Multiple Subject Behavior in Pest and Disease Control Outsourcing from the Perspective of Government Intervention: Based on Evolutionary Game and Simulation Analysis

Abstract

Pest and disease control outsourcing has become an effective means to restore damaged arable land and guarantee agroecological benefits. However, it is adopted at a relatively low rate in China. The purpose of this study is to explore, from the perspective of government intervention, behavioral logic, and the game relationship among farmers, service organizations and the government in the pest and disease control outsourcing system as well as the endogenous motivation of each subject. The results indicate that when the degree of policy implementation is low, the government’s policy is ineffective, but, after reaching a certain level, the higher the degree of policy implementation is, the stronger the farmers’ willingness to choose outsourcing control and the service organizations’ willingness to provide positive control services are, and the faster the stable state of tripartite joint pest and disease control is formed. In the case of implementing a single policy tool, the convergence rate of each party that implements the regulatory policy alone is fast but may be unstable, while the rate is slow but more stable when a guidance- or incentive-based policy is solely applied. The effect of a combination of policy tools being applied is much better than that of a single policy tool being applied. The simultaneous implementation of the three types of policy tools can form a policy system with both positive and negative mechanisms, which can maximize the complementary and superposition effects.

1. Introduction

For over 70 years, China has been faced with the increasing severity of pest disasters, together with a rise in pest species, and there is a tendency that the occurrence of pest damage grows more intense [1]. As an important production factor to control agricultural pests and diseases, chemical pesticides have played an indelible role in recovering agricultural losses and ensuring stable and abundant yields. However, due to decentralized operations and limited awareness and capabilities, small farmers are unable to master the professional knowledge required for pesticide application, which leads to widespread pesticide abuse [2]. As revealed by the Ministry of Agriculture and Rural Affairs, the utilization rate of pesticides in China’s three staple foods was 40.6% in 2020 (data source: the website of the Ministry of Agriculture and Rural Affairs: http://www.moa.gov.cn/xw/bmdt/202101/t20210119_6360102.htm, accessed on 18 April 2023). China is the world’s largest producer and consumer of pesticides [3], but its long-term excessive and inefficient use of pesticides has aggravated agricultural non-point source pollution, which has undermined the quality of arable land and the health of workers and eaten away at social welfare from agricultural economic growth [3]. Moreover, a series of risk hazards, such as produce quality and safety and ecological environment degradation, have been induced [4]. Practical dilemmas, such as “pesticide overdependence” and “increasing ecological imbalance”, need to be solved urgently. Exploring effective countermeasures for pesticide reduction and efficiency has become an urgent task for the high-quality development of agriculture and the transformation to green production.

With the gradual deepening of specialized labor division, the separability of agricultural production and management activities has been continuously enhanced, and the development of producer services has offered a new path to help pesticide reduction and increase efficiency. Compared with individual farmers, pest and disease control outsourcers have a stronger ability to collect and screen essential information [5], for they are better equipped with professional pesticide application techniques and devices [6]. At the same time, pest and disease control outsourcing (hereafter referred to simply as PDCO) can regulate application behaviors and reverse excessive pesticide use [5,7]. Therefore, the PDCO has now become an effective means to restore damaged arable land and guarantee agroecological benefits. However, PDCO is characterized by complexity and effect uncertainty [8]. The PDCO has been adopted at a relatively low rate, which was about 42.4% coverage for the three major food crops in 2021 (data source: Farmers Daily Edition 001, 31 August 2022). While governments at all levels pour in a lot of resources and energy to make up for the shortcomings of producer services, they are constrained by different demands and the behavior-oriented conflicts of all interest subjects; the development of PDCO is consequently sluggish, making it difficult for it to play its role in ensuring produce quality and safety and consolidating ecological benefits. Based on the above situation, the clarification of the behavioral logic and game relationship among the government, service organizations, and farmers in the PDCO system can help to break the practical dilemma and accelerate the popularization and application of modern pest and disease control measures.

Recent discussions between the government and academic circles focused on how the restraining effect of existing policies can be fully exerted on the production behavior of relevant subjects and how such policies can promote the transformational mode of modern agriculture, namely, from the extensive pattern, which relies on chemical elements, to the green and high-quality production mode. There is a relative lack of research results at home and abroad on the outsourcing behaviors of pest and disease control based on the policy level. Within such a context, this research tries to review the situation from the following three aspects:

Firstly, in terms of pesticide application behavior, the established results, which aimed at a single guidance-based policy [9,10,11], regulatory policy [12,13], and incentive-based policy [14], analyzed the ameliorative effects of farmers’ excessive pesticide application and confirmed that the above policies were particularly important for regulating safe application behaviors. In addition, some scholars tried to reveal the superposition effect of various policies by incorporating them into a unified framework, but they generated mixed findings. Skevas et al. explored the effects of regulatory and incentive-based policies, confirming that only regulatory policies slightly reduced pesticide application by Dutch growers [15]. Hruska and Wang et al. found that regulatory, guidance-, and incentive-based policies all regulate farmers’ application behaviors [16,17]. Huang et al. found that there were differences in the effects of various policies, among which guidance-based and command-and-control policies were able to regulate farmers’ label reading before application and their behaviors during application, respectively, while incentive-based policies had significant effects on the entire application process [18].

Secondly, for the outsourcing of agricultural production, its rapid development is inseparable from government regulation and policy norms [19,20,21]. However, prominent problems were found in the recent outsourcing of agricultural production, such as weakened incentives in the operation process [22]. In this regard, many scholars analyzed the boosting of outsourcing behaviors by using incentive-based policies, and Zhang and Du confirmed the positive role of subsidy tools in promoting productive service choices of family farms when the market development is at a low state [23]. Jiao and Liu and Han et al. agreed that subsidies for key production links could effectively enhance the participation behavior of land trusts. In addition, some scholars also focused on the impact of guidance-based policies on the outsourcing of agricultural production chain [24,25]. Wang and Li believed that the government’s formulation of such policies could strengthen the decisive role of market mechanism in the agricultural service system [26]. Duan et al. found that government technical training had facilitated farmers’ adoption of topdressing outsourcing service but inhibited seeding outsourcing [27].

Thirdly, by focusing on PDCO, many scholars verified the positive effects of farmers’ participation in social services on pesticide reduction behaviors through empirical studies [5,7,28,29,30] and put forward policy suggestions to promote farmers’ adoption of outsourcing based on their respective priorities. For example, Ying and Xu stressed the need to strengthen training and guidance for professional farmers in pest and disease control [7]. Sun et al. suggested that incentives should be provided to large-scale farmers, while highlighting the need to ensure relevant government subsidies should be transferred to farmers rather than outsourcing organizations [28]. However, the existing literature rarely addressed the mechanisms of government and related policies on outsourcing behaviors in agricultural pest and disease control. Duan et al. only introduced the variable of “whether or not to receive technical training” when exploring the factors influencing the outsourcing in technology-intensive links, but the results showed that the guidance policy for technical training provided by the government had no effect on the adoption of outsourced pest and disease control services by farmers [27]. Zheng and Zhao, based on the conventional game analysis framework, confirmed that the government’s intervention in the pest risk control system could effectively reduce the cost of pest and disease control for all parties. In addition, the study found that subsidies or penalties could regulate outsourcing organizations’ market behaviors [31].

To sum up, the existing academic results provide a useful reference for this study to explore governmental actions in PDCO, but there is still room for more exploration. Firstly, the studies on PDCO often ended up with policy recommendations, failing to evaluate the effects of various policies. Secondly, the existing literature focused on the behavioral responses of farmers, but few researchers included government, service organizations, and farmers into the same analytical framework, inevitably causing a lack of related research on modern pest and disease control systems. Thirdly, each game player constantly improves its own strategy through dynamic cost-benefit adjustment, but traditional game studies ignored such a dynamic process, so the picture of the change process of each player’s strategy at different policy levels tends to become ambiguous. In view of this, this study attempts to extend the above studies. Firstly, based on the scientific division of the different control policy tools for PDCO, the mechanism of these policies on PDCO is to be clarified. Secondly, from the perspective of an effective control subject, the dynamic relationship of the tripartite game model, which consists of a government, outsourcing organizations, and farmers, for PDCO and the equilibrium stability of the strategy combination are to be constructed, together with further exploration into the endogenous motivation of each subject in PDCO. Finally, numerical simulation analysis is conducted to obtain the dynamic mechanism for the different amounts of initial willingness of all subjects and for different combinations of policy tools on these subjects, in order to deeply reveal the evolutionary characteristics of the decision-making behaviors of the multiple interest subjects in China’s agricultural pest and disease control system, thus hopefully providing theoretical reference for the construction of a policy system for efficient PDCO.

2. Materials and Methods

2.1. Analysis of the Path and Mechanism of Policy Tools to Regulate PDCO

PDCO involves three subjects: farmers, service organizations, and the governments, and a logical relationship is formed among the stakeholders, as shown in Figure 1. Firstly, farmers, who are decision makers of pesticide application, are not sensitive to the perception of ecological benefits in pest and disease control but weigh the economic benefits to determine application amount and operation mode. Secondly, agricultural socialized service organizations, as the promotion subject of PDCO, face the constraints of asset specificity and professional and technical levels of their service personnel, and they are prone to breed “opportunistic behaviors” when considering the goal of maximizing their operating benefits in actual service process. In addition, the government plays a vital role in regulating farmers’ use of chemical inputs [16]. In order to ensure the quality and safety of agricultural products and protect the ecological environment, the government has implemented a number of policy tools to promote outsourcing services for pest and disease control.

