Subsidy Policy Interactions in Agricultural Supply Chains: An Interdepartmental Coordination Perspective

Abstract

The efficacy of government subsidy programs in agriculture is frequently compromised by internal policy conflicts that arise between competing government departments. This challenge is addressed herein, with a focus on the policy environment in China, through the development of a game-theoretic model of an agricultural supply chain. This model explicitly incorporates two competing government bodies—the Agriculture and Rural Affairs Department (ARAD) and the Development and Reform Commission (DRC)—each with distinct objectives and performance indicators. Within this framework, the strategic interactions of four subsidy types are analyzed: production and cold-chain subsidies (ARAD), and platform operation and blockchain subsidies (DRC). The findings reveal that department-specific performance indicators can significantly distort the overall effectiveness of subsidies. While individual subsidies may achieve their intended departmental goals, their combined impact is shown to be complex and frequently suboptimal in the absence of higher-level coordination. Notably, a subsidy portfolio combining production and platform operation subsidies is found to consistently yield superior performance in maximizing social welfare. Ultimately, this research contributes a new framework for understanding subsidy policies and provides actionable insights for optimizing interdepartmental coordination to enhance supply chain performance.

1. Introduction

Although agriculture serves as a primary source of income in many developing countries, government subsidies have become a cornerstone of agricultural policy worldwide. Recently, the scope of these subsidies has diversified beyond simple production support to encompass investments in technology, such as cold-chain logistics and blockchain for food safety. Although the impact of individual subsidies on farm-level decisions and welfare has been extensively analyzed in agricultural economics and operations management (e.g., Chintapalli and Tang [1], Fan et al. [2]), a prevailing assumption in these studies is that the government acts as a single, monolithic decision-maker. This simplification represents a notable gap in the literature. Specifically, a critical and pragmatic challenge is frequently overlooked by this conventional approach: internal policy conflict arising from interdepartmental competition, which often leads to policy failure. To the best of our knowledge, how the competing objectives and performance metrics of different government bodies influence the design and ultimate effectiveness of subsidy portfolios has not been sufficiently investigated. This study addresses this gap by explicitly modeling the government as a system composed of departments with conflicting interests.

For instance, in China, the Agriculture and Rural Affairs Department (ARAD) might promote subsidies to boost grain output, while the Development and Reform Commission (DRC) concurrently supports land-use policies that can inadvertently cause farmers to abandon traditional farming [3,4]. Consequently, these conflicting objectives, driven by disparate departmental mandates and performance indicators, can result in policy neutralization, resource waste, and suboptimal outcomes for the entire agricultural supply chain. This interdepartmental tension is further exacerbated in modern supply chains featuring powerful platform enterprises. Consequently, emerging technologies, such as blockchain, are often adopted by these platforms to enhance food safety and supply chain transparency. However, the practical application of blockchain for traceability is not a standalone solution, as integration with a broader technological ecosystem is frequently required. For example, complementary technologies like Near Field Communication (NFC) are often necessary to establish a link between physical products and their digital identities, thereby enhancing product authenticity and consumer trust. The strategic value and consumer acceptance of such integrated systems have been empirically validated, for instance, in the wine industry [5]. The significant investment required for these advanced traceability infrastructures has created a new focal point for policy debate, posing a dilemma for higher-level government: whether to subsidize traditional production (an ARAD priority) or a platform’s adoption of new technology (a DRC priority). This dilemma’s resolution is not merely technical but fundamentally political, as it is rooted in the unique goals of each department.

To address this critical research gap, our study is guided by an overarching question: How do interactions and coordination within the government shape the effectiveness of agricultural subsidies in a modern supply chain? Specifically, we seek to answer the following detailed research questions:

• Under various subsidy policies and their combinations, how are the decisions of supply chain members (supplier, platform) and the government (higher-level department) formulated, and what are the resulting impacts on social welfare, stakeholder profits, and departmental utility?
• What are the differential impacts of various subsidy policies on the respective performance indicators of the two competing government departments?
• How can the higher-level department optimally allocate its budget across different subsidy combinations to improve key outcomes, such as social welfare and overall supply chain performance?

To this end, a game-theoretic framework is developed to model an agricultural supply chain composed of a supplier, a platform enterprise, and a government structure with two competing departments (ARAD and DRC) overseen by a higher-level authority. Through this structure, the policy-making process can be formalized not as a simple optimization problem but as a multi-level game where departmental interests and performance metrics assume a central role.

In this study, four distinct subsidy types are analyzed, both individually and in combination: production and cold-chain subsidies from the ARAD, and platform operation and blockchain subsidies from the DRC. Department-specific performance indicators are also explicitly incorporated: an increase in agricultural output for the ARAD and market price stability for the DRC. This approach makes it possible to explore how a higher-level authority can utilize budgetary allocation as a mechanism to coordinate these departments and align their conflicting objectives toward maximizing social welfare.

Table 1. Summary of representative policies relevant to this study.

Subsidy Programs in This Study	Representative Policies from Different Countries	Affiliated Department
Production subsidies	China [6], USA [7], Ghana [8]	ARAD
Cold-chain logistics investment subsidies	China [9], India [10]	ARAD
Platform operation cost subsidies	China [11]	DRC
Blockchain technology subsidies	China [12], UK [13], India [14]	DRC

summarizes representative real-world policies that correspond to the subsidy types examined in this study.

This study makes the following contributions. First, a new analytical framework is pioneered by modeling the government not as a monolith but as a multi-agent system with internal conflicts, thereby bridging a crucial gap between public administration theory and supply chain management. Second, this study is one of the first to explicitly incorporate and quantify the impact of department-specific performance indicators on subsidy design, revealing how these metrics can create policy distortions. Third, the findings provide actionable insights for policymakers by demonstrating how different subsidy combinations perform and offering a tool to optimize interdepartmental coordination for enhanced supply chain efficiency and social welfare.

The structure of this paper is outlined as follows: Section 2 reviews the relevant literature on subsidy programs, agricultural supply chain, and interdepartmental coordination within government. Section 3 introduces the agricultural supply chain model, detailing its assumptions and indices. Section 4 examines a baseline model without blockchain integration, a baseline model incorporating blockchain, and four individual subsidy models, followed by a comparative analysis. In Section 5, two subsidy combinations are selected for detailed analysis, informed by the findings in Section 4 and practical considerations. Section 6 evaluates the equilibrium solutions of each model, emphasizing the effects of policy interactions on supply chain profits, social welfare, and departmental performance indicators. Section 7 discusses the implications of our findings, connecting them to real-world policy challenges and the existing literature. Finally, Section 8 presents the research conclusions, managerial implications, and prospective avenues for future research.

2. Literature Review

This study’s relevant literature primarily addresses three aspects: subsidy programs, agricultural supply chain, and interdepartmental coordination within government.

2.1. Subsidy Programs

In line with the research focus of this paper, subsidy programs are categorized into agricultural subsidies and non-agricultural subsidies.

Agricultural subsidies have consistently been a focal point in agricultural economics research. The primary focus of this literature is on the macroeconomic impacts of subsidies, as explored by scholars such as Hoekman et al. [15], Anderson et al. [16]. These studies primarily evaluate subsidies through their effects on income distribution [17], productivity levels [18,19], and social welfare [20], employing predominantly empirical methods. In contrast to these studies, this paper employs an analytical model, considering the current state of smart agriculture and incorporating non-agricultural subsidies into the analysis. It investigates how these subsidies and their combinations influence the decision-making of agricultural supply chain members and key indicators such as social welfare, serving as a complement to existing empirical studies.

Subsidy programs have also been examined in diverse contexts, such as drug allocation [21,22], green technology adoption [23,24], bilateral coordination [25], and live streaming businesses [26]. While these studies primarily investigate single subsidy types, this paper examines both agricultural and non-agricultural subsidies, analyzing their mechanisms, effects, and combinations.

2.2. Agricultural Supply Chain

Extensive research on agricultural supply chain has primarily addressed aspects such as pricing decisions [27], logistics and transportation strategies [28], preservation efforts [29], supply chain coordination mechanisms [30], information disclosure [31], and farmer incentive programs [32]. Specifically, Chintapalli and Tang [33] introduced a minimum support price framework grounded in a credit mechanism, evaluating its impact on both farmer surplus and consumer surplus. Similarly, Chintapalli and Tang [1] examined cost subsidies, minimum support prices, and their combinations, revealing that cost subsidies diminish farmer surplus. Fan et al. [2] employed a Stackelberg model to investigate the effects of planting, harvesting, comprehensive, and selective subsidies on budget allocation, social welfare, farmer output, and wealth distribution. Aligned with these studies, this paper examines the impacts of various subsidy types and their combinations on social welfare and profit levels. However, this study uniquely integrates performance indicators of different departments and their interdepartmental coordination in subsidy combinations, addressing a gap in agricultural supply chain literature.

