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BY 4.0 license Open Access Published by De Gruyter Open Access January 25, 2024

Evolutionary game analysis of government, businesses, and consumers in high-standard farmland low-carbon construction

  • Yuting Dai EMAIL logo , Jinbao Liu and Yichun Du
From the journal Open Geosciences

Abstract

Soil is an important carbon reservoir, and high-standard farmland construction projects have significant potential to promote low-carbon development. In order to study the management and implementation of low-carbon production in high-standard farmland construction projects, the tripartite evolution game model of government, business, and consumer is constructed based on the tripartite bounded rationality. Then, the behavior strategy of tripartite stakeholders is analyzed with the method of system dynamics. Finally, the evolution process of tripartite interaction behavior is simulated using the MATLAB tool. The results show that: (1) The subsidy and punishment mechanism of the government must be aligned. In addition, the net income of government regulation is higher than the sum of the government’s environmental governance fees and fines of non-regulation; (2) The government, business, and consumers all choose their own behavioral strategies based on their own interests. (3) When the government’s environmental governance fee reaches a particular value, the system will appear imbalanced. In light of this, it is suggested that the government should increase support for business and use media publicity, consumer subsidies, and other measures to promote the consumption of low-carbon products. The business should constantly reduce the cost of carbon emission reduction through technological innovation.

1 Introduction

With the rapid development of China’s economy, there has been a significant increase in industrialization and urbanization. However, this “fast economy” has also resulted in numerous environmental problems. One of the most pressing issues for China’s sustainable development is carbon emissions. Agriculture, as a crucial component, also carries a significant responsibility for carbon emissions. Consequently, finding ways to reduce carbon emissions in farmland and enhance resource utilization efficiency has become a prominent research focus in the agricultural field [1]. High-standard farmland construction projects can not only increase industrial capacity but also reduce carbon emissions from farmlands [2]. However, the management and implementation of low-carbon production in high-standard farmland construction projects still need to be studied. The greenhouse effect, which leads to extreme weather, significantly impacts the economy, environment, and production activities of countries. CO2, CH4, and NO2 are important greenhouse gases in the atmosphere, contributing approximately 80% to the greenhouse effect [3]. Article 4 of the Paris Agreement proposes reducing carbon emissions and increasing foreign exchange. As a result, many countries are prioritizing carbon emission reduction [4]. Agricultural systems, being open ecosystems, are a significant source of carbon emissions [5]. Agriculture in Poland accounts for 7.7% of the country’s greenhouse gas emissions [6]. In Russia, agriculture contributed 7% of the country’s greenhouse gases in 2004 [7]. In China, agricultural production causes approximately 15% of the total greenhouse gas emissions [8]. To reduce agricultural carbon emissions, improving the quality of the factors that contribute to these emissions is necessary. This can be achieved by addressing the impact of human activities on farming systems. A demonstrated that a 1% increase in agricultural productivity in Kazakhstan from 1996 to 2020 resulted in a 0.34% reduction in CO2 emissions [9]. Scholars studied carbon emissions in different agricultural and rural areas. They analyzed the variability and convergence of carbon emissions and carbon intensity, aiming to provide a foundation for improving agricultural technical efficiency and achieving a sustainable reduction in carbon emissions in the future [10]. Johnson et al. summarized how to reduce agricultural greenhouse gas emissions and explored the impact of agricultural policies and practices on greenhouse gas emissions [11]. From 2010 to 2019, empirical tests concluded that improving agricultural production efficiency in China can reduce carbon emissions in the agricultural economy. As a result, the policy of constructing high-standard farmland was implemented [12].

The construction of high-standard farmland is a powerful tool to reduce carbon emissions in agriculture. It is also a critical government initiative aiming at improving agricultural production conditions in a planned and organized manner. In recent years, the central government has invested nearly 100 billion Yuan annually in constructing high-standard farmland. Most of this investment is allocated to constructing “water, road, and forestry networks” and “soil improvement.” Another portion is dedicated to enhancing infrastructure and upgrading the organic content of farmland. These measures aim to increase the farmland’s ability to absorb greenhouse gases and sequester carbon dioxide. This will increase the capacity of farmland to absorb greenhouse gases and sequester carbon dioxide, transforming farmland from a carbon source into a carbon sink. Based on the SARR model and data from 280 urban agricultural sectors in China [13], this study analyzes the role of high-standard farmland projects in agricultural carbon reduction from the perspectives of policy and carbon emissions [14].

In the process of high-standard farmland construction, the government is the main body for implementing carbon emission reduction in high-standard farmland projects and constantly transforms its policies based on public interests; businesses, as the main body of construction, focus on their interests. Therefore, to reduce carbon emissions from high-standard farmland, it is essential to understand the interplay and dynamic evolution process between stakeholders. This understanding forms the basis for developing reasonable and practical measures to reduce carbon emissions. Under the government’s low-carbon policy regulation, industrial adjustment can be effectively carried out to force businesses to carry out low-carbon production [15] and only when businesses get certain rewards for low-carbon production will they choose to implement the policy of low-carbon production [16,17], and consumers’ consumption of low-carbon production products will also directly influence the implementation of the government and businesses, the dynamic of interest subjects in the context of low-carbon policy coordination remains a crucial issue [18,19,20].