The essential attribute of regulation exists in its “binding nature” [32]. According to related research conducted by Zhao et al. [32], Wang et al. [17], and Huang et al. [18], combined with actual policy measures implemented by the Chinese agricultural and rural authorities in PDCO, the policy tools implemented by the government are classified into three types according to impact path and mechanism setting of policy tools, with the regulatory path and mechanism shown in Figure 2.

The first type is guidance-based policy. The government implements a guidance-based policy to provide technical guidance, training, publicity, and education to farmers and service organizations, so both can develop their production awareness and master production techniques. In doing so, the government can effectively transmit information to strengthen the awareness and participation of farmers and organizations in outsourcing agricultural pest and disease control. In 2020, Premier Li Keqiang signed the Decree of the State Council, requiring relevant departments at or above the county level to provide technical training and guidance for specialized pest and disease control service organizations in the published Regulation on the Prevention and Control of Crop Disease and Pests. In December 2022, the Ministry of Agriculture and Rural Affairs of the People’s Republic of China held a national video training course on the prevention and control of wheat and rape diseases and insect pests, aiming to enhance the awareness and knowledge skills of grassroots agricultural technicians and farmers and improve the prevention and control capacity.

The second type is incentive-based policy. Such policies are implemented with an aim to provide market-based incentives to organizations and farmers to change relative prices of production factors, to generate income effects, and ultimately to choose control methods as advocated by the government. Farmers’ adoption of positive pest and disease control services provided by service organizations can produce environmental effects, which can be shared by others, and some economists, who follow Pigou’s tradition, advocate government intervention and subsidies to internalize the positive externalities of environmental improvements [33]. If the organization provides positive PDCO services, it needs to purchase more professional equipment and machinery, equip higher quality service personnel, and invest more time and energy into the service. The government provides corresponding machinery purchase subsidies or loan subsidies for the positive control services of the organization. If farmers purchase PDCO services, the government provides incentives for farmers’ outsourcing control attitude and provides corresponding service subsidies or pesticide subsidies to farmers. In 2017, the state introduced the subsidy policy for agricultural production trusteeship, which was intended to be an incentive tool, with the aid of subsidy, to make up for the weakness of agricultural production trusteeship [25].

The third type involves regulatory policy. Such policies regulate the non-standard conduct of the subjects through coercive means, which, in return, urge them to participate in modern pest and disease control. Under the decentralized management pattern, there are a large number of small farmers in China, and the non-point source pollution caused by pesticide application by the farmers is in a hidden and scattered state, so it is difficult and costly for the government to control it [34]. Therefore, considering the difficulties in practical governance, regulatory policies in this study are only used to regulate service organizations. When a service organization provides negative services, the government charges a fine for it, restrains its negative service behavior by increasing the service cost of the organization, and promotes the organization to provide positive and effective services in the reverse direction. However, negative prevention and control services provided by organizations that were regulated and punished are considered as uncertain events. The reason is that the information on ineffective services of the organizations cannot be easily accessible in a timely and effective manner. In addition, due to economic performance assessment, some village leaders may ignore or shield unscientific pesticide application by service organizations.

2.2. Problem Description and Model Setting

Classical game theory requires acting subjects to be fully rational and to have complete information when making decisions, but that is difficult to obtain in reality. Evolutionary game theory is different from classical game theory in that it focuses on static equilibrium and comparative static equilibrium but emphasizes dynamic equilibrium. Therefore, in evolutionary game theory, participants are not required to be completely rational, and the conditions of complete information are not required. This study assumes that farmers, outsourcing organizations, and the government all have bounded rationality. All three stakeholders have two behavioral strategies; among them, farmers can choose outsourcing control or self control, which is recorded as $\left(\mathrm{H}, \overline{\mathrm{H}}\right)$; a service organization can provide positive or negative pest and disease control services, which is recorded as $\left(\mathrm{S}, \overline{\mathrm{S}}\right)$; and a government behavior strategy involves the application or non-application of policy tools, which are noted as $\left(\mathrm{A}, \overline{\mathrm{A}}\right)$. It is assumed that the total number of farmers, service organizations, and local governments remains relatively stable in a given region. At time T, the probability of farmers choosing outsourcing control strategy is $\mathrm{X}$, and $0\le \mathrm{X}\le 1$; the probability of the service organization choosing active control service strategy is $\mathrm{Y}$, and $0\le \mathrm{Y}\le 1$; and the probability of the local government choosing to apply policy tools and strategies is $\mathrm{Z}$, and $0\le \mathrm{Z}\le 1$.

2.2.1. Setting of the Profit and Loss Variables for the Farmers

When farmers control pests and diseases on their own, the cost and the benefit are ${\mathrm{C}}_{\mathrm{F}}$ and ${\mathrm{B}}_{\mathrm{F}}$, respectively, and ${\mathrm{B}}_{\mathrm{F}}>{\mathrm{C}}_{\mathrm{F}}$. If farmers purchase outsourced services, they need to pay service fees, ${\mathrm{S}}_{\mathrm{F}}$. If positive services are purchased, they help to scientifically apply pesticides, thus promoting the improvements in crop yield and quality, and helping to improve farmers’ production efficiency, at which point farmers gain additional benefits, $\Delta {\mathrm{B}}_{\mathrm{F}} \left(\Delta {\mathrm{B}}_{\mathrm{F}}>{\mathrm{S}}_{\mathrm{F}}\right)$, while no additional benefits are gained if negative services are purchased.

2.2.2. Setting of the Profit and Loss Variables for the Service Organization

When the service organization provides a negative service, the production and operation cost is ${\mathrm{C}}_{\mathrm{T}}$. If a positive service is provided, the production and operation cost increases on top of negative prevention and control, $\Delta {\mathrm{C}}_{\mathrm{T}}$. Regardless of the services provided, the organization benefits ${\mathrm{S}}_{\mathrm{F}}$ and gains ${\mathrm{C}}_{\mathrm{T}}+\Delta {\mathrm{C}}_{\mathrm{T}}<{\mathrm{S}}_{\mathrm{F}}$, as long as the farmer adopts the outsourced service. When a negative service is provided to and adopted by the farmer, the service organization suffers from reputational damage for providing such a service, ${\mathrm{R}}_{\mathrm{T}} \left({\mathrm{R}}_{\mathrm{T}}>\Delta {\mathrm{C}}_{\mathrm{T}}\right)$.

2.2.3. Setting of the Profit and Loss Variables for the Government

The cost for the government to implement the outsourcing control policy of pest and disease control is taken as ${\mathrm{C}}_{\mathrm{G}}$. In addition, when providing a guidance-based policy, the government provides technical promotion trainings, publicity, and education activities to outsourcing organizations and farmers by the units ${\mathrm{U}}_{\mathrm{T}}$ and ${\mathrm{U}}_{\mathrm{F}}$, respectively, with a unit input being $\mathrm{I}$, assuming that the benefits of the service organization and the farmer are equal to what the government contributes. When an incentive-based policy is provided, if the service organization provides positive services and the farmer purchases such outsourced control, the government offers both ${\mathrm{F}}_{\mathrm{T}}$ and ${\mathrm{F}}_{\mathrm{F}}$ subsidies, respectively. When providing a regulatory policy, if the outsourcing organization provides negative services, the government charges it the penalty, ${\mathrm{P}}_{\mathrm{T}}$, assuming ${\mathrm{P}}_{\mathrm{T}}>{\mathrm{S}}_{\mathrm{F}}$, and the probability of being regulated and penalized is $\mathrm{Q} \left(0<\mathrm{Q}<1\right)$. When the state introduces relevant policy tools, it needs to take into account pricing that does not affect market services, so this paper assumes ${\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}<{\mathrm{S}}_{\mathrm{F}}$. In addition, farmers’ adoption of positive control services provided by service organizations is beneficial to the improvement of ecological environment, and the government obtains ecological benefits, ${\mathrm{B}}_{\mathrm{E}}$. However, if the government fails to curb the negative control behavior of service organizations, the loss of trust and reputation from the public results. At this point of time, the total loss of the government is ${\mathrm{R}}_{\mathrm{G}}$, and ${\mathrm{R}}_{\mathrm{G}}>{\mathrm{C}}_{\mathrm{G}}$. When the three parties cooperate on pest and disease control, the special subsidies and incentives given by the superior government to the local government amount to $\mathrm{K}$.

2.3. Model Building and Strategy Solution

Based on the model hypothesis, the game payment matrix of three subjects involved in agricultural pest and disease control under different strategies is constructed from the perspective of government intervention, as shown in

Table 1. Benefit matrix of the game among farmers, service organizations, and the government.

