Digital Policy for Sustainable Agricultural Modernization: A Three-Party Evolutionary Game and Stackelberg Game Analysis

Abstract

Digital policy has become an important instrument for promoting sustainable agricultural modernization. However, its effectiveness depends on the strategic responses of the government, agricultural operators, and farmers. This study develops a theoretical framework to examine how digital policy affects sustainable agricultural modernization through multi-agent interaction. Specifically, it constructs a three-party evolutionary game model and a Stackelberg game model to analyze strategy evolution under different implementation costs, subsidies, and penalties, as well as the government’s first-mover role in subsidy design. The results show that digital policy does not promote sustainable agricultural modernization through a simple linear pathway. Instead, it operates by reshaping the incentive structures of agricultural operators and farmers. Lower government implementation costs increase the likelihood of active policy implementation, while subsidies for agricultural operators and farmers strengthen their willingness to adopt digital tools, engage in standardized production, and participate in digital agricultural activities. However, the marginal effect of subsidies weakens as participation and digitalization increase, indicating that unlimited subsidy expansion may reduce policy efficiency and increase fiscal pressure. This study contributes to the literature by linking digital policy design, multi-agent strategic interaction, and sustainable agricultural modernization within a unified theoretical framework. It highlights that effective digital agricultural policy requires incentive compatibility, fiscal sustainability, inclusive participation, and adaptive governance, rather than reliance solely on digital technology investment or subsidy expansion.

1. Introduction

Digital technologies are reshaping agricultural production, rural governance, and agricultural value chains. Big data, the Internet of Things, and artificial intelligence are increasingly being applied to agricultural production, operation, and circulation. As a result, agriculture is shifting from experience-based management toward data-driven decision-making, more precise resource use, and improved coordination across the entire value chain. The development of digital villages, rural information infrastructure, rural e-commerce, and modern agriculture pilot policies further indicates that digitalization is no longer merely a technical tool. It has become an important policy instrument that influences resource allocation, industrial organization, and rural governance. In this study, sustainable agricultural modernization is defined as a modernization process through which agricultural production enhances efficiency, resilience, and resource-use performance while ensuring inclusive participation and long-term policy viability. This concept therefore extends beyond output growth or technology adoption alone. It refers to the integrated advancement of economic efficiency, social inclusion, environmental governance, and institutional coordination within the process of agricultural digital transformation.

Digital policy may improve production efficiency, facilitate green transformation, strengthen rural resilience, and enhance the allocation and use of agricultural resources. It may also enable farmers and agricultural operators to access markets, services, and public support systems more effectively. However, rural areas often remain constrained by uneven infrastructure provision, limited digital skills, weak policy implementation capacity, and unequal access to digital benefits. Such constraints may produce uneven patterns of digital transformation and weaken the long-term effectiveness of digital policy.

The central issue is not simply whether digital technology can be introduced into agriculture, but how digital policy reshapes the behavioral incentives of different actors. Sustainable agricultural modernization is contingent on the strategic choices made by the government, agricultural operators, and farmers. The government provides policy support, subsidies, and regulatory oversight; agricultural operators decide whether to adopt digital tools and standardized production practices; and farmers determine whether to participate in digital agricultural activities. These choices jointly influence the cost, pace, and outcomes of agricultural digitalization. Against this background, the key question is how digital policy can guide the choices of the government, agricultural operators, and farmers in a sustainable manner. A sustainable digital policy should not only encourage digital adoption, but also control implementation costs, improve subsidy efficiency, support weaker actors, and reduce unequal access to digital resources.

Existing studies on agricultural digital transformation and sustainable agricultural modernization can be broadly grouped into three main streams.

The first focuses on the technological empowerment of agricultural production and management. Digital technologies, including artificial intelligence (AI), machine learning (ML), big data, the Internet of Things (IoT), blockchain, drones, robotics, and digital twins, have been increasingly incorporated into smart farming systems. By improving agricultural monitoring, production decision-making, resource allocation, and farm management, these technologies facilitate the transition toward data-driven, precise, and intelligent agricultural production. The second stream examines the policy effects of the digital economy, digital finance, broadband infrastructure, rural e-commerce, and related pilot policies. Econometric methods are commonly used in this literature to assess whether digital development contributes to agricultural modernization and rural transformation. Existing evidence suggests that digital development can enhance sustainable agricultural modernization, agricultural resilience, green total factor productivity, and industrial upgrading. The third stream focuses on multi-agent governance in agricultural digital transformation. This line of research examines how governments, agricultural firms, farmers, platforms, and other actors make strategic choices under policy incentives, regulatory constraints, and market conditions. Evolutionary game models, policy network analysis, and other analytical frameworks have been used to investigate interactions among different actors and their implications for digital policy implementation.

From a datafication perspective, IoT-based sensors, unmanned aerial vehicles, and intelligent devices enable the continuous collection of heterogeneous field-level data, including soil moisture, temperature, crop growth conditions, livestock behavior, and meteorological information [1,2,3]. Such streaming data constitute the empirical foundation of agricultural big data systems. Big data analytics platforms further support data storage, integration, and mining, thereby enabling more precise and evidence-based agricultural decision-making [4,5]. From the perspective of precision management, AI and ML algorithms transform multi-source agricultural data into predictive insights and operational decisions. In irrigation management, for instance, AI-based systems can integrate soil moisture sensor data with weather forecasts to generate precise irrigation plans, thereby reducing water consumption and improving resource-use efficiency [6,7]. In fertilization and plant protection, AI can identify crop diseases, pests, and growth abnormalities through image recognition and sensor-based data analysis, which helps farmers determine more appropriate pesticide and fertilizer application strategies [5,8,9]. Such data-driven precision management reduces the inefficiencies associated with uniform input application and contributes to lower production costs and reduced environmental pressure [9,10]. From the perspective of intelligent production, the integration of AI and IoT is accelerating the transition of agriculture from human–machine interaction toward autonomous decision-making. Intelligent agricultural machinery, autonomous navigation robots, and automated greenhouse control systems can monitor and adjust crop growth environments in real time [1,7,11]. In livestock production, AI- and IoT-enabled systems can continuously monitor animal health, behavior, and environmental conditions, thereby supporting refined feeding management and product traceability [12]. In addition, emerging technologies such as digital twins have begun to be applied to agriculture by constructing virtual farm models to simulate, monitor, and optimize real production processes [1]. However, some studies have also cautioned that the growing centrality of algorithms in agricultural decision-making may weaken the traditional decision-making authority of farmers and agronomists, raising concerns about the social consequences of smart farming [13].

Overall, this body of literature demonstrates that digital technologies can improve agricultural production and management by enhancing monitoring capacity, enabling precision decision-making, reducing resource waste, and promoting intelligent production. Nevertheless, most existing studies remain largely technology-oriented and descriptive. They tend to emphasize the functional advantages of digital technologies, while paying relatively limited attention to policy costs, subsidy efficiency, heterogeneous actor responses, and coordination mechanisms among governments, agricultural operators, and farmers. Therefore, although this literature explains how digital technologies empower agricultural development, it does not fully clarify how digital policy can guide different actors toward sustainable agricultural modernization.

The second stream examines the effects of the digital economy, digital finance, and related digital policies on agricultural green total factor productivity (GTFP). Existing empirical studies generally indicate that digital development can promote green productivity growth by improving financial accessibility, facilitating technological innovation, optimizing resource allocation, and strengthening environmental governance. For instance, digital inclusive finance has been found to improve agricultural GTFP by alleviating financing constraints, optimizing resource allocation, and promoting rural e-commerce [14]. The digital economy can also enhance agricultural GTFP through agricultural technological innovation, although its effects vary across regions [15]. Similarly, digital finance has been shown to improve agricultural GTFP by facilitating agricultural resource allocation and technological innovation [16]. Other studies further suggest that the positive effect of the digital economy on GTFP may depend on innovation capacity, the institutional environment, and environmental expenditure [17,18].

The mechanisms through which digital development improves GTFP are multidimensional. Green technological innovation is widely regarded as a key transmission channel, as the digital economy can enhance knowledge diffusion, technology adoption, and green production innovation [15,19]. Industrial structure upgrading represents another important pathway, through which digital development promotes the rationalization and advancement of industrial structures and subsequently improves green productivity [20,21]. In addition, rural e-commerce plays a mediating role between digital inclusive finance and agricultural GTFP by easing financing constraints, improving resource allocation, and encouraging the adoption of green technologies [14]. Human capital accumulation, environmental regulation, land transfer, and digital village construction have also been identified as important mechanisms linking digital development to green productivity improvement [22,23,24,25].

It is also important to note that the impact of digital development on GTFP may not be strictly linear. Some studies have identified a U-shaped relationship, suggesting that digital development may initially suppress green productivity because of adjustment costs and resource mismatches, but may later promote productivity once digital infrastructure, innovation capacity, and institutional conditions reach certain thresholds [26]. Other studies emphasize the spatial spillover effects of digital finance and the digital economy, indicating that digital development in one region may influence green productivity in neighboring regions through technology diffusion, capital flows, and industrial linkages [20,27].

Although this stream of research provides important empirical evidence on the positive role of digital development in agricultural green modernization, it mainly focuses on the average effects of the digital economy or digital finance on productivity-related outcomes. Relatively limited attention has been paid to the strategic interactions among heterogeneous actors. Existing studies have not sufficiently explained how policy costs, subsidy intensity, punishment mechanisms, and heterogeneous participation decisions jointly shape the sustainability of agricultural digital transformation. Therefore, further research is needed to reveal the multi-agent mechanism through which digital policy guides sustainable agricultural modernization.

The third stream focuses on multi-agent governance and strategic interaction in platform-based, environmental, and cluster-based governance contexts. Evolutionary game theory has been widely applied to examine how governments, enterprises, platforms, consumers, farmers, and other stakeholders adjust their strategies under bounded rationality. In platform governance, flexible government–platform collaborative regulation has been shown to be more effective than a simple binary choice between regulation and non-regulation in promoting merchant compliance and improving product quality [28]. Related studies further suggest that government access to market information, detection probability, platform effort, public participation, technological improvement, and institutional design are key factors shaping the effectiveness of multi-agent governance on Internet platforms [29]. Government regulation plays a central role in multi-agent governance systems. Studies show that regulatory costs and punishment intensity significantly influence regulatory efficiency [30]. Research further indicates that moderate regulatory intensity is essential: excessive regulation may weaken platform supervision incentives, whereas insufficient regulation may fail to create effective deterrence [31]. In environmental governance, punishment mechanisms imposed by different levels of government may generate heterogeneous effects on local governments and enterprises [32]. Moreover, compared with subsidy policies, punishment mechanisms may be more effective in restraining opportunistic or greenwashing behavior among heterogeneous enterprises [33]. Platform enterprises also play a dual role as both regulated entities and governance participants. When platforms regulate merchants within their ecosystems, the government functions as a meta-regulator, while consumer complaints can help suppress illegal business behavior [28]. However, excessive joint liability may weaken platforms’ incentives to perform their regulatory responsibilities. Therefore, improving platform effort, public participation, technological empowerment, and institutional design is essential for achieving effective multi-agent governance [29,34].

The participation of farmers, consumers, non-governmental organizations, and the public also shapes governance outcomes. In farmland consolidation under public–private partnership arrangements, farmer supervision can compensate for insufficient government regulation and constrain opportunistic behavior [35]. In environmental governance, public participation can accelerate the transition of enterprises toward active governance strategies [32]. However, when the participation level of industry organizations or platform users is too low, such participation may only delay the evolution toward undesirable outcomes rather than fundamentally reverse it [31]. Maintaining stakeholder participation above a certain threshold and strengthening punishment mechanisms are therefore important for guiding multi-agent systems toward positive and stable states [36].

Overall, the multi-agent governance literature provides useful theoretical and methodological support for analyzing strategic interactions among heterogeneous actors. It shows that governance outcomes are not determined by a single policy instrument, but by the combined effects of regulatory costs, information acquisition, incentive design, punishment mechanisms, platform responsibility, public participation, and actor responses. However, most existing studies focus on platform governance, antitrust regulation, environmental governance, or enterprise cluster behavior. Relatively limited attention has been paid to agricultural digital policy, and few studies place the government, agricultural operators, and farmers within a unified policy interaction framework. Consequently, although this literature offers important methodological insights, it does not fully explain how digital policy coordinates different agricultural actors and promotes sustainable agricultural modernization.

Based on the above discussion, existing research has provided valuable insights into the technological foundations, productivity effects, and governance logic of digital transformation. Nevertheless, several research gaps remain. First, technology-oriented studies explain the functional advantages of AI, IoT, big data, and related technologies, but they do not sufficiently examine the policy mechanisms required for large-scale and sustainable adoption. Second, empirical studies on the digital economy and agricultural GTFP mainly focus on macro-level productivity outcomes, while the micro-level strategic responses of heterogeneous actors remain underexplored. Third, multi-agent governance studies provide useful analytical tools, but their application to agricultural digital transformation remains limited. Therefore, it is necessary to construct a unified multi-agent analytical framework that incorporates government regulation, agricultural operator participation, farmer adoption decisions, subsidy policies, punishment mechanisms, and digital transformation costs. Such a framework can better explain how digital policy guides the strategic choices of different actors and promotes sustainable agricultural modernization.

This study investigates how digital policy drives sustainable agricultural modernization through multi-agent interaction. The core question is not whether digital policy directly improves sustainable agricultural modernization, but how it reshapes the strategic choices of the government, agricultural operators, and farmers. This process involves policy costs, subsidies, punishment mechanisms, behavioral responses, and coordination benefits. Meanwhile, this study focuses on three key actors: the government, agricultural operators, and farmers. The main variables include government implementation cost, subsidies for agricultural operators, subsidies for farmers, punishment intensity, actor participation, agricultural digitalization, and sustainable agricultural modernization performance. Policy costs, subsidies, and punishment mechanisms reflect the strength and structure of government policy supply, while the participation of agricultural operators and farmers captures micro-level behavioral responses. Agricultural digitalization and sustainable agricultural modernization performance represent the main outcomes of digital policy implementation.

First, this study constructs a three-party evolutionary game model to examine the stable states of the system under different costs, subsidies, and punishment mechanisms, as well as the dynamic evolution of the strategies adopted by the government, agricultural operators, and farmers. Second, this study develops a Stackelberg game model in which the government acts as the first mover and agricultural operators and farmers act as followers. This model is used to examine how the government can guide the responses of agricultural operators and farmers through subsidy design.

Overall, this study aims to explain the mechanism underlying the effects of digital policy. It links policy supply with actor responses and connects incentive design with sustainable agricultural modernization. This framework helps explain why effective digital policy requires cost control, appropriate subsidy design, and stable participation by agricultural operators and farmers. It also shows how digital policy can support a more inclusive and sustainable transformation of agriculture.

2. Literature Review

Digital policy-driven sustainable agricultural modernization is a multidimensional research field. It involves technological transformation, policy intervention, institutional governance, and multi-agent behavioral responses. To build the theoretical basis of this study, the literature review is organized around three related strands. The first strand examines how digital technologies reshape agricultural production systems and provide the technical basis for smart and sustainable agriculture. The second strand reviews empirical studies on digital policy, digital infrastructure, the digital economy, and agricultural modernization. It focuses on whether digitalization improves agricultural development outcomes and how these effects are produced. The third strand discusses multi-agent governance, digital divides, platform power, and strategic interaction. It shows that digital policy implementation depends not only on technological availability, but also on actor coordination and incentive compatibility. This structure enables the review to progress logically from technological conditions to policy effects, from policy effects to governance mechanisms, and finally to the model motivation of this study.