Game theory is originally a theory of mathematics, which is a process of using the method of mathematical design to find the optimal solution when the participants choose strategies in the process of game. From 1928 to 1950, mathematicians primarily focused on studying the existence of equilibrium and the rationality of participants in two-person non-zero-sum games. In 1994, the game theory research conducted by mathematicians and economists, notably John Nash, significantly expanded the scope of applicable research. It was proposed that nearly all problems solvable through mathematical modelling can be considered game problems to some degree [21,22]. Therefore, evolutionary game theory has been widely used in various daily activities and urban utilization. Xu and Lv are committed to promoting the evolution of the ideal low-carbon operation model, using the theory and method of evolutionary game to analyze the results of game interaction among businesses, governments, and consumers [23]. Some scholars integrated digital green innovation into agricultural high-end equipment manufacturing system or other systems [24,25]. Zhang et al. investigated the dynamic changes in oil prices and corporate carbon reduction behavior by establishing an evolutionary game model. This study provides a theoretical reference for the government to formulate reasonable low-carbon policies [26]. Barari et al. applied evolutionary game theory to study the cooperative relationship between producers and retailers and seek the balance between environmental interests and commercial interests [27]. In the evolutionary game, an important concept is evolutionary strategy, and the other is dynamics, which provides a powerful means for studying the stable strategy of evolutionary games [28,29]. Xu et al. established a multi-objective optimization design model for low-carbon products, which realized the government’s supervision of enterprise carbon emissions and met the win–win needs of stakeholders [30]. Wu et al. established a tripartite game model, discussed the relationship between stakeholders in urban land use using the concept of evolutionary game theory, and analyzed the conditions and outcomes of achieving game balance [31]. A game model is first used to analyze the decision-making game and its stability strategy among multiple stakeholders in the recycling of construction waste [28,32]. Some scholars constructed a three-player game model for enterprises [33]. The quantum evolutionary game model for new energy enterprises and village collectives was constructed. It provides a theoretical basis for scientific and effective cooperation [34]. The above analysis results laid the foundation for the evolutionary game of high-standard farmland low-carbon production.

To sum up, domestic and foreign scholars have made valuable explorations on carbon emission reduction using evolutionary game theory, providing a theoretical basis for this study. However, there are also some limitations: first, domestic and foreign scholars are studying high-standard farmland low-carbon production, but most of them focus on the effects and measures of low-carbon production, while the management of low-carbon production is rarely mentioned. But this is the key to whether high-standard farmland will adopt low-carbon production. Second, most scholars are based on the game relationship between daily activities and stakeholders in urban utilization, and there are few studies on the game relationship between stakeholders in the construction of high-standard farmland projects. However, the dynamic coordination of low-carbon production of high-standard farmland projects is the key issue for the government to improve agricultural production conditions. Third, few works of literature realize that high-standard farmland construction plays a vital role in carbon reduction behavior, and there is no systematic evaluation index system for high-standard farmland carbon emission measurement and net carbon sequestration value. Under realistic conditions, it is challenging for the government to regulate strictly based on probability, and it is also complicated for businesses to strictly reduce emissions based on probability.

Given this, and based on the bounded rationality hypothesis, this study focuses on a high-standard farmland construction project as the research subject. It fully combines the advantages of dynamic game theory and MATLAB simulation analysis methods to construct an evolutionary game model of stakeholders adopting different behavior strategies under low-carbon background, discusses the interaction mechanism and long-term evolution trend among stakeholders, and puts forward a method to calculate the value of high-standard farmland net carbon sequestration. It is the theoretical basis and useful reference for the sustainable development of agriculture in China.

2 Evolutionary game theory

Evolutionary game theory combines the analysis of game theory with the analysis of dynamic evolutionary processes. Unlike game theory, which focuses on static and comparative static equilibrium, it emphasizes a dynamic equilibrium. Evolutionary game theory has two main elements: replication dynamic equation and evolutionary stable equilibrium strategy.

Replication dynamics (RD) is a dynamic evolution mechanism first proposed by Su et al. [35]. The process of dynamically adjusting the strategy is described, and the RD equation expresses the law of evolution. The value of the strategy is proportional to the proportion x in which it is chosen and is also proportional to the difference between the expected return E(x) and the mean return. RD can accurately describe the behavior change trend of bounded rational individuals. Hofbauer and Sigmund argue that the stability of the internal equilibrium of the RD equation in the evolutionary game system is in line with the stability of the evolutionary strategy [36].

Evolutionary stability strategy (ESS) is a basic concept proposed by Maynard Smith to characterize the stable state of evolutionary games. For multi-party evolutionary games, Lyapunov stability theory is usually used to determine whether the internal equilibrium point of the RD equation is ESS. The Jacobian matrix and the set of internal equilibrium points are obtained from the RD equations of the evolutionary game system. If the real parts of all eigenvalues of the Jacobian matrix at an internal equilibrium point are negative. in that case, that is, when the determinant of the Jacobian matrix is positive. The sum of the elements on the diagonal is negative, then the pure strategy represented by the internal equilibrium point of the corresponding RD equation must be the system’s evolutionarily stable equilibrium point (sink). The ESS can be obtained at the equilibrium point. If the real part of all eigenvalues is positive, the internal equilibrium point is referred to as evolutionarily unstable (source). Suppose the real part of all eigenvalues is positive or negative (or zero), in that case, it is called the saddle point (or center, still an unstable equilibrium state) [37,38].

