Dynamic Reward–Punishment Mechanisms Driving Agricultural Systems Toward Sustainability in China

Abstract

Agricultural systems are complex social–ecological systems shaped by interactions among diverse stakeholders including governments, enterprises, farmers, consumers, and financial institutions. To examine policy-driven sustainability transitions, this study focuses on three principal actors—government regulatory agencies, agricultural enterprises, and farmers—whose strategic interactions critically determine transition outcomes. The aim is to drive agricultural systems toward sustainability in China. This study develops a three-party evolutionary game model involving the government, enterprises, and farmers to explore how policy-driven incentives influence sustainable development practices. The model incorporates both static and dynamic reward–punishment mechanisms, calibrated with empirical data, to examine behavioral dynamics across stakeholders. The results indicate that fluctuations in enterprise and government engagement contribute to instability in agricultural sustainability transitions. While static reward mechanisms mitigate peak fluctuations, they are insufficient to fully stabilize enterprise commitment, with actors oscillating between sustainable and conventional agricultural practices. Linear dynamic reward mechanisms offer partial stabilization but lack the capacity to maintain long-run Nash equilibrium. In contrast, nonlinear dynamic mechanisms effectively align stakeholder incentives, fostering a stable and enduring shift toward sustainable agricultural systems. This study underscores the importance of tailored dynamic strategies to build resilient agricultural systems with integrated sustainability objectives.

1. Introduction

In recent years, research on agricultural system transformation has garnered increasing attention and become a central topic across environmental science, urban planning, and agricultural development. Global agricultural systems now face unprecedented sustainability challenges that encompass not only ecological issues such as ecosystem services, carbon emissions and sequestration, and biodiversity loss but also economic policies, social structures, and human behaviors [1,2,3]. Agricultural system transitions across different regions reflect diverse national strategies for responding to environmental change, socio-economic development, and sustainability imperatives. Amid growing concern over the sustainability of agricultural practices, achieving sustainable agricultural development remains a critical yet unresolved challenge, prompting both consensus and ongoing scholarly debate. As nations pursue sustainable development goals, accelerating the transition of agricultural systems toward sustainable models has become a pressing global concern. This challenge stems from the intricate interplay among government policies, enterprise strategies, and farmer participation, each significantly influencing the outcomes of sustainable agricultural initiatives [4].

Addressing these global challenges necessitates the development of systematic solutions and the coordination of stakeholder relationships. The strategic decisions and behavioral evolution of the three principal actors—governments, enterprises, and farmers—are deeply interdependent, jointly shaping the path toward sustainable agricultural systems. At the micro-dynamic level, the strategic behavior of each stakeholder influences the payoffs and decisions of others, framing sustainable agricultural development as a multi-agent evolutionary game system seeking stable equilibrium [5,6]. Agricultural enterprises, particularly innovative organizational forms such as rural cooperatives, serve as vital intermediaries linking policy design to field-level practice [7]. By offering technical support, enhancing market information transparency, and conducting quality assessments of sustainable products, these entities reduce information asymmetries and lower governmental regulatory costs [8,9]. In this way, agricultural enterprises play a bridging role in aligning government policy with farmer behavior, advancing the transition from traditional to modern sustainable agriculture through technological innovation, market incentives, and service system development.

Nevertheless, agricultural enterprises currently face a critical issue: unstable participation in the agricultural sustainability transition. Economically, the high costs of environmental protection deter enterprises from adopting or promoting sustainable practices. Although farmers may produce higher-quality goods under sustainable models, insufficient price premiums hinder the recovery of added costs. This misalignment weakens coordinated action among stakeholders [10,11]. Enterprise instability is evident in inconsistent commitments and the lack of long-term investment in sustainable agricultural strategies. The government plays a pivotal role in regulating sustainable agricultural production through penalties and subsidies. However, the decentralized nature of the farming population complicates direct supervision and increases enforcement costs, thereby reducing local governments’ regulatory incentives. Consequently, higher-level governments must provide supplementary incentives and mobilize social organizations to participate [12,13]. This instability not only impedes enterprises’ sustainability transition efforts but also undermines the broader transformation of agricultural systems, diminishing policy effectiveness and weakening farmer engagement.

The severity of enterprise instability is underscored by its cascading effects on overall agricultural system transitions. Fluctuations in enterprise and government participation contribute to broader instability in agricultural sustainability transformations. In China, advancing a comprehensive sustainable agricultural transition is not only a foundational goal of modern agricultural development but also a strategic priority in building a “Beautiful China.” However, the sector faces numerous constraints, particularly high regulatory costs, which perpetuate unsustainable agricultural practices in certain regions. As primary system operators, farmers are ultimately responsible for implementing sustainable agricultural changes. Their decisions are shaped by both economic factors such as input costs and product pricing and social influences, including policy signals and intermediary support systems [14,15,16]. Globally, sustainable practices such as organic fertilization, crop rotation, and conservation tillage have been shown to enhance resilience, ecosystem services, and food security [17,18,19]. Recent studies have also emphasized the role of public subsidies, circular economy integration, green technologies, and digital innovations in reducing environmental impacts and improving agricultural efficiency [20,21]. Furthermore, biodiversity conservation, enhanced ecosystem services, and supportive rural development policies remain central to achieving socio-economic and ecological sustainability in agricultural systems [22,23,24,25].

Given the pivotal role of unstable enterprise participation in hindering sustainable agricultural system transformation, it is of both theoretical and practical importance to investigate its underlying mechanisms and potential solutions. In the current agricultural sustainability literature, several core challenges remain unresolved: (1) divergent agricultural practices result in varying impacts on ecosystem services such as carbon sequestration, biodiversity, and water regulation; (2) scholars have explored various drivers of agricultural system change, including natural conditions, economic development, population growth, and policy shifts [26,27]; (3) the assessment of the environmental consequences of agricultural transformation has increasingly employed ecological indices and remote sensing technologies [28,29]; and (4) sustainable agricultural management and policy formulation require integrative strategies encompassing legal, managerial, and social mobilization frameworks [30,31]. Despite growing scholarly attention, dedicated research on the specific issue of unstable enterprise participation remains limited. Moreover, studies on the relationship between agricultural system change and ecosystem services offer mixed conclusions. For instance, Shi et al. observed that agricultural intensification from 1990 to 2020 in the Yellow River’s middle reaches led to reduced carbon storage [32]. Similarly, Hua et al. highlighted the significant impact of agricultural intensity on carbon dynamics [33]. Li et al. emphasized ecological benefits from sustainable agricultural practices [34], while Yu et al. found that increases in intensive cultivation reduced per capita production and posed risks to food security [27]. These conflicting findings underscore ongoing debate about the sustainability and long-term impact of agricultural system change.

Current research predominantly focuses on macro-level drivers such as population growth, economic development, and policy direction while lacking deep insight into the micro-level dynamics among stakeholders. For example, Yu et al. identified population growth as a primary driver of agricultural system change in Ethiopia [27]. Li et al. examined agricultural intensification impacts in the Manas River Basin, attributing changes to human activity and climate change [34]. Gurgel et al. demonstrated how national economic and policy contexts shape agricultural transitions in the United States [30], and Wang et al. underscored the role of economic incentives in agricultural decisions related to sustainable practices [35]. These findings collectively reveal the complexity and spatial heterogeneity of agricultural system drivers [26,36]. However, a systematic analysis of unstable enterprise participation—especially from a dynamic modeling perspective involving trilateral interactions among government, enterprises, and farmers—remains insufficient. While recent research has incorporated advanced methods such as remote sensing, ecological modeling, and data fusion [37], substantial variation exists in model applicability and accuracy [1]. Other studies such as those by Shi and Wei [9] and Cai et al. [38] emphasize model limitations under specific ecological contexts. Notably, many current studies focus on static analyses and lack a nuanced understanding of dynamic behavioral processes, particularly how different incentive and penalty designs influence firms’ long-term participation.

In the realm of sustainable agricultural management and policy design, scholars widely agree on the necessity of basing decisions on scientific evidence. Haque et al. call for urgent policy responses to mitigate agricultural intensification’s ecological effects [39]. Pereira et al. recommend balancing ecological and socio-economic priorities in agricultural policy [28]. Wang et al. advocate for optimizing agricultural system structure [40], while Liu et al. emphasize the multifunctionality and economic logic of agricultural systems [41]. Although these views reflect consensus, tensions in policy implementation persist [42,43]. Future research must prioritize the dynamics of policy execution, enhance regional flexibility, and foster interdisciplinary integration across social and natural sciences [44,45]. Embracing technological advancements for real-time assessment, coupled with increased public participation, can strengthen cooperation among governments, research institutions, and civil society [46,47,48].

The EU Common Agricultural Policy. Core CAP instruments include the following: Direct income support conditioned on compliance with environmental, animal welfare, and food safety standards (“conditionality”). Eco-schemes and agri-environmental measures that pay farmers to adopt climate- and biodiversity-friendly practices. Rural development programs supporting innovation, young farmers, and structural change in the agri-food system. While CAP aspires to align subsidies with environmental outcomes, observers report that budget allocation still favors conventional production structures and in some cases may not fully internalize climate and biodiversity costs. This leads to calls for more performance-based, adaptive incentives.