Gaming Party				Government
				$\mathbf{Application} \mathbf{of} \mathbf{Policy} \mathbf{Tools} \left(\mathit{Z}\right)$	$\mathbf{Non}-\mathbf{Application} \mathbf{of} \mathbf{Policy} \mathbf{Tools} (1-\mathit{Z})$
Farmers	Outsourced prevention and control ($\mathrm{X}$)	Service organizations	Positive prevention and treatment services ($\mathrm{Y}$)	$\left(\mathrm{H}, \mathrm{S}, \mathrm{A}\right)$ $\left[\begin{array}{c}{\mathrm{B}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{F}}-{\mathrm{S}}_{\mathrm{F}}+\Delta {\mathrm{B}}_{\mathrm{F}}+{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}},\\ {\mathrm{S}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{T}}-\Delta {\mathrm{C}}_{\mathrm{T}}+{\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}},\\ {\mathrm{B}}_{\mathrm{E}}-{\mathrm{C}}_{\mathrm{G}}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}-{\mathrm{F}}_{\mathrm{F}}-{\mathrm{F}}_{\mathrm{T}}+\mathrm{K}\end{array}\right]$	$\left(\mathrm{H}, \mathrm{S}, \overline{\mathrm{A}}\right)$ $\left[\begin{array}{c}{\mathrm{B}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{F}}-{\mathrm{S}}_{\mathrm{F}}+\Delta {\mathrm{B}}_{\mathrm{F}},\\ {\mathrm{S}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{T}}-\Delta {\mathrm{C}}_{\mathrm{T}},\\ {\mathrm{B}}_{\mathrm{E}}\end{array}\right]$
			Negative prevention and control services ($1-\mathrm{Y}$)	$\left(\mathrm{H}, \overline{\mathrm{S}}, \mathrm{A}\right)$ $\left[\begin{array}{c}{\mathrm{B}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{F}}-{\mathrm{S}}_{\mathrm{F}}+{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}},\\ {\mathrm{S}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{T}}-{\mathrm{R}}_{\mathrm{T}}-{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}},\\ {\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}-{\mathrm{C}}_{\mathrm{G}}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}-{\mathrm{F}}_{\mathrm{F}}\end{array}\right]$	$\left(\mathrm{H}, \overline{\mathrm{S}}, \overline{\mathrm{A}}\right)$ $\left[\begin{array}{c}{\mathrm{B}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{F}}-{\mathrm{S}}_{\mathrm{F}},\\ {\mathrm{S}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{T}}-{\mathrm{R}}_{\mathrm{T}},\\ -{\mathrm{R}}_{\mathrm{G}}\end{array}\right]$
Farmers	Self prevention and control ($1-\mathrm{X}$)	Service organizations	Positive prevention and treatment services ($\mathrm{Y}$)	$\left( \overline{\mathrm{H}}, \mathrm{S}, \mathrm{A}\right)$ $\left[\begin{array}{c}{\mathrm{B}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{F}},\\ -{\mathrm{C}}_{\mathrm{T}}-\Delta {\mathrm{C}}_{\mathrm{T}}+{\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}},\\ -{\mathrm{C}}_{\mathrm{G}}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}-{\mathrm{F}}_{\mathrm{T}}\end{array}\right]$	$\left( \overline{\mathrm{H}}, \mathrm{S}, \overline{\mathrm{A}}\right)$ $\left[\begin{array}{c}{\mathrm{B}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{F}},\\ -{\mathrm{C}}_{\mathrm{T}}-\Delta {\mathrm{C}}_{\mathrm{T}},\\ 0\end{array}\right]$
			Negative prevention and control services ($1-\mathrm{Y}$)	$\left( \overline{\mathrm{H}}, \overline{\mathrm{S}}, \mathrm{A}\right)$ $\left[\begin{array}{c}{\mathrm{B}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{F}},\\ -{\mathrm{C}}_{\mathrm{T}}-{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}},\\ {\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}-{\mathrm{C}}_{\mathrm{G}}\end{array}\right]$	$\left( \overline{\mathrm{H}}, \overline{\mathrm{S}}, \overline{\mathrm{A}}\right)$ $\left[\begin{array}{c}{\mathrm{B}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{F}},\\ -{\mathrm{C}}_{\mathrm{T}},\\ -{\mathrm{R}}_{\mathrm{G}}\end{array}\right]$

Notes: The meaning of the parameters is shown in Section 2.2. The contents of the table were derived by the authors.

.

When farmers choose outsourced control strategy $\left(\mathrm{H}\right)$ and self-control strategy $\left(\overline{\mathrm{H}}\right)$ in pest and disease control, the expected returns are

$$\begin{gathered} {\mathrm{U}}_{\mathrm{F}\left(\mathrm{H}\right)}= \mathrm{Y}\ast \mathrm{Z} \ast \left({\mathrm{B}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{F}}-{\mathrm{S}}_{\mathrm{F}}+\Delta {\mathrm{B}}_{\mathrm{F}}+{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)+\mathrm{Y}\ast \left(1-\mathrm{Z}\right) \\ \begin{array}{l}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\ast \left({\mathrm{B}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{F}}-{\mathrm{S}}_{\mathrm{F}}+\Delta {\mathrm{B}}_{\mathrm{F}}\right)+\left(1-\mathrm{Y}\right)\ast \mathrm{Z}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\ast \left({\mathrm{B}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{F}}-{\mathrm{S}}_{\mathrm{F}}+{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)+\left(1-\mathrm{Y}\right)\ast \left(1-\mathrm{Z}\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\ast \left({\mathrm{B}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{F}}-{\mathrm{S}}_{\mathrm{F}}\right)\end{array} \\ {\mathrm{U}}_{\mathrm{F}\left(\overline{\mathrm{H}}\right)}= \mathrm{Y}\ast \mathrm{Z} \ast \left({\mathrm{B}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{F}}\right)+\mathrm{Y} \ast \left(1-\mathrm{Z}\right)\ast \left({\mathrm{B}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{F}}\right)+\left(1-\mathrm{Y}\right)\ast \mathrm{Z} \ast \left({\mathrm{B}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{F}}\right) \\ +\left(1-\mathrm{Y}\right)\ast \left(1-\mathrm{Z}\right)\ast \left({\mathrm{B}}_{\mathrm{F}}-{\mathrm{C}}_{\mathrm{F}}\right) \end{gathered}$$

The average expected returns from pest and disease control for farmers are

$${\mathrm{U}}_{\mathrm{F}}={ \mathrm{X}\ast \mathrm{U}}_{\mathrm{F}\left(\mathrm{H}\right)}+\left(1-\mathrm{X}\right) {\ast \mathrm{U}}_{\mathrm{F}\left(\overline{\mathrm{H}}\right)}$$

Then, the replicator dynamics equation for the farmer’s behavioral strategy is

$$\begin{gathered} \mathrm{F}\left(\mathrm{X}\right)= \mathrm{dX}/\mathrm{dt}= \mathrm{X} \ast \left({\mathrm{U}}_{\mathrm{F}\left(\mathrm{H}\right)}-{\mathrm{U}}_{\mathrm{F}}\right)= \mathrm{X} \ast \left(1-\mathrm{X}\right)\ast \left({\mathrm{U}}_{\mathrm{F}\left(\mathrm{H}\right)}-{\mathrm{U}}_{\mathrm{F}\left(\overline{\mathrm{H}}\right)}\right) \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=\mathrm{X} \ast \left(1-\mathrm{X}\right)\ast \left[-{\mathrm{S}}_{\mathrm{F}}+\mathrm{Y} \ast \Delta {\mathrm{B}}_{\mathrm{F}}+\mathrm{Z} \ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)\right] \end{gathered}$$

Similarly, the replicator dynamics equations for the service organization and government behavior strategies are obtained as

$$\begin{gathered} \mathrm{F}\left(\mathrm{Y}\right)=\mathrm{dY}/\mathrm{dt}= \mathrm{Y}\ast \left(1-\mathrm{Y}\right)\ast \left[-\Delta {\mathrm{C}}_{\mathrm{T}}+{\mathrm{X}\ast \mathrm{R}}_{\mathrm{T}}+\mathrm{Z} \ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}\right)\right] \\ \mathrm{F}\left(\mathrm{Z}\right)=\mathrm{dZ}/\mathrm{dt}= \mathrm{Z} \ast \left(1-\mathrm{Z}\right)\ast \left[\begin{array}{c}-{\mathrm{C}}_{\mathrm{G}}+\mathrm{Q}\ast {\mathrm{P}}_{\mathrm{T}}+{\mathrm{R}}_{\mathrm{G}}-\mathrm{Y}\ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}+{\mathrm{R}}_{\mathrm{G}}\right)\\ -\mathrm{X}\ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)+\mathrm{X}\ast \mathrm{Y}\ast \mathrm{K}\end{array}\right] \end{gathered}$$

3. Results

3.1. Analysis of the Stability of the Strategy of the Three Game Subjects

3.1.1. Analysis of the Stability of Farmers’ Strategies

Taking the derivation of the farmer’s replicator dynamics equation $\mathrm{F}\left(\mathrm{X}\right)$, with respect to $\mathrm{X}$, we can obtain

$$\mathrm{dF}\left(\mathrm{X}\right)/\mathrm{dX}=\left(1-2\mathrm{X}\right)\ast \left[-{\mathrm{S}}_{\mathrm{F}}+\mathrm{Y} \ast \Delta {\mathrm{B}}_{\mathrm{F}}+\mathrm{Z} \ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)\right]$$