3 Methods

3.1 Basic assumptions of the game model

In the context of reducing carbon emissions, conflicting objectives create multi-player problems among the government, businesses, and consumers.

The decision-making problems faced by the government mainly include how to regulate and control carbon emissions, what kind of cost regulations to implement, and what kind of punishment system to establish for businesses with excessive carbon emissions. On the other hand, the decision-making problems faced by businesses mainly revolve around whether to actively reduce emissions while considering the cost of emission reduction. The public must want a safe and green environment if there is the problem of illegal emissions, as an important force of supervision. We hope that businesses can vigorously reduce emissions.

However, in this process, each participant is a bounded rational game subject with incomplete information and insufficient computing power. Therefore, the probability of determining the optimal strategy by only one game is very low. Only through continuous trial and error, summary, and other continuous searches for a better strategy can finally form a relatively stable strategy.

Therefore, it is more meaningful to study the process of behavior evolution in different subjects from the perspective of a dynamic game. In the process of constructing high-standard farmland, the government, businesses, and consumers have their own interests and behavioral strategies when faced with low-carbon policies. The three parties adopt different behavioral strategies to interact and influence each other based on their interests. To analyze the evolution of the game in the low-carbon context, the following assumptions are made.

3.2 Game model subjects

It is assumed that the interest subjects of the model are the government, business, and consumers, respectively (Figure 1). The government refers to the government at all levels, mainly including government departments related to the construction of high-standard farmland; businesses refer to the agricultural businesses that implement the construction of high-standard farmland; consumers refer to the group that consumes the products formed after the construction of high-standard farmland. These three participating groups all have limited rationality and seek to maximize their interests.

Figure 1 
                  Tripartite evolutionary game.
Figure 1

Tripartite evolutionary game.

3.3 Behavioral strategies of game subjects

For the government, there are two behavioral strategies: regulation and non-regulation. The set of behavioral strategies is S 1 = {T 1 regulate, T 2 non-regulate}, one is regulation, the government invests a certain amount of cost to encourage businesses to build high standard farmland projects, encourages businesses to implement low carbon production and gives rewards, encourages consumers to consume low carbon products and gives subsidies, and adopts a punishment mechanism for businesses that do not implement low carbon production. The second is non-regulation, which means that the government does not take any measures to interfere with the behavior of businesses and consumers.

There are two behavioral strategies for firms: implement and non-implement, S 2 = {L 1 implement, L 2 non-implement}. The first approach is to implement government policies, promote technological innovation, and adopt more low-carbon and environmentally friendly measures in the construction of high-standard farmland. The second is to rely on traditional construction methods and not adhere to policies for low-carbon production. However, this approach is not aligned with the development of urban construction in a low-carbon context and may result in penalties under government regulations.

For consumers, there are two behavioral strategies: purchase and non-purchase. S 3 = {G 1 purchase, G 2 non-purchase}. Consumers’ purchase behavior is a voluntary choice, and the government and businesses do not intervene.

3.4 Probability of occurrence of behavioral strategies

Assume that in the initial stage of the game between the government and business consumers, the probability of the government choosing the “regulation” strategy is x, the probability of choosing the “non-regulation” strategy is 1–x. Similarly, the probability of a firm choosing the “implement” strategy is y, and the probability of choosing the “non- implement” strategy is 1–y. Finally, the probability of a consumer choosing the “purchase” strategy is z, and the probability of choosing the “non-purchase” strategy is 1–z, where 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ z ≤ 1.

3.5 Relevant parameter assumptions and their implications in the evolutionary game model

(i) Benefits and costs for the government: The government incurs costs (C 1) for human, material, and financial resources to promote the development of high-standard farmland. Additionally, there is an environmental treatment fee (C 2). The government also regulates through subsidies or rewards. Subsidies (S 1) are provided to businesses that adopt low-carbon production practices, while fines (p) are imposed on businesses that do not implement low-carbon production. Furthermore, subsidies (S 2) are given to consumers who opt for low-carbon products. If low-carbon policies are implemented in the construction of high-standard farmland, they can enhance the overall agricultural production capacity and improve environmental quality, resulting in social benefits for the government as well.

(ii) The benefits and costs of businesses vary depending on their production methods. Businesses that adopt low-carbon production techniques may incur costs for adopting new technologies and purchasing new equipment (C 3), but they can also reap benefits (S 4) and have access to government subsidies (S 1). On the other hand, businesses that rely on traditional means to cultivate farmland may face costs (C 4) but also enjoy benefits (S 5). These businesses are subject to government regulations and may be fined for non-compliance (p).

(iii) Benefits and costs for consumers: According to consumer utility theory, their benefits include both direct and indirect benefits. Assume that the indirect benefits of consumers consuming low-carbon products are S 6, while the indirect benefits of not consuming are S 7. The main direct benefit is the government’s subsidies for consumers who purchase low-carbon products, such as S 2.