2.1. Digital Technologies and the Transformation of Agricultural Production

The first strand of literature examines how digital technologies have reshaped agricultural production systems. Existing studies generally agree that big data, the Internet of Things, artificial intelligence, digital twins, and platform technologies are shifting agriculture from experience-based and fragmented management toward data-driven, predictive, and integrated decision-making [37,38,39,40,41,42,43]. From a technological perspective, IoT platforms, wireless sensors, cloud computing, machine learning, and farm management information systems enable real-time monitoring, multi-source data integration, crop forecasting, irrigation control, soil management, and machinery optimization [44,45,46,47,48,49,50,51,52,53]. Jayaraman et al. integrated wireless sensors, weather stations, cameras, smartphones, and other IoT devices into a cloud-based smart farming platform, showing that multi-source agricultural data can be filtered, integrated, and transformed into crop forecasts and personalized planting advice [44]. Köksal and Tekinerdogan, using design-driven research, feature-driven domain analysis, and two case studies in Turkey, proposed an IoT-based farm management information system architecture and demonstrated that digital systems can support data collection, processing, monitoring, planning, decision-making, recording, and farm business management [49]. Collectively, these studies provide important evidence that digital technologies can improve production efficiency, reduce operational uncertainty, and support the transition from traditional agriculture to smart agriculture.

At the same time, this body of literature also reveals clear differences in research focus and methodological orientation. Engineering-oriented studies mainly emphasize the technical feasibility and functional performance of smart farming systems, including data collection, algorithmic prediction, automation, and system architecture [44,49,51,52]. Review-based studies broaden this perspective by showing that agricultural digitalization is no longer confined to field-level production, but increasingly extends to the entire agri-food supply chain, including production planning, resource allocation, logistics coordination, and business process transformation [45,46,53]. Nevertheless, these studies tend to conceptualize digital transformation primarily as a technology-driven process, while paying relatively limited attention to the institutional and behavioral conditions under which digital technologies are adopted, sustained, and governed. In particular, they do not sufficiently explain how governments, agricultural operators, platforms, and farmers strategically respond to digital policy incentives.

International research provides a more critical perspective on this issue. In Europe, digitalization is closely associated with the redesign of agricultural policy instruments. Drawing on a theoretical framework and European agricultural policy cases, Ehlers et al. argued that digital technologies enable more spatially targeted, adaptive, and results-based policy tools, suggesting that smart agriculture is not only a technological transformation but also a process of policy innovation [54]. In North America, studies on agricultural automation indicate that sensors, artificial intelligence, robotics, and digital platforms can improve efficiency, but may also reshape farm labour, rural communities, and the control of agricultural data [55,56]. Evidence from Brazil and other developing regions further shows that digital agriculture may produce unequal outcomes. Coggins et al., drawing on interviews with digital extension tool developers across 21 countries and user interviews with smallholder farmers in Bihar, India, found that digital advisory tools can improve farmers’ access to agricultural information, but their use is constrained by access to devices, electricity, mobile networks, digital literacy, language, trust, and socioeconomic conditions [57].

Taken together, digital technologies provide an important technical basis for sustainable agricultural modernization, particularly by improving monitoring capacity, decision accuracy, and resource-use efficiency. Yet when policy incentives and governance mechanisms are poorly designed, the same process of digital transformation may reinforce digital divides, deepen data-control asymmetries, and produce unequal access to technological benefits. Therefore, the contribution of digital technology to sustainable agricultural modernization depends not only on technological availability, but also on infrastructure provision, platform governance, policy design, and the strategic responses of different agricultural actors. This provides the theoretical basis for this study to move beyond a purely technology-centered explanation and to examine digital policy-driven sustainable agricultural modernization from a multi-agent perspective.

2.2. Digital Policy, Agricultural Modernization, and Empirical Evidence

Digitalization can promote sustainable agricultural modernization by improving agricultural production efficiency, optimizing factor allocation, strengthening rural entrepreneurship, and facilitating industrial upgrading [58,59,60,61,62,63,64,65,66,67,68,69]. However, these studies differ considerably in their policy contexts, empirical strategies, and explanatory mechanisms. Most China-based studies focus on the digital economy, digital inclusive finance, broadband infrastructure, and pilot policies, whereas international studies pay greater attention to broadband access, digital infrastructure subsidies, results-based policy instruments, and digital extension services [54,66,67,70]. This difference suggests that digital policy does not operate through a single universal channel. Rather, its effects depend on institutional settings, infrastructure conditions, farmer participation, and the incentives faced by different actors. Liu et al., based on an index system of the digital economy, new agricultural productivity, and sustainable agricultural modernization, showed that sustainable agricultural modernization acts as a mediating mechanism through which the digital economy promotes new agricultural productivity, with this effect exhibiting a clear regional gradient across different development stages [59]. Fu and Guo, based on annual data and empirical identification of digital inclusive finance, showed that digital inclusive finance promotes sustainable agricultural modernization through urban–rural integration and higher informatization levels [62]. Collectively, these studies confirm that digitalization can improve agricultural modernization performance. However, their emphasis remains largely on macro-level effects and mediating channels rather than on the strategic choices of governments, agricultural operators, and farmers. Some studies examine the role of digital finance and digital infrastructure in strengthening agricultural resilience, productivity, and entrepreneurial activity. Using panel data, empirical tests, and robustness checks, Gao et al. found that digital inclusive finance enhances agricultural economic resilience, with rural industrial integration serving as a key mediating channel [63]. Xu and Yang, through spatial effect analysis, showed that digital finance promotes rural industrial revitalization and generates industrial upgrading effects by improving agricultural socialized services [64]. Wu et al., using a mediation model, found that digital finance improves agricultural total factor productivity by promoting capital deepening, land transfer, farmer organization, and agricultural socialized services [65]. These findings indicate that digital finance and digital infrastructure can improve agricultural performance by reshaping factor allocation and service provision. Yet they also point to a methodological limitation: while econometric studies are well suited to estimating average treatment effects and mediation pathways, they are less able to explain how policy incentives are converted into behavioral responses by different actors.

From an international perspective, LoPiccalo, using county-level panel data, found that higher broadband penetration significantly increases corn and soybean yields and reduces some operating costs, suggesting that digital infrastructure can directly improve agricultural production performance [66]. Kim and Paudel, drawing on an event study design based on U.S. broadband grant programs, provided causal evidence that broadband subsidies improve crop productivity, particularly in areas with weaker initial conditions [67]. In Europe, Ehlers et al., based on a theoretical framework and European agricultural policy cases, argued that digitalization enables more spatially targeted, adaptive, and results-based agricultural policy instruments, indicating that digital policy can improve not only agricultural production but also the precision and accountability of policy intervention [54]. In India, Cole and Fernando, using evidence from mobile-based agricultural advisory services, showed that digital extension tools can influence farmers’ information acquisition, input adoption, and production practices, although their effectiveness depends on farmers’ access to digital services, trust in information, and sustained technology use [70]. These international studies indicate that digital policy promotes agricultural modernization through multiple channels, including infrastructure provision, targeted subsidies, policy instrument redesign, and digital advisory services.

Still, this literature contains some unresolved tensions. First, most empirical studies report positive effects of digitalization, but the size and channels of these effects vary across regions, policy types, and development stages [58,59,66,67]. This shows that digital policy is not effective by itself. Its performance depends on supporting conditions such as infrastructure quality, fiscal support, human capital, farmer participation, and service accessibility. Second, China-based studies often emphasize industrial structure upgrading, rural industrial integration, digital finance, and entrepreneurship as key channels [61,62,63,64,65,66,67,68,69], while international studies place more direct attention on broadband infrastructure, policy design, and farmer-facing digital services [54,66,67,70]. This difference shows that the relationship between digital policy and agricultural modernization is shaped by both macro-level institutions and micro-level behavioral responses. Third, existing econometric studies mainly explain whether digital policy works, but they do not fully explain why different actors choose to participate in, delay, or resist digital transformation under different cost, subsidy, and punishment conditions.

Therefore, although the empirical literature provides strong evidence that digital policy can improve agricultural modernization, it is still limited in explaining the changing interaction among governments, agricultural operators, and farmers. Macro-level econometric models are useful for identifying average effects and transmission channels, but they cannot fully capture incentive compatibility, strategic adjustment, or equilibrium formation among multiple actors. These gaps justify the need for a multi-agent analytical framework. By introducing an evolutionary game model and a Stackelberg game structure, this study further examines how government subsidies, implementation costs, penalties, and actor responses jointly determine the transition from a low-coordination state to a high-coordination state in digital policy-driven sustainable agricultural modernization.

2.3. Multi-Agent Governance, Digital Divide, and Strategic Interaction

The third strand of literature shifts the analytical focus from the performance effects of digital policy to the strategic interactions among governments, agricultural operators, farmers, platforms, and other actors. Compared with macro-level empirical studies, this line of research pays greater attention to the mechanisms through which digital policy incentives are translated into behavioral responses. A common finding is that digital policy implementation is not a linear process. Its effectiveness depends on multi-actor coordination, the alignment between policy tools and regional development stages, and the capacity of policy design to address digital divides, incentive compatibility, and governance conflicts. Drawing on the principles of digital policy implementation in the context of the Russian digital economy, Shcherbakova et al. argued that digital policy should be flexible, stage-based, and responsive to changing institutional and technological conditions [71]. This argument implies that digital policy should not be treated merely as a technical intervention, but rather as a dynamic governance process shaped by heterogeneous actors and evolving incentive structures.

Existing studies further indicate that the conceptualization of digital policy varies across institutional contexts. In the European context, Ehlers et al., drawing on a theoretical framework and agricultural policy cases, showed that agricultural digitalization can reshape the selection and design of policy instruments by enabling spatially precise subsidies, targeted interventions, and results-oriented policy tools [54]. This research highlights the role of digital technologies in improving policy precision and accountability. By contrast, Tian et al., using policy instrument classification and policy network analysis based on China’s digital agriculture policies, identified imbalances among supply-side, environment-side, and demand-side instruments, as well as weak coordination and interest conflicts among actors in the policy network [72]. The contrast between these studies indicates that digital policy does not automatically improve governance capacity. Its effectiveness depends on whether policy instruments are balanced and whether different actors can establish stable coordination relationships.

International studies further show that digital governance may generate both efficiency gains and distributional risks. Rotz et al., drawing on literature and field data from North America, particularly Canada, found that sensors, artificial intelligence, and automation can improve agricultural efficiency, but may also intensify labor differentiation, land concentration, and data-control asymmetries [55]. Coca et al., using online surveys and field visits in Minas Gerais, Brazil, found clear differences between large agribusinesses and family farmers in their expectations of Agriculture 4.0, suggesting that digitalization may further marginalize family farmers if the digital divide is not actively reduced [56]. These studies challenge the technology-optimistic assumption that digital agriculture benefits all actors in the same way. Rather, they suggest that digital policy must address the distributional questions of who controls digital resources, who bears the costs of adoption, and who captures the gains from digital transformation.

Game-theoretic and system-dynamics studies offer useful analytical tools for examining these strategic interactions, while also revealing several limitations. Zheng et al., using a tripartite evolutionary game model involving the government, farmer cooperatives, and consumers, found that government incentives constitute important external conditions for guiding the system toward a positive equilibrium [73]. Mei et al., through a three-party evolutionary game model and scenario analysis, showed that the digital transformation of farmer cooperatives depends more heavily on policy support in the short term, whereas consumption upgrading and market demand become more important in the long term [74]. This finding implies that policy effects are both time-dependent and threshold-sensitive. Zheng and Mei using a two-party evolutionary game model and MATLAB-based numerical simulation, found that government subsidies and cooperative adoption can generate an optimal stable state, although excessive subsidy intensity may destabilize the system [75]. Taken together, these studies indicate that stronger policy intervention is not necessarily more effective. Digital policy must instead balance incentive intensity, fiscal cost, and behavioral response.

Related work has extended this discussion to digital governance tools, particularly blockchain applications and value-chain coordination. Cao et al., using a blockchain-driven tripartite game model involving the government, water rights service companies, and farmers, found that coordinated incentives, information transparency, and moderate subsidies can improve the stability of participation in agricultural water-saving governance [76]. Tan et al., using an evolutionary game model of farmers and blockchain platforms in agricultural product traceability, showed that downstream actors’ preference for traceability authenticity can reduce farmers’ cheating behavior and increase platforms’ supervision willingness [77]. Cooper et al., using a system dynamics model and Monte Carlo simulation, found that internal project adjustment alone cannot simultaneously achieve higher small-market supply, higher farmer profits, and sustainable organizational operation; external retail demand and supporting conditions are also necessary [78]. Collectively, these studies show that digital agricultural governance requires cross-actor coordination rather than single-point intervention. However, the existing game-theoretic literature still has several limitations. First, many studies treat government subsidies, penalties, and regulatory intensity as exogenous parameters, while giving insufficient attention to how governments strategically design these policies in response to the expected reactions of agricultural operators and farmers. Second, most evolutionary game studies focus on the stability of actor strategies under given parameter settings, but rarely explain the sequential decision-making process in which the government acts as a first mover and other actors subsequently adjust their strategies. Third, existing models often focus on specific digital applications, such as smart spraying, blockchain traceability, or water-saving governance, while paying less attention to the broader policy problem of sustainable agricultural modernization driven by digital policy.

International studies on platform governance and data governance further strengthen the need for a multi-agent analytical framework. Alessa et al., based on evidence from Saudi dairy firms and the technology-organization-environment framework, found that perceived costs and benefits, access to credit, extension services, government policy, and market pressure all influence the adoption of milk-traceability technologies [79]. Wiseman et al., examining farmers’ reluctance to share data through the lens of laws affecting smart farming, found that uncertainty over data ownership, control, access, and use weakens farmers’ willingness to participate in digital agriculture [80]. Kos and Kloppenburg, focusing on digital technologies and hyper-transparency in global value chains, showed that digital tools may improve smallholder inclusion, but may also create new forms of exclusion when smallholders lack data access, digital skills, or bargaining power [81].

Taken together, the literature reveals a clear tension. On the one hand, digital policy and digital platforms can improve coordination, transparency, monitoring capacity, and resource allocation in agricultural systems. On the other hand, they may also generate new forms of dependency, unequal bargaining power, data-control asymmetries, and the exclusion of smallholders. This tension cannot be fully explained by descriptive policy analysis or macro-level empirical models. Instead, it requires an analytical framework capable of capturing how heterogeneous actors adjust their strategies under different costs, subsidies, penalties, and expected benefits. Therefore, the existing literature collectively supports the necessity of the model proposed in this study. By constructing a multi-agent evolutionary game model involving the government, agricultural operators, and farmers, this study analyzes the dynamic adjustment of actor strategies under digital policy incentives. By further introducing a Stackelberg game structure, it captures the government’s role as a first mover in subsidy design and policy intervention. This combined framework helps explain how digital policy may guide the system from a low-coordination state toward a high-coordination equilibrium that supports sustainable agricultural modernization.

