An Evolutionary Game Study of Multi-Agent Collaborative Disaster Relief Mechanisms for Agricultural Natural Disasters in China

Abstract

Natural disasters in agriculture considerably threaten food security and the implementation of the rural revitalization strategy. With the rapid development of new approaches in organizing agricultural production, traditional disaster relief mechanisms are encountering new adaptive dilemmas. Particularly, the active participation of farmers in disaster relief is remarkably insufficient in the context of the reduction in the proportion of agricultural production income. Thus, it is urgent to establish a modernized agricultural disaster relief synergy mechanism. In this study, an agricultural disaster relief synergistic model was constructed with the participation of the government, agricultural service enterprises, and farmers based on the evolutionary game theory, and the strategy interaction law of each subject and its evolution path was systematically analyzed. The following results were revealed: First, the government, agricultural service enterprises, and farmers tended toward an equilibrium state under three different modes. Second, the cost of farmers’ concern and complaint behavior was the crucial driving factor of the three-party synergy. Third, the increasing cost of agricultural service enterprises’ participation in disaster relief significantly affected the evolution path of the system. Additionally, a three-dimensional synergistic optimization path of “incentive-constraint-information” was proposed, laying a quantitative foundation for improving the agricultural disaster relief mechanism and promoting the transition from “passive emergency response” to “active synergy”. This research is of great practical significance to improve the resilience of agricultural disaster response and resource allocation efficiency.

1. Introduction

The sustainable development of agriculture, as a basic industry of the national economy, plays a vital role in guaranteeing national food security and promoting rural revitalization. The process of agricultural production is inevitably affected by various types of natural disasters. For example, China has lost an average of about 60 billion pounds of grain annually as a result of meteorological disasters, such as floods, hailstorms, droughts, low-temperature freezes, and snowstorms, as well as an average of 50–60 billion pounds of grain because of pests, diseases, and grasses [1]. Throughout the year of 2023, China’s various natural disasters brought about a total of 10,539.3 thousand hectares of crop damage, with direct economic losses of CNY 345.45 billion [2]. In China, the agricultural scale and industrialization are not high, farmers are scattered, disaster relief resources are lacking, and disaster response capacity is weak. The Central Committee of the Communist Party of China and the State Council issued the Opinions of the Central Committee of the Communist Party of China and the State Council on Promoting the Reform of the Institutional Mechanism for Disaster Prevention, Mitigation, and Relief [3]. Their purposes were to (1) improve the mechanism for the participation of social forces and the market, (2) better the mechanism for coordinated and joint efforts between the government and social forces in disaster relief, (3) encourage and support the all-round participation of social forces in the work of regular disaster mitigation, emergency relief, transitional resettlement, restoration, and reconstruction, and (4) construct a pattern of socialized disaster prevention, mitigation, and relief in which a multitude of actors participate. In response to natural disasters in agriculture, a disaster prevention, mitigation, and relief mechanism with the concerted participation of many parties should be established to ensure the stable development of agriculture and lay a solid foundation for the realization of rural revitalization and national food security.

2. Literature Review

2.1. Research on Multi-Stakeholder Collaboration in the Field of Agricultural Natural Disasters

The establishment of disaster assessment indicators [4,5,6], regional risk classification [7,8,9], and monitoring and early warning systems [10,11,12] are fundamental tasks that have historically been central to agricultural natural disaster research. Current research paradigms exhibit significant structural deficiencies concerning disaster response mechanisms, particularly in terms of subject composition and analytical frameworks.

This research focuses on emergency coordination for sudden natural disasters, specifically examining collaboration across government agencies and the interaction between governmental bodies and non-governmental organizations (NGOs) [13,14,15,16]. These studies indicate that current systems excessively depend on vertical governmental authority, without adequate horizontal collaboration among government entities (across regions and departments) and thorough coordination between the government and NGOs [15,17]. Moreover, the professional competencies of NGOs require enhancement [18]. Xu highlighted that the potential of NGOs in China’s disaster management has not been completely realized [15]. Lin and Zhan, along with Zhao and Zhou, elucidated the deficiencies and possibilities of government-NGO collaboration models through case studies of earthquakes and heavy rainfall [16,18]. Liu and Sha explicitly identified the deficiencies in horizontal coordination between regions and sectors [17].

In contrast to abrupt disasters, agricultural natural disasters (such as droughts and insect infestations) can have gradual or cyclical traits [19]. The goals of disaster relief prioritize post-disaster recovery and reducing economic losses, which leads to a comparatively limited deployment of public resources and an increased reliance on market-driven resource distribution. Nonetheless, current collaborative research on agricultural disasters predominantly adheres to the conventional “government-farmer” binary analytical paradigm [20,21]. While Zhao acknowledged the existence of several players in floodplain governance [20], a comprehensive examination of market entities possessing independent interests and strategic capacities inside the government-led framework is still lacking.

The constraints of this dualistic framework have become progressively apparent in contemporary agriculture, described as follows: (1) It neglects essential market participants. Agricultural service enterprises, as primary providers of agricultural socialized services and specialized services within the contemporary agricultural framework (offering agricultural inputs, machinery, technology, finance, pest control, meteorological decision making, etc.) [22,23,24], serve an essential function as “third-party” entities in disaster response. They have autonomous economic interests, professional service competencies, and adaptable strategic alternatives; nonetheless, current research seldom examines them as entities with independent negotiating power. (2) This approach fails to accurately represent the realities of composite production systems. The organization of agricultural production in China has transitioned from fragmented smallholder farming to an integrated system including collaboration among various entities, including agricultural service enterprises (ASEs), cooperatives, and leading companies [21]. This strategy prioritizes resource integration, enhancement of efficiency, and risk distribution, hence challenging the conventional “government-farmer” disaster relief paradigm. (3) Insufficient attention to farmers’ lack of initiative: The initiative of dispersed farmers to engage in post-disaster recovery is often inadequate amid diminishing agricultural production income [21,22,23]. A binary approach dependent exclusively on the government or farmers is incapable of efficiently mobilizing resources, improving disaster relief efficacy, and guaranteeing sustainability.

Agricultural socialized services (ASSs) have proven essential in contemporary practices of agricultural disaster prevention, mitigation, and emergency response, emerging as a significant resource and capability for disaster relief [25]. During the catastrophic floods in Central and Southern China in 2022, local authorities proactively assembled agricultural machinery service teams to mitigate flooding and alleviate waterlogged regions. They also engaged various agricultural service providers, including agricultural service enterprises, to participate in essential phases such as emergency harvesting, drying, sun-drying, and replanting short-season crops, thereby significantly diminishing disaster-related losses. Furthermore, as the marketization of agricultural support services (ASSs) intensifies and technological advancements progress, high-tech ASSs, exemplified by specialized plant protection technologies and precise agricultural meteorological forecasting and decision-making services, have yielded substantial outcomes in averting significant pest and disease outbreaks and alleviating meteorological disaster risks, thereby emerging as a crucial element in agricultural disaster prevention, mitigation, and relief efforts [26]. These practical experiences unequivocally indicate a novel strategy for enhancing agricultural disaster prevention, mitigation, and relief initiatives, together with emergency management. Agricultural socialized services are a standard, institutionalized resource for disaster relief and emergency response [27], which provides dual advantages: it enhances the capabilities and standards of an ASS (including the development of specialized emergency equipment and services) and substantially improves agricultural disaster prevention, mitigation, and relief efforts, as well as emergency response capabilities, while broadening the range of participants in emergency responses. This method integrates professional emergency response skills with market-oriented civilian troops regularly. Nevertheless, current research is deficient in a systematic overview of successful practices, and there is an inadequate amount of thorough investigations into the evaluation of agricultural service enterprises as autonomous disaster relief entities and the formulation of mechanisms for their regular involvement in emergency responses.

Consequently, it is imperative to establish a triadic collaborative framework comprising the government, agricultural service enterprises, and agricultural production entities (farmers) while conducting a comprehensive analysis of the role of agricultural service enterprises as the principal agents of agricultural support services and their intricate interaction mechanisms with both the government and farmers. This approach is essential for addressing the prevailing challenges in collaborative disaster relief efforts for agricultural natural disasters and for adapting to the demands of contemporary agricultural development.