4 Game model construction

According to the behavioral strategies of the government, businesses, and consumers, eight game combinations can be introduced. These combinations are: T 1 regulation, L 1 implementation, and G 1 purchase; T 1 regulation, L 1 implementation, and G 2 non-purchase; T 1 regulation, L 2 non-implementation, and G 1 purchase; T 1 regulation, L 2 non-implementation, and G 2 non-purchase; T 2 non-regulation, L 1 implementation, and G 1 purchase; T 2 non-regulation, L 2 non-implementation, and G 1 purchase; T 2 non-regulation, L 1 implementation, and G 2 non-purchase; and T 2 non-regulation, L 2 non-implementation, and G 2 non-purchase. According to the assumptions of the relevant parameters of the evolutionary game model, when the strategy combination is T 1 regulation, L 1 implementation, and G 1 purchase, the government needs to pay the cost of regulation C 1, provide subsidies S 1 to businesses implementing low-carbon production, provide subsidies S 2 to businesses choosing low-carbon products, and can obtain social benefits S 3 from the implementation of low-carbon policies. Similarly, the benefits obtained by other strategies can be deduced, as shown in Table 1.

Table 1

Combination of government, business, and consumer behavioral strategies and benefits matrix

Strategy combinations Government benefits Business benefits Consumer benefits
(T1, L1, G1) S 3C 1S 1S 2 S 4 + S 1C 3 S 6 + S 2
(T1, L1, G2) S 3C 1S 1 S 1C 3 0
(T1, L2, G1) S 3C 1 + P S 5C 4P S 7
(T1, L2, G2) S 3C 1 + P S 5C 4P 0
(T2, L1, G1) C 2 S 4C 3 S 6
(T2, L2, G1) C 2 S 5C 4 S 7
(T2, L1, G2) C 2 S 4C 3 0
(T2, L2, G2) C 2 S 5C 4 0

5 Game model analysis

The RD equation is a prerequisite for the evolutionary game and serves as the endogenous driving force behind the evolutionary game process. The following dynamic equation of replication is constructed for the behavioral strategies of the government, businesses, and consumers.

5.1 Stability analysis of the government’s strategy

Let the expected return of the government’s “regulation” strategy be V 11, the expected return of the “no regulation” strategy be V 12, and the average expected return to be V 1, then

V 11 = y z ( S 3 C 1 S 1 S 2 ) + y ( 1 z ) ( S 3 C 1 S 1 ) + z ( 1 y ) ( S 3 C 1 + P ) + ( 1 y ) ( 1 z ) ( S 3 C 1 + P ) ,

V 12 = y z ( C 2 ) + z ( 1 y ) ( C 2 ) + y ( 1 z ) ( C 2 ) + ( 1 y ) ( 1 z ) ( C 2 ) ,

V 1 = x V 11 + ( 1 x ) V 12 .

The replicated dynamic equation for constructing the behavioral strategy of the businesses is as follows:

F ( x ) = d x /d t = x ( V 11 V 1 )

= x ( x 1 ) [ y z S 2 + y ( S 1 + p ) + C 1 S 3 C 2 p ] .

According to the stability theorem of the differential equation, if the probability of the government choosing to regulate low carbon policy is in a steady state, the equation must satisfy: F(x) = 0 and d(F(x))/dx < 0, at which point

d ( F ( x ) ) d x = ( 2 x 1 ) [ y z S 2 + y ( S 1 + p ) + C 1 S 3 C 2 p ] ,

G ( y ) = y z S 2 + y ( S 1 + p ) + C 1 S 3 C 2 p .

According to the equation, it is easy to see that when x = 0, or x = 1, y = ( S 3 C 1 + C 2 + p ) / ( S 1 + p + z S 2 ) = y , F ( x ) = d x /d t = 0 , according to evolutionary stability theory, when F ( x ) = 0 and F ( x ) < 0 , the probability of government regulation in low carbon is in dynamic equilibrium and is called ESS, that is, x = ESS.

(i) When y = ( S 3 C 1 + C 2 + p ) / ( S 1 + p + z S 2 ) = y , F ( x ) = d x /d t = 0 , all levels are in steady states.

(ii) When y ( S 3 C 1 + C 2 + p ) / ( S 1 + p + z S 2 ) = y , let F ( x ) =d x /d t = 0 , we obtain x = 0 and x = 1 two stable points, at this time d ( F ( x ) ) d x = ( 2 x 1 ) [ y z S 2 + y ( S 1 + p ) + C 1 S 3 C 2 p ] , there are two cases.

When y > ( S 3 C 1 + C 2 + p ) / ( S 1 + p + z S 2 ) = y , F ( 1 ) > 0 , F ( 0 ) < 0 , then x = 0 is the equilibrium point and x = 1 is not a stable point.

When y < ( S 3 C 1 + C 2 + p ) / ( S 1 + p + z S 2 ) = y , F ' ( 1 ) < 0 , F ' ( 0 ) > 0 , then x = 1 is the equilibrium point, x = 0 is not a stable point.

5.2 Analysis of the stability of the company’s strategy

Let the expected return of a firm choosing the “implement” strategy be V 21, the expected return of a firm choosing the “non-implement” strategy be V 22, and the average expected return be V 2.