2.3. Interdepartmental Coordination Within Government

The literature concerning interdepartmental coordination within government predominantly emphasizes public administration. Key topics include the differentiation of departmental interests [34], the distribution of political power among local governments [35], power structures [36], mutual influence among departmental leaders [37], and interdepartmental games [38]. However, the majority of studies fail to examine the behavioral-level impacts of interdepartmental coordination relationships. Notable exceptions include Zheng et al. [38], Qian and Mok [39], Gilli et al. [40]. Qian and Mok [39] identified crowding-out effects between social welfare policies caused by the segmentation of departmental interests, using unemployment insurance and the “minimum livelihood guarantee” as examples. Similarly, Gilli et al. [40] observed that interest exchanges between the National Health Commission and the Ministry of Civil Affairs diminished the efficiency of social security and medical insurance coverage when examining rural medical insurance and the “minimum livelihood guarantee”. Additionally, Zheng et al. [38] provided a novel characterization of the gaming behaviors between two higher-level government departments, considering resource allocation, interaction strategies, and output levels through a three-tier model encompassing higher-level government, lower-level government, and enterprises. They further validated their proposed theory of departmental coordination consistency using large-sample empirical evidence. In contrast, this paper focuses on the coordination between two lower-level departments, mediated by a higher-level department through fund allocation. This perspective offers significant novelty within the domain of supply chain operations management.

3. Model Setup and Assumptions

3.1. Model Setup

As shown in Figure 1, this paper examines an agricultural supply chain consisting of government departments, an agricultural product supplier, and a platform enterprise. The agricultural product supplier (denoted as F) cultivates q units of agricultural products at a total cost of $c{q}^2$ and sells them to an intermediary platform enterprise (denoted as P). A wholesale contract at a unit price of w is adopted between these two entities, and the platform sells the product at a unit retail price of p, where $p>w>c$. It is assumed that the platform purchases all output produced by the supplier, a standard assumption in agricultural supply chain models. The “14th Five-Year Plan for National Economic and Social Development and the Long-Range Objectives Through the Year 2035” of the People’s Republic of China [41] outlines development goals, including promoting farmers’ income growth, enhancing the modernization of industrial and supply chains, establishing cold-chain logistics systems, developing the platform economy, and supporting blockchain infrastructure construction. Aligned with this policy framework, multiple subsidies have been implemented by provincial-level departments. Building on this policy context, this paper develops an agricultural supply chain model driven by platform enterprise. The study first examines the impact of different subsidy policies on the agricultural supply chain in relation to the performance indicators of government departments at the same level, and subsequently analyzes how the higher-level department coordinates subsidies and resources between these departments.

The selection of the four subsidy types for analysis—production, cold-chain, platform operation, and blockchain—is based on the current policy landscape of China. These selected subsidies reflect the dual priorities of the central government, which are outlined in major policy directives such as the “14th Five-Year Plan for National Economic and Social Development and the Long-Range Objectives Through the Year 2035” [41]. On the one hand, production and cold-chain subsidies are considered established, critical tools for ensuring food security and improving the circulation of agricultural goods—mandates that are central to the ARAD. On the other hand, subsidies for platform operations and the adoption of new technologies like blockchain are aligned with the national strategic push towards developing the digital economy and modernizing industrial supply chains—initiatives that are typically championed by the DRC. As shown in Table 1, each of these subsidy types corresponds to real-world policies implemented at national or provincial levels. Consequently, their relevance for examining the dynamics of interdepartmental coordination is well established.

Specifically, Section 4 analyzes the impact of agricultural subsidies provided by a single department on the agricultural supply chain, while Section 5 examines the effects of subsidies offered simultaneously by two departments. The scenarios examined in Section 4 include six models, designated as OA, OB, AA, AB, FA, and FB.

(1) Baseline Models OA and OB: Neither involves subsidies. In scenario OB, the platform enterprise adopts blockchain to enhance market demand and reduce recall costs, whereas in scenario OA, blockchain is not utilized.

(2) Scenarios with subsidies from the ARAD: Subsidies based on the volume of agricultural products are denoted as Model AA, while subsidies for cold-chain logistics construction are denoted as Model AB.

(3) Scenarios with subsidies from the DRC: Subsidies for platform enterprise operating costs are denoted as Model FA, while subsidies for blockchain application costs (including one-time and variable costs) are denoted as Model FB.

For clarity, the models examined in this study and their key characteristics are summarized in

Table 2. Summary of Models and Scenarios.

Model Acronym	Subsidizing Department(s)	Key Characteristics
Section 4: Single-Department Subsidy Scenarios
OA	None (Baseline)	No blockchain, no subsidies.
OB	None (Baseline)	Blockchain adopted by the platform, no subsidies.
AA	ARAD	Production subsidy for the supplier.
AB	ARAD	Cold-chain investment subsidy for the platform.
FA	DRC	Platform operation cost subsidy.
FB	DRC	Blockchain technology subsidy for the platform.
Section 5: Interdepartmental Coordination Scenarios
GA	ARAD + DRC	Coordinated subsidies: Production (ARAD) + Platform Operation (DRC).
GB	ARAD + DRC	Coordinated subsidies: Production (ARAD) + Blockchain (DRC).

.

Section 5 primarily focuses on the following scenarios:

(1) The ARAD offers subsidies based on agricultural product volume, while the DRC provides subsidies for platform enterprise operating costs, denoted as Model GA.

(2) The ARAD provides subsidies based on agricultural product volume, while the DRC provides subsidies for blockchain application costs (including one-time and variable costs), denoted as Model GB.

The decision-making sequences are presented in Figure 2 and Figure 3. All parameters, symbols, and their corresponding explanations are detailed in the online Supplementary. Superscripts OA, OB, AA, AB, FA, FB, GA, and GB indicate different models. For clarity: ‘O’ denotes baseline models, the first ‘A’ denotes subsidies by the ARAD, ‘F’ denotes subsidies by the DRC, and ‘G’ represents scenarios with subsidies from both departments.

3.2. Model Assumptions

Assumption 1.

This paper examines the impact of crop yield uncertainty on decision-making processes and social welfare with respect to agricultural product pricing. To address these uncertainties and derive tractable results, this paper, following the setups in Alizamir et al. [42], Arya and Mittendorf [43] and Chintapalli and Tang [33], assumes that the inverse demand function for agricultural products is $p=a-bqX$, where a denotes the market potential of agricultural products, which is assumed to be sufficiently large. Here, q represents the cultivated area (or production quantity) of agricultural products, i.e., the production decision of agricultural product supplier; p is the retail price of agricultural products; b is the retail price elasticity coefficient; and X is the yield uncertainty factor, capturing variations in yield due to environmental factors and agricultural practices (e.g., rainfall, irrigation, pest infestations, and seed quality). Furthermore, the density function of X is assumed to be denoted as $f_X(·)$. Without loss of generality, it is defined that $E\left(X\right)=\mu$ and $D\left(X\right)={\sigma }^2$. Thus, when the production quantity of agricultural products is q, the inverse demand function can be expressed as $p=a-b\mu q$.

Assumption 2.

Agricultural products are subject to a probability of contamination during both the production and distribution processes. The probabilities of contamination during transportation from supplier to the platform enterprise’s warehouse and from the warehouse to the market are denoted by ${\rho }_f$ and ${\rho }_p$, respectively. In the absence of blockchain technology for product traceability, the responsible entity (i.e., the platform enterprise) requires significant time to identify the source of contamination, investigate the issue, and gather the necessary information for resolution. During this period, the platform enterprise incurs a cost of $({\rho }_f+{\rho }_p)c_{r}q$ to recall all products, while the agricultural product supplier bears a loss of $({\rho }_f+{\rho }_p)gq$, where $c_r$ denotes the recall cost per unit product, and g represents the unit loss to supplier due to contamination, including reputational damage or downstream claims, with $c_r>g>0$. To efficiently identify the contamination source, contaminated batches, and responsible entities, while minimizing recall costs, the platform enterprise invests a fixed cost F in blockchain infrastructure, which simultaneously increases market demand by s. Following the adoption of blockchain technology, an agricultural product quality traceability system is established, facilitating the identification of contaminated batches and responsible parties for recalls, thereby enabling flexible recall processes [44,45,46]. Under this scenario, only the contaminated batches are recalled, reducing the number of recalled products from q to $(1-\delta )q$. Thus, blockchain adoption reduces supply chain costs by minimizing recall losses, albeit with the introduction of a variable cost per unit of $c_b$. At this stage, the recall costs incurred by the platform enterprise and agricultural product supplier are ${\rho }_p{c}_r(1-\delta )q$ and ${\rho }_f{c}_r(1-\delta )q$, respectively, where $\delta \in (0,1)$ denotes the proportion of uncontaminated agricultural products.

Assumption 3.

