Farmers’ Cognition of and Satisfaction with Policy Affect Willingness of Returning Straw to Field: Based on Evolutionary Game Perspective

Abstract

As an important measure to promote the black soil protection strategy, returning straw to the fields is the choice of government policy to affect the decision-making behavior of farmers, and the policy implementation process is a dynamic game equilibrium process between farmers and the government. In order to explore the influence of policies on farmers’ straw-returning decision-making and stability processes, this paper used a logit model to analyze the influencing factors on farmers’ straw-returning decision-making behavior based on the survey data of 397 farmers in Hailun City, Heilongjiang Province. This study also constructs the evolutionary game model between farmers and government, carrying out a stability strategy analysis and numerical simulation. The results evidence that farmers’ cognition of fertilization technology, ecological protection, policy satisfaction and cognition of straw returning recipients have a significant negative influence on their willingness to return to the field, and the effect intensity decreases successively. What is more, cognition of crop disease resistance has a positive effect on the willingness of returning straw to the field. It is found that the game balancing process of farmers’ behavior and government straw returning policy evolution can be divided into three stages. At present, China’s straw returning policy is in the intermediate stage, and government needs to provide comprehensive compensation for returning straw to the field according to local conditions such as farmers’ willingness, crop conditions and so on.

1. Introduction

In China, straw production is huge, which provides sufficient raw materials for the comprehensive utilization of straw, and also provides a broad space for the development of the comprehensive utilization of straw. In 2022, China’s straw resources were 977 million tons, and the collectible amounts are 737 million tons. It is expected that Chinese straw resources will reach 1.014 billion tons. Since the promulgation of the Opinions on Accelerating the Comprehensive Utilization of Crop Straw in 2008, many cities have successively introduced an implementation policy of local returning straw to the field. The No. 1 document of the Central Committee of the Communist Party of China in 2022 proposed the promotion of green development of agriculture and rural areas and support for the comprehensive utilization of straw. The Ministry of Agriculture and Rural Affairs has proposed building about 400 national key counties for comprehensive straw utilization and 1600 straw comprehensive utilization display bases, which made the comprehensive utilization rate of straw nationwide remain above 86% in 2023. This means that higher goals have been proposed for straw return technology and services. However, due to the small number of farmers in China’s large territory, as the direct implementers of straw returning, farmers have different knowledge about and understanding of straw returning policies in the process of step-by-step policy distribution, resulting in differences in cognition, and ultimately leading to differences in decision-making behaviors of farmers. Therefore, it is necessary to explore the influencing factors on farmers’ returning straw decisions from theoretical and empirical perspectives. In this paper, a logit regression model is constructed to identify the factors affecting farmers’ straw-returning decisions, and an evolutionary game model is used to analyze the equilibrium process between farmers and local governments in the straw-returning process, in order to reveal the path of policy on farmers’ straw-returning behavior.

The decision-making choice of farmers’ straw treatment behavior directly affects the efficiency of straw return to field. Governments of various countries have actively formulated effective policies to enhance farmers’ willingness to return straw to the field. Domestic and foreign scholars have conducted a series of studies on how government policies affect farmers’ straw disposal behavior, mainly focusing on the following aspects:

Joyce analyzed farmers’ behavioral decision of returning straw to the field from the perspective of psychology [1]. According to the study of Jallow MFA, the age factor can affect the decision-making of farmers [2]. Doss C. R. found that gender also had a great impact on farmers’ decision-making [3]. According to Merwe R. V., factors such as public opinion have a significant impact on farmers’ decision-making in social networks [4]. Supaporn found that education level, technical cognition and the number of family members in the labor force are the main factors affecting farmers’ decision-making behavior of returning straw to the field [5,6,7]. Education level and household land quantity have a negative impact on farmers’ decision-making and choice behavior [8,9,10,11,12]. Tong Hongzhi found that the willingness of farmers in non-plain areas to adopt returning straw to the field is restricted by family poverty, and the government’s restrictive supervision and punitive measures have a positive impact on them, while farmers in plain areas are more sensitive to government subsidies and penalties, and the punitive measures have a negative impact due to the substitution effect of other resource utilization methods [13]. In the study of multiple factors that have a significant impact on farmers’ willingness to return straw, it is found that the level and structure of farmers’ capital endowment are important factors restricting the rate of returning straw to the field [14]. Social learning and social trust not only have a direct positive impact on farmers’ willingness of returning straw to the field, but also have an indirect positive impact on farmers’ willingness to return straw to the field through ecological cognition [15]. Implementing government regulations and increasing farmers’ positive perceived value can effectively improve farmers’ willingness to return straw to the field [16].