V 21 = x z ( S 4 + S 1 C 3 ) + x ( 1 z ) ( S 1 C 3 ) + z ( 1 x ) ( S 5 C 4 P ) + ( 1 x ) ( 1 z ) ( S 5 C 4 P ) ,

V 22 = x z ( S 4 C 3 ) + z ( 1 x ) ( S 5 C 4 ) + x ( 1 z ) ( S 4 C 3 ) + ( 1 x ) ( 1 z ) ( S 5 C 4 ) ,

V 2 = y V 21 + ( 1 y ) V 22 .

Construct the RD equation for the firm’s behavioral strategy as follows:

F ( y ) = dy/d t = y ( V 21 V 2 ) ,

= y ( y 1 ) [ x ( S 4 S 1 ) x z S 4 + ( 1 x ) p ] ,

When y = 0, y = 1, z = [ S 4 S 1 + p [ ( 1 x ) / x ] ] / S 4 , F ( y ) = d y /d t = 0 , according to evolutionary stability theory, when F ( y ) = 0 and F ( y ) < 0 , the probability of government regulation of low carbon is in dynamic equilibrium called ESS, i.e., y = ESS.

(i) When z = [ S 4 S 1 + p [ ( 1 x ) / x ] ] / S 4 , F ( y ) = d y/ d t = 0 , all levels are in steady states.

(ii) When z [ S 4 S 1 + p [ ( 1 x ) / x ] ] / S 4 , let F ( y ) = d y /d t = 0 , we obtain two stable points, y = 0 and y = 1 at this time, d ( F ( y ) ) d y = ( 2 y 1 ) [ S 4 S 1 + p [ ( 1 x ) / x ] ] / S 4 , there are two cases.

When z > [ S 4 S 1 + p [ ( 1 x ) / x ] ] / S 4 , F ( 1 ) > 0 , F ( 0 ) < 0 , then y = 0 is the equilibrium point and y = 1 is not a stable point.

When z < [ S 4 S 1 + p [ ( 1 x ) / x ] ] / S 4 , F ' ( 1 ) < 0 , F ' ( 0 ) > 0 , then y = 1 is the equilibrium point, y = 0 is not a stable point.

5.3 Consumer strategy stability analysis

Let the expected return of consumers choosing the “consumption” strategy be V 31, the expected return of consumers choosing the “non-consumption” strategy be V 32, and the average expected return to be V 3, then

V 31 = x y ( S 6 + S 2 ) + x ( 1 y ) S 7 ,

V 32 = ( 1 x ) S 6 + y S 7 ,

V 3 = z V 31 + ( 1 z ) V 32 .

The RD equation for the consumer behavior strategy is

F ( z ) = dz/d t = z ( V 31 V 3 ) , = z ( z 1 ) [ x y ( S 7 S 2 S 6 ) + S 6 x S 6 x S 7 + y S 7 ] .

When z = 0, z = 1, x = ( y S 7 + S 6 ) / ( S 7 + S 6 + y S 2 + y S 6 y S 7 ) = x , F ( z ) = d z /d t = 0 according to evolutionary stability theory, when F ( z ) = 0 , F ( z ) < 0 , the probability of government regulation of low carbon is in dynamic equilibrium and is called ESS, that is, z = ESS.

(i) When x = ( y S 7 + S 6 ) / ( S 7 + S 6 + y S 2 + y S 6 y S 7 ) = x , F ( z ) = d z /d t = 0 , all levels are in steady states.

(ii) When x ( y S 7 + S 6 ) / ( S 7 + S 6 + y S 2 + y S 6 y S 7 ) = x , let F ( z ) = d z /d t = 0 , we obtain two stable points, z = 0 and z = 1 at this time, d ( F ( z ) ) d z = ( 2 x 1 ) ( y S 7 + S 6 ) / ( S 7 + S 6 + y S 2 + y S 6 y S 7 ) , there are two cases.

When x < ( y S 7 + S 6 ) / ( S 7 + S 6 + y S 2 + y S 6 y S 7 ) = x , F ( 1 ) > 0 , F ( 0 ) < 0 , then z = 0 is the equilibrium point and z = 1 is not a stable point.

When x > ( y S 7 + S 6 ) / ( S 7 + S 6 + y S 2 + y S 6 y S 7 ) = x , F ( 1 ) < 0 , F ( 0 ) > 0 , then z = 1 is the equilibrium point and z = 0 is not a stable point.

5.4 Stability analysis of the equilibrium point of the three-party evolutionary game

To maximize their interests, the three-party game subject constantly adjusts the game strategy and finally reaches the equilibrium state, which is called the ESS. Let F(x) = 0, F(y) = 0, and F(z) = 0 to obtain the system equilibrium point, respectively, D 1 (0, 0, 0), D 2 (1, 0, 0), D 3 (0, 1, 0), D 4 (0, 0, 1), D 5 (1, 1, 0), D 6 (1, 0, 1), D 7 (0, 1, 1), D 8 (1, 1, 1), D9 (P/(P + S 1), – S 7/( S 2 + S 6 – 2S 7),1), D 10(1, 1 –(S 1S 4)/S 4), D 11(P/(P + S 1S 4), (C 2C 1 + P + S 3)/(P + S 1),0), D 12((S 6 + S 7)/(S 2 + 2S 6), 1, (C 1C 2 + S 1S 3)/S 2), for the above equilibrium points, it is only necessary to discuss D 1(0, 0, 0), D 2(1, 0, 0), D 3(0, 1, 0), D 4(0, 0, 1), D 5(1, 1, 0), D 6(1, 0, 1), D 7(0, 1, 1), D 8(1, 1, 1), which correspond to one evolutionary game equilibrium each, and the other points are non-asymptotically stable and need not be discussed.