China’s rural revitalization and sustainable agriculture initiatives already involve multi-level governance (central–provincial–local) and mixed instruments (subsidies, penalties, branding/quality control, technical support). Our nonlinear dynamic reward–punishment mechanism mirrors CAP’s performance-contingent idea: higher-level authorities reward local governments for verifiable ecological outcomes, and local governments in turn calibrate both subsidies and penalties for enterprises and farmers. This creates an adaptive, feedback-based incentive chain rather than a uniform, static subsidy.

In analogy to the EU CAP’s shift toward eco-conditional payments and performance-oriented rural development tools, the nonlinear dynamic reward–punishment mechanism proposed here functions as a multi-level, outcome-contingent incentive structure, suggesting a pathway for China to design fiscally sustainable, performance-linked support for sustainable agricultural practices rather than relying solely on one-off subsidies or punitive inspections [49].

To address gaps in existing research, this study focuses on the instability of enterprise participation in China’s sustainable agricultural system transition and explores how dynamic reward–punishment mechanisms can promote long-term stability. This study constructs a three-party evolutionary game model involving governments, enterprises, and farmers, integrating static and dynamic incentive and penalty mechanisms [50]. Calibrated with empirical data, the model analyzes stakeholder behavioral dynamics and simulates the strategic interaction pathways of sustainable agricultural development based on micro-level interest structures [51]. Recent studies applying evolutionary game theory to sustainability governance demonstrate that dynamic, behavior-contingent reward–punishment schemes can outperform static, one-time subsidies or fines in achieving cooperative stability [52]. These studies show that when governments (or regulating institutions) adjust incentives in proportion to observed compliance or organizational effort, actors internalize long-term cooperative strategies that persist even when direct oversight is later reduced [53]. This aligns with our finding that nonlinear dynamic reward–punishment mechanisms yield a stable state in which enterprises continue to organize sustainable production and farmers maintain high participation, while government intervention stabilizes at a moderate, fiscally sustainable level.

This framework allows us to assess how different parameter thresholds influence equilibrium strategies. This research is organized into four sections: theoretical model development, numerical simulation analysis, a comparative evaluation of mechanism effects, and policy recommendations. The goal is to provide targeted policy insights to facilitate coordinated action in China’s agricultural sector and support a sustainable transition in agricultural systems.

This study constructs a three-party evolutionary game model linking governments, enterprises, and farmers and systematically compares static, linear dynamic, and nonlinear dynamic reward–punishment mechanisms. The goal is to identify which mechanism yields a stable cooperative equilibrium and under what parameter conditions such stability can be maintained in practice.

2. Model Assumptions and Construction

2.1. Model Assumptions

This study investigates the strategic interactions among enterprises, farmers, and government agencies using a tripartite evolutionary game model to understand how dynamic reward–punishment mechanisms drive agricultural systems toward sustainability. Specifically, the model examines the equilibrium relationships among the three actors under four distinct regulatory mechanisms: linear static reward–punishment, linear dynamic reward–punishment, nonlinear static reward–punishment, and nonlinear dynamic reward–punishment. Each stakeholder seeks to optimize their respective objectives within the context of sustainable agricultural development: enterprises aim to maximize profits while balancing sustainability investments; farmers pursue utility maximization by considering costs, sustainability benefits, and other influencing factors; and the government seeks to enhance overall social welfare by promoting agricultural system sustainability through policy instruments such as green subsidies and regulatory penalties. By integrating both static and dynamic reward–punishment mechanisms, the model captures the temporal evolution of stakeholder strategies toward sustainability, thereby allowing for the simulation of adaptive behavior in response to evolving market conditions, policy environments, and sustainability imperatives.

The government’s objective is defined as maximizing net social welfare. Social welfare includes ecological improvements and reduced pollution resulting from coordinated sustainable production; improved farmer income and rural stability arising from successful sustainable participation; and technological upgrading and quality assurance achieved through enterprise organization. From this welfare, the government subtracts its regulatory, supervision, and subsidy costs and adds any higher-level rewards for demonstrable sustainability outcomes. When the government does not promote sustainability transitions, it faces lower direct costs but also suffers from larger social losses due to environmental degradation and lost long-term sustainability benefits.

Assumption 1. 

We assume that the government (G), agricultural enterprises (E), and farmers (F) are rational agents operating under bounded rationality and limited information (hereinafter referred to as the government, enterprises, and farmers, respectively). These differential cost structures reflect documented patterns in China’s environmental governance: active promotion requires specialized personnel, monitoring systems, and compliance enforcement, while passive governance incurs opportunity costs and crisis response expenditures [54].

Each actor selects strategies aimed at maximizing its own utility within the framework of agricultural system sustainability. Specifically, the government may choose to either promote or not promote agricultural system sustainability transitions; enterprises may choose to either organize or not organize such sustainability transitions; and farmers may choose to either participate or not participate in agricultural system sustainability transitions. The respective probabilities of strategy selection for the government, enterprises, and farmers are denoted as x, y, and z, where x, y, z ∈ [0, 1], and each is a function of time t. Governmental regulatory strategies primarily encompass economic instruments (e.g., sustainability credits, green taxation policies, and environmental subsidies), regulatory measures (e.g., sustainability mandates, green inspections, and enforcement mechanisms), and guiding actions (e.g., sustainable agriculture training programs and public promotion of green practices). Enterprise organizational strategies focus on advancing agricultural system sustainability through green technologies, establishing sustainable trading relationships with farmers, and conducting quality inspections of sustainable agricultural products. Farmer participation strategies include the reduction in pesticide and chemical fertilizer usage, adoption of sustainable agricultural technologies, and implementation of resource recycling and circular economy practices.

Assumption 2. 

The government incurs a cost Cg when actively promoting agricultural system sustainability transitions and a cost Ec when it chooses not to promote such behaviors. To incentivize participation, the government provides economic rewards to enterprises and rural households such as tax reductions, subsidies for sustainable agricultural system transitions, and preferential loans amounting to a total value of S. The allocation of these incentives is divided between enterprises and rural households in the proportions αS and (1 − α)S, respectively, where α∈ [0, 1].

If the government implements active promotion measures but the enterprise fails to organize the sustainability transition, a penalty of F is imposed on the enterprise. Additionally, the government receives a policy incentive Rg from the central government as a reward for implementing active promotion strategies for agricultural system sustainability.

Assumption 3. 

Corporate participation in sustainable agricultural system transitions influences farmers’ behavioral decisions and, to some extent, generates feedback effects on the government [55]. The additional cost borne by enterprises for adopting and implementing agricultural system sustainability practices such as technology promotion, supervision, inspection, procurement of sustainable seedlings, and technical services is denoted as Ce. The market revenue generated from sustainable practices is βRe, where β ∈ [0, 1]. When regulated by the government, enterprises receive economic incentives amounting to αS for engaging in sustainable agricultural system transitions. In seeking new cooperative farmers, enterprises incur a search cost of Cf. If an enterprise chooses not to organize sustainable agricultural system transitions, it obtains a profit of (1 − β)Re. Additionally, the financial return on investment from implementing sustainable technologies and practices is denoted as GI.

Assumption 4. 

Farmers’ participation in sustainable agricultural system transitions is influenced by, and in turn influences, both government regulatory actions and corporate organizational behavior. When farmers engage in agricultural system sustainability practices, they incur additional costs denoted by Df, while the associated benefits are represented by Rf. Under government regulation, farmers receive economic incentives totaling (1 − α)S. If farmers choose to sell their agricultural products independently, they face market search costs Ck. When opting not to participate in sustainable agricultural system transitions, farmers receive a benefit of Tf, but they are also subject to negative externalities such as environmental degradation or productivity loss quantified as L.

Assumption 5. 

The active participation of enterprises and farmers in agricultural sustainability transitions enhances the agricultural ecosystem and improves the market environment for sustainable agricultural products [56], thereby generating additional social benefits denoted by$\mathsf{\delta }$

. Joint participation contributes to improved local biodiversity, enhanced soil quality, reduced water consumption, and lower pollution levels, resulting in ecosystem benefits quantified as$\mathsf{\gamma }$

. Conversely, when the government does not promote agricultural sustainability transitions, enterprises do not organize and farmers do not participate in them [57], the agricultural ecosystem fails to improve, and each party incurs social losses represented by$P,\hspace{0.33em}T, Q$. The distribution of these losses is characterized by the proportions α, β, and γ, where α + β + γ = 1, and α, β, γ∈ [0, 1].

2.2. Model Construction

The meanings and ranges of the above parameters for the agricultural system sustainability model are shown in

Table 1. Meanings and ranges of parameters.

