2.1 Connotation and composition of agricultural innovation ecosystem

The innovation ecosystem is an extension of the business ecosystem [17], which was formally proposed by the U.S. President’s Council of Advisors on Science and Technology (PCAST) in 2004. Since then, the research on innovation ecosystems have become a hot topic in academic circles. At present, the definition of an innovation ecosystem is relatively loose and fragmented [18], and can be roughly divided into theoretical perspectives from systematics [19], factor flows [20], innovation networks [21], collaboration [22], responsible innovation [23], and so on. Scholars generally refer to the ideas of ecology and regard the innovation ecosystem as a dynamic and complex system formed by the interconnected and collaborative evolution of different stakeholders and the external environment [24]. With the deepening of research, the concept of an innovation ecosystem has been used more and more commonly to study the collaborative innovation of multiple actors in value co-creation [25]. Some scholars have stated that an innovation ecosystem is a collaborative innovation network centered on value co-creation [26]. Some other scholars believe that innovation ecosystem is an alliance structure formed through the cooperation of heterogeneous subjects, in order to realize core value propositions [27, 28].

As one of the important branches of innovation ecosystem, agricultural innovation ecosystem is an inevitable choice to deepen the reform of science and technology system, and an important support for the development of Chinese agricultural innovation. In recent years, scholars have begun to focus on the study of agricultural innovation ecosystems, which has laid the theoretical foundation for this paper. Pigford (2018) proposed an umbrella concept that defines agricultural innovation ecosystems as interdependent and nested interconnected innovation networks formed by multiple innovation players in pursuit of common value creation [29]. Wen (2019) considered agricultural innovation ecosystem as an innovation network composed of agro-involved firms, suppliers, consumers, and the external environment in which they were located, which was loose in nature [30]. Based on the architect theory, Li (2022) divided the agricultural innovation ecosystem into three parts: internal architects, external architects, and the environment, each of which interacts with each other to achieve resource integration and thus promote the value co-creation of the system [31]. Thus, on the one hand, it can be seen that agricultural innovation ecosystem contains some common elements of innovation ecosystem, and involves diversified innovation subjects such as agriculture-related enterprises, government, universities and research institutions [32]. In the whole process from technological research and development to commercialization, multiple innovation subjects are connected with each other, forming a network structure with multiple cycles, reciprocation, and cooperation of multiple subjects [33]. An agricultural innovation ecosystem aims to promote the improvement of agricultural innovation capacity, ultimately achieving the improvement of economic, social, and ecological benefits. In order to adapt to changes in the innovation environment, the innovation main body must facilitate the exchange of substances, energy, and information, thus creating a system with ecological and dynamic characteristics. Through cooperation, the realization of resource sharing, and complementary advantages, the value pursuits of various subjects can be satisfied, thus promoting internal value consensus of the system and, finally, realizing value co-creation. On the other hand, from the reality of China, there are still some limitations of innovation resources in the agricultural industry compared with other industries, leading to some special features of the agricultural innovation ecosystem. Agricultural innovation activities should take into account regional characteristics [34]; only the participation of government forces can ensure that innovation activities can be carried out smoothly [35]; it is necessary to rely on collaborative innovation between industry, academia and research to promote the improvement of independent innovation capacity [36]; special industries should be used as a grasp to highlight the competitive advantages of unique regional resources, make the regional brand bigger and stronger, and consolidate and strengthen the basic position of agriculture [12].

In summary, based on a large amount of literature, this paper defines the agricultural innovation ecosystem for developing countries from the actual Chinese agricultural industry as follows: Within the scope of a certain time and space, agricultural-related enterprises, universities, and research institutions (e.g., the multivariate innovation main body with industry–university–institution cooperation as the core), under the guidance of the government and community interactions, promote agriculture industry innovation and create an innovation environment which more effectively fosters material, energy, and information flows, leading to a symbiotic, creative, and co-prosperous common evolution of the system.

2.2 Integration framework for agricultural innovation ecosystem

Agricultural innovation is a complex system involving the economy, society, and ecology. Addressing the problems of agriculture, rural areas, and farmers cannot be completed by a single subject, but must rely on the joint participation of multiple innovation subjects. The structural relationship between agricultural innovation ecosystem elements is depicted in Fig 1.