The Jacobi matrix of the tripartite evolutionary game model is as follows:

Jacobi = F ( x ) x F ( x ) y F ( x ) z F ( y ) x F ( y ) y F ( y ) z F ( z ) x F ( z ) y F ( z ) z = ( 2 x 1 ) [ y z S 2 + y ( S 1 + p ) + C 1 S 3 C 2 p ] x ( x 1 ) [ z S 2 + ( S 1 + p ) ] x ( x 1 ) y S 2 y ( y 1 ) ( S 4 S 1 z S 1 p ) ( 2 y 1 ) [ x ( S 4 S 1 ) x z S 4 + ( 1 x ) p ] y ( y 1 ) ( S 4 ) z ( z 1 ) [ y ( S 7 S 2 S 6 ) S 6 S 7 ] z ( z 1 ) [ x ( S 7 S 2 S 6 ) + S 7 ] ( 2 z 1 ) [ x y ( S 7 S 2 S 6 ) + S 6 x S 6 x S 7 + y S 7 ]

The stability of the equilibrium point of the system can be determined by analyzing the positive and negative eigenvalues of the Jacobi matrix. When all eigenvalues are negative, the equilibrium point is asymptotically stable. If there is a positive eigenvalue, the equilibrium point is unstable. When there is a zero eigenvalue, the stability of the equilibrium point cannot be determined.

According to Table 2, it is easy to understand the benefits and costs of the industry. Businesses that engage in low-carbon production and adopt new technologies not only incur costs (C 3) but also receive benefits (S 4) and have access to government subsidies (S 1). On the other hand, businesses that rely on traditional methods to develop farmland not only face costs (C 4) but also receive benefits (S 5). Additionally, government regulations include fines for businesses that fail to comply (p).

Table 2

Equilibrium point stability analysis

Equilibrium point λ 1 λ 2 λ 3 Type of equilibrium point Stability
D 1 (0, 0, 0) p S 6 C 2C 1 + P + S 3 (−, −, −) ESS (λ 3 < 0)
D 2 (1, 0, 0) S 7 S 1S 4 C 1C 2PS 3 (+, ×, +) Unstable point
D 3 (0, 1, 0) p S 6S 7 C 2C 1S 1 + S 3 (+, −, ×) Unstable point
D 4 (0, 0, 1) S 7 S 1S 4 C 1C 2PS 3 (+, ×, ×) Unstable point
D 5 (1, 1, 0) S 4S 1 S 2 + S 6S 7 C 1C 2 + S 1S 3 (−, −, −) ESS (λ1 < 0, λ2 < 0, λ3 < 0)
D 6 (1, 0, 1) S 1 S 7 C 1C 2PS 3 (+, −, ×) Unstable point
D 7 (0, 1, 1) P S 6 + S 7 C 2C 1S 1S 2 + S 3 (+, +, ×) Unstable point
D 8 (1, 1, 1) C 1C 2 + S 1 + S 2S 3 S 1 S 7S 6S 2 (−, −, −) ESS (λ1 < 0, λ3 < 0)

Corollary 1: When C 2C 1 + P + S 3 < 0, the net income from government regulation exceeds the combined amount of the government’s environmental management fee and the fines imposed on businesses in the absence of regulation. At this point, there exists a system asymptotic stability point D 1 (0, 0, 0). If the fines imposed on businesses are increased or the net income from government regulation is higher, it may alter the stability state of the system.

Corollary 2: If S 4S 1 < 0, S 2 + S 6S 7 < 0, C 1C 2 + S 1S 3 < 0, D 5(1, 1, 0) is the system’s asymptotic stability point. This means that the government will choose to regulate when the net benefits gained from regulating are higher than the penalty costs and environmental treatment costs are incurred when the government does not regulate low-carbon policies. Additionally, when the benefits gained by businesses adopting low-carbon production coexist with government subsidies, consumers will not choose to consume low-carbon products if the benefits of traditional products outweigh the benefits of low-carbon production. Therefore, consumer behavior is not influenced by whether the government regulates or not, or whether businesses implement low-carbon production or not. Reason 2: The revised text clarifies the relationships and improves the technical accuracy of the original text. It also enhances readability and clarity by breaking down the complex sentence into smaller, more understandable sentences.

Corollary 3: C 1C 2 + S 1 + S 2S 3 < 0 and S 7S 6S 2 < 0, D 8 (1, 1, 1) is the point of asymptotic stability of the system. This means that the government will choose to regulate when the net benefit gained from regulating is higher than the cost of penalties incurred when the government does not regulate the low-carbon policy and the cost of environmental treatment. Additionally, when the benefit of consumers consuming low-carbon products exceeds the benefit of traditional products, consumers will choose to consume low-carbon products. At this point, companies will choose to implement low-carbon policies. Therefore, in order to promote the adoption of low-carbon behavior, the government needs to implement consistent regulations to maximize social benefits and offer increased subsidies to consumers.

