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Research Article
The Evolutionary Game Analysis of Multiple Stakeholders in the
Low-Carbon Agricultural Innovation Diffusion
Lixia Liu ,
1
Yuchao Zhu,
1
and Shubing Guo
2
1
School of Economics, Tianjin University of Commerce, Tianjin 300134, China
2
College of Management and Economics, Tianjin University, Tianjin 300072, China
Correspondence should be addressed to Lixia Liu; liulixia77@163.com and Shubing Guo; sbguo20160831@126.com
Received 20 September 2019; Revised 12 December 2019; Accepted 27 January 2020; Published 22 February 2020
Academic Editor: Yan-Ling Wei
Copyright ©2020 Lixia Liu et al. is is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Encouraging the adoption and diffusion of low-carbon agricultural technology innovation is an important measure to cope with
climate change, reduce environmental pollution, and achieve sustainable agricultural development. Based on evolutionary game
theory, this paper establishes a game model among agricultural enterprises, government, and farmers and analyzes the dynamic
evolutionary process and evolutionary stable strategies of the major stakeholders. e impact of innovation subsidies, carbon
taxes, and adoption subsidies on low-carbon agricultural innovation diffusion is simulated using Matlab software. e results
show that the government’s reasonable subsidies and carbon taxes for agricultural enterprises and farmers can increase the
enthusiasm of agricultural enterprises and farmers to participate in low-carbon agriculture. is study can be used as a basis for
the government to formulate more targeted policies to promote the diffusion of low-carbon agricultural innovation.
1. Introduction
With the rapid development of the global economy, global
warming has become an issue of great concern to the in-
ternational community. According to the IPCC’s fifth as-
sessment report, excessive carbon dioxide emission from
human activities is the leading cause of climate warming [1].
For a long time, governments have been developing low-
carbon economy with practical actions and taking the
second and third industries as key sectors of carbon emission
management [2]. In recent years, with the acceleration of
agricultural modernization, the impact of agriculture on
global climate change is increasing. According to statistics,
agriculture directly contributes 10%–12% of global green-
house gas emissions [3, 4]. Low-carbon agriculture is a new
development mode featuring low energy consumption, low
emission, and low pollution. e development of low carbon
agriculture is the inevitable choice to realize the sustainable
development of agriculture [5].
Research and development, promotion, and application
of low-carbon agricultural technologies are the key measures
to achieve carbon sequestration and emission reduction in
agricultural production [6]. In recent years, many countries
have adopted policies to stimulate the innovation and dif-
fusion of low-carbon agricultural technologies, such as
subsidies, tax incentives, and public loans [7–12]. However,
the diffusion of low-carbon agricultural technologies is still
slow, especially in developing countries. is situation is
mainly due to the following two reasons. First, as demanders
of low-carbon agricultural technologies, farmers are not
enthusiastic about adopting low-carbon agricultural tech-
nologies affected by their knowledge level, income level, land
size, and external environment [7–11]. Second, as providers
of low-carbon agricultural means of production and tech-
nical services, agricultural enterprises are less motivated in
low-carbon innovation due to the long cycle, high cost, and
high-risk characteristics of low-carbon agricultural tech-
nology innovation [12]. erefore, the obstacles to low-
carbon agricultural technology innovation and technology
promotion and the implementation effect of the govern-
ment’s low-carbon agricultural policy have attracted much
attention [11–15].
Although the importance and value of low-carbon ag-
ricultural innovation diffusion has been confirmed, there are
Hindawi
Complexity
Volume 2020, Article ID 6309545, 12 pages
https://doi.org/10.1155/2020/6309545
very limited literatures on the diffusion of low-carbon ag-
ricultural technology innovation from the perspective of the
dynamic system [16]. Different from the existing literature,
we analyze the diffusion of low-carbon agricultural inno-
vation based on evolutionary game theory. We consider the
roles of key stakeholders in the process of low-carbon ag-
ricultural innovation diffusion, analyze the relationship
between agricultural enterprises, farmers, and the govern-
ment, explore the causes of the slow diffusion of low-carbon
agricultural innovation, and reveal the evolutionary mech-
anism of low-carbon agricultural innovation diffusion. On
the basis of theoretical analysis, the complexity scientific
method was introduced and the evolutionary game model of
low-carbon agricultural innovation diffusion was established
[17, 18]. en, we use the numerical simulation method to
examine the dynamic evolution path of the game system and
to analyze the impact of low-carbon policies on the behavior
of agricultural enterprises, government, and farmers. is
paper explains two issues that are not fully addressed in the
previous literature. First, what is the diffusion mechanism of
low-carbon agricultural technology through agricultural
enterprises and farmers? Second, how does the government’s
low-carbon policy affect the diffusion of low-carbon agri-
cultural innovation? Based on the findings, the paper pro-
vides recommendations for low-carbon scholars and
policymakers.
e remainder of this paper is organized as follows.
