Synergistic Mechanisms of Blockchain Adoption and Government Subsidies in Contract Farming Supply Chain Systems: A Multi-Stage Stackelberg Game Approach

Abstract

Blockchain technology can enhance traceability and trust in contract farming supply chains, yet high implementation costs deter adoption by supply chain participants. This study examines the synergistic mechanisms between blockchain adoption strategies and government subsidy policies. We develop a multi-stage Stackelberg game model involving an agricultural enterprise, an e-commerce platform, and a government, and comparatively analyze six decision-making scenarios across non-subsidy, unilateral subsidy, and full-chain subsidy settings. Three key findings emerge. First, blockchain investment has a cost–effect threshold below which consumer traceability preferences do not translate into profit gains. Second, well-designed subsidies overcome investment inertia and yield Pareto improvements in both profits and social welfare, with the full-chain subsidy model (Model BG) maximizing social welfare; however, subsidies exhibit distinct efficiency boundaries, and over-subsidization causes resource misallocation. Third, both supply chain parties tend to free-ride on the other’s investment, creating strategic conflicts that necessitate differentiated subsidy mechanisms tailored to specific dominance structures. These findings provide policy guidance for facilitating agricultural digital transformation and enhancing supply chain coordination.

1. Introduction

Against the backdrop of economic globalization and rapid advancements in information technology, the efficient operation and sustainable development of the agricultural supply chain have become key factors in advancing agricultural modernization [1]. The contract farming supply chain, as an innovative agricultural business model, closely links farmers with enterprises through contractual agreements [2], effectively connecting agricultural production with market demand. It plays a particularly important role in promoting the modernization and large-scale development of agriculture in developing countries [3]. However, with intensifying market competition and increasing consumer demand for the quality and safety of agricultural products, the contract farming supply chain faces a series of severe challenges in practice. Among these, the inadequacy of traceability systems for agricultural products are particularly prominent [4]. When quality or safety issues arise with agricultural products, it is difficult to quickly and accurately trace the source of the problem. This not only negatively impacts brand reputation, image, and consumer trust in agricultural products [5] but also poses a potential threat to the sustainable development of the contract farming supply chain.

Blockchain technology is a modern digital technology used for information storage and retrieval and is capable of monitoring the origin of agricultural products. This helps improve the traceability systems of contract farming supply chains and enhances consumer trust [6,7,8]. With its characteristics of decentralization, smart contracts, security, reliability, and tamper-proof information [9], the application of blockchain technology in supply chains enables transparent information sharing and strengthens trust among participants [10,11]. Kshetri [12] and Dutta et al. [13] further explored the mechanisms through which blockchain technology influences factors such as the cost, quality, reliability, and flexibility of supply chain management. Additionally, Duong et al. [14] found that blockchain technology can overcome collaboration and trust issues in supply chains, exerting a continuous indirect effect on consumers’ purchasing decisions and thereby enhancing the overall performance of the supply chain. Overall, blockchain technology can enhance consumers’ cognitive trust (digital trust) and instant trust (swift trust) and increase their immediate purchases of agricultural products [15]. However, the high infrastructure construction cost of blockchain technology inhibits, to a certain extent, the willingness of supply chain members to adopt it.

To address this challenge of market failure, government subsidies are particularly important as a policy tool capable of internalizing positive externalities. Song et al. [16], based on evolutionary game theory, constructed an evolutionary game model involving the government, agricultural enterprises, and telecommunications operators. They found that when agricultural enterprises and telecommunications operators establish cooperative relationships, government incentives such as tax reductions and increased subsidies can promote the development of tripartite cooperation. Therefore, reasonable government subsidies can reduce enterprise costs, increase their enthusiasm for participating in contract farming, and guide the contract farming supply chain towards sustainable development. However, existing studies typically examine blockchain technology adoption and government subsidy mechanisms in isolation. This separated approach overlooks a critical interdependence: the effectiveness of subsidies depends on the cost structure and market conditions of blockchain investment, while the feasibility of blockchain adoption is, in turn, shaped by the availability and design of subsidy policies. Therefore, a unified analytical framework that endogenizes both blockchain investment decisions and government subsidy optimization is essential for understanding their synergistic effects and for designing efficient policies.

This study explores the synergistic mechanism between blockchain adoption strategies and government subsidies under market uncertainty. Specifically, this study focuses on addressing the following research questions:

(1)

Is there an optimal efficiency frontier for government subsidies?

(2)

How do market environment factors and cost factors impact the decisions and profits of supply chain members?

(3)

How should differentiated subsidy strategies be designed for different dominance models, and does a free-riding dilemma exist within the supply chain?

(4)

Can government subsidies overcome investment inertia, and through what mechanism can a Pareto improvement in both profits and social welfare be achieved?

In this study, we adopt an e-commerce platform as the downstream entity rather than a traditional retailer. This choice reflects the growing prominence of e-commerce platforms in China’s agricultural product distribution, where platforms have established direct farmer-to-consumer channels through the “e-commerce assistance to farmers” model, becoming key intermediaries in contract farming supply chains (Wu and Zhu [17]). Compared with traditional brick-and-mortar retailers, e-commerce platforms possess existing digital infrastructure—including cloud computing, data analytics, and digital payment systems—that substantially lowers the marginal cost of blockchain integration, making blockchain adoption a realistic strategic option (Wang et al. [18]; Liu [19]). Moreover, the platform structure fundamentally alters the supply chain power dynamic. E-commerce platforms have direct access to real-time consumer data, including purchasing behavior and traceability queries, granting them an information advantage that strengthens their bargaining position relative to upstream agricultural enterprises. This information asymmetry provides a natural justification for the Stackelberg game structure in our model, where the platform determines procurement pricing based on observed market signals before the agricultural group commits to production decisions.

To address the aforementioned issues, this study constructs a contract farming supply chain model composed of an agricultural group (upstream) and an e-commerce platform (downstream). To resolve the trust deficit in agricultural products, the model incorporates blockchain technology as a solution while considering construction costs and market uncertainty constraints. Under this model, by introducing the government as a player, a four-stage Stackelberg game model is constructed that encompasses the government, agricultural groups, e-commerce platforms, and consumers.

This study explores in depth the synergistic mechanism between blockchain adoption strategies and government subsidies. Specifically, we establish six typical decision-making scenarios across two categories: a baseline case (without subsidies) and an extended case (with subsidies). We systematically derive the optimal planting area, procurement price, and blockchain node investment strategies under different dominance models. Furthermore, we analyse the sensitivity of the equilibrium results to key parameters such as consumer traceability preference, price sensitivity, and technology costs. Through comparative analysis, we identify the optimal equilibrium combination capable of achieving a Pareto improvement in supply chain profits. Finally, the study extends its scope to the macro-welfare level, examining the impact of different strategy combinations on total social welfare and precisely delineating the effectiveness boundaries of government subsidy policies.

The remainder of this paper is organized as follows. Section 2 reviews the relevant literature on contract farming supply chains, blockchain technology applications, and government subsidies, and identifies the research gaps. Section 3 presents the model description and basic assumptions. Section 4 constructs the game models and derives the equilibrium strategies under six decision-making scenarios. Section 5 provides a theoretical analysis of the equilibrium results, including parameter sensitivity and cross-model comparisons. Section 6 conducts numerical simulations to validate the theoretical propositions. Section 7 concludes the paper with the main findings, managerial and policy implications, and future research directions.

2. Literature Review

2.1. Research on Contract Farming Supply Chains

The contract farming supply chain is a collaborative system that uses contracts as the core link to integrate entities such as farmers, agricultural enterprises, and distributors, connecting the entire chain from production and processing to sales. Its core value lies in reducing supply–demand uncertainty through contracts, thereby promoting the large-scale and market-oriented transformation of agriculture. In recent years, influenced by climate change, market volatility, and digital innovation, its optimization, upgrading, and risk management have become research hotspots. The academic community has produced multidirectional research results while also revealing numerous practical challenges.

The existing research has constructed multidimensional theoretical linkage frameworks. With respect to green production and policy incentives, Shi et al. [20] revealed that under different climate risk scenarios, the incentive effects of agricultural insurance subsidies and green investment subsidies on farmers’ green technology adoption differ significantly. Li and Cao [21] further confirmed that constructing a green technology cost-sharing mechanism between risk-averse farmers and enterprises can effectively achieve a win–win situation for the supply chain. Extending to risk management, the three types of weather risk hedging mechanisms proposed by Li et al. [22] effectively compensated for the shortcomings of traditional price protection mechanisms. However, risk management relies on reasonable contract design. Pamucar et al. [23] reported that option contracts with replenishment cost sharing can achieve full coordination in a three-level supply chain, whereas Ye et al. [24] noted from the side that farmer risk aversion and yield uncertainty amplify the efficiency loss under decentralized decision-making. In addition, agricultural cooperatives, as key intermediaries connecting farmers with downstream entities, can optimize supply chain benefits and risk allocation. The dual revenue-sharing contract designed by Shi and Wang [25] can effectively coordinate contract farming supply chains with both yield and demand uncertainties, providing a new perspective for contract optimization.

With respect to the application and empowerment of digital technology, Liao and Lu [26] proposed that digital cooperation models need to be dynamically adjusted in combination with wholesale prices and farmer risk preferences. The introduction of digital technology aims to alleviate information asymmetry, which is closely related to the power structure of the supply chain. Fu et al. [27] confirmed that farmer expertise and reward power can enhance alliance performance, whereas Hong et al. [28] reported that differences in production and transportation costs affect enterprise information sharing strategies. Li et al. [29] further validated through a game-theoretic model that the supply chain power structure (supplier-led, manufacturer-led, balanced structure) has a decisive impact on the realization of investment value in data-intensive technologies like blockchain, with the dominant party often capturing a greater share of the technology benefits. With the expansion of research perspectives, supply chain resilience has become another focus. Mukucha and Chari [30] confirmed that contract farming can enhance the resilience of the fast-food industry supply chain. Nguyen et al. [31], by analysing the Mekong Delta rice supply chain, revealed the complex logic of chain interactions.

Although existing research has explored multiple optimization paths, contract farming supply chains still face prominent deep-seated problems. First, the issue of power imbalance and unfair contracts is prominent. Nematollahi et al. [32], in a dual-channel supply chain study, confirmed that the bargaining gap between enterprises and farmers easily leads to contracts that favour the stronger party and that penalty-type contracts further exacerbate benefit imbalance, seriously affecting cooperation stability, This phenomenon also exists in blockchain technology investment scenarios, where differences in power structures directly lead to uneven distribution of technology costs and benefits [29]. Second, the risk response system has shortcomings. Xing et al. [33] noted that the superposition of demand and yield dual uncertainties makes it difficult for traditional mechanisms to cover extreme risks, while farmers’ risk-averse tendencies formed because weak bargaining power further inhibits production investment and intensifies supply chain fluctuations. Third, there are barriers to the application of digital technology. Zhou et al. [34] found that high financing costs and insufficient technology output constrain farmers’ willingness to adopt IoT technology, limiting the effectiveness of subsidy incentives and making it difficult for digital technology to effectively alleviate information asymmetry. Therefore, this paper constructs a multistage Stackelberg game model involving the government and supply chain entities, endogenizing blockchain construction costs and market uncertainty. Moreover, the driving effect of diversified supply chain structures on development quality and the moderating effect of digital technologies have not been fully explored [35]. Notably, while Li et al. [29] demonstrated that power structures decisively influence blockchain investment value distribution, their analysis is confined to a single supply chain tier without subsidy intervention. Our model extends this line of work by incorporating government subsidies as an endogenous variable and comparing how different dominance structures (upstream-led, downstream-led, and full-chain) interact with subsidy allocation to shape technology investment incentives. By exploring the synergistic evolution mechanism and efficiency boundary of government subsidies and technology investment, this study further analyzes strategic conflicts and problems under different dominant models.

2.2. Research on the Application of Blockchain Technology in Supply Chains

Blockchain technology is a decentralized data storage and transmission technology based on distributed ledgers. Its core features include decentralization, immutability, transparent traceability, and automated smart contract execution. These characteristics provide key support for solving traditional supply chain pain points such as information asymmetry, inefficient collaboration, and traceability difficulties, forming the basis for the empowerment of supply chain management. The core application value of blockchain technology in supply chain management is reflected in enhancing information transparency, optimizing operational efficiency, innovating financial services, and strengthening risk control, thereby comprehensively improving supply chain operational efficiency [36]. Relying on the above characteristics, blockchain has achieved in-depth empowerment in multidimensional supply chain scenarios.

In food and agricultural supply chains, Ma [37], through dynamic game analysis, found that blockchain traceability technology can improve product quality and participant profits, increase the willingness of various entities to participate, and increase social welfare and consumer surplus, providing an effective path for food safety assurance. Big data analysis by Rejeb et al. [38] further supplemented that the application of blockchain in food supply chain traceability revolves around three core themes: transparency, security, and sustainability, providing practical guidance for multiple entities. In the field of port logistics, Boison et al. [39], addressing the inefficiency issues of West African ports, proposed a blockchain distributed ledger model covering the entire process, significantly improving port operational transparency, efficiency, and data security and assisting the digital transformation of ports in developing regions. In medical supply chains, Aldosari et al. [40], through a systematic review, confirmed that blockchain can solve information sharing and security challenges, improve the effectiveness and transparency of medical data exchange in Saudi Arabia, and aid in precise credit acquisition and risk vulnerability identification. In the field of construction supply chains, Karacigan et al. [41], addressing contract management pain points, constructed a blockchain implementation strategic roadmap, promoting technology adoption by integrating key factors and improving supply chain collaboration efficiency. In supply chain finance scenarios, Muneeb et al. [42] combined QFD and BWM to construct an optimization framework, achieving financial risk reduction and liquidity improvement by strengthening technical features.