Norton, Illac, Hellin J., Mueller and other studies show that improving the level of government subsidies can improve farmers’ willingness to return straw to the field [17,18,19,20]. Ekboir J. concluded that the natural environment, soil situation, technological development and other factors have a significant impact on the straw disposal of farmers [21]. Cao Guangqiao found that the government’s compulsory or subsidy measures, the degree of grain commercialization and the health of the household members have a positive impact on the tendency of farmers to return straw to the field. Whether there is an economic value of straw and the amount of land for farmers have a negative impact on farmers’ willingness of returning straw to the field [22]. Qi Jun proposed to improve the comprehensive utilization efficiency of straw by strengthening the knowledge publicity of straw’s comprehensive utilization, increasing the upgrading and promotion of technology relating to returning straw to the field, and government enterprises and third-party organizations jointly improving the straw collection, storage and transportation system [23]. The information of media channels and social communication can help increase the probability of farmers adopting returning straw to the field, and the interaction between the two is also positive [24].

The straw returning behavior of farmers has a scale economy effect [25]. There is a robust inverted “U” relationship between the scale of land management and the implementation of environmentally friendly production behavior of farmers, and the moderate expansion of land scale is conducive to the straw returning behavior of farmers [26]. The extension service of grassroots agricultural technology stimulates farmers’ willingness to take social responsibility, and enhances farmers’ willingness to return straw to the field to a certain extent [27,28], which has a partial spillover effect and more obvious positive effect on small-scale farmers [29].

In summary, most of the existing studies explore the strength and direction of the influence of external factors such as individual family circumstances, government supervision and subsidies, technology promotion, and social networks. Few studies have been conducted exploring the influence of policies on farmers’ willingness to return straw from the perspective of internal factors. Even so, there is a lack of relevant research about the operating mechanism and successful conditions of policies on encouraging returning straw. Currently, there are many outstanding difficulties in the implementation of policies on returning straw to the field. The traditional habit of burning straw is deeply rooted, leading to a discrepancy between farmers’ environmental awareness and behavior. What is worse, the immaturity of relevant public service, the accumulation of resources in a large amount of straw affecting spring ploughing and the information asymmetry between the government and farmers are all existing problems. Under the basic agricultural situation of small farmers in large countries, to promote the modernization of small scale farmers and agricultural resources, the grassroots organization structure must be adapted to it. Heilongjiang Provincial government has incorporated the task of returning straw to the field into the management of the “field chief system”. It guided all localities to establish a leadership responsibility system and special administrator system of straw resource ledger, but the solutions to many problems directly related to farmers’ behavior are still being explored.

2. Theoretical Analysis and Research Hypothesis

2.1. The Influence of Internal Cognition on Farmers’ Willingness of Returning Straw to the Field

According to the theory of planned behavior, behavioral intention is the most direct factor affecting behavior, and in turn is influenced by behavioral attitude [30]. Studies have shown that socially preferred farmers are staunch practitioners of returning to the land [31]. Socially preferred farmers not only pay attention to their own interests but also pay attention to the ecological environment. Farmers’ cognition of environmental changes and crop conditions affect their attitudes towards straw returning behavior [32]. As the “surplus” of crops, straw is rich in nitrogen, phosphorus, potassium and other nutrients, and has the characteristics of “use is benefit, abandon is harm”. As the direct straw returning technology is mature, straw returning can increase soil organic matter, improve soil structure, enhancing soil fertilizer and water retention performance. When farmers find that the surrounding ecological environment becomes better after returning straw to the field, they will inevitably have a favorable impression of the return behavior. However, because it does not produce a direct economic value in addition to the farmers’ grain production, income targets and their educational level being low, their perception and acceptance of new technologies are weak. Therefore, in this paper, the effects of internal cognition on farmers’ willingness of returning straw to the field are investigated from three aspects: compensation cognition, environmental change cognition and crop state cognition.

H_1a: 

The recognition of straw returning to the field affects farmers’ willingness of returning straw to the field;

H_1b: 

The cognition of environmental changes after straw returning to the field affects farmers’ willingness of returning straw to the field;

H_1c: 

The cognition of the change in chemical fertilizer applied after straw returning to the field affects farmers’ willingness to return straw to the field;

H_1d: 

The change in crop disease resistance after straw returning affects farmers’ willingness to return straw to the field.

H_1e: 

The cognition of crop yield change after straw returning to the field affects farmers’ willingness to return straw to the field.