Based on the research by Yun and Wei [47] and Yu and Xiao [48], a positive correlation between market demand and cold-chain service preservation efforts has been established. Accordingly, the demand function is expressed as $p=a-bqX+h\beta e$, where h denotes the sensitivity of market demand to freshness, β represents the efficiency of cold-chain logistics service preservation efforts, and e is the decision variable for preservation efforts, with $e\in (0,1)$. By letting $\eta =h\beta$, η is defined as the sensitivity of market demand to variations in cold-chain logistics service preservation efforts. This study assumes that the platform enterprise is responsible for providing cold-chain logistics preservation services, a premise that aligns with practical industry scenarios. Leading companies such as Meicai.com [49], JD.com [50], and Walmart [51] have developed their own cold-chain logistics systems, serving as illustrative examples of platform enterprises. Drawing from the frameworks proposed by Wu et al. [52], Yang and Tang [53] and Yu and Xiao [48], the investment cost associated with the platform enterprise’s cold-chain logistics preservation services is given by ${\displaystyle \frac{1}{2}}k{e}^2$, where k denotes the cost coefficient.

Assumption 4.

The social welfare function is composed of four key components: the profits of entities within the agricultural supply chain (${\pi }_f+{\pi }_p$), consumer surplus ($CS$), government subsidy expenditures (E), and government performance indicators (G). The subsidy recipients and amounts for the contract farming supply chain vary under different subsidy policies. With respect to government subsidy expenditures (E), this paper makes the following assumptions: according to Table 1, four primary types of subsidy policies are selected for study: subsidies provided by the ARAD based on agricultural product output (Model AA) and cold-chain logistics construction costs (Model AB), and subsidies provided by the DRC based on platform enterprise operating costs (Model FA) and blockchain application costs (Model FB). Notably, the ARAD and the DRC are parallel departments within the same governmental hierarchy. Performance indicators are measurable metrics that indicate the achievement of specific objectives over time. Teams use performance indicators to set goals and track the progress being made. This information can assist personnel from different departments, such as finance or marketing, in making more informed decisions. The government uses performance indicators to measure the outcomes, effectiveness, and efficiency of socio-economic management activities, reflecting its management capabilities in exercising its functions and implementing its policies. These include political, economic, cultural, and social performance. In summary, performance indicators serve as a method for measuring success and guiding improvements across various domains within an organization. Due to varying definitions and indicator frameworks across countries and government departments, the U.S. Department of Agriculture includes food security [54] and rural economic development within its performance indicators, while the UK government categorizes its environmental indicators into four areas: air emissions, land, water quality, and energy usage [55]. This study uses China as an example. Regarding the government performance indicators (G), the following assumptions are made: drawing on several government reports, including the “Self-Evaluation Report on the Overall Expenditure Performance of the Yueyang County Agriculture and Rural Affairs Bureau in 2020" [56], the “Performance Evaluation Report on the Overall Expenditure of the Jianghua Yao Autonomous County Agriculture and Rural Affairs Bureau in 2023" [57], the “Self-Evaluation Table on the Overall Expenditure Performance of the Wanzai County Development and Reform Commission" published by the Bengbu Yuhui District Development and Reform Commission [58], and the “Self-Evaluation Report on the Overall Expenditure Performance of the Linli County Development and Reform Bureau in 2023" [59], the performance indicator for subsidies provided by the agriculture and rural affairs departments is defined as the increase in agricultural product output (compared to Model OB), expressed as $G_A^i=q^i-q^{OB*}$, where $i=AA,AB$. For subsidies provided by the development and reform commissions, the performance indicator is defined as a penalty for market price instability, expressed as $G_A^j=-\alpha {(p^j-p_0)}^2$, where $p_0$ is the exogenously determined stable price level set by the government, and $j=FA,FB$.

Assumption 5.

To ensure that the model can obtain an equilibrium solution, the following conditions must also be satisfied: ${\displaystyle \frac{2bk\left({\sigma }^2+1\right)+4ck-{\eta }^2}{4c^2}}>0$, $-{\displaystyle \frac{-2k\left(b{\sigma }^2+b+2c\right)+2k{t}_2\left(b{\sigma }^2+b+2c\right)+{\eta }^2}{4c^2}}>0$.

4. Model Solving and Discussions

In this section, backward induction will be employed to solve the model. Given the multiple models examined in this paper, the inverse demand functions, profit functions, and social welfare functions for the models studied in this section (namely OA, OB, AA, AB, FA, and FB) are summarized in

Table 3. Summary of demand, profit and social welfare functions in scenarios where only one type of subsidy is provided.

Models	Inverse Demand, Profit and Social Welfare Functions
OA	$p^{OA}=a-bX{q}^{OA}+\eta e^{OA}$
	$E\left({\pi }_f\right)=E[w^{OA}{q}^{OA}X-{c{q}^{OA}}^2-({\rho }_f+{\rho }_p)g{q}^{OA}X]$
	$E\left({\pi }_p^{OA}\right)=E[(p^{OA}-w^{OA}-c_p)q^{OA}X-{\displaystyle \frac{1}{2}}k{e}^{O{A}^2}-({\rho }_f+{\rho }_p)c_r{q}^{OA}X]$
	$E\left(S{W}^{OA}\right)=E({\pi }_f^{OA}+{\pi }_p^{OA}+C{S}^{OA})$
OB	$p^{OB}=a-bX{q}^{OB}+\eta e^{OB}+s$
	$E\left({\pi }_f^{OB}\right)=E[w^{OB}{q}^{OB}X-{c{q}^{OB}}^2-{\rho }_f{c}_r(1-\delta )q^{OB}X]$
	$E\left({\pi }_p^{OB}\right)=E[(p^{OB}-w^{OB}-c_p-c_b)q^{OB}X-{\displaystyle \frac{1}{2}}k{e}^{O{B}^2}-{\rho }_p{c}_r(1-\delta )q^{OB}X-F]$
	$E\left(S{W}^{OB}\right)=E({\pi }_f^{OB}+{\pi }_p^{OB}+C{S}^{OB})$
AA	$p^{AA}=a-bX{q}^{AA}+\eta e^{AA}+s$
	$E\left({\pi }_f^{AA}\right)=E[w^{AA}{q}^{AA}X-{c{q}^{AA}}^2-{\rho }_f{c}_r(1-\delta )q^{AA}X+t_1{q}^{AA}X]$
	$E\left({\pi }_p^{AA}\right)=E[\left(p^{AA}-w^{AA}-c_p-c_b\right)q^{AA}X-{\displaystyle \frac{1}{2}}k{e}^{A{A}^2}-{\rho }_p{c}_r(1-\delta )q^{AA}X-F]$
	$E\left(S{W}^{AA}\right)=E({\pi }_f^{AA}+{\pi }_p^{AA}+C{S}^{AA}-t_1{q}^{AA}X+q^{AA}-q^{{OB}^{*}})$
AB	$p^{AB}=a-bX{q}^{AB}+\eta e^{AB}+s$
	$E\left({\pi }_f^{AB}\right)=E[w^{AB}{q}^{AB}X-{c{q}^{AB}}^2-{\rho }_f{c}_r(1-\delta )q^{AB}X]$
	$E\left({\pi }_p^{AB}\right)=E[(p^{AB}-w^{AB}-c_p-c_b)q^{AB}X-{\displaystyle \frac{1}{2}}k{e}^{A{B}^2}-{\rho }_p{c}_r\left(1-\delta \right)qX-F+{\displaystyle \frac{1}{2}}k{t}_2{e}^{A{B}^2}]$
	$E\left(S{W}^{AB}\right)=E({\pi }_f^{AB}+{\pi }_p^{AB}+C{S}^{AB}-{\displaystyle \frac{1}{2}}k{t}_2{e}^{A{B}^2}+q^{AB}-q^{{OB}^{*}})$
FA	$p^{FA}=a-bX{q}^{FA}+\eta e^{FA}+s$
	$E\left({\pi }_f^{FA}\right)=E[w^{FA}{q}^{FA}X-{c{q}^{FA}}^2-{\rho }_f{c}_r(1-\delta )q^{FA}X]$
	$E\left({\pi }_p^{FA}\right)=E[(p^{FA}-w^{FA}-c_p-c_b)q^{FA}X-{\displaystyle \frac{1}{2}}k{e}^{F{A}^2}-{\rho }_p{c}_r(1-\delta )q^{FA}X-F+t_3{q}^{FA}X{c}_p]$
	$E\left(S{W}^{FA}\right)=E[{\pi }_f^{FA}+{\pi }_p^{FA}+C{S}^{FA}-t_3{q}^{FA}X{c}_p-\alpha {(p^{FA}-p_0)}^2]$
FB	$p^{FB}=a-bX{q}^{FB}+\eta e^{FB}+s$
	$E\left({\pi }_f^{FB}\right)=E[w^{FB}{q}^{FB}X-{c{q}^{FA}}^2-{\rho }_f{c}_r\left(1-\delta \right)q^{FB}X]$
	$E\left({\pi }_p^{FB}\right)=E[(p^{FB}-w^{FB}-c_p-c_b)q^{FB}X-{\displaystyle \frac{1}{2}}k{e}^{F{B}^2}-{\rho }_p{c}_r(1-\delta )q^{FB}X-F+t_4(c_b{q}^{FB}X+F)]$
	$E\left(S{W}^{FB}\right)=E[{\pi }_f^{FB}+{\pi }_p^{FB}+C{S}^{FB}-t_4(c_b{q}^{FB}X+F)-\alpha {(p^{FA}-p_0)}^2]$

Note that: $E\left(C{S}^i\right)=E({\int }_0^{q^i}{p}^{i}d{q}^i-p^i{q}^{i}X)$, where $i=AA,AB,FA,FB$.

for clarity.