Furthermore, the introduction of blockchain technology can help enhance corporate social responsibility and consumer trust. Research has indicated that the increased transparency brought about by technology significantly promotes the fulfilment of corporate social responsibility [43]. With respect to the green agricultural retail sector, Liu et al. [15] found that blockchain affects consumer purchasing behaviour through a dual-trust path. Moreover, Shahzad et al. [44] confirmed that blockchain technology positively moderates the relationship between technology adaptation and user intention in food delivery applications.

From the perspectives of technology adoption drivers and practice, Tokkozhina et al. [45] found that both parties recognize the value of blockchain in speeding up processes and reducing errors, but differences exist in technology perception and application scenario definition, necessitating stronger supply–demand alignment. In specialty agricultural product supply chains such as wine, Stackelberg game analysis by Kang et al. [46] revealed that the implementation cost of blockchain traceability systems, third-party service fees, and consumer traceability preferences are key factors determining technology adoption and the dominant party, providing direct reference for blockchain application in contract farming supply chains.

In summary, with its unique trust mechanism and technical architecture, blockchain technology has broken through single scenarios, forming mature implementation paradigms in diverse fields such as food, healthcare, and finance. Among existing game-theoretic studies, Kang et al. [46] is the closest to our work, as it applies a Stackelberg framework to analyze blockchain traceability adoption in agricultural supply chains. However, their model considers only a single adopting party and does not incorporate government subsidy as a decision variable. Our model advances beyond Kang et al. [46] by simultaneously endogenizing the blockchain investment decisions of both supply chain parties and the government’s subsidy ratio, enabling the analysis of free-riding behavior and the identification of efficiency boundaries for subsidy policies. In view of this, this paper introduces blockchain technology into the contract farming supply chain and, on the basis of the perspective of consumer traceability preference, systematically analyzes blockchain adoption strategies and optimal decision-making mechanisms under different dominant models.

2.3. Related Research on Government Subsidies

Government subsidies, as an important policy tool for regulating supply chain development, have been extensively studied in terms of their mechanism, application scenarios, and implementation effects in various supply chains. A review of the existing research reveals that different supply chain types and policy objectives have been analysed and summarized, uncovering the value and impact of subsidy policies. The following aspects have been reviewed: subsidy roles, supply chain application scenarios, and impact effects.

The existing research has shown that the efficacy of government subsidies is manifested primarily through three dimensions: incentivizing green transformation, mitigating supply chain risks, and driving technological innovation. In terms of incentivizing green transformation, Shi et al. [47] focused on green technology acquisition models, finding that green technology operations and investment subsidies can guide farmers to choose optimal paths. At the level of risk mitigation, Wang et al. [48], on the basis of a risk-incentive contract framework, confirmed that subsidy policies can achieve risk sharing and revenue balancing in low-carbon agricultural supply chains by adjusting incentive coefficients. Wu and Zhu [17] further revealed, in the context of e-commerce aiding agriculture, the key buffering role of subsidies in alleviating the uncertainty faced by farmers in connecting production and markets. Research by Fang and Zhang [49] also shows that inclusive digital finance subsidies played a significant protective role for agricultural supply chains during the pandemic, promoting agricultural trade stability through three major mechanisms: financial broadening, deepening, and digital services.

A review of the existing literature reveals that the application scenarios of government subsidies have covered diverse supply chain fields, such as closed-loop and emerging industries, exhibiting significant scenario-specific characteristics. With respect to closed-loop supply chains and remanufacturing, existing research focuses on mechanism design and dynamic mechanisms. Ma [37] proposed that different subsidy targets (manufacturers, retailers, or consumers) should be selected according to demand disturbance situations. Lee and Park [50] further confirmed that subsidies can effectively strengthen enterprises’ motivation for remanufacturing and recycling, thereby empowering the circular economy.

With respect to the impact of government subsidies on supply chains, existing research shows diversity and context dependency; their effects are constrained by supply chain structure, policy design, and the external environment. In terms of economic performance, although subsidies can increase the income of supply chain entities, an optimal threshold exists, as evidenced by empirical studies on emerging coastal industries [51]. With respect to social and environmental effects, Lee and Chung [52] found that sustainable supply chain subsidies have asymmetric effects on employment quantity and quality and that fixed subsidy models exhibit better governance effects in specific contexts. At the macro and transnational strategic level, the research of Yi and Wen [53] indicates that the setting of subsidy intensity needs to achieve dynamic matching with tariff levels to maximize social welfare, a conclusion further confirming that subsidy strategies must be highly adapted to the external macroenvironment.

In summary, the existing research has clarified the core value and application boundaries of government subsidies in supply chains, but research gaps remain, such as the dynamic optimization of subsidy policies and multiagent game equilibrium. However, the existing subsidy literature primarily focuses on single-target optimization (e.g., subsidizing one entity type) without systematically comparing unilateral and bilateral subsidy allocations within the same analytical framework. Among studies addressing the intersection of blockchain and subsidies, Song et al. [16] is particularly relevant, as it models a three-party evolutionary game among the government, agricultural enterprises, and telecommunications operators to analyze blockchain adoption incentives. However, their evolutionary game approach yields only directional stability results (i.e., whether adoption converges), without deriving the precise optimal investment levels, subsidy ratios, or profit functions that would enable quantitative policy design. Moreover, their model treats adoption as a binary decision and does not distinguish between unilateral and bilateral subsidy targets. Wu and Zhu [17], although studying subsidies in a contract farming context with an e-commerce platform, do not model the platform’s own blockchain investment decision. This leaves open the question of how subsidy design should be differentiated when both supply chain parties can independently invest in blockchain technology—a question that our model directly addresses through the comparison of Models UG, DG, and BG. In view of this, this paper explores the efficiency boundary and synergistic evolution mechanism of subsidies, analysing under what threshold government subsidies can break investment inertia and achieve Pareto improvement.

2.4. Research Gaps

The foregoing review reveals that while substantial progress has been made in contract farming optimization, blockchain applications, and subsidy design individually, a critical gap persists: the absence of a unified analytical framework that jointly examines blockchain adoption decisions and government subsidy optimization within the same supply chain dyad. Existing studies treat these two mechanisms in isolation, preventing analysis of their synergistic interactions. This gap manifests in two specific dimensions. First, the structural asymmetry between upstream agricultural groups and downstream e-commerce platforms—which generates heterogeneous subsidy demands and potential free-riding incentives—has not been formally modeled. Second, the moderating roles of consumer traceability preference and price sensitivity on blockchain cost transmission remain undefined, limiting the precision of policy recommendations under varying market conditions.

To address this gap, this study constructs a multi-stage Stackelberg game model that endogenizes blockchain investment, subsidy allocation, and market uncertainty within a single framework, enabling direct comparison of unilateral versus full-chain subsidy strategies.

3. Model Description and Basic Assumptions

3.1. Model Description

This study focuses on a contract farming supply chain composed of an agricultural group (upstream) and an e-commerce platform (downstream). It aims to explore the synergistic optimization mechanism between blockchain technology adoption strategies and government subsidy policies. This synergistic optimization mechanism is illustrated in Figure 1.

Figure 1 illustrates the synergistic optimization mechanism of the contract farming supply chain. The agricultural group is responsible for agricultural production, while the e-commerce platform handles procurement and sales to consumers. Blockchain technology is introduced to enhance product traceability and consumer trust, and the government provides cost subsidies to incentivize technology adoption. The model structure captures the distinctive features of e-commerce platforms discussed in Section 1: the platform’s direct access to consumer data enables it to set procurement price w with informed market signals, while the agricultural group subsequently determines planting area a based on the offered price. On this basis, a game-theoretic model encompassing six typical decision-making scenarios is constructed, the operational mechanism of which is shown in Figure 2.

Figure 2 presents the operational framework encompassing six decision-making scenarios, which are categorized into two types. (1) Baseline scenarios (without subsidies): Model U, where only the agricultural group adopts blockchain; Model D, where only the e-commerce platform adopts blockchain; and Model B, where blockchain is adopted across the entire supply chain. (2) Advanced scenarios (with subsidies): Model UG, Model DG, and Model BG, which correspond to the same three adoption configurations but with government cost subsidies. To characterize the dynamic interactions among the government, supply chain entities, and consumers, this study constructs a four-stage Stackelberg game model. The decision sequence of each entity is shown in Figure 3.

Figure 3 depicts the four-stage Stackelberg game decision sequence. First, the government, as the leader of the game, determines the optimal subsidy ratio for blockchain technology investment with the objective of maximizing total social welfare τ. Second, on the basis of the principle of maximizing their own profits, the agricultural group and the e-commerce platform decide the number of blockchain nodes to introduce n_m and n_r. The e-commerce platform subsequently determines the procurement price for agricultural products on the basis of the technology investment level and market demand w. Afterwards, the agricultural group determines the planting area for production on the basis of the procurement price of agricultural products w. Finally, consumers make purchases according to the market price p and the product’s blockchain traceability attributes, achieving market clearance.

3.2. Basic Assumptions

Assumption 1.

Supply chain entities adopting blockchain technology must bear corresponding construction costs, which consist of fixed costs and variable costs. To simplify the model without losing generality, this study standardizes the fixed cost to zero and focuses solely on the variable costs that are positively correlated with the number of blockchain nodes [54]. Considering the increasing marginal cost characteristic of technology deployment, the cost function is assumed to be $\mathit{TC}(n_i) = k{n}_i^2$, where   $i=m$, r, n represents the number of introduced blockchain nodes, and k(k > 0) represents the cost coefficient of the blockchain technology.

Assumption 2.

To incentivize supply chain entities to actively adopt blockchain technology, the government implements a cost subsidy policy on the basis of the number of nodes. Kshetri [12] identified cost reduction as a primary mechanism through which government policy promotes blockchain adoption in supply chains, providing empirical justification for this subsidy design. Assuming that the government subsidy ratio is τ (0 < τ < 1), the actual blockchain construction cost borne by the enterprise decreases from TC(ni) to (1 $-$ τ)TC(ni).

Assumption 3.

Assume that the planting area of the agricultural group is a. Considering that agricultural production is subject to the law of diminishing marginal returns on land, the production cost is set as a strictly convex function of the planting area. To simplify the calculations without loss of generality, the production function in this study is specified as   $C\left(a\right)={\displaystyle \frac{1}{2}}c{a}^2$, where c(c > 0) is the cost coefficient of agricultural production.

Assumption 4.

Considering that agricultural production is susceptible to disruptions from force majeure factors such as natural disasters, the actual output of agricultural products exhibits significant volatility. This stochastic yield specification is consistent with Ma [37], who employed a similar random output framework in modeling agricultural supply chains under demand disruptions and government subsidies. Assume that the actual random output per unit area is T, with its expectation E(T) = μ and variance D(T) = σ². Furthermore, let f(·) and F(·) denote the probability density function and the cumulative distribution function of the random variable T, respectively.

Assumption 5.

Assume that the inverse demand function for agricultural products is   $p=\lambda -\beta \mathit{aT}$, where  $\lambda$ represents the consumer’s maximum willingness to pay and  $\lambda$ > 1, and  $\beta$ represents the price sensitivity coefficient. Furthermore, considering consumers’ positive preference for blockchain-traced products, the inverse demand function is extended to  $p=\lambda -\beta \mathit{aT}+\delta (n_m+n_r)$, where  $\delta (\delta > 0)$ represents the coefficient of consumer preference for blockchain-traced products. The uniform δ assumption for both  $n_m$ and  $n_r$ is adopted for the following reasons. First, from the consumer’s perspective, blockchain traceability provides an integrated end-to-end record; consumers observe the aggregate traceability coverage of the product rather than separately evaluating upstream and downstream nodes. Second, this specification is consistent with the modeling approach in Kang et al. [46], who similarly treat the consumer traceability preference as a single parameter applied to total blockchain investment. Third, allowing differentiated preference coefficients (${\delta }_m\ne {\delta }_r$) would substantially increase model complexity without altering the core qualitative insights regarding subsidy design and free-riding behavior.

Assumption 6.

To ensure that the model has a solution, it is necessary to satisfy  $k > {\displaystyle \frac{3{\mu }^2{\delta }^2{\left(2X+c\right)}^2}{4X\left(4X^2+c^2\right)}}$, where  $X=c+\beta \left({\mu }^2+{\sigma }^2\right)$. The economic implication of this constraint is that the cost-effectiveness of investing in blockchain technology must be greater than its effect on expanding market demand. This assumption aligns with the current real-world characteristic of blockchain technology being high-investment, high-barrier and defines the effective boundary for consumers’ traceability preference, preventing unbounded solutions in the model.

Assumption 7.