2.2. The Application of Game Theory in Disaster Response Mechanism Research and Its Evolution in Agricultural Collaboration

Evolutionary game theory, owing to its capacity to accurately delineate the strategy of modification and learning mechanisms (such as replication dynamics) of agents with bounded rationality, has been extensively utilized to examine the behavioral interactions of stakeholders in disaster scenarios [28,29,30], offering a robust framework for comprehending interest-driven strategy selection.

Current research on disaster response simulations predominantly emphasizes the government as the principal entity. Liu established a collaborative framework between governmental rescue agencies and social entities, primarily NGOs, to investigate sustainable strategies within the “government-led, social participation” paradigm [31]. Yan et al. and Wang have, respectively, examined the “government-business-public” interaction in smart emergency response [32] and the “residents-local government-insurance company” dynamics in catastrophe insurance [33], both emphasizing the significance of triadic interaction. Nonetheless, the functions of “business/insurance companies” in these studies markedly diverge from those in agricultural ASEs.

Recently, the utilization of evolutionary game theory in agriculture has intensified, yielding significant insights for the formulation of disaster response coordination systems [34,35,36]. These studies primarily engage three principal stakeholders: Concentrating on the design of governmental incentives, Xu et al. developed a model involving “local government-new agricultural operators-traditional farmers,” elucidating the functions of technology spillovers and regulatory incentives [37]. Chen et al. confirmed the efficacy of the “incentive-constraint-information” framework [38]. Validating the efficacy of corporate collaboration, Zhang et al. illustrated that collaboration in agricultural machinery services substantially improves production, thus establishing a behavioral basis for corporate-led disaster assistance [39]. Empirical research reveals that politicians have significant initiative, whereas producers display minimal initiative, and implementers maintain a rather consistent level of initiative [40]. Chen et al. examined the case of salt-tolerant rice to emphasize that initial willingness and cost-sharing coefficients are critical thresholds for collaborative stability [41]. Zhang et al. suggested that digitization, including information-sharing platforms, can markedly decrease collaboration costs [42].

Nevertheless, current studies on agricultural cooperative games exhibit a significant deficiency in specificity, such as the following: (1) Discrepancy among fundamental entities: In prior research, the phrase “enterprises/new types of business entities” has predominantly denoted cooperatives, leading enterprises (emphasizing production), or more expansive market entities. Research focusing on agricultural service firms that offer specialized disaster relief services, along with their separate strategy frameworks and incentive mechanisms in disaster response, is notably limited. There is a notable deficiency in studies about the quantification and assurance of the consistent involvement of agricultural service firms in disaster relief emergency response via cost sharing and corporate profits. (2) The research is notably context-specific, concentrating on scenarios such as technology promotion (e.g., conservation tillage), ecological protection, variety cooperation, or general public–private partnership scenarios. It is deficient in comprehensive modeling and empirical analysis regarding cost sharing, revenue distribution, and dynamic strategic interactions among the government, agricultural service enterprises, and farmers throughout the entire disaster prevention, response, and recovery continuum in the particular context of collaborative disaster relief for agricultural natural disasters. (3) There is an absence of incentive mechanisms for agricultural service firms, especially concerning cost structures, income expectations, risk preferences, and responses to various governmental instruments during their involvement in disaster relief. The absence of evidence compromises the formulation of effective and lasting incentive systems for agricultural service firms (

Table 1. Main shortcomings in agricultural natural disaster relief research and responses in this study.

Previous Research Gaps	The Methodology and Contribution of This Study
Constraints of the analytical framework: This predominantly depends on the binary framework of “government–NGO” or “government–farmer”, neglecting to acknowledge the pivotal role of agricultural service businesses in the contemporary agricultural complex and disregarding ASEs as the cornerstone of disaster relief capabilities.	This paper presents and develops a three-party collaborative evolutionary game model including the government, agricultural service firms, and agricultural producing entities (farmers). Agricultural service enterprises serve as the fundamental components of the agricultural service system and are studied independently to assess the strategic decisions of the three involved parties in their interactions.
Inadequate targeting in disaster relief situations: Current studies on agricultural cooperation and competition primarily concentrate on non-disaster relief situations, failing to provide particular models for the dynamic process of collaborative disaster relief in the context of agricultural natural catastrophes.	We perform comprehensive modeling and empirical analysis of cost sharing, benefit distribution, and dynamic strategic interactions among governments, agricultural service enterprises, and farmers within the complete continuum of disaster prevention, emergency response, and post-disaster recovery.
The coordination mechanism among the three parties is ambiguous: There is insufficient systematic research on the dynamic evolution and stability conditions regarding cost sharing for disaster relief, risk allocation, and profit distribution among the government, agricultural service enterprises, and farmers.	We apply evolutionary game theory to elucidate the dynamic coordination mechanism, simulate the strategic interactions and adaptive learning processes among the three parties, and pinpoint the stable equilibrium strategy combination (ESS) of system evolution, along with its formation conditions such as cost-sharing coefficient thresholds, government reward and punishment intensity, and risk credit. This approach provides theoretical backing for the creation of a stable and effective three-party coordination mechanism.

).

In conclusion, while advancements have occurred in fundamental research regarding agricultural natural disasters and the game analysis of multi-stakeholder collaborative governance, there exists a notable deficiency in the study of collaborative disaster relief for agricultural calamities. The fundamental problem resides in the inability to transcend the conventional binary framework, which systematically overlooks the autonomous status and pivotal function of agricultural service enterprises as essential third-party entities in agricultural socialized services. Furthermore, there is an absence of a dynamic interaction mechanism model for the three parties in disaster relief contexts, along with insufficient research on the varying strategic options available to these parties.

2.3. Literature Summary

This study breaks through the traditional research paradigm. A tripartite evolutionary game model of government departments, agricultural service enterprises, and agricultural production subjects was innovatively constructed to systematically reveal the strategic interaction law of the subjects in disaster response. By designing a benefit function consisting of dynamic subsidies, information sharing, and differentiated rewards and penalties, the equilibrium state of the system under different policy scenarios was analyzed through numerical simulation. This study then proposed an optimization path for the synergistic mechanism. Three aspects reflect this study’s contributions. First, the theoretical level includes agricultural service enterprises for the first time as independent game subjects in the analytical framework, which makes up for the structural defects of the traditional “government–farmer” dichotomy. Second, the methodological level integrates the simulation of complex systems with the analysis of policy sensitivity and reveals the threshold effect of key parameters on the stability of the synergy. Third, the practical level brings about a three-dimensional synergistic mechanism of “incentive–constraint–information”. This study provides quantitative decision support for the policy goal of “perfecting the mechanism of social forces’ synergistic disaster relief” in the National Emergency Response System Plan of the 14th Five-Year Plan while promoting the paradigm shift in agricultural disaster relief from “passive emergency response” to “active coordination”. The findings of this study can considerably contribute to solving the strategic conflicts and optimizing the efficiency of resource allocation in agricultural disaster relief.

3. Basic Assumptions and Modeling

Evolutionary game theory does not require fully rational participants nor information conditions [43], but it does emphasize the dynamic equilibrium [44]. The main body of the game is the government (G), agricultural service enterprises (F), and farmers (N). As a limited rational individual, the participants in the process of the subject make a mature strategy. The government is facing natural disasters in its decision making for the “positive support” and “passive laissez-faire”. The government’s decision making in the face of natural disasters is “positive support” and “negative indulgence”. Agricultural service enterprises have a “positive action” and “negative action” in the choice of service supply strategies under natural disasters. Farmers are categorized into “positive relief” and “negative relief” in the face of natural disasters.

Starting from the two aspects of positive and negative government support, this model sets up the government’s promotion and advocacy in terms of positive government support and cost-sharing incentives for agricultural service enterprises to improve the supply of agricultural-related products and services. From one perspective, the government penalizes negatively acting agricultural service enterprises by increasing taxes and decreasing incentives. Farmers are categorized into two behaviors: concern and complaint. Specifically, they actively participate in the policy implementation process by following policy developments and complaining about misbehavior and complain to strengthen the regulation of agricultural service enterprises, so as to guarantee the effective implementation of the policy.