2.4. Research Gaps and Model Motivation

The above literature provides an important foundation for understanding the relationship between digital policy and sustainable agricultural modernization. Existing studies have made valuable contributions from technological, empirical, and governance perspectives. Technology-oriented research has shown that big data, the Internet of Things, artificial intelligence, digital twins, and platform technologies can enhance agricultural monitoring, improve production decision-making, optimize resource allocation, and strengthen supply-chain coordination. Empirical studies have further shown that the digital economy, digital finance, broadband infrastructure, and related digital policies may improve agricultural modernization performance through industrial upgrading, factor reallocation, rural entrepreneurship, and the expansion of agricultural services. This evidence suggests that digitalization affects agriculture not only through technological inputs, but also through changes in economic organization and resource allocation. From a governance perspective, digital policy implementation has also been understood as a coordination process involving governments, agricultural operators, farmers, platforms, and market actors. Taken together, these studies provide both theoretical and empirical foundations for understanding how digitalization contributes to agricultural transformation.

Despite these contributions, several important gaps remain. The first concerns the distinction between effect identification and mechanism explanation. Macro-level empirical studies are useful for identifying the average effects of digital policy or the digital economy on agricultural green development, agricultural productivity, rural entrepreneurship, and agricultural modernization. However, such studies often treat governments, agricultural operators, and farmers as implicit or aggregated actors. As a result, they provide limited insight into how different actors make strategic choices under specific policy conditions. In particular, existing empirical studies rarely integrate policy costs, subsidy intensity, punishment mechanisms, adoption costs, expected benefits, and behavioral responses into a unified analytical framework. This limitation makes it difficult to explain why digital policy can generate coordinated participation in some contexts but fail to do so in others.

The second gap lies in the limitations of existing game-theoretic studies. Evolutionary game models have been widely used to examine multi-actor strategy adjustment in digital agriculture, farmer cooperative transformation, blockchain traceability, and resource-saving governance. Compared with econometric studies, these models are better suited to capturing bounded rationality, dynamic learning, and strategy evolution. However, many existing studies still treat government subsidies, penalties, and regulatory intensity as exogenous parameters, and they mainly rely on static parameter settings and numerical simulations. They pay insufficient attention to the sequential nature of digital policy implementation, in which the government often acts as the first mover by designing subsidy schemes and regulatory rules, while agricultural operators and farmers subsequently adjust their participation strategies. Therefore, existing evolutionary game studies do not fully explain how government first-mover decisions shape the strategic responses of other actors.

The third gap concerns the policy scope of digital agricultural modernization. Existing studies tend to focus on the digital economy, digital finance, broadband infrastructure, or individual digital pilot policies. These studies offer important insights into specific policy instruments, but they pay less attention to how digital policy functions as a coordinated set of governance tools for sustainable agricultural modernization. In practice, digital policy does not operate through a single channel. It involves infrastructure investment, financial incentives, technical services, platform governance, regulatory supervision, and inclusive participation. Therefore, a more integrated framework is needed to explain how different policy instruments jointly affect the strategic interactions among governments, agricultural operators, and farmers.

Moreover, from the standpoint of agricultural sustainability, many studies emphasize the positive effects of digital policy on agricultural output, productivity, and efficiency, but fewer studies examine whether the policy process itself is sustainable. Digital policy may improve agricultural performance in the short term, yet poorly designed subsidies may generate fiscal pressure, inefficient resource allocation, weak participation, or dependency on government support. At the same time, if policy incentives mainly benefit large agricultural operators, digital transformation may widen the gap between large-scale operators and small farmers. Therefore, sustainable agricultural modernization requires not only efficiency improvement, but also fiscal sustainability, policy efficiency, inclusive participation, and digital divide mitigation.

To move beyond the limitations of macro-level effect estimation and static game analysis, this paper constructs a three-party evolutionary game model involving the government, agricultural operators, and farmers. This framework makes it possible to examine how the three actors adjust their strategies under different costs, subsidies, punishments, and expected benefits, and to identify the conditions under which the system evolves toward a stable equilibrium. Furthermore, this paper introduces a Stackelberg game structure to capture the government’s role as the first mover in digital policy design. In this framework, the government first determines the subsidy policy, after which agricultural operators and farmers make their participation decisions in response. By combining evolutionary game analysis with Stackelberg game logic, this study explains how digital policy can guide the system from a low-coordination state to a high-coordination state. In doing so, it contributes to the literature by linking digital policy design, multi-agent strategic interaction, and sustainable agricultural modernization within a unified analytical framework.

3. Construction and Simulation Analysis of the Multi-Agent Evolutionary Game Model

3.1. Agent Setting and Parameter Description

In the process through which digital policy supports sustainable agricultural modernization, the government, agricultural operators, and farmers constitute the core game players. Each player seeks to maximize its own interests, and its strategic choices are shaped by policy incentives, cost constraints, and expected benefits. The interaction among these strategic choices forms a dynamic process that shapes the effectiveness of digital policy implementation. In this process, the government is mainly responsible for policy design, resource allocation, and regulatory supervision. Agricultural operators carry out digital transformation, adjust production and operation models, and respond to market conditions. Farmers are the main participants in agricultural production, and their behavioral choices directly affect both policy implementation and agricultural economic performance. The government has two strategic options: active implementation and passive implementation. Active implementation means strengthening policy support, improving institutional arrangements, and increasing resource input to support the effective implementation of digital policy. Passive implementation means adopting a more cautious and gradual policy approach to reduce implementation costs and control policy risks.

Agricultural operators also have two strategic options: active response and passive response. These choices reflect whether they actively optimize business models, adopt digital technologies, and improve standardized operations under government policy guidance. Farmers, similarly, can choose either active participation or passive participation. This distinction reflects whether they actively cooperate with policy implementation, participate in agricultural economic activities, and respond to the requirements of digital development. Under different combinations of strategies, the three players interact dynamically, and their interaction jointly determines the actual effect of digital policy on sustainable agricultural modernization.

Assume that the government has two strategies in the implementation of the digital policy: strict regulation and loose regulation. The probabilities of choosing these two strategies are x and 1 − x, respectively. Agricultural operators have two strategies: standardized production and non-standardized production. The probabilities of choosing these two strategies are y and 1 − y, respectively. Farmers have two strategies: active participation and passive participation. The probabilities of choosing these two strategies are z and 1 − z, respectively, where 0 ≤ x, y, z ≤ 1. Based on the above model assumptions, the key parameters and their definitions used in the three-party evolutionary game model are summarized in Table 1.

Table 1. Parameter description of the three-party evolutionary game model for digital policy-driven sustainable agricultural modernization.

Parameter	Definition
E1	Governance cost paid by the government for strongly implementing the digital policy.
E2	Cost incurred by agricultural operators when they actively support and cooperate with the implementation of the digital policy.
E3	Cost incurred by agricultural operators when they moderately support the digital policy and make only local adjustments based on big data analysis results.
E4	Cost incurred by farmers when they support and participate in the implementation of the digital policy.
S1	Subsidies or policy incentives received from higher-level authorities when the government actively promotes the management of agricultural economic activities in the big data pilot zone.
S2	Subsidies provided by the government to agricultural operators for their active support, digital transformation, and standardized production under the digital policy.
S3	Subsidies provided by the government to farmers who actively participate in the implementation of the digital policy.
F1	Penalty cost imposed by higher-level authorities on the government due to poor management and insufficient regulation.
F2	Fines imposed by the government on agricultural operators for non-standardized behavior.
F3	Fines imposed by the government on farmers for non-standardized behavior in agricultural economic activities.

The selection of model parameters is grounded in the economic logic of digital policy implementation and the institutional process of sustainable agricultural modernization. In this study, digital agricultural policy is not regarded as a purely technological intervention. Rather, it is conceptualized as a multi-agent governance process involving public implementation costs, policy incentives, regulatory enforcement, technology adoption costs, and heterogeneous behavioral responses. Accordingly, the parameters in the model are designed to capture the key economic and institutional conditions under which the government, agricultural operators, and farmers decide whether and how to participate in digital transformation.

First, the government-related parameters reflect the fiscal and administrative logic of policy implementation. The implementation cost E₁ represents the public resources required for policy design, digital infrastructure construction, data platform operation, technical training, administrative coordination, and regulatory supervision. In practice, promoting digital agriculture requires not only fiscal expenditure, but also administrative capacity and continuous governance input. Therefore, E₁ captures the fiscal and administrative sustainability of digital policy implementation. The parameter S₁ denotes the incentives or policy support that the government may receive from higher-level authorities when it actively promotes digital agricultural modernization, such as fiscal transfers, policy rewards, pilot-zone support, or performance-based incentives. By contrast, F₁ represents accountability pressure or penalties imposed by higher-level authorities when policy implementation is ineffective. These parameters reflect a vertical governance structure in which local governments respond simultaneously to upper-level incentives and accountability constraints.

Second, the subsidy parameters S₂ and S₃ reflect the incentive mechanism through which the government encourages agricultural operators and farmers to participate in digital policy implementation. From the perspective of incentive compatibility, digital transformation often requires agricultural actors to bear additional costs before the benefits are fully realized. Agricultural operators may need to invest in digital equipment, standardized production systems, data reporting mechanisms, traceability systems, and managerial adjustment. Farmers may need to acquire new knowledge, change production habits, use digital platforms, and participate in digital advisory or extension services. Without appropriate subsidies, these actors may lack sufficient motivation to participate actively. Therefore, S₂ and S₃ represent policy instruments used to reduce adoption costs and strengthen the participation incentives of agricultural operators and farmers, respectively.

Third, the cost parameters of agricultural operators and farmers capture the economic burden of digital adoption. For agricultural operators, E₂ denotes the cost of actively cooperating with digital policy implementation and adopting standardized digital production practices. This may include investment in digital equipment, data management, traceability systems, production standardization, and organizational adjustment. E₃ denotes the lower cost of limited or partial response, reflecting a more passive strategy in which agricultural operators make only local adjustments without fully engaging in digital transformation. This distinction matters because, in practice, agricultural operators rarely make a binary choice between participation and non-participation. More often, they may adopt symbolic, partial, or low-intensity forms of compliance when the expected benefits of full participation are uncertain or insufficient. For farmers, E₄ denotes the cost of active participation, including learning costs, time costs, technology-use costs, and adjustments in production behavior. Such costs are particularly relevant for small farmers, who often face limited digital literacy, weaker financial capacity, and inadequate access to digital infrastructure.

Fourth, the penalty parameters F₂ and F₃ capture the role of regulatory enforcement in sustaining standardized agricultural production and ensuring policy effectiveness. Digital agricultural modernization is not confined to technology adoption; it also requires improvements in production quality, transparency, traceability, and standardization. If agricultural operators engage in non-standardized production, false data reporting, weak quality control, or opportunistic behavior, the effectiveness of digital governance may be weakened. Similarly, if farmers fail to follow standardized production requirements or engage in irregular agricultural economic activities, the implementation effect of digital policy may be reduced. Therefore, F₂ and F₃ represent government penalties imposed on non-standardized behavior by agricultural operators and farmers, respectively. These penalties are included to capture the regulatory mechanism that complements subsidy-based incentives.

The relationships among these variables reflect the basic economic mechanism of digital policy implementation. Government subsidies reduce the participation costs of agricultural operators and farmers, while penalties increase the costs of passive participation or non-standardized behavior. Government implementation cost affects the government’s willingness and capacity to actively promote digital policy. At the same time, upper-level incentives and accountability pressures shape government policy choices. Agricultural operators compare the costs and benefits of standardized digital transformation, while farmers compare the costs and benefits of active participation. Therefore, the strategic interaction among the three actors is jointly determined by implementation costs, subsidies, penalties, and expected benefits.

Above all, these parameters are also closely connected with the sustainability dimensions of agricultural modernization. Government implementation cost E₁ reflects fiscal and administrative sustainability. Subsidies S₂ and S₃ reflect the efficiency of policy incentives. Farmers’ active participation reflects inclusive participation and digital divide reduction. Agricultural operators’ standardized production reflects the quality of digital transformation and the improvement of agricultural governance. The transition from a low-coordination equilibrium to a high-coordination equilibrium reflects the enhancement of digital governance capacity. In this sense, the model does not merely describe strategy evolution among multiple actors. It also explains whether digital policy can support a more efficient, inclusive, and sustainable process of agricultural modernization.

The game process through which digital policy supports sustainable agricultural modernization reflects the independent decision-making of the government, agricultural operators, and farmers under policy incentives, cost constraints, and benefit distribution. It also captures the interactions and dynamic interdependence among these three actors. Their strategic choices jointly determine the effectiveness of policy implementation and the level of coordination in sustainable agricultural modernization. By constructing a three-party game framework, this study further examines the behavioral response mechanisms of each actor under different institutional settings. It also provides a theoretical basis for improving policy design, strengthening coordinated participation, and promoting sustainable agricultural modernization.

3.2. Construction of the Payoff Matrix and Dynamic Equations

To clarify the economic meaning of the payoff matrix, the three-party evolutionary game can be interpreted as a dynamic policy interaction among the government, agricultural operators, and farmers. Let (x) denote the probability that the government adopts strict regulation, (y) denote the probability that agricultural operators choose standardized production, and (z) denote the probability that farmers choose active participation. The payoff matrix therefore describes how each actor’s expected payoff changes under different combinations of policy regulation, production behavior, and farmer participation. The payoff matrix therefore describes how each actor’s expected payoff changes under different combinations of policy regulation, production behavior, and farmer participation, as shown in Table 2.

Table 2. Payoff matrix of the government–agricultural operator–farmer three-party evolutionary game in digital policy-driven sustainable agricultural modernization.

		Agricultural Operators	Farmers
			Active Participation	Passive Participation
Government	Strict regulation	Standardized production	$-{\mathrm{E}}_1+{\mathrm{S}}_1-{\mathrm{S}}_2-{\mathrm{S}}_3$	$-{\mathrm{E}}_1+{\mathrm{S}}_1-{\mathrm{S}}_2+{\mathrm{F}}_3$
			${\mathrm{S}}_2-{\mathrm{E}}_2$	${\mathrm{S}}_2-{\mathrm{E}}_2$
			$-{\mathrm{E}}_4+{\mathrm{S}}_3$	$-{\mathrm{F}}_3$
		Non-standardized production	$-{\mathrm{E}}_1+{\mathrm{S}}_1+{\mathrm{F}}_2-{\mathrm{S}}_3$	$-{\mathrm{E}}_1+{\mathrm{S}}_1+{\mathrm{F}}_2+{\mathrm{F}}_3$
			$-{\mathrm{F}}_2-{\mathrm{E}}_3$	$-{\mathrm{F}}_2-{\mathrm{E}}_3$
			$-{\mathrm{E}}_4+{\mathrm{S}}_3$	$-{\mathrm{F}}_3$
	Loose regulation	Standardized production	$-{\mathrm{F}}_1$	$-{\mathrm{F}}_1$
			$-{\mathrm{E}}_2$	$-{\mathrm{E}}_2$
			$-{\mathrm{E}}_4$	0
		Non-standardized production	$-{\mathrm{F}}_1$	$-{\mathrm{F}}_1$
			$-{\mathrm{E}}_3$	$-{\mathrm{E}}_3$
			$-{\mathrm{E}}_4$	0

For the government, strict regulation entails both fiscal burdens and expected policy returns. On the cost side, the government bears the implementation cost E₁ and provides subsidies S₂ and S₃ to agricultural operators and farmers participating in digital policy implementation. These expenditures reflect not only direct fiscal outlays, but also the administrative coordination, digital infrastructure support, and regulatory supervision required to sustain policy implementation. On the benefit side, strict regulation enables the government to obtain policy support or performance incentives ${\mathrm{S}}_1$ from higher-level authorities and to impose penalties F₂ and F₃ on non-standardized behavior by agricultural operators and farmers. If the government chooses loose regulation, it avoids direct implementation costs and subsidy payments, but may face accountability pressure or penalties F₁ due to insufficient policy implementation. Therefore, the government’s strategic choice reflects a trade-off among fiscal and administrative costs, upper-level incentives, accountability pressure, and regulatory effectiveness.