6 Results

Based on theoretical analysis and the literature [39,40], the evolutionary game strategies of the government, businesses, and consumers are numerically simulated using MATLAB tools. This is done according to the parameter conditions and replicated dynamic equations in order to analyze the influence of each factor on the evolutionary outcome.

First, the constraints in Corollary 1, Corollary 2, and Corollary 3 are dynamically evolved by being set.

Array 1:

C 1 = 200, C 2 = 30, C 3 = 210, C 4 = 200, S 1 = 20, S 2 = 10, S 3 = 100, S 4 = 250, S 5 = 250, S 6 = 5, S 7 = 3, P = 10;

Array 2:

C 1 = 150, C 2 = 200, C 3 = 210, C 4 = 200, S 1 = 20, S 2 = 10, S 3 = 100, S 4 = 250, S 5 = 250, S 6 = 5, S 7 = 3, P = 10;

Array 3:

C 1 = 150, C 2 = 200, C 3 = 210, C 4 = 200, S 1 = 60, S 2 = 10, S 3 = 100, S 4 = 40, S 5 = 250, S 6 = 5, S 7 = 3, P = 10;

The three sets of values evolved 50 times over a period of time from different initial strategy combinations. The results are shown in Figure 2.

Figure 2 
               Evolution diagram.
Figure 2

Evolution diagram.

As shown in Figure 2, Array 1 is dynamically stable at (0, 0, 0), Array 2 is dynamically stable at (1, 1, 0), and Array 3 is dynamically stable at (1, 1, 1). This indicates that the government will opt for regulation when the net benefits of government regulation outweigh the costs of penalties and environmental treatment in the absence of regulation for low-carbon policies. Furthermore, the government will choose to regulate when the benefits of low-carbon production exceed the costs of implementing low-carbon production. In turn, companies will choose to implement low-carbon policies when the benefits of low-carbon production surpass the government’s subsidies for such implementation. It can be seen that the simulation analysis is consistent and valid with the conclusions drawn from the analysis of the stability of each party’s strategy, and it provides practical guidance for the implementation of low-carbon policies.

Based on theoretical analysis, MATLAB tools can be utilized to numerically simulate the evolution of the interaction behavior among the government, businesses, and consumers. The influence of the change of each parameter on the evolution result can be analyzed. taking array 1 as an example.

The simulation test is shown in Figure 3. Both the 2D and 3D simulation plots validate the analysis of the equilibrium point (0, 0, 0). When the government incurs higher penalty costs and environmental treatment fees, the system tends to reach equilibrium faster. This implies that the government will receive economic incentives to accelerate the implementation of low-carbon policies. Conversely, when the costs imposed on the government are higher, the system tends to reach equilibrium slower. Additionally, the higher government subsidies lead to a faster equilibrium in the system and increase the likelihood of businesses choosing low-carbon production. If the penalty suffered by the government for not regulating low-carbon policies exceeds a certain value, the system evolves towards an unstable state.

Figure 3 
               Simulation test. (a) Simulation of the effect of increasing government fines on the evolutionary outcome of the system, (b) simulation of the impact of government regulation of low carbon policy costs on the evolution of the system, (c) simulation of the impact of government subsidies on the evolutionary outcome of the system, and (d) simulation of the effect of government non-regulation of penalty costs on the evolutionary outcome of the system.
Figure 3

Simulation test. (a) Simulation of the effect of increasing government fines on the evolutionary outcome of the system, (b) simulation of the impact of government regulation of low carbon policy costs on the evolution of the system, (c) simulation of the impact of government subsidies on the evolutionary outcome of the system, and (d) simulation of the effect of government non-regulation of penalty costs on the evolutionary outcome of the system.

7 Discussion

First of all, the results of using MATLAB tools to simulate the interactive behavior of government, businesses, and consumers are consistent with the findings of theoretical analysis. The dynamic evolution game theory is employed to support the arguments presented in this study.

As can be seen from Figure 3a, in the process of the evolution of the system to a stable point, increasing the fine on businesses that do not implement p can slow down the speed at which the government chooses to regulate and control low-carbon production. With the increase in p, the likelihood of businesses implementing low-carbon production increases, while the likelihood of government regulation and control of low-carbon policies decreases. Therefore, when the government fines businesses that have low-carbon production, it needs to strengthen the regulation and control of the low-carbon policy. Specifically, for uncooperative businesses, the regulation and control policy can be appropriately relaxed to alleviate the production pressure they face.

Figure 3c shows that if the government increases the subsidy to businesses (S 1), the likelihood of businesses opting for low-carbon production increases, while the likelihood of consumers choosing to consume low-carbon products decreases. Therefore, while increasing support for businesses, the government should also utilize media publicity, consumer subsidies, and other measures to promote the consumption of low-carbon products.

In addition, in Figure 3d, results of the evolution of dynamic equations with time are provided to C 2 employees, as shown in the figure. When the environmental governance fee reaches a certain threshold without government regulation, the system becomes unbalanced and the resulting environmental damage becomes irreversible. Currently, no measures can be taken to restore balance to the system. Therefore, the government, businesses, and consumers must actively respond to the low-carbon policy and protect the environment.