Section 2 reviews the literature related to low-carbon ag-
ricultural innovation diffusion. Section 3 describes these
problems in the diffusion of low-carbon agricultural tech-
nology, puts forward the theoretical hypothesis of the model,
and provides the parameters and variables of the model.
Section 4 establishes a trilateral evolutionary game theory
model of the interaction among agricultural enterprises,
government, and farmers and assesses the stability of the
model. Section 5 describes the results of evolutionary game
simulation. Section 6 presents the conclusion and some
policy suggestions.
2. Literature Review
2.1. Obstacles to the Diffusion of Low-Carbon Agricultural
Innovation. Rogers first put forward the theory of inno-
vation diffusion [19]. He defines innovation diffusion as a
process in which innovation can spread over time among
members of the social system through certain channels.
Innovative technology will affect economic and social de-
velopment only when it is diffused and widely applied [20].
Since the theory is proposed, it has attracted significant
scholarly attention in the past decades [21, 22].
In recent years, this theory has also attracted the at-
tention of agriculturists and environmentalist. Mannan et al.
believed that innovative attributes play an active role in the
promotion and adoption of green fertilizer technology in
rice cultivation in Malaysia [23]. High-input agriculture not
only increases greenhouse gas emissions but also causes
huge economic losses and environmental damage in many
countries [24]. For example, excessive use of nitrogen fer-
tilizer has resulted in excessive nitrate in groundwater and
surface water, which has a negative impact on human health
[25]. e management of aquatic ecosystems with excessive
nitrates will cost a lot of money [26]. It is generally accepted
that the use of low-carbon technology in agriculture is of
great significance to agricultural progress. Reducing carbon
in agriculture and improving soil nutrients and productivity
of agroecosystems through the use of organic fertilizers and
low-carbon technologies are crucial for developing sus-
tainable, low-carbon, and climate-adaptive agriculture
[27, 28].
However, there are great obstacles on the development
and popularization of low-carbon agricultural technology.
From the perspective of farmers, individual characteristics,
family characteristics, information channels, and psycho-
logical characteristics are considered to be important factors
affecting farmers’ low-carbon behavior [9, 29, 30]. On the
one hand, the adoption of low-carbon technology requires
capital investment, and insufficient funds are an important
factor restricting farmers to adopt low-carbon technology
[31]. On the other hand, farmers’ enthusiasm for using low-
carbon technologies is low due to lack of awareness or
knowledge [7]. Furthermore, time and learning costs re-
quired to use new technologies also reduce the adoption of
low-carbon technologies by farmers to a certain extent
[8, 9, 32]. From the perspective of agricultural enterprises,
due to the long cycle, high cost, and high risk of low-carbon
technology innovation, the low-carbon innovation enthu-
siasm of agricultural enterprises is not high [11]. erefore,
the development of low-carbon agricultural technology
cannot be separated from the support of government pol-
icies [10].
2.2. e Impact of Low-Carbon Policy on the Diffusion of
Agricultural Low-Carbon Innovation. e theory of market
failure has occupied a central position in public policy re-
search [33]. According to the theory, the pursuit of private
interests will lead to inefficient outcomes due to monopoly,
externality, and information asymmetry [34]. erefore, the
government intervention is needed to solve these problems.
Freibauer et al. showed that increasing the organic input of
cultivated land, encouraging farmers to grow organic crops,
and strengthening the government’s low-carbon policy can
improve the carbon sequestration function of the agricul-
tural land [35]. Adzawla et al. indicated that the adoption of
agricultural technologies can increase production while
reducing greenhouse gas emissions. erefore, in addition to
greenhouse gas reduction initiatives or climate stabilization
policies, carbon tax policies should be deemed as a strategic
choice to promote the diffusion of low-carbon technologies
[36]. Innovation subsidy for emission reduction is an ef-
fective measure to achieve food security and reduce agri-
cultural pollution in China [37]. Qiao et al. found that
government subsidy has a significant positive effect on the
low-carbon agricultural technology adoption [38]. However,
Liu et al. believed that the current economic incentives have
not greatly improved the adoption rate of sustainable ag-
ricultural practices at the farm level, and technical training
for farmers can increase the likelihood of low-carbon
2Complexity
agricultural technology adoption [13]. Some scholars sug-
gested that farmers are the main body of the diffusion of low-
carbon agricultural innovation, so it is more important to
change farmers’ views on environmental issues and climate
change [7, 32]. Lybbert and Sumner argued that national and
international policymakers must incorporate a global per-
spective into agricultural policies in order to better address
global climate change. From innovation to technology
transfer and access to agricultural innovation technologies
for small farmers in developing countries, agricultural
policies play an important role at all levels [6].