After deriving the equilibrium solution, a sensitivity analysis was conducted on the model, followed by a comparison with the benchmark model. Given that this is a routine analysis, the detailed results have been summarized in Supplementary S5 and Supplementary S6 respectively.

4.1. Discussions

4.1.1. A Comparison Between Model AA and Model AB

Proposition 1.

$w^{{AA}^{*}}<w^{{AB}^{*}}$ and $p^{{AA}^{*}}<p^{{AB}^{*}}$ always holds. When $t_2<\dot{t_2}$, we have $e^{{AA}^{*}}>e^{{AB}^{*}}$, otherwise, $e^{{AA}^{*}}<e^{{AB}^{*}}$. When $t_2<\ddot{t_2}$, we have $q^{{AA}^{*}}>q^{{AB}^{*}}$ and ${\pi }_f^{{AA}^{*}}>{\pi }_f^{{AB}^{*}}$, otherwise, $q^{{AA}^{*}}<q^{{AB}^{*}}$, ${\pi }_f^{{AA}^{*}}<{\pi }_f^{{AB}^{*}}$. When $t_2<\stackrel{⃛}{t_2}$, ${\pi }_p^{{AA}^{*}}>{\pi }_p^{{AB}^{*}}$, otherwise, ${\pi }_p^{{AA}^{*}}<{\pi }_p^{{AB}^{*}}$. The expressions for $\dot{t_2}, \ddot{t_2}, \stackrel{⃛}{t_2}$ are provided in Online Supplementary S2. Due to the complexity of the analytical solution for SW, we used simulations to demonstrate that $S{W}^{{AA}^{*}}>S{W}^{{AB}^{*}}$. The simulation figures can be found in Online Supplementary S6.

Proposition 1 reveals the impact of different subsidy rates $t_2$ on key supply chain indicators and social welfare in the Model AA and the Model AB. When $t_2$ is low, the Model AA significantly reduces farmers’ production costs through direct subsidies on the output of agricultural product supplier, allowing supplier to sell agricultural products at reduced wholesale and retail prices. This reduction increases investment in cold-chain logistics and production volumes, thereby optimizing supply chain efficiency and enhancing the profits of agricultural product supplier. This direct form of subsidy provides more evident support to the production side, making the Model AA outperform the Model AB in terms of supplier profits, agricultural product output, and other indicators.

As the subsidy rate $t_2$ increases, the Model AB gradually gains an advantage. By subsidizing the construction costs of cold-chain logistics for platform enterprise, the Model AB allows platform enterprise to allocate more resources to optimize logistics services, improving product freshness and supply chain coordination efficiency. This optimization further stimulates agricultural product supplier to increase production and drives the economic growth of platform enterprise. Therefore, at high levels of $t_2$, the Model AB surpasses the Model AA in terms of production volume, supplier profits, and platform enterprise profits.

However, in terms of social welfare, simulation results indicate that the Model AA consistently outperforms the Model AB. The output subsidies in the Model AA directly promote an increase in agricultural product output, significantly improving the performance metrics of the rural agricultural sector, thereby providing it with a distinct advantage in social welfare evaluation. Furthermore, the increase in agricultural product output has a direct impact on meeting the basic demand for agricultural products in society, a benefit that is highly weighted in social welfare assessments.

In contrast, although the Model AB improves supply chain efficiency through cold-chain logistics subsidies, the main beneficiaries of its subsidies are platform enterprise, and it does not directly increase agricultural output to the same extent, which limits its overall contribution to social welfare. The differences in social welfare performance between the two models stem from different priorities in the allocation of subsidy resources. The Model AA, by directly promoting agricultural output, can more effectively enhance social welfare, especially under the goal of increasing agricultural income and production.

4.1.2. A Comparison Between Model FA and Model FB

Proposition 2.

When $t<\dot{t_4}$, we have $w^{{FA}^{*}}>w^{{FB}^{*}}$, $p^{{FA}^{*}}<p^{{FB}^{*}}$, $e^{{FA}^{*}}>e^{{FB}^{*}}$, $q^{{FA}^{*}}>q^{{FB}^{*}}$, ${\pi }_f^{{FA}^{*}}>{\pi }_f^{{FB}^{*}}$ and $S{W}^{{FA}^{*}}>S{W}^{{FB}^{*}}$, otherwise, $w^{{FA}^{*}}<w^{{FB}^{*}}$, $p^{{FA}^{*}}>p^{{FB}^{*}}$, $e^{{FA}^{*}}<e^{{FB}^{*}}$, $q^{{FA}^{*}}<q^{{FB}^{*}}$, ${\pi }_f^{{FA}^{*}}<{\pi }_f^{{FB}^{*}}$ and $S{W}^{{FA}^{*}}<S{W}^{{FB}^{*}}$. When $t_4<\ddot{t_4}$, we have ${\pi }_p^{{FA}^{*}}>{\pi }_p^{{FB}^{*}}$, otherwise, ${\pi }_p^{{FA}^{*}}<{\pi }_p^{{FB}^{*}}$.

From the analysis of Proposition 2, it is evident that variations in the subsidy rate t significantly affect the performance of Model FA and Model FB. When the subsidy rate t is less than the critical value $\dot{t_4}$, Model FA outperforms Model FB in key indicators such as wholesale price, cold-chain logistics investment, agricultural product production quantity, supplier profit, and social welfare. At this stage, by subsidizing the operating costs of the platform enterprise, Model FA directly improves the production efficiency of the platform enterprise and enhances overall supply chain effectiveness, fostering the expansion of agricultural product production and supply, thereby enhancing social welfare.

Regarding retail prices, when $t_4<\dot{t_4}$, Model FA places greater emphasis on optimizing the operating costs of the platform enterprise, resulting in a lower wholesale price. This advantage is directly reflected in the retail market, where the retail price of Model FA is lower than that of Model FB, thereby effectively lowering consumer expenditure. However, when the subsidy rate t exceeds the critical value $\dot{t_4}$, Model FB outperforms Model FA in key indicators such as wholesale price, cold-chain logistics investment, and agricultural product production quantity.

At this stage, subsidies aimed at blockchain technology not only enhance the logistics efficiency of the platform enterprise but also improve overall production efficiency and supply chain responsiveness through improved transparency and information sharing. Consequently, Model FB emerges as the more competitive model under high subsidy rates.

5. Interdepartmental Coordination Within Government

In this section, a new role is introduced—the higher-level department (typically the Ministry of Finance)—which oversees and coordinates subsidies provided by two peer departments: the ARAD and the DRC. The structural relationship is illustrated in Figure 4. Following the framework established by Zheng et al. [38], $\theta$ represents the degree of importance the higher-level department assigns to the ARAD, while $1-\theta$ reflects the emphasis placed on the DRC, where $0\le \theta \le 1$. As $\theta$ increases, the higher-level department prioritizes the ARAD, thereby allocating a larger proportion of subsidies to it. The total subsidy allocation is subject to the budget constraint L, such that $\theta E_A^{GA}+\left(1-\theta \right)E_F^{GA}\le L$.

According to information disclosed by the Department of Financial and Planning, the coverage rate of improved varieties of major crops in China had already reached 96% as early as 2016 [60]. This indicates that subsidies provided by the ARAD based on production volume represent the most widely implemented and representative type of agricultural subsidies in China’s current policy landscape. Building on this policy context, this section examines two scenarios. The first scenario involves the ARAD providing subsidies based on production volume, while the DRC offers subsidies based on blockchain-related costs (denoted as Model GA). The second scenario examines subsidies provided by the ARAD based on production volume, combined with subsidies from the DRC targeting the operating costs of the platform enterprise (denoted as Model GB).

It is important to note that in the models studied in this section, the allocation of subsidies is determined by the higher-level department, which considers only the budgetary constraint without evaluating whether the performance indicators of the ARAD or the DRC meet the required standards. Subsequently, in Section 6.4, Models GA and GB are extended to incorporate the performance indicators of the subordinate departments. This extension aims to more comprehensively capture how changes in the utility function of the higher-level department influence its benefit evaluation. Furthermore, this analysis reveals the critical role and significance of subordinate departments’ performance indicators in shaping policy objectives and priorities.