2.2. The Influence of Policy Satisfaction on Farmers’ Willingness of Returning Straw to the Field

The higher the degree of government support for a certain behavior, the easier it is for farmers to make that decision. Farmers’ satisfaction with the policy also reflects acceptance of the policy [33,34,35]. At this stage, household-based farmers are still the main body of agricultural production in China [36]. Under the rational economic participant assumption, farmers are bound to be very concerned about whether the economic benefits generated by returning straw to the land can cover or even exceed the cost. Due to the cost of straw return and the existence of positive externalities, the enthusiasm of farmers to participate in it is not high, and economic compensation can stimulate farmers’ behavior [37,38]. The government not only makes up for the cost of returning straw to the field by issuing subsidies, alleviating the pressure on farmers in terms of technology and capital, but also provides technical, financial and other services for farmers to return straw to the field, ensuring that farmers feel better than the traditional model of policy care in the process of returning to the field. Therefore, this paper examines the influence of policy satisfaction on farmers’ willingness of returning straw to the land from both subsidy policy and service policy. Based on this, the following research hypothesis is proposed.

H_2a: 

The satisfaction with the field returning service policy affects the farmers’ willingness to return the straw to the field;

H_2b: 

The satisfaction with the subsidy policy affects farmers’ willingness to return straw to the field.

Based on the above hypothesis, the research framework is constructed as shown in Figure 1.

3. Model Construction, Data Sources, and Variable Description

3.1. Model Setting

This paper mainly discusses the influence of farmers’ internal cognition and policy satisfaction on farmers’ willingness to return straw to the field. The explained variables belong to dichotomous variables, so the binary logit model based on the micro level is selected for regression. The model is set as follows:

$$Logit\left(retur{n}_i=1\right)=\Phi \left({\beta }_0+{\beta }_{1}Cognitio{n}_i+{\beta }_{2}Satisfactio{n}_i+{\beta }_3{X}_i+{\epsilon }_i\right)$$

(1)

where β₁, β₂, β₃ are the parameters to be estimated; i means different farmers; $retur{n}_i$ represents the binary dummy variable of whether farmer i returns straw to the field; $Cognitio{n}_i$ and $Satisfactio{n}_i$ show two key variables of internal cognition and policy satisfaction; X_i is the relevant control variables for farmer i; ε_i is a random disturbance term.

3.2. Regional Characteristics and Data Sources

Hailun is located in the northeast region which is a county-level city under the jurisdiction of Suihua in Heilongjiang Province and is also an important national commodity grain base. In 2021, the total output of straw in the city was 1.6 million tons, and the collection amount can reach 1.3655 million tons. With the goal of 100 percent of corn, rice and soybean returning to the field, exploring the willingness and mode selection of farmers’ returning straw to the field can help the Hailun Municipal government to better guide the work. The original data of this paper come from the survey of Dongfeng, Donglin, Haibei, Qianjin and Zhyinhe in Hailun, Heilongjiang Province from January to March 2022. The contents of the survey include information about the head of the household, information about the family, the internal cognition and satisfaction with the policy. A total of 500 questionnaires were distributed in this survey, 100 in each place, and 397 valid questionnaires were obtained after sorting, with an effective rate of 79.4%, indicating that the survey was effective.

3.3. Variable Descriptive Statistics

3.3.1. Dependent Variable

The dependent variable is “farmers’ willingness of returning straw to the field”, and the questionnaire is “ Which straw disposal method do you prefer to adopt?” This question was characterized, and the sample answering “straw returning to the field” was assigned a value of 1, and “straw leaving the field” was assigned a value of 0.

3.3.2. Key Variables

On one hand, farmers’ cognition of compensation, environmental change and crop status after returning straw to the field all play a significant role in their willingness to return straw to the field. Therefore, the internal cognition of farmers was investigated from the above three aspects, and was characterized by variables such as “cognition of compensation”, “cognition of environmental change” and so on. On the other hand, farmers’ satisfaction with service and the subsidy policy of returning straw to field both play a driving role. Therefore, the influence of policy satisfaction on farmers’ willingness of returning straw to field was investigated from the above two aspects, which are service and subsidy.

3.3.3. Controlled Variables

Referring to existing studies [39,40,41], we further controlled the characteristics of household heads such as gender, age, education level, political status, and household characteristics such as participation organization, annual income, and labor force, as well as additional service variables such as transportation services and recovery services. The implications and assignments of the variables are shown in

Table 1. Variable definitions and assignments.