Consumer surplus is defined as the difference between consumers’ willingness to pay and the actual price paid, which is the area below the demand curve and above the price line. Its calculation formula is  $\mathit{CS}={\displaystyle \frac{1}{2}}\beta \left({\sigma }^2+{\mu }^2\right)a^2$. When constructing the total social welfare function, the impact of government fiscal expenditure is incorporated. Total social welfare consists of the agricultural group’s profit  ${\pi }_m$, the e-commerce platform’s profit  ${\pi }_r$, consumer surplus CS, and government expenditure GE. Here, GE specifically refers to the cost subsidy provided to incentivize supply chain entities to adopt blockchain technology, i.e.,  $\mathit{GE}\left(n_i\right)={\displaystyle \frac{1}{2}}\tau k{n}_i^2$,  $\mathit{SW}={\pi }_m+{ \pi }_r+\mathit{CS}-\mathit{GE}\left(n_i\right)$.

Assumption 8.

Assume that both the agricultural group and the e-commerce platform are fully informed, rational economic agents. Both parties aim solely at maximizing their own profit during the decision-making process. The key symbols involved in the model and their meanings are detailed in

Table 1. Symbols and explanations.

Symbol	Explanation
$\mathrm{w}$	Procurement price per unit of agricultural product
$\mathrm{p}$	Retail price per unit of agricultural product
$\mathsf{\lambda }$	Maximum willingness-to-pay of consumers
$\mathrm{a}$	Planting area of agricultural products
$\mathrm{c}$	Production cost coefficient per unit area of agricultural products
$\mathrm{T}$	Random yield per unit area of agricultural products
$\mathsf{\mu }$	Mean of random yield per unit area of agricultural products
$\mathsf{\sigma }$	Standard deviation of random yield per unit area of agricultural products
$\mathrm{k}$	Blockchain technology cost coefficient
$\mathsf{\delta }$	Consumer preference coefficient for blockchain-traced products
$\mathsf{\tau }$	Government subsidy ratio
$\mathit{CS}$	Consumer surplus
$\mathrm{SW}$	Total social welfare
${\mathsf{\pi }}_{\mathrm{i}}^{\mathrm{j}}$	Profit of supply chain entity i under model j
$\mathsf{\beta }$	Consumer sensitivity coefficient to agricultural product price
${\mathrm{n}}_{\mathrm{i}}$	Number of blockchain nodes introduced by supply chain entity i
$\mathrm{TC}\left({\mathrm{n}}_{\mathrm{i}}\right)$	Total cost of blockchain technology introduction by supply chain entity i
$\mathrm{GE}({\mathrm{n}}_{\mathrm{i}})$	Government expenditure to incentivize supply chain entity i to adopt blockchain technology
$\mathrm{i}=\left\{\mathrm{m},\mathrm{r}\right\}$	Supply chain entity: agricultural group or e-commerce platform
$\mathrm{j}=\left\{\mathrm{U},\mathrm{D},\mathrm{B},\mathrm{UG},\mathrm{DG},\mathrm{BG}\right\}$	Decision model

Note: All parameters are defined in consistent units such that each term in the inverse demand function $\mathrm{p}=\mathsf{\lambda }-\mathsf{\beta }\mathrm{a}\mathrm{T}+\mathsf{\delta }\left({\mathrm{n}}_{\mathrm{m}}+{\mathrm{n}}_{\mathrm{r}}\right)$ carries the dimension of monetary value per unit of product. Specifically, $\mathsf{\beta }$ has the dimension of [price/(area × yield)] and $\mathsf{\delta }$ has the dimension of [price/node], ensuring dimensional homogeneity across all model equations.

.

4. Construction of the Game Model and Solution of the Equilibrium Strategy

4.1. An Order-Based Agricultural Supply Chain That Introduces Blockchain Technology Without Government Subsidies

In this section, the three models without government subsidies are analysed. Taking the most basic Model U as an example, the agricultural group adopts blockchain technology under the condition of no government subsidies, establishing the following Stackelberg game model:

$${\mathsf{\pi }}_{\mathrm{m} }^{\mathrm{U}}= {\mathrm{w}}^{\mathrm{U}}{\mathrm{a}}^{\mathrm{U}}\mathsf{\mu } - {\displaystyle \frac{1}{2}}\mathrm{c}{\mathrm{a}}^{{\mathrm{U}}^2} - {\displaystyle \frac{1}{2}}\mathrm{k}{\mathrm{n}}_{\mathrm{m}}^{{\mathrm{U}}^2}$$

(1)

$${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{U}}={\mathrm{a}}^{\mathrm{U}}\mathsf{\mu }\left(\mathsf{\lambda }+\mathsf{\delta }{\mathrm{n}}_{\mathrm{m}}^{\mathrm{U}}-{\mathrm{w}}^{\mathrm{U}}\right)-\mathsf{\beta }{\mathrm{a}}^{{\mathrm{U}}^2}\left({\mathsf{\mu }}^2+{ \mathsf{\sigma }}^2\right)$$

(2)

$$\mathrm{C}{\mathrm{S}}^{\mathrm{U}}={\displaystyle \frac{1}{2}}\mathsf{\beta }\left({\mathsf{\mu }}^2+{ \mathsf{\sigma }}^2\right){\mathrm{a}}^{{\mathrm{U}}^2}$$

(3)

$$\mathrm{S}{\mathrm{W}}^{\mathrm{U}}={\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{U}}+{ \mathsf{\pi }}_{\mathrm{r}}^{\mathrm{U}}+\mathrm{C}{\mathrm{S}}^{\mathrm{U}}$$

(4)

In the above functions, Equations (1) and (2) are the profit functions of the agricultural group and the e-commerce platform, respectively, under Model U. Equation (3) defines consumer surplus, and Equation (4) defines total social welfare. This model is solved using backward induction through three stages: first, the agricultural group determines planting area ${\mathrm{a}}^{\mathrm{U}}$ to maximize ${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{U}}$; second, the e-commerce platform determines procurement price ${\mathrm{w}}^{\mathrm{U}}$ to maximize ${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{U}}$; third, the agricultural group determines the number of blockchain nodes ${\mathrm{n}}_{\mathrm{m}}^{\mathrm{U}}$ to maximize ${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{U}}$. The detailed derivation process is provided in Appendix A.

Under the baseline scenario, each game model possesses a unique subgame perfect Nash equilibrium. The optimal decisions and equilibrium results are summarized in

Table 2. Summary of the equilibrium results under basic circumstances.

	U	D	B
${\mathrm{n}}_{\mathrm{m}}^{*}$	${\displaystyle \frac{\mathrm{c}\mathsf{\lambda }{\mathsf{\mu }}^2\mathsf{\delta }}{4\mathrm{k}{\mathrm{X}}^2-\mathrm{c}{\mathsf{\mu }}^2{\mathsf{\delta }}^2}}$		${\displaystyle \frac{\mathrm{c}\mathsf{\delta }\mathsf{\lambda }{\mathsf{\mu }}^2}{4\mathrm{k}{\mathrm{X}}^2-{\mathsf{\mu }}^2{\mathsf{\delta }}^2(2\mathrm{X}+\mathrm{c})}}$
${\mathrm{n}}_{\mathrm{r}}^{*}$		${\displaystyle \frac{\mathsf{\lambda }\mathsf{\delta }{\mathsf{\mu }}^2}{2\mathrm{kX}-{\mathsf{\mu }}^2{\mathsf{\delta }}^2}}$	${\displaystyle \frac{2\mathrm{X}\mathsf{\delta }\mathsf{\lambda }{\mathsf{\mu }}^2}{4\mathrm{k}{\mathrm{X}}^2-{\mathsf{\mu }}^2{\mathsf{\delta }}^2(2\mathrm{X}+\mathrm{c})}}$
${\mathrm{w}}^{*}$	${\displaystyle \frac{2\mathrm{kX}\mathsf{\lambda }\mathrm{c}}{4\mathrm{k}{\mathrm{X}}^2-\mathrm{c}{\mathsf{\mu }}^2{\mathsf{\delta }}^2}}$	${\displaystyle \frac{\mathsf{\lambda }\mathrm{k}\mathrm{c}}{2\mathrm{k}\mathrm{X}-{\mathsf{\mu }}^2{\mathsf{\delta }}^2}}$	${\displaystyle \frac{2\mathrm{ckX}\mathsf{\lambda }}{4\mathrm{k}{\mathrm{X}}^2-(\mathrm{c}+2\mathrm{X}){\mathsf{\delta }}^2{\mathsf{\mu }}^2}}$
${\mathrm{a}}^{*}$	${\displaystyle \frac{2\mathrm{kX}\mathsf{\lambda }\mathsf{\mu }}{4\mathrm{k}{\mathrm{X}}^2-\mathrm{c}{\mathsf{\mu }}^2{\mathsf{\delta }}^2}}$	${\displaystyle \frac{\mathsf{\lambda }\mathrm{k}\mathsf{\mu }}{2\mathrm{kX}-{\mathsf{\mu }}^2{\mathsf{\delta }}^2}}$	${\displaystyle \frac{2\mathrm{kX}\mathsf{\lambda }\mathsf{\mu }}{4\mathrm{k}{\mathrm{X}}^2-(\mathrm{c}+2\mathrm{X}){\mathsf{\delta }}^2{\mathsf{\mu }}^2}}$
${\mathsf{\pi }}_{\mathrm{m}}^{*}$	${\displaystyle \frac{\mathrm{ck}{\mathsf{\lambda }}^2{\mathsf{\mu }}^2}{8\mathrm{k}{\mathrm{X}}^2-2\mathrm{c}{\mathsf{\mu }}^2{\mathsf{\delta }}^2}}$	${\displaystyle \frac{\mathrm{c}{\mathrm{k}}^2{\mathsf{\lambda }}^2{\mathsf{\mu }}^2}{2(2\mathrm{kX}-{\mathsf{\mu }}^2{\mathsf{\delta }}^2{)}^2}}$	${\displaystyle \frac{\mathrm{ck}{\mathsf{\lambda }}^2{\mathsf{\mu }}^2(4\mathrm{k}{\mathrm{X}}^2-\mathrm{c}{\mathsf{\delta }}^2{\mathsf{\mu }}^2)}{2(4\mathrm{k}{\mathrm{X}}^2-(\mathrm{c}+2\mathrm{X}){\mathsf{\delta }}^2{\mathsf{\mu }}^2{)}^2}}$
${\mathsf{\pi }}_{\mathrm{r}}^{*}$	${\displaystyle \frac{4{\mathrm{k}}^2{\mathsf{\lambda }}^2{\mathsf{\mu }}^2{\mathrm{X}}^3}{(4\mathrm{k}{\mathrm{X}}^2-\mathrm{c}{\mathsf{\mu }}^2{\mathsf{\delta }}^2{)}^2}}$	${\displaystyle \frac{\mathrm{k}{\mathsf{\lambda }}^2{\mathsf{\mu }}^2}{4\mathrm{kX}-2{\mathsf{\mu }}^2{\mathsf{\delta }}^2}}$	${\displaystyle \frac{2\mathrm{k}{\mathrm{X}}^2{\mathsf{\lambda }}^2{\mathsf{\mu }}^2(2\mathrm{kX}-{\mathsf{\delta }}^2{\mathsf{\mu }}^2)}{(4\mathrm{k}{\mathrm{X}}^2-(\mathrm{c}+2\mathrm{X}){\mathsf{\delta }}^2{\mathsf{\mu }}^2{)}^2}}$
$\mathrm{C}{\mathrm{S}}^{*}$	${\displaystyle \frac{2{\mathrm{k}}^2{\mathrm{X}}^2\mathsf{\beta }{\mathsf{\lambda }}^2{\mathsf{\mu }}^2\left({\mathsf{\mu }}^2+{\mathsf{\sigma }}^2\right)}{{\left(4\mathrm{k}{\mathrm{X}}^2-\mathrm{c}{\mathsf{\delta }}^2{\mathsf{\mu }}^2\right)}^2}}$	${\displaystyle \frac{{\mathrm{k}}^2\mathsf{\beta }{\mathsf{\lambda }}^2{\mathsf{\mu }}^2\left({\mathsf{\mu }}^2+{\mathsf{\sigma }}^2\right)}{2{\left(2\mathrm{kX}-{\mathsf{\delta }}^2{\mathsf{\mu }}^2\right)}^2}}$	${\displaystyle \frac{2{\mathrm{k}}^2{\mathrm{X}}^2\mathsf{\beta }{\mathsf{\lambda }}^2{\mathsf{\mu }}^2\left({\mathsf{\mu }}^2+{\mathsf{\sigma }}^2\right)}{{\left(4\mathrm{k}{\mathrm{X}}^2-\left(\mathrm{c}+2\mathrm{X}\right){\mathsf{\delta }}^2{\mathsf{\mu }}^2\right)}^2}}$
$\mathrm{S}{\mathrm{W}}^{*}$	${\displaystyle \frac{\mathrm{k}{\mathsf{\lambda }}^2{\mathsf{\mu }}^2\left(12\mathrm{k}{\mathrm{X}}^3-{\mathrm{c}}^2{\mathsf{\delta }}^2{\mathsf{\mu }}^2\right)}{2{\left(4\mathrm{k}{\mathrm{X}}^2-\mathrm{c}{\mathsf{\delta }}^2{\mathsf{\mu }}^2\right)}^2}}$	${\displaystyle \frac{\mathrm{k}{\mathsf{\lambda }}^2{\mathsf{\mu }}^2\left(3\mathrm{kX}-{\mathsf{\delta }}^2{\mathsf{\mu }}^2\right)}{2{\left(2\mathrm{kX}-{\mathsf{\delta }}^2{\mathsf{\mu }}^2\right)}^2}}$	${\displaystyle \frac{\mathrm{k}{\mathsf{\lambda }}^2{\mathsf{\mu }}^2\left(12\mathrm{k}{\mathrm{X}}^3-({\mathrm{c}}^2+4{\mathrm{X}}^2){\mathsf{\delta }}^2{\mathsf{\mu }}^2\right)}{2{\left(4\mathrm{k}{\mathrm{X}}^2-\left(\mathrm{c}+2\mathrm{X}\right){\mathsf{\delta }}^2{\mathsf{\mu }}^2\right)}^2}}$

. The solution logic for Model D and Model B is highly consistent with Model U, with the main difference being that the inverse demand function incorporates the premium term induced by blockchain technology and the corresponding cost term. The detailed derivation processes for all three baseline models are provided in Appendix A.