2.3. Application of Evolutionary Game in Low-Carbon In-
novation Diffusion. As an analytical tool, game theory has
been applied to various fields of research studies to explain
social phenomena [39–42]. Evolutionary game theory
originated as an application of game theory to evolving
populations of life forms in biology. e evolutionary game
model based on the bounded rationality assumption might
have more realistic significance than the game theory model
based on the complete rational assumption. In recent years,
the application of evolutionary game theory in the field of
low-carbon economy has been increasing. For example,
Mahmoudi and Rasti-Barzoki established the evolutionary
game models between government and enterprise and an-
alyzed the impact of government policies on enterprise
behavior [43]. Zhang et al. examined the impact of low-
carbon policies on green technology diffusion in enterprise
alliances [44].Wang and Zheng studied low-carbon diffusion
from the perspective of network characteristics and con-
sumer environmental awareness [45]. Fan and Dong
established an evolutionary game model between enterprises
and consumers and discussed the impact of government
subsidy policies on the diffusion of new energy vehicles [46].
As can be seen from the abovementioned literature
review, the evolutionary game model has been applied to the
study of low-carbon diffusion, but the related research
mainly focuses on the industrial sector and pays less at-
tention to the agricultural sector [47]. Prior studies mainly
considered the relationship between government and
manufacturing enterprises or between consumers and
manufacturing enterprises. However, few scholars analyzed
the diffusion of low-carbon agricultural innovation from the
perspective of multistakeholder relationship. It is difficult to
see the application of evolutionary game in low-carbon
agriculture [15].
3. Problem Description and Assumptions
3.1. Problem Description. e process of diffusion of low-
carbon agriculture innovation is also the process of adoption
of low-carbon agricultural technology. is is a long process,
which requires the joint efforts of agricultural enterprises,
farmers, and the government [12, 15]. e government is the
promoter and beneficiary of innovation diffusion in low-
carbon agriculture. e government can promote low-car-
bon innovation of agricultural enterprises and encourage
farmers to adopt low-carbon technology through the
implementation of policy tools such as low-carbon subsidies
and tax rebates [14].
Agricultural enterprises that provide low-carbon agri-
cultural means of production and technical services are the
main body of low-carbon agricultural technology innova-
tion. Agricultural production materials mainly include ag-
ricultural machinery and equipment, semimechanized
agricultural tools, small and medium-sized agricultural
tools, pesticides, fertilizers, and agricultural plastic film.
Low-carbon innovation of agricultural enterprises is to
improve the energy efficiency of resource utilization of
agricultural enterprises and achieve effective management of
all aspects of agricultural production through the R&D of
energy-saving technologies, waste recycling technologies,
and biotechnology [48–51]. Due to the high cost, long cycle,
high risk, and uncertain benefits of agricultural low-carbon
technology R&D, the innovation enthusiasm of agricultural
enterprises is not high [13]. Agricultural enterprises avoid
risks and seek to maximize their own interests. ere is great
uncertainty about whether agricultural enterprises choose
low-carbon innovation strategy. erefore, effective gov-
ernment policies need to be formulated and implemented in
order to guide and standardize the low-carbon innovation of
the agricultural enterprises.
Farmers are users of low-carbon agricultural technolo-
gies. Farmers’ adoption of low-carbon innovative technol-
ogies is essential for promoting the development of
low-carbon agriculture [52–56]. For the farmers, the main
determinant of low-carbon technology adoption is the
profitability and feasibility of greenhouse gas emission re-
duction measures. In particular, the early use of low-carbon
agricultural technology may not bring about a rapid increase
in farmers’ income, but a decline in farmers’ output and
income [47]. At the same time, due to farmers’ lack of
awareness of low-carbon agriculture and the high cost of
barriers to adopting low-carbon agricultural technology, the
diffusion of low-carbon agricultural technology is facing
greater resistance from farmers [7–9]. us, it is more
important for the government to increase publicity on low-
carbon agriculture and compensate for the decline in
farmers’ income by subsidizing the adopters of low-carbon
agricultural technologies. In addition, while providing low-
carbon technology and products to farmers, agricultural
enterprises are required to provide corresponding technical
services to farmers.
In short, the government, agricultural enterprises, and
farmers are the main stakeholders in the process of low-
carbon agricultural innovation diffusion [15]. ese stake-
holders are all bounded rationality. ey choose their own
behavioral strategies from the perspective of maximizing
their own interests, thus forming a complex game rela-
tionship. is will be a long-term and complex game process.
3.2. Model Assumptions. We assume that the strategies of
agricultural enterprises are {Low-carbon innovation, Not
low-carbon innovation}. e strategies of government are
{Regulation, Not regulation}, while the strategies of farmers
are {Adoption, Not adoption}. x, y, and zrepresent the
Complexity 3
probability of agricultural enterprises’ choice of low-carbon
innovation, government regulation, and farmers’ adoption
low-carbon technology, respectively. Correspondingly, 1 −
x, 1−y, and 1 −zrepresent that the probability that agri-
cultural enterprises do not choose low-carbon innovation,
that the government does not regulate, and that farmers do
not adopt low-carbon technology, respectively.