Type	Variable	Assignment	Mean	Standard Deviation
Interpreted variable	Willingness to return the straw to the field	Which straw disposal method do you prefer to use? Straw leaving the field = 0; Straw returning to field = 1	0.529	0.500
Key variables
Internal cognition	Cognition of compensation	Do you know the subsidy policy for comprehensive utilization of straw? Don’t know = 1; Attention only after the autumn harvest = 2; Pay close attention to and understand that = 3	2.778	0.478
	Cognition of environmental change	Changes in the surrounding ecological environment after straw resource utilization? Worse = 1; No change = 2; Better = 3	2.751	0.445
	Cognition of crop fertilization	Change in chemical fertilizer application after returning straw to the field? Reduce = 1; Constant = 2; Increase = 3	1.398	0.490
	Cognition of crop disease resistance	Changes in crop disease resistance after returning straw to field? Worse = 1; No change = 2; Better = 3	2.577	0.592
	Cognition of crop yield	Change in organic crop yield after returning straw to field? Decrease = 1; Constant = 2; Increase = 3	2.625	0.597
Satisfaction of the policy	Returning service policy	What is the satisfaction of returning straw service in this region? No = 1; Generally = 2; Yes = 3	2.605	0.601
	Returning subsidy policy	What is the satisfaction of the government subsidy policy of returning straw to the field? No = 1; Generally = 2; Yes = 3	2.390	0.820
Controlled variable
Householder characteristics	Gender	Female = 0; male = 1	0.887	0.317
	Age	≤30 = 1; 31–40 = 2; 41–50 = 3; 51–60 = 4; ≥61 = 5	3.385	0.873
	Education level	Primary school and below = 1; junior high school education = 2; high school, junior college and above = 3;	1.929	0.432
	Political status	Are you a member of the Communist Party of China? No = 0; Yes = 1	0.151	0.359
Family characteristics	Participating organization	Does your family join the various cooperatives? No = 0; Yes = 1	0.118	0.323
	Labor number	Number of household workers	2.249	0.644
	Annual gross income	CNY 20,000 and less = 1; CNY 20,000–50,000 = 2; CNY 50,000–100,000 = 3; CNY 100,000 and above = 4	2.743	0.659
Additional services	Transportation services	How convenient is the transport level? Inconvenient = 1; general = 2; convenient = 3	2.242	0.836
	Recycling services	Are there any straw purchasing and storage enterprises or units near the planting area? No = 0; Yes = 1	0.796	0.403

.

4. Results and Analysis

4.1. Results and Analysis of the Binary Logit Regression

A multi-collinearity test was conducted before using the logit model estimation, and the maximum value of variance inflation factor column was 3.85 < 10, so there is no multicollinearity situation.

Table 2. Logit regression results.

Type	Variable	Regression (1)	Regression (2)	Marginal Effect
Internal cognition	Cognition of compensation		−0.644 * (0.072)	−0.0885 (0.068)
	Cognition of environmental change		−2.017 *** (0.003)	−0.277 ** (0.002)
	Cognition of crop fertilization		−3.502 *** (0)	−0.481 *** (0.000)
	Cognition of crop disease resistance		1.077 ** (0.024)	0.148 * (0.020)
	Cognition of crop yield		0.161 (0.76)	0.0221 (0.760)
Satisfaction with the policy	Returning service policy		0.463 (0.237)	0.0636 (0.233)
	Returning subsidy policy		−1.567 *** (0)	−0.215 *** (0.000)
Householder characteristics	Gender	0.485 (0.172)	0.689 (0.115)	0.0947 (0.110)
	Age	−0.343 ** (0.012)	−0.351 ** (0.043)	−0.0483 * (0.039)
	Education level	−0.696 ** (0.016)	−0.176 (0.662)	−0.0242 (0.662)
	Political status	0.935 *** (0.006)	1.208 ** (0.014)	0.166 * (0.012)
Family characteristics	Participating organization	0.729 * (0.061)	0.857 * (0.076)	0.118 (0.072)
	Labor number	−0.072 (0.68)	−0.303 (0.241)	−0.0417 (0.238)
	Annual gross income	0.477 ** (0.016)	0.418 (0.108)	0.0575 (0.104)
Additional services	Transportation services	−0.36 ** (0.016)	−0.561 * (0.097)	−0.0771 (0.092)
	Recycling services	1.697 *** (0)	1.354 *** (0.001)	0.186 *** (0.000)
Constant term		0.284 (0.786)	12.135 *** (0)
chi-square		60.179 ***	215.510 ***
Quasi R2		0.110	0.393
Observational values		397	397	397

Note: ***, ** and * are significant at 1%, 5%, and 10%, respectively.

shows the estimated results, and regression (1) is the benchmark regression for the control variables. Regression (2) is the result of the included key variables including internal cognition and policy satisfaction variables. In addition, the regression results of the marginal effect of each variable on the interpreted variable were obtained according to the regression (2). By comparing regression (2) with regression (1), it was found that the quasi-R2 increased from 0.110 to 0.393, which showed that the inclusion of key variables had an significant impact on the regression results.

From the regression results (2), environmental change cognition, crop fertilization cognition and returning subsidy policy satisfaction were statistically significant at 1%. Crop resistance cognition was statistically significant at 5% and compensation cognition was statistically significant at 10%. Crop yield cognition, returning service policy satisfaction, and burning regulatory policy satisfaction were not significant. Moreover, according to the regression results of marginal effect, the variables that strengthen the farmers’ willingness of returning straw from high to low are: crop fertilization cognition, ecological cognition, satisfaction with returning subsidy policy, and crop disease resistance cognition.