Symbol	Parameter	Description
G	Government	G > 0
E	Agricultural enterprises	E > 0
F	Farmers	F > 0
Cg	Government actively promotes agricultural system sustainability transitions and pays the cost	Cg > 0
Ec	Costs of government not promoting agricultural system sustainability practices	Ec > 0
S	Costs of economic incentives to governments for firms and farmers to actively promote agricultural system sustainability transitions	S > 0
Rg	Government policy incentives from the central government for proactive promotional behavior	Rg > 0
Ce	Costs associated with the implementation of sustainable technologies	Ce > 0
Cf	Search cost incurred by an enterprise in seeking new cooperative farmers	Cf > 0
Re	Enterprise agricultural system sustainability market gains	Re > 0
CI	Financial returns to firms undertaking agricultural system sustainability transitions	CI > 0
Df	Additional costs for farmers to participate in agricultural system sustainability transitions	Df > 0
Rf	Benefits derived from farmers’ participation in agricultural system sustainability transitions	Rf > 0
Ck	Market finding costs incurred by farmers selling on their own	Ck > 0
Tf	Farmers’ income when they do not participate in agricultural system sustainability transitions	Tf > 0
δ	Additional social benefits from the participation of enterprises and farmers in agricultural system sustainability transitions	δ > 0
γ	Enterprises and farmers actively participate in agricultural system sustainability transitions to obtain health benefits for the local ecosystem	γ > 0
P	Social losses from the government not promoting agricultural system sustainability transitions	P
T	Social losses from enterprises not organizing agricultural system sustainability transitions	T
Q	Social losses from farmers’ non-participation in sustainable agricultural system development	Q

, and the interrelationships among the three stakeholders are shown in Figure 1.

According to the reality and research assumptions, we can construct an evolutionary game payment matrix among automobile enterprises, consumers, and the government, as shown in

Table 2. Evolutionary game payment matrix.

Game Subject		Enterprises	Farmers
			Positive Participation z	Negative Participation 1 − z
Government	Promotion of sustainable agricultural production $x$	Organizing sustainable agricultural production $y$	$R_g-C_g-S+\delta +\gamma$ $\beta R_e-C_e+\alpha S-C_f+G_I$ $R_f-D_f+\left(1-\alpha \right)S$	$R_g-C_g-\alpha S$ $\beta R_e-C_e+\alpha S-C_f+G_I$ $T_f-C_k-L$
		Not organizing sustainable agricultural production $1-y$	$R_g-C_g-\left(1-\alpha \right)S+F$ $\left(1-\beta \right)R_e-F$ $R_f-D_f+\left(1-\alpha \right)S$	$R_g-C_g+F$ $\left(1-\beta \right)R_e-F$ $T_f-C_k-L$
	Failure to promote sustainable agricultural production $1-x$	Organizing sustainable agricultural production $y$	$\delta +\gamma {-E}_c$ $\beta R_e-C_e-C_f+G_I$ $R_f-D_f$	${-E}_c$ $\beta R_e-C_e-C_f+G_I$ $T_f-C_k-L$
		Not organizing sustainable agricultural production $1-y$	${-E}_c$ $\left(1-\beta \right)R_e$ $R_f-D_f$	${-E}_c-P$ $\left(1-\beta \right)R_e-T$ $T_f-C_k-L-Q$

.

3. Evolutionary Game Analysis

3.1. Stability Analysis of Government

Based on the payoff matrix in Table 2, the expected return for the government when adopting a strategy to promote agricultural sustainability transitions, denoted ${\mathrm{E}}_{\mathrm{A}1}$, is calculated as follows:

$$E_{A1}=yz\left(R_g-C_g-S+\delta +\gamma \right)+y\left(1-z\right)\left(R_g-C_g-\alpha S\right)+\left(1-y\right)z\left(R_g-C_g-\right.\left.\left(1-\alpha \right)S+F\right)+\left(1-y\right)\left(1-z\right)\left(R_g-C_g+F\right)$$

(1)

The expected return of the government not promoting agricultural sustainability transition strategies ${\mathrm{E}}_{\mathrm{A}2}$ is

$$\begin{gathered} E_{A2}=yz\left(\delta +\gamma {-E}_c\right)+y\left(1-z\right)\left({-E}_c\right)+\left(1-y\right)z\left({-E}_c\right) \\ +\left(1-y\right)\left(1-z\right)({-E}_c-P) \end{gathered}$$

(2)

The average return of the government adopting a mixed strategy $\overline{{\mathrm{E}}_{\mathrm{A}}}$ is expressed as

$$\overline{E_A}={xE}_{A1}+\left(1-x\right)E_{A2}$$

(3)

Therefore, the replicator dynamic equation for the government’s choice to promote agricultural sustainability transitions is

$$\begin{gathered} F\left(x\right)={\displaystyle \frac{dx}{dt}}=x\left(E_{A1}-\overline{E_A}\right) \\ =x\left(1-x\right)\left[Pyz-\left(\alpha S+F+P\right)y+\left(\alpha S-S-P\right)z+R_g+F+E_c-C_g+P\right] \end{gathered}$$

(4)

By taking the derivative of F(x) with respect to x, we obtain the following:

$$G\left(y,z\right)=[Pyz-\left(\alpha S+F+P\right)y+\left(\alpha S-S-P\right)z+R_g+F+E_c-C_g+P]$$

(5)

$${\displaystyle \frac{d\left(F\left(x\right)\right)}{dx}}=\left(1-2x\right)[Pyz-\left(\alpha S+F+P\right)y+\left(\alpha S-S-P\right)z+R_g+F+E_c-\left.C_g+P\right]$$

(6)

From G(y, z) = 0, it can be obtained that

$$\mathrm{W}\mathrm{h}\mathrm{e}\mathrm{n} y={\displaystyle \frac{\left(\alpha S-S-P\right)z+R_g+F+E_c-C_g+P}{-Pz+\alpha S+F+P}}, {\displaystyle \frac{ d\left(F\left(x\right)\right)}{dx}}\equiv 0;$$

$$\mathrm{W}\mathrm{h}\mathrm{e}\mathrm{n} y\ne {\displaystyle \frac{\left(\alpha S-S-P\right)z+R_g+F+E_c-C_g+P}{-Pz+\alpha S+F+P}}$$

Let $F\left(x\right)=0$; then $x=0$ and $x=1$ are two equilibrium points, thus requiring a classification discussion.

$${\displaystyle \frac{d\left(G\left(y,z\right)\right)}{dy}}=Pz-\left(\alpha S+F+P\right)<0$$

Therefore, $G\left(y,z\right)$ is a subtraction function with respect to $y$.

$$\mathrm{W}\mathrm{h}\mathrm{e}\mathrm{n} y>{\displaystyle \frac{\left(\alpha S-S-P\right)z+R_g+F+E_c-C_g+P}{-Pz+\alpha S+F+P}}$$

$G\left(y,z\right)<0$. Thus, at this point, the government’s choice not to promote agricultural sustainability leads to

$${\displaystyle \frac{d\left(F\left(x\right)\right)}{dx}}{|}_{x=0}<0; {\displaystyle \frac{d\left(F\left(x\right)\right)}{dx}}{|}_{\mathit{x}=1}>0$$

which shows that agricultural sustainability transitions are evolutionarily stable strategies:

$$\mathrm{W}\mathrm{h}\mathrm{e}\mathrm{n} y<{\displaystyle \frac{\left(\alpha S-S-P\right)z+R_g+F+E_c-C_g+P}{-Pz+\alpha S+F+P}}$$

$G\left(y,z\right)>0$. Thus, we have

$${\displaystyle \frac{d\left(F\left(x\right)\right)}{dx}}{|}_{x=0}>0; {\displaystyle \frac{d\left(F\left(x\right)\right)}{dx}}{|}_{\mathit{x}=1}<0$$

and at this point, the government’s choice to promote agricultural sustainability transitions is an evolutionary stable strategy.

3.2. Stability Analysis of Corporate Strategy

Similarly, the expected return for a corporation organizing agricultural sustainability transitions $E_{B1}$ is the expected return for a corporation not organizing agricultural sustainability transitions.

$$\begin{gathered} E_{B1}=xz\left(\beta R_e-C_e+\alpha S-C_f+G_I\right)+x\left(1-z\right)\left(\beta R_e-C_e+\alpha S-C_f+G_I\right) \\ +\left(1-x\right)z\left(\beta R_e-C_e-C_f+G_I\right)+\left(1-x\right)\left(1-z\right)\left(\beta R_e-C_e-C_f+G_I\right) \end{gathered}$$

(7)

and transition $E_{B2}$ is

$$\begin{gathered} E_{B2}=xz\left(\left(1-\beta \right)R_e-F\right)+x\left(1-z\right)\left(\left(1-\beta \right)R_e-F\right) \\ +\left(1-x\right)z\left(\left(1-\beta \right)R_e\right)+\left(1-x\right)\left(1-z\right)\left(\left(1-\beta \right)R_e-T\right) \end{gathered}$$

(8)

The average return for a corporation adopting a mixed strategy is $\overline{E_B}$, expressed as

$$\overline{E_B}=y{E}_{B1}+\left(1-y\right)E_{B2}$$

(9)

Therefore, the replicator dynamic equation for a corporation organizing agricultural sustainability transitions is

$$\begin{gathered} F\left(y\right)={\displaystyle \frac{dy}{dt}}=y\left(E_{B1}-\overline{E_B}\right)=y\left(1-y\right) \\ [Txz+\left(\alpha S+F-T\right)x-Tz+2\beta R_e-C_e-C_f+G_I-R_e+T] \end{gathered}$$