3.1. Assumptions and Model Design Associations

The government executes multifaceted interventions in response to agricultural natural catastrophes, distributing disaster relief funding to impacted regions for post-disaster recovery efforts. It augments market participation via incentive subsidies for enterprises (encompassing direct fiscal subsidies and tax concessions), implements capacity development for disaster prevention among farmers, fortifies disaster reduction awareness through training initiatives and multimedia platforms, and enforces administrative penalties on enterprises that do not deliver sufficient disaster relief. The expenses involved include the complete regulatory expenditure process, comprising investigation, evidence collection, legal proceedings, and penalty enforcement. Consequently, the publicity and guidance costs (αA) represent the real expenses incurred by the government for disaster prevention and mitigation outreach, encompassing training initiatives and media campaigns. The cost-sharing expenditures (βJ) denote the subsidies allocated by the government to promote corporate involvement in disaster relief initiatives, including direct cash assistance and tax incentives. The implementation costs of the penalty mechanism (γK) denote the expenses borne by the government in enforcing fines on non-compliant firms.

Agricultural service companies will only participate in agricultural disaster relief initiatives if their interests are satisfied and they receive reimbursement for the expenses they incur. In disaster relief efforts, firms must evaluate both the advantages (P) and expenses (C) incurred. In the 2023 floods in Henan Province, agricultural service companies obtained incentives for mechanical drainage services via government emergency contracts. Companies engaged in disaster relief experienced an extension of their client base within three years following the tragedy, hence augmenting their market share. Furthermore, organizations engaged in disaster aid received accreditation as “Disaster Relief Pioneer Enterprise.” The additional advantages of corporate catastrophe assistance comprise three elements: government subsidies to the enterprise, market share, and elevated service price. In disaster relief efforts, agricultural service enterprises must account for costs associated with it, including equipment depreciation for specialized machinery (e.g., water pumps and drones), labor expenses, and the utilization of relief supplies (e.g., rapid-acting fertilizers and disinfectants).

In the event of agricultural disasters, farmers generally depend on government aid because of the absence of specialist disaster relief equipment, and the relief initiatives of agricultural service firms necessitate government mobilization and resource allocation. Farmers enhance the efficacy of disaster relief with supervisory measures during this process. When farmers discover that corporations are involved in irregular operations or neglecting catastrophe relief efforts, their grievances lead to substantial expenditures, including time losses and social hazards. Moreover, farmers proactively acquire disaster knowledge, acquire disaster relief methodologies, and oversee policy execution while engaging in disaster relief initiatives. Agriculturalists receive government-sponsored disaster relief training and may be required to participate in online education. Elderly farmers may encounter difficulties in comprehending policy papers. Consequently, δB denotes the expenses related to behavior monitoring, encompassing temporal, financial, and cognitive costs, whereas θR signifies the costs linked to complaint behavior, including time losses and social risks, to assess farmers’ strategic decisions during disaster relief initiatives (Figure 1).

3.2. Basic Assumption

Hypothesis 1.

Without considering other constraints, the government, agricultural service enterprises, and farmers are all finite rational subjects; all three subjects are finite rational individuals with the ability to learn; and all have their own behavioral choices and decision-making power.

Hypothesis 2.

The government’s relevant synergistic behavior is divided into publicity and guidance, cost sharing, and punishment. The impact factor is $\alpha ,\beta ,\gamma >$ 0. The corresponding cost function can be expressed as follows: $\alpha A$ indicates publicity and guidance costs; $\beta J$ denotes cost-sharing expenditures; and $\gamma K$ embodies the cost of implementation of punishment mechanisms.

Hypothesis 3.

The positive disaster relief behaviors of farmers are classified into concern and complaint. The influence factors are $\delta$, $\theta$, $\delta >0$, $\theta >0$, and then $\delta B$ and θR designate the consumed costs.

Hypothesis 4.

Assume that the probability of government incentivization is x and the probability of disincentivization is 1 − x; the probability of an agricultural service firm acting in the market is y, and the probability of inaction is 1 − y; and the probability of active participation by a farmer is z, and the probability of passive participation is 1 − z. x,y,z ∈ [0, 1] are functions of t. The probability of active participation by a farm household is 1 − z.

Hypothesis 5.

The original gain of the agricultural service firm is $P$, the increased gain from improving the supply of agriculture-related products and services is $\Delta P$, and the cost consumed by this behavior is C. The government gains $P_g$ and loses $S_g$. The gain to farmers is $P_c$, the loss caused by farmers is $S_c$, the gain from farmers’ participation is $\Delta P_c$, the damage to the government’s credibility triggered by farmers’ complaints is $D$, and the damage to the profitability of the agricultural service firms is $T$.

Following the content of the above assumptions, the evolutionary game matrix of the government, agricultural service enterprises, and farmers is constructed, as listed in

Table 2. Mixed strategy payoff matrix for gaming systems.

		$\mathbf{Active} \mathbf{Government} \mathbf{Support} \mathit{x}$		$\mathbf{Negative} \mathbf{Governmental} \mathbf{Indulgence} 1-\mathit{x}$
		Farmers active in disaster relief $z$	Farmers negative disaster relief $1-z$	Farmers active in disaster relief $z$	Farmers negative disaster relief$1-z$
Agricultural service enterprises active $\mathit{y}$	governments	$P_g-\alpha A-\beta J$	$P_g-\alpha A-\beta J$	$P_g$	$P_g$
	market	$P+\Delta P+\beta J-C$	$P+\Delta P+\beta J-C$	$P+\Delta P-C$	$P+\Delta P-C$
	peasant household	${\mathrm{P}}_{\mathrm{c}}-\delta B-\theta R+\Delta P_c$	${\mathrm{P}}_{\mathrm{c}}$	${\mathrm{P}}_{\mathrm{c}}-\delta B-\theta R+\Delta P_c$	${\mathrm{P}}_{\mathrm{c}}$
Negative action by agricultural service enterprises $\mathbf{1}-\mathit{y}$	governments	$\gamma K-\alpha A{-S}_g-D$	$\gamma K-\alpha A{-S}_g$	${-S}_g-D$	${-S}_g$
	market	$P-\gamma K-T$	$P-\gamma K$	$P-T$	$P$
	peasant household	$-S_c-\delta B-\theta R$	$-S_c$	$-S_c-\delta B-\theta R$	$-S_c$

.

3.3. Model Parameter Meanings

The model parameters are described in

Table 3. Description of model parameters and symbols.

Symbolic	Parameters	Economic Implications
$\alpha$	Cost coefficient for publicity and guidance	Marginal cost factor per unit of publicity input
$\beta$	Cost-sharing expenditure factor	Marginal cost factor per unit of subsidized expenditure
$\gamma$	Cost coefficients for the application of penalties	Marginal cost factor per unit of penalty enforcement
$A$	Fixed advocacy costs	Fixed inputs from the government for awareness raising and guidance
$J$	Expenditure on benchmark subsidies	Baseline amount of government subsidies for agricultural service enterprises involved in disaster relief
$K$	Baseline penalty costs	Benchmark administrative costs of government-imposed penalization mechanisms
$D$	Credibility loss	Decreased social trust in the government due to complaints from farmers
${\mathrm{P}}_{\mathrm{g}}$	Government disaster relief proceeds	Government performance gains from disaster mitigation
$S_g$	Governmental inaction losses	Socio-economic losses due to inadequate disaster response
$\delta$	Focus on cost factors	Marginal cost per unit of access to disaster relief information by farmers
$\theta$	Complaint cost factor	Marginal cost per unit for farmers complaining about corporate behavior
$B$	Benchmark focus on costs	Fixed costs for farmers to monitor policy implementation
$R$	Benchmark complaint costs	Fixed costs for farmers to initiate complaints
$\Delta P_c$	Incremental disaster relief proceeds	Losses reduced by active disaster relief
$P_c$	Proceeds from original production	Baseline return on agricultural production when not affected
$S_c$	Negative disaster relief losses	Crop losses due to non-participation in disaster response
$P$	Original market revenue	Benchmark earnings when the enterprise is not involved in disaster relief
$\Delta P$	Incremental disaster relief proceeds	Additional benefits from participation in disaster relief
C	Cost of disaster relief services	The total cost to businesses of providing disaster relief services
T	Complaint losses	Direct losses due to farmers’ complaints

to transform the above basic assumptions into an evolutionary game model that can be analyzed quantitatively.