4.1.1. Intrinsic Cognitive Analysis

The perception of crop disease resistance positively affects farmers’ willingness to return straw to the field at 5% level of significance. When farmers find that crops have stronger resistance to disease after returning straw to the field, they will be more inclined to return straw to the field. Environmental change cognition and crop fertilization cognition significantly negatively affect farmers’ willingness to return straw to the field. The possible reason is that farmers believe that the environmental condition has nothing to do with their own interests, and only after they know that the environmental condition is better, farmers are reluctant to return straw to the field. The amount of crop fertilizer is related to the planting costs for farmers, so it is reasonable to find that farmers do not return straw to the field when the amount of fertilizer is increased. Farmers’ perception of compensation negatively affects their willingness to return straw to the field at the 10% level. The possible reason is that the more farmers understand the content of the subsidy policy for comprehensive utilization of straw, the more dissatisfied they are with the existing subsidy scope and amount, and then refuse to return straw to the field.

4.1.2. Policy Satisfaction Analysis

From the perspective of farmers’ satisfaction with the subsidy policy about returning straw to the field, the negative impact on willingness indicates that though farmers accept the subsidy, they still refuse to carry out the policy. It may because farmers know little about the subsidy policy or they do not expect to depend on subsidy fundamentally. Subsequent interviews have confirmed these reasons. From the perspective of farmers’ satisfaction with straw return services, the current service of returning straw has no significant impact on farmers’ willingness, indicating that the returning straw service has not yet formed a professional division of labor service embodiment and farmers cannot find a returning straw service at expected costs.

4.1.3. Control Variables Analysis

The influence of personal characteristics: Compared with the traditional incineration disposal method, returning straw to the field belongs to the application of new technology, whereas older farmers are more accustomed to traditional practices, therefore, it is understandable that it is difficult to change behavior to that of returning straw to the field. Farmers with political status as Party members are more active in responding to government policies and responding to the government’s call for straw to be returned to the field, so it is easier to have the will to return straw to the field.

The influence of family characteristics: Agricultural cooperatives provide services for small-scale farmers, making up for the high cost of returning straw to the field, so they are more inclined to do it. Farmers with a higher annual income also have a stronger sense of social responsibility, and are more likely to return straw to the field considering environmental issues and responding to the government’s call.

The impact of additional services: Some local enterprises provide straw recycling services, and the recycling price may not be as high as the subsidy price given by the government. In addition, various transportation and labor costs, such as inconvenient transportation, make farmers more inclined to return straw to the field.

4.2. Robustness Test

In this paper, the model replacement method was used to test robustness (

Table 3. The robustness test.

Variable	Model Replacement (Probit)		Model Replacement (ols)
	Coefficient	Standard Error	Coefficient	Standard Error
Cognition of compensation	−0.373 *	0.2	−0.085 *	0.047
Cognition of environmental change	−1.132 ***	0.351	−0.223 ***	0.07
Cognition of crop fertilization	−1.927 ***	0.26	−0.47 ***	0.05
Cognition of crop disease resistance	0.66 **	0.274	0.149 **	0.061
Cognition of crop yield	0.101	0.294	0.021	0.064
Returning service policy	0.243	0.223	0.081 *	0.049
Returning subsidy policy	−0.89 ***	0.171	−0.22 ***	0.041
Controlled variable	Controlled	Controlled	Controlled	Controlled
Constant term	6.477 ***	1.45	1.911 ***	0.304
chi-square	215.776 ***		17.641 *** (F value)
Quasi R2	0.393		0.426
Observational values	397		397

Note: ***, ** and * are significant at 1%, 5% and 10%, respectively.

). Probit regression and OLS regression were performed on the original data to verify the robustness of the model. The results show that there is no significant difference between robustness test and regression results.

5. Evolutionary Game

From the above analysis results, we can see that there is information asymmetry between farmers’ willingness to return straw to the field and government policies. First of all, farmers have a certain understanding of the environmental changes after straw is returned to the field, but they pay more attention to the economic benefits brought through this behavior, and do not understand the huge economic, ecological and social benefits of straw returning technology and services that have been promoted. Secondly, farmers do not understand the policies and regulations of national and local governments at all levels on the utilization of straw resources. Due to information asymmetry, the policies of returning straw are not carried out sufficiently, leading to a low willingness level. It ultimately causes the rate of returning straw not to achieve the expected effect. Therefore, this paper uses the two decision-making subjects of farmers and local government to construct the game model to find out the policy conditions for farmers to form a stable willingness to return straw to the field, and uses numerical simulation to verify the conclusion.

5.1. Game Model Assumption and Payment Matrix Construction

Hypothesis 1:

Behavior decision-making subject and strategy choice.