According to the stability theorem of the differential equation, the probability of farmers choosing outsourced control is in a stable state and must meet $\mathrm{F}\left(\mathrm{X}\right)=0$ and $\mathrm{dF}\left(\mathrm{X}\right)/\mathrm{dX}<0$. Therefore, when $\mathrm{Y} ={\mathrm{Y}}_0=[{\mathrm{S}}_{\mathrm{F}}-\mathrm{Z} \ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)]/\Delta {\mathrm{B}}_{\mathrm{F}}$, $\mathrm{F}\left(\mathrm{X}\right)=0$ and $\mathrm{dF}\left(\mathrm{X}\right)/\mathrm{dX}=0$; at this time, whatever value $\mathrm{X}$ takes is in the evolutionary stable state. When $\mathrm{Y}>{\mathrm{Y}}_0$, $\mathrm{dF}\left(\mathrm{X}\right)/\mathrm{dX}{|}_{\mathrm{X} =0}>0$ and $\mathrm{dF}\left(\mathrm{X}\right)/\mathrm{dX}{|}_{\mathrm{X} =1}<0$; at this time, $\mathrm{X} =1$ is the farmer’s evolutionary stabilization strategy. Conversely, $\mathrm{dF}\left(\mathrm{X}\right)/\mathrm{dX}{|}_{\mathrm{X}=1}>0$ and $\mathrm{dF}\left(\mathrm{X}\right)/\mathrm{dX}{|}_{\mathrm{X} =0}<0$ when $\mathrm{Y}<{\mathrm{Y}}_0$, at which point $\mathrm{X} =0$ is the farmers’ evolutionary stabilization strategy. The evolution phase diagram of farmers is shown in Figure 3:

Figure 3 shows that the probability of farmers steadily choosing outsourced control and self control are the volumes of ${\mathrm{V}}_{12}$ and ${\mathrm{V}}_{11}$, respectively. Through computation, we can obtain

$$\begin{gathered} {\mathrm{V}}_{11}={{\displaystyle \int }}_0^1{{\displaystyle \int }}_0^1\frac{{\mathrm{S}}_{\mathrm{F}}-\mathrm{Z} \ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)}{\Delta {\mathrm{B}}_{\mathrm{F}}}\mathrm{dZdX} =\frac{2{\mathrm{S}}_{\mathrm{F}}-\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)}{2\Delta {\mathrm{B}}_{\mathrm{F}}} \\ {\mathrm{V}}_{12}=1-{\mathrm{V}}_{11}=1-\frac{2{\mathrm{S}}_{\mathrm{F}}-\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)}{2\Delta {\mathrm{B}}_{\mathrm{F}}} \end{gathered}$$

Inference 1: The probability of farmers’ stable choice of outsourced prevention and control is positively correlated with the government’s guidance and incentive supports $\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)$ and to the additional benefits, $\Delta {\mathrm{B}}_{\mathrm{F}}$, brought by positive control services but is negatively correlated with the service costs, ${\mathrm{S}}_{\mathrm{F}}$.

Demonstration: According to the expression of the probability, ${\mathrm{V}}_{12}$, that the farmer chooses to outsource the control, the first-order partial derivatives of each element can be obtained as $\mathsf{\partial }{\mathrm{V}}_{12}/\mathsf{\partial }\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)>0$, $\mathsf{\partial }{\mathrm{V}}_{12}/\mathsf{\partial }\Delta {\mathrm{B}}_{\mathrm{F}}>0$, and $\mathsf{\partial }{\mathrm{V}}_{12}/\mathsf{\partial }{\mathrm{S}}_{\mathrm{F}}<0$. Therefore, the increase in $\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)$ and $\Delta {\mathrm{B}}_{\mathrm{F}}$ or the decrease in ${\mathrm{S}}_{\mathrm{F}}$ can increase the probability of farmers choosing outsourced control.

Inference 1 suggests that the guarantee of farmers’ economic benefits can promote their choice of outsourced control. Firstly, the government implements guidance-based policies to change farmers’ perceptions and awareness, while the related price of the services is changed through subsidies, which, in turn, stimulates farmers to evolve toward outsourced control; secondly, farmers gain additional benefits by adopting positive control services, which is directly contributive to the outsourced control; and, thirdly, the reduction in the cost of outsourced control services cuts down farmers’ operating expenses, which also helps to promote the choice of outsourced control.

Inference 2: In the evolution process, the probability, X, of farmers choosing to outsource the prevention and control increases with the probability, Y, of service organizations providing positive services and with the probability, Z, of the government applying policy tools.

Demonstration: According to the stability analysis of the farmer’s strategy, ${\mathrm{Y}}_0={ \mathrm{S}}_{\mathrm{F}}-\mathrm{Z} \ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)/\Delta {\mathrm{B}}_{\mathrm{F}}$ indicates that ${\mathrm{Y}}_0$ is negatively correlated with Z, when $\mathrm{Y}<{\mathrm{Y}}_0$, $\mathrm{X} =0$ is the evolutionary stabilization strategy for farmers. Conversely, when $\mathrm{Y}>{\mathrm{Y}}_0$, $\mathrm{X} =1$ is the evolutionary stabilization strategy for farmers. Thus, as Y and Z gradually increase, the stabilization strategy of farmers evolves from self-control to outsourced control.

Inference 2 suggests that enhancing the probability of service organizations to provide positive control services and the probability of the government to apply policy tools helps farmers choose outsourced control as a stabilization strategy. Government departments can not only positively promote service organizations to provide positive services through guidance- and incentive-based tools but also increase the service cost for organizations with the help of regulatory penalties, which in turn inhibits their negative service behaviors. Namely, the government’s application of policy tools can help form a positive and orderly market for efficient services and enhance the probability of service organizations to provide positive control services; farmers can gain additional benefits from these services, thus further driving them to choose outsourced control.

3.1.2. Analysis of the Stability of Service Organizations

The derivation of the replicator dynamics equation $\mathrm{F}\left(\mathrm{Y}\right)$ for the service organization, with respect to $\mathrm{Y}$, can obtain

$$\mathrm{dF}\left(\mathrm{Y}\right)/\mathrm{dY}=\left(1-2\mathrm{Y}\right)\ast \left[-\Delta {\mathrm{C}}_{\mathrm{T}}+{\mathrm{X}\ast \mathrm{R}}_{\mathrm{T}}+\mathrm{Z} \ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}\right)\right]$$

Similarly, according to the stability theorem of differential equations, when $\mathrm{X} ={\mathrm{X}}_0=\left[\Delta {\mathrm{C}}_{\mathrm{T}}-\mathrm{Z} \ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}\right)\right]/{\mathrm{R}}_{\mathrm{T}}$, $\mathrm{F}\left(\mathrm{Y}\right)=0$, and $\mathrm{dF}\left(\mathrm{Y}\right)/\mathrm{dY}=0$, whatever value Y takes is in an evolutionary stable state; when $\mathrm{X}>{\mathrm{X}}_0$, $\mathrm{dF}\left(\mathrm{Y}\right)/\mathrm{dY}{|}_{\mathrm{Y} =0}>0$, and $\mathrm{dF}\left(\mathrm{Y}\right)/\mathrm{dY}{|}_{\mathrm{Y} =1}<0$, $\mathrm{Y} =1$ is the evolutionary stable strategy; when $\mathrm{X}<{\mathrm{X}}_0$, $\mathrm{dF}\left(\mathrm{Y}\right)/\mathrm{dY}{|}_{\mathrm{Y} =1}>0$, and $\mathrm{dF}\left(\mathrm{Y}\right)/\mathrm{dY}{|}_{\mathrm{Y} =0}<0$, $\mathrm{Y} =0$ is the evolutionary stabilization strategy. The evolutionary phase diagram of the service organization is shown in Figure 4.

Figure 4 shows that the probability of the stability section of positive and negative control services is volume ${\mathrm{V}}_{22}$ and ${\mathrm{V}}_{21}$, respectively. Through computation, we can obtain

$$\begin{gathered} {\mathrm{V}}_{21}={{\displaystyle \int }}_0^1{{\displaystyle \int }}_0^1\frac{\Delta {\mathrm{C}}_{\mathrm{T}}-\mathrm{Z} \ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}\right)}{{\mathrm{R}}_{\mathrm{T}}}\mathrm{dZdY} =\frac{2\Delta {\mathrm{C}}_{\mathrm{T}}-\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}\right)}{2{\mathrm{R}}_{\mathrm{T}}} \\ {\mathrm{V}}_{22}=1-{\mathrm{V}}_{21}=1-\frac{2\Delta {\mathrm{C}}_{\mathrm{T}}-\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}\right)}{2{\mathrm{R}}_{\mathrm{T}}} \end{gathered}$$

Inference 3: The probability of service organizations stabilizing their choice of positive control services is positively correlated with government-directed support, incentive subsidies, regulatory penalties $\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}\right)$, and reputation loss, ${\mathrm{R}}_{\mathrm{T}}$, when negative services are provided, and is negatively correlated with the increased cost of positive services relative to negative services, $\Delta {\mathrm{C}}_{\mathrm{T}}$.

Demonstration: According to the expression of the probability of the service organization choosing positive control services, ${\mathrm{V}}_{22}$, the first-order partial derivative of each element is obtained as $\mathsf{\partial }{\mathrm{V}}_{22}/\mathsf{\partial }\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}\right)>0$, $\mathsf{\partial }{\mathrm{V}}_{22}/\mathsf{\partial }{\mathrm{R}}_{\mathrm{T}}>0$, and $\mathsf{\partial }{\mathrm{V}}_{22}/\mathsf{\partial }\Delta {\mathrm{C}}_{\mathrm{T}}<0$. Thus, either an increase in $\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}\right)$ and ${\mathrm{R}}_{\mathrm{T}}$ or a decrease in $\Delta {\mathrm{C}}_{\mathrm{T}}$ can increase the probability that a service organization chooses positive control services.