For agricultural operators, standardized production requires a higher level of digital investment and organizational adjustment, represented by E₂. This includes the costs of digital equipment, data management, traceability systems, production standardization, and operational restructuring. If agricultural operators respond passively or choose non-standardized production, they bear a lower cost E₃; however, under strict government regulation, they may be subject to penalties F₂. Therefore, the strategic choice of agricultural operators depends on whether government subsidies and penalties are sufficient to offset the additional cost of standardized digital transformation.

For farmers, active participation requires learning new technologies, adjusting production behavior, using digital platforms, and participating in digital extension services. These participation costs are represented by E₄. Under strict regulation, farmers who actively participate may receive subsidies S₃, while passive participation or non-standardized behavior may lead to penalties F₃. Therefore, farmers’ participation decisions depend on whether the combined effect of subsidies and regulatory pressure can compensate for their participation costs. This is particularly important for small farmers, who often face stronger digital literacy constraints and more limited access to digital infrastructure.

$$\begin{array}{c}{\mathrm{U}}_{11}=\mathrm{y}\mathrm{z}(-{\mathrm{E}}_1+{\mathrm{S}}_1-{\mathrm{S}}_2-{\mathrm{S}}_3)+\mathrm{y}(1-\mathrm{z})(-{\mathrm{E}}_1+{\mathrm{S}}_1-{\mathrm{S}}_2+{\mathrm{F}}_3)\\ +(1-\mathrm{y})\mathrm{z}(-{\mathrm{E}}_1+{\mathrm{S}}_1+{\mathrm{F}}_2-{\mathrm{S}}_3)+(1-\mathrm{y})(1-\mathrm{z})(-{\mathrm{E}}_1+{\mathrm{S}}_1+{\mathrm{F}}_2+{\mathrm{F}}_3)\end{array}$$

(1)

$${\mathrm{U}}_{12}=-\mathrm{y}\mathrm{z}{\mathrm{F}}_1-\mathrm{y}(1-\mathrm{z}){\mathrm{F}}_1-(1-\mathrm{y})\mathrm{z}{\mathrm{F}}_1+(1-\mathrm{y})(1-\mathrm{z})(-{\mathrm{F}}_1)$$

(2)

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

(3)

$$\mathrm{F}(\mathrm{x})={\displaystyle \frac{\mathrm{d}\mathrm{x}}{\mathrm{d}\mathrm{t}}}=\mathrm{x}({\mathrm{U}}_{11}-\overline{{\mathrm{U}}_1})=\mathrm{x}(\mathrm{x}-1)({\mathrm{E}}_1-{\mathrm{F}}_1-{\mathrm{F}}_2-{\mathrm{F}}_3-{\mathrm{S}}_1+{\mathrm{F}}_2\mathrm{y}+{\mathrm{F}}_3\mathrm{z}+{\mathrm{S}}_2\mathrm{y}+{\mathrm{S}}_3\mathrm{z})$$

(4)

Equations (1)–(4) indicate that the probability of strict regulation increases when the net payoff of strict regulation exceeds that of loose regulation. Specifically, stronger upper-level incentives S₁, greater accountability pressure F₁, and higher penalties for non-standardized behavior, represented by F₂ and F₃, encourage the government to adopt strict regulation. By contrast, higher implementation cost E₁ and larger subsidy payments S₂ and S₃ reduce the government’s willingness to regulate strictly. The terms (y) and (z) further indicate that the behaviors of agricultural operators and farmers feed back into government decision-making. When more agricultural operators choose standardized production and more farmers participate actively, the government needs to provide more subsidies, thereby increasing its fiscal burden. However, when non-standardized behavior or passive participation is widespread, strict regulation becomes more attractive because the government can obtain greater regulatory benefits through penalties and improved governance effectiveness.

$${\mathrm{U}}_{21}=\mathrm{x}\mathrm{z}({\mathrm{S}}_2-{\mathrm{E}}_2)+\mathrm{x}(1-\mathrm{z})({\mathrm{S}}_2-{\mathrm{E}}_2)+(1-\mathrm{x})\mathrm{z}(-{\mathrm{E}}_2)+(1-\mathrm{x})(1-\mathrm{z})(-{\mathrm{E}}_2)$$

(5)

$${\mathrm{U}}_{22}=\mathrm{x}\mathrm{z}(-{\mathrm{F}}_2-{\mathrm{E}}_3)+\mathrm{x}(1-\mathrm{z})(-{\mathrm{F}}_2-{\mathrm{E}}_3)+(1-\mathrm{x})\mathrm{z}(-{\mathrm{E}}_3)+(1-\mathrm{x})(1-\mathrm{z})(-{\mathrm{E}}_3)$$

(6)

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

(7)

$$\mathrm{F}(\mathrm{y})={\displaystyle \frac{\mathrm{d}\mathrm{y}}{\mathrm{d}\mathrm{t}}}=-\mathrm{y}(\mathrm{y}-1)({\mathrm{E}}_3-{\mathrm{E}}_2+{\mathrm{F}}_2\mathrm{x}+{\mathrm{S}}_2\mathrm{x})$$

(8)

Equations (5)–(8) indicate that standardized production will diffuse among agricultural operators when the expected benefits of standardization exceed its additional costs. Since E₂ is generally greater than E₃, agricultural operators may lack sufficient incentives to adopt standardized digital production without government intervention. However, as the probability of strict regulation (x) increases, the combined effect of subsidy S₂ and penalty F₂ enhances the relative attractiveness of standardized production. Therefore, government regulation plays a crucial role in shifting agricultural operators’ behavior from passive adjustment toward standardized digital production.

$${\mathrm{U}}_{31}=\mathrm{x}\mathrm{y}(-{\mathrm{E}}_4+{\mathrm{S}}_3)+\mathrm{x}(1-\mathrm{y})(-{\mathrm{E}}_4+{\mathrm{S}}_3)+(1-\mathrm{x})\mathrm{y}(-{\mathrm{E}}_4)+(1-\mathrm{x})(1-\mathrm{y})(-{\mathrm{E}}_4)$$

(9)

$${\mathrm{U}}_{32}=\mathrm{x}\mathrm{y}(-{\mathrm{F}}_3)+\mathrm{x}(1-\mathrm{y})(-{\mathrm{F}}_3)$$

(10)

$$\overline{{\mathrm{U}}_3}=\mathrm{z}{\mathrm{U}}_{31}+(1-\mathrm{z}){\mathrm{U}}_{32}$$

(11)

$$\mathrm{F}(\mathrm{z})={\displaystyle \frac{\mathrm{d}\mathrm{z}}{\mathrm{d}\mathrm{t}}}=-\mathrm{z}(\mathrm{z}-1)({\mathrm{F}}_3\mathrm{x}-{\mathrm{E}}_4+{\mathrm{S}}_3\mathrm{x})$$

(12)

Equations (9)–(12) show that farmers’ active participation increases when the expected subsidy and avoided penalty under strict regulation exceed the cost of participation. If government regulation is weak, farmers may have limited incentives to bear the learning costs, time costs, and behavioral adjustment costs associated with digital policy participation. However, when strict regulation becomes more likely, subsidy S₃ and penalty F₃ jointly increase the relative payoff of active participation. Thus, the evolution of farmers’ behavior is strongly shaped by the credibility and intensity of government policy implementation.

Overall, the three replicator dynamic equations reveal a feedback mechanism among the three actors. The government influences agricultural operators and farmers through subsidies and penalties, while agricultural operators and farmers, in turn, affect the government’s expected payoff through their production and participation choices. When government implementation costs are high, subsidies are weak, or penalties are insufficient, the system may remain in a low-coordination state characterized by loose regulation, non-standardized production, and passive participation. When government incentives are sufficiently strong, regulatory enforcement is credible, and subsidies effectively lower adoption costs, agricultural operators and farmers are more likely to participate actively. Under these conditions, the system may gradually move toward a high-coordination state, in which strict regulation, standardized production, and active farmer participation reinforce one another.

The intermediate variables (H), (K), and (L) in the Jacobian matrix can be understood as the net evolutionary incentives faced by the three actors. Specifically, (H) denotes the net incentive for the government to adopt strict regulation, (K) denotes the net incentive for agricultural operators to choose standardized production, and (L) denotes the net incentive for farmers to participate actively. When these net incentives are positive, the corresponding strategy tends to expand within the population; when they are negative, the corresponding strategy tends to decline. Therefore, the stability analysis based on the Jacobian matrix is not only a mathematical procedure, but also an economic assessment of whether the policy system can generate self-reinforcing coordination among government regulation, operator standardization, and farmer participation.

$$\mathrm{H}={\mathrm{F}}_1+{\mathrm{F}}_2+{\mathrm{F}}_3+{\mathrm{S}}_1-{\mathrm{E}}_1-({\mathrm{F}}_2+{\mathrm{S}}_2)\mathrm{y}-({\mathrm{F}}_3+{\mathrm{S}}_3)\mathrm{z}$$

(13)

$$\mathrm{K}={\mathrm{E}}_3-{\mathrm{E}}_2+({\mathrm{F}}_2+{\mathrm{S}}_2)\mathrm{x}$$

(14)

$$\mathrm{L}=({\mathrm{F}}_3+{\mathrm{S}}_3)\mathrm{x}-{\mathrm{E}}_4$$

(15)

$$\begin{gathered} \mathrm{J}=\left(\begin{array}{ccc}{\mathrm{J}}_1& {\mathrm{J}}_2& {\mathrm{J}}_3\\ {\mathrm{J}}_4& {\mathrm{J}}_5& {\mathrm{J}}_6\\ {\mathrm{J}}_7& {\mathrm{J}}_8& {\mathrm{J}}_9\end{array}\right)=\left(\begin{array}{ccc}{\displaystyle \frac{\partial \mathrm{F}\left(\mathrm{x}\right)}{\partial \mathrm{x}}}& {\displaystyle \frac{\partial \mathrm{F}\left(\mathrm{x}\right)}{\partial \mathrm{y}}}& {\displaystyle \frac{\partial \mathrm{F}\left(\mathrm{x}\right)}{\partial \mathrm{z}}}\\ {\displaystyle \frac{\partial \mathrm{F}\left(\mathrm{y}\right)}{\partial \mathrm{x}}}& {\displaystyle \frac{\partial \mathrm{F}\left(\mathrm{y}\right)}{\partial \mathrm{y}}}& {\displaystyle \frac{\partial \mathrm{F}\left(\mathrm{y}\right)}{\partial \mathrm{z}}}\\ {\displaystyle \frac{\partial \mathrm{F}\left(\mathrm{z}\right)}{\partial \mathrm{x}}}& {\displaystyle \frac{\partial \mathrm{F}\left(\mathrm{z}\right)}{\partial \mathrm{y}}}& {\displaystyle \frac{\partial \mathrm{F}\left(\mathrm{z}\right)}{\partial \mathrm{z}}}\end{array}\right) \\ =\left(\begin{array}{ccc}(1-2\mathrm{x})\mathrm{H}& -\mathrm{x}(1-\mathrm{x})({\mathrm{F}}_2+{\mathrm{S}}_2)& -\mathrm{x}(1-\mathrm{x})({\mathrm{F}}_3+{\mathrm{S}}_3)\\ \mathrm{y}(1-\mathrm{y})({\mathrm{F}}_2+{\mathrm{S}}_2)& (1-2\mathrm{y})\mathrm{K}& 0\\ \mathrm{z}(1-\mathrm{z})({\mathrm{F}}_3+{\mathrm{S}}_3)& 0& (1-2\mathrm{z})\mathrm{L}\end{array}\right) \end{gathered}$$

3.3. Equilibrium Stability Analysis

Since the eight pure-strategy equilibrium points all satisfy x, y, z ∈ {0, 1}, the off-diagonal elements of the Jacobian matrix are all 0. The Jacobian matrix then becomes a diagonal matrix, and its eigenvalues are the diagonal elements. According to evolutionary game stability theory, an equilibrium point is an evolutionarily stable strategy only when all eigenvalues at this point are less than 0.

$${\mathrm{E}}_1>{\mathrm{F}}_1+{\mathrm{F}}_2+{\mathrm{F}}_3+{\mathrm{S}}_1,\hspace{1em}{\mathrm{E}}_3<{\mathrm{E}}_2,\hspace{1em}{\mathrm{E}}_4>0$$

(16)

The eigenvalues of the Jacobian matrix and the stability results for each equilibrium point are summarized in Table 3.

Table 3. Eigenvalues of the Jacobian matrix and stability analysis of each equilibrium point in the three-party evolutionary game system.

Evolutionarily Stable Point	Eigenvalues of the Jacobian Matrix	Stability
	${\mathsf{\lambda }}_{\mathbf{1}},{\mathsf{\lambda }}_{\mathbf{2}},{\mathsf{\lambda }}_{\mathbf{3}}$
${\mathrm{E}}_1(\mathrm{0,0},0)$	${\mathrm{F}}_1-{\mathrm{E}}_1+{\mathrm{F}}_2+{\mathrm{F}}_3+{\mathrm{S}}_1,{\mathrm{E}}_3-{\mathrm{E}}_2,-{\mathrm{E}}_4$	$(*,-,-)$
${\mathrm{E}}_2(0,1,0)$	${\mathrm{F}}_1-{\mathrm{E}}_1+{\mathrm{F}}_3+{ \mathrm{S}}_1-{\mathrm{S}}_2, {\mathrm{E}}_2-{\mathrm{E}}_3, -{\mathrm{E}}_4$	$(*,+,-)$
${\mathrm{E}}_3(0,0,1)$	${\mathrm{F}}_1-{\mathrm{E}}_1+{\mathrm{F}}_2+{\mathrm{S}}_1-{\mathrm{S}}_3, {\mathrm{E}}_3-{\mathrm{E}}_2, {\mathrm{E}}_4$	$(*,-,+)$
${\mathrm{E}}_4(0,1,1)$	${\mathrm{F}}_1-{\mathrm{E}}_1+{\mathrm{S}}_1-{\mathrm{S}}_2,{ \mathrm{E}}_2-{\mathrm{E}}_3,{ \mathrm{E}}_4$	$(*,+,+)$
${\mathrm{E}}_5(1,0,0)$	${\mathrm{E}}_1-{\mathrm{F}}_1-{\mathrm{F}}_2-{\mathrm{F}}_3-{\mathrm{S}}_1, {\mathrm{E}}_3-{\mathrm{E}}_2+{\mathrm{F}}_2+{\mathrm{S}}_2,{ \mathrm{F}}_3-{\mathrm{E}}_4+{\mathrm{S}}_3$	$(*,*,*)$
${\mathrm{E}}_6(1,1,0)$	${\mathrm{E}}_1-{\mathrm{F}}_1-{\mathrm{F}}_3-{\mathrm{S}}_1+{\mathrm{S}}_2,{ \mathrm{E}}_2-{\mathrm{E}}_3-{\mathrm{F}}_2-{\mathrm{S}}_3,{ \mathrm{F}}_3-{\mathrm{E}}_4+{ \mathrm{S}}_3$	$(*,*,*)$
${\mathrm{E}}_7(1,0,1)$	${\mathrm{E}}_1-{\mathrm{F}}_1-{\mathrm{F}}_2-{\mathrm{S}}_1+{\mathrm{S}}_3,{ \mathrm{E}}_3-{\mathrm{E}}_2+{\mathrm{F}}_2+{ \mathrm{S}}_2, {-\mathrm{F}}_3+{\mathrm{E}}_4-{\mathrm{S}}_3$	$(*,*,*)$
${\mathrm{E}}_8(1,1,1)$	${\mathrm{E}}_1-{\mathrm{F}}_1-{\mathrm{S}}_1+{ \mathrm{S}}_2+{ \mathrm{S}}_3,{ \mathrm{E}}_2-{\mathrm{E}}_3-{\mathrm{F}}_2-{\mathrm{S}}_2,{-\mathrm{F}}_3+{ \mathrm{E}}_4-{\mathrm{S}}_3$	$(*,*,*)$

Note: * indicates that the sign of the corresponding eigenvalue depends on parameter values and cannot be directly determined.