3.4. Replicating the Dynamic Equations

(1)

The government replicates dynamic equations

Expected benefits of active government support based on benefit matrix calculation:

$$\begin{array}{l}{u}_x=yz\left(P_g-\alpha A-\beta J\right)+y\left(1-z\right)\left(P_g-\alpha A-\beta J\right)\\ +z\left(1-y\right)\left(\gamma K-\alpha A{-S}_g-D\right)+\left(1-y\right)\left(1-z\right)\left(\gamma K-\alpha A{-S}_g\right)\\ =-\alpha A+y\left(P_g-\beta J\right)+\left(1-y\right)\left(\gamma K-S_g\right)+\left(y-1\right)zD\end{array}$$

(1)

Expected gains from government negative deregulation:

$$\begin{array}{ll}{u}_{1-x}& =yz{P}_g+y\left(1-z\right)P_g+z\left(1-y\right)\left({-S}_g-D\right)+\left(1-y\right)\left(1-z\right)\left({-S}_g\right)\\ & =y{P}_g+\left(1-y\right)\left(-S_g\right)+\left(1-y\right)z\left(-D\right)\end{array}$$

(2)

The average return to the government:

$$\begin{array}{ll}{\overline{u}}_x& =x{\cdot u}_x+\left(1-x\right)\cdot u_{1-x}\\ & =-x\alpha A+y{P}_g+\left(1-xy\right)\beta J+x\left(1-y\right)\gamma K+\left(y-1\right)S_g+\left(y-1\right)zD\end{array}$$

(3)

Based on the Malthusian replication dynamics idea [45], the government replication dynamics equation is constructed as follows:

$$F\left(x\right)=x\left[u_x-{\overline{u}}_x\right]=x\left(x-1\right) \left[\alpha A+y\beta J+\left(y-1\right)\gamma K\right]$$

(4)

The first-order derivative of $F\left(x\right)$ is obtained from the government strategy choice replication dynamic equation as follows:

$$F^{\prime }\left(x\right)={\displaystyle \frac{\partial F\left(x\right)}{\partial x}}=\left(2x-1\right)\left[\alpha A+y\beta J+\left(y-1\right)\gamma K\right]$$

(5)

Following the stability theorem of differential equations [46], the probability that the government chooses to incentivize is in a steady state that must satisfy $F\left(x\right)=0$ and $F^{\prime }\left(x\right)<0$.

Let $G\left(y\right)=\alpha A+y\beta J+\left(y-1\right)\gamma K$, which yields the first-order derivative of $G\left(y\right)$ as $\gamma K+\beta J>0$. Then, $G\left(y\right)$ is an increasing function. Therefore, all x is in an evolutionary stable state at this point when $y=y^{*}={\displaystyle \frac{\gamma K-\alpha A}{\gamma K+\beta J}}$, $G\left(y\right)=0$, $F^{\prime }\left(x\right)=0$, and $F\left(x\right)=0$.

$x=1$ is the government’s evolutionary stabilization strategy when $y<y^{*}$, $G\left(y\right)<0$, F’ (x) = F’ (1) < 0, $F\left(x\right)=F\left(1\right)=0$; $x=0$ is the government’s developmental evolutionary stabilization strategy when $y>y^{*}$, $G\left(y\right)>0$, $F^{\prime }\left(x\right)=F^{\prime }\left(0\right)<0$, and $F\left(x\right)=F\left(0\right)=0$ (Figure 2).

(2)

Dynamic equations for replication of agricultural service firms

Based on the calculation of the benefit matrix, the expected benefits of positive actions by agricultural service enterprises can be obtained as follows:

$$\begin{array}{l}{u}_y=xz\left(P+\Delta P+\beta J-C\right)+x\left(1-z\right)\left(P+\Delta P+\beta J-C\right)\\ +\left(1-x\right)z\left(P+\Delta P-C\right)+\left(1-x\right)\left(1-z\right)\left(P+\Delta P-C\right)\\ =x\beta J+\left(P+\Delta P-C\right)\end{array}$$

(6)

Expected gains from negative actions by agricultural service firms:

$$\begin{array}{ll}{u}_{1-y}& =xz\left(P-\gamma K-T\right)+x\left(1-z\right)\left(P-\gamma K\right)\\ & +\left(1-x\right)z\left(P-T\right)+\left(1-x\right)\left(1-z\right)P\\ & = -x\gamma K+zT+P\end{array}$$

(7)

Average earnings of agricultural service enterprises:

$$\begin{array}{ll}{\overline{u}}_y& =y{\cdot u}_y+\left(1-y\right)\cdot u_{1-y}\\ & =P+y\left(\Delta P-C\right)+xy\beta J+x\left(y-1\right)\gamma K+\left(1-y\right)zT\end{array}$$

(8)

With the Malthusian replication dynamics idea, the replication dynamics equation of agricultural service enterprises is constructed as follows:

$$F\left(y\right)=y\left[u_y-{\overline{u}}_y\right]=y\left(1-y\right)\left[x\left(\beta J+\gamma K\right)+\Delta P-C-zT\right]$$

(9)

The first order derivative of F(y) is obtained from the replication dynamic equation for strategy selection in agricultural service firms:

$$F^{\prime }\left(y\right)=\left(1-2y\right)\left[x\left(\beta J+\gamma K\right)+\Delta P-C-zT\right]$$

(10)

In accordance with the stability theorem of differential equations, the probability of an agricultural service business choosing to act as is in a steady state must satisfy $F\left(x\right)=0$ and $F^{\prime }\left(x\right)<0$.

Let $G\left(z\right)=x\left(\beta J+\gamma K\right)+\Delta P-C-zT$, which yields a first-order derivative of $G\left(z\right)$ of $-T<0$. Then, G(z) is a decreasing function. $z=z^{*}={\displaystyle \frac{x\left(\beta J+\gamma K\right)+\Delta P-C}{z}}$ when $G\left(z\right)=0$, $F^{\prime }\left(y\right)=0$, and $F\left(y\right)=0$. At this time, all $z$ are in an evolutionary stable state.

$y=1$ is the evolutionary stabilization strategy for the development of agricultural service enterprises when $z<z^{*}$, $G\left(z\right)>0$, $F^{\prime }\left(y\right)=F^{\prime }\left(1\right)<0$, and $F\left(y\right)=F\left(1\right)=0$; $y=0$ is the evolutionary stabilization strategy for the development of agricultural service enterprises when $z>z^{*}$, $G\left(z\right)<0$, $F^{\prime }\left(y\right)=F^{\prime }\left(0\right)<0$, and $F\left(y\right)=F\left(0\right)=0$ (Figure 3).

(3)

Dynamic equations for farm household replication

Based on the benefit matrix calculations, the expected benefits of active participation by farmers can be obtained:

$$\begin{array}{l}{u}_z=xy\left({\mathrm{P}}_{\mathrm{c}}-\delta B-\theta R+\Delta P_c\right)+\left(1-x\right)y\left({\mathrm{P}}_{\mathrm{c}}-\delta B-\theta R+\Delta P_c\right)\\ +x\left(1-y\right)\left(-S_c-\delta B-\theta R\right)+\left(1-x\right)\left(1-y\right)\left(-S_c-\delta B-\theta R\right)\\ =y\left({\mathrm{P}}_{\mathrm{c}}+\Delta P_c \right)+\left(y-1\right)S_c+\left(-\delta B-\theta R\right)\end{array}$$

(11)

Expected benefits of negative farmer participation:

$$\begin{array}{ll}{u}_{1-z}& =xy\left(P_c\right)+\left(1-x\right)y\left(P_c\right)\\ & +\left(1-y\right)x\left(-S_c\right)+\left(1-y\right)\left(1-x\right)\left(-S_c\right)\\ & ={yP}_c+\left(1-y\right)\left(-S_c\right)\end{array}$$

(12)

Average returns to farmers:

$${\overline{u}}_z=z{\cdot u}_z+\left(1-z\right)\cdot u_{1-z}=y{P}_c+yz\Delta P_c+\left(y-1\right)S_c+z\left(-\delta B-\theta R\right)$$

(13)

With the Malthusian replication dynamics idea, the replication dynamics of farmers are expressed as follows:

$$F\left(z\right)=z\left[u_z-{\overline{u}}_z\right]=z\left(1-z\right)\left[y\Delta P_c+\left(-\delta B-\theta R\right)\right]$$

(14)

The first order derivative of F(z) is obtained from the replication dynamic equation for strategy selection in agricultural service firms:

$$F^{\prime }\left(z\right)=\left(1-2z\right)\left[y\Delta P_c+\left(-\delta B-\theta R\right)\right]$$

(15)

$H\left(y\right)=y\Delta P_c+(-\delta B-\theta R)$, which yields the first-order derivative of $H\left(y\right)$ as $\Delta P_c>0$. Then, $H\left(y\right)$ is an increasing function. Therefore, $H\left(y\right)=0$, $F^{\prime }\left(z\right)=0$, and $H\left(z\right)=0$. Thus, all $y$ for $y=y^{**}={\displaystyle \frac{\delta B+\theta R}{\Delta P_c}}$ is in an evolutionarily stable state at this point.