Inference 3 suggests that ensuring the operating benefits of service organizations can promote service organizations to choose positive control services. Firstly, the government enables the organizations to master advanced techniques and improve their professionalism through guidance-based policies, while the incentive-based policies guarantee that organizations can receive subsidies when they positively serve, thus prompting them to provide positive control services. In addition, regulatory penalties increase the cost of negative services and help to reduce opportunistic behavior. Secondly, the greater the loss of reputation of service organizations in providing negative services is, the more difficult it is for them to secure their operating profits, which, in turn, motivates them to provide positive and effective services. Thirdly, the greater the difference between the costs of positive and negative services is, the greater the room for service organizations to profitably provide negative services is, and, consequently, the organizations may take risks and choose to provide negative service to seek high profits.

Inference 4: In the evolution process, the probability, Y, of service organizations providing positive control services increases with the probability, X, of farmers outsourcing the services and with the probability, Z, of the government applying policy tools.

Demonstration: Through the stability analysis on service organization strategies, ${\mathrm{X}}_0=\left[\Delta {\mathrm{C}}_{\mathrm{T}}-\mathrm{Z} \ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}\right)\right]/{\mathrm{R}}_{\mathrm{T}}$ indicates that ${\mathrm{X}}_0$ is negatively correlated with Z. When $\mathrm{Y}<{\mathrm{Y}}_0$, $\mathrm{X} =0$ is the evolutionary stabilization strategy for farmers; conversely, when $\mathrm{Y}>{\mathrm{Y}}_0$, $\mathrm{X} =1$ is the evolutionary stabilization strategy for farmers. Thus, as X and Z gradually increase, the stabilization strategy of the outsourcing organization evolves from negative to positive control services.

Inference 4 suggests that increasing the probability that farmers choose outsourced control and that the government applies policy tools can prompt service organizations to provide positive control services as a stabilization strategy. Therefore, to promote the formation and healthy development of the agricultural PDCO market and to ensure that service organizations provide positive and effective services, it is necessary for the government to implement policy tools to guide and motivate farmers to raise production awareness, reduce service costs, and adopt outsourced control.

3.1.3. Analysis of the Stability of the Government’s Strategies

Taking the derivative of the government’s replication dynamic equation $\mathrm{F}\left(\mathrm{Z}\right)$, with respect to $\mathrm{Z}$, we can obtain

$$\begin{gathered} \mathrm{dF}\left(\mathrm{Z}\right)/\mathrm{dZ}=\left(1-2\mathrm{Z}\right)\ast \left[-{\mathrm{C}}_{\mathrm{G}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}+{\mathrm{R}}_{\mathrm{G}}-\mathrm{Y}\ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}+{\mathrm{R}}_{\mathrm{G}}\right) \\ -\mathrm{X} \ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)+\mathrm{X}\ast \mathrm{Y}\ast \mathrm{K}\right] \end{gathered}$$

Similarly, according to the stability theorem of differential equations, in the case of $\mathrm{Y}\ast \mathrm{K}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}-{\mathrm{F}}_{\mathrm{F}}<0$, when $\mathrm{X} ={\mathrm{X}}_{\mathrm{O}}^{\prime }=\left[\mathrm{Y}\ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}+{\mathrm{R}}_{\mathrm{G}}\right)+{\mathrm{C}}_{\mathrm{G}}-{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}-{\mathrm{R}}_{\mathrm{G}}\right]/\left[\mathrm{Y}\ast \mathrm{K}-\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)\right]$, $\mathrm{F}\left(\mathrm{Z}\right)=0$, and $\mathrm{dF}\left(\mathrm{Z}\right)/\mathrm{dZ}=0$, whatever value $\mathrm{Z}$ takes is in an evolutionary stable state. When $\mathrm{X}>{\mathrm{X}}_{\mathrm{O}}^{\prime }$, $\mathrm{dF}\left(\mathrm{Z}\right)/\mathrm{dZ}{|}_{\mathrm{Z} =1}>0$, $\mathrm{dF}\left(\mathrm{Z}\right)/\mathrm{dZ}{|}_{\mathrm{Z} =0}<0$, $\mathrm{Z} =0$ is the evolutionary stable strategy. When $\mathrm{X}<{\mathrm{X}}_{\mathrm{O}}^{\prime }$, $\mathrm{dF}\left(\mathrm{Z}\right)/\mathrm{dZ}{|}_{\mathrm{Z} =0}>0, \mathrm{and} \mathrm{dF}\left(\mathrm{Z}\right)/\mathrm{dZ}{|}_{\mathrm{Z} =1}<0$, $\mathrm{Z} =1$ is the evolutionary stabilization strategy. The evolutionary phase diagram of the government is shown in Figure 5.

Figure 5 shows that when $\mathrm{Y}\ast \mathrm{K}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}-{\mathrm{F}}_{\mathrm{F}}<0$, the probability that the government stably chooses the application or non-application of policy tools is the volume of ${\mathrm{V}}_{32}$ and ${\mathrm{V}}_{31}$, respectively. Through computation, it can be obtained that

$$\begin{gathered} {\mathrm{V}}_{32}={{\displaystyle \int }}_0^1{{\displaystyle \int }}_0^1\frac{\mathrm{Y}\ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}+{\mathrm{R}}_{\mathrm{G}}\right)+{\mathrm{C}}_{\mathrm{G}}-{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}-{\mathrm{R}}_{\mathrm{G}}}{\mathrm{Y}\ast \mathrm{K}-\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)}\mathrm{dYdZ} =\frac{{\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}+{\mathrm{R}}_{\mathrm{G}}}{\mathrm{K}} \\ +\left[\frac{\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}+{\mathrm{R}}_{\mathrm{G}}\right)\ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)}{{\mathrm{K}}^2}+\frac{{\mathrm{C}}_{\mathrm{G}}-{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}-{\mathrm{R}}_{\mathrm{G}}}{\mathrm{K}}\right]\ast \ln \left(1-\frac{\mathrm{K}}{{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}}\right) \\ {\mathrm{V}}_{31}=1-{\mathrm{V}}_{32}=\frac{\mathrm{K}-\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}+{\mathrm{R}}_{\mathrm{G}}\right)}{\mathrm{K}} \\ -\left[\frac{\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}+{\mathrm{R}}_{\mathrm{G}}\right)\ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)}{{\mathrm{K}}^2}+\frac{{\mathrm{C}}_{\mathrm{G}}-{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}-{\mathrm{R}}_{\mathrm{G}}}{\mathrm{K}}\right]\ast \ln \left(1-\frac{\mathrm{K}}{{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}}\right) \end{gathered}$$

In addition, when $\mathrm{Y}\ast \mathrm{K}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}-{\mathrm{F}}_{\mathrm{F}}>0$, the probability of the government stabilizing the application or non-application of policy tools is shown in the volume of ${\mathrm{V}}_{31}$ and ${\mathrm{V}}_{32}$, respectively, as shown in Figure 5, but, at this time, $1-\mathrm{K}/\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)<0$, while the volume formula for ${\mathrm{V}}_{31}$ and ${\mathrm{V}}_{32}$ includes $\ln \left[1-\mathrm{K}/\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)\right]$; thus, the discussions on farmers’ evolutionary strategies at $\mathrm{Y}\ast \mathrm{K}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}-{\mathrm{F}}_{\mathrm{F}}>0$ become meaningless. To sum up, only the relevant cases at the time of $\mathrm{Y}\ast \mathrm{K}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}-{\mathrm{F}}_{\mathrm{F}}<0$ are subsequently discussed.

Inference 5: The probability of the government’s stable selection of policy tool application is positively correlated with the reputation loss, ${\mathrm{R}}_{\mathrm{G}}$, when negative services from service organizations are not regulated; with the revenue from fines, ${\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}$, on negative services; and with special subsidies and incentives, $\mathrm{K}$, earned in the tripartite concerted control. However, the probability of the government’s stable selection of policy tool application is negatively correlated with the total cost of implementing regulatory policies, ${\mathrm{C}}_{\mathrm{G}}$; with inputs in promoting guidance-based policies, ${\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}{ \mathrm{and} \mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}$; and with subsidies, ${\mathrm{F}}_{\mathrm{F}}$ and ${\mathrm{F}}_{\mathrm{T}}$, when implementing incentive-based policies.

Demonstration: According to the expression of the probability, ${\mathrm{V}}_{32}$, of the government’s stabilization of the application of policy tools, the first-order partial derivatives of each element are obtained as follows: $\mathsf{\partial }{\mathrm{V}}_{32}/\mathsf{\partial }{\mathrm{R}}_{\mathrm{G}}>0$, $\mathsf{\partial }{\mathrm{V}}_{32}/\mathsf{\partial }\left({\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}\right)>0$, $\mathsf{\partial }{\mathrm{V}}_{32}/\mathsf{\partial }\mathrm{K}>0$, $\mathsf{\partial }{\mathrm{V}}_{32}/\mathsf{\partial }{\mathrm{C}}_{\mathrm{G}}<0$, $\mathsf{\partial }{\mathrm{V}}_{32}/\mathsf{\partial }\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}\right)<0$, $\mathsf{\partial }{\mathrm{V}}_{32}/\mathsf{\partial }\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}\right)<0$, $\mathsf{\partial }{\mathrm{V}}_{32}/\mathsf{\partial }{\mathrm{F}}_{\mathrm{F}}<0$, and $\mathsf{\partial }{\mathrm{V}}_{32}/\mathsf{\partial }{\mathrm{F}}_{\mathrm{T}}<0$. Therefore, the increase in ${\mathrm{R}}_{\mathrm{G}}$, ${\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}$, and $\mathrm{K}$ or the decrease in ${\mathrm{C}}_{\mathrm{G}}$, ${\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}$, ${\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}$, ${\mathrm{F}}_{\mathrm{F}}$, and ${\mathrm{F}}_{\mathrm{T}}$ can all increase the probability of the government choosing to apply policy tools.