H1represents the benefit obtained by the agricultural
enterprises, when they do not choose low-carbon innovation
strategies. Δh11 and Δh12, respectively, represents the benefit
increase that the agricultural enterprises can obtain through
low-carbon innovation, when the government chooses the
“Regulate” strategies and the “Not regulation” strategies. C
1
represents the cost of agricultural enterprises when they
choose low-carbon innovation strategy.
H2represents the social benefit obtained by the gov-
ernment, when the enterprises do not choose low-carbon
innovation. Under the case of enterprises choosing low-
carbon innovations, Δh21 and Δh22, respectively, represent
the benefit increase of the government, when the govern-
ment adopts the “Regulate” strategies and the “Not regu-
lation” strategies.
H3represents the utility obtained by the farmers,
when they do not adopt low-carbon technology. Δh3
represents the utility increase of the farmers, when they
adopt low-carbon technology. When agricultural enter-
prises select “Low-carbon innovation” strategies, the
farmers can gain wthe social effect, regardless of whether
they adopt low-carbon technology.
In the case of government regulation, the amount of
innovation subsidies for the agricultural enterprises is αC1,
when the agricultural enterprises choose low-carbon in-
novate strategies. e government levies βFcarbon tax on
agricultural enterprises, when the agricultural enterprises do
not choose low-carbon innovation strategies. e amount of
adoption subsidies for the farmers is cC3, when the farmers
adopt low-carbon technology. According to the actual sit-
uation in economies, we suppose that Δh11 >Δh12,
Δh21 >Δh22, and 0 ≤α,β,c≤1. e corresponding param-
eters are shown in Table 1.
According to the abovementioned analysis, the payoff
matrix among agricultural enterprises, government, and
farmers is established, as shown in Table 2.
4. The Evolutionary Game Model Solution
and Analysis
4.1. e Replicated Dynamic Equation. Let Ue1 and Ue2
represent, respectively, the expected earnings of “Low-car-
bon innovation” and “Not low-carbon innovation” for ag-
ricultural enterprises. According to the payoff matrix, the
fitness of agricultural enterprises with two different strate-
gies can be calculated as follows:
Ue1 �H1−C1+Δh12z+αC1y+Δh11 −Δh12
yz,
Ue2 �H1−βFy. (1)
e average expected earnings of agricultural enterprises
can be calculated as
Ue�xUe1 +(1−x)Ue2 .(2)
e replication dynamics equation for agricultural en-
terprises can be achieved as follows:
F(x) � x(1−x)Ue1 −Ue2
�x(1−x)αC1+βF
y
+Δh12z+Δh11 −Δh12
yz −C1.
(3)
Similarly, the expected earnings of “Regulation” and
“Not regulation” for government can be calculated as
follows:
Ug1 �H2+βF+Δh21 −αC1−βF
x−cC3z,
Ug2 �H2+Δh22x. (4)
e average expected earnings of government can be
calculated as
Ug�yUg1 +(1−y)Ug2.(5)
e replication dynamics equation for the government
can be achieved as follows:
F(y) � y(1−y)Ug1 −Ug2
�y(1−y)βF+Δh21 −Δh22
−αC1−βFx−cC3z.
(6)
e expected earnings of “Adoption” and “Not adop-
tion” for farmers can be calculated as follows:
Uc1 �H3+Δh3−C3+wx +cC3y,
Uc2 �H3+wx. (7)
e average expected earnings of farmers can be cal-
culated as
Uc�zUc1 +(1−z)Uc2.(8)
e replication dynamics equation for farmers can be
achieved as follows:
F(z) � z(1−z)Uc1 −Uc2
�z(1−z)Δh3−C3+cC3y
.
(9)
e replication dynamics equation of each stakeholder
has the following form:
F(x) � x(1−x)αC1+βF
y+Δh12z+Δh11 −Δh12
yz −C1
,
F(y) � y(1−y)βF+Δh21 −Δh22 −αC1−βF
x−cC3z
,
F(z) � z(1−z)Δh3−C3+cC3y
.
⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩
(10)
4.2. Model Analysis. To seek the system’s stable strategy, let
the replicated dynamic equation of agricultural enterprises,
government, and farmers be zero, that is, F(x) � 0,
F(y) � 0,and F(z) � 0. According to the evolutionary
game theory, we obtain nine local equilibrium points
of replicated dynamic equation: U1(1,1,1),U2(1,1,0),
U3(1,0,1),U4(0,1,1),U5(1,0,0),U6(0,1,0),U7(0,0,1),
4Complexity
U8(0,0,0), and U9(x∗, y∗, z∗).U9(x∗, y∗, z∗)is the solution
of
αC1+βF
y+Δh12z+Δh11 −Δh12
yz −C1�0,
βF+Δh21 −Δh22 −αC1−βF
x−cC3z�0,
Δh3−C3+cC3y�0.