In this game model, the decision-making subjects are farmers and local government departments, and are limited rational. The fertilizer utilization of returning straw to the field has obvious ecological, economic and social benefits, which is the most likely way to achieve the large-scale utilization of straw under the current technical conditions. Therefore, this paper takes (straw returning, no straw returning to the field) as the selection strategy of farmers to dispose of straw. This paper assumes that the government’s choice strategy is (comprehensive subsidy, cash subsidy), respectively. Among them, comprehensive subsidy refers to the government not only providing a cash subsidy to farmers, but also providing an agricultural machinery financial subsidy, service subsidy and so on. Cash subsidy refers to the government only providing a cash subsidy to farmers who return straw to the field.

Hypothesis 2:

The probability of the strategy selection.

The probability of farmers returning straw to the field is x(0 ≤ x ≤ 1), and the probability of not returning straw is (1 − x).

The probability of local governments choosing comprehensive subsidies is y(0 ≤ y ≤ 1), and the probability of choosing a cash subsidy is (1 − y).

Hypothesis 3:

The payment of the subjects.

When the farmer returns straw to the field, the income is R₁, and the cost C₁ will occur. When farmers use burning and leaving the field without returning straw to the field, the income is R₂, the cost is C₂, and R₁ > R₂. For the government, the comprehensive subsidy will have a fixed cost M₁, and the cash subsidy will cost M₂, M₁ > M₂. If the farmers return straw to the field, the local government will receive the reward from the higher government T. If the farmers do not return straw to the field, the comprehensive subsidy and cash subsidy will produce the hidden environmental cost M₃ and M₄, respectively, as the performance loss caused by straw burning cannot be measured, so the relationship between M₃ and M₄ is uncertain, which will be further discussed in the future.

Based on the above assumptions, the payment matrix under the different strategies of farmers and government departments is shown in

Table 4. Payment Matrix.

	Comprehensive Subsidies for Local Governments	Cash Subsidies from Local Governments
Farmers choose to return straw to the field	R1 − C1, T − M1	R2 − C1, T − M2
Farmers choose non-straw returning to the field	R3 − C2, −M3	R3 − C2, −M4

.

5.2. Evolutionary Game Model Construction

Behavior analysis of the farmers: If y adopts the proportion of comprehensive subsidy strategy for the government, then 1 − y adopts the proportion of cash subsidy strategy for the government. Therefore, the expected return of the straw returning strategy U₁₁ is:

$$U_{11}=y\left(R_1-C_1\right)+\left(1-y\right)\left(R_2-C_1\right)=R_2-C_1+y\left(R_1-R_2\right)$$

(2)

When the straw is not returned to the field, the farmers’ expected income U₁₂ is:

$$U_{12}=y\left(R_3-C_2\right)+\left(1-y\right)\left(R_3-C_2\right)=R_3-C_2$$

(3)

The average expected income of straw disposal $\overline{U_1}$ for farmers is:

$$\overline{U_1}=x{U}_{11}+\left(1-x\right)U_{12}$$

(4)

From Equations (2)–(4), the dynamic equation of returning straw to the field is:

$$G\left(X\right)=\frac{\partial x}{\partial t}=x\left(1-x\right)\left[R_2-C_1+y\left(R_1-R_2\right)-R_3+C_2\right]$$

(5)

From Equation (5), when $x=1,0$ or $y^{*}=\frac{-R_2+C_1+R_3-C_2}{R_1-R_2}$, farmers adopt the policy of returning straw to the field, achieving local balance.

Government behavior analysis: Assuming that x is the proportion of farmers picking and returning straw to the field, then 1 − x is the proportion of farmers not returning straw to the field. Therefore, the government adopts the comprehensive subsidy period.

$$U_{21}=x\left(T-M_1\right)+\left(1-x\right)\left(-M_3\right)$$

(6)

Expected income U₂₂ when the government adopts cash subsidy is:

$$U_{22}=x\left(T-M_2\right)+\left(1-x\right)\left(-M_4\right)$$

(7)

Average expected return of the government subsidy strategy $\overline{U_2}$:

$$\overline{U_2}=y{U}_{21}+\left(1-y\right)U_{22}$$

(8)

From Equations (6)–(8), the dynamic equation of the government taking comprehensive subsidy is:

$$G\left(Y\right)=\frac{\partial y}{\partial t}=y\left(1-y\right)\left[x\left(-M_1+M_2+M_3-M_4\right)-M_3+M_4\right]$$

(9)

From Equation (9), when $y=0,1$ or $x^{*}=\frac{M_3-M_4}{-M_1+M_2+M_3-M_4}$ the government’s comprehensive subsidy policy can achieve a local equilibrium.

In the point (0, 0), (0, 1), (1, 0), (1, 1), (x, y), G (X) = 0 and G (Y) = 0. These are the local equilibrium points of the evolutionary system. With reference to the method proposed by Friedman, the stability of equilibrium points of an evolutionary system can be obtained from the local stability analysis of the Jacobian matrix of the system.