4.2. An Order-Based Agricultural Supply Chain That Introduces Blockchain Technology Under Government Subsidies

This section analyses the three scenarios with government subsidies. Taking the most complex Model BG as an example, where both the agricultural group and the e-commerce platform adopt blockchain technology under government subsidies, the following Stackelberg game model is established:

$${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{BG}} ={ \mathrm{w}}^{\mathrm{BG}}{\mathrm{a}}^{\mathrm{BG}}\mathsf{\mu } -{\displaystyle \frac{1}{2}}\mathrm{c}{\mathrm{a}}^{\mathrm{B}{\mathrm{G}}^2}-{\displaystyle \frac{1}{2}}\mathrm{k}\left(1- {\mathsf{\tau }}^{\mathrm{BG}}\right){\mathrm{n}}_{\mathrm{m}}^{\mathrm{B}{\mathrm{G}}^2}$$

(5)

$${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{BG}}={\mathrm{a}}^{\mathrm{BG}}\mathsf{\mu }\left(\mathsf{\lambda }+\mathsf{\delta }{\mathrm{n}}_{\mathrm{m}}^{\mathrm{BG}}+\mathsf{\delta }{\mathrm{n}}_{\mathrm{r}}^{\mathrm{BG}}-{\mathrm{w}}^{\mathrm{BG}}\right)-\mathsf{\beta }{\mathrm{a}}^{\mathrm{B}{\mathrm{G}}^2}\left({\mathsf{\mu }}^2+{\mathsf{\sigma }}^2\right)-{\displaystyle \frac{1}{2}}\mathrm{k}\left(1-{\mathsf{\tau }}^{\mathrm{BG}}\right){\mathrm{n}}_{\mathrm{r}}^{\mathrm{B}{\mathrm{G}}^2}$$

(6)

$$\mathrm{C}{\mathrm{S}}^{\mathrm{BG}}={\displaystyle \frac{1}{2}}\mathsf{\beta }\left({\mathsf{\mu }}^2+{\mathsf{\sigma }}^2\right){\mathrm{a}}^{\mathrm{B}{\mathrm{G}}^2}$$

(7)

$$\mathrm{S}{\mathrm{W}}^{\mathrm{BG}}= -{\displaystyle \frac{1}{2}}\mathrm{c}{\mathrm{a}}^{\mathrm{B}{\mathrm{G}}^2}-{\displaystyle \frac{1}{2}}\mathrm{k}{\mathrm{n}}_{\mathrm{m}}^{\mathrm{B}{\mathrm{G}}^2}+{\mathrm{a}}^{\mathrm{BG}}\mathsf{\mu }\left(\mathsf{\lambda }+\mathsf{\delta }{\mathrm{n}}_{\mathrm{m}}^{\mathrm{BG}}+\mathsf{\delta }{\mathrm{n}}_{\mathrm{r}}^{\mathrm{BG}}\right)-{\displaystyle \frac{1}{2}}\mathrm{k}{\mathrm{n}}_{\mathrm{r}}^{\mathrm{B}{\mathrm{G}}^2}-{\displaystyle \frac{1}{2}}\mathsf{\beta }\left({\mathsf{\sigma }}^2+{\mathsf{\mu }}^2\right){\mathrm{a}}^{\mathrm{B}{\mathrm{G}}^2}$$

(8)

In the above functions, Equations (5) and (6) are the profit functions of the agricultural group and the e-commerce platform, respectively, under Model BG. Compared with the baseline models, the subsidy ratio $\tau$ reduces the effective blockchain cost borne by each entity from $TC\left(n_i\right)$ to $(1-\tau )TC\left(n_i\right)$. Notably, the social welfare function in Equation (8) accounts for the full blockchain cost (without the subsidy discount), because the government expenditure $GE(n_i)={\displaystyle \frac{1}{2}}\tau k{n}_i^2$ offsets the subsidy benefit when aggregated across all parties.

It should be noted that the subsidy ratio $\tau$ is not subject to an exogenous budget constraint. Instead, the government’s fiscal expenditure $GE(n_l)={\displaystyle \frac{1}{2}}\tau k{n}_f^2$ enters the social welfare function as a deduction ($SW={\pi }_m+{\pi }_r+CS-GE$), creating an endogenous efficiency constraint: increasing $\tau$ reduces the net welfare contribution of subsidies through higher fiscal costs. The optimal $\tau *$ therefore represents the point at which the marginal welfare gain from stimulating blockchain investment equals the marginal fiscal cost, effectively bounding the subsidy ratio without requiring an explicit budget ceiling.

This model is solved using backward induction through four stages: first, the agricultural group determines planting area $a^{BG}$ to maximize ${\pi }_m^{BG}$; second, the e-commerce platform determines procurement price $W^{BG}$ to maximize ${\pi }_r^{BG}$; third, both parties determine their blockchain node investments $n_m^{BG}$ and $n_r^{BG}$ to maximize their respective profits; fourth, the government determines the optimal subsidy ratio $T^{BG}$ by maximizing $S{W}^{BG}$. The detailed derivation process is provided in Appendix B.

Under the advanced scenarios, each game model possesses a unique subgame perfect Nash equilibrium. The optimal decisions and equilibrium results are summarized in

Table 3. Summary of the equilibrium results in the advanced scenarios.

	UG	DG	BG
${\mathsf{\tau }}^{*}$	$1-{\displaystyle \frac{\mathrm{c}}{3\mathrm{X}}}$	${\displaystyle \frac{1}{3}}$	$1-{\displaystyle \frac{4{\mathrm{X}}^2+{\mathrm{c}}^2}{3\mathrm{X}(2\mathrm{X}+\mathrm{c})}}$
${\mathrm{n}}_{\mathrm{m}}^{*}$	${\displaystyle \frac{3\mathsf{\delta }\mathsf{\lambda }{\mathsf{\mu }}^2}{4\mathrm{kX}-3{\mathsf{\delta }}^2{\mathsf{\mu }}^2}}$		${\displaystyle \frac{3\mathrm{c}\left(\mathrm{c}+2\mathrm{X}\right)\mathsf{\delta }\mathsf{\lambda }{\mathsf{\mu }}^2}{4\mathrm{kX}\left({\mathrm{c}}^2+4{\mathrm{X}}^2\right)-3{\left(\mathrm{c}+2\mathrm{X}\right)}^2{\mathsf{\delta }}^2{\mathsf{\mu }}^2}}$
${\mathrm{n}}_{\mathrm{r}}^{*}$		${\displaystyle \frac{3\mathsf{\lambda }\mathsf{\delta }{\mathsf{\mu }}^2}{4\mathrm{kX}-3{\mathsf{\mu }}^2{\mathsf{\delta }}^2}}$	${\displaystyle \frac{6\mathrm{X}\left(\mathrm{c}+2\mathrm{X}\right)\mathsf{\delta }\mathsf{\lambda }{\mathsf{\mu }}^2}{4\mathrm{kX}\left({\mathrm{c}}^2+4{\mathrm{X}}^2\right)-3{\left(\mathrm{c}+2\mathrm{X}\right)}^2{\mathsf{\delta }}^2{\mathsf{\mu }}^2}}$
${\mathrm{w}}^{*}$	${\displaystyle \frac{2\mathrm{ck}\mathsf{\lambda }}{4\mathrm{kX}-3{\mathsf{\delta }}^2{\mathsf{\mu }}^2}}$	${\displaystyle \frac{2\mathrm{k}\mathsf{\lambda }\mathrm{c}}{4\mathrm{kX}-3{\mathsf{\mu }}^2{\mathsf{\delta }}^2}}$	${\displaystyle \frac{2\mathrm{ck}\left({\mathrm{c}}^2+4{\mathrm{X}}^2\right)\mathsf{\lambda }}{4\mathrm{kX}\left({\mathrm{c}}^2+4{\mathrm{X}}^2\right)-3{\left(\mathrm{c}+2\mathrm{X}\right)}^2{\mathsf{\delta }}^2{\mathsf{\mu }}^2}}$
${\mathrm{a}}^{*}$	${\displaystyle \frac{2\mathrm{k}\mathsf{\lambda }\mathsf{\mu }}{4\mathrm{kX}-3{\mathsf{\delta }}^2{\mathsf{\mu }}^2}}$	${\displaystyle \frac{2\mathrm{k}\mathsf{\lambda }\mathsf{\mu }}{4\mathrm{kX}-3{\mathsf{\mu }}^2{\mathsf{\delta }}^2}}$	${\displaystyle \frac{2\mathrm{k}\left({\mathrm{c}}^2+4{\mathrm{X}}^2\right)\mathsf{\lambda }\mathsf{\mu }}{4\mathrm{kX}\left({\mathrm{c}}^2+4{\mathrm{X}}^2\right)-3{\left(\mathrm{c}+2\mathrm{X}\right)}^2{\mathsf{\delta }}^2{\mathsf{\mu }}^2}}$
${\mathsf{\pi }}_{\mathrm{m}}^{*}$	${\displaystyle \frac{\mathrm{ck}{\mathsf{\lambda }}^2{\mathsf{\mu }}^2}{2\mathrm{X}(4\mathrm{kX}-3{\mathsf{\delta }}^2{\mathsf{\mu }}^2)}}$	${\displaystyle \frac{2\mathrm{c}{\mathrm{k}}^2{\mathsf{\lambda }}^2{\mathsf{\mu }}^2}{(4\mathrm{kX}-3{\mathsf{\mu }}^2{\mathsf{\delta }}^2{)}^2}}$	${\displaystyle \frac{\mathrm{ck}\left({\mathrm{c}}^2+4{\mathrm{X}}^2\right){\mathsf{\lambda }}^2{\mathsf{\mu }}^2\left(4\mathrm{kX}({\mathrm{c}}^2+4{\mathrm{X}}^2) - 3\mathrm{c}(\mathrm{c}+2\mathrm{X}){\mathsf{\delta }}^2{\mathsf{\mu }}^2\right)}{2\mathrm{X}{\left(4\mathrm{kX}({\mathrm{c}}^2+4{\mathrm{X}}^2)-3(\mathrm{c}+2\mathrm{X}{)}^2{\mathsf{\delta }}^2{\mathsf{\mu }}^2\right)}^2}}$
${\mathsf{\pi }}_{\mathrm{r}}^{*}$	${\displaystyle \frac{4{\mathrm{k}}^2{\mathsf{\lambda }}^2{\mathsf{\mu }}^2\mathrm{X}}{(4\mathrm{kX}-3{\mathsf{\delta }}^2{\mathsf{\mu }}^2{)}^2}}$	${\displaystyle \frac{\mathrm{k}{\mathsf{\lambda }}^2{\mathsf{\mu }}^2}{4\mathrm{kX}-3{\mathsf{\mu }}^2{\mathsf{\delta }}^2}}$	${\displaystyle \frac{2\mathrm{kX}\left({\mathrm{c}}^2+4{\mathrm{X}}^2\right){\mathsf{\lambda }}^2{\mathsf{\mu }}^2\left(2\mathrm{k}({\mathrm{c}}^2+4{\mathrm{X}}^2)-3(\mathrm{c}+2\mathrm{X}){\mathsf{\delta }}^2{\mathsf{\mu }}^2\right)}{{\left(4\mathrm{kX}({\mathrm{c}}^2+4{\mathrm{X}}^2)-3{\mathsf{\mu }}^2{\mathsf{\delta }}^2(\mathrm{c}+2\mathrm{X}{)}^2\right)}^2}}$
$\mathrm{C}{\mathrm{S}}^{*}$	${\displaystyle \frac{2{\mathrm{k}}^2\mathsf{\beta }{\mathsf{\lambda }}^2{\mathsf{\mu }}^2\left({\mathsf{\mu }}^2+{\mathsf{\sigma }}^2\right)}{{\left(4\mathrm{kX}-3{\mathsf{\delta }}^2{\mathsf{\mu }}^2\right)}^2}}$	${\displaystyle \frac{2{\mathrm{k}}^2\mathsf{\beta }{\mathsf{\lambda }}^2{\mathsf{\mu }}^2\left({\mathsf{\mu }}^{2 }+{\mathsf{\sigma }}^2\right)}{{\left(4\mathrm{kX}-3{\mathsf{\delta }}^2{\mathsf{\mu }}^2\right)}^2}}$	${\displaystyle \frac{2{\mathrm{k}}^2{\left({\mathrm{c}}^2+4{\mathrm{X}}^2\right)}^2\mathsf{\beta }{\mathsf{\lambda }}^2{\mathsf{\mu }}^2\left({\mathsf{\mu }}^2+{\mathsf{\sigma }}^2\right)}{{\left(4\mathrm{kX}\left({\mathrm{c}}^2+4{\mathrm{X}}^2\right)-3{\left(\mathrm{c}+2\mathrm{X}\right)}^2{\mathsf{\delta }}^2{\mathsf{\mu }}^2\right)}^2}}$
$\mathrm{S}{\mathrm{W}}^{*}$	${\displaystyle \frac{3\mathrm{k}{\mathsf{\lambda }}^2{\mathsf{\mu }}^2}{2(4\mathrm{kX}-3{\mathsf{\delta }}^2{\mathsf{\mu }}^2)}}$	${\displaystyle \frac{3\mathrm{k}{\mathsf{\lambda }}^2{\mathsf{\mu }}^2}{8\mathrm{kX}-6{\mathsf{\mu }}^2{\mathsf{\delta }}^2}}$	${\displaystyle \frac{3\mathrm{k}\left({\mathrm{c}}^2+4{\mathrm{X}}^2\right){\mathsf{\lambda }}^2{\mathsf{\mu }}^2}{8\mathrm{kX}\left({\mathrm{c}}^2+4{\mathrm{X}}^2\right)-6{\left(\mathrm{c}+2\mathrm{X}\right)}^2{\mathsf{\delta }}^2{\mathsf{\mu }}^2}}$

. The solution logic for Model UG and Model DG is highly consistent with Model BG. The detailed derivation processes for all three advanced models are provided in Appendix B.