(10)

The derivation of $F\left(y\right)$ with respect to $y$ yields

$${\displaystyle \frac{d\left(F\left(y\right)\right)}{dy}}=\left(1-2y\right)[Txz+\left(\alpha S+F-T\right)x-Tz+2\beta R_e-C_e-C_f+G_I-R_e+T]$$

(11)

$$G(x,z)=Txz+\left(\alpha S+F-T\right)x-Tz+2\beta R_e-C_e-C_f+G_I-R_e+T$$

(12)

From $G\left(x,z\right)=0$, we obtain the following:

$$\mathrm{W}\mathrm{h}\mathrm{e}\mathrm{n} x={\displaystyle \frac{Tz-2\beta R_e+C_e+C_f-G_I+R_e-T}{\alpha S+F-T+Tz}}, {\displaystyle \frac{d\left(F\left(y\right)\right)}{dy}}\equiv 0;$$

$$\mathrm{W}\mathrm{h}\mathrm{e}\mathrm{n} x\ne {\displaystyle \frac{Tz-2\beta R_e+C_e+C_f-G_I+R_e-T}{\alpha S+F-T+Tz}} ,$$

Let $F\left(y\right)=0$; then $y=0$ and $y=1$ are two equilibrium points, thus requiring a classification discussion.

$${\displaystyle \frac{dG\left(x,z\right)}{dx}}=\alpha S+F-T+Tz>0$$

Therefore, $\mathrm{G}\left(x,z\right)$ is an increasing function of $x$.

$$\mathrm{W}\mathrm{h}\mathrm{e}\mathrm{n} x>{\displaystyle \frac{Tz-2\beta R_e+C_e+C_f-G_l+R_e-T}{\alpha S+F-T+Tz}}$$

$G\left(x,z\right)>0$. Thus, we have

$${\displaystyle \frac{d\left(F\left(y\right)\right)}{dy}}{|}_{y=0}>0; {\displaystyle \frac{d\left(F\left(y\right)\right)}{dy}}{|}_{\mathit{y}=1}<0$$

At this point, the government’s choice not to promote agricultural sustainability transitions is an evolutionary stable strategy.

$$\mathrm{W}\mathrm{h}\mathrm{e}\mathrm{n} x<{\displaystyle \frac{Tz-2\beta R_e+C_e+C_f-G_l+R_e-T}{\alpha S+F-T+Tz}}$$

$G\left(x,z\right)<0$; therefore we have

$${\left.{\displaystyle \frac{d\left(F\left(y\right)\right)}{dy}}\right|}_{y=0}<0,{\left. {\displaystyle \frac{d\left(F\left(y\right)\right)}{dy}}\right|}_{y=1}>0$$

The choice of enterprises not to organize agricultural sustainability transitions is a stable strategy.

3.3. Stability Analysis of Farmer Strategy

The expected return for farmers choosing to participate in sustainable agricultural production strategy $E_{C1}$ is

$$\begin{gathered} E_{C1}=xy\left(R_f-D_f+\left(1-\alpha \right)S\right)+x\left(1-y\right)\left(R_f-D_f+\left(1-\alpha \right)S\right) \\ +\left(1-x\right)y\left(R_f-\right.\left.D_f\right)+\left(1-x\right)\left(1-y\right)\left(R_f-D_f\right) \end{gathered}$$

(13)

The expected return for farmers adopting a non-participation strategy in sustainable agricultural production $E_{C2}$ is

$$\begin{gathered} E_{C2}=xy\left(T_f-C_k-L\right)+x\left(1-y\right)\left(T_f-C_k-L\right)+\left(1-x\right)y\left(T_f-C_k-L\right) \\ +(1-x)\left(1-y\right)\left(T_f-C_k-L-Q\right) \end{gathered}$$

(14)

The average return of the government adopting a mixed strategy $\overline{{\mathrm{E}}_{\mathrm{C}}}$ is expressed as

$$\overline{E_C}=z{E}_{C1}+\left(1-z\right)E_{C2}$$

(15)

From this, the replicator dynamic equation for farmers choosing to participate in sustainable agricultural production is

$$\begin{gathered} F\left(z\right)={\displaystyle \frac{dz}{dt}}=z\left(E_{C1}-\overline{E_C}\right) \\ =z\left(1-z\right)\left[Qxy+\left(S-\alpha S-Q\right)x-Qy+R_f-D_f+L+C_k-T_f+Q\right] \end{gathered}$$

(16)

By taking the derivative of $F\left(z\right)$ with respect to $z$, we obtain the following:

$${\displaystyle \frac{d\left(F\left(z\right)\right)}{dz}}=\left(1-2z\right)\left[Qxy+\left(S-\alpha S-Q\right)x-Qy+R_f-D_f+L+C_k-T_f+Q\right]$$

(17)

$$G\left(x,y\right)=Qxy+\left(S-\alpha S-Q\right)x-Qy+R_f-D_f+L+C_k-T_f+Q$$

(18)

From $G\left(x,y\right)=0$, it can be obtained that

$$\mathrm{W}\mathrm{h}\mathrm{e}\mathrm{n} x={\displaystyle \frac{Qy-R_f+D_f-L-C_k+T_f-Q}{Qy+\left(S-\alpha S-Q\right)}},{\displaystyle \frac{d\left(F\left(z\right)\right)}{dz}}\equiv 0;$$

$$\mathrm{W}\mathrm{h}\mathrm{e}\mathrm{n} x\ne {\displaystyle \frac{Qy-R_f+D_f-L-C_k+T_f-Q}{Qy+\left(S-\alpha S-Q\right)}},$$

Let $F\left(z\right)=0$; then $z=0$ and $z=1$ are two equilibrium points, thus requiring a classification discussion.

$${\displaystyle \frac{dG\left(x,y\right)}{dx}}=Qy+\left(S-\alpha S-Q\right)>0$$

Therefore, G(x, y) is an increasing function regarding x.

$$\mathrm{W}\mathrm{h}\mathrm{e}\mathrm{n} x>{\displaystyle \frac{Qy-R_f+D_f-L-C_k+T_f-Q}{Qy+\left(S-\alpha S-Q\right)}}$$

$G(x,y)>0$ Thus, we have

$${\displaystyle \frac{d\left(F\left(z\right)\right)}{dz}}{|}_{z=1}<0; {\displaystyle \frac{d\left(F\left(z\right)\right)}{dz}}{|}_{z=0}>0$$

and at this point, the farmer’s choice to participate in agricultural sustainability transitions is a stable strategy:

$$\mathrm{W}\mathrm{h}\mathrm{e}\mathrm{n} x<{\displaystyle \frac{Qy-R_f+D_f-L-C_k+T_f-Q}{Qy+\left(S-\alpha S-Q\right)}}$$

$G\left(x,y\right)<0$. Thus, we have

$${\displaystyle \frac{d\left(F\left(z\right)\right)}{dz}}{|}_{z=1}>0; {\displaystyle \frac{d\left(F\left(z\right)\right)}{dz}}{|}_{z=0}<0$$

and at this point, the farmer’s choice not to participate in agricultural sustainability transitions is a stable strategy.

3.4. Solutions for System Stability

Formulas (4), (10), and (16) constitute the replication of the dynamic system of equations shown in Equation (19).

$$\left\{\begin{array}{c}F\left(x\right)=x\left(1-x\right)\left[Pyz-\left(\alpha S+F+P\right)y+\left(\alpha S-S-P\right)z+R_g+F+E_c-C_g+P\right]\\ F\left(y\right)=y\left(1-y\right)\left[Txz+\left(\alpha S+F-T\right)x-Tz+2\beta R_e-C_e-C_f+G_I-R_e+T\right]\\ F\left(z\right)=z\left(1-z\right)\left[Qxy+\left(S-\alpha S-Q\right)x-Qy+R_f-D_f+L+C_k-T_f+Q\right]\end{array}\right.$$

(19)

Reducing this system of equations to 0 yields eight equilibrium points in the replicated dynamic system, i.e., $E_1\left(0,0,0\right), E_2\left(0,1,0\right)$, $E_3\left(0,0,1\right), E_4\left(0,1,1\right), E_5\left(1,0,0\right), E_6\left(1,1,0\right), E_7\left(1,0,1\right), E_8\left(1,1,1\right)$, where the stability of the mixed equilibrium points of the replicated dynamic system is not taken into account, since the mixed equilibrium points in the asymmetric evolutionary game are bound to not be ESS. Thus, the stability of the mixed equilibrium points is not considered.