⎧⎪
⎪
⎨
⎪
⎪
⎩
(11)
e equilibrium points are not necessarily the evolu-
tionary stable strategies (ESS). According to research by
Friedman [53], the stability of the equilibrium points can be
judged from the Jacobin matrix. e Jacobin matrix of
replication dynamics equation and its eigenvalues are as
follows:
J�
F11 F12 F13
F21 F22 F23
F31 F32 F33
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦,(12)
where
Table 1: Parameter descriptions.
Stakeholders Parameters Descriptions
Agricultural
enterprises
xe probability that agricultural enterprises carry out low-carbon innovation
H1e benefits when agricultural enterprises do not carry out low-carbon innovation
Δh11
e benefit increase when the government chooses “regulation” strategies and the farmers adopt low-
carbon technology
Δh12
e benefit increase when the government choose “not regulation” strategies and the farmers adopt
low-carbon technology
C1e costs increase when agricultural enterprises carry out low-carbon innovation
Government
ye probability that government regulates low-carbon innovation
H2e social benefit when the agricultural enterprises adopt general innovation
Δh21
e benefit increase when the government adopts “regulation” strategies and the agricultural
enterprises carry out low-carbon innovation
Δh22
e benefit increase when the government does not regulate and the agricultural enterprises adopt low-
carbon innovation
Fe amount of carbon taxes levied on agricultural enterprises adopting “not low-carbon innovation”
strategies
αe ratio of innovation subsidies to agricultural enterprises’ low-carbon innovation input cost
βCarbon tax rate
ce ratio of adoption subsidies to farmers’ low-carbon technology purchase cost
Farmers
ze probability that farmers adopt low-carbon technology
H3e benefits when farmers do not adopt low-carbon technology
Δh3e increase benefits when farmers adopt low-carbon technology
C3e costs increase when farmers adopt low-carbon technology
we benefits increase when agricultural enterprises carry out low-carbon innovation, regardless of
whether farmers adopt low-carbon technology
Table 2: e payoff matrix among agricultural enterprises, government, and farmers.
Agricultural enterprises Government Farmers
Adoption (z) Not adoption (1 −z)
Low-carbon innovation (x)
Regulation (y)
H1+Δh11 − (1−α)C1H1− (1−α)C1
H2+Δh21 −αC1−cC3H2+Δh21 −αC1
H3+w−Δh3− (1−c)C3H3+w
Not regulation (1 −y)
H1+Δh12 −C1H1−C1
H2+Δh22 H2+Δh22
H3+w−Δh3−C3H3+w
Not low-carbon innovation (1 −x)
Regulation (y)
H1−βF H1−βF
H2+βF−cC3H2+βF
H3+Δh3− (1−c)C3H3
Not regulation (1 −y)
H1H1
H2H2
H3+Δh3−C3H3
Complexity 5
F11 �zA(x)
zx� (1−2x)αC1+βF
y+Δh12z
+Δh11 −Δh12
yz −C1,
F12 �zA(x)
zy�x(1−x)αC1+βF+Δh11 −Δh12
z
,
F13 �zA(x)
zz�x(1−x)Δh12 +Δh11 −Δh12
y
,
F21 �zB(y)
zx�Δh21 −Δh22 −αC1−βF
y(1−y),
F22 �zB(y)
zy� (1−2y)βF+Δh21 −Δh22 −αC1−βF
·x−cC3z,
F23 �zB(y)
zz� − cC3y(1−y),
F31 �zC(z)
zx�0,
F32 �zC(z)
zy�cC3z(1−z),
F33 �zC(z)
zz� (1−2z)Δh3−C3+cC3y
.
(13)
According to Lyapunov’s indirect method, the equi-
librium point is an evolutionary stable strategy (ESS),
when F11,F22, and F33 are negative; the equilibrium point
is an unstable point, when F11,F2 2, and F33 are positive; the
equilibrium point is a saddle point, when there are one or
two positive numbers in F11,F22 , and F33 . We only
consider the equilibrium points U1to U8because the
equilibrium resolution of three-party evolutionary game is
a strict Nash equilibrium. e main eigenvalues of the
Jacobian matrix at different equilibrium points are shown
in Table 3.
Since C1>0 and βF>0, the equilibrium points (1, 0, 0)
and (0, 0, 0) may be a saddle point or an unstable point. e
equilibrium points (1, 1, 1), (1, 1, 0), (1, 0, 1), (0, 1, 1), (0, 1, 0),
and (0, 0, 1) may be the potential evolutionary stability
strategies of the three-party game model. Among these
potential stabilization strategies, the strategies that agri-
cultural enterprises carry out low-carbon innovation and
farmers adopt low-carbon technology are ideal stabilization
strategies. erefore, we only discuss the equilibrium points
(1, 0, 1) and (1, 1, 1).