When the cost of strong policy implementation by the government is much higher than its subsidies and regulatory benefits, and the cost of full support by agricultural operators is higher than that of moderate support, the system tends to (0,0,0). In this state, the government chooses moderate implementation, agricultural operators choose passive cooperation, and farmers show low participation. Thus, ${\mathrm{E}}_1$ = (0,0,0) is stable.

$${\mathrm{E}}_1<{\mathrm{F}}_1+{\mathrm{F}}_3+{\mathrm{S}}_1-{\mathrm{S}}_2,\hspace{1em}{\mathrm{E}}_2-{\mathrm{E}}_3<{\mathrm{F}}_2+{\mathrm{S}}_2,\hspace{1em}{\mathrm{E}}_4>{\mathrm{F}}_3+{\mathrm{S}}_3$$

(17)

When the benefits of strong policy implementation by the government can cover its extra costs, agricultural operators tend to fully support the policy under subsidies and penalties. At the same time, farmers’ participation costs are still higher than the benefits from incentives and constraints. In this case, the system evolves to (1,1,0), which means that the government and agricultural operators adopt positive strategies, while farmers adopt a negative strategy. This point is a local stable equilibrium that is likely to occur, and ${\mathrm{E}}_6$ = (1,1,0) becomes stable.

$${\mathrm{E}}_1<{\mathrm{F}}_1+{\mathrm{F}}_2+{\mathrm{S}}_1-{\mathrm{S}}_3,\hspace{1em}{\mathrm{E}}_3-{\mathrm{E}}_2<-({\mathrm{F}}_2+{\mathrm{S}}_2),\hspace{1em}{\mathrm{E}}_4<{\mathrm{F}}_3+{\mathrm{S}}_3$$

(18)

This point means that the government and farmers take active actions, while agricultural operators take passive actions. Since the strong condition ${\mathrm{E}}_3-{ \mathrm{E}}_2< -({\mathrm{F}}_2+{\mathrm{S}}_2)$ is still required, ${\mathrm{E}}_7$ = (1,0,1) is also unlikely to become a stable state.

$${\mathrm{E}}_1<{\mathrm{F}}_1+{\mathrm{S}}_1-{\mathrm{S}}_2-{\mathrm{S}}_3,\hspace{1em}{\mathrm{E}}_2-{\mathrm{E}}_3<{\mathrm{F}}_2+{\mathrm{S}}_2,\hspace{1em}{\mathrm{E}}_4<{\mathrm{F}}_3+{\mathrm{S}}_3$$

(19)

The ideal state is that the government strongly implements the policy, agricultural operators actively support it, and farmers take part widely. If the net benefit of strong policy implementation by the government is higher than its governance cost, agricultural operators have enough incentive to provide full support under the subsidy and penalty mechanism, and the cost of farmer participation is lower than the combined incentive formed by government subsidies and penalties, the system will gradually evolve to ${\mathrm{E}}_8$ = (1,1,1) and become stable.

The stable state of the three-party evolutionary game system depends on the relative relationship among government implementation cost, support benefits of agricultural operators, and farmer participation cost. With the improvement of government incentives and constraints, the system may move from the low-level equilibrium ${\mathrm{E}}_1$ = (0,0,0) to the transitional equilibrium ${\mathrm{E}}_6$ = (1,1,0), and then to the fully coordinated equilibrium ${\mathrm{E}}_8$ = (1,1,1). This shows that the effective implementation of the digital policy is a dynamic coordination process led by the government and jointly driven by the response of agricultural operators and the participation of farmers.

The three scenarios indicate that the stability of the evolutionary game equilibrium points varies significantly under different constraints, leading to different possible strategy combinations. At different stages of system evolution, the government, agricultural operators, and farmers adjust their strategies according to changes in expected benefits, thereby influencing both the evolutionary path and the final stable state of the system. Therefore, coordinated participation among the government, agricultural operators, and farmers is essential for achieving a stable and positive equilibrium in sustainable agricultural modernization.

To further examine how changes in key parameters affect strategy evolution paths and system stability, this study uses MATLAB to conduct numerical simulations of the three-party evolutionary game model. In addition, the sensitivity of key parameters, including government implementation cost and incentive intensity, is analyzed to clarify their effects on system evolution.

This study further conducts a numerical simulation analysis for the high-coordination stable equilibrium (${\mathrm{E}}_8$ = (1,1,1)). The parameter values used in the benchmark simulation are not intended to be direct empirical estimates. Rather, they are scenario-based benchmark values designed to reflect the relative economic relationships among policy implementation costs, digital adoption costs, subsidies, penalties, and upper-level incentives in the process of digital policy-driven agricultural modernization.

Specifically, the initial values of the model parameters are set as follows: ${\mathrm{E}}_1$ = 80, ${\mathrm{E}}_2$ = 50, ${\mathrm{E}}_3$ = 30, ${\mathrm{E}}_4$ = 10, ${\mathrm{S}}_1$ = 40, ${\mathrm{S}}_2$ = 8, ${\mathrm{S}}_3$ = 6, ${\mathrm{F}}_1$ = 60, ${\mathrm{F}}_2$ = 14, and ${\mathrm{F}}_3$ = 7. These values are assigned on a common payoff scale and are mainly used to examine the evolutionary direction of the system under a theoretically consistent policy scenario. The government implementation cost ${\mathrm{E}}_1$ is assigned a relatively high value because digital policy implementation entails public expenditure on infrastructure construction, platform operation, technical training, administrative coordination, and regulatory supervision. The cost of standardized digital production for agricultural operators, ${\mathrm{E}}_2$, is higher than the cost of limited response, ${\mathrm{E}}_3$, reflecting the fact that full digital transformation requires greater investment in equipment, data management, traceability systems, and organizational adjustment. The participation cost of farmers, ${\mathrm{E}}_4$, is set lower than that of agricultural operators, but remains positive because farmers still need to bear learning costs, time costs, and behavioral adjustment costs. The subsidy parameters ${\mathrm{S}}_2$ and ${\mathrm{S}}_3$ are set lower than the corresponding adoption costs, indicating that government subsidies reduce but do not fully offset the costs borne by agricultural operators and farmers. The penalty parameters ${\mathrm{F}}_2$ and ${\mathrm{F}}_3$ represent the regulatory pressure imposed on non-standardized behavior. Together with subsidies, these penalties are expected to improve the relative payoff of standardized production and active participation. The upper-level incentive ${\mathrm{S}}_1$ and accountability pressure ${\mathrm{F}}_1$ are introduced to reflect the vertical governance structure in which local governments are encouraged to promote digital agricultural modernization and may face penalties when policy implementation is insufficient.

The selected parameter values satisfy the theoretical conditions required for the system to evolve toward the high-coordination equilibrium. For the government, the net incentive for strict regulation at (${\mathrm{E}}_8$ = (1,1,1)) is positive because (${\mathrm{S}}_1$ + ${\mathrm{F}}_1$ − ${\mathrm{E}}_1$ − ${\mathrm{S}}_2$ − ${\mathrm{S}}_3$ = 40 + 60 − 80 − 8 − 6 = 6 > 0). For agricultural operators, the net incentive for standardized production under strict regulation is positive because (${\mathrm{S}}_2$ + ${\mathrm{F}}_2$ − (${\mathrm{E}}_2$ − ${\mathrm{E}}_3$) = 8 + 14 − (50 − 30) = 2 > 0). For farmers, the net incentive for active participation under strict regulation is also positive because (${\mathrm{S}}_3$ + ${\mathrm{F}}_3$ − ${\mathrm{E}}_4$ = 6 + 7 − 10 = 3 > 0). These inequalities indicate that, under the benchmark parameter setting, strict government regulation, standardized production by agricultural operators, and active farmer participation can generate mutually reinforcing incentives.

After these initial values are substituted into the replicator dynamic system, the simulation results are shown in Figure 1. The evolutionary trajectories of the government, agricultural operators, and farmers gradually converge to (${\mathrm{E}}_8$ = (1,1,1)), indicating that the system evolves toward a high-coordination state characterized by strict regulation, standardized production, and active participation. This result is consistent with the stability analysis and confirms that, when policy incentives and regulatory constraints are sufficiently strong to compensate for implementation and adoption costs, digital policy can guide the agricultural modernization system toward a stable and coordinated equilibrium.

Figure 1. Evolutionary stability trajectories of the three-party game system in sustainable agricultural modernization driven by digital policy.

3.4. Sensitivity Analysis and Simulation Test

To analyze the effect of digital policy on sustainable agricultural modernization, this paper selects three key parameters in the tripartite evolutionary game model for sensitivity analysis: government implementation cost ${\mathrm{E}}_1$, government subsidy ${\mathrm{S}}_2$ for the supportive behavior of agricultural operators, and government subsidy ${\mathrm{S}}_3$ for farmers’ participation behavior. ${\mathrm{E}}_1$ reflects the cost constraint faced by the government in promoting digital policy. ${\mathrm{S}}_2$ represents the strength of government incentives for agricultural operators’ digital cooperation and standardized operation. ${\mathrm{S}}_3$ reflects the guiding and incentive role of the government in encouraging farmers to participate in agricultural economic activities. These three parameters correspond respectively to the cost constraint on the government side, the incentive intensity for agricultural operators, and the incentive intensity for farmers. Together, they help reveal the transmission path through which digital policy affects sustainable agricultural modernization.

To ensure clear comparison, this paper changes the values of ${\mathrm{E}}_1$, ${\mathrm{S}}_2$, and ${\mathrm{S}}_3$ separately while keeping the other parameters unchanged. Two-dimensional time evolution diagrams and three-dimensional evolutionary trajectory diagrams are then used to examine changes in the system’s evolutionary path and stable state.

Based on the above analysis, this paper proposes the following research hypotheses.

Hypothesis 1.

The implementation cost E₁ of government promotion of digital policy can be adjusted within a certain range. The government may adjust the intensity of policy implementation in response to changes in implementation cost. As E₁ increases, the government’s willingness to promote policy implementation is expected to decline. This may further reduce the willingness of agricultural operators and farmers to participate, thereby weakening the effect of digital policy on sustainable agricultural modernization.

Hypothesis 2.

The participation willingness of agricultural operators is strongly influenced by government subsidy S₂. When the government increases subsidies for agricultural operators, they have stronger incentives to carry out digital transformation, standardized operation, and policy cooperation. When subsidies are insufficient, their willingness to respond actively may decline, which may affect the level of sustainable agricultural modernization.

Hypothesis 3.

Farmers’ participation behavior is directly affected by government incentive S₃. As government subsidies or guiding incentives for farmers increase, farmers are more likely to participate in agricultural economic activities, thereby improving the level of system coordination. At the same time, higher farmer participation may influence the behavior of agricultural operators and the overall effect of digital policy on sustainable agricultural modernization through strategic interaction, further promoting the system’s evolution toward a higher level of coordinated equilibrium.

To examine the effect of government implementation cost on the evolutionary trajectories of the three-party system, the corresponding simulation results are presented in Figure 2.

Figure 2. (a) Three-dimensional evolutionary trajectory of the tripartite evolutionary game system under different levels of government implementation cost. (b) Time evolution of the strategy variable of agricultural operators under different levels of government implementation cost.

The simulation results show that changes in the government implementation cost of digital policy have a significant effect on the strategic evolution of the three actors and the convergence speed of the system. When the government implementation cost ${\mathrm{E}}_1$ is low, the net benefit of adopting an active implementation strategy is relatively high, making the system more likely to evolve toward coordinated participation among multiple actors. As ${\mathrm{E}}_1$ increases, the cost burden of policy implementation rises. This weakens the government’s motivation to adopt an active implementation strategy and further reduces its positive driving effect on agricultural operators and farmers.

The two-dimensional time evolution results show that the evolutionary trend of the strategy variable (y) for agricultural operators differs clearly under different levels of ${\mathrm{E}}_1$. Lower government implementation cost helps agricultural operators shift more rapidly toward active support. By contrast, higher implementation cost slows the convergence of their strategy toward a stable state and may weaken their willingness to participate in policy implementation. This occurs because higher government implementation cost reduces the intensity and credibility of policy enforcement, making it more difficult for agricultural operators to form stable expectations regarding policy incentives.

The three-dimensional evolutionary trajectories further show that an increase in ${\mathrm{E}}_1$ shifts the system’s evolutionary path toward a low-coordination region and reduces the likelihood of convergence to a high-level coordinated equilibrium. These results indicate that government implementation cost is a key constraint affecting whether digital policy can effectively promote sustainable agricultural modernization. If the cost of policy implementation is too high, even clearly defined policy objectives may fail to support digital transformation and coordinated governance in the agricultural economy because of weakened governance efforts. Thus, Hypothesis 1 is supported.

To examine the effect of government subsidies for agricultural operators on the evolutionary trajectories of the three-party system, the corresponding simulation results are presented in Figure 3.

Figure 3. (a) Three-dimensional evolutionary trajectory of the tripartite evolutionary game system under different subsidy levels for agricultural operators. (b) Time evolution of the strategy variable of agricultural operators under different subsidy levels for agricultural operators.

$${\mathrm{E}}_1<{\mathrm{F}}_1+{\mathrm{F}}_2+{\mathrm{S}}_1-{\mathrm{S}}_3, {\mathrm{E}}_3-{\mathrm{E}}_2<-({\mathrm{F}}_2+{\mathrm{S}}_2), {\mathrm{E}}_4<{\mathrm{F}}_3+{\mathrm{S}}_3$$

The simulation results show that government subsidy ${\mathrm{S}}_2$ for agricultural operators’ supportive behavior has a clear positive effect on their strategic choices. As the subsidy level increases, the probability that agricultural operators actively support and cooperate with policy implementation rises significantly, and the system converges more rapidly. This indicates that agricultural operators, as important supply-side actors in agricultural economic activities, are highly responsive to policy incentives.

The two-dimensional time evolution graph shows that, when ${\mathrm{S}}_2$ is higher, the strategy variable (y) of agricultural operators converges more rapidly to a higher level. This suggests that subsidies can reduce the marginal costs associated with digital transformation, data access, and standardized operation, thereby strengthening agricultural operators’ willingness to respond to digital policy. When ${\mathrm{S}}_2$ is low, agricultural operators lack sufficient income compensation, making active support difficult to sustain and slowing the evolutionary speed of the system.

The three-dimensional evolutionary trajectory further indicates that, as ${\mathrm{S}}_2$ increases, the overall system path moves more clearly toward the high-coordination region. This means that increasing subsidies for agricultural operators not only promotes their own strategy optimization, but also drives the strategic choices of the government and farmers in a positive direction through the game interaction mechanism. Therefore, subsidies for agricultural operators play an important incentive role in the effect of digital policy on sustainable agricultural modernization. They serve as a key policy instrument for encouraging supply-side actors in the agricultural economy to participate actively. Thus, Hypothesis 2 is supported.