The inverse demand function, profit functions, and the utility function of the higher-level department for Model GA are as follows:

$$p^{GA}=a-b{q}^{GA}X+\eta e^{GA}+s$$

(1)

$$E\left({\pi }_f^{GA}\right)=E[w^{GA}{q}^{GA}X-c{q}^{G{A}^2}-{\rho }_f{c}_r(1-\delta )q^{GA}X+{\theta }^{GA}{t}_1{q}^{GA}]$$

(2)

$$E\left({\pi }_p^{GA}\right)=E[(p^{GA}-w^{GA}-c_p-c_b)q^{GA}X-{\displaystyle \frac{1}{2}}k{e}^{G{A}^2}-{\rho }_p{c}_r(1-\delta )q^{GA}X-F+(1-{\theta }^{GA})t_3{c}_p{q}^{GA}X]$$

(3)

$$E\left(C{S}^{GA}\right)=E({\int }_0^{q^{GA}}{p}^{GA}d{p}^{GA}-p^{GA}{q}^{GA}X)$$

(4)

$$\begin{array}{ccc}& E\left(U_H^{GA}\right)& =E[{\pi }_f^{GA}+{\pi }_p^{GA}+C{S}^{GA}-{\theta }^{GA}{t}_1{q}^{GA}-(1-{\theta }^{GA})t_3{c}_p{q}^{GA}X]\hfill \\ & s.t.& {\theta }^{GA}{t}_1{q}^{GA}X+(1-{\theta }^{GA})t_3{c}_b{q}^{GA}X\le L\hfill \end{array}$$

(5)

The inverse demand function, profit functions, and the utility function of the higher-level department for Model GB are as follows:

$$p^{GB}=a-b{q}^{GB}X+\eta e^{GB}+s$$

(6)

$$E\left({\pi }_f^{GB}\right)=E[w^{GB}{q}^{GB}X-c{q}^{G{B}^2}-{\rho }_f{c}_r(1-\delta )q^{GB}X+{\theta }^{GB}{t}_1{q}^{GB}]$$

(7)

$$E\left({\pi }_p^{GB}\right)=E[(p^{GB}-w^{GB}-c_p-c_b)q^{GB}X-{\displaystyle \frac{1}{2}}k{e}^{G{B}^2}-{\rho }_p{c}_r(1-\delta )q^{GB}X-F+(1-{\theta }^{GB})t_4(c_b{q}^{FB}X+F)]$$

(8)

$$E\left(C{S}^{GB}\right)=E({\int }_0^{q^{GB}}{p}^{GB}d{p}^{GB}-p^{GB}{q}^{GB}X)$$

(9)

$$\begin{array}{ccc}& E\left(U_H^{GB}\right)& =E[{\pi }_f^{GB}+{\pi }_p^{GB}+C{S}^{GB}-{\theta }^{GB}{t}_1{q}^{GB}-(1-{\theta }^{GB})t_4(c_b{q}^{FB}X+F)]\hfill \\ & s.t.& {\theta }^{GB}{t}_1{q}^{GB}X+(1-{\theta }^{GB})t_4(c_b{q}^{FB}X+F)\le L\hfill \end{array}$$

(10)

A Comparison Between Model GA and Model GB

Due to the complexity of the equilibrium solutions, this subsection employs simulation to compare Model GA and Model GB. The parameter values used in the simulation are as follows: $a=100$, $b=1$, $k=50$, $\eta =0.5$, $c=1$, ${\rho }_f=0.02$, ${\rho }_p=0.02$, $c_p=2$, $\delta =0.2$, $g=1$, $c_b=3$, $F=500$, $c_r=3$, $s=8$, $\sigma =0.1$, $\alpha =0.1$, $p_0=50$, $t_1=0.5$, and $t_2=t_3=t_4=0.3$. The range of L is set between $L_1$ and $L_2$. The optimal decisions and equilibrium profits of Models GA and GB are summarized in Figure 5.

From Figure 5, within the range from $L_1$ to $L_2$, the following relationships are observed: $w^{{GB}^{*}}<w^{{GA}^{*}}$, $p^{{GB}^{*}}>p^{{GA}^{*}}$, $e^{{GB}^{*}}<e^{{GA}^{*}}$, $q^{{GB}^{*}}<q^{{GA}^{*}}$, ${\theta }^{{GB}^{*}}>{\theta }^{{GA}^{*}}$, ${\pi }_f^{{GB}^{*}}<{\pi }_f^{{GA}^{*}}$, ${\pi }_p^{{GB}^{*}}>{\pi }_p^{{GA}^{*}}$, and $U_H^{{GB}^{*}}<U_H^{{GA}^{*}}$. The simulation results reveal significant differences between Model GA and Model GB in terms of resource allocation, pricing strategies, cold-chain logistics investment, and the profits of supply chain participants.

In the comparison of weight factors, it is evident that ${\theta }^{{GB}^{*}}>{\theta }^{{GA}^{*}}$, indicating that the higher-level department assign greater importance to production subsidies for the ARAD in Model GB compared to Model GA, while the relative support for the DRC is weaker. However, this does not imply that more resources are allocated to the ARAD in Model GB; rather, it reflects a tendency to assign higher weights to the ARAD relative to Model GA. This tendency is closely related to the subsidy structure characteristics of Model GB. Specifically, subsidies provided by the DRC in Model GB are based on blockchain-related costs, and the inherent rigidity of blockchain construction and operational costs influences this allocation. For instance, the infrastructure construction of blockchain technology entails high initial fixed costs, while operational and maintenance costs remain significant. This rigidity results in blockchain subsidies occupying a large proportion of resource allocation, thereby limiting the flexibility of the higher-level department in allocating additional subsidies to the DRC. To achieve a balance in resource allocation and prevent the ARAD from experiencing insufficient support, the higher-level department tend to assign higher weights to the ARAD in Model GB, ensuring a degree of policy balance within the overall resource framework.

These shifts in weight factors are also reflected in the comparisons of wholesale prices, retail prices, and cold-chain logistics investment. In Model GB, wholesale prices are lower than in Model GA, while retail prices are higher. This indicates that the platform enterprise in Model GB may purchase agricultural products from supplier at lower wholesale prices but compensates for this cost difference through higher retail prices, thereby maintaining its profitability. Furthermore, the cold-chain logistics investment in Model GA exceeds that in Model GB, suggesting that the platform enterprise in Model GA receives greater resource support for optimizing logistics efficiency. In contrast, the lower investment in cold-chain logistics in Model GB adversely affects the overall circulation efficiency of the agricultural product supply chain and market supply.

In terms of profits and social utility, the profits of agricultural product supplier in Model GB are lower than those in Model GA, signifying that although higher weights are assigned to the ARAD in Model GB, this support has not fully translated into direct income benefits for supplier. Meanwhile, the platform enterprise achieves higher profits in Model GB, largely due to its ability to offset the lower wholesale prices by adopting retail pricing strategies. However, this imbalance in resource allocation ultimately results in lower utility for the higher-level department in Model GB compared to Model GA, highlighting that the subsidy strategy tilt in Model GB has not fully maximized the overall efficiency of the supply chain.

In summary, regarding resource allocation and subsidy strategies, the balanced advantage of Model GA highlights that resource investment in cold-chain logistics can substantially enhance supply chain efficiency and supplier returns, thereby improving overall social welfare. While Model GB provides greater support to the ARAD, its resources are disproportionately allocated to the high rigid costs of blockchain technology, resulting in insufficient direct incentives for supplier. This imbalance ultimately leads to lower supply chain efficiency and reduced social welfare compared to Model GA. Policymakers should consider optimizing resource allocation based on the specific characteristics of the subsidy structure, ensuring that resource imbalances do not negatively impact supply chain efficiency or economic returns.

6. Analysis

In this section, the equilibrium solutions derived earlier will be analyzed in greater depth, and Models GA and GB will be extended to uncover additional insights and conclusions.

6.1. Impact of Subsidy Rate Interactions on Supply Chain Members’ Profits and Social Welfare Under the Scenario of Providing a Single Subsidy

We use simulations to analyze the impact of subsidy rate interactions on the profits of supply chain members and social welfare when only one type of subsidy is provided. The simulation results for Models AA and AB are summarized in Figure 6, with the following parameter values: $a=100$, $b=1$, $k=50$, $\eta =0.5$, $c=1$, ${\rho }_f=0.02$, ${\rho }_p=0.02$, $c_p=2$, $\delta =0.2$, $g=1$, $c_b=3$, $F=200$, $c_r=3$, $s=8$, and $\sigma =0.1$. Figure 6a,b illustrate how the combination of subsidy rates, $t_1$ (production subsidy) and $t_2$ (cold-chain logistics subsidy), affects the profit distribution of agricultural product supplier and platform enterprise. When $t_1$ is high and $t_2$ is low, Model AA demonstrates superior performance in terms of both supplier profits and platform enterprise profits. This advantage arises because the production subsidy directly lowers the production costs for supplier, thereby enhancing procurement efficiency and increasing the profit levels of platform enterprise through the supply chain transmission mechanism. However, as $t_2$ increases, Model AB begins to exhibit greater advantages. This is attributable to the cold-chain logistics subsidy, which improves supply chain efficiency and reduces logistics losses, thereby driving joint profit growth for both supplier and platform enterprise. Notably, Figure 6c reveals that, regardless of the combination of $t_1$ and $t_2$, Model AA consistently outperforms Model AB in terms of social welfare. While cold-chain logistics subsidies enhance the economic benefits of supply chain members by improving efficiency, their marginal contribution to social welfare is not as substantial as that of direct production subsidies.