8 Conclusion

Aiming to address the issue of carbon emission reduction in farmland, this study presents a tripartite evolutionary game dynamic model involving the government, businesses, and consumers. The model analyzes the stability of each strategy choice and the relationship between various factors. The equilibrium point of the model is calculated using the MATLAB tool, and the validity of the theoretical results is verified through numerical simulation analysis in MATLAB. The study also determines the stable strategies for each party. According to the influence of a variety of factors, the government, businesses, and consumers all put forward suggestions for low-carbon production. The main conclusions are as follows:

  1. The cost of government regulation for carbon reduction on farmland directly affects businesses’ decision to choose low-carbon production. When the cost of government regulation is higher than the sum of the government’s environmental management fee and the fine imposed on businesses when there is no regulation, i.e., when government regulation has little impact on the environment or not, the regulation does not work. Businesses will still choose not to invest in low-carbon, high-standard farmland projects. If the fine imposed on businesses is increased, it may change the stability of the system.

  2. Government, businesses, and consumers all choose their behavioral strategies based on their interests. The increase in government subsidies and penalties is conducive to promoting businesses to choose low-carbon production. However, increasing subsidies slows down the government’s regulation of low-carbon production. The government’s subsidy and punishment mechanism must align with the sum of the government’s environmental governance fees and fines. This ensures that the net income from government regulation is higher than that of non-regulation, thereby ensuring the evolution and stability of stakeholders in the low-carbon context. The higher the cost of low-carbon production, the more the government will promote businesses to adopt low-carbon production. However, while increasing support for businesses, the government should also utilize media publicity, consumer subsidies, and other measures to promote the consumption of low-carbon products.

  3. When the income of low-carbon production coexists with government subsidy, the enthusiasm for low-carbon production is higher, so if businesses reduce the cost of carbon emission reduction and increase income through technological innovation, the probability of low-carbon production will increase. When the income of consumers consuming low-carbon products is less than that of traditional products, consumers will not choose to consume low-carbon products. At this time, whether the government regulates or not and whether the businesses are implemented or not are not related to the behavior of consumers.

  4. When low-carbon production is accompanied by government subsidies, it tends to generate higher enthusiasm. Therefore, if businesses can lower the cost of carbon emission reduction and increase income through technological innovation, the likelihood of engaging in low-carbon production will increase. When the income of consumers who consume low-carbon products is lower than that of traditional products, consumers will not choose to consume low-carbon products. At this time, the behavior of consumers is not related to whether the government regulates or not, or whether businesses are implemented or not.

  5. For the popularization of low-carbon behavior, the government needs to continue regulating in order to maximize social benefits. Additionally, businesses should focus on making technological innovations to reduce the cost of carbon emissions. This will help accelerate the market for low-carbon production and move towards stability.

8.1 Managerial implication

Managers pay great attention to low-carbon production. Low-carbon is regarded by the country as a new direction of production, and it is bound to affect various fields. First of all, government managers should increase support for businesses and utilize media publicity, consumer subsidies, and other measures to promote the consumption of low-carbon products. When imposing fines on low-carbon production businesses, it is necessary to strengthen the regulation and control of low-carbon policies. However, for uncooperative businesses, the regulation and control policy can be appropriately relaxed to reduce the production pressure they face.

Second, through technological innovation, enterprise managers should continuously reduce the cost of carbon emission reduction, increase revenue, and consistently improve the likelihood of businesses opting for low-carbon production.

Finally, the government, businesses, and consumers must actively respond to the high-standard farmland low-carbon policy in order to achieve agricultural carbon reduction.

8.2 Practical/social implications

Carbon emissions have become a pressing issue in China’s pursuit of sustainable development. As an important part of the national economy and basic industries, agriculture also bears considerable responsibility for carbon emissions. Therefore, finding ways to reduce carbon emissions in farmland and improve resource utilization efficiency has become a research priority in agriculture.

This work examines the evolution process of the tripartite subject in the context of carbon emissions. It aims to enhance the government, businesses, and the public’s understanding of the significance of farmland carbon emissions and the urgent need to address global climate change actively. At the same time, it encourages businesses to implement high-standard farmland low-carbon transformation and promote the sustainable development of the farmland economy.


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Acknowledgements

The authors would like to thank the Shaanxi Industry Innovation Center of Cultivated Land Protection and Quality Improvement for helpful discussions on topics related to this work. This research was partially supported by the Key Technology Integration and demonstration of Water Control, weight loss, Drug reduction, quality improvement and efficiency of staple Grain crops in Guanzhong Plain: 2023-ZDLNY-52, and Research and Innovation team of farmland Standardization Construction in Weibei Arid Plateau: DJTD-2022-5, and Study on mechanism of effects of soil physicochemical optimization on crop yield: DJNY2024-55, and Technical integration and demonstration of farmland soil structure optimization and healthy plough layer construction: 2021YFD1900701-04.

  1. Author contributions: Yuting Dai: data analysis and writing; Yichun Du: formal analysis; and Jinbao Liu: validation.

  2. Conflict of interest: Authors state no conflict of interest.

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Received: 2023-07-12
Revised: 2023-11-26
Accepted: 2023-12-01
Published Online: 2024-01-25

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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