e equilibrium point (1, 0, 1) is the ESS, when
Δh12 −C1>0,Δh21 −Δh22 −αC1−cC3<0 , and Δh3−C3
>0. e equilibrium point (1, 0, 1) is an unstable point,
when Δh12 −C1<0,Δh21 −Δh22 −αC1−cC3>0, and
Δh3−C3<0. And the equilibrium point (1, 0, 1) is a saddle
point, when C1−Δh12,Δh21 −Δh22 −αC1−cC3, and C3−
Δh3have one or two positive numbers. Under the conditions
of government nonregulation, the agricultural enterprises
adopt low-carbon innovation strategy, when their earnings
of nonlow-carbon innovation are less than those of low-
carbon innovation. e government chooses “Not regulation”
strategy, when its regulatory benefit is less than the on-
regulatory benefit. e farmers select “Adoption” strategy,
when their benefits of adopting low-carbon technology are
higher than the benefits of adopting nonlow-carbon tech-
nology. Combined with the current social reality, the social
benefits of the government adopting “Regulation” strategy
must be greater than the gains from the choice of “Not
regulation” strategy. erefore, we will not consider this
situation in depth.
e equilibrium point U8(1,1,1)is also analyzed with
this method. When (Δh11 +βF− (1−α)C1)>0, Δh21−
Δh22 −αC1−cC3>0 , and Δh3− (1−c)C3>0, the equi-
librium point (1, 1, 1) is the ESS. When (Δh11 +βF−
(1−α)C1)<0, Δh21 −Δh22 −αC1−cC3<0 , and Δh3−
(1−c)C3<0, the equilibrium point (1, 1, 1) is an unstable
point. When Δh3− (1−c)C3<0, Δh21−Δh22 −αC1−cC3,
and Δh3− (1−c)C3have one or two positive numbers, the
equilibrium point (1, 1, 1) is a saddle point. e results
indicate that the agricultural enterprises adopt low-carbon
innovation strategy, when its earnings of nonlow-carbon
innovation is less than that of low-carbon innovation; the
government accept “Regulation” strategy, when its regula-
tory benefit is higher than the nonregulatory benefit; the
farmers choose “Adoption” strategy, when their benefits
adopting low-carbon technology is larger than the benefits
adopting nonlow-carbon technology.
5. Simulation Analysis
e numerical simulations are carried out using Matlab
software. We only discuss the equilibrium point (1, 1, 1) and
consider the effect of initial strategy selection and influence
factors on evolution results. According to Section 4, when
(Δh11 +βF− (1−α)C1)>0, Δh21 −Δh22 −αC1−cC3>0,
and Δh3− (1−c)C3>0, the system finally achieves to the
ideal state, that is, the ESS is the strategy set {Low-carbon
innovation, Regulation, Adoption}. We set Δh11 �6,
Δh21 �5, Δh22 �2,Δh12 �5,Δh3�0.8, C1�4, C3�0.5,
F�1, α�0.3, β�0.2, c�0.3, and ω�0.1. e time is set
to t�20.
5.1. Effect of Initial Strategy Selection. When the initial value
of the strategy combination (x,y,z) is set as
U0� (0.5,0.5,0.5), the strategy selection results of stake-
holders are shown in Figure 1. From the two-dimensional
and three-dimensional simulation diagrams, we can find
that the probabilities of participants choosing strategy 1
increase with time. Ultimately, the agricultural enterprises
choose “Low-carbon innovation” strategy, the government
chooses “Regulation” strategy, and the farmers choose
“Adoption” strategy, and thus reaching ESS point
U1� (1,1,1).
6Complexity
5.2. Effect of Government Behavior on the Strategy Selection.
Government subsidies to agricultural enterprises and
farmers, as well as government carbon tax requirements for
nonlow-carbon innovative enterprises, may have an effect
on the strategy choices of agricultural enterprises and
farmers. We discuss the influence of the abovementioned
factors on the evolutionary results.
5.2.1. Innovation Subsidies for Agricultural Enterprises.
In order to examine the impact of innovation subsidies for
agricultural enterprises, we set the parameter αin the in-
terval [0, 1], while fixing the value of the other parameters.
e simulation results shown in Figure 2 suggest that when
the ratio of innovation subsidies to agricultural enterprises’
low-carbon innovation input cost increase from 0.1 to 0.9,
the “Low-carbon innovation” strategy ratio of agricultural
enterprises and the “Adoption” strategy ratio of farmers will
increase, but the “Regulation” strategy ratio of government
will decrease. e results of simulation coincide with the
explanation that market failure is the fundamental reason for
the government to subsidize low-carbon innovation activ-
ities, which creates a gap between private interests and social
interests [33]. e government can obtain more societal
benefits through supporting firms’ innovation. However, the
government will select “Not regulation” strategy, when the
amount of government subsidies is greater than the social
benefits obtained by the government. From abovementioned
analysis, we can see that government subsidies may have a
substitution effect in the initial stage and reduce the en-
thusiasm of low-carbon innovation of agricultural enter-
prises, but with the passage of time it will play an incentive
role and promote low-carbon innovation of agricultural
enterprises. At the same time, innovation subsidies have an
incentive effect on farmers to adopt low-carbon technolo-
gies. However, if the amount of financial subsidies is too
large, it will affect the enthusiasm of government subsidies.