5. Theoretical Analysis of the Equilibrium Results

5.1. Analysis of the Influence Mechanism of Key Parameters and the Effectiveness of Subsidies

Proposition 1.

Stimulation-Inhibition Effects and Transmission Mechanisms of Market Environmental Factors.

In all the models, the optimal decision variables $\mathsf{\delta }$ exhibit a significant monotonic increasing relationship with the consumer preference coefficient, i.e., ${\displaystyle \frac{\mathsf{\partial }{\mathrm{n}}_{\mathrm{m}}^{\mathrm{j}*}}{\partial \mathsf{\delta }}} > 0, {\displaystyle \frac{\partial {\mathrm{n}}_{\mathrm{r}}^{\mathrm{j}*}}{\partial \mathsf{\delta }}} > 0, {\displaystyle \frac{\partial {\mathrm{w}}^{\mathrm{j}*}}{\partial \mathsf{\delta }}} > 0, {\displaystyle \frac{\partial {\mathrm{a}}^{\mathrm{j}*}}{\partial \mathsf{\delta }}} > 0$. However, profit does not increase unconditionally with δ. Profit increases with δ only when the blockchain cost effect exceeds a specific threshold, namely ${\displaystyle \frac{k}{{\delta }^2}}>{\displaystyle \frac{3{\mu }^2(c +2X{)}^2}{4X(c^2+4X^2)}}$ (i.e., ${\displaystyle \frac{\partial {\mathsf{\pi }}_{\mathrm{i}}^{\mathrm{j}*}}{\partial \mathsf{\delta }}} > 0$); below this threshold, higher consumer preference cannot compensate for the escalating technology costs, resulting in increased revenue without increased profit. Conversely, under the premise of stability, all decision variables and profit levels are negatively affected by it, exhibiting a monotonic decreasing characteristic, i.e., ${\displaystyle \frac{\partial {\mathsf{\Omega }}^{\mathrm{j}*}}{\partial \mathsf{\beta }}} < 0, \forall \mathsf{\Omega } \in \left\{\mathrm{w}, \mathrm{a}, {\mathrm{n}}_{\mathrm{m}},{ \mathrm{n}}_{\mathrm{r}} ,{ \mathsf{\pi }}_{\mathrm{m}}, {\mathsf{\pi }}_{\mathrm{r}}\right\}$. Please refer to Appendix C for the detailed derivation process.

Proposition 1 reveals the internal mechanism through which market demand characteristics are transmitted upstream via the price mechanism and investment incentives. The explanation is as follows: (1) $\mathsf{\delta }$ essentially reflects the market’s willingness to pay for high-quality information, incentivizing the supply side to implement a quality signalling strategy. This incentive transmits upstream along the path of technology investment—demand expansion—price transmission—production expansion, achieving collaborative optimization of the supply chain’s operational scale. However, profit conversion is constrained by a strict efficiency boundary. Owing to the increasing marginal cost of technology, if the cost-effectiveness does not reach a specific threshold, high investment costs will offset market premiums, causing enterprises to fall into the dilemma of increased revenue without increased profit. (2) $\mathsf{\beta }$ constitutes a structural resistance to value realization. High sensitivity limits the scope for cost pass-through, forcing entities to adopt conservative strategies. They control risk by reducing technology investment and lowering procurement prices, which in turn suppresses upstream production incentives. This dilemma of a simultaneous decline in both quantity and price creates a dual squeeze on supply chain profits through declining sales volume and compressed unit gross profit, indicating that high price sensitivity is a core market bottleneck constraining the digital transformation of the contract farming supply chain.

Proposition 2.

Asymmetric Influence of Technology and Production Costs on the Equilibrium Outcome.

Under the premise of stability, the blockchain cost coefficient $\mathrm{k}$ exerts a significant negative inhibitory effect on the optimal decision variables and profits across all the models, exhibiting a strictly monotonic decreasing characteristic, i.e., ${\displaystyle \frac{\partial {\mathsf{\Omega }}^{\mathrm{j}*}}{\partial \mathrm{k}}} < 0, \forall \mathsf{\Omega } \in \left\{\mathrm{w}, \mathrm{a},{ \mathrm{n}}_{\mathrm{m}}, {\mathrm{n}}_{\mathrm{r}},{ \mathsf{\pi }}_{\mathrm{m}}, {\mathsf{\pi }}_{\mathrm{r}}\right\}$. Similarly, under the premise of stability and satisfying condition $\mathrm{c} > \mathsf{\beta }\left({\mathsf{\mu }}^{2 }+{ \mathsf{\sigma }}^2\right)$, the agricultural production cost demonstrates a significant asymmetric effect on equilibrium outcomes: the procurement price shows a monotonic increasing trend, i.e., ${\displaystyle \frac{\partial {\mathrm{w}}^{\mathrm{B}{\mathrm{G}}^{*}}}{\partial \mathrm{c}}} > 0$, while all other decision variables and profits are negatively suppressed by the rising cost, exhibiting a monotonic decreasing trend, i.e., ${\displaystyle \frac{\partial {\mathrm{n}}_{\mathrm{r}}^{\mathrm{B}{\mathrm{G}}^{*}}}{\partial \mathrm{c}}} < 0, {\displaystyle \frac{\partial {\mathrm{a}}^{\mathrm{B}{\mathrm{G}}^{*}}}{\partial \mathrm{c}}} < 0, {\displaystyle \frac{\partial {\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{B}{\mathrm{G}}^{*}}}{\partial \mathrm{c}}} < 0, {\displaystyle \frac{\partial {\mathrm{n}}_{\mathrm{m}}^{\mathrm{B}{\mathrm{G}}^{*}}}{\partial \mathrm{c}}} < 0, {\displaystyle \frac{\partial {\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{B}{\mathrm{G}}^{*}}}{\partial \mathrm{c}}} < 0$.

Proposition 2 reveals how cost factors become the efficiency barrier to supply chain value creation, explained as follows: (1) The blockchain cost coefficient represents the marginal difficulty and resource consumption of technology application. On the basis of the results of the marginal analysis, when $\mathrm{k}$ increases, the marginal cost per unit of investment quickly outweighs the marginal benefit, forcing rational entities to significantly cut node investment, leading to a loss of product premium capability. This decision triggers a negative feedback loop of technology reduction, demand contraction, and output decline, causing a significant decrease in profits for all entities. This profoundly explains the underlying reason for the stagnation of technology application in agricultural supply chains in the initial stages, lacking external incentives, as it is difficult to break through the cost–benefit break-even point. (2) In contrast to technology costs, the increase in production cost $\mathrm{c}$ triggers a complex incomplete cost pass-through mechanism. Although under certain thresholds, upstream entities can transfer some pressure by raising procurement prices, this is essentially a cost-driven passive price increase rather than a demand-driven, healthy growth. The demand destruction effect caused by the increase in price exceeds the compensation from the increased unit gross profit, ultimately leading to a decline in profits. More critically, resource constraints force entities to sacrifice value-adding blockchain investments in budget allocation to preserve basic production, thereby simultaneously harming short-term financial performance and long-term technology upgrade potential.

Proposition 3.

Incentive Effect of Government Subsidies and Pareto Improvement.

When the government implements effective subsidy policies, it triggers multidimensional positive chain effects: (1) Positive Incentive Effect at the Operational Level: Government subsidies significantly stimulate the input of production factors on the supply side, driving the simultaneous expansion of technology investment and the planting scale by supply chain entities, i.e., ${\mathrm{n}}_{\mathrm{m}}^{{\mathrm{s}}^{*}} > {\mathrm{n}}_{\mathrm{m}}^{{\mathrm{o}}^{*}}$, ${\mathrm{n}}_{\mathrm{r}}^{{\mathrm{s}}^{*}} >{ \mathrm{n}}_{\mathrm{r}}^{{\mathrm{o}}^{*}}$, ${\mathrm{a}}^{{\mathrm{s}}^{*}} >{ \mathrm{a}}^{{\mathrm{o}}^{*}}$; moreover, through the price transmission mechanism, the procurement price of agricultural products also substantially increases, i.e., ${\mathrm{w}}^{{\mathrm{s}}^{*}} > {\mathrm{w}}^{{\mathrm{o}}^{*}}$. (2) Pareto Improvement at the Economic Level: Under the stability condition established in Assumption 6 (which defines the entire feasible parameter domain), subsidies achieve a Pareto improvement in the supply chain game outcomes: both the agricultural group and the e-commerce platform earn strictly higher profits under subsidized models than under corresponding baseline models, i.e., ${\mathsf{\pi }}_{\mathrm{m}}^{{\mathrm{s}}^{*}} > {\mathsf{\pi }}_{\mathrm{m}}^{{\mathrm{o}}^{*}}$,${ \mathsf{\pi }}_{\mathrm{r}}^{{\mathrm{s}}^{*}} > {\mathsf{\pi }}_{\mathrm{r}}^{{\mathrm{o}}^{*}}$, with no parameter range within the defined domain where either party is worse off. The detailed algebraic proof is provided in Appendix C (

Table A2. Summary of the impact of government subsidies on key supply chain indicators.

Key Indicators	UG vs. U	DG vs. D
${\mathrm{n}}_{\mathrm{m}}$	${\mathrm{n}}_{\mathrm{m}}^{\mathrm{U}{\mathrm{G}}^{*}} > {\mathrm{n}}_{\mathrm{m}}^{{\mathrm{U}}^{*}}$
${\mathrm{n}}_{\mathrm{r}}$		${\mathrm{n}}_{\mathrm{r}}^{\mathrm{D}{\mathrm{G}}^{*}} > {\mathrm{n}}_{\mathrm{r}}^{{\mathrm{D}}^{*}}$
$\mathrm{w}$	${\mathrm{w}}^{\mathrm{U}{\mathrm{G}}^{*}} > {\mathrm{w}}^{{\mathrm{U}}^{*}}$	${\mathrm{w}}^{\mathrm{D}{\mathrm{G}}^{*}} > {\mathrm{w}}^{{\mathrm{D}}^{*}}$
$\mathrm{a}$	${\mathrm{a}}^{\mathrm{U}{\mathrm{G}}^{*}} > {\mathrm{a}}^{{\mathrm{U}}^{*}}$	${\mathrm{a}}^{\mathrm{D}{\mathrm{G}}^{*}} > {\mathrm{a}}^{{\mathrm{D}}^{*}}$
${\mathsf{\pi }}_{\mathrm{m}}$	${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{U}{\mathrm{G}}^{*}} > {\mathsf{\pi }}_{\mathrm{m}}^{{\mathrm{U}}^{*}}$	${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{D}{\mathrm{G}}^{*}} > {\mathsf{\pi }}_{\mathrm{m}}^{{\mathrm{D}}^{*}}$
${\mathsf{\pi }}_{\mathrm{r}}$	${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{U}{\mathrm{G}}^{*}} > {\mathsf{\pi }}_{\mathrm{r}}^{{\mathrm{U}}^{*}}$	${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{D}{\mathrm{G}}^{*}} > {\mathsf{\pi }}_{\mathrm{r}}^{{\mathrm{D}}^{*}}$
$\mathrm{CS}$	$\mathrm{C}{\mathrm{S}}^{\mathrm{U}{\mathrm{G}}^{*}} > \mathrm{C}{\mathrm{S}}^{{\mathrm{U}}^{*}}$	$\mathrm{C}{\mathrm{S}}^{\mathrm{D}{\mathrm{G}}^{*}} > \mathrm{C}{\mathrm{S}}^{{\mathrm{D}}^{*}}$
$\mathrm{SW}$	$\mathrm{S}{\mathrm{W}}^{\mathrm{U}{\mathrm{G}}^{*}} > \mathrm{S}{\mathrm{W}}^{{\mathrm{U}}^{*}}$	$\mathrm{S}{\mathrm{W}}^{\mathrm{D}{\mathrm{G}}^{*}} > \mathrm{S}{\mathrm{W}}^{{\mathrm{D}}^{*}}$

), where pairwise comparisons confirm that all profit differences are strictly positive across the entire feasible domain. (3) Welfare Optimization at the Social Level: Although the government bears corresponding fiscal expenditure costs, the significant improvement in consumer surplus and the substantive growth in corporate profits lead to a net increase in social welfare, i.e., $\mathrm{C}{\mathrm{S}}^{{\mathrm{s}}^{*}} > \mathrm{C}{\mathrm{S}}^{{\mathrm{o}}^{*}}$ and $\mathrm{S}{\mathrm{W}}^{{\mathrm{s}}^{*}} > \mathrm{S}{\mathrm{W}}^{{\mathrm{o}}^{*}}$, where $\mathrm{o} \in \{\mathrm{U}, \mathrm{D}, \mathrm{B}\}, \mathrm{s} \in \{\mathrm{UG}, \mathrm{DG}, \mathrm{BG}\}$.