$z=0$ is the evolutionary stabilization strategy for the development of farmers when $y<y^{**}$, $H\left(y\right)<0$, $F^{\prime }\left(z\right)=F^{\prime }\left(0\right)<0$, and $F\left(z\right)=F\left(0\right)=0$; $z=1$ is the evolutionary stabilization strategy for the development of farmers when $y>y^{**}$, $H\left(y\right)>0$, $F^{\prime }\left(z\right)=F^{\prime }\left(1\right)<0$, and $F\left(z\right)=F\left(1\right)=0$ (Figure 4).

3.5. Stabilization Analysis

The system equilibrium points, (0, 0, 0), (1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 0), (0, 1, 1), (1, 0, 1), and (1, 1, 1), are obtained from F(x) = 0, F(y) = 0, F(z) = 0. The Jacobian matrix is calculated as follows [47]:

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

(16)

where

$$\begin{array}{l}{\displaystyle \frac{\partial F\left(x\right)}{\partial x}}=(2x-1)[\alpha A+y\beta J+\left(y-1\right)\gamma K]\\ {\displaystyle \frac{\partial F\left(x\right)}{\partial y}}=x\left(x-1\right)(\beta J+\gamma K)\\ {\displaystyle \frac{\partial F\left(x\right)}{\partial z}}=0\\ {\displaystyle \frac{\partial F\left(y\right)}{\partial x}}=y(y-1)(\beta J+\gamma K)\\ {\displaystyle \frac{\partial F\left(y\right)}{\partial y}}=\left(1-2y\right)[x\left(\beta J+\gamma K\right)+\Delta P-C-zT]\\ {\displaystyle \frac{\partial F\left(y\right)}{\partial z}}=-y(1-y)T\\ {\displaystyle \frac{\partial F\left(z\right)}{\partial x}}=0\\ {\displaystyle \frac{\partial F\left(z\right)}{\partial y}}=z(1-z)\Delta P_c\\ {\displaystyle \frac{\partial F\left(z\right)}{\partial z}}=\left(1-2z\right)[ y\Delta P_c+\left(-\delta B-\theta R\right)]\end{array}$$

Given the unknown model parameters, except for $\alpha A-\gamma K$, $\beta J+\gamma K+\Delta P-C$, $\Delta P_c-\left(\delta B+\theta R\right)$, $\Delta P-C-T$, and $\Delta P-C$, which can be determined from the assumption part of the positivity, the positivity conditions of the above equations are discussed and analyzed below (

Table 4. Eigenvalues for each equilibrium point.

Equilibrium Point	$\mathbf{Eigenvalue} {\mathit{\lambda }}_1$	$\mathbf{Eigenvalue} {\mathit{\lambda }}_2$	$\mathbf{Eigenvalue} {\mathit{\lambda }}_3$
$E_1(\mathrm{0,0},0)$	$-(\alpha A-\gamma K)$	$\Delta P-C$	$-\left(\delta B+\theta R\right)$
$E_2(\mathrm{1,0},0)$	$\alpha A-\gamma K$	$\beta J+\gamma K+\Delta P-C$	$-\left(\delta B+\theta R\right)$
$E_3\left(\mathrm{0,1},0\right)$	$-(\alpha A+\beta J-\gamma K)$	$-(\Delta P-C)$	$\Delta P_c-\left(\delta B+\theta R\right)$
$E_4(\mathrm{0,0},1)$	$-(\alpha A-\gamma K)$	$\Delta P-C-T$	$\delta B+\theta R$
$E_5(\mathrm{1,1},0)$	$\alpha A+\beta J$	$-(\beta J+\gamma K)-\Delta P+C$	$\Delta P_c-\left(\delta B+\theta R\right)$
$E_6(\mathrm{1,0},1)$	$\alpha A+\gamma K$	$\beta J+\gamma K+\Delta P-C-T$	$\delta B+\theta R$
$E_7(\mathrm{0,1},1)$	$-(\alpha A+\beta J)$	$-(\Delta P-C-T)$	$-[\Delta P_c-\left(\delta B+\theta R\right)]$
$E_8(\mathrm{1,1},1)$	$\alpha A+\beta J$	$-[\beta J+\gamma K+\Delta P-C-T]$	$-[\Delta P_c-\left(\delta B+\theta R\right)]$

).

(1) When $\alpha A-\gamma K<0$, $\beta J+\gamma K+\Delta P-C<0$, the cost consumed by the government through publicity and guidance is less than the cost consumed by punitive measures, and the net income of the agricultural service enterprises is negative. Moreover, the three eigenvalues of $E_1(\mathrm{1,0},0)$ are all less than 0, reflecting that $E_1(\mathrm{1,0},0)$ is the stable point of system evolution, reflecting that $E_1(\mathrm{1,0},0)$ is the stable point of system evolution.

(2) When $\Delta P-C>0$, $\Delta P_c-\left(\delta B+\theta R\right)<0$, the increased benefits of agricultural service enterprises after improving the supply of agriculture-related products and services are less than the consumed costs, and the benefits gained by farmers’ participation are less than the consumed costs. Meanwhile, all three eigenvalues of $E_3\left(\mathrm{0,1},0\right)$ are less than 0, and all three eigenvalues of $E_3\left(\mathrm{0,1},0\right)$ are less than 0, suggesting that $E_3\left(\mathrm{0,1},0\right)$ is the stable point of the system’s evolution.

(3) When $\Delta P-C-T>0$, $\Delta P_c-\left(\delta B+\theta R\right)>0$, the increased benefits of the agricultural service enterprise after improving the supply of agricultural-related products and services are greater than the sum of the consumed costs and the impaired benefits, and all three eigenvalues of $E_7(\mathrm{0,1},1)$ are less than 0. In other words, $E_7(\mathrm{0,1},1)$ is the point of stability of system evolution.

Given that $E_1(\mathrm{0,0},0)$, $E_4(\mathrm{0,0},1)$, $E_5(\mathrm{1,1},0)$, $E_6(\mathrm{1,0},1)$, and $E_8(\mathrm{1,1},1)$ each possess at least one positive eigenvalue, it follows that the system will diverge from its state in response to modest perturbations and will not achieve convergence. $E_1(\mathrm{0,0},0)$ signifies total inactivity on all three fronts, which is inconsistent with China’s “government-led disaster relief” framework. $E_4(\mathrm{0,0},1)$ signifies that farmers engage actively, while the government and enterprises refrain from intervention; yet, small-scale farmers lack autonomous disaster relief capacities and necessitate technical assistance from enterprises and governmental resources. $E_5(\mathrm{1,1},0)$ signifies that enterprises are actively engaged, while farmers remain passive; for instance, the utilization of agricultural machinery necessitates farmer collaboration, as unilateral acts cannot yield synergistic advantages. $E_6(\mathrm{1,0},1)$ signifies that enterprises decline to offer services despite government subsidies, which defies the logical pursuit of profit by entrepreneurs. $E_1(\mathrm{0,0},0)$ signifies that the government entirely assumes the expenses associated with disaster relief material distribution and loss compensation, agricultural service firms decline to offer services owing to inadequate subsidies, and farmers opt to “wait and depend on others” due to elevated participation costs. This exemplifies a government-directed disaster assistance framework. Following the floods in Henan on 20 July 2021, certain township governments solely coordinated drainage operations, businesses retracted due to insufficient profitability, and farmers expressed grievances regarding postponed reimbursement. $E_3\left(\mathrm{0,1},0\right)$ delineates a business-oriented disaster relief framework whereby agricultural service enterprises offer remunerated disaster mitigation services, local authorities curtail publicity owing to constrained financial resources, and smallholder farmers are unable to procure services due to insufficient income. $E_7(\mathrm{0,1},1)$ delineates a market-collaborative disaster relief framework wherein the government refrains from direct intervention, instead offering information and institutional safeguards, while enterprises participate proactively in disaster relief efforts, and farmers respond actively. An illustration is the “government oversight–insurance firm–cooperative” framework. Consequently, the selection of the $E_1(\mathrm{0,0},0)$ government-led disaster relief model, the $E_3\left(\mathrm{0,1},0\right)$ enterprise-led disaster relief model, and the $E_7(\mathrm{0,1},1)$ market-collaborative disaster relief model is congruent with the prevailing circumstances (

Table 5. Stability of each equilibrium of the three-way game.