5.2.2. Carbon Taxes for Agricultural Enterprises. Carbon tax
policy is an important measure to reduce carbon emissions
[54, 55]. In order to examine the effect of the carbon tax rate,
Table 3: Main eigenvalues of the Jacobian matrix.
x,y,zF11 F22 F33
1, 1, 1 − (Δh11 +βF− (1−α)C1) − (Δh21 −Δh22 −αC1−cC3) − (Δh3− (1−c)C3)
1, 1, 0 − (βF− (1−α)C1) − (Δh21 −Δh22 −αC1)Δh3− (1−c)C3
1, 0, 1 − (Δh12 −C1)Δh21 −Δh22 −αC1−cC3− (Δh3−C3)
0, 1, 1 Δh11 +βF− (1−α)C1− (βF−cC3) − (Δh3− (1−c)C3)
1, 0, 0 C1Δh21 −Δh22 −αC1Δh3−C3
0, 1, 0 βF− (1−α)C1−βFΔh3− (1−c)C3
0, 0, 1 Δh12 −C1βF−cC3− (Δh3−C3)
0, 0, 0 −C1βFΔh3−C3
Note: F12 �F13 �F21 �F23 �F31 �F32 �0.
400 20 60 80 100
Time (t)
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Strategy ratio
x
y
z
(a)
0.5
P0 (0.5, 0.5, 0.5)
1.2
0.6
0.7
11.2
P1 (1, 1, 1)
Z
0.8
1
Y
0.9
0.8 0.8
X
1
0.6
0.6 0.4
0.4 0.2
(b)
Figure 1: e dynamic evolution of the tripartite game model when x�0.5, y �0.5,and z�0.5. (a) Time evolutions of x,y, and z; (b) time
evolutions of (x,y,z).
Complexity 7
we set the parameter βin the interval [0, 1], while fixing the
other parameters. e results shown in Figure 3 indicate that
when the carbon tax rate increases from 0.1 to 0.9, the “Low-
carbon” strategy ratio of agricultural enterprises and the
“Regulation” strategy ratio of government increase, while the
“Adoption” strategy ratio of farmers decreases. e results
suggest that the higher the carbon tax rate, the higher the
willingness of agricultural enterprises to carry out low-
carbon innovation and the higher the probability of gov-
ernment choosing regulatory strategies. However, the in-
crease of the carbon tax has a negative impact on farmers’
adoption of low-carbon technology. e reason may be that,
on the one hand, the increase of the carbon tax has led to the
decrease in the supply of nonlow-carbon technology and the
increase in the price of nonlow-carbon technology. e
inertia of farmers in choosing agricultural technology has
stimulated the increase of market demand for nonlow-
carbon technology. On the other hand, the farmers do not
have sufficient awareness of the importance of the envi-
ronment, and the diffusion of low-carbon agricultural
technology will take longer. erefore, it is difficult to im-
prove the speed and scope of agricultural low-carbon
technology in the short term by relying solely on the carbon
tax policy. Carbon tax policy needs are combined with other
low-carbon policy tools to promote the popularization of
low-carbon technology in agriculture.
5.2.3. Adoption Subsidies for Farmers. In order to examine
the effect of adoption subsidies for farmers, we set the pa-
rameter cin the interval [0, 1], while keeping all other
parameters constant. e simulation results shown in
Figure 4 indicate that the ratio of government subsidies to
farmers’ low-carbon product purchase cost increases from
0.1 to 0.9, the “Low-carbon innovation” strategy ratio of
agricultural enterprises and the “Adoption” strategy ratio of
farmers increase, while the “Regulation” strategy ratio of
government decrease. e results indicate that government
subsidies increase farmers’ enthusiasm for adopting low-
carbon technology. e more subsidies farmers receive, the
higher is their demand for low-carbon technology products
and the higher is the enthusiasm of agricultural enterprises
for low-carbon innovation. Similar to the analysis of gov-
ernment subsidies for agricultural enterprises, the larger the
Time (t)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
x
α = 0.1
α = 0.3
α = 0.6
α = 0.9
0 102030405060708090100
(a)
α = 0.1
α = 0.3
α = 0.6
α = 0.9
Time (t)
–0.2
0
0.2
0.4
0.6
0.8
1
1.2
y
0 102030405060708090100
(b)
α = 0.1
α = 0.3
α = 0.6
α = 0.9
0 102030405060708090100
Time (t)
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
z
(c)
Figure 2: e effect of innovation subsidies on the evolutionary strategies.
8Complexity
Time (t)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
x
100 2030405060
β = 0.1
β = 0.2
β = 0.6
β = 0.9
(a)
Time (t)
0.5
0.6
0.7
0.8
0.9
1
1.1
y
100 2030405060
β = 0.1
β = 0.2
β = 0.6
β = 0.9
(b)
100 2030405060
Time (t)
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
z
β = 0.1
β = 0.2
β = 0.6
β = 0.9
(c)
Figure 3: e effect of the carbon tax rate on the evolutionary strategies.