Inference 5 suggests that the key to the government’s application or non-application of policy tools is limited by fiscal pressures. The greater the reputation loss caused by the government’s inaction in the service organization’s negative control is, and the higher the amounts of the special subsidies and rewards given by higher authorities are, the more it can motivate the government to strictly implement policy tools. In addition, setting a heavier penalty amount and a greater penalty probability for negative services from service organizations can promote the strict fulfillment of policy tools by government regulators. However, the higher the cost of implementing policies is, the higher the inputs into the settings of incentive- and guidance-based policies are, and the higher the financial burden is that the government faces, these, in turn, reduce the probability of applying policy tools.

Inference 6: In the evolution process, the probability, Z, of the government applying policy tools decreases with the increase in the probability, X, of farmers outsourcing control services, and with the probability, Y, of service organizations providing positive control services.

Demonstration: From the analysis on the government’s strategy stability, when $\mathrm{Y}\ast \mathrm{K}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}-{\mathrm{F}}_{\mathrm{F}}<0$, ${\mathrm{X}}_{\mathrm{O}}^{\prime }=\left[\mathrm{Y}\ast \left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}+{\mathrm{R}}_{\mathrm{G}}\right)+{\mathrm{C}}_{\mathrm{G}}-{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}-{\mathrm{R}}_{\mathrm{G}}\right]/\left[\mathrm{Y}\ast \mathrm{K}-\left({\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}\right)\right]$ indicates that ${\mathrm{X}}_{\mathrm{O}}^{\prime }$ is negatively correlated with Y. When $\mathrm{X}<{\mathrm{X}}_{\mathrm{O}}^{\prime }$, $\mathrm{Z} =1$ is the government’s evolutionary stability strategy; conversely, when $\mathrm{X}>{\mathrm{X}}_{\mathrm{O}}^{\prime }$, $\mathrm{Z} =0$ is its evolutionary stabilization strategy. Thus, as X and Y gradually increase, the government’s stabilization strategy evolves from the application of policy tools to the non-application of policy tools.

Inference 6 suggests that increasing the probability that farmers choose to outsource control services and that service organizations adopt positive control services can both prompt the government to opt for the non-application of policy tools as a stabilization strategy. After the probability that farmers choose outsourcing and that service organizations opt for positive control services reaches a certain level, government departments choose not to use policy tools as a stabilization strategy, in order to improve capital utilization and reduce financial burden. Therefore, when farmers and service organizations can effectively promote the benign operation of PDCO, the government chooses not to intervene in the PDCO system.

3.2. Stability Analysis of Equilibrium Point of Three-Party Evolutionary Game System

From the replicator dynamics equation of the behavioral strategies of farmers, service organizations, and the government, the replicator dynamics system for the three main players in agricultural pest and disease control can be obtained.

$$\left\{\begin{array}{c}F\left(X\right)=X\ast \left(1-X\right)\ast \left[-S_F+Y\ast \Delta B_F+Z\ast \left(I\ast U_F+F_F\right)\right]\\ F\left(Y\right)=Y\ast \left(1-Y\right)\ast \left[-\Delta C_T+X\ast R_T+Z\ast \left(I\ast U_T+F_T+Q\ast P_T\right)\right]\\ F\left(Z\right)=Z\ast \left(1-Z\right)\ast \left[\begin{array}{c}-C_G+Q\ast P_T+R_G-Y\ast \left(I\ast U_T+F_T+Q\ast P_T+R_G\right)\\ -X\ast \left(I\ast U_F+F_F\right)+X\ast Y\ast K\end{array}\right]\end{array}\right.$$

The Jacobian matrix, $J$, of agricultural pest and disease control is

$$J=\left[\begin{array}{ccc}\frac{\mathsf{\partial }F\left(X\right)}{\mathsf{\partial }X}& \frac{\mathsf{\partial }F\left(X\right)}{\mathsf{\partial }Y}& \frac{\mathsf{\partial }F\left(X\right)}{\mathsf{\partial }Z}\\ \frac{\mathsf{\partial }F\left(Y\right)}{\mathsf{\partial }X}& \frac{\mathsf{\partial }F\left(Y\right)}{\mathsf{\partial }Y}& \frac{\mathsf{\partial }F\left(Y\right)}{\mathsf{\partial }Z}\\ \frac{\mathsf{\partial }F\left(Z\right)}{\mathsf{\partial }X}& \frac{\mathsf{\partial }F\left(Z\right)}{\mathsf{\partial }Y}& \frac{\mathsf{\partial }F\left(Z\right)}{\mathsf{\partial }Z}\end{array}\right]$$

$$=\left[\begin{array}{ccc}\left(1-2X\right) \ast \left[\begin{array}{c}-S_F+Y \ast {∆B}_F+\\ Z \ast \left(I \ast U_F+F_F\right)\end{array}\right]& X \ast \left(1-X\right) \ast {∆B}_F& X \ast \left(1-X\right) \ast \left(I \ast U_F+F_F\right)\\ Y \ast \left(1-Y\right) \ast R_T& \left(1-2Y\right) \ast \left[\begin{array}{c}-∆C_T+X \ast R_T+\\ Z \ast \left(\begin{array}{c}I \ast U_T+\\ F_T+Q \ast P_T\end{array}\right)\end{array}\right]& Y \ast \left(1-Y\right) \ast \left(\begin{array}{c}I \ast U_T+F_T\\ +Q \ast P_T\end{array}\right)\\ Z \ast \left(1-Z\right) \ast \left[\begin{array}{c}-\left(I \ast U_F+F_F\right)\\ +Y \ast K\end{array}\right]& Z \ast \left(1-Z\right) \ast \left[\begin{array}{c}-\left(\begin{array}{c}I \ast U_T+F_T\\ +Q \ast P_T+R_G\end{array}\right)\\ +X \ast K\end{array}\right]& \left(1-2Z\right) \ast \left[\begin{array}{c}-C_G+Q \ast P_T+R_G-\\ Y \ast \left(\begin{array}{c}I \ast U_T+F_T+\\ Q \ast P_T+R_G\end{array}\right)\\ -X \ast \left(I \ast U_F+F_F\right)\\ +X \ast Y \ast K\end{array}\right]\end{array}\right]$$

According to Lyapunov’s first methodology, when all the eigenvalues of Jacobian matrix, $J$, are negative, the equilibrium point is the asymptotic stability point; when at least one of the eigenvalues of the Jacobian matrix, $J$, is positive, the equilibrium point is unstable. However, when the Jacobian matrix, $J$, has a zero eigenvalue, and all the other eigenvalues are negative, the stability of the point cannot be determined. When $F\left(X\right)=F\left(Y\right)=F\left(Z\right)=0$, 8 equilibrium points from the replicator dynamics system for agricultural pest and disease control can be obtained. The evolution of mixed equilibrium points is not considered here, because the mixed equilibrium points must have the characteristic value of 0, which does not fit the evolutionary stability strategy (ESS). Combined with the profit and loss variables’ settings and the descriptions of the three subjects, the stability analysis of the equilibrium point is shown in

Table 2. Stability analysis of equilibrium points.