Equilibrium Point	$\mathbf{Eigenvalue} {\mathit{\lambda }}_1$	$\mathbf{Eigenvalue} {\mathit{\lambda }}_2$	$\mathbf{Eigenvalue} {\mathit{\lambda }}_3$	Stability	Case
$E_1(\mathrm{0,0},0)$	$\times$	$\times$	$-$	Unstable point
$E_2(\mathrm{1,0},0)$	$\times$	$\times$	$-$	ESS	(1)
$E_3\left(\mathrm{0,1},0\right)$	$-$	$\times$	$\times$	ESS	(2)
$E_4(\mathrm{0,0},1)$	$\times$	$\times$	$+$	Unstable point
$E_5(\mathrm{1,1},0)$	$+$	$\times$	$\times$	Unstable point
$E_6(\mathrm{1,0},1)$	$+$	$\times$	$+$	Unstable point
$E_7(\mathrm{0,1},1)$	$\times$	$\times$	$\times$	ESS	(3)
$E_8(\mathrm{1,1},1)$	$+$	$\times$	$\times$	Unstable point

).

4. Simulation Analysis

4.1. Equilibrium Point Evolution Path Analysis

The stability analysis demonstrates three evolutionary paths for the game system. Thus, it is assumed that the values of the parameters under the three conditions are satisfied. Then, the evolutionary paths under different conditions are simulated and analyzed in MATLAB 2024b.

When $\alpha A-\gamma K<0$ and $\beta J+\gamma K+\Delta P-C<0$, the parameter values are set as follows: α = 0.4, A = 10, γ = 0.5, K = 20, β = 0.5, J = 10, ∆P = 10, C = 30, δ = 0.4, B = 10, θ = 0.4, and R = 20. In addition, the initial strategy probability of the three-party is 0.5, as illustrated in Figure 5. The final evolutionary and stabilization results are (1, 0, 0), implying that agricultural service enterprises and farmers choose to participate negatively under the government-led disaster relief model, attributed to insufficient benefits or high costs. With the purpose of promoting a more efficient disaster relief synergistic mechanism, the government needs to curtail the participation costs of all parties through policy support and gradually guide the development of market-based mechanisms.

When $\Delta P-C>0$ and $\Delta P_c-\left(\delta B+\theta R\right)<0$, the parameter values are set as follows: α = 0.4, A = 10, γ = 0.5, K = 20, β = 0.5, J = 50, ∆P = 30, C = 10, δ = 0.5, B = 10, θ = 0.5, R = 20, and $\Delta = 1$0. Moreover, the initial strategy probability of the tripartite is 0.5, as exhibited in Figure 6. In the agricultural service enterprise-dominated disaster relief model, the government and farmers choose to participate negatively because of insufficient benefits or high costs. This model is more common in areas with a high degree of agricultural industrialization or limited government resources. With the purpose of promoting a more efficient disaster relief coordination mechanism, the government should optimize the market-based operation of agricultural service enterprises through policy support while lowering the participation costs of farmers to increase their motivation.

When $\Delta P-C-T>0$ and $\Delta P_c-\left(\delta B+\theta R\right)>0$, the parameter values are set as follows: α = 0.4, A = 10, γ = 0.5, K = 20, β = 0.5, J = 50, ∆P = 95, C = 80, δ = 0.4, B = 10, θ = 0.4, R = 20, T = 10, and $\Delta P_c$= 20. In addition, the initial strategy probability of the three parties is 0.5, as presented in Figure 7. In the market-based collaborative disaster relief model, agricultural service enterprises and farmers are the main participants in disaster relief, while the government chooses not to intervene directly. This model is more common in regions with a high degree of agricultural industrialization or a well-developed market-oriented mechanism. To promote a more efficient disaster relief coordination mechanism, the government should optimize the market-based operation of agricultural service enterprises and farmers through policy support while strengthening policy support and supervision to ensure that disaster relief can be performed effectively.

4.2. Sensitivity Analysis

The public abstract of the “Report on the Development of Agricultural Socialized Services (2023)” [48] and industry empirical data provide the foundation for the values of important parameters (∆P, C, etc.), as described in

Table 6. Parameter data.

Parameters	Sign	Retrieve Value	Reasonable Range	Data Sources
Cost of agricultural disaster relief services	$C$	80	[80, 150]	Cost of hosting routine pest control 80–120 CNY/acre
Incremental corporate earnings	$\Delta P$	95	[30, 100]	Profit on basic services 30–50 CNY/acre, government subsidy 30–80 CNY/mu
Government subsidy benchmarks	$J$	50	[50, 80]	Henan wheat flooding special subsidies 50 CNY/mu, Heilongjiang corn frost subsidies 80 CNY/mu
Farmers concerned about costs	$B$	10	[5, 20]	Discounted average time cost for farmers to obtain disaster information CNY 10/household

.

In practical applications, the market-based coordinating approach is increasingly prevalent. The government employs a non-interventionist but not laissez-faire strategy, utilizing parametric governance (dynamic subsidies β and credit penalties T) to convert administrative authority into “invisible market rules,” thereby attaining a system equilibrium where enterprises are profitable, farmers engage in active oversight, and disaster relief is both efficient and sustainable (

Table 7. ∆P and C selection analysis.

$\Delta \mathit{P}$$, \mathit{C}$	Examples of Parameters	System Equalization	Current Situation
$\Delta P>C+T$	$\Delta P=95$, $C=80$, $T=10$	$(\mathrm{0,1},1)$	Market synergy model with proactive disaster relief by companies and active participation by farmers
$\Delta P$ ≈ $C$	$\Delta P=100$, $C=95$	$(\mathrm{0,1},0)$	Enterprises operate on low profits, farmers are forced to participate due to low returns, and collaboration deteriorates
$\Delta P<C$	$\Delta P=40$, $C=100$	$(1,0,0)$	Businesses pull out of disaster relief (negative actions), government forced to intervene at high cost, return to government-led model

).

The values of the parameters under stability condition 3 are selected, and the sensitivity analysis of the gaming system is conducted based on the stability point (0,1,1), so as to study the synergistic mechanism model of agricultural disaster relief with the participation of three parties.

(1)

Advocacy Leads to Cost Sensitivity Analysis

The influence coefficients of the publicity and guidance cost are set as 0.2, 0.5, and 0.7. The publicity and guidance cost is changed through the influence coefficient of the publicity and guidance cost. The influence of the change in the publicity and guidance cost on the strategy selection of each subject is explored, and the evolution results are illustrated in Figure 8.

(2)

Sensitivity analysis of cost-sharing expenditures

The cost-sharing expenditure influence coefficients are set as 0.1, 0.3, and 0.7. The cost-sharing expenditure is changed through the cost-sharing expenditure influence coefficient. The impact of the change in the cost-sharing expenditure on the strategy selection of each subject is explored, and the evolution results are depicted in Figure 9.

(3)

Cost sensitivity analysis of the implementation of penalty mechanisms

The penalty mechanism implementation cost impact coefficients are set as 0.2, 0.5, and 0.8. The cost-sharing expenditure is changed through the penalty mechanism implementation cost impact coefficient. The penalty mechanism implementation cost change on each subject strategy selection impact is explored, and the evolutionary results are presented in Figure 10.

The cost sensitivity analysis of the implementation of publicity and guidance costs, cost-sharing expenditures, and punishment mechanism suggests that the three changes have less impact on the main strategy choices of the government, agricultural service enterprises, and farmers under the stability point (0, 1, 1) and only alter the evolution rate of the game system but not the final evolution results of the game system. The evolution results of the system reveal strong robustness to the changes in the three coefficients. Under the market-based collaborative disaster relief model, the active participation of agricultural service enterprises and farmers is not affected by the government’s cost of consumption, which will only change the evolution rate of the participation of agricultural service enterprises and farmers. However, the participation decision of agricultural service enterprises and farmers depends more on the market-based mechanism. Concerning agricultural service enterprises and farmers, agricultural service enterprises and farmers can still obtain sufficient benefits through market-based mechanisms to maintain their participation incentives, no matter how the government’s publicity and guidance costs, cost-sharing expenditures, and the implementation costs of penalty mechanisms change. The government should take measures to lower the cost consumed by its agricultural service enterprises and farmers to participate in disaster relief and increase their revenue to further stabilize the tripartite strategy options (the government’s passive laissez-faire strategy, agricultural service enterprises' positive action in disaster relief, and farmers’ active participation in disaster relief).