According to Equations (8) and (9), the Jacobian matrix can be obtained as:

$$J=\left[\begin{array}{cc}{G^{\prime }}_x\left(X\right)& {G^{\prime }}_y\left(X\right)\\ {G^{\prime }}_x\left(Y\right)& {G^{\prime }}_y\left(Y\right)\end{array}\right]=\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right]$$

(10)

$$\{\begin{array}{l}{a}_{11}=\left(1-2x\right)\left[R_2-C_1+y\left(R_1-R_2\right)-R_3+C_2\right]\\ a_{22}=\left(1-2y\right)\left[x\left(-M_1+M_2+M_3-M_4\right)-M_3+M_4\right]\\ a_{12}=x\left(1-x\right)\left[R_1-R_2\right]\\ a_{21}=y\left(1-y\right)\left(-M_1+M_2+M_3-M_4\right)\end{array}$$

(11)

The stability of matrix J at the above five equilibrium points is analyzed (

Table 5. Analysis of the stability results of the evolutionary game of farmers’ and governments’ strategy choices.

Equilibrium Point	Condition 1			Condition 2			Condition 3			Condition 4
	DetJ	TrJ	Stability	DetJ	TrJ	Stability	DetJ	TrJ	Stability	DetJ	TrJ	Stability
A(0, 0)	+	-	ESS	-	unsteady	saddle point	+	+	unstable	-	unsteady	saddle point
B(0, 1)	-	unsteady	saddle point	+	-	ESS	-	unsteady	saddle point	+	+	unstable
C(1, 0)	-	unsteady	saddle point	-	unsteady	saddle point	+	-	ESS	+	-	ESS
D(1, 1)	+	+	unstable	+	+	unstable	-	unsteady	saddle point	-	unsteady	saddle point
E(x*, y*)	unsteady	0	\	-	0	\	-	0	\	unsteady	0	\

Note: “\” means that point E (x*, y*) does not fall within the ABCD range.

). Condition 1 (R₂ − C₁ < R₁ − C₁ < R₃ − C₂, M₃ > M₄) and condition 2 (R₂ − C₁ < R₁ − C₁ < R₃ − C₂, M₃ < M₄) means that the net income of the farmer derived from returning straw to the field is lower than the net income of not returning straw to the field, and when the farmers do not return straw to the field, the government adopts comprehensive subsidies and cash subsidies of profit and loss is different. Condition 3 (R₁ − C₁ > R₂ − C₁ > R₃ − C₂, M₃ < M₄) and condition 4 (R₁ − C₁ > R₂ − C₁ > R₃ − C₂, M₃ > M₄) indicate that when the farmers do not return the straw to the field, the net income of returning straw to the field is higher than the net income of not returning straw under the government cash subsidy. The government adopts comprehensive subsidies or cash subsidies for different profit and loss.

Since this paper expects farmers to stably and steadily adopt the measures of returning straw to the field, the evolution path map based on condition 3 and condition 4 and the corresponding result analysis are presented below.

The value of y* under condition 3 and condition 4 is always less than 0. When M₃ < M₄, x* exists, the instability points are A (0, 0), and the saddle points are B (0, 1) and D (1, 1), as shown in Figure 2A. When local governments and farmers are in the initial state of “zero experience” in the practice of straw returning policy, the government needs to first issue comprehensive subsidy standards to encourage farmers to return straw to the field. Under such conditions, according to different initial states of farmers, in the evolutionary game between farmers and local governments, when the initial state of the game is x = x* in the right region, farmers are more likely than x* to choose the straw returning strategy. When the initial state of the game is in the left region of x = x*, the possibility of farmers choosing the straw returning strategy is lower than x*. The two initial states will eventually converge to C (1, 0). The difference lies in the different evolutionary paths of government decision-making, as shown in Figure 2A path (a) and (b). It can be concluded that the evolutionary path of the game between farmers and local governments has a great correlation with the location of x*. If the value of x* becomes smaller, the probability of farmers choosing straw to return to the field will increase, and the government can directly tend to cash subsidies to ease the financial pressure, and the game will tend to be stable faster. When M₃ > M₄, the x* value is in the interval other than [0, 1], the instability point is B (0, 1), and the saddle point is A (0, 0) and D (1, 1), as shown in Figure 2B. The results show that under the background of the Ministry of Agriculture and Rural Affairs promoting returning straw to the field, local governments responded positively and publicized the straw returning policy to farmers with comprehensive subsidies as the starting point. No matter what the initial state of the game is, it will eventually converge to C (1, 0).

5.3. Simulation and Analysis of the Evolutionary Game Model

In order to more intuitively describe the path of the game between farmers and local governments to reach the evolutionarily stable equilibrium strategy under different conditions, this paper uses MATLAB (version 2021) to simulate and analyze the evolutionary game model.