Equilibrium Point	Eigenvalue of Jacobian Matrix		Stability Conclusion	Condition
	${\mathbf{\lambda }}_1,{\mathbf{\lambda }}_2,{\mathbf{\lambda }}_3$	Real Part Symbol
(0, 0, 0)	$-{\mathrm{S}}_{\mathrm{F}}$, $-\Delta {\mathrm{C}}_{\mathrm{T}},{\mathrm{R}}_{\mathrm{G}}-{\mathrm{C}}_{\mathrm{G}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}$	($-$, $-$, $+$)	Instability point	/
(0, 1, 0)	$\Delta {\mathrm{B}}_{\mathrm{F}}-{\mathrm{S}}_{\mathrm{F}}$, $\Delta {\mathrm{C}}_{\mathrm{T}}$, $-{\mathrm{C}}_{\mathrm{G}}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}-{\mathrm{F}}_{\mathrm{T}}$	($+$, $+$, $-$)	Instability point	/
(0, 0, 1)	${\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}-{\mathrm{S}}_{\mathrm{F}}$, ${\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}-\Delta {\mathrm{C}}_{\mathrm{T}}$, ${\mathrm{C}}_{\mathrm{G}}-{\mathrm{R}}_{\mathrm{G}}-{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}$	($-$, $\times$, $-$)	ESS	①
(0, 1, 1)	$\Delta {\mathrm{B}}_{\mathrm{F}}+{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}-{\mathrm{S}}_{\mathrm{F}},$ $\Delta {\mathrm{C}}_{\mathrm{T}}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}-{\mathrm{F}}_{\mathrm{T}}-{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}$, ${\mathrm{C}}_{\mathrm{G}}+{\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}$	($+$, $\times$, $+$)	Instability point	/
(1, 0, 0)	${\mathrm{S}}_{\mathrm{F}}$, ${\mathrm{R}}_{\mathrm{T}}-\Delta {\mathrm{C}}_{\mathrm{T}},$ ${\mathrm{R}}_{\mathrm{G}}-{\mathrm{C}}_{\mathrm{G}}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}-{\mathrm{F}}_{\mathrm{F}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}$	($+$, $+$, $\times$)	Instability point	/
(1, 1, 0)	${\mathrm{S}}_{\mathrm{F}}-\Delta {\mathrm{B}}_{\mathrm{F}}$, $\Delta {\mathrm{C}}_{\mathrm{T}}-{\mathrm{R}}_{\mathrm{T}}$, $\mathrm{K}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}-{\mathrm{F}}_{\mathrm{F}}-{\mathrm{F}}_{\mathrm{T}}-{\mathrm{C}}_{\mathrm{G}}$	($-$, $-$, $\times$)	ESS	②
(1, 0, 1)	${\mathrm{S}}_{\mathrm{F}}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}-{\mathrm{F}}_{\mathrm{F}}$, ${\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}+{\mathrm{R}}_{\mathrm{T}}-\Delta {\mathrm{C}}_{\mathrm{T}}$, ${\mathrm{C}}_{\mathrm{G}}+{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{F}}-{\mathrm{R}}_{\mathrm{G}}-{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}$	($+$, $+$, $\times$)	Instability point	/
(1, 1, 1)	${\mathrm{S}}_{\mathrm{F}}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}-{\mathrm{F}}_{\mathrm{F}}-\Delta {\mathrm{B}}_{\mathrm{F}}$, $\Delta {\mathrm{C}}_{\mathrm{T}}-{\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}-{\mathrm{F}}_{\mathrm{T}}-{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}-{\mathrm{R}}_{\mathrm{T}}$, ${\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{C}}_{\mathrm{G}}-\mathrm{K}$	($-$, $-$, $\times$)	ESS	③
Condition ①: ${\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{Q}\ast \mathrm{P}}_{\mathrm{T}}<\Delta {\mathrm{C}}_{\mathrm{T}}$; Condition ②: $\mathrm{K}<{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{C}}_{\mathrm{G}}$; Condition ③: $\mathrm{K}>{\mathrm{I}\ast \mathrm{U}}_{\mathrm{F}}+{\mathrm{I}\ast \mathrm{U}}_{\mathrm{T}}+{\mathrm{F}}_{\mathrm{F}}+{\mathrm{F}}_{\mathrm{T}}+{\mathrm{C}}_{\mathrm{G}}$.

Note: $\times$ indicates that the symbol is uncertain. The meaning of the parameters is shown in Section 2.2. The contents of the table were derived by the authors.

. From Table 2, it is easy to obtain that at equilibrium points (0, 0, 0), (0, 1, 0), (0, 1, 1), (1, 0, 0), and (1, 0, 1) there exists at least one positive eigenvalue; therefore, these five equilibrium points are not evolutionarily stable strategies.

Inference 7: When condition ① is met, (0, 0, 1) in the replicator dynamics system is the equilibrium point.

Demonstration: Under condition ①, the equilibrium points of (0, 0, 1) have negative eigenvalues; thus, (0, 0, 1) is the asymptotically stable point of the system.

Inference 7 shows that when the cost difference between a positive service and a negative service is higher than the sum of the government’s guidance, subsidies, rewards, and penalties, it indicates that the potential benefits obtained by the organization from the government for the positive service cannot cover the organization’s increased cost, so the organization chooses to provide negative ones. Farmers, because of the negative control services provided by service organizations, cannot receive additional benefits from yield and quality, and the government’s guidance and incentive supports can hardly offset the service cost of outsourced control; as a result, farmers turn to self control after comprehensive consideration of the economic benefits. At this point of time, although the government applies policy tools, the guidance, rewards, and penalties from the policy tools are low, which has little effect on changing the behavior of farmers and outsourcing organizations.

Inference 8: When condition ② is satisfied, (1, 1, 0) in the replicator dynamic system is the equilibrium point.

Demonstration: Under condition ②, the equilibrium points (1, 1, 0) have negative eigenvalues; thus, (1, 1, 0) is the asymptotically stable point of the system.

Inference 8 shows that, when the sum of the cost of implementing the government’s PDCO policy is greater than the supports and rewards from the superior government, that is, when the government sets the guidance- and incentive-based policy tools at a higher level of support, the government eventually does not intervene in the pest and disease control system through the evolutionary game, and, at the same time, both farmers and service organizations can achieve an ideal pest and disease control state on their own, indicating that both farmers and service organizations can gain higher benefits from it. After a benign and effective market operation system is formed between farmers and service organizations, the government no longer imposes policy tools in consideration of fiscal savings.

Inference 9: When condition ③ is satisfied, (1, 1, 1) in the replicator dynamic system is the equilibrium point.

Demonstration: Under condition ③, the eigenvalues of the equilibrium point (1, 1, 1) are all negative; thus, (1, 1, 1) is the asymptotically stable points of the system.

Inference 9 shows that when the sum of the government expenditures on policy tools is less than that of the special subsidies and rewards from higher-level governments, that is, the regulation of policy tools is relatively small, the government can effectively regulate the behaviors of farmers and organizations by applying policy tools. This suggests that a “gradual and incremental” policy tool does not impose a fiscal burden on the government and guarantees a market order free from disturbance. The “one-step but anticlimactic” policy tool may quickly achieve a good governance, but it causes serious financial pressure to government departments, and, most importantly, it may disrupt the order on the service market; thus, it is not conducive to the stable and sustainable development of the modern pest and disease control system.

3.3. Numerical Simulation and Analysis

In order to assess the validity of the evolutionary stability analysis, the model is numerically assigned in combination with the realistic situation, and the numerical evolutionary simulation analysis is carried out using Matlab2021a. The values of the profit and loss parameters are assigned as shown in

Table 3. Assignment of profit and loss parameters.

Parameter	${\mathbf{S}}_{\mathbf{F}}$	$\Delta {\mathbf{B}}_{\mathbf{F}}$	$\Delta {\mathbf{C}}_{\mathbf{T}}$	${\mathbf{R}}_{\mathbf{T}}$	${\mathbf{C}}_{\mathbf{G}}$	$\mathbf{I}$	${\mathbf{U}}_{\mathbf{T}}$	${\mathbf{U}}_{\mathbf{F}}$	${\mathbf{F}}_{\mathbf{T}}$	${\mathbf{F}}_{\mathbf{F}}$	${\mathbf{P}}_{\mathbf{T}}$	$\mathbf{Q}$	${\mathbf{R}}_{\mathbf{G}}$	$\mathbf{K}$
Value	18	32	8.5	10	2	1	3	2	1	2	20	0.2	3	10.5

Note: The meaning of the parameters is shown in Section 2.2. The data in the table are set by the authors according to the sensitivity of the tripartite strategy to changes in exogenous variables.

.

3.3.1. Simulation Analysis of the Effect of Initial Willingness on Stabilization Strategy

Figure 6 simulates the effect of simultaneous changes in the initial willingness of the three subjects on the ultimately stable evolution results. It can be concluded that the initial willingness of the three parties is at a lower level (0.4), which eventually evolves into (0, 0, 1). At this point, the convergence rate is fastest for farmers, intermediate for the government, and slowest for service organizations. When the initial willingness of the three subjects is increased to 0.6 and 0.8, the final evolution result is (1, 1, 1). A detailed analysis of the evolutionary process at these two willingness levels reveals that the higher the initial willingness is, the faster the convergence rate of the three parties to 1 is, and the earlier the state of the three-party collaborative pest and disease control can be achieved. In the process of evolution, the convergence rate of farmers is slightly faster than that of service organizations, while the government is at the slowest rate. Thus, it can be seen that when the initial willingness of all parties is low, although the government applies policy tools to try to regulate the behaviors of the other two parties, the effect of the policy tools remains invisible. After the initial willingness of all parties reaches a certain level, the application of policy tools by the government can effectively coordinate the behavioral choices of farmers and service organizations, thus contributing to the formation of a good outsourcing environment for pest and disease control.

3.3.2. Simulation Analysis of the Impact of Single Policy Tool on Stabilization Strategies

The initial willingness of the three parties is set to 0.6, the impact of implementing only a single policy tool on the final stabilization evolutionary outcome is compared and analyzed, and the changes in each parameter and the evolution result are shown in Figure 7. When the three policies are at a low level, i.e., ${\mathrm{U}}_{\mathrm{F}}=1$, ${\mathrm{U}}_{\mathrm{T}}=2$, ${\mathrm{F}}_{\mathrm{F}}=1$, and ${\mathrm{F}}_{\mathrm{T}}=0.5$ and ${\mathrm{F}}_{\mathrm{F}}=2$, ${\mathrm{F}}_{\mathrm{T}}=1$, $\mathrm{Q} =0.1$, and ${\mathrm{P}}_{\mathrm{T}}=19$, the final evolution of the results is (0, 0, 1). When the level of guidance, incentive, and regulation is further improved, it can effectively promote the tripartite subjects to collaborate in efficient pest and disease control, which eventually evolves to (1, 1, 1). The reason for this is that at a low policy level, government support is difficult to offset the increased cost when farmers and service organizations choose positive externality behaviors, and, in order to maximize profits, each chooses negative externalities with higher returns.