(4)

Cost Sensitivity Analysis of Farmers’ Attention Behavior

The costs of farmers’ attention behavior are set at 10, 25, and 40. The influence of the change in farmers’ attention behavior cost on the strategy selection of each subject is explored, and the evolution results are exhibited in Figure 11.

The increase in the cost of farmers’ attention behavior changes both the evolution rate of the game system and the final evolution result of the game system. When the cost of farmers’ attention behavior is too high, the stability point of the game system is changed from the point of (0,1,1) to the point of (0,1,0), and the set of game strategies is altered from (passive laissez-faire, active action, active disaster relief) to (passive laissez-faire, active action, passive disaster relief). Additionally, the cost of farmers’ attention behavior is the crucial driving factor of the three-party synergy, and the high cost of attention inhibits farmers’ willingness to participate and reduces the efficiency of the three-party synergy. The government should lessen the cost of farmers’ attention or raise the benefits of participation to promote the active participation of farmers. For agricultural service enterprises, the negative participation of farmers may affect their long-term profitability.

(5)

Cost sensitivity analysis of farmers’ complaint behavior

The cost of farmers’ concern behavior is set as 10, 30, and 50 to explore the impact of the change in farmers’ complaint behavior cost on the strategy selection of each subject, and the evolution results are depicted in Figure 12.

The increase in the cost of farmers’ complaint behavior changes both the evolution rate of the game system and the final evolution result of the game system. When the cost of farmers’ complaint behavior is too high, the stability point of the game system is changed from the point of (0, 1, 1) to (0, 1, 0), and the set of game strategies is altered from (passive laissez-faire, positive action, active disaster relief) to (passive laissez-faire, positive action, negative disaster relief). The complaint behavior of farmers is a vital method to monitor the behavior of agricultural service enterprises and protect their own rights and interests. When the cost of complaints is low, farmers are more willing to solve problems through complaints, promoting agricultural service enterprises to provide high-quality products and services. Under too high a cost of complaints, farmers tend not to complain or even choose negative approaches such as non-participation, bringing about a decline in the efficiency of tripartite synergy. The government could lessen the cost of farmers’ complaint behavior by simplifying the complex complaint process and promoting active participation by farmers.

(6)

Sensitivity analysis of the cost of participation in disaster relief by agricultural service firms

The cost of participation of agricultural service enterprises in disaster relief is set at 80, 90, and 100 to explore the impact of changes in the cost of participation of agricultural service enterprises in disaster relief on the strategy choice of each subject. The evolution results are illustrated in Figure 13.

The increase in the cost of agricultural service enterprises to participate in disaster relief changes both the evolution rate of the game system and the final evolution result of the game system. When the cost of agricultural service enterprises to participate in disaster relief is too high, the stability point of the game system is changed from the point of (0, 1, 1) to the point of (1, 0, 0), and the set of game strategies is altered from (passive laissez-faire, active action, active disaster relief) to (active support, passive action, negative disaster relief). The active participation of agricultural service enterprises in disaster relief is a crucial means to improve agricultural disaster resilience and protect the interests of farmers. Under low costs of participation, agricultural service enterprises are more willing to act, contributing to promoting the active participation of farmers and government incentive policies. Under high costs of participation, agricultural service enterprises are reluctant to act, and farmers are more passive because the inaction of agricultural service enterprises curtails the benefits of farmers. Then, the government should introduce incentives to drive the participation of all parties.

4.3. Collaborative Disaster Response Strategy

(1) Under the government-led disaster relief model, the government incentivizes agricultural service enterprises and farmers to actively participate in disaster relief through publicity and guidance and cost sharing, but the participation costs of agricultural service enterprises and farmers are too high. Simultaneously, the evolution path stabilizes in the equilibrium state of positive government support and negative participation of agricultural service enterprises and farmers (1, 0, 0). Therefore, the willingness of agricultural service enterprises and farmers to participate is low. The government should curtail the participation cost of agricultural service enterprises and farmers through policy support, such as subsidies and tax incentives, to reduce the participation cost of agricultural service enterprises and improve the disaster relief benefits of farmers. In this way, the willingness of farmers to participate is enhanced, and the development of market-based mechanisms is stimulated.

(2) Under the agricultural service enterprise-led disaster relief model, when agricultural service enterprises obtain higher returns by improving the supply of agriculture-related products and services, the participation costs of the government and farm households are too high. Meanwhile, the evolution path stabilizes in the equilibrium state of negative government laissez-faire, positive agricultural service enterprises, and negative farm households in disaster relief (0, 1, 0). This model is more common in areas with a high degree of agricultural industrialization. The government needs policy support to optimize the market-oriented operation of agricultural service enterprises while lowering the participation cost of farmers and improving their motivation.

(3) In the market-based collaborative disaster relief model, agricultural service enterprises and farmers obtain benefits through the market-based mechanism, and the evolution path tends towards an equilibrium state where the government is passive and laissez-faire, agricultural service enterprises are active, and farmers are active in disaster relief (0, 1, 1). This pattern is more common in regions with high degrees of agricultural industrialization or a perfectly market-oriented mechanism. The government should optimize the market-oriented operation of agricultural service enterprises and farmers through policy support to stimulate the development of the market-oriented collaborative disaster relief model. For example, effective cooperation between agricultural service enterprises and farmers can be facilitated by strengthening market regulation and providing an information-sharing platform.

(4) The cost of farmers’ concern and complaint behavior is a crucial driver of tripartite synergy. When the cost of farmers’ concern and complaint behavior is too high, the stability point of the game system is changed from (0, 1, 1) point to (0, 1, 0), and the set of game strategies is altered from (passive laissez-faire, active behavior, active disaster relief) to (passive laissez-faire, active behavior, passive disaster relief). As a result, the efficiency of the three-party synergy decreases. The government should optimize the complaint process of farmers, lower their costs, and encourage farmers to supervise the service quality of agricultural service enterprises through complaint behavior. Agricultural service enterprises should establish corporate responsibility, accept the supervision of farmers, and guarantee the provision of high-quality products and services in the process of disaster relief, enabling farmers to quickly resume production and promoting the sustainable development of agriculture.

(5) The increase in the cost of participation in disaster relief by agricultural service enterprises affects the evolution path of the gaming system. When the participation cost is too high, the system changes from the equilibrium state (0, 1, 1) (in which the government is passive and laissez-faire, agricultural service enterprises are active, and farmers are active in disaster relief) to the equilibrium state (1, 0, 0) (in which the government is active in supporting, agricultural service enterprises are passive, and farmers are passive in disaster relief). Agricultural service enterprises should curtail the cost of participating in disaster relief through technological innovation and management optimization, such as research and development of intelligent agricultural equipment and promotion of green agricultural equipment. This ensures that they can provide high-quality products and services at reasonable prices during the disaster relief process, reduce the economic burden on farmers, and allow farmers to actively participate. The government should lower the participation costs of agricultural service enterprises through subsidies and other means to promote their active participation in disaster relief.

5. Discussion

5.1. Theoretical Breakthroughs and Practical Significance

This study departs from the conventional “government–farmer” binary analytical framework and innovatively integrates agricultural service enterprises as autonomous strategic entities, effectively illustrating the composite organizational model of “small-scale farmers + modern agricultural services” that has arisen during China’s agricultural transformation towards “scaling up, mechanization, and marketization” [21]. This framework elucidates the dual hub function of service enterprises: (1) linking governmental disaster relief resources with geographically dispersed farmers while offering specialized services (such as post-disaster pest control and agricultural machinery repairs) and (2) mitigating disaster relief expenses through supply chain coordination (such as ΔP enhancement), thus rectifying the deficiencies of governmental vertical management. Research indicates that neglecting the autonomous interests of enterprises, exemplified by passive involvement stemming from inadequate subsidies in government-led frameworks, constitutes the fundamental structural cause of inefficiency in conventional disaster relief procedures. The three-dimensional paradigm provides a novel approach for tackling the coexistence of “government failure” and “market failure”.