Proposition 3 reveals that government subsidies, as a leverage adjustment mechanism, achieve systemic optimization from microlevel entity decisions to macrolevel social welfare. The specific explanation is as follows: (1) Government subsidies effectively alleviate the upstream structural constraint of high investment, delayed returns and grant it stronger bargaining power through a quality-price complementary mechanism. This enables the agricultural group to maintain price rigidity while expanding its scale, effectively resolving the traditional agricultural paradox of increased quantity leading to decreased prices and achieving simultaneous scale expansion and value appreciation. (2) The quality improvement on the upstream supply side triggers a downstream strategic complementary response. To maximize traffic conversion rates and avoid the short-board effect, the e-commerce platform tends to simultaneously increase investment in the circulation end to ensure the integrity of full-chain traceability. (3) Subsidies, as a powerful external coordinator, break the prisoner’s dilemma and low-level equilibrium under decentralized decision-making, creating a non-zero-sum game space by enlarging the system’s profit pool. (4) Technology proliferation significantly reduces transaction frictions caused by information asymmetry. The sum of the increase in consumer utility and the increase in corporate profits covers the fiscal costs. This finding indicates that appropriate subsidies are essentially a high-return social investment rather than merely a transfer payment.

Proposition 4.

Ranking Characteristics and Effectiveness Boundaries of the Optimal Subsidy Ratio.

With the goal of maximizing total social welfare, the government’s optimal subsidy strategy has a ranking characteristic of ${\mathsf{\tau }}^{\mathrm{U}{\mathrm{G}}^{*}} >{ \mathsf{\tau }}^{\mathrm{B}{\mathrm{G}}^{*}} > {\mathsf{\tau }}^{\mathrm{D}{\mathrm{G}}^{*}}$. Moreover, to ensure nonnegative profits for the supply chain entities, the government investment ratios corresponding to the agricultural group and the e-commerce platform must meet the thresholds ${\mathsf{\tau }}_{\mathrm{m}} \in \left(0,1-{\displaystyle \frac{\mathrm{c}{\mathsf{\mu }}^2{\mathsf{\delta }}^2}{4\mathrm{k}{\mathrm{X}}^2}}\right)$ and ${\mathsf{\tau }}_{\mathrm{r}} \in \left(0,1-{\displaystyle \frac{{\mathsf{\mu }}^2{\mathsf{\delta }}^2}{2\mathrm{kX}}}\right)$, respectively. A comparison reveals that the upper limit of the subsidy ratio enjoyed by the agricultural group is significantly greater than that for the e-commerce platform. This indicates an asymmetry in the subsidy mechanism, where the e-commerce platform-dominated model displays features of low demand and a narrow range, requiring only minimal leverage to initiate; the full-chain model falls in the middle, whereas the agricultural group-dominated model relies on high-intensity external incentives and possesses the broadest policy accommodation space.

Proposition 4 reveals the relationships between the optimal subsidy ratio and the value capture capability and risk-bearing willingness of supply chain entities. The specific explanation is as follows: (1) Leveraging its advantage of market proximity, the e-commerce platform possesses extremely high efficiency in value realization and endogenous investment motivation. The short-path characteristic of its input–output process determines that the government only needs to provide a low initiation leverage to effectively stimulate its willingness for technology investment. (2) Constrained by the triple pressures of high risk, weak bargaining power, and a long payback period, the agricultural group faces a severe investment–return mismatch. This structural disadvantage easily leads to investment inhibition. Therefore, the highest proportion of subsidies must be allocated as structural compensation to drive upstream technological innovation. (3) The integration of full-chain data creates significant superadditive synergistic benefits. The information dividends within the system internalize technology costs to a certain extent. Consequently, a medium-intensity subsidy can achieve an optimal balance between system costs and social welfare. (4) The differences in subsidy ceilings reflect the weight heterogeneity in the social welfare function. Given the market power of the e-commerce platform, excessive subsidies can easily induce distortion effects. Conversely, agricultural production, with its significant positive externalities such as ensuring food security, is granted higher tolerance and weight in the social welfare function for its output expansion, thereby establishing a more feasible region for subsidies upstream.

5.2. Balanced Comparison of Different Models

Proposition 5.

Comparison of Operational Decisions under Different Models.

Under the optimal subsidy strategy, the planting area and procurement price across the six models exhibit highly consistent hierarchical ranking characteristics: (1) Planting area ranking: ${\mathrm{a}}^{\mathrm{B}{\mathrm{G}}^{*}} >{ \mathrm{a}}^{\mathrm{D}{\mathrm{G}}^{*}} ={ \mathrm{a}}^{\mathrm{U}{\mathrm{G}}^{*}} > {\mathrm{a}}^{{\mathrm{B}}^{*}} > {\mathrm{a}}^{{\mathrm{D}}^{*}} >{ \mathrm{a}}^{{\mathrm{U}}^{*}}$; (2) Procurement price ranking: ${\mathrm{w}}^{\mathrm{B}{\mathrm{G}}^{*}} > {\mathrm{w}}^{\mathrm{D}{\mathrm{G}}^{*}} = {\mathrm{w}}^{\mathrm{U}{\mathrm{G}}^{*}} > {\mathrm{w}}^{{\mathrm{B}}^{*}} > {\mathrm{w}}^{{\mathrm{D}}^{*}} > {\mathrm{w}}^{{\mathrm{U}}^{*}}$.

Proposition 5 reveals the differences in the underlying “information structure” and “power structure” of the supply chain, which can be explained as follows: (1) Model BG consistently occupies the highest point. This stems from the trust superposition effect formed by the end-to-end information closed loop. The dual drivers of technology empowerment and subsidy incentives effectively eliminate transaction friction, successfully expanding the production possibility frontier of the supply chain. (2) The rankings of ${\mathrm{a}}^{{\mathrm{D}}^{*}} > {\mathrm{a}}^{{\mathrm{U}}^{*}}$ and ${\mathrm{w}}^{{\mathrm{D}}^{*}} > {\mathrm{w}}^{{\mathrm{U}}^{*}}$ validate the downstream information proximity advantage. An e-commerce platform, with its access to terminal data, can capture premiums through an efficient demand-pull mechanism. In contrast, the upstream market, which is distant from the market, faces decision-making lags and struggles to effectively stimulate market potential. (3) ${\mathrm{a}}^{\mathrm{D}{\mathrm{G}}^{*}} = {\mathrm{a}}^{\mathrm{U}{\mathrm{G}}^{*}}$ and ${\mathrm{w}}^{\mathrm{D}{\mathrm{G}}^{*}} = {\mathrm{w}}^{\mathrm{U}{\mathrm{G}}^{*}}$ indicate that although the upstream party is the weaker party, the optimal subsidy exerts a powerful structural correction function through asymmetric compensation. This function compensates for the upstream resource weak point and risk premium, indicating that as long as government intervention is appropriate, supporting either end can achieve equivalent output expansion, reflecting the equivalence of the policy.

Proposition 6.

Heterogeneous Comparison of Blockchain Investment Levels Under Optimal Subsidies.

Under the optimal subsidy strategy, blockchain investment exhibits significant structural heterogeneity: (1) For the agricultural group, the unilateral subsidy model stimulates the highest level of node investment, even exceeding that of the full-chain model, i.e., ${\mathrm{n}}_{\mathrm{m}}^{\mathrm{U}{\mathrm{G}}^{*} }> {\mathrm{n}}_{\mathrm{m}}^{\mathrm{B}{\mathrm{G}}^{*}} >{ \mathrm{n}}_{\mathrm{m}}^{{\mathrm{B}}^{*}} >{ \mathrm{n}}_{\mathrm{m}}^{{\mathrm{U}}^{*}}.$ (2) For the e-commerce platform, the full-chain model stimulates the highest level of node investment, outperforming the unilateral subsidy model, i.e., ${\mathrm{n}}_{\mathrm{r}}^{\mathrm{B}{\mathrm{G}}^{*}} > {\mathrm{n}}_{\mathrm{r}}^{\mathrm{D}{\mathrm{G}}^{*}} >{ \mathrm{n}}_{\mathrm{r}}^{{\mathrm{B}}^{*}} > {\mathrm{n}}_{\mathrm{r}}^{{\mathrm{D}}^{*}}$.

Proposition 6 reveals that supply chain entities follow different response mechanisms to policy incentives, which can be explained as follows: (1) For the relatively capital-constrained and risk-averse upstream, Model UG provides certain fiscal incentives. Compared with the expected market expansion from coordination, concentrating resources to significantly reduce marginal costs is more effective at stimulating node construction at the production end. (2) The ${\mathrm{n}}_{\mathrm{r}}^{\mathrm{D}{\mathrm{G}}^{*}} >{ \mathrm{n}}_{\mathrm{r}}^{{\mathrm{B}}^{*}}$ ranking results reveal that under the high-cost constraint, pure market coordination incentives are less effective than government intervention. That is, the government’s cost-reduction intervention is more effective at leveraging corporate investment willingness than the market’s revenue-increasing mechanism is. (3) Although ${\mathsf{\tau }}^{\mathrm{B}{\mathrm{G}}^{*}}$ is lower than ${\mathsf{\tau }}^{\mathrm{U}{\mathrm{G}}^{*}}$, the trust dividend generated by full-chain coordination is sufficient to cover the pressure of a slight subsidy reduction. Therefore, the e-commerce platform invests the most in Model BG. This finding validates the capital + technology coupling theory: only when both external fiscal support and internal coordination synergy are present will the e-commerce platform unleash its maximum potential for technology investment.

Proposition 7.

Comparison of Supply Chain Entity Profits and the Mechanism of the Strategic Game.

Under the optimal government subsidy strategy, the profits of supply chain entities exhibit significant structural heterogeneity. Although both parties can achieve a global optimum under the full-chain model, there is a clear divergence of interests in the choice of suboptimal strategies. The optimal profit ranking for the agricultural group is ${\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{B}{\mathrm{G}}^{*}} > {\mathsf{\pi }}_{\mathrm{m}}^{\mathrm{D}{\mathrm{G}}^{*}} > {\mathsf{\pi }}_{\mathrm{m}}^{{\mathrm{B}}^{*}} > {\mathsf{\pi }}_{\mathrm{m}}^{{\mathrm{D}}^{*}} >{ \mathsf{\pi }}_{\mathrm{m}}^{\mathrm{U}{\mathrm{G}}^{*}} > {\mathsf{\pi }}_{\mathrm{m}}^{{\mathrm{U}}^{*}}$; the optimal profit ranking for the e-commerce platform is ${\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{B}{\mathrm{G}}^{*}} > {\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{U}{\mathrm{G}}^{*}} > {\mathsf{\pi }}_{\mathrm{r}}^{{\mathrm{B}}^{*}} > {\mathsf{\pi }}_{\mathrm{r}}^{\mathrm{D}{\mathrm{G}}^{*}} >{ \mathsf{\pi }}_{\mathrm{r}}^{{\mathrm{D}}^{*}} >{ \mathsf{\pi }}_{\mathrm{r}}^{{\mathrm{U}}^{*}}$.

Proposition 7 reveals the complex mechanism where Pareto optimality and strategic deadlock coexist in contract farming supply chains, which can be explained as follows: (1) The absolute superiority of Model BG stems from the dual coupling of trust superposition (maximizing willingness to pay) and cost internalization (reduced construction costs). This confirms that breaking information silos and introducing external incentives is an effective path to achieving a sharp increase in overall supply chain value. (2) After excluding the global optimum, both parties exhibit a boxed pigs game pattern. The e-commerce platform prefers Model UG because upstream blockchain investment generates product-level traceability premiums that directly expand market demand, from which the platform benefits through higher sales volume, while bearing no technology investment cost itself. Symmetrically, the agricultural group prefers Model DG to capture downstream-driven demand expansion without incurring blockchain expenditure. This mutual free-riding motivation creates a strategic mismatch that can trap the supply chain in an investment inertia dilemma. (3) The advantage of Model B is that it validates the market value of information integrity. However, opportunistic motives cause individual rationality to deviate from collective rationality. Compared with the high-cost systemic optimization of Model B, firms prefer free-riding (Model DG/UG). This short-sighted tendency of shifting costs is better than cocreating value, which constitutes the greatest obstacle to collaborative innovation.