Similarly, we analyzed the profits of supply chain members and social welfare for Models FA and FB using simulation. The simulation results are summarized in Figure 7. The specific parameter values used in the analysis are as follows: $a=100$, $b=1$, $k=30$, $\eta =0.5$, $c=1$, ${\rho }_f=0.02$, ${\rho }_p=0.02$, $c_p=2$, $\delta =0.2$, $g=1$, $c_b=3$, $F=200$, $c_r=3$, $s=8$, $\sigma =0.1$, $\alpha =0.1$, and $p_0=30$. This figure highlights the effects of subsidy strategy interactions by examining the impact of subsidy rates $t_3$ (operating cost subsidy for platform enterprise) and $t_4$ (blockchain subsidy) on the profits of supply chain members and social welfare. Figure 7a,c demonstrate that when the subsidy rate $t_4$ is high, Model FB significantly outperforms Model FA in terms of both agricultural product supplier profits and social welfare. This superiority can be attributed to the application of blockchain technology, which not only reduces recall costs but also enhances supply chain transparency and consumer confidence, thereby driving an expansion in market demand. In contrast, an increase in the subsidy rate $t_3$ only provides a distinct advantage to Model FA when $t_4$ is low, as the benefits of operating cost subsidies are primarily limited to improving the short-term operating income of platform enterprise, with minimal impact on overall supply chain efficiency and social welfare. Figure 7b further illustrates that in nearly all combinations of subsidy rates (except when $t_4$ is small), the profits of platform enterprise are higher in Model FB. This result underscores the significant role of blockchain subsidies in enhancing the long-term competitiveness and market responsiveness of platform enterprise.

These two sets of simulation results reveal the interactions between different subsidy mechanisms and their differentiated impacts on various supply chain entities and overall social welfare. For the comparison between Models AA and AB, although cold-chain logistics subsidies improve supply chain efficiency by reducing logistical losses and enhancing product freshness, production subsidies have a stronger and more direct effect on increasing social welfare due to their immediate support for the production side. In the comparison between Models FA and FB, blockchain subsidies demonstrate significantly greater comprehensive value than operating cost subsidies, primarily by enhancing supply chain transparency, fostering market trust, and reducing recall costs. These findings suggest that the combination and prioritization of different subsidy mechanisms play a critical role in achieving policy objectives. For instance, in Models AA and AB, moderately increasing cold-chain logistics subsidies can further optimize supply chain efficiency, while in Models FA and FB, prioritizing blockchain subsidies can significantly enhance the modernization of the supply chain and deliver higher social benefits.

In summary, the design of subsidy strategies should be optimized by taking into account the interactions between different subsidies and the specific policy objectives. In scenarios where the primary goal is to increase grain production, production subsidies should be prioritized due to their direct and immediate impact. Conversely, in scenarios where the focus is on improving supply chain efficiency and transparency, subsidies supporting cold-chain logistics and blockchain technology are more critical. Policymakers must carefully balance these subsidy mechanisms to simultaneously enhance supply chain performance and maximize social welfare. Similarly, enterprise should adapt their strategies in alignment with evolving policy directions, particularly by leveraging emerging technologies such as blockchain to gain competitive advantages and promote the sustainable development of the agricultural supply chain.

6.2. Comparison of Performance Indicators

Proposition 3.

When $t_1<\dot{t_1}$, we have $G_A^{{AA}^{*}}<G_A^{{AB}^{*}}$, otherwise, $G_A^{{AA}^{*}}>G_A^{{AB}^{*}}$. When $t_4<\dot{t_4}$, we have $G_F^{{FA}^{*}}>G_F^{{FB}^{*}}$, otherwise, $G_F^{{FA}^{*}}<G_F^{{FB}^{*}}$.

Proposition 3 examines the comparison of performance indicators between Model AA and Model AB, as well as between Model FA and Model FB, under varying subsidy conditions, introducing the concept of a subsidy rate threshold to illustrate the impact of subsidy strategies on performance indicators. First, for the agricultural product output increase indicator ($G_A$), when $t_1<\dot{t_1}$, the increase in agricultural product output in Model AA is smaller than that in Model AB. This is because, at lower levels of production subsidies, cold-chain logistics facility subsidies (Model AB) more effectively enhance the market supply of agricultural products by improving transportation efficiency and reducing losses within the supply chain, thereby resulting in increased output. However, when $t_1>\dot{t_1}$, the agricultural product output increase in Model AA surpasses that in Model AB. This shift reflects that at higher levels of production subsidies, their direct incentive effect on the production side becomes more pronounced. As suppliers is motivated to expand production, this directly drives a larger increase in agricultural product output, exceeding the indirect effects of cold-chain logistics subsidies.

Second, regarding the market price stability penalty indicator ($G_F$), when $t_4<\dot{t_4}$, $G_F^{FA*}$ is greater than $G_F^{FB*}$, indicating that Model FB performs better in reducing market price instability. This advantage arises from the role of blockchain technology in enhancing supply chain information transparency, which improves the supply chain’s responsiveness and its ability to match market demand, thereby mitigating price instability and reducing government penalties for price fluctuations. However, when $t_4>\dot{t_4}$, platform enterprise operating cost subsidies (Model FA) become more effective in stabilizing market prices. High levels of operating cost subsidies directly alleviate cost pressures on platform enterprise, enabling them to optimize their pricing strategies, which in turn contributes to more stable market price fluctuations.

In conclusion, Proposition 3 highlights that subsidy strategy selection should align with specific policy objectives. For increasing agricultural product output, cold-chain logistics subsidies are more effective at lower production subsidy levels due to their indirect effects, while production subsidies yield greater benefits at higher levels due to their direct influence on production. For improving market price stability, platform operating cost subsidies have a stronger impact at lower blockchain subsidy levels, whereas blockchain application subsidies are more effective in alleviating market price fluctuations at higher subsidy levels. These findings provide valuable guidance for policymakers to balance supply chain efficiency, production incentives, and market price stability in the design of subsidy strategies.

In addition, we analyzed the impact of the two subsidies on performance indicators through simulation plotting, as shown in Figure 8, with parameter values consistent with those in Figure 7. Figure 8a illustrates the effect of two different subsidy combinations on the performance indicators of the two sectors. The left panel reflects the performance indicator of the ARAD, specifically the increase in agricultural product output, highlighting the differing impacts of the combination of $t_1$ and $t_2$ on these benefits. As shown in the figure, when $t_1$ is high, Model AA demonstrates a more significant advantage, indicating that production-based subsidies are more effective in directly increasing agricultural product output. However, as $t_2$ increases, the advantage of Model AB gradually becomes evident, reflecting that cold-chain logistics subsidies can indirectly promote agricultural product output by enhancing supply chain efficiency.

Figure 8b presents the performance indicator of the DRC, represented by the penalty for market price instability, analyzing the impacts of $t_3$ and $t_4$. When $t_4$ is high, Model FB significantly outperforms Model FA, demonstrating that blockchain subsidies play a greater role in improving market transparency and stability. Conversely, the increase in $t_3$ offers only a slight advantage to Model FA when $t_4$ is low, indicating that operating cost subsidies have a relatively limited contribution to stabilizing market prices.

These analyses provide critical management implications for policy formulation. For the ARAD, production-based subsidies should be prioritized to directly enhance agricultural product output, while cold-chain logistics subsidies can be employed as a complementary approach to indirectly support agricultural development by improving supply chain efficiency. Meanwhile, the DRC should focus on supporting blockchain technology applications, as higher $t_4$ subsidies significantly reduce market price fluctuations, enhance market transparency, and boost consumer confidence, thereby effectively achieving the policy objective of price stability.

6.3. Analysis of Weighting Factors

In this subsection, we analyze the changes in the weighting factors influenced by two key parameters in Model GA and Model GB. As previously discussed, the weighting factor $\theta$ represents the level of importance attached by the higher-level department to the ARAD. A higher value of $\theta$ indicates greater emphasis on the ARAD, while $1-\theta$ reflects the level of importance assigned to the DRC. The simulation results are summarized in Figure 9, where the total budget L is set to 10, and all other parameter values remain consistent with those in Section 6.2.

Figure 9a illustrates the influence of $t_1$ and the total subsidy budget L on the weighting factor $\theta$. The results indicate that Model GB dominates most of the parameter space, suggesting that the higher-level department tends to assign greater importance to the ARAD in Model GB compared to Model GA. Model GA only demonstrates an advantage when $t_1$ approaches 0.5. This phenomenon can be attributed to the indirect efficiency enhancements provided by blockchain-related subsidies ($t_4$) in Model GB. Specifically, blockchain technology enhances supply chain transparency and information sharing, which in turn improves collaboration efficiency and market responsiveness, contributing to the long-term development potential of the supply chain. As a result, even when $t_1$ is low, the blockchain subsidies from the DRC can partially offset the insufficient support for supply chain production caused by low production subsidies, leading the higher-level department to maintain a higher weighting for the ARAD in Model GB. However, when $t_1$ approaches 0.5, the impact of production subsidies becomes more pronounced, particularly in scenarios with a smaller budget. The combination of platform operation subsidies ($t_3$) and production subsidies in Model GA provides more direct benefits for agricultural production and the basic operation of the supply chain, thereby increasing the importance attached to the ARAD in Model GA.