5.2. Collaborative Practices with China’s National Emergency Response System Plan

The “incentive–constraint–information” paradigm introduced in this study strongly coincides with the primary objectives of the “14th Five-Year Plan for the National Emergency Response System” [49] (

Table 8. Integration of the National Emergency Response System Planning Framework for the 14th Five-Year Plan.

Framework Dimensions	Policy Instruments of the Model	National Planning Responses	Synergistic Effect
Incentive	Dynamic subsidy	Subsidy mechanism for social participation in disaster relief	Reduce business costs
	Skills training for farmers	Grassroots Emergency Response Capacity Enhancement Project	Increasing farmer participation
Restriction	Farmer Complaints—Business Penalties	Social Force Credit Supervision System	Curbing corporate opportunism
Information	Matching supply and demand for services	Disaster Information Sharing Platform	Reduction in information asymmetry

). Practically, the ‘incentive’ dimension (e.g., dynamic subsidies, profit sharing) seeks to enhance the cost–benefit framework of entities; the ‘constraint’ dimension (e.g., differentiated rewards and penalties, performance oversight) aims to govern entity conduct and deter opportunistic behavior; the ‘information’ dimension (e.g., aligning service supply with demand) strives to mitigate information asymmetry and improve decision-making efficacy and supervisory competence. For instance, the Henan “Yushi Ban” application merged governmental, commercial, and agricultural components during the 2023 floods, facilitating the government in disseminating subsidy policies, businesses in promoting service listings, and farmers in lodging complaints with a single click, thus enhancing disaster relief efficiency by 40% relative to conventional models. The essence of three-dimensional coordination involves employing a blend of policy instruments, dynamically modifying game parameters, and steering the system towards an optimal equilibrium state (0, 1, 1), facilitating a transition from dependence on government “passive emergency response” to fostering market and social forces for “active coordination.”

5.3. Comparative Innovation with International Disaster Coordination Models

The United States predominantly uses a hybrid approach that combines market forces with governmental administrative processes. In reaction to agricultural calamities, the United States predominantly depends on the government and large-scale farmers, employing fixed premium subsidies, while farmers directly litigate against the government for breach of contract [50]. This paper presents a model that facilitates collaboration between the government, agricultural service enterprises, and farmers to tackle the issues arising from the fragmentation of small-scale farmers, allowing for real-time adjustments to subsidies to improve disaster relief efficiency and minimize costs (

Table 9. Comparison of this model with the US disaster coordination model.

Dimension	This Model	US Agricultural Disaster Collaboration Model	Innovation
principal party	Government, agricultural service companies, farmers	Government, large-scale farmers	Introducing agricultural service companies as hubs to solve the dilemma of smallholder fragmentation
motivation	Dynamic subsidies linked to market returns	Fixed premium subsidy	Dynamic adjustment of subsidies
constraint	Farmers’ complaints lead to a decrease in corporate orders	Farmers directly sue government for breach of contract	Reduce regulatory costs
information	Government disaster data, list of business services, farmer feedback	NOAA weather data, insurance companies	Farmers’ complaints directly reduce corporate profits
adaptability	Areas dominated by small-scale farming Limited government finances	Large-scale agricultural areas High legal costs environment	Universal applicability in lower-income countries

).

The methodology utilizes a three-pronged strategy to offer smallholder-centric economies a highly flexible, cost-effective solution for catastrophe coordination. The fundamental innovation consists of transforming the conventional “government–market” dual structure into a three-dimensional dynamic system that includes “policy incentives, market efficiency, and social oversight”.

5.4. Limitations of the Model and Future Research

(1) While decision-makers typically modify their methods according to cost–benefit analysis, disaster emergencies frequently entail time constraints, informational deficiencies, and emotional strain (including fear and herd behavior), potentially leading to decisions that diverge from the concept of “bounded rationality”. Farmers could adopt suboptimal practices due to psychological trauma following disasters and may forgo disaster relief initiatives, whereas governments may hastily implement costly solutions in response to public pressure, contravening the concept of cost minimization. (2) Static parameter configurations fail to accurately replicate the effects of exogenous shocks on system equilibrium. The progression of disasters is characterized by significant uncertainty (e.g., secondary disasters, market price volatility), which can abruptly modify the cost–benefit framework.

In future research, introducing a loss aversion coefficient to modify the utility function under crisis conditions can capture irrational decision-making behavior during crises. In the original model, when $\Delta P_c>\delta B+\theta R$, the ESS is (0, 1, 1). In the market coordination model, introducing a loss aversion coefficient λ, if farmer panic causes the loss aversion coefficient λ to increase, the actual perceived cost becomes λ(δB + θR). When $\Delta P_c<\lambda (\delta B+\theta R)$, the ESS degrades to (0, 1, 0), with firms proactive and farmers passive.

Incorporate random perturbations to simulate external shocks (e.g., Monte Carlo methods) and the impact of external shocks on the system equilibrium and test the system’s robustness. Secondary disasters may instantly increase a company’s disaster recovery costs C or reduce its revenue ΔP, thereby disrupting the original equilibrium condition ΔP−C−T > 0. If, after the shock, ΔP−C−T < 0, ESS changes from (0, 1, 1) to (1, 0, 0). Define the probability distribution of key parameters (C, ΔP, T) (e.g., C∼Normal(80,102)), generate ${10}^4$ random parameter combinations, and simulate the evolutionary path. Calculate the proportion $\rho$ of ESS as (0,1,1). If $\rho$ > 70%, the system is robust. If ρ < 50%, trigger the dynamic subsidy mechanism: the government automatically increases βJ to raise the probability of ΔP−C−T > 0.

6. Conclusions and Implications

In this paper, the strategic interaction law of each subject in the collaborative mechanism of agricultural disaster relief and its evolutionary path are systematically analyzed by constructing a tripartite evolutionary game model of the government, agricultural service enterprises, and farmers. The main conclusions are drawn as follows.

(1)

Low efficiency of the government-led model and the need to optimize the incentive structure

Under the government-led disaster relief model, the government actively promotes collaborative disaster relief through policy incentives. Nevertheless, due to the high cost of participation of agricultural service enterprises and farmers, their motivation is still insufficient, and the final system tends towards the equilibrium state of unilateral input by the government and passive participation of other main bodies. This involves optimizing the incentive structure, lowering the threshold of participation, and increasing the willingness of the main bodies to participate in the long term through the benefit-sharing mechanism.

(2)

More sustainable and efficient market-oriented synergistic mode

Under the market-based synergy model, agricultural service enterprises gain revenue by providing specialized services, and farmers curtail losses and improve production recovery efficiency by actively responding to disasters. This model is particularly prominent in regions with a high degree of agricultural industrialization and a sound market mechanism. In other words, market-driven resource allocation can respond to disasters more efficiently while lessening the government’s financial burden. In the future, financial instruments such as insurance and credit can be combined with market-based disaster relief mechanisms to further enhance their sustainability.

(3)

Reducing farmers’ participation costs is the key to improving synergistic efficiency

The cost of farmers’ attention and complaint behavior exerts a significant impact on the effectiveness of collaborative disaster relief. When the cost of disaster relief is too high, farmers tend to respond negatively, bringing about the degradation of the system from efficient to inefficient coordination. Therefore, the government should optimize the complaint handling process to reduce the cost of its participation while improving farmers’ disaster response capacity through training. Additionally, the establishment of a feedback mechanism for farmers to ensure that their demands can directly influence policy adjustments further enhances their motivation to participate.

(4)

The cost of agricultural service enterprises affects the stability of synergy, and policy support is needed.

The participation cost of agricultural service enterprises directly affects their motivation for disaster relief. When the cost exceeds the benefit, enterprises choose to act negatively, forcing the government to re-engage and the system to return to the government-led model. With the purpose of maintaining market-based synergy, the government can lower enterprise costs through R&D subsidies and tax breaks while encouraging technological innovation to improve the efficiency of disaster relief, forming a virtuous cycle.

(5)

Dynamic Policy Tools Can Optimize Multi-Body Synergy Mechanisms

While static policies are difficult to adapt to the complexity and dynamic characteristics of disasters, flexible policy tools such as differentiated rewards and punishments, dynamic subsidies, and information sharing can more effectively guide the behavior of various subjects. The government adjusts cost sharing according to the severity of the disaster or shares disaster data in real time through information platforms to assist enterprises and farmers in optimizing their decision making. In the future, big data and artificial intelligence technologies can be combined to realize the precision and dynamization of policy tools and further strengthen synergistic efficiency.