To examine the effect of government subsidies for farmer participation on the evolutionary trajectories of the three-party system, the corresponding simulation results are presented in Figure 4.

Figure 4. (a) Three-dimensional evolutionary trajectories of the three-party evolutionary game system under different farmer subsidy levels. (b) Time evolution of the strategy variable of agricultural operators under different farmer subsidy levels.

The simulation results show that government subsidy ${\mathrm{S}}_3$ for farmer participation has a significant effect on farmers’ strategic choices and further influences the overall coordination level of the system. As government subsidies or guiding incentives for farmers to participate in agricultural economic activities increase, farmers are more likely to choose active participation, and the system is more likely to converge toward a high-level coordinated equilibrium.

The two-dimensional evolution results indicate that although ${\mathrm{S}}_3$ first affects the payoff structure of farmers, changes in ${\mathrm{S}}_3$ also indirectly influence the behavior of agricultural operators and the overall evolutionary speed of the system through strategic interaction. A higher level of ${\mathrm{S}}_3$ enhances farmers’ willingness to participate and strengthens the participation-side effect of digital policy, thereby improving information feedback and social coordination in agricultural economic activities.

The three-dimensional evolutionary trajectory further shows that, as ${\mathrm{S}}_3$ increases, the system’s evolutionary path gradually moves toward a region characterized by high participation and high coordination. This indicates that stronger farmer incentives help improve the external environment for sustainable agricultural modernization and build a stronger social foundation for policy implementation. Compared with relying solely on government promotion or the response of agricultural operators, stronger incentives for farmer participation can further enhance system stability and coordination. Therefore, in the process through which digital policy supports sustainable agricultural modernization, greater attention should be paid to the design of farmer-oriented incentive mechanisms by lowering participation barriers and increasing participation benefits. Thus, Hypothesis 3 is supported.

${\mathrm{E}}_1$, ${\mathrm{S}}_2$, and ${\mathrm{S}}_3$ affect the dynamic evolution of the tripartite evolutionary game system from three dimensions: government cost constraints, the incentive mechanism for agricultural operators, and the incentive mechanism for farmers. An increase in ${\mathrm{E}}_1$ inhibits the evolution of the system toward a high-coordination state, whereas increases in ${\mathrm{S}}_2$ and ${\mathrm{S}}_3$ enhance the willingness of agricultural operators and farmers to participate and promote convergence toward a higher level of coordinated equilibrium. This indicates that the effect of digital policy on sustainable agricultural modernization is not driven by a single actor, but results from the interactive adjustment among the government, agricultural operators, and farmers.

When government implementation costs are too high, the motivation to promote policy implementation is constrained, and the system may fall into a low-coordination state. When the government provides effective incentives by increasing subsidies for agricultural operators and farmers, the effect of policy implementation can be significantly improved. This can promote coordinated development in agricultural governance standardization, business digitalization, and diversified participation. Therefore, the key for digital policy to promote sustainable agricultural modernization lies not only in the introduction of policy tools, but also in reasonable cost control and incentive design, which can strengthen the internal motivation of each actor to participate in policy implementation.

Based on the tripartite evolutionary game analysis, this paper further introduces a Stackelberg game to describe the government’s first-mover decision-making behavior as a policy maker. Since digital policy formulation, subsidy arrangements, and implementation guidance are mainly led by the government, this paper sets the government as the leader and agricultural operators and farmers as followers. The government first determines the incentive levels for agricultural operators and farmers. After observing the government’s policy signal, agricultural operators and farmers make their optimal responses, which jointly determine the final state of sustainable agricultural modernization.

To measure the effect on sustainable agricultural modernization, this paper introduces an index of the sustainable agricultural modernization level. This index is specified as a function of the participation degree of agricultural operators, the participation degree of farmers, and the coordination effect between them. By constructing a Stackelberg game model in which the government acts as the first mover and agricultural operators and farmers act as followers, this paper further explains how big data policy tools affect sustainable agricultural modernization by changing the behavioral choices of micro-level actors.

4. Government First-Mover Decision, Subsidy Optimization, and Stackelberg Equilibrium Analysis

4.1. Model Setting and Research Hypotheses

This study identifies the government, agricultural operators, and farmers as the game players. The government acts as the leader and first determines the level of policy incentives, while agricultural operators and farmers act as followers and make their optimal responses after observing the government’s policy decisions. The government is modeled as the leader because digital policy formulation, subsidy arrangements, resource allocation, and regulatory guidance are mainly initiated and coordinated by the government. Agricultural operators and farmers then adjust their behavior in response to these policy signals.

The Stackelberg framework does not mean that governments have perfect information or unlimited ability to optimize policy in practice. Instead, it is used as a basic model of a sequential policy process. In this process, the government usually sets subsidy schemes, allocates policy resources, and makes regulatory rules before agricultural operators and farmers adjust their behavior. This setting fits the institutional logic of digital agricultural policy implementation. Policy incentives are first introduced by the government and then passed to agricultural operators and farmers through subsidies, regulation, technical services, and platform governance. This study also recognizes that real government decisions are limited by political priorities, fiscal capacity, administrative capacity, institutional arrangements, and information constraints. Therefore, the optimal subsidy levels derived from the Stackelberg model should be interpreted as theoretical benchmark values rather than precise policy prescriptions. The purpose of the model is not to assume that the government can perfectly calculate and implement the optimal subsidy combination, but to reveal the mechanism through which government subsidy decisions reshape the payoff structures of agricultural operators and farmers, thereby influencing the level of sustainable agricultural modernization.

To keep the model consistent with the previous evolutionary game model, this study still uses $\mathrm{y}$ to represent the active response level of agricultural operators and $\mathrm{z}$ to represent the active participation level of farmers, where $0 \le \mathrm{y} \le 1$ and $0 \le \mathrm{z} \le 1$. A larger $\mathrm{y}$ means that agricultural operators are more willing to support and cooperate with the implementation of digital policy. A larger $\mathrm{z}$ means that farmers are more willing to take part in agricultural economic activities and respond to policy guidance.

The core pathway through which digital policy affects sustainable agricultural modernization lies in the transmission of policy incentives. This study selects the government subsidy for agricultural operators, ${\mathrm{S}}_2$, and the government subsidy for farmers, ${\mathrm{S}}_3$, as the government’s first-mover decision variables. ${\mathrm{S}}_2$ represents the incentive intensity provided by the government to encourage agricultural operators to engage in digital transformation, data access, and standardized operation. ${\mathrm{S}}_3$ represents the incentive intensity provided by the government to encourage farmers to participate in agricultural economic activities and respond to digital guidance.

To enhance the practical relevance of the model, this study further adjusts the payoff functions of agricultural operators and farmers. The participation levels of these two types of actors do not increase without limit; instead, they are constrained by diminishing marginal returns and increasing marginal costs. Therefore, this study introduces subsidy incentive terms and quadratic cost terms to capture the continuous decision-making characteristics of agricultural operators and farmers. Within this framework, the government acts as the leader and first determines the subsidy levels ${\mathrm{S}}_2$ and ${\mathrm{S}}_3$, while agricultural operators and farmers act as followers and choose their optimal participation levels (y) and (z), respectively.

Hypothesis 4.

When other conditions remain unchanged, an increase in the government subsidy $S_2$ for agricultural operators will significantly increase the optimal participation level $y^{*}$ of agricultural operators.

Hypothesis 5.

When other conditions remain unchanged, an increase in the government subsidy $S_3$ for farmers will significantly increase the optimal participation level $z^{*}$ of farmers.

Hypothesis 6.

Increasing government subsidies for agricultural operators and farmers can increase their participation levels and further promote sustainable agricultural modernization through the coordination effect, but this effect shows diminishing marginal returns.

4.2. Setting of Sustainable Agricultural Modernization Level and Payoff Functions

To clarify the link between the proposed model and sustainable development outcomes, this study conceptualizes sustainable agricultural modernization as a multidimensional construct rather than as a single output indicator. In the model, the level of sustainable agricultural modernization, (N), serves as a theoretical representation of the combined economic, social, and environmental effects generated by digital policy implementation. The economic dimension is reflected in improved production efficiency, reduced operational uncertainty, better resource allocation, and higher modernization returns resulting from the digital transformation of agricultural operators and the participation of farmers. The social dimension is reflected in inclusive participation, particularly whether farmers and weaker agricultural operators are able to engage in digital agricultural activities rather than being excluded by digital barriers. The environmental dimension is reflected indirectly through standardized production, digital monitoring, data-based management, and more efficient resource use, all of which can support greener and more sustainable agricultural practices.

Within this framework, the participation level of agricultural operators, (y), mainly captures the quality of digital transformation and standardized production. A higher value of (y) indicates that agricultural operators are more likely to adopt digital tools, improve data management, and comply with standardized production requirements, thereby contributing to both economic efficiency and environmental governance. The participation level of farmers, (z), captures the inclusiveness and social foundation of digital policy implementation. A higher value of (z) indicates that farmers are more willing and able to participate in digital agricultural activities, which helps reduce exclusion and improve the social sustainability of agricultural modernization. The interaction term (yz) captures the coordination effect between agricultural operators and farmers. It reflects the idea that sustainable agricultural modernization depends not only on the independent participation of each actor, but also on whether their actions are mutually reinforcing.

Therefore, the model does not directly measure environmental, social, and economic sustainability indicators in an empirical sense. Instead, it provides a theoretical mechanism for explaining how digital policy may influence these dimensions through actor participation, standardized production, incentive compatibility, and coordination. Let the level of sustainable agricultural modernization be defined as

$$N=\alpha y+\beta z+\gamma yz$$

(20)

where $\mathsf{\alpha }$> 0, $\mathsf{\beta }$> 0, $\mathsf{\gamma }$> 0 represent the contributions of agricultural business entity participation, farmer participation, and their coordination effect to sustainable agricultural modernization, respectively.

The government payoff function is set as:

$${\mathrm{U}}_{\mathrm{g}}=\mathrm{a}\mathrm{N}-\mathrm{b}{\mathrm{S}}_2-\mathrm{c}{\mathrm{S}}_3-{\mathrm{E}}_1$$

(21)

where $\mathrm{a}$ > 0 represents the overall benefit that sustainable agricultural modernization brings to the government, $\mathrm{b}$ > 0, $\mathrm{c}$ > 0 represent the weights of government subsidy expenditure, and ${\mathrm{E}}_1$ represents the cost of government implementation of the big data policy.

The payoff function of agricultural operators is revised as:

$${\mathrm{U}}_{\mathrm{b}}=\mathrm{d}\mathrm{N}+\mathsf{\theta }{\mathrm{S}}_2\mathrm{y}-{\mathrm{E}}_2{\mathrm{y}}^2$$

(22)

where $\mathrm{d}$ > 0 represents the effect of sustainable agricultural modernization on the operating income of agricultural operators, $\mathsf{\theta }$ > 0 represents the incentive coefficient of government subsidies for their active participation, and ${\mathrm{E}}_2{\mathrm{y}}^2$ represents the increasing marginal cost caused by the higher participation level of agricultural operators.

The payoff function of farmers is revised as:

$${\mathrm{U}}_{\mathrm{p}}=\mathrm{e}\mathrm{N}+\mathsf{\varphi }{\mathrm{S}}_3\mathrm{z}-{\mathrm{E}}_4{\mathrm{z}}^2$$

(23)

where $\mathrm{e}$ > 0 represents the effect of sustainable agricultural modernization on farmers’ utility, $\mathsf{\varphi }$ > 0 represents the incentive coefficient of subsidies for farmer participation, and ${\mathrm{E}}_4{\mathrm{z}}^2$ represents the increasing marginal cost faced by farmers as their participation level increases.

4.3. Solving the Optimal Response Functions of Followers

Substitute $\mathrm{N}$ into the payoff functions of agricultural operators and farmers.

The payoff function of agricultural operators can be written as:

$${\mathrm{U}}_{\mathrm{b}}=\mathrm{d}(\mathsf{\alpha }\mathrm{y}+\mathsf{\beta }\mathrm{z}+\mathsf{\gamma }\mathrm{y}\mathrm{z})+\mathsf{\theta }{\mathrm{S}}_2\mathrm{y}-{\mathrm{E}}_2{\mathrm{y}}^2$$

(24)

After simplification, we obtain:

$${\mathrm{U}}_{\mathrm{b}}=\mathrm{d}\mathsf{\alpha }\mathrm{y}+\mathrm{d}\mathsf{\beta }\mathrm{z}+\mathrm{d}\mathsf{\gamma }\mathrm{y}\mathrm{z}+\mathsf{\theta }{\mathrm{S}}_2\mathrm{y}-{\mathrm{E}}_2{\mathrm{y}}^2$$

(25)

Taking the first-order derivative with respect to $\mathrm{y}$, we obtain:

$${\displaystyle \frac{\partial {\mathrm{U}}_{\mathrm{b}}}{\partial \mathrm{y}}}=\mathrm{d}\mathsf{\alpha }+\mathrm{d}\mathsf{\gamma }\mathrm{z}+\mathsf{\theta }{\mathrm{S}}_2-2{\mathrm{E}}_2\mathrm{y}$$

(26)

Set the first-order condition equal to 0. The optimal response function of agricultural operators can be obtained as follows:

$${\mathrm{y}}^{\mathrm{*}}={\displaystyle \frac{\mathrm{d}\mathsf{\alpha }+\mathrm{d}\mathsf{\gamma }\mathrm{z}+\mathsf{\theta }{\mathrm{S}}_2}{2{\mathrm{E}}_2}}$$

(27)

Because

$${\displaystyle \frac{{\partial }^2{\mathrm{U}}_{\mathrm{b}}}{\partial {\mathrm{y}}^2}}=-2{\mathrm{E}}_2<0$$

(28)

Thus, the payoff function of agricultural operators is strictly concave in $\mathrm{y}$, so the above result is indeed the optimal response.

Similarly, the payoff function of farmers is:

$${\mathrm{U}}_{\mathrm{p}}=\mathrm{e}(\mathsf{\alpha }\mathrm{y}+\mathsf{\beta }\mathrm{z}+\mathsf{\gamma }\mathrm{y}\mathrm{z})+\mathsf{\varphi }{\mathrm{S}}_3\mathrm{z}-{\mathrm{E}}_4{\mathrm{z}}^2$$

(29)

After simplification, we obtain:

$${\mathrm{U}}_{\mathrm{p}}=\mathrm{e}\mathsf{\alpha }\mathrm{y}+\mathrm{e}\mathsf{\beta }\mathrm{z}+\mathrm{e}\mathsf{\gamma }\mathrm{y}\mathrm{z}+\mathsf{\varphi }{\mathrm{S}}_3\mathrm{z}-{\mathrm{E}}_4{\mathrm{z}}^2$$

(30)

Taking the first-order derivative with respect to $\mathrm{z}$:

$${\displaystyle \frac{\partial {\mathrm{U}}_{\mathrm{p}}}{\partial \mathrm{z}}}=\mathrm{e}\mathsf{\beta }+\mathrm{e}\mathsf{\gamma }\mathrm{y}+\mathsf{\varphi }{\mathrm{S}}_3-2{\mathrm{E}}_4\mathrm{z}$$

(31)

Set it equal to 0. The optimal response function of farmers can be obtained as follows:

$${\mathrm{z}}^{\mathrm{*}}={\displaystyle \frac{\mathrm{e}\mathsf{\beta }+\mathrm{e}\mathsf{\gamma }\mathrm{y}+\mathsf{\varphi }{\mathrm{S}}_3}{2{\mathrm{E}}_4}}$$

(32)

Since

$${\displaystyle \frac{{\partial }^2{\mathrm{U}}_{\mathrm{p}}}{\partial {\mathrm{z}}^2}}=-2{\mathrm{E}}_4<0$$

(33)

The payoff function of farmers is also strictly concave in $\mathrm{z}$, so the above result is also the optimal response.