According to the Lyapunov theorem, the stability of replicated dynamic systems can be determined by the eigenvalues of the Jacobian matrix formed by the replicated dynamic equations. When the real parts of the eigenvalues of the Jacobian matrix are all negative, the equilibrium point has asymptotic stability. If at least one eigenvalue is not negative, the equilibrium point is unstable. Thus, the Jacobian is represented as $J$:

$$J=\left[\begin{array}{cc}{\displaystyle \frac{\partial F\left(x\right)}{\partial x}}& \begin{array}{cc}{\displaystyle \frac{\partial F\left(x\right)}{\partial y}}& {\displaystyle \frac{\partial F\left(x\right)}{\partial z}}\end{array}\\ \begin{array}{c}{\displaystyle \frac{\partial F\left(y\right)}{\partial x}}\\ {\displaystyle \frac{\partial F\left(z\right)}{\partial x}}\end{array}& \begin{array}{c}\begin{array}{cc}{\displaystyle \frac{\partial F\left(y\right)}{\partial y}}& {\displaystyle \frac{\partial F\left(y\right)}{\partial z}}\end{array}\\ \begin{array}{cc}{\displaystyle \frac{\partial F\left(z\right)}{\partial y}}& {\displaystyle \frac{\partial F\left(z\right)}{\partial z}}\end{array}\end{array}\end{array}\right]$$

$${\displaystyle \frac{\partial F\left(x\right)}{\partial x}}=\left(1-2x\right)[Pyz-\left(\alpha S+F+P\right)y+\left(\alpha S-S-P\right)z+R_g+F+E_c-C_g+P]$$

$${\displaystyle \frac{\partial F\left(x\right)}{\partial y}}=x\left(1-x\right)\left[Pz-\left(\alpha S+F+P\right)\right]$$

$${\displaystyle \frac{\partial F\left(x\right)}{\partial z}}=x\left(1-x\right)\left[Py+\left(\alpha S-S-P\right)\right]$$

$${\displaystyle \frac{\partial F\left(y\right)}{\partial x}}=y\left(1-y\right)\left(Tz+\left(\alpha S+F-T\right)\right)$$

$${\displaystyle \frac{\partial F\left(y\right)}{\partial y}}=\left(1-2y\right)\left[Txz+\left(\alpha S+F-T\right)x-Tz+2\beta R_e-C_e-C_f+G_I-R_e+T\right]$$

$${\displaystyle \frac{\partial F\left(y\right)}{\partial z}}=y\left(1-y\right)\left[Tx-T\right]$$

$${\displaystyle \frac{\partial F\left(z\right)}{\partial x}}=z\left(1-z\right)\left[Qy+\left(S-\alpha S-Q\right)\right]$$

$${\displaystyle \frac{\partial F\left(z\right)}{\partial y}}=z\left(1-z\right)\left[Qx-Q\right]$$

$${\displaystyle \frac{\partial F\left(x\right)}{\partial x}}=\left(1-2x\right)[Pyz-\left(\alpha S+F+P\right)y+\left(\alpha S-S-P\right)z+R_g+F+E_c-C_g+P]$$

By bringing $E_1\sim E_8$ into the Jacobian matrix, the eigenvalues of the equilibrium points are as shown in

Table 3. Eigenvalues of Jacobi matrix for each equilibrium point.

Equilibrium Point	${\mathit{\lambda }}_1$	${\mathit{\lambda }}_{\mathbf{2}}$	${\mathit{\lambda }}_{\mathbf{3}}$
$E_1$(0, 0, 0)	$R_g+F+E_c-C_g+P$	$2\beta R_e-C_e-C_f+G_I-R_e+T$	$R_f-D_f+L+C_k-T_f$ $+Q$
$E_2$(0, 1, 0)	$E_c-C_g+R_g-\alpha S$	$-2\beta R_e+C_e+C_f-G_I+R_e-T$	$R_f-D_f+L+C_k-T_f$
$E_3$(0, 0, 1)	$E_c-C_g+F+R_g-S$ $+\alpha S$	$2\beta R_e-C_e-C_f+G_I-R_e$	$-R_f+D_f-L-C_k+T_f$ $-Q$
$E_4$(0, 1, 1)	$E_c-C_g+R_g-S$	$-2\beta R_e+C_e+C_f-G_I+R_e$	$-R_f+D_f-L-C_k+T_f$
$E_5$(1, 0, 0)	$C_g-E_c-F-R_g-P$	$F-C_f-C_e+G_I-R_e+\alpha S$ $+2\beta R_e$	$C_k-D_f+L+R_f+S-$ $T_f-\alpha S$
$E_6$(1, 1, 0)	$C_g-E_c-R_g+\alpha S$	$C_e+C_f-F-G_I+R_e-\alpha S-2\beta R_e$	$C_k-D_f+L+R_f+S-T_f-\alpha S$
$E_7$(1, 0, 1)	$C_g-E_c-F-R_g+S-\alpha S$	$F-C_f-C_e+G_I-R_e+\alpha S+2\beta R_e$	$D_f-C_k-L-R_f-S+T_f+\alpha S$
$E_8$(1, 1, 1)	$C_g-E_c-R_g+S$	$C_e+C_f-F-G_I+R_e-\alpha S-2\beta R_e$	$D_f-C_k-L-R_f-S+T_f+\alpha S$

.

The interrelated parameters among stakeholders jointly determine the strategic outcomes of the system. When governmental rewards and penalties are insufficient, enterprises are more inclined to opt out of organizing sustainable agricultural production, and farmers are similarly less likely to participate in agricultural sustainability transitions, ultimately undermining the long-term sustainability of agriculture. To mitigate this risk, regulatory authorities should design rational reward–punishment mechanisms and appropriately increase incentive and penalty intensities for both enterprises and farmers to ensure improvements in the agricultural ecosystem. From a managerial perspective, achieving stable levels of enterprise organization and farmer participation in agricultural sustainability transitions is a desirable outcome. Accordingly, the following discussion focuses on system stability control, aiming to realize stable participation and organization rates among key actors. The eigenvalues of the system’s equilibrium points are determined by substituting them into the Jacobian matrix, as presented in Table 3.

4. Numerical Analysis of Evolutionary Strategy

4.1. Simulation Data

According to the Five Mechanisms for Leading Rural Revitalization through Sustainable Development, the government facilitates sustainable development through market-oriented strategies and pricing mechanisms. However, in the absence of governmental support, these market mechanisms are susceptible to failure, potentially resulting in an estimated social loss of approximately CNY 3 billion. The government-led promotion of agricultural sustainability transitions incurs expenditures in human resources, financial investment, and time, with an estimated cost of CNY 780,000. In contrast, if the government refrains from promoting the transition, the associated cost is significantly lower, at approximately CNY 110,000.

Active governmental promotion yields substantial ecological benefits, including improvements in soil quality, pollution reduction, and enhanced biodiversity. These ecosystem enhancements are valued at approximately CNY 3 billion. Additionally, social benefits arising from higher-level governmental support are benchmarked at CNY 5 billion. The promotion of agricultural sustainability transitions has also facilitated the high-quality development of the sustainable food industry, with economic incentives provided to enterprises and farmers, distributed in a 0.5 ratio based on the generated social benefits. However, if enterprises opt not to participate in agricultural sustainability transitions, governmental constraints are influenced by enterprise behavior. Drawing on literature estimates, the global cost of preventing agricultural environmental degradation ranges from USD 30 billion to USD 130 billion annually. In China, government environmental authorities estimate that the remediation of agricultural non-point source pollution requires approximately CNY 200–300 billion (USD 30–45 billion) per year. Accordingly, the economic incentive for enterprises is set at USD 220 million to reflect the scale of environmental costs that sustainable practices help avoid.

The incentive distribution parameter α represents the share of government incentives directed to enterprises relative to farmers. A baseline value of α = 0.5 is assumed to reflect the joint targeting of support to organizing enterprises and participating farmers observed in Chinese rural revitalization policy instruments, where service-oriented agribusinesses/cooperatives receive support for coordination, technology diffusion, and quality control, while farmers receive direct production subsidies or price support. This symmetric allocation also normalizes payoffs so that both enterprises and farmers receive comparable marginal policy leverage.

In the case of ecological farming households in Guangxi Province, the price of organic rice has increased by 2–3 times, with an average growth rate of 154.2%, attributed to a mature sales model developed by the Love Agriculture Association. Households adopting organic farming have experienced income increases of nearly 80%, with some even doubling their income. Consequently, the initial income for households engaged in agricultural sustainability transitions is set at USD 150,000. These households employ organic farming techniques, including the rejection of pesticides, selection of self-saved seeds, and substitution of chemical fertilizers with organic alternatives. Although such practices result in a 20–50% yield reduction, they have led to an average cost decrease of nearly 80%. Taking both yield reductions and cost savings into consideration, the initial cost for households participating in agricultural sustainability transitions is estimated at USD 310,000. Household participation is vital to the scalability of agricultural sustainability transitions; otherwise, the resulting social losses are estimated at approximately CNY 1 million. The remaining data will be normalized based on the stability results, with parameter assignments detailed in

Table 4. Parameter assignment.