In the evolutionary convergence process of the three subjects, regulatory-type policies have the fastest convergence rate, while the evolution of guidance- and incentive-based policies is relatively slow. This is because the regulatory policy is different from the guidance- and incentive-based policies, which cannot fundamentally solve the technical and financial constraints faced by other subjects. Scholars pointed out that a high-intensity regulatory restraint policy may lead to resistance among other agents [35], so the implementation of regulatory policies alone may make it difficult to maintain a cooperative state in the long run. In this way, cooperation is in a more stable state, although the evolution of each subject is relatively slower after the implementation of guidance- and incentive-based policies.

3.3.3. Simulation Analysis of the Impact of Policy Tool Combinations on Stabilization Strategies

The implementation of one certain policy consists of a series of combined policy tools, so this part explores the impact of the combination of policy tools on the final stable evolutionary outcome of each subject, followed by the analysis on the complementary relationship and superposition effects among policy tools. The initial willingness of the three parties is set to 0.6, and the changes and evolution results of the other parameters are shown in Figure 8. Compared with the application of a single policy tool, the absence of the (0, 0, 1) evolutionary state after the combination of the three types of policy tools suggests that the policy inefficiencies, which may be faced during the implementation of a single policy tool, can be effectively eliminated after the superposition of policy tools.

When the regulatory policy is paired with the guidance- or incentive-based policies, it evolves to (1, 1, 1) under low, medium, and high parameter settings, and the evolution of each party to 1 accelerates as the parameter setting value increases. In contrast, the combination of guidance- and incentive-based policies evolves to (1, 1, 1) at low and medium parameter settings and to a more optimal state (1, 1, 0) at a high parameter setting, i.e., farmers and service organizations can reach an ideal pest and disease control state on their own without government intervention. The evolutionary state of the combination of the three types of policy instruments is the same as the evolutionary state when the guidance-based policy is combined with the incentive-based one, but the evolutionary rates of farmers and service organizations are higher at this time.

4. Discussion

Compared with farming and harvesting practice, where specialized services are relatively mature and standardized, the service quality of PDCO is difficult to assess in a timely manner, the operational effects can only be seen afterwards, and its implementation is usually irreversible, thus causing complexity and uncertainty [8], so opportunistic behavior is easy to breed when PDCO is carried out. Due to information asymmetry and subject interest conflict, farmers and service organizations have a typical principal–agent relationship when trading PDCO services. At present, the adoption rate of PDCO among Chinese farmers is still low, and the promotion of PDCO is still in its infancy. According to the research results, the behavioral choices of farmers and service organizations are affected by internal economic perception, which is mainly affected by external policies. Among them, the rational perception of farmers mainly comes from increasing income and then realizing the maximization of economic effect. The rational perception of service organization mainly lies in the maximization of operating benefits. However, farmers and service organizations do not have the ecological rationality to actively protect the environment. In summary, farmers and service organizations tend to make rational decisions under the role of “economic man”.

As an ecological environment has the attribute of public goods, its property rights are difficult to be clearly defined. Therefore, the free competition market mechanism advocated by Coase cannot realize efficient resource allocation, and it is difficult to comprehensively promote the spontaneous trading of PDCO between farmers and service organizations. Therefore, the government needs to implement policy tools to mobilize the enthusiasm of farmers and service organizations. The research results show that the government’s separate implementation of guidance-based policies, incentive-based policies, and regulatory policies can promote the realization of a modernized PDCO system. Huang et al. found that these three kinds of policies have standardized effects on farmers’ pesticide application behavior [18]. At present, the Chinese government attaches great importance to the implementation of guidance- and incentive-based policies in agricultural pest and disease control. Guidance-based policies can change the selection behavior of participating subjects from the very beginning through technical training and other means, while incentive-based policies, similar to agricultural production trust subsidies, effectively solve the problem of the financial constraints of other subjects. In addition, the implementation of regulatory policies, driven by coercive measures, can quickly achieve the goal of the tripartite joint control of pests and disease. However, the implementation of the regulatory policy alone has not yet fundamentally solved the technical and financial constraints faced by the other subjects in practice.

Scholars further discussed the effects of different policy combinations and proposed that incentives and constraints should be equal in the formulation of relevant policies [35]. Huang et al. compared and analyzed the influence of different policies on the pesticide spraying behavior of Chinese farmers and believed that the comprehensive management mechanism of “combining rewards and punishments” could give full play to the effectiveness of policies [18]. This study also reached a similar conclusion, finding that when guidance-based policies, incentive-based policies, and regulatory policies are simultaneously implemented, a policy system with both positive and negative mechanisms can be formed. The reverse push from regulatory policies can further strengthen the positive effects of guidance- and incentive-based policies, maximizing the complementary and superposition effects among the policies.

Of course, in the long run, to realize a green, modern, and efficient PDCO system, we must build a long-term mechanism of PDCO, so that farmers and service organizations can spontaneously trade positive and effective PDCO services without government intervention. That is to say, on the premise of ensuring that PDCO can satisfy the economic effect of farmers and the operating benefits of service organizations, the endogenous power of farmers and service organizations seeking sustainable development is gradually stimulated. However, in the initial stage of ecological capital accumulation, the market cannot guarantee the interests of farmers and service organizations. The goal of turning ecological dividends into sustainable benefits is only possible if ecological accumulation continues over a long period of time, and, until then, policy tools must be relied upon to achieve a smooth transition.

5. Conclusions and Revelations

In this paper, the dynamic relationship of the tripartite game model of farmers, service organizations, and the government regarding PDCO, together with the equilibrium stability of the strategy combination, were constructed and deeply analyzed. The study reached the following conclusions:

Firstly, the government’s provision of guidance-based policy, incentive-based policy, and regulatory policy can help to enhance farmers’ willingness to choose outsourcing control and service organizations’ willingness to provide positive control services, thus helping to achieve a stable state of joint pest and disease control by farmers, service organizations, and the government. In addition, when the degree of policy implementation is low, the government’s policy is ineffective, but, after reaching a certain level, the higher the degree of policy implementation is, the stronger the willingness of each subject is, and the faster the stable state of tripartite joint pest and disease control is formed.

Secondly, when implementing a single policy tool, after the implementation of a mandatorily regulatory policy, the convergence of all parties is the fastest, but the cooperative state may not be maintained for a long time, while the convergence of guidance- and incentive-based policies is slower, but the cooperation tends to be in a more stable state.

Thirdly, the effect of a policy tool combination is much better than that of a single policy tool being applied. When tools are combined in pairs, the combination of guidance-based policy and incentive-based policy is more effective than the other two combinations, and the addition of regulatory policy on top of this can produce a better effect.

Based on the above findings, certain insights have, thus, been obtained.

Firstly, give full play to government functions and strengthen the evaluation of the achievements and effects of PDCO. Under the realistic background that PDCO practice is still in its infancy in China, farmers and service organizations lack the motivation to actively change the behavior of pesticide application and the service mode. At this time, the government’s policy regulation becomes the key to implement PDCO. The government should introduce guiding policies such as publicity and training; incentive policies such as service subsidies, machinery subsidies, and pesticide subsidies; and regulatory policies such as fines and taxes, to reduce information asymmetry and conflicts of interest when farmers and service organizations deal with PDCO. This can gradually establish a PDCO system in which “farmers gain additional benefits, service organizations gain customers, and the government wins praise”.

Secondly, specific to different regions and groups, it is advisable to formulate policy tools that meet individual characteristics and needs. For regions with a low development level of PDCO, the government should focus on implementing guidance-based policy to strengthen the cognitive level of farmers and service organizations. For poor farmers, the government should focus on implementing incentive-based policy to ease the financial constraints they face when purchasing PDCO services. For regions with a high level of PDCO development but a low level of regulation, the government should focus on implementing regulatory policies.

Thirdly, policy combination can be tried, to achieve complementarity and the superposition effect between policy tools. Each type of policy tool may have certain disadvantages while performing specific functions. Therefore, the policy tools should complement one another to exert the superposition effect. The combination of guidance-based policy and incentive-based policy should be emphasized. If possible, regulatory policy can be added. In addition, the government should flexibly adjust its policy implementation, combination mode, and policy details in accordance with the strategic choices of the other subjects. When the PDCO trading behaviors of farmers and service organizations tend to be stable and produce ecological effects, the government can gradually reduce the intensity of policy intervention.

6. Limitations and Further Research

This study provides theoretical support for the government to build an efficient policy system for PDCO, but it still has some limitations and needs to be expanded and improved in the future.

On the one hand, this study does not compare and analyze the PDCO two-party evolutionary game model between farmers and service organizations when the government does not intervene. However, for the future development of PDCO, if farmers and service organizations fail to establish an operation system and produce economic benefits by themselves, it is difficult to achieve sustainable and stable development by relying on policy support alone. Therefore, the next step is to build a two-party evolutionary game model to analyze the behavioral logic of farmers and service organizations forming PDCO on their own without government intervention, which is also one of our next research directions.

On the other hand, this study found that guidance-based policy, incentive-based policy, and regulatory policy can effectively promote coordinated management among farmers, service organizations, and the government in modern pest and disease control. However, excessive policy support may disturb the market, make farmers and service organizations rely on policies, and also bring too heavy a financial burden to the government, thus affecting the implementation effect of the policy. Therefore, it is crucial to find an appropriate level of policy support, and future studies can further explore the optimal range of policy support to make up for the shortcomings of existing studies.