In the revised model, the optimal responses of agricultural operators and farmers are no longer fixed values. They are functions of the government subsidy levels ${\mathrm{S}}_2$, ${\mathrm{S}}_3$. This means that government policy tools can directly affect follower behavior, which is more consistent with the real logic of how digital policy affect sustainable agricultural modernization.

Solving the followers’ response functions jointly.

Since the optimal responses of agricultural operators and farmers affect each other, they need to be solved jointly.

$$\mathrm{y}={\displaystyle \frac{\mathrm{d}\mathsf{\alpha }+\mathrm{d}\mathsf{\gamma }\mathrm{z}+\mathsf{\theta }{\mathrm{S}}_2}{2{\mathrm{E}}_2}}$$

(34)

$$\mathrm{z}={\displaystyle \frac{\mathrm{e}\mathsf{\beta }+\mathrm{e}\mathsf{\gamma }\mathrm{y}+\mathsf{\varphi }{\mathrm{S}}_3}{2{\mathrm{E}}_4}}$$

(35)

By solving the two equations jointly, the equilibrium responses of agricultural operators and farmers to the government subsidy levels can be obtained. Substituting the first equation into the second equation gives

$${\mathrm{z}}^{\mathrm{*}}={\displaystyle \frac{\mathrm{e}\mathsf{\beta }+\frac{\mathrm{e}\mathsf{\gamma }(\mathrm{d}\mathsf{\alpha }+\mathrm{d}\mathsf{\gamma }\mathrm{z}+\mathsf{\theta }{\mathrm{S}}_2)}{2{\mathrm{E}}_2}+\mathsf{\varphi }{\mathrm{S}}_3}{2{\mathrm{E}}_4}}$$

(36)

After further simplification, the expression of ${\mathrm{z}}^{\mathrm{*}}$ with respect to ${\mathrm{S}}_2$ and ${\mathrm{S}}_3$ can be obtained. Similarly, by substituting ${\mathrm{z}}^{\mathrm{*}}$ back into the response function of agricultural operators, the expression of ${\mathrm{y}}^{\mathrm{*}}$ with respect to ${\mathrm{S}}_2$ and ${\mathrm{S}}_3$ can be derived.

For a simpler presentation, the equilibrium response functions of agricultural operators and farmers are denoted as follows:

$${\mathrm{y}}^{\mathrm{*}}=\mathrm{Y}({\mathrm{S}}_2,{\mathrm{S}}_3)$$

(37)

$${\mathrm{z}}^{\mathrm{*}}=\mathrm{Z}({\mathrm{S}}_2,{\mathrm{S}}_3)$$

(38)

Then, the level of sustainable agricultural modernization can be written as:

$${\mathrm{N}}^{\mathrm{*}}=\mathsf{\alpha }\mathrm{Y}({\mathrm{S}}_2,{\mathrm{S}}_3)+\mathsf{\beta }\mathrm{Z}({\mathrm{S}}_2,{\mathrm{S}}_3)+\mathsf{\gamma }\mathrm{Y}({\mathrm{S}}_2,{\mathrm{S}}_3)\mathrm{Z}({\mathrm{S}}_2,{\mathrm{S}}_3)$$

(39)

4.4. Equilibrium Responses and the Government’s Optimal Subsidy Decision

Substitute ${\mathrm{y}}^{*}=\mathrm{Y}({\mathrm{S}}_2,{\mathrm{S}}_3)$, ${\mathrm{z}}^{*}=\mathrm{Z}({\mathrm{S}}_2,{\mathrm{S}}_3)$ into the government payoff function. The government optimization problem can be written as:

$${\mathrm{U}}_{\mathrm{g}}^{\mathrm{*}}=\mathrm{a}{\mathrm{N}}^{\mathrm{*}}-\mathrm{b}{\mathrm{S}}_2-\mathrm{c}{\mathrm{S}}_3-{\mathrm{E}}_1$$

(40)

that is:

$${\mathrm{U}}_{\mathrm{g}}^{\mathrm{*}}=\mathrm{a}\left[\mathsf{\alpha }\mathrm{Y}({\mathrm{S}}_2,{\mathrm{S}}_3)+\mathsf{\beta }\mathrm{Z}({\mathrm{S}}_2,{\mathrm{S}}_3)+\mathsf{\gamma }\mathrm{Y}({\mathrm{S}}_2,{\mathrm{S}}_3)\mathrm{Z}({\mathrm{S}}_2,{\mathrm{S}}_3)\right]-\mathrm{b}{\mathrm{S}}_2-\mathrm{c}{\mathrm{S}}_3-{\mathrm{E}}_1$$

(41)

The economic meaning of the government’s optimization problem is that the government does not seek to maximize subsidy expenditure itself, but rather to maximize the net policy return generated by sustainable agricultural modernization. An increase in ${\mathrm{S}}_2$ can raise the participation level of agricultural operators by reducing the relative costs of digital transformation, standardized production, data access, and organizational adjustment. Similarly, an increase in ${\mathrm{S}}_3$ can encourage farmers to participate more actively by compensating for learning costs, time costs, technology-use costs, and behavioral adjustment costs. In this sense, subsidies affect sustainable agricultural modernization by reshaping the marginal incentives of agricultural operators and farmers.

However, higher subsidies also increase government fiscal expenditure. Moreover, because the payoff functions of agricultural operators and farmers include quadratic cost terms, the marginal effect of subsidies on participation gradually weakens as participation levels increase. Therefore, the optimal subsidy policy is not to increase ${\mathrm{S}}_2$ and ${\mathrm{S}}_3$ without limit, but to balance the additional modernization benefits generated by higher participation against the additional fiscal cost of subsidy provision. The equilibrium subsidy levels ${\mathrm{S}}_2^{*}$ and ${\mathrm{S}}_3^{*}$ can thus be interpreted as the policy balance point at which the marginal policy gain from higher participation equals the marginal fiscal cost of additional subsidies.

Based on this economic interpretation, the first-order conditions are:

$${\displaystyle \frac{\partial {\mathrm{U}}_{\mathrm{g}}^{\mathrm{*}}}{\partial {\mathrm{S}}_2}}=0 \mathrm{and} {\displaystyle \frac{\partial {\mathrm{U}}_{\mathrm{g}}^{\mathrm{*}}}{\partial {\mathrm{S}}_3}}=0.$$

Based on these conditions, the optimal subsidy strategies ${\mathrm{S}}_2^{*}$ and ${\mathrm{S}}_3^{*}$ can be obtained. The Stackelberg equilibrium is then given by:

$$({\mathrm{S}}_2^{*},{\mathrm{S}}_3^{*};{\mathrm{y}}^{*},{\mathrm{z}}^{*}).$$

The model shows that big data policy does not directly determine the final outcome of sustainable agricultural modernization. Instead, it influences agricultural operators and farmers by reshaping their payoff structures, thereby affecting their participation levels. In general, higher subsidy levels increase the marginal benefits of participation for agricultural operators and farmers, which strengthens their willingness to engage in digital policy implementation. However, continuous increases in subsidies also raise government fiscal expenditure and create fiscal constraints. Therefore, the optimal policy choice is not to expand subsidies without limit, but to achieve a balance between incentive effects and fiscal costs.

Based on the revised Stackelberg game model, the following propositions can be obtained.

For Hypothesis 4, the optimal response function of agricultural operators

$${\mathrm{y}}^{\mathrm{*}}={\displaystyle \frac{\mathrm{d}\mathsf{\alpha }+\mathrm{d}\mathsf{\gamma }\mathrm{z}+\mathsf{\theta }{\mathrm{S}}_2}{2{\mathrm{E}}_2}}$$

(42)

$${\displaystyle \frac{\partial {\mathrm{y}}^{\mathrm{*}}}{\partial {\mathrm{S}}_2}}={\displaystyle \frac{\mathsf{\theta }}{2{\mathrm{E}}_2}}>0$$

(43)

Since $\mathsf{\theta }>0$, ${\mathrm{E}}_2>0$, ${\displaystyle \frac{\partial {\mathrm{y}}^{\mathrm{*}}}{\partial {\mathrm{S}}_2}}>0$. This means that a higher government subsidy for agricultural operators can increase their willingness to take part in the implementation of big data policy. Hypothesis 4 is supported.

For Hypothesis 5, according to the optimal response function of farmers,

$${\mathrm{z}}^{\mathrm{*}}={\displaystyle \frac{\mathrm{e}\mathsf{\beta }+\mathrm{e}\mathsf{\gamma }\mathrm{y}+\mathsf{\varphi }{\mathrm{S}}_3}{2{\mathrm{E}}_4}}$$

(44)

$${\displaystyle \frac{\partial {\mathrm{z}}^{\mathrm{*}}}{\partial {\mathrm{S}}_3}}={\displaystyle \frac{\mathsf{\varphi }}{2{\mathrm{E}}_4}}>0$$

(45)

Since $\mathsf{\varphi }>0$, ${\mathrm{E}}_4>0$, ${\displaystyle \frac{\partial {\mathrm{z}}^{\mathrm{*}}}{\partial {\mathrm{S}}_3}}>0$. This shows that a higher government subsidy for farmers helps increase their willingness to take part in agricultural economic activities. Hypothesis 5 is supported.

For Hypothesis 6, the function of sustainable agricultural modernization level is:

$$\mathrm{N}=\mathsf{\alpha }\mathrm{y}+\mathsf{\beta }\mathrm{z}+\mathsf{\gamma }\mathrm{y}\mathrm{z}$$

(46)

Since

$${\displaystyle \frac{\partial \mathrm{N}}{\partial \mathrm{y}}}=\mathsf{\alpha }+\mathsf{\gamma }\mathrm{z}>0$$

(47)

$${\displaystyle \frac{\partial \mathrm{N}}{\partial \mathrm{z}}}=\mathsf{\beta }+\mathsf{\gamma }\mathrm{y}>0$$

(48)

It can be seen that higher participation by agricultural operators and farmers can both promote sustainable agricultural modernization. Since the payoff functions of agricultural operators and farmers include the quadratic cost terms ${\mathrm{E}}_2{\mathrm{y}}^2$ and ${\mathrm{E}}_4{\mathrm{z}}^2$, their marginal costs increase as participation rises. Thus, although subsidy policies can increase $\mathrm{y}$ and $\mathrm{z}$, their marginal effect will gradually weaken as participation continues to rise. Hypothesis 6 is supported.

From a practical policy perspective, the Stackelberg equilibrium provides a decision-making logic for subsidy design in digital agricultural modernization. Subsidies may be used by governments not simply as fiscal transfers, but as incentive instruments through which agricultural operators and farmers are encouraged to move toward standardized production and active participation. When participation costs are high, well-designed subsidies can reduce the first barriers to digital adoption. Once participation has reached a relatively high level, however, further subsidy expansion may become less efficient, since marginal gains in participation decline while fiscal pressure continues to rise. For this reason, digital agricultural policy should place greater emphasis on incentive efficiency, fiscal sustainability, and targeted support, rather than relying on the continuous expansion of subsidy expenditures. This interpretation also helps clarify the relationship between the evolutionary game and the Stackelberg game frameworks. The evolutionary game captures how the system evolves under different combinations of government regulation, agricultural operators’ strategic behavior, and farmers’ participation decisions. In contrast, the Stackelberg game explains how the government, as the policy leader, can shape this evolutionary process by pre-setting subsidy levels and influencing the initial payoff structure. In other words, the evolutionary game describes the dynamic process of strategic adjustment among actors, while the Stackelberg game focuses on how policy design can guide and structure this adjustment process.

5. Discussion

5.1. From Policy Incentives to Multi-Agent Coordination

This study examines how digital policy affects sustainable agricultural modernization through strategic interactions among the government, agricultural operators, and farmers. The main finding suggests that digital policy does not promote sustainable agricultural modernization through a simple linear pathway. Instead, its effectiveness depends on whether policy incentives, implementation costs, regulatory constraints, and actor responses are aligned within a coordinated incentive structure. Accordingly, digital agricultural transformation should not be understood solely as a technological process, but also as an institutional and behavioral coordination process shaped by multi-actor interactions. This coordination perspective also helps clarify the relationship between the modelling framework and the sustainability dimensions of agricultural modernization. The model does not conceptualize sustainability as purely an environmental concern, nor does it reduce agricultural modernization to economic output growth alone. Instead, it links sustainability to three interrelated dimensions.

From an economic perspective, digital policy can enhance production efficiency and reduce operational uncertainty by encouraging digital adoption and standardized production practices. From a social perspective, it can improve inclusiveness by enabling farmers and smaller agricultural operators to participate in digital transformation, rather than being excluded due to digital barriers. From an environmental perspective, standardized production processes, digital monitoring systems, and data-driven management practices can contribute to more efficient resource utilization and more sustainable agricultural practices. Therefore, the transition from a low-coordination state to a high-coordination state represents not only a change in actor strategies, but also an improvement in the economic, social, and environmental foundations of sustainable agricultural modernization.

The evolutionary game results show that the system may evolve toward either a low-coordination state or a high-coordination state. The theoretical significance of this result lies in demonstrating that digital policy may face a coordination dilemma. When government implementation costs are high, subsidies are insufficient, or penalties are weak, agricultural operators and farmers may have limited incentives to participate in digital transformation. In this situation, the government may also reduce its regulatory effort because the expected return from policy implementation is low. As a result, the system may remain in a low-coordination equilibrium characterized by loose regulation, non-standardized production, and passive participation. Therefore, policy failure does not necessarily result from the absence of digital technology itself, but may instead arise from a mismatch between policy incentives and the actual costs faced by different actors.

By contrast, the high-coordination equilibrium indicates that strict government regulation, standardized production by agricultural operators, and active farmer participation can become mutually reinforcing when the incentive structure is appropriately designed. In this state, government regulation helps stabilize policy expectations, subsidies reduce the costs of digital adoption, and penalties increase the cost of non-compliant or non-standardized behavior. As a result, agricultural operators and farmers are more likely to adjust their strategies toward digital participation and standardized production. This finding further extends the understanding of sustainable agricultural modernization by highlighting that modernization is shaped not only by digital infrastructure and technological tools, but also by incentive compatibility and strategic interaction among multiple actors.

The Stackelberg analysis further develops this argument. It indicates that the government is not merely one participant in the evolutionary process, but also a policy designer that can shape the strategic environment before other actors make their decisions. The model, however, does not imply that subsidies should be expanded without constraint. Instead, the optimal subsidy decision requires the government to balance the marginal modernization benefits generated by higher participation against the marginal fiscal costs of additional subsidies. The central policy issue is therefore not subsidy expansion per se, but subsidy efficiency. Excessive subsidies may generate fiscal pressure, policy dependency, and inefficient resource allocation, whereas insufficient subsidies may fail to mobilize agricultural operators and farmers. Therefore, the key contribution of the Stackelberg analysis is to clarify the economic logic of optimal subsidy design under fiscal and behavioral constraints.