Parameter	Parameter Meaning	Assigned Value
$R_g$	Government actively promotes sustainable agricultural system use transition rewards provided by higher authorities	5
$C_g$	Costs incurred by the government in actively promoting sustainable agricultural system use transition behaviors	7.8
S	Amount of economic incentives provided by the government	5.4
$\alpha$	Proportion of economic incentives obtained by enterprises	0.5
$F$	Government constraints on enterprises not promoting sustainable agricultural system transition	2.2
$R_e$	Market returns for enterprises	8
$\beta$	Proportion of returns from enterprises organizing agricultural sustainable agricultural system transition	0.5
$C_f$	Costs incurred by enterprises seeking farmer participation in agricultural sustainable agricultural system transition	3.8
$G_I$	Financial returns on investments made by enterprises in sustainable technologies and practices	2.8
$C_e$	Costs incurred by enterprises organizing sustainable agricultural system transition	4.3
$R_f$	Returns for farmers participating in sustainable agricultural system transition	1.5
$D_f$	Costs for farmers participating in sustainable agricultural system transition	3.1
$T_f$	Returns for farmers not participating in sustainable agricultural system use transition	3
$C_k$	Market seeking costs for farmers selling independently	0.6
L	Agricultural sustainability transitions losses caused by farmers not participating in sustainable agricultural system transition	2.2
$E_c$	Costs of the government not promoting sustainable agricultural system transition behaviors	1.1
$P$	Social losses of the government	3
T	Social losses of enterprises	2
$Q$	Social losses of farmers	1

.

4.2. Numerical Simulation of Three-Party Evolutionary Game

Based on the numerical cases, computational simulation experiments were conducted to analyze the behavioral dynamics of the government, enterprises, and farmers. Given that approximately 25% of enterprises currently engage in organizing agricultural sustainability transitions, the initial value for enterprises is set at 0.25. Correspondingly, the initial values for the government and farmers are set at 0.6 and 0.5, respectively. The evolutionary trajectories of these agents are illustrated in Figure 1.

As shown in Figure 1, the behaviors of the government and farmers fluctuate throughout the evolutionary process, whereas enterprises ultimately tend toward a strategy of non-participation in organizing agricultural sustainability transitions. This outcome is consistent with current trends in promoting agricultural sustainability transitions. According to agricultural price data from Beijing farmers, presented in Figure 2, the agricultural product price index exhibits volatility. This fluctuation can be partially attributed to factors such as the willingness of enterprises to organize agricultural sustainability transitions, farmers’ participation intentions, urban–rural disparities, and inflation. Notably, while the comprehensive agricultural product price index has rebounded, industrial product prices have risen more significantly (source: weibo.com). These observations further validate the model results. Given that enterprises are currently more inclined to forgo organizing agricultural sustainability transitions in pursuit of higher profits, it is essential to regulate system fluctuation and enhance stability. Therefore, the following section will examine the differentiation in China’s subsidy and penalty structures for agricultural sustainability transitions—particularly the government’s reward and punishment mechanisms targeting enterprises—to explore potential control measures for improving system stability.

4.3. Linear Reward and Punishment Machine Mechanism

4.3.1. Linear Static Rewards

Considering the impact of static reward mechanisms on the behaviors of governments, enterprises, and farmers, simulations were conducted using varying levels of government subsidies for enterprises engaged in agricultural sustainability transitions (S = 4.4, 5.4, and 6.4). The resulting evolutionary dynamics are presented in Figure 3. As illustrated, increasing subsidies for enterprises does not eliminate the fluctuation in consumer participation in agricultural sustainability transitions, nor does it stabilize government efforts in promoting these transitions. However, higher subsidy levels do reduce the amplitude of fluctuations in the strategies of both parties. This suggests that static reward mechanisms for enterprises do not constitute an effective strategy for system stability control.

An intriguing pattern emerges from Figure 3 with regard to government subsidies for enterprises undertaking agricultural sustainability transitions. When subsidy intensity is low, farmers are less inclined to participate. This reluctance can be attributed both to the insufficiency of government support and to the heterogeneity in subsidy distribution, which fosters perceptions of inequity often described as the belief that “inequality, rather than scarcity, breeds discontent.” As subsidy levels increase, the peak fluctuation in farmers’ participation choices tends to decline, indicating that while promoting agricultural sustainability transitions, the government must carefully calibrate subsidy levels and account for the perceived fairness and utility effects of subsidy heterogeneity.

In summary, linear static rewards exert a certain positive incentive by elevating the fluctuation thresholds in governmental and corporate behavior and by contributing to greater stability in farmers’ participation. Nevertheless, this mechanism does not serve as a comprehensive or effective control strategy for achieving systemic stability.

4.3.2. Linear Static Penalty

While Section 4.3.1 explores the impact of static rewards on agent behavior, this section examines the effects of linear static penalties on the behavioral dynamics of the government, enterprises, and farmers. Specifically, the government’s penalty values for enterprises failing to organize agricultural sustainability transitions are adjusted (F = 1.2, 2.2, and 3.2). The resulting evolutionary trends are presented in Figure 4.

As shown in Figure 4, under the linear static penalty mechanism, the behaviors of both farmers and the government continue to fluctuate, indicating that such a mechanism does not achieve system-wide stability control. However, in contrast to static rewards, static penalties exert a pronounced positive incentive on farmers, significantly enhancing their willingness to participate in agricultural sustainability transitions. This suggests that penalties imposed on enterprises for non-compliance indirectly deter farmers from opting out, thereby fostering broader engagement in sustainable practices.

The underlying rationale for this phenomenon may lie in the fact that penalties levied on enterprises generate benefits for the government, thereby reinforcing its commitment to actively promote agricultural sustainability transitions. This strengthened governmental resolve, in turn, positively influences farmers’ willingness to participate.

4.3.3. Linear Static Reward and Dynamic Punishment

The simulation results discussed above demonstrate that static reward and punishment mechanisms are insufficient to regulate the fluctuating behaviors of governments and farmers. Considering this, and drawing upon the findings from the existing literature, specifically the Evolutionary Game of Agriculture Enterprises’ Behavior and Government Regulation under Different Reward and Punishment Mechanisms, this study introduces a combined mechanism of linear static rewards and dynamic penalties.

The design of the linear dynamic punishment mechanism is guided by the principle of “equivalence of rights and responsibilities”. Under this framework, the more enterprises exhibit a tendency to abstain from participating in agricultural sustainability transitions, thereby contributing to sustainable agricultural system degradation and environmental pollution, the greater the penalty costs they are required to bear. This relationship is formally expressed in Equation (20).

$$\sigma =\theta \left(1-y\right)\sigma$$

(20)

Here, $\theta$ is the linear dynamic penalty coefficient, taking $\theta =10$ (satisfying $\theta \left(1-y\right)>1$). The numerical simulation results for the linear static reward–dynamic penalty mechanism are presented in Figure 5. As illustrated, this mechanism effectively enhances system stability, with the system converging to a steady state of (0.71, 0, 0.49). At this equilibrium, the mechanism functions as a valid strategy for controlling system fluctuations.

However, it is noteworthy that enterprises ultimately converge toward a non-participation strategy in organizing agricultural sustainability transitions. This outcome is counterproductive to the goals of carbon reduction and the development of a circular system for sustainable agricultural systems. Therefore, although the linear static reward–dynamic penalty mechanism provides system stability, it remains insufficient for fully promoting sustainable transition goals and thus requires further optimization.

4.3.4. Linear Dynamic Reward and Static Penalty

The results from Section 4.3.3 demonstrate that the linear dynamic punishment–static reward mechanism can regulate the behaviors of the government and farmers. However, it ultimately causes enterprises to gravitate toward non-participation in agricultural sustainability transitions. To address this shortcoming, further analysis is conducted using a linear dynamic reward–static punishment mechanism. This section investigates the effects of implementing a linear dynamic reward mechanism in combination with a static punishment strategy, evaluating its influence on the fluctuating behaviors of the government, enterprises, and farmers. The linear dynamic reward mechanism is designed according to the principle that the government provides real-time, responsive rewards based on the willingness of enterprises to organize and the willingness of farmers to participate in agricultural sustainability transitions. This relationship is formally represented in Equation (21).

$$S=\delta yS$$

(21)

Here, $\delta$ is the linear dynamic reward coefficient for enterprises, and $\epsilon$ considers the effectiveness of subsidies, taking the reward coefficient $\delta =5$ (satisfying $\delta y>1$). The numerical simulation results for the linear dynamic reward–static penalty mechanism are presented in Figure 6. As shown, the system ultimately converges to a stable state of (1, 0, 0). This indicates that the mechanism functions effectively as a system stability control strategy. However, under this mechanism, enterprises tend to choose not to organize agricultural sustainability transitions, and farmers similarly opt not to participate. Such behavioral tendencies are detrimental to the development of sustainable agricultural ecosystems. Therefore, although the linear dynamic reward–static penalty mechanism achieves system stability, it fails to promote positive engagement from key stakeholders and thus requires further optimization.

4.3.5. Linear Dynamic Reward and Dynamic Penalty

Both the linear dynamic reward–static penalty mechanism and the static reward–dynamic penalty mechanism influence the stability of control systems; however, each exhibits limitations that hinder the effective construction of agricultural sustainability transitions. In response, this study further explores a combined approach of the linear dynamic reward–dynamic penalty mechanism with its formulation and parameter settings detailed in Equations (19) and (20), and the corresponding evolutionary results are illustrated in Figure 7.

As shown in Figure 7, the fluctuation patterns under this combined mechanism reveal that its performance is less favorable than the individual implementations of the linear dynamic reward–static penalty and the static reward–dynamic penalty mechanisms. The system continues to exhibit a fluctuating trajectory and fails to converge toward an evolutionary stable strategy. This persistent instability presents a challenge for the effective governmental promotion of agricultural sustainability transitions.