Table 6. Value setting based on the parameters of conditions 3 and 4.

	R1	R2	R3	C1	C2	M1	M2	M3	M4	(x,y)
Condition 3-1	10	9.5	8	5	4	10	8	6	10	(0.3, 0.8)
Condition 3-2	10	9.5	8	5	4	10	8	6	10	(0.7, 0.8)
Condition 4-1	10	9.5	8	5	4	10	8	10	6	(0.3, 0.8)
Condition 4-2	10	9.5	8	5	4	15	8	10	6	(0.3, 0.8)

shows the initial value. After several iterations, the evolutionary strategies of both farmers and local governments converge to C(1, 0), and the final evolutionary stability strategy is as follows: local governments provide adequate cash subsidies, and farmers are 100% willing to return straw to the field. In addition, there are significant differences in evolution speed under different parameter conditions, as shown in Figure 3.

Due to the spread of smog and other invisible damage caused by burning straw, it is difficult to quantify the loss of political performance, which means the relationship between the size of M₃ and M₄ is uncertain. Therefore, in reality, it is uncertain whether the stable path of straw return policy and farmers’ willingness to return straw in a specific region belongs to condition 3 or condition 4. In order to make both sides of the game reach the evolutionary stable strategy as soon as possible, it is necessary to control the value of x* as close to 0 as possible. Because $x^{*}=\frac{{\mathrm{M}}_3-{\mathrm{M}}_4}{{-\mathrm{M}}_1+{\mathrm{M}}_2+{\mathrm{M}}_3-{\mathrm{M}}_4}$, even if the difference between M₁ and M₂ is as large as possible, the local government needs to increase the comprehensive subsidy in reality. Secondly, in terms of the income and cost to farmers, it is necessary to control the net income of farmers who return straw to the field when the government only provides cash subsidies, which is higher than that of those who do not return straw to the field. In fact, in the short term, the cash subsidies provided by the government cannot have a large increase. The only way to start is to reduce the cost of returning farmland and improve the value recognition of farmers on straw to the field.

6. Conclusions and Policy Recommendations

In this study, a logit regression model was established to analyze the effects of internal cognition and policy satisfaction on farmers’ willingness of returning straw to the field. According to the empirical conclusion, the payment matrix of the game between farmers and the government was constructed, and the paper further discussed how local governments can effectively make farmers stably choose straw to return to the field. The main conclusions are as follows:

• The cognition of crop fertilization, ecological cognition, satisfaction with the subsidy policy and cognition of compensation had significant negative effects on the willingness of farmers to return straw, and their utility intensity decreased successively. However, crop disease resistance cognition had a positive effect on farmers’ willingness to return straw to the field.
• The equilibrium process of the evolutionary game between farmers’ behavior and the government’s straw returning policy can be divided into three stages. In the primary stage, the government only provides cost subsidies in the form of cash, and the willingness of farmers to return straw depends on the net income that comes from returning land. In the intermediate stage, the government provides comprehensive compensation through various forms such as cash subsidies, technical services, agricultural machinery purchase subsidies and financial services. The comprehensive compensation of the government and farmers’ willingness to return straw to the field will increase simultaneously. In the advanced stage, the straw returning technology and special services gradually mature, and the comprehensive income from the reduction in straw returning costs increases and at this time, cash subsidies provided by the government to farmers can make up for the cost of returning straw to the field, and farmers’ willingness has reached a stable state. At present, China’s straw returning policy is in the intermediate stage.

Based on this, this study has the following suggestions:

• In order to improve the willingness of farmers to return straw to the field, local governments need to strengthen the implementation of policies, ensure that the policy of straw returning to the field is implemented and improve the pertinence of policies at the level of farmers. As for the specific implementation subject of returning straw to the field, farmers’ cognition of the policy mainly depends on the implementation and communication of the grass-root governments of villages and towns. It is very important to give play to the promoting role of village cadres, actively participate in the promotion of straw returning technology and the interpretation of resource returning policies, and focus on the demonstration and leading role of large farmers and new business entities in the village, thus guiding farmers to rationally view the long-term and short-term interests generated by returning straw.
• At present, to improve farmers’ willingness returning straw to the field, local governments should improve the fiscal subsidy policy, improve the use efficiency of subsidy funds, expand the scope of non-cash subsidies, increase subsidies for the purchase of agricultural machinery for returning straw to the field and support farmers to participate in straw industries including the production of organic fertilizer, feed processing and edible fungi. On the other hand, it is very important to establish and improve the social service organization system of straw returning to the field. Straw returning technical service subsidies should be supported as well as relevant enterprises and third-party straw technical service institutions should be united to form a straw comprehensive service organization, which can accept the supervision of the main management department, with reasonable service quality and service price.