5.2. Comparison with Previous Studies

This study indicates that digital technologies and digital policies can improve agricultural modernization. Technology-oriented studies have shown that IoT platforms, big data analytics, machine learning, digital twins, and farm management information systems can enhance real-time monitoring, crop forecasting, soil management, irrigation control, machinery optimization, and supply-chain coordination [46,47,48,49,50,51,52,53,54,55]. Moreover, it further suggests that the availability of digital technologies alone is insufficient to ensure sustainable agricultural modernization. Digital technologies can generate modernization benefits only when agricultural operators and farmers have sufficient incentives and capacity to adopt them. In this sense, this study moves beyond a technology-centered explanation and emphasizes the behavioral and institutional conditions under which digital technologies become effective.

Firstly, this study is closely related to macro-level empirical research on the digital economy, digital finance, broadband infrastructure, and agricultural modernization. In previous studies, Ye [58] shows that the digital economy and digital inclusive finance can promote sustainable agricultural modernization, high-quality agricultural development, and urban–rural integration. Gao et al. [63], Xu and Yang [64], and Wu et al. [65] further demonstrate that digital finance can improve agricultural resilience, rural industrial revitalization, and agricultural total factor productivity by reshaping factor allocation and service provision. International evidence from LoPiccalo [66] and Kim and Paudel [67] also indicates that broadband infrastructure and broadband subsidies can improve agricultural productivity. These studies provide important evidence of the positive average effects of digitalization. However, they mainly address whether digitalization improves agricultural outcomes. The present study complements this literature by explaining how such effects may be generated through strategic interactions among the government, agricultural operators, and farmers. It shows that the effects of digital policy depend on whether policy incentives can offset implementation costs, adoption costs, and participation costs.

Secondly, the results explain why the effects of digital policy may vary across regions and policy contexts. Existing empirical studies have found that the effects of digitalization differ across regions, development stages, and infrastructure conditions [68,69,70]. The model developed in this study provides a mechanism-based interpretation of this heterogeneity. In regions with stronger digital infrastructure, lower government implementation costs, and lower participation costs for relevant actors, digital policy is more likely to move the system toward a high-coordination equilibrium. By contrast, in regions where implementation costs are high, subsidies are insufficient, or farmers and agricultural operators lack digital capacity, the same type of digital policy may fail to generate coordinated participation. Therefore, this study extends existing empirical findings by linking regional heterogeneity to incentive compatibility and multi-agent strategic responses.

Thirdly, the study contributes to governance-oriented research on digital divides, data governance, and unequal access to the benefits of digital agriculture. Rotz et al. [55] show that agricultural automation and digital technologies may reshape farm labour, rural communities, and data control. Coca et al. [56] and Coggins et al. [57] further suggest that digital agriculture may reinforce inequalities when smallholders face barriers related to infrastructure access, digital literacy, trust, and socioeconomic conditions. Similarly, studies on platform governance and agricultural data governance indicate that digital platforms may create new power asymmetries and data-control problems. The present study provides a formal mechanism-based explanation of these concerns. If subsidies and digital resources are mainly captured by large agricultural operators with stronger capital and technological capacity, small farmers and weaker operators may remain outside the high-coordination path. Therefore, digital policy may improve overall efficiency while also generating unequal outcomes unless inclusive participation is explicitly incorporated into policy design.

Finally, compared with existing evolutionary game studies, this study provides a further methodological extension. Previous studies have used evolutionary game models to examine the digital transformation of farmer cooperatives, blockchain traceability, water-saving governance, and agricultural technology adoption. These studies show that government incentives, market demand, information transparency, and moderate subsidies can influence actor strategies and equilibrium outcomes. However, most of them treat government subsidies and regulatory intensity as exogenous parameters. The present study differs by introducing a Stackelberg framework to capture the government’s first-mover role in subsidy design. This allows the analysis to move from examining how actors evolve under given policy parameters to explaining how the government can design subsidy instruments to shape the payoff structures of agricultural operators and farmers before their participation decisions are made.

Overall, this study confirms the positive role of digital policy identified in previous research, but it also qualifies this conclusion. Digital policy does not automatically lead to sustainable agricultural modernization. Its effectiveness depends on the alignment among policy incentives, government implementation capacity, agricultural operators’ adoption costs, and farmers’ participation constraints. The main contribution of this study is therefore to connect macro-level digital policy effects with micro-level behavioral responses and to explain how multi-agent coordination determines whether digital agricultural modernization moves toward a low-coordination or high-coordination equilibrium.

5.3. Policy Implications for Sustainable Digital Agricultural Governance

The policy implications of this study should be read with caution. The results do not mean that higher subsidies or lower government implementation costs will always improve coordination. Instead, they show that digital agricultural policy should focus on incentive compatibility, fiscal sustainability, differentiated support, and inclusive governance. First, reducing government implementation costs should not mean reducing necessary public investment. In the early stages of agricultural digitalization, public investment in digital infrastructure, data platforms, technical training, and regulatory capacity may still be necessary. The main policy question is not how to reduce all public spending, but how to reduce inefficient implementation costs. Implementation efficiency can be improved by strengthening coordination across departments, avoiding repeated platform construction, improving data-sharing mechanisms, and using digital tools for monitoring and evaluation. In this way, lower implementation costs should come from stronger governance capacity, not from weaker public support. Second, subsidy policy should focus on incentive efficiency rather than subsidy expansion. The model shows that subsidies can increase the willingness of agricultural operators and farmers to participate, but their marginal effect may decline as participation levels rise. Therefore, subsidies should not be given as unconditional financial transfers. They should be linked to actual digital adoption, standardized production, data reporting quality, participation performance, and measurable modernization outcomes.

Third, policy design should account for the heterogeneity of agricultural actors. Large agricultural operators usually have stronger financial capacity, better access to digital technologies, and greater ability to absorb subsidies. By contrast, small farmers and weaker agricultural operators may face higher learning costs, lower digital literacy, limited access to services, and greater risk exposure. If a uniform subsidy standard is applied to all actors, digital policy may unintentionally widen the gap between large-scale operators and smallholders. Therefore, governments should adopt differentiated policy instruments, including targeted subsidies, digital training, low-cost technical services, simplified digital tools, and support for small farmers in less developed regions.

Fourth, regulatory penalties should be combined with supportive services. Penalties can increase the cost of non-standardized behavior and improve policy discipline, but excessive reliance on punishment may discourage participation, especially among actors with limited digital capacity. Effective digital governance should therefore combine incentives, supervision, and capacity building. Regulation should not only punish non-compliance, but also help agricultural operators and farmers acquire the capacity to comply with digital and standardized production requirements.

Finally, digital agricultural policy should address the risk of unequal digitalization. If policy incentives mainly benefit actors with better infrastructure, stronger capital, and higher digital literacy, digital transformation may reinforce existing inequalities. Therefore, sustainable agricultural modernization requires not only improvements in productivity and efficiency, but also the protection of inclusive participation. Policy makers should pay particular attention to small farmers, weaker agricultural operators, and regions with poor digital infrastructure.

5.4. Limitations of the Modelling Approach

This study builds a theoretical framework based on evolutionary game theory and a Stackelberg game. It studies how digital policy affects sustainable agricultural modernization. The model helps explain incentive relations among the government, agricultural operators, and farmers. Some limits should be stated when the results are interpreted.

First, the analysis is mainly theoretical and based on simulation. It does not use empirical estimation or causal analysis from real policy data. So the results should be seen as explanations of possible mechanisms and strategic interactions. They should not be seen as exact measures of real policy effects. Second, the simulation uses scenario-based benchmark parameters. These parameters are set to show relative relations among key variables such as implementation costs, adoption costs, subsidies, penalties, and expected benefits. But they are not based on large real datasets. If the parameters change, the results can also change. The system may show different paths, different speeds, and different final states. So the results are only examples under specific settings. Third, the model simplifies the system by focusing on three main actors: government, agricultural operators, and farmers. This helps make the model clear and easier to analyze. It also highlights the main incentive links. But real digital agriculture also includes other actors. These include digital platforms, technology providers, financial institutions, cooperatives, extension agencies, data governance bodies, and consumers. Leaving these actors out reduces the ability of the model to show full real-world complexity in coordination, services, finance, and data flow. Fourth, differences across regions and actors are only partly included. In reality, policy effects can be different in developed regions and less-developed regions. They can also be different in grain-producing areas and non-grain-producing areas. Actors also differ in size, capital, digital ability, education level, and risk preference. These differences can affect costs, response to subsidies, and adoption behavior. They can also affect whether a high-coordination state is reached. Using one set of parameters can hide these differences. Fifth, the Stackelberg model assumes the government is the first mover in setting subsidy policy. This helps to study how government decisions affect other actors. But in real practice, government decisions are also limited by fiscal capacity, institutions, information limits, and coordination problems between departments. So the results should be seen as theoretical reference points, not direct policy rules.

Overall, the model gives a structured way to understand incentive relations in digital agricultural policy. It shows how alignment among actors can support coordinated participation in sustainable agricultural modernization. The assumptions, parameter settings, and simplifications should be considered when the results are used or interpreted.

5.5. Future Directions for Empirical Validation

Building on the theoretical framework developed in this study, future research should prioritize strengthening empirical validation to enhance the robustness and practical relevance of the model. A key step in this direction is to test whether the mechanisms identified in the evolutionary game and Stackelberg framework hold in real-world policy contexts. This can be achieved using provincial panel data, county-level policy records, farmer survey data, field experiments, and quasi-natural experimental designs. Such empirical evidence would help determine whether digital policy indeed drives the strategic responses of governments, agricultural operators, and farmers in the manner suggested by the model, and whether transitions between low-coordination and high-coordination equilibria can be observed in practice.

In addition to validation, parameter calibration using real-world data represents an important avenue for improving model realism. Government implementation costs could be approximated through fiscal expenditures on digital agriculture initiatives, rural digital infrastructure, smart village programs, data platforms, technical training, and agricultural extension services. Similarly, the adoption costs of agricultural operators may be inferred from investments in digital equipment, traceability systems, data management platforms, and production standardization processes. Farmers’ participation costs can be assessed using survey-based indicators such as learning time, digital literacy levels, platform usage costs, perceived risks, and behavioral adjustment burdens. Policy instruments such as subsidies and penalties can be derived from official policy documents, administrative implementation records, and local regulatory guidelines. By grounding these parameters in observed data, the explanatory power and empirical relevance of the simulation results can be significantly improved.

Another important research direction is the incorporation of actor heterogeneity into the analytical framework. In practice, agricultural operators vary substantially in scale, financial capacity, organizational structure, and technological readiness. Large agribusinesses and cooperatives are generally better positioned to absorb the costs of digital transformation, while smallholders and small service providers may face higher relative barriers and greater uncertainty. Farmers also differ in education level, income, production scale, digital literacy, and risk preferences, all of which can shape their responsiveness to policy incentives. Accounting for such heterogeneity would allow for a more refined understanding of how digital policy may either reduce or widen the digital divide in agricultural modernization.

Future research could also expand the set of actors included in the model to better reflect the complexity of digital agricultural governance. Beyond governments, operators, and farmers, key stakeholders such as digital platforms, technology service providers, financial institutions, agricultural cooperatives, extension organizations, and data governance agencies play critical roles in shaping infrastructure provision, technology diffusion, financing conditions, and service accessibility. Incorporating these actors would provide a more comprehensive representation of institutional interactions and better capture the multi-layered governance structure underlying digital agricultural transformation.

A further promising direction lies in integrating theoretical modelling with empirical identification strategies. The current framework can be used to generate testable hypotheses regarding subsidy effectiveness, penalty intensity, participation thresholds, and equilibrium stability. These hypotheses can then be examined using methods such as panel data econometrics, policy evaluation designs, structural estimation, field surveys, and experimental approaches. This combined strategy would preserve the explanatory strengths of theoretical modelling while enhancing empirical credibility and policy relevance.

Future research should aim to more closely integrate theoretical models, empirical evidence, and policy implementation. Such integration would not only validate the mechanisms proposed in this study, but also help identify the institutional and economic conditions under which digital policy can effectively promote sustainable agricultural modernization, while avoiding excessive fiscal pressure, weak participation incentives, or unequal distribution of digital benefits.

6. Conclusions

This study examines how digital policy contributes to sustainable agricultural modernization by shaping strategic interactions among the government, agricultural operators, and farmers. Rather than treating digital policy as a purely technological input or an external shock, it is conceptualized as a multi-actor governance mechanism in which outcomes are jointly determined by implementation costs, subsidy incentives, regulatory enforcement, and behavioral responses. By integrating a three-party evolutionary game framework with a Stackelberg game structure, the study explains how incentive design and strategic interaction jointly drive system-level coordination in agricultural modernization.

From a substantive perspective, the findings suggest that digital agricultural modernization is fundamentally an incentive-compatible coordination process. When implementation costs are high, subsidies are insufficient, or regulatory enforcement lacks credibility, the system tends to remain in a low-coordination equilibrium. In this state, agricultural operators have weak incentives to adopt standardized digital production practices, farmers show limited willingness to participate, and policy implementation becomes fragmented and unstable. By contrast, when policy incentives are sufficiently strong and well-aligned with actor-specific costs, and when regulatory mechanisms are credible, the system can evolve toward a high-coordination equilibrium. This state is characterized by active governmental implementation, widespread standardized digital adoption by operators, and sustained participation from farmers. These results highlight that the effectiveness of digital policy depends not only on technological readiness, but also on the compatibility between policy instruments and heterogeneous actor incentives.

Methodologically, the study contributes by combining evolutionary game theory with a Stackelberg decision-making framework. The evolutionary game model shows how strategies change over time among the three actors under different costs, subsidies, penalties, and behavior conditions. The Stackelberg framework sets the government as the first mover in subsidy and incentive design. It shows how government decisions change payoffs before other actors adjust their strategies. Together, these methods explain how policy tools affect behavior and system coordination outcomes.

The analysis also yields several policy implications. First, improving the effectiveness of digital policy requires enhancing implementation efficiency rather than simply increasing fiscal input. This includes strengthening inter-departmental coordination, reducing duplication across digital platforms, integrating fragmented infrastructure, and leveraging digital tools to lower supervision costs. Second, subsidy systems should link more closely to clear performance indicators. These include digital adoption, standardized production behavior, data reporting quality, and participation results. Third, policy design should differ across regions and actor groups. It should consider differences in digital ability, adoption costs, and participation limits. Targeted support for farmers is important for inclusive participation and system stability.

Furthermore, several limitations of the present study warrant careful consideration. The study is based on theoretical modelling and numerical simulation rather than empirical estimation using observed data. The simulation parameters are scenario-based and not calibrated using large-scale datasets. Moreover, the model includes only three core actors and does not explicitly incorporate other important stakeholders such as digital platforms, cooperatives, financial institutions, extension organizations, or consumers. In addition, heterogeneity across regions and actors is only partially represented. Building on these limitations, future research should prioritize empirical validation using panel data, survey data, field experiments, or quasi-natural experimental designs. More broadly, theoretical modelling can also be combined with empirical identification methods. This can improve the ability to explain results. It can also improve the policy relevance of research on digital policy and agricultural modernization.

In summary, this study reframes digital policy-driven agricultural modernization as a process of multi-actor strategic coordination rather than a simple technological diffusion outcome. The study shows that successful modernization depends on an incentive-compatible system among governments, agricultural operators, and farmers. This perspective helps explain why digital policy performs effectively under certain institutional conditions, while under others it may lead to weak coordination, inefficiency, or uneven participation.