Consequently, while the linear dynamic reward–dynamic penalty mechanism integrates the features of the prior two strategies, it still does not offer a satisfactory solution for system stabilization. Further optimization is required to develop more effective control strategies.

4.4. Nonlinear Dynamic Reward and Penalty

4.4.1. Nonlinear Dynamic Reward and Penalty Mechanism

Section 4.3 presents the results of the linear dynamic reward and punishment mechanism, demonstrating that while it has a certain degree of effectiveness in stabilizing the system, further refinement is necessary. In response, this paper introduces a nonlinear dynamic reward and punishment mechanism and validates its effectiveness in enhancing system stability through both numerical simulations and theoretical analysis.

Drawing on the principles used to construct the linear mechanism and the methodologies described earlier, this approach assumes that the greater the government’s efforts to promote agricultural sustainability transitions, the stronger the corresponding rewards and penalties it applies. The formulation of the nonlinear dynamic reward and punishment mechanism, including its parameter settings, is presented in Equations (22) and (23).

$$\mathrm{S}={\displaystyle \frac{S}{1-x}}+\delta {\displaystyle \frac{y}{S}}$$

(22)

$$F={\displaystyle \frac{F}{1-x}}+\theta \left(1-y\right)F$$

(23)

The numerical simulation results for the nonlinear dynamic reward and punishment mechanism, illustrating its impact on the behaviors of the government, enterprises, and farmers, are presented in Figure 8. As shown, the system converges to a relatively stable state around (0.43, 0.17, 1). This outcome indicates that the mechanism successfully mitigates the previously observed issue of enterprises consistently opting out of organizing agricultural sustainability transitions. Therefore, the nonlinear dynamic reward and punishment mechanism serves as an effective and ideal stability control strategy for the system.

However, despite achieving overall system stabilization, the simulation reveals a relatively low level of willingness among farmers to participate. As such, the next step involves appropriately adjusting relevant parameters to further increase the likelihood of stable and sustained farmer participation.

By setting the reward from higher-level government departments to local government agencies for promoting agricultural sustainability transitions at a value of 15, the evolutionary results are as illustrated in Figure 9. As shown, the system converges to a relatively optimal state of (0.48, 1, 0.75), reflecting improved coordination among the government, enterprises, and farmers.

These results indicate that, following appropriate parameter adjustments within the nonlinear dynamic reward and punishment mechanism, government departments are effectively incentivized to actively promote agricultural sustainability transitions. This, in turn, enhances farmers’ willingness to participate. Moreover, the behavioral evolution of enterprises demonstrates that increased incentives from higher government levels significantly improve the likelihood of enterprises choosing to organize agricultural sustainability transition efforts.

Overall, these findings suggest that higher-level government rewards exert a positive incentive effect on all three stakeholders—government departments, enterprises, and farmers—thereby reinforcing the collective advancement of agricultural sustainability transitions.

To further verify that the nonlinear dynamic reward and punishment mechanism constitutes a valid stability control strategy, the initial values for the strategy selections of the government, enterprises, and farmers were set at 0.2, 0.5, and 0.8, respectively. The corresponding evolutionary results are depicted in Figure 10.

As illustrated, the system consistently converges to a stable state around (0.48, 1, 0.75) despite variations in initial conditions. This demonstrates that the system’s convergence outcome is robust to changes in initial strategy distributions. Therefore, the nonlinear dynamic reward and punishment mechanism, after adjusting the rewards from higher government departments, can be confirmed as an effective stability control strategy for promoting agricultural sustainability transitions.

Section 4.4.1 partially demonstrated, through numerical simulations, that the nonlinear dynamic reward and punishment mechanism serves as a valid stability control strategy for the system. To further substantiate this conclusion, the effectiveness of the nonlinear dynamic reward and punishment mechanism is now examined through theoretical analysis. Specifically, this involves substituting the expressions of the nonlinear dynamic reward and punishment mechanism into the system’s evolutionary equations to formally verify the stability conditions.

$$F\left(x\right)=x\left(1-x\right)\left[\begin{array}{c}Pyz-\left(\alpha \left({\displaystyle \frac{S}{1-x}}+\delta {\displaystyle \frac{y}{S}}\right)+\left({\displaystyle \frac{F}{1-x}}+\theta \left(1-y\right)F\right)+P\right)y+\left(\alpha \left({\displaystyle \frac{S}{1-x}}+\delta {\displaystyle \frac{y}{S}}\right)-\left({\displaystyle \frac{S}{1-x}}+\delta {\displaystyle \frac{y}{S}}\right)-P\right)z\\ +R_g+\left({\displaystyle \frac{F}{1-x}}+\theta \left(1-y\right)F\right)+E_c-C_g+P\end{array}\right]$$

$$F\left(y\right)=y\left(1-y\right)\left[Txz+\left(\alpha \left({\displaystyle \frac{S}{1-x}}+\delta {\displaystyle \frac{y}{S}}\right)+\left({\displaystyle \frac{F}{1-x}}+\theta \left(1-y\right)F\right)-T\right)x-Tz+2\beta R_e-C_e-C_f+G_I-R_e+T\right]$$

(24)

$$F\left(z\right)=z\left(1-z\right)\left[Qxy+\left(\left({\displaystyle \frac{S}{1-x}}+\delta {\displaystyle \frac{y}{S}}\right)-\alpha \left({\displaystyle \frac{S}{1-x}}+\delta {\displaystyle \frac{y}{S}}\right)-Q\right)x-Qy+R_f-D_f+L+C_k-T_f+Q\right]$$

Setting the system of equations in (24) to zero, we obtain eight equilibrium points ${\mathrm{E}}_1^{\mathrm{*}}\left(\mathrm{0,0},0\right), {\mathrm{E}}_2^{\mathrm{*}}\left(\mathrm{0,1},0\right), {\mathrm{E}}_3^{\mathrm{*}}\left(\mathrm{0,0},1\right)$,${\mathrm{E}}_4^{\mathrm{*}}\left(\mathrm{0,1},1\right), {\mathrm{E}}_5^{\mathrm{*}}\left(\mathrm{1,0},0\right), {\mathrm{E}}_6^{\mathrm{*}}\left(\mathrm{1,1},0\right), {\mathrm{E}}_7^{\mathrm{*}}\left(\mathrm{1,0},1\right), {\mathrm{E}}_8^{\mathrm{*}}\left(\mathrm{1,1},1\right)$. The Jacobian matrix of Equation (24) at the initial value (0.8, 1, 0.5) is as follows.

$$J^{*}=\left[\begin{array}{ccc}-8.6133& -4.3452& -2.2341\\ 0& -14.8704& 0\\ 16.9907& 0.0426& 0\end{array}\right]$$

The eigenvalue ${\lambda }_1=-4.3067+4.4058i,{ \lambda }_2=-4.3067-4.4058i,{ \lambda }_3=-$14.8704, where ${\lambda }_{1,2,3}<0$. According to Lyapunov’s stability theory, a sufficient condition for the asymptotic stability of a three-dimensional system at an equilibrium point is that all three eigenvalues of the system’s Jacobian matrix have negative real parts. Based on this criterion, it can be demonstrated that the saddle point under the nonlinear dynamic reward and punishment mechanism satisfies the stability condition. Therefore, the evolutionary dynamics of the system exhibit asymptotic stability, and the theoretical proof is thus complete.

Integrating dynamic and static reward and punishment mechanisms, this study examines interactions among the government, enterprises, and farmers in advancing sustainable agricultural production. The findings reveal several critical insights: The government’s active promotion through various mechanisms significantly influences enterprise participation in agricultural sustainability transitions. However, when government actions fluctuate, this leads to an unstable equilibrium where enterprises intermittently engage in sustainable practices. This instability hinders the long-term sustainability of sustainable agriculture, highlighting the need for consistent government incentives.

Static reward and punishment mechanisms, while capable of reducing fluctuations in enterprise participation, are insufficient to stabilize the system entirely. Government incentives may temporarily encourage enterprise involvement, but they lack the sustained impact necessary for continuous agricultural sustainability transitions. Consequently, a purely static approach is inadequate as a standalone solution.

Dynamic rewards and punishments offer some degree of stability but risk driving the system toward an unfavorable equilibrium. For example, discontinuing rewards may lead to reduced participation in sustainable practices. This outcome suggests that while dynamic policies have potential, they must be carefully designed to avoid unintended, counterproductive effects.

The nonlinear dynamic reward and punishment mechanism proves the most effective in achieving stable agricultural sustainability transitions. By dynamically adjusting incentives based on stakeholder participation levels, this approach fosters a favorable equilibrium where the government, enterprises, and farmers consistently engage in sustainable practices. This mechanism not only stabilizes the system but also promotes a balanced evolution toward sustainable agricultural practices.

The convergence state (0.48, 1, 0.75) implies that long-run stability does not require permanent full-intensity promotion by government. Instead, once enterprises reliably organize sustainable production and most farmers participate, a moderate, cost-effective level of public oversight (x < 1) is sufficient to maintain coordination. This suggests that the policy goal is not maximal continuous intervention but calibrated, performance-contingent support that can be fiscally sustained.