Time (t)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
x
0 102030405060708090100
γ = 0.1
γ = 0.3
γ = 0.6
γ = 0.9
(a)
100
Time (t)
0
0.2
0.4
0.6
0.8
1
1.2
y
0 102030405060708090
γ = 0.1
γ = 0.3
γ = 0.6
γ = 0.9
(b)
Figure 4: Continued.
Complexity 9
amount of adoption subsidies is, the lower the enthusiasm of
government subsidies is.
6. Conclusions and Suggestions
Developing low-carbon agriculture is an inevitable choice to
reduce greenhouse gas emissions, improve agricultural
ecological environment, and realize agricultural moderni-
zation. e innovation and diffusion of low-carbon agri-
cultural technologies cannot be separated from the
participation of relevant stakeholders such as agricultural
enterprises, government, farmers, and intermediaries.
However, current research on the interrelationship of
multiple stakeholders in low-carbon agricultural technology
innovation and diffusion is very limited. Different from
previous studies, this paper establishes a tripartite game
model involving agricultural enterprises, government, and
farmers using evolutionary game theory. en, simulation
analysis based on MATLAB software is implemented to
explore the impact of government policies on the innovation
diffusion of low-carbon agriculture. e results show that
(1) e cost of low-carbon innovation, the increased
revenue from low-carbon innovation, and govern-
ment regulation (including carbon taxes and inno-
vation subsidies) are the main factors affecting the
low-carbon innovation of agricultural enterprises.
(2) Low-carbon production costs, additional benefits
from low-carbon production, and adoption subsidies
for low-carbon are the principal factors affecting
farmers’ adoption of low-carbon technologies.
(3) e probability of government regulation is mainly
affected by the cost and benefit of low-carbon reg-
ulation, which decreases with the increase of regu-
lation costs and increases with the increase of
regulatory benefits.
(4) Government subsidies for low-carbon innovation,
carbon taxes, and government subsidies for low-
carbon technology adoption are effective means to
promote the diffusion of low-carbon technologies in
agriculture. High-level of innovation subsidies and
adoption subsidies inspires the enthusiasm of agri-
cultural enterprises for low-carbon innovation and
farmers for low-carbon technology adoption. e
high level of carbon taxes arouses the enthusiasm of
low-carbon innovation of agricultural enterprises.
However, it inhibits farmers’ adoption of low-carbon
technologies in the short term.
is study contributes to the present literature on in-
novation diffusion theory in two areas. First, evolutionary
game theory is utilized to study the diffusion of low-carbon
agricultural innovation based on multiple stakeholders. e
reduction of agricultural greenhouse gas emissions depends
not only on farmers’ low-carbon production but also on the
innovation of low-carbon agricultural technology. It is
significance to reveal the mechanism of the interaction
between agricultural enterprises and farmers in low-carbon
agricultural innovation diffusion. is study compensates
for the current lack of application of innovation diffusion
theory in agriculture [47]. Second, the effects of low-carbon
policy instruments (innovation subsidies, carbon taxes, and
adoption subsidies) on low-carbon agricultural technology
innovation diffusion are studied, which is of great value in
the formulation and implementation low-carbon agricul-
tural policies.
is study also has policy implications. First, the gov-
ernment should increase the propaganda of the importance
of low-carbon agriculture and low-carbon agriculture pol-
icies through training, meetings, and public service adver-
tisements and strengthen the awareness of agricultural
enterprises and farmers to low-carbon agriculture. In order
to reduce the cost of government regulation, the public,
media, and nongovernmental organizations should be fully
mobilized to participate in the production regulation of
agricultural enterprises. Second, the appropriate subsidy
level should be committed to prevent agricultural enterprises
and farmers from defrauding low-carbon subsidies caused
by excessive subsidies. is policy can be combined with
other policies such as carbon trading market to avoid
marketing problems caused by insufficient supply of
0 102030405060708090100
Time (t)
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
z
γ = 0.1
γ = 0.3
γ = 0.6
γ = 0.9
(c)
Figure 4: e effect of adoption subsidies on the evolutionary strategies.
10 Complexity
nonlow-carbon production materials in the short term.
ird, a communication platform should be built for agri-
cultural enterprises, scientific research institutions, farmers,
and financial institutions, which can promote the R&D and
industrialization of low-carbon agricultural technologies.
e farmers can get the latest market information of low-
carbon agricultural technologies and choose the applicable
low-carbon agricultural technology.
Data Availability
e data used to support the findings of this study are
available from the corresponding author upon request.
Conflicts of Interest
e authors declare no conflicts of interest regarding the
publication of this paper.
Authors’ Contributions
All authors have read and approved the final manuscript.
Acknowledgments
is paper was supported by the Tianjin Planning Leading
Group Office of Philosophy and Social Sciences under Grant
no. TJYY17-017.
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