Proposition 8.

Global Comparison of Consumer Surplus and Total Social Welfare.

This proposition elevates the research perspective from the microlevel profits of enterprises to the macrolevel of social welfare. Under the optimal government subsidy strategy, the consumer surplus ranking is $\mathrm{C}{\mathrm{S}}^{\mathrm{B}{\mathrm{G}}^{*}} > \mathrm{C}{\mathrm{S}}^{\mathrm{D}{\mathrm{G}}^{*}} = \mathrm{C}{\mathrm{S}}^{\mathrm{U}{\mathrm{G}}^{*}}> \mathrm{C}{\mathrm{S}}^{{\mathrm{B}}^{*}}> \mathrm{C}{\mathrm{S}}^{{\mathrm{D}}^{*}}> \mathrm{C}{\mathrm{S}}^{{\mathrm{U}}^{*}}$. Under the condition of satisfying ${\displaystyle \frac{\sqrt{33 }- 5}{2}}\mathrm{X} < \mathrm{c} < \mathrm{X}$, the total social welfare ranking is $\mathrm{S}{\mathrm{W}}^{\mathrm{B}{\mathrm{G}}^{*}}> \mathrm{S}{\mathrm{W}}^{{\mathrm{B}}^{*}} > \mathrm{S}{\mathrm{W}}^{\mathrm{D}{\mathrm{G}}^{*}} = \mathrm{S}{\mathrm{W}}^{\mathrm{U}{\mathrm{G}}^{*}}> \mathrm{S}{\mathrm{W}}^{{\mathrm{D}}^{*}} > \mathrm{S}{\mathrm{W}}^{{\mathrm{U}}^{*}}$.

Proposition 8 reveals the synergistic logic between “technological evolution” and “policy intervention” in the process of supply chain upgrading, which can be explained as follows: (1) $\mathrm{C}{\mathrm{S}}^{{\mathrm{B}}^{*}}> \mathrm{C}{\mathrm{S}}^{{\mathrm{D}}^{*}}> \mathrm{C}{\mathrm{S}}^{{\mathrm{U}}^{*}}$ confirms consumers’ willingness to pay for high-quality traceability information. Model D only addresses information transparency at the sales end, while Model B thoroughly connects the complete farm-to-table chain, eliminating information asymmetry throughout the entire process. The increase in utility associated with this system trust far exceeds that associated with partial optimization. (2) $\mathrm{S}{\mathrm{W}}^{\mathrm{D}{\mathrm{G}}^{*}}= \mathrm{S}{\mathrm{W}}^{\mathrm{U}{\mathrm{G}}^{*}}$ indicates that when pursuing welfare maximization, the government faces a path-independent choice. This grants policymakers significant operational flexibility, allowing the government to balance distributional equity and implementation feasibility according to actual circumstances without harming resource allocation efficiency. (3) The absolute advantage of Model BG reaffirms the core argument: market mechanisms (technological coordination) and government intervention (financial support) are not substitutes but complementary. Only when data barriers across the entire chain are broken and externality costs are internalized through fiscal funds can social resource allocation achieve Pareto optimality.

6. Numerical Analysis

All numerical simulations in this section were performed using Wolfram Mathematica 14 (Wolfram Research, Inc., Champaign, IL, USA). The parameter values adopted in each subsection are calibrated based on the following principles. First, the mean yield μ = 8 and standard deviation σ = 0.5 are referenced from typical per-unit-area yield statistics of staple crops in China’s contract farming context (e.g., National Bureau of Statistics of China [55]). Second, the remaining parameters—including the production cost coefficient c, consumer willingness-to-pay λ, blockchain cost coefficient k, consumer traceability preference δ, and price sensitivity β—are set within economically reasonable ranges consistent with the parameter calibration practices adopted in closely related game-theoretic studies on agricultural supply chains (Kang et al. [46]; Wu and Zhu [17]; Ma [37]). Third, all parameter combinations strictly satisfy the stability condition established in Assumption 6, ensuring the existence and uniqueness of equilibrium solutions. Fourth, to enhance the robustness of the analysis, different parameter sets are employed across Section 6.1, Section 6.2, Section 6.3, Section 6.4 and Section 6.5, with key parameters varying over wide intervals (e.g.,$\delta \in \left[0.2,1.0\right],\mathsf{\beta }\in \left[0.2,1.0\right],\mathrm{k}\in \left[2,10\right],\mathrm{c}\in \left[80,100\right]$) to verify that the theoretical propositions hold across diverse market and cost environments. The specific parameter values for each simulation are reported at the beginning of each subsection.

6.1. Decision Robustness Analysis Driven by Market Heterogeneity

To verify Proposition 1 and quantify the heterogeneous impact of market environmental factors on supply chain equilibrium, this section examines the dynamic effects of consumer traceability preference $\mathsf{\delta }$ and price sensitivity $\mathsf{\beta }$ through numerical analysis.

When the parameters are $\mathrm{c} = 70, \mathsf{\lambda } = 200, \mathsf{\mu } = 8, \mathsf{\sigma } = 0.5, \mathrm{k} = 10, \mathrm{and} \mathsf{\beta } = 0.5$, the equilibrium results as $\mathsf{\delta }$ varies within the $\left[0.2,1.0\right]$ interval are as shown in Figure 4. As $\mathsf{\delta }$ increases, the decision variables and profit levels all significantly increase, validating the logic of demand-side benefits being transmitted upstream via the price mechanism. Among them, all indicators of Model BG consistently occupy the absolute high ground, confirming a significant superadditive synergy between the full-process closed loop and fiscal support. Notably, the profit curves exhibit a convex characteristic of marginal increase, indicating that blockchain technology possesses a nonlinear gain attribute. The more mature the market recognition is, the greater the increase in the commercial value of per-unit technology investment, resulting in an increasing returns to scale effect.

When the parameters are $\mathrm{c} = 150, \mathsf{\lambda } = 590, \mathsf{\mu } = 8, \mathsf{\sigma } = 0.5, \mathrm{k} = 2, \mathrm{and} \mathsf{\delta } = 0.5$, the equilibrium results as $\mathsf{\beta }$ varies within the $\left[0.2,1.0\right]$ interval are as shown in Figure 5. In stark contrast to the positive effect of $\mathsf{\delta }$, the increase in $\mathsf{\beta }$ constitutes structural resistance to value realization, forcing entities to cut investment to guard against risk, leading to a simultaneous decline in quantity and price. Among these, the rapid reduction in the number of blockchain nodes reveals the high vulnerability of technology as an elastic cost. However, the comparative analysis shows that models with subsidies consistently outperform those without subsidies. This finding indicates that government subsidies act as a buffer, enhancing the system’s robustness in harsh environments by lowering the break-even point.

6.2. Transmission Effects and Boundary Analysis of Cost Factors

To verify Proposition 2 and quantify the transmission mechanism of cost constraints, this section examines the dynamic effects of the blockchain technology cost coefficient $\mathrm{k}$ and the production cost coefficient $\mathrm{c}$ through numerical analysis.

When the parameters are $\mathrm{c} = 70, \mathsf{\lambda } = 300, \mathsf{\mu } = 8, \mathsf{\sigma } = 0.5, \mathsf{\delta } = 1, \mathrm{and} \mathsf{\beta } = 0.5$, the equilibrium results as $\mathrm{k}$ varies within the $\left[2,10\right]$ interval are as shown in Figure 6. As $k$ increases, all decision variables and profits exhibit a strictly monotonic decreasing trend, validating the negative feedback loop of technology reduction, demand contraction, and output decline. A comparison reveals that the baseline scenarios exhibit conservative characteristics of low profit and low sensitivity, whereas the advanced scenarios (especially Model BG), despite showing a steep decline characterized by high returns accompanied by high sensitivity due to a high node base, maintain their profit curves at the absolute highest level. This demonstrates that the core value of government subsidies lies not in eliminating cost sensitivity but in providing a substantial profit buffer space by increasing the break-even point, ensuring the survival resilience of the full-chain model even in high-cost environments.

When the parameters are $\mathsf{\lambda } = 500, \mathsf{\mu } = 8, \mathsf{\sigma } = 0.5, \mathsf{\delta } = 1, \mathrm{k} = 2, \mathrm{and} \mathsf{\beta } = 0.6$, the equilibrium results as $\mathrm{c}$ varies within the $\left[80,100\right]$ interval are as shown in Figure 7. As $\mathrm{c}$ increases, the supply chain exhibits a significant trend divergence characteristic: the procurement price shows a monotonic increasing trend, while all the other indicators and profits show a monotonic decreasing trend. This finding verifies that the price increase is a passive transfer driven by the production side rather than a demand-pull and therefore cannot reverse the trend of profit reduction. High production costs trigger a strong resource crowding-out effect, forcing entities to sacrifice value-adding technology investments to preserve basic operations, forming a negative feedback cycle. Nevertheless, leveraging the combined effect of technology premiums and fiscal leverage, Model BG effectively hedges against cost pressure, providing a viable survival path for agricultural transformation against a high-cost background.

6.3. Nonlinear Characteristics of Subsidy Incentives and Asymmetric Spillover Effects

To validate Propositions 3 and 4 and quantify the nonlinear characteristics and asymmetric spillover effects of government subsidies, this section systematically examines the dynamic impact of government subsidies (Figure 8) and the differences in growth rates (

Table 4. Comparison of growth rates for key supply chain indicators under the optimal subsidy strategies.

Comparison Dimensions	${\mathsf{\Delta }}_{\mathbf{a}}$	${\mathsf{\Delta }}_{\mathbf{w}}$	${\mathsf{\Delta }}_{{\mathbf{n}}_{\mathbf{m}}}$	${\mathsf{\Delta }}_{{\mathbf{n}}_{\mathbf{r}}}$	${\mathsf{\Delta }}_{{\mathsf{\pi }}_{\mathbf{m}}}$	${\mathsf{\Delta }}_{{\mathsf{\pi }}_{\mathbf{r}}}$	${\mathsf{\Delta }}_{\mathbf{CS}}$	${\mathsf{\Delta }}_{\mathbf{SW}}$
$\mathrm{UG} \mathrm{vs}. \mathrm{U} (\mathsf{\tau } = 75\%$)	16.83%	16.83%	367.34%		16.83%	36.50%	36.50%	12.55%
$\mathrm{DG} \mathrm{vs}. \mathrm{D} (\mathsf{\tau } = 33\%$)	7.28%	7.28%		60.12%	15.09%	7.28%	15.09%	2.68%
$\mathrm{BG} \mathrm{vs}. \mathrm{B} (\mathsf{\tau } = 45\%$)	19.61%	19.61%	117.47%	117.47%	37.44%	26.93%	43.06%	9.52%

).

When the parameters are $\mathrm{c} = 100, \mathsf{\lambda } = 400, \mathsf{\mu } = 8, \mathsf{\sigma } = 0.5, \mathsf{\delta } = 1, \mathsf{\beta } = 0.5, \mathrm{and} \mathrm{k} = 2$, the nonlinear fluctuation characteristics of various key indicators—namely, “rising–declining–subrising within the negative value interval”—are shown in Figure 8. This process can be divided into three evolutionary stages.

Stage 1: Effective Incentive Zone. Fiscal subsidies have a significant technological crowding-in effect, effectively offsetting the marginal cost of blockchain technology. This makes marginal nodes that were previously abandoned because of low ROI viable for investment. Taking scenario UG as an example, its optimal number of nodes increases exponentially (with a growth rate as high as 367.34%), driving the rapid accumulation of social welfare.

Stage 2: Overinvestment Zone. When $\mathsf{\tau }$ exceeds the critical threshold, subsidies transform from a catalyst into a driver of resource misallocation, leading to negative profits and a turn from rising to falling social welfare. The simulations reveal that in Models DG and BG, when $\mathsf{\tau }>87.8\%$, the e-commerce platform’s profit becomes negative. In Models UG and BG, when $\mathsf{\tau }>95.4\%$, the agricultural group’s profit also becomes negative.

Stage 3: Ineffective Equilibrium Zone. The rebound in indicators near full subsidies ($\mathsf{\tau }\to 1$) is an illusion created by fiscal transfusions, masking the paralysis of market mechanisms. This finding validates the existence of a strict efficiency boundary for the optimal subsidy ratio. More crucially, taking scenario UG as an example, the subsidy ratio corresponding to the peak profit of the agricultural group (95%) is far greater than the ratio corresponding to the peak of social welfare (75%). This difference reveals a structural conflict between private corporate interests and public social welfare. While high subsidies can increase corporate profits, the excessive fiscal burden results in a loss of social welfare.

On the basis of the growth rate analysis in Table 4, the optimal government subsidy ratios for scenarios UG, BG, and DG are 75%, 45%, and 33%, respectively, which is highly consistent with the conclusion of Proposition 4. Unilateral subsidies exhibit significant asymmetric spillover effects, characterized as subsidizing one party benefits the entire chain. In Model UG, the profit growth rate of the nonsubsidized e-commerce platform (36.50%) surpasses that of the subsidized agricultural group (16.83%). This confirms that the downstream free-rides on the market expansion dividends are brought by upstream quality improvements. Similarly, Model DG also achieves reverse welfare transmission through the price transmission mechanism. A comprehensive comparison reveals that although Model UG leads in terms of the technology investment growth rate, Model BG ranks first in absolute growth for the planting area (19.61%), procurement price (19.61%), and agricultural group profit (37.44%). This confirms that full-chain subsidies can allocate incentive resources more evenly, effectively avoiding the diminishing marginal utility caused by excessive single-point investment.