Figure 9b presents the influence of $t_3$ and $t_4$ on the weighting factor $\theta$. When both $t_3$ and $t_4$ are low, or when $t_3$ is high and $t_4$ is low, the higher-level department attaches greater importance to the ARAD in Model GA compared to Model GB. This outcome can be explained by the limited marginal contributions of low-level blockchain subsidies ($t_4$) to supply chain efficiency and social welfare, which make it challenging to significantly enhance the operational performance of the supply chain. In contrast, platform operation cost subsidies ($t_3$) directly reduce the basic operational costs of the supply chain, ensuring the circulation and market supply of agricultural products. This direct impact leads the higher-level department to favor the ARAD in Model GA. However, as $t_4$ increases and $t_3$ remains relatively low, the advantages of blockchain subsidies in Model GB become increasingly evident. At higher subsidy levels, blockchain technology significantly enhances supply chain transparency and efficiency, yielding substantial benefits for the entire supply chain. Once these technology-driven gains materialize, the higher-level department assigns significantly greater importance to the ARAD in Model GB compared to Model GA.

In summary, variations in subsidy combinations and funding levels have a direct impact on the resource allocation preferences of the higher-level department. Model GA prioritizes short-term agricultural production and supply chain operations by leveraging production subsidies and platform operation subsidies. In contrast, the blockchain subsidies in Model GB focus on enhancing long-term collaboration efficiency and supply chain transparency through technological advancements. Policymakers should carefully balance the trade-off between ensuring short-term production stability and pursuing long-term technological upgrades, aligning resource allocation with priority objectives to maximize overall benefits.

6.4. Extended Analysis

In the extended model presented in this section, the utility indicators of the two subordinate departments are incorporated into the utility function of the superior department. This adjustment is designed to more comprehensively capture the superior department’s emphasis on the performance outcomes of subordinate departments during policy implementation. It is important to note that this modification neither influences the allocation tendencies of supply chain resources nor alters the relative performance of supply chain members. Instead, the focus of the study lies in analyzing how the transformation of the superior department’s utility function affects its own revenue evaluation. This analysis further elucidates the role and significance of the utility indicators of subordinate departments in shaping policy objectives. The extended models are represented as $U_H^{G{A}^{\prime }}$ and $U_H^{G{B}^{\prime }}$, and the revised utility functions are as follows:

$$\begin{array}{ccc}& E\left(U_H^{G{A}^{\prime }}\right)& =E[{\pi }_f^{GA}+{\pi }_p^{GA}+C{S}^{GA}-{\theta }^{GA}{t}_1{q}^{GA}-(1-{\theta }^{GA})t_3{c}_p{q}^{GA}X+q^{GA}-q^{{OB}^{*}}-\alpha {(p^{GA}-p_0)}^2]\hfill \\ & s.t.& {\theta }^{GA}{t}_1{q}^{GA}+(1-{\theta }^{GA})t_3{c}_b{q}^{GA}X\le L\hfill \end{array}$$

(11)

$$\begin{array}{ccc}& E\left(U_H^{G{B}^{\prime }}\right)& =E[{\pi }_f^{GB}+{\pi }_p^{GB}+C{S}^{GB}-{\theta }^{GB}{t}_1{q}^{GB}-(1-{\theta }^{GB})t_4(c_b{q}^{FB}X+F)+q^{GB}-q^{{OB}^{*}}-\alpha {(p^{GB}-p_0)}^2]\hfill \\ & s.t.& {\theta }^{GB}{t}_1{q}^{GB}+(1-{\theta }^{GB})t_4(c_b{q}^{FB}X+F)\le L\hfill \end{array}$$

(12)

Through simulation plotting, we compared the cross-impacts of key parameters on the utility function of the superior department under scenarios both with and without incorporating the performance indicators of subordinate departments. Figure 10 presents the comparative results of the utility functions of the superior department between Model GA and Model GB in these two scenarios. The upper section illustrates the scenario where the performance indicators of subordinate departments are not considered. The steep slope of the dividing line in this image indicates that $t_1$ (production subsidy) and L (total subsidy budget) are the dominant factors influencing the utility comparison between the two models. This outcome reflects that, in the absence of performance indicators, the utility function of the superior department solely focuses on the direct economic benefits derived from resource allocation, with the structural characteristics of the two subsidy types being the primary determinants of model performance.

In contrast, the lower section of the figure reflects the scenario after introducing the performance indicators of subordinate departments. In this context, Model GA demonstrates an absolute advantage across all parameter combinations. This shift is primarily driven by the revised evaluation method of the superior department’s utility function. When performance indicators are considered, the superior department evaluates not only the direct economic outcomes of resource allocation but also the specific performance impacts on the ARAD and the DRC. As highlighted in prior analyses, while ${\theta }^{{GB}^{*}}>{\theta }^{{GA}^{*}}$ in Model GB—indicating that the superior department places greater emphasis on the ARAD in Model GB—the utility function of the superior department, $U_H^{{GA}^{*}}$, remains higher in Model GA. This discrepancy is primarily attributed to differences in resource allocation efficiency between the two subsidy combinations. As noted in Section 6.2, simulation analyses of the performance indicators in the extended Models GA and GB reveal that the performance indicators for both subordinate departments in Model GA consistently outperform those in Model GB, irrespective of key parameter combinations.

Specifically, in Model GA, the production subsidy $t_1$ and the platform enterprise operation cost subsidy $t_3$ directly impact agricultural production and platform operations, respectively. The production subsidy $t_1$ substantially increases agricultural product output, while $t_3$ alleviates operational pressures on platform enterprise, indirectly enhancing supply chain efficiency and aligning market supply with demand. Conversely, while the blockchain subsidy $t_4$ in Model GB improves long-term outcomes by enhancing supply chain transparency and collaboration efficiency, its high rigid costs constrain short-term resource flexibility. This limitation reduces the immediate production benefits for the ARAD. Furthermore, to sustain supply chain operations, Model GB compensates for lower wholesale prices through higher retail prices, further diminishing overall supply chain benefits.

Although Model GB attempts to strengthen support for the ARAD by assigning a higher weight ${\theta }^{{GB}^{*}}$, the direct and flexible resource allocation strategy in Model GA ensures that the utility function of the superior department achieves superior overall performance compared to Model GB.

In summary, incorporating the performance indicators of subordinate departments significantly alters the evaluation framework employed by the superior department to assess the effectiveness of subsidy policies. In the scenario where the performance indicators of subordinate departments are not considered, the utility function of the superior department focuses solely on the direct economic benefits derived from resource allocation. As a result, model performance is predominantly influenced by parameters such as the subsidy rate $t_1$ and the total budget L, which explains the steep slope of the dividing line observed in the upper part of Figure 10. However, when the performance indicators of subordinate departments are introduced, the superior department’s evaluation expands to include not only the direct returns of resource allocation but also the specific performance impacts on the ARAD and the DRC. This shift in evaluation methodology gives Model GA a clear and consistent advantage, as reflected in the lower part of the figure. It should be noted that, beyond the parameters analyzed in Figure 10, additional simulations were conducted to examine the interactions among $\alpha$, $p_0$, and other key parameters. The results consistently demonstrated that Model GA maintains a distinct advantage. Therefore, the corresponding images for this analysis are not included here.

7. Discussion

In this section, the practical implications of the theoretical findings are discussed by connecting the model’s results to observed phenomena and existing literature, thereby providing potential explanations for real-world policy challenges.

A key finding from the model is that a decline in overall social welfare can be caused by uncoordinated subsidy programs driven by conflicting departmental objectives, even when each department successfully meets its own performance targets. This theoretical outcome offers a compelling explanation for the widely reported issue of policy neutralization in practice. For instance, there have been documented cases where agricultural production subsidies (an ARAD priority) were rendered less effective by concurrent land-use planning or industrial development policies (a DRC priority) that incentivized the conversion of farmland to other uses [4]. The proposed framework suggests that such suboptimal outcomes are not necessarily the result of a single flawed policy but rather are a predictable consequence of a fragmented governance structure in which departmental goals are not aligned with overarching social welfare. Furthermore, it is demonstrated by the model that these conflicts can be mitigated and the system steered toward a more desirable state by a higher-level coordinating authority through the strategic allocation of budgets.