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Fig 1. Integration framework for agricultural innovation ecosystem.

https://doi.org/10.1371/journal.pone.0289408.g001

As seen from Fig 1, in the agricultural innovation ecosystem, industry-university-research is at the most central position. This is due to the limited independent innovation capacity of agriculture-related enterprises, which must rely on collaborative innovation among industry, academia and research to obtain sustainable innovation sources.

Agriculture-related enterprises constitute the basic unit of the agricultural industry, including not only those directly engaged in agricultural production, but also those providing various services for agricultural production and processing agricultural products [37]. As the main body of benefit innovation of the system, agriculture-related enterprises can create economic benefits for the system by absorbing agricultural intellectual property technologies and transforming them into innovative products [38]. The social benefits of the system may be improved through taxation and employment opportunities. In addition, agriculture-related enterprises can carry out agricultural production in a large-scale, intensive, and standardized way; make more effective use of agricultural resources; reduce agricultural non-point source pollution; and promote the improvement of system ecological benefits [39]. It can be seen that agriculture-related enterprises are the core group of an agricultural innovation ecosystem, who are the main actors maintaining the economic, social, and ecological benefits of the agricultural innovation ecosystem, as well as the dominant leaders and main driving force of agricultural innovation activities.

Universities & scientific research institutions are the providers of innovation achievements in an agricultural innovation ecosystem. Compared with other industries, agricultural R&D investment and the innovation talent reserve are significantly insufficient, while agriculture-related enterprises have limited independent innovation ability and, thus, lack the ability to fully undertake independent innovation [40]. They can only rely on the advantages of academic and research institutions, in terms of knowledge and technical personnel to support the agricultural innovation ecosystem to produce sustainable innovation. Colleges and universities are mainly engaged in the basic research of agriculture, which aims at innovating the frontiers of agricultural science theory. However, scientific research in colleges and universities should not be divorced from social needs, and should be guided by market demands. On the basis of industry–university–research cooperation, universities should possess a deep understanding of key technical problems, and then carry out basic research work in relevant areas [41]. In addition, agriculture-related colleges and universities shoulder the important task of training agricultural science and technology talents, thus providing a steady stream of high-quality talents for agricultural research and practice. Scientific research institutions are directly involved in the process of agricultural innovation. With the help of good platforms and resources provided by agriculture-related enterprises, scientific research institutions carry out the development of agricultural technology and the planning of research, transforming the achievements of agricultural scientific research into technological achievements that can be applied by enterprises and their industries, in order to enhance the content and added value of agricultural science and technology while promoting the high-quality development of agriculture.

The government acts as the strategy- and policy-maker and plays an important role, in terms of policy guidance and providing subsidies in the agricultural innovation ecosystem [42]. Due to the weak nature of agriculture itself, it is characterized by a long growth cycle, large investment, low industry barriers, and high risks. Besides the government, other innovation subjects are limited by objectives, interests, and resources, and may not be competent. Only the participation of the government can ensure the smooth development of innovation activities [33]. In the process of system operations, the government is not directly involved in agricultural technology innovation; however, it can, through system design and policy support, constrain and incentivize the innovation main body, fully combined with the local actual situation, in order to provide proactive strategies, clear agricultural innovation development directions, more targeted allocation of resources, and organization and coordination [43]. Therefore, in many cases, the government plays an important role in organizing and investing in agricultural innovation activities. When agricultural innovation resources are scarce, it is particularly important for the government to provide policy support, introduction of and investment into innovation resources, and social services.

In addition, financial institutions and intermediary institutions also play an indispensable role in the agricultural innovation ecosystem [44]. Financial institutions are the main support to promote agricultural innovation and provide indispensable financial support for the interior of the agricultural innovation ecosystem. Intermediary agencies play roles involving communication, coordination, integration, and promotion among multiple innovation subjects, and provide professional services such as agricultural technical consultation, evaluation, and industrialization of achievements for agriculture, rural areas, and farmers. Of course, farmers, as the main operating subject in agricultural development, are the demanders of agricultural innovation technology, and carry out re-innovation according to their actual agricultural technology demand, thus accelerating the sustainable development of the agricultural innovation ecosystem.