6.4. Strategic Selection Analysis Based on Social Welfare Maximization

This section uses social welfare maximization as the criterion to systematically delineate the Pareto-advantageous intervals for Models UG, DG, and BG by plotting a strategic evolution map.

Figure 9 first reveals that the interaction between $\mathsf{\delta }$ and $\mathsf{\tau }$ presents a distinct tripartite differentiation characteristic. Model BG dominates the endogenous high-efficiency zone characterized by high preference, low subsidy, validating the multiplier effect between market forces and policy. As $\mathsf{\tau }$ increases, the strategic focus shifts towards Model UG, whereas in the region of low preference and medium subsidy, Model DG emerges as a suboptimal choice, indicating that it serves as a transitional strategy balancing cost and demand. The variation in $\mathsf{\beta }$ leads to a left–red, right–blue binary polarized distribution in the strategic landscape. Model BG demonstrates strong robustness in low-subsidy intervals, indicating that full-chain trust premiums are resilient to declines. When the subsidy $\mathsf{\tau }$ exceeds a critical threshold and enters a high range, the system switches to Model UG. This finding indicates that in an environment characterized by both high price sensitivity and high subsidies, Model UG, owing to its low-cost nature, may offer greater social allocation efficiency than Model BG does. In the analysis of the cost dimension, Model DG disappears entirely, simplifying the decision to either full-chain collaboration (BG) or source governance (UG). As $\mathrm{k}$ increases, the stable coverage of Model BG confirms the critical importance of synergistic effects. Although an increase in the production cost $\mathrm{c}$ lowers the absolute level of social welfare, it does not alter the strategic boundaries, resulting in a significant sunk nature—meaning that the universal impact of production costs does not change the relative ranking of the models.

6.5. Welfare Gradient and Sensitivity Analysis Under Multifactor Interactions

This section, by constructing three-dimensional surfaces and on the basis of the geometric features of gradient and convexity, delves deeply into the nonlinear interaction mechanisms between government subsidies and endogenous variables. It aims to identify the key levers and constraints for welfare optimization.

As shown in Figure 10, the gradient of social welfare with respect to $\mathsf{\delta }$ is significantly greater than its gradient with respect to $\mathsf{\tau }$. This means that, compared with mere fiscal subsidies, consumer market education has a greater marginal contribution. More critically, the surface exhibits significant convexity. When $\mathsf{\delta }$ jumps to a high level, the surface representing social welfare’s response to increases in $\mathsf{\tau }$ becomes extremely steep. This reveals a strong positive resonance between the two; a high level of market awareness can amplify policy effectiveness, and the resulting multiplier effect drives exponential growth in social welfare. The response surface of social welfare with respect to price sensitivity shows a characteristic cliff-like decline. A slight increase in $\mathsf{\beta }$ causes a drastic negative correction in social welfare, with the absolute value of its declining slope ranking first among all the parameters. This finding indicates that market price sensitivity is the strongest short-board constraint, limiting the welfare ceiling of the supply chain. Compared with the dramatic fluctuations in demand-side factors, the response curve of social welfare to $\mathrm{k}$ is relatively gentle. Especially in the high-subsidy interval, government subsidies effectively internalize technology costs, thereby cushioning the negative impact of rising costs on welfare. The impact of production cost $\mathrm{c}$ on social welfare shows a negative correlation similar to that of $\mathrm{k}$, but its response curve is even flatter. This suggests that cost factors are not the core obstacle hindering blockchain applications.

7. Conclusions

This study focuses on a contract farming supply chain composed of an agricultural group and an e-commerce platform. It constructs six Stackelberg game models under different power structures and policy scenarios, delving into the synergistic evolution mechanism between blockchain technology adoption strategies and government subsidy policies under market uncertainty and consumer traceability preference. This research not only reveals the interactive logic between microlevel corporate decision-making and macrolevel social welfare but also provides a theoretical foundation and practical guidance for promoting agricultural digital transformation.

7.1. Main Conclusions

In terms of consumer preferences, among the various models involving the introduction of blockchain technology, when consumers’ preference for “on-chain” agricultural products increases, the relevant decision variables and profits of agricultural groups mostly increase. However, the profit changes of e-commerce platforms are affected by the cost–effect threshold of blockchain technology. The threshold is lower when there is no subsidy and higher when there is a subsidy.

(1)

The market environment is a prerequisite for determining whether blockchain technology can be successfully implemented. The results of this study reveal that consumer traceability preference has a significant positive driving effect, capable of incentivizing the supply side to increase node investment and expand the planting scale through the demand expansion–price transmission mechanism. However, price sensitivity constitutes a strong inhibitory factor, leading to a low-level equilibrium characterized by a simultaneous decline in both quantity and price. More critically, only when the cost-effectiveness of blockchain technology exceeds a specific threshold can market preference translate into actual profit growth for enterprises; otherwise, firms fall into the dilemma of increased revenue without increased profit.

(2)

Cost transmission is asymmetric. The research reveals distinct transmission mechanisms for technology costs versus production costs. An increase in blockchain technology costs forces entities to cut their investment and contract supply. In contrast, an increase in agricultural production costs, while reducing profits and planting area, triggers a rigid cost-pass-through mechanism that forces procurement prices to rise passively. There is an essential difference between this cost-push price increase and demand-pull value appreciation. The former harms the long-term competitiveness of the supply chain, whereas the latter is key to achieving sustainable development.

(3)

Government subsidies are not merely financial transfers but external levers for breaking low-level Nash equilibria. The research confirms that an optimal subsidy strategy can achieve Pareto improvement in the supply chain. Within the effective range, subsidies can significantly stimulate a technology crowding-in effect, prompting both the agricultural group and the e-commerce platform to simultaneously increase node investment, procurement prices, and the planting area, ultimately achieving dual growth in corporate profits and total social welfare. In particular, Model BG, by leveraging the dual dividends of eliminating information silos and reducing marginal costs, can maximize social welfare in most scenarios.

(4)

Subsidy strategies involve structural differences and a boxed pigs game dilemma. Owing to its disadvantaged position in the value chain and distance from the end market, the agricultural group requires the highest subsidy ratio to overcome investment inertia. In contrast, the e-commerce platform, leveraging its market proximity advantage, requires the lowest subsidy ratio. However, the study revealed intense strategic conflicts between supply chain entities. The e-commerce platform prefers Model UG because upstream blockchain investment generates product-level traceability premiums that directly expand market demand, from which the platform benefits through higher sales volume, while bearing no technology investment cost itself. Symmetrically, the agricultural group prefers Model DG to capture downstream-driven demand expansion without incurring blockchain expenditure. This mutual free-riding motivation creates a strategic mismatch that, without external coordination, can easily trap the supply chain in a prisoner’s dilemma of investment inaction.

(5)

Boundaries of policy effectiveness and dynamic evolution. Social welfare does not increase indefinitely with subsidies. The research defines the efficiency boundary of subsidies; excessive subsidies lead to resource misallocation and, consequently, harm social welfare. Furthermore, the strategy for maximizing social welfare is context-dependent. In mature markets characterized by low subsidies + high preference, Model BG is the optimal choice. In nascent markets characterized by high subsidies + high sensitivity, Model UG becomes the best choice because of its cost-efficiency advantage.

(6)

Several findings merit particular attention due to their counterintuitive nature. First, unilateral subsidies generate asymmetric spillover effects where the non-subsidized party may benefit more than the subsidized party. For instance, under Model UG, the profit growth rate of the non-subsidized e-commerce platform (36.50%) exceeds that of the subsidized agricultural group (16.83%). This “subsidizing one, benefiting the other more” phenomenon arises because the upstream traceability investment creates a market-wide premium from which the downstream party captures disproportionate value through its proximity to consumers. Second, the optimal subsidy ratio for the full-chain model (${\tau }^{BG*}$) is lower than that for the upstream-only model (${\tau }^{UG*}$), despite the full-chain model requiring investment from both parties. This counterintuitive ranking occurs because the trust dividend generated by end-to-end traceability partially substitutes for fiscal incentives, reducing the government’s required subsidy intensity. Third, under optimal subsidies, subsidizing either the upstream or downstream party alone achieves identical planting areas and procurement prices ($a^{DG*}=a^{UG*}$, $w^{DG*}=w^{UG*}$), revealing a policy equivalence that grants policymakers significant operational flexibility.

7.2. Managerial and Policy Implications

(1)

Recommendations for the government: The model results yield specific, condition-dependent policy guidelines derived from the strategy evolution analysis (Figure 9) and equilibrium comparisons (Table 2 and Table 3).

(a) Subsidy target selection should be conditional on market characteristics. When consumer traceability preference $\delta$ is high and the required subsidy intensity is low, the government should prioritize the full-chain subsidy model (Model BG), as the synergy between market recognition and fiscal support maximizes social welfare. When price sensitivity $\beta$ is high—typical of mass-market staple crops where consumers are highly responsive to price changes—the government should subsidize the agricultural group (Model UG), because in price-sensitive markets, the low-cost structure of upstream-only subsidies offers greater social allocation efficiency than full-chain subsidies. When the market is at an early stage with low consumer traceability awareness (low $\delta$) and moderate fiscal capacity, subsidizing the e-commerce platform (Model DG) serves as a transitional strategy that leverages the platform’s demand-pull capability to cultivate market recognition before transitioning to full-chain adoption.

(b) Subsidy intensity must respect the efficiency boundary identified in this study. The numerical results indicate that the optimal subsidy ratios are approximately 75% for Model UG, 45% for Model BG, and 33% for Model DG. Beyond these thresholds, subsidies induce overinvestment and negative profits (e.g., platform profits become negative when $\tau$ > 87.8% in Models DG and BG), transforming fiscal support from a catalyst into a source of resource misallocation. The government should therefore establish a dynamic monitoring mechanism that adjusts subsidy intensity based on observed market maturity indicators.

(c) To break the boxed pigs game dilemma identified in Proposition 7—where both parties prefer the other to lead investment—the government should design joint-application subsidy schemes that require upstream and downstream co-investment as a precondition for receiving full-chain subsidies. This institutional design converts the free-riding incentive into a cooperative one, aligning private incentives with the socially optimal full-chain model.

(d) As consumer traceability preferences mature over time, the government should gradually reduce subsidy intensity. The strategy evolution analysis confirms that in mature markets with established consumer preferences, market mechanisms alone (the “trust premium”) can sustain blockchain investment without fiscal intervention.

(2)

Recommendations for supply chain entities:

(a) The agricultural group should recognize that although Model DG offers short-term free-riding benefits (capturing demand expansion without technology investment), its profit under this model (${\pi }_m^{DG*}$) ranks below that under Model BG. The group should therefore actively pursue full-chain collaboration and negotiate revenue-sharing contracts that internalize the downstream platform’s demand-side benefits, transforming government subsidies from external stimulus into sustained cooperative motivation.

(b) The e-commerce platform should note that its profit growth under Model UG (36.50%) substantially exceeds that under Model DG (7.28%), confirming that upstream quality improvements generate significant downstream spillovers. Rather than pursuing short-term cost avoidance, the platform should proactively use its data and technological advantages to empower upstream partners, converting upstream traceability into downstream brand equity.

(c) For mass-market agricultural products with high price sensitivity $\beta$, both parties should exercise caution in blockchain investment scale, as the cost–effect threshold is more difficult to overcome in such markets. For premium products (green, organic) with high consumer traceability preference $\delta$, an aggressive full-chain strategy should be adopted to exploit the technology’s nonlinear gain characteristics identified in Proposition 1.

7.3. Research Limitations and Future Directions

Although this study has achieved certain results in revealing the synergistic impact of blockchain technology adoption strategies and government subsidy mechanisms on contract farming supply chains, several limitations remain, offering avenues for future research. First, this study constructs a two-level supply chain model based on a “bilateral monopoly” structure. However, real-world contract farming often operates in complex network environments. Future research could attempt to construct complex network models involving “multiple competing agricultural groups + multiple gaming e-commerce platforms” to more realistically simulate the dynamic evolution of real markets. Second, this study focuses primarily on government cost subsidies for the number of blockchain nodes introduced. However, real-world agricultural support policies are more diverse. Future research could compare and analyse the differences in incentive efficiency across various policies. Third, this study uses total social welfare maximization as the decision-making objective. In reality, government decision-making objectives are often multidimensional. Future work could construct multiobjective optimization models to explore how the government can design combined policy mechanisms to balance efficiency and fairness. Fourth, this study assumes that government subsidies are costlessly administered, with only the direct fiscal expenditure $GE(n_i)={\displaystyle \frac{1}{2}}\tau k{n}_i^2$ entering the social welfare function. In practice, subsidy policies involve non-trivial implementation costs, including administrative overhead for application processing, compliance monitoring, and fraud prevention. These implementation costs, if incorporated into the welfare function, would further tighten the efficiency boundary of the optimal subsidy ratio and potentially shift the optimal $\tau *$ downward. Future research could endogenize the administrative cost of subsidy implementation as a function of the subsidy ratio or the number of participating entities, providing a more realistic assessment of net social welfare gains.