4.4.2. Sensitivity Analysis of Incentive Allocation and Penalty Intensity

We re-simulated the nonlinear dynamic reward–punishment mechanism (Equations (22) and (23)) under each α and recorded the long-run convergence states (x*, y*, z*). Here, x, y, and z are, respectively, the probabilities of the government promoting, enterprises organizing, and farmers participating in sustainable agricultural system transitions.

Preliminary results from our re-analysis: When α decreases (α = 0.3 more subsidy directed to farmers), farmer participation z tends to increase, but enterprise willingness y weakens, risking coordination failure. When α increases (α = 0.7 more subsidy directed to enterprises), enterprise organization y stabilizes at higher levels, but farmer participation z can fall if direct farmer incentives become too weak; α = 0.5 maintains a balance in which both enterprise organization and farmer participation remain simultaneously non-zero under the nonlinear dynamic mechanism.

Building on Section 4.3.2’s static penalties, we quantify how stronger penalties on non-organizing enterprises influence convergence. As F increases, enterprise non-cooperation becomes less attractive, which supports higher y. However, if F is set excessively high, the system drifts toward a corner solution in which enterprises nominally “comply”, but farmers’ participation z plateaus at a suboptimal level. This is consistent with the intuition that over-punishment without matching positive incentives may trigger “formal compliance” rather than true cooperative engagement.

Sensitivity analysis on α (incentive split between enterprises and farmers) and F (penalty intensity on non-cooperative enterprises) confirms that the qualitative ranking of mechanisms remains unchanged: the nonlinear dynamic reward–punishment mechanism continues to dominate static or purely linear schemes in achieving the joint stability of x, y, and z. However, excessively asymmetric incentives (very high or very low α) or overly harsh penalties (very high F) can erode either farmer participation or enterprise cooperation. This indicates that policy design should avoid “all-to-enterprise” or “all-to-farmer” transfers and instead target a calibrated balance.

5. Discussion

The baseline evolutionary trajectory reproduces an empirically observed coordination problem in China’s sustainable agriculture initiatives: enterprises frequently scale back or exit coordination roles after initial engagement because they bear the upfront costs of quality control, farmer supervision, and branding, while the market does not always deliver a price premium sufficient to recover these investments. Meanwhile, farmers alone cannot sustain standardized green production, and local governments face rising supervision costs over time. This cyclical instability, reported in multiple provincial pilot programs of ecological rice, organic tea, and low-input horticulture, is consistent with our model’s finding that—without adaptive incentives—enterprise organization probability y declines toward zero.

When higher-level governments reward local governments for verifiable sustainability outcomes, and when penalties/rewards are adjusted dynamically in proportion to observed enterprise and farmer behavior, the system converges to a cooperative equilibrium. This mirrors policy discussions in China emphasizing performance-based transfers and differentiated environmental supervision, where local cadres receive incentives tied to ecological outcomes and enterprises gain structured, conditional support rather than one-off subsidies.

The model provides a formal analytical result: using the Jacobian stability analysis, in which all eigenvalues have negative real parts, it is shown that a nonlinear dynamic reward–punishment mechanism can yield an asymptotically stable cooperative equilibrium in a three-party evolutionary game linking government promotion (x), enterprise organization (y), and farmer participation (z). In other words, stability is not assumed; it is mathematically demonstrated.

Practical contribution. The Discussion translates these theoretical stability conditions into implementable governance tools. Specifically, it identifies the following: Calibrated subsidies that reduce enterprise coordination costs without creating permanent fiscal burdens. Escalating behavior-contingent penalties for non-compliant enterprises to deter strategic free-riding. Performance-based incentives from higher-level government to local government so that local promotion efforts can be maintained at a sustainable intensity rather than requiring constant maximum intervention. These instruments map directly onto the parameters in the model (S, αS, F, R_g) and outline how policymakers could operationalize nonlinear dynamic reward–punishment schemes in practice.

These instruments map directly onto the model’s payoff parameters: subsidies and guaranteed procurement (S, αS) reduce the enterprise cost of organizing; dynamic penalties (θ(1 − y)F) deter free-riding; performance-based higher-level rewards (R_g) encourage local governments to keep promoting with fiscally sustainable intensity (x = 0.5 rather than x = 1); and targeted farmer incentives ((1 − α)S) plus marketing support reduce individual adoption barriers (D_f, C_k). Together, these levers operationalize the nonlinear dynamic reward–punishment mechanism as a feasible multi-level governance toolkit.

6. Conclusions

This study addresses the critical challenge of achieving transitions toward sustainable agricultural systems in China by developing a three-party evolutionary game model to examine how policy-driven incentives influence strategic interactions among governments, enterprises, and farmers. Through a systematic analysis of both static and dynamic reward–punishment mechanisms, we investigate the behavioral dynamics governing stakeholder participation in sustainable agricultural practices and their implications for long-term agricultural system sustainability.

Our key findings demonstrate that the stability of sustainable agricultural system transitions is fundamentally contingent on the design and implementation of reward–punishment mechanisms. The analysis reveals that fluctuations in government engagement and enterprise participation introduce inherent instability into the transition process, with stakeholders oscillating between sustainable and conventional agricultural practices under inadequate policy frameworks. While static reward mechanisms partially mitigate peak fluctuations, they prove insufficient for maintaining sustained enterprise commitment to sustainable practices. Linear dynamic reward mechanisms offer modest improvements in system stability but lack the robustness required for long-term equilibrium. Most notably, nonlinear dynamic reward–punishment mechanisms emerge as the most effective approach, successfully aligning stakeholder incentives and fostering stable, enduring transitions toward sustainable agricultural systems.

These findings carry significant implications for agricultural policy design and sustainable development strategies in China and comparable contexts. The demonstrated efficacy of nonlinear dynamic mechanisms suggests that policymakers should prioritize adaptive governance strategies capable of responding flexibly to shifts in stakeholder participation and market conditions. This research emphasizes the necessity of moving beyond static, one-size-fits-all policies toward sophisticated and responsive mechanisms that sustain long-term engagement. Furthermore, the critical role of enterprise stability in facilitating transitions highlights the importance of targeted interventions that address the unique challenges confronting agricultural enterprises in adopting and maintaining sustainable practices.

This study also acknowledges several limitations that may influence the interpretation of the results. Although the evolutionary game model is comprehensive, it relies on assumptions regarding stakeholder behavior and preferences that may not fully reflect the complexity of real-world decision-making. Similarly, while empirically calibrated with available data, the model may not capture regional variations in agricultural practices, economic conditions, or policy implementation across China’s diverse landscapes. Additionally, the model focuses on three principal stakeholder groups, excluding other potentially influential actors such as consumers, financial institutions, and international market forces, which may also impact sustainable agricultural system transitions.

Future research should pursue several directions to expand upon these findings. First, longitudinal empirical studies are essential to validate the theoretical predictions and evaluate the real-world performance of different reward–punishment mechanisms across various agricultural regions. Second, subsequent research should explore the inclusion of additional stakeholders and external variables to account for more complex, multi-actor dynamics. Third, comparative studies assessing the effectiveness of nonlinear dynamic mechanisms across national and regional contexts would strengthen the generalizability of the results. Finally, investigations into the design parameters and implementation strategies of nonlinear dynamic reward–punishment systems would offer practical insights for policy development.

(i)

Mechanism ranking. The analysis shows that nonlinear dynamic reward–punishment mechanisms outperform linear dynamic mechanisms, and linear dynamic mechanisms outperform purely static reward or static penalty schemes. Nonlinear dynamic mechanisms are therefore identified as the most effective approach for achieving a stable cooperative equilibrium among government, enterprises, and farmers.

(ii)

Policy relevance. The Conclusions emphasize that effective agricultural sustainability governance should not rely on uniform, one-size-fits-all subsidies or fixed penalties. Instead, the most robust outcomes emerge from calibrated, performance-contingent incentives that adapt to observed behavior. This reflects a shift from continuous maximal intervention by government to targeted, fiscally sustainable guidance that still maintains enterprise organization and farmer participation.

(iii)

Limitations and future work. The Conclusions explicitly acknowledge the current study’s scope and remaining gaps. First, although the model captures patterns observed in practice (e.g., unstable enterprise participation), full empirical validation using longitudinal policy and market data is identified as a priority for future research. Second, the present model focuses on three stakeholders—government, enterprises, and farmers—and does not yet incorporate other influential actors such as financial institutions, downstream retailers, or consumers. Third, region-specific heterogeneity in China is not yet parameterized. These issues are now clearly identified as directions for subsequent work.

In conclusion, this research makes a significant contribution to the understanding of sustainable agricultural system transitions by demonstrating the superior effectiveness of nonlinear dynamic reward–punishment mechanisms in achieving stable stakeholder coordination. The findings establish a robust theoretical foundation for designing more effective policy interventions and underscore the importance of adaptive governance approaches in addressing complex sustainability challenges. By illuminating the pivotal role of mechanism design in shaping stakeholder behavior, this study advances both theoretical insight and practical policy development in the pursuit of resilient, sustainable agricultural systems that simultaneously support ecological protection, economic viability, and social equity.