Furthermore, the growing body of literature on technology adoption in agricultural supply chains is extended by this research. Prior studies, such as that of Cao et al. [61], have established that the value of blockchain-based platforms is contingent on their ability to mitigate specific operational risks (e.g., financing and counterparty risks) and bolster consumer trust. While these studies establish the conditions under which the technology is beneficial—often noting that its value is contingent on factors such as the business environment’s credibility and operational costs—our work introduces a critical public policy dimension. Specifically, it is shown that even when a technology like blockchain is potentially beneficial, its successful implementation via government support is heavily dependent on the internal coordination among government departments. This dependency is underscored by the superior performance of the production and platform operation subsidy combination (Model GA), which highlights a crucial policy trade-off: balancing long-term technological upgrades with robust support for core production activities is a complex task profoundly shaped by the government’s internal governance structure.

To consolidate the multifaceted results from the preceding analysis, the key findings from our policy comparisons are summarized in

Table 4. Summary of Key Findings from Policy Comparisons.

Policy Comparison/Topic	Key Finding/Insight	Primary Driver/Condition
ARAD Subsidies (Production vs. Cold-chain)	The production subsidy (AA) is more effective for social welfare; firm profitability is contingent on the cold-chain subsidy rate ($t_2$).	Greater effectiveness of direct output support for social welfare. High subsidy rates ($t_2$) make the cold-chain option more profitable for the platform. (See Proposition 1)
DRC Subsidies (Platform Operation vs. Blockchain)	The blockchain subsidy (FB) is superior for welfare and profits at high subsidy rates ($t_4$); the platform operation subsidy (FA) is preferable only when $t_4$ is low.	Systemic benefits from blockchain investment (e.g., transparency, efficiency) are greater than benefits from simple operational cost reductions. (See Proposition 2)
Interdepartmental Coordination (GA vs. GB)	The Production + Platform Operation subsidy combination (GA) generates consistently higher social welfare than the Production + Blockchain combination (GB).	High fixed costs and inflexibility of blockchain investment can “crowd out” resources, leading to lower efficiency than the direct and flexible subsidies in the GA model. (See Section 5)
Role of Departmental Performance Indicators	The superiority of the GA subsidy combination is reinforced when departmental performance indicators are explicitly incorporated into the analysis.	Inclusion of subordinate performance indicators aligns the higher-level department’s utility more closely with overall supply chain health, thereby favoring the balanced GA model. (See Section 6.4)

.

8. Concluding Remarks

8.1. Conclusions

This paper investigates an agricultural supply chain model comprising platform enterprise, agricultural product supplier, and government departments, including the ARAD, the DRC, and higher-level department. Drawing on various subsidy policies currently implemented in China, the study examines four distinct subsidy policies while incorporating market demand sensitivity to cold-chain logistics services, blockchain-enabled product recalls for food safety, performance indicators for the two government departments, government subsidy budget constraints, and the higher-level authority’s weight preferences for the two peer departments. This research analyzes the effects of these four subsidy policies on the agricultural supply chain and further explores the two most representative subsidy combinations. It evaluates their impacts on the agricultural supply chain and investigates how the higher-level department allocates and coordinates subsidy amounts between the two peer departments. The main conclusions of this study are as follows:

(1) Government subsidies exert substantial and multi-faceted effects on the agricultural supply chain, particularly in enhancing key performance indicators. Firstly, subsidies provided by the ARAD based on agricultural product output significantly reduce production costs for supplier. This reduction promotes an increase in cultivated area and production volume, effectively boosting agricultural output. Such direct output subsidies alleviate the economic burden on supplier, incentivizing them to expand production and thereby driving overall supply chain efficiency and social welfare improvements. Secondly, subsidies for cold-chain logistics facility construction, also provided by the ARAD, enhance transportation efficiency and market demand stability within the supply chain. These cold-chain subsidies indirectly promote agricultural product output and supply chain efficiency by optimizing logistics operations, further contributing to agricultural output growth. Meanwhile, subsidies provided by the DRC based on platform enterprise’s operating costs and blockchain application costs optimize platform enterprise’s operational decisions, enhance supply chain transparency and collaboration efficiency, increase the profits of both platform enterprise and supplier, and improve the performance indicator of market price stability.

(2) The analysis of performance indicators reveals that different subsidy policies have distinct and significant impacts on the agricultural supply chain’s key performance metrics—agricultural product output growth and market price stability. Output subsidies are highly effective in directly increasing agricultural product output, while cold-chain logistics subsidies play a crucial role in enhancing supply chain efficiency and stabilizing market demand. On the other hand, technical subsidies, such as those supporting blockchain applications, indirectly promote market demand and overall supply chain benefits by improving supply chain transparency and building consumer trust.

(3) Dual-department subsidies offer a more balanced and efficient optimization of the agricultural supply chain by coordinating resource allocation between the ARAD and the DRC. The combination of output subsidies and operating cost subsidies demonstrates significant advantages in increasing agricultural product output and supply chain efficiency, leading to maximized social welfare. Although the combination of output subsidies and blockchain technology subsidies has the potential to enhance supply chain transparency and collaboration efficiency, the high fixed costs of blockchain technology constrain flexible resource allocation. This limitation results in insufficient direct support for agricultural product output and ultimately leads to lower social welfare compared to the former combination. Notably, in the extended analysis of Models GA and GB, when the higher-level department incorporates the performance indicators of subordinate departments into its utility function, the combination of output subsidies and platform enterprise operating cost subsidies achieves higher social welfare. This combination enhances agricultural product output and supply chain efficiency through more effective resource allocation, while the combination of output subsidies and blockchain-related cost subsidies faces certain limitations in improving social welfare due to the rigid cost structure of blockchain technology.

8.2. Management Implications

This study provides valuable insights for optimizing the management of agricultural supply chain through a thorough analysis of the roles and interactions of various subsidy policies. The following are the key contributions and implications of this research for agricultural supply chain management:

(1) Synergistic effects of subsidy policies in agricultural supply chain: this research demonstrates how different types of subsidies—such as production subsidies, cold-chain logistics subsidies, and blockchain technology subsidies—interact to influence the overall efficiency of agricultural supply chain. Specifically, combining production subsidies with platform operational cost subsidies can simultaneously enhance agricultural output and supply chain efficiency, maximizing social welfare. These findings provide policymakers with a theoretical foundation for considering the synergistic effects of various subsidies when designing policies, ensuring more efficient resource allocation.

(2) Impact of subsidy policy interactions on supply chain efficiency: through sensitivity analysis of subsidy combinations, this research uncovers the complex interactions between different subsidy policies and their long-term effects on supply chain efficiency. For instance, when blockchain technology subsidies are higher, both platform enterprises and agricultural suppliers experience increased profits, and market price stability is improved. However, excessively high blockchain subsidies may restrict flexible resource allocation, affecting direct support for agricultural production. This highlights the need for policymakers to consider both long- and short-term effects when configuring subsidy policies, ensuring that they meet the specific demands of the supply chain.

(3) Dynamic resource allocation: dual-department subsidies, coordinating resources between the ARAD and DRC, promote balanced and efficient optimization. Combining output subsidies with operational cost subsidies enhances agricultural output and supply chain efficiency. While blockchain-related subsidies boost transparency and collaboration, their high fixed costs constrain flexibility and direct agricultural support. Managers should dynamically adjust subsidy allocations based on performance to maximize policy impact.

(4) Contributions to the long-term development of agricultural supply chain: Through the analysis of subsidy policy interactions and impact evaluations, this study provides actionable policy recommendations that not only focus on improving short-term production outcomes but also ensure the long-term stability and efficiency of the agricultural supply chain. Notably, subsidies for technology (such as blockchain) enhance transparency, information flow, market responsiveness, and supply chain resilience. By promoting technological progress, this research lays a solid foundation for the long-term innovation and growth of the agricultural sector, ensuring that the supply chain can adapt to future challenges and opportunities.

8.3. Limitations and Future Research

While this study provides a novel framework for analyzing interdepartmental policy coordination, it is acknowledged that several limitations exist, which in turn present opportunities for future research.

First, the analysis is predicated on a game-theoretic model. Although the model’s assumptions and structure are grounded in real-world policy contexts, its quantitative predictions are not empirically validated. This limitation stems from the significant challenges associated with accessing sensitive firm-level and department-level decision-making data, as attempts to obtain such information proved unsuccessful due to confidentiality policies. Consequently, the numerical simulations presented herein serve primarily to illustrate the model’s mechanics and sensitivities, rather than to validate it against a specific case. A significant avenue for future research, therefore, would be to calibrate the model with real-world data from a particular agricultural sector or region, should such data become accessible. Furthermore, econometric analysis could be employed to empirically test the key relationships and trade-offs proposed by the model.

Second, to ensure analytical tractability, certain aspects of the supply chain were simplified. For example, the model considers a single supplier and a single platform. Future research could extend the model to incorporate competition at both the supplier and platform levels, enabling an exploration of how market structure influences the effectiveness of different subsidy combinations.

Finally, in the current model, subsidy rates are treated as exogenous parameters in some scenarios. An interesting extension would be to endogenize these rates as decision variables for the government departments, which would allow for a deeper analysis of optimal subsidy design under budgetary and political constraints.