The innovation ecosystem is self-organizing and evolutionary [45], so is the agricultural innovation ecosystem as one of its branches. The innovation subjects and innovation elements in the agricultural innovation ecosystem interact with the external environment in the process of continuous development and change [46], which in turn causes structural changes in the whole system, leading to further renewal and enrichment of innovation subjects and innovation elements, expansion of the system scope and presentation of new environmental forms. The agricultural innovation ecosystem also has the attributes of a natural ecosystem. Through industry-university-research synergistic innovation, materials and energy in the natural ecosystem are transformed into economic materials and energy with exchange value, so as to promote the upgrading of science and technology [47]. Therefore, the agricultural innovation ecosystem will change and evolve dynamically over time, in a spiraling process from low level to high level. On this basis, it is of great significance to reveal the evolutionary relationship among innovation subjects in the agricultural innovation ecosystem from a dynamic perspective. However, existing studies mainly focus on static perspective analysis. In order to make up for the shortcomings of the existing research, and to deepen and expand the theoretical system of agricultural innovation ecosystem and evolution more systematically, the following is carried out in this paper: (1) We analyze the connotation of an agricultural innovation ecosystem, deconstruct its constituent elements and structure, and identify the role, relationship, and positioning of the collaborative innovation subject of the system; (2) The evolutionary game model is applied to explore and analyze the synergistic evolutionary behavior of the government, agriculture-related enterprises, universities & research institutions in order to explore the influencing factors of synergistic innovation [48]; and (3) the MATLAB software is used to conduct numerical simulation of the collaborative innovation evolution game of government, agriculture-related enterprises, universities & research institutions, in order to verify the effect of the collaborative innovation game process and influencing factors on collaborative innovation evolution of the agricultural innovation ecosystem. The relevant research results are expected to be helpful, in terms of reducing the opportunity cost and externalities of innovation subjects in the process of participating in synergistic innovation, improving the ability for collaborative innovation and co-evolution among subjects, guaranteeing the sustainable development of the system, and providing reference for the formulation of local government agricultural innovation development strategy planning.

3.1 Role identification

The development of regional agricultural innovation ecosystem in developed countries has been relatively mature, which provides valuable practical experience for our country. For example, the United States has built a sound innovation ecosystem with strong multinational companies such as Monsanto, Bunge and Novus International as the core, supported by universities, scientific research institutions and governments, and brought about the continuous emergence of modern agricultural products and technologies such as crop varieties, agricultural biotechnology, microbial technology and biological agents. It can be seen that the high degree of agricultural science and technology industrialization in developed countries is mainly due to the cultivation of a large number of enterprise innovation subjects integrating agricultural science and technology research and development and achievement transformation [49]. The practice of developed countries is more in line with the development process of the industrial innovation ecosystem in China, which relies mainly on large enterprises with strong strength as the core, complemented by innovative R&D in academic and research institutions. However, unlike developed countries, agricultural innovation ecosystem in China is in its infancy, and there is a lack of agricultural-related enterprises with independent innovation capabilities, which must rely on universities & research institutions as the main source of innovation to engage in industry-university-research cooperation. In addition, as a policy leader, although the government does not directly participate in the industry-university-research synergistic innovation, it will maintain the stability of the industry-university-research collaborative innovation through legal, economic and administrative means. Therefore, the roles of government, agriculture-related enterprises, universities & research institutions are indispensable in the agricultural innovation ecosystem.

In the agricultural innovation ecosystem, the collaborative innovation intention among the multiple subjects is usually long-term. Agriculture-related enterprises carry out in-depth cooperation with relevant innovation subjects and reach cooperation agreements. The collaborative innovation behaviors among agents is limited by these cooperation agreements, and is restricted and influenced by the strategy choices of all involved parties, each of which cannot fully realize the goal of maximizing their own interests. Thus, their collaborative innovation behaviors conform to the bounded rationality hypothesis of evolutionary game theory [50]. In this paper, the government, agriculture-related enterprises, universities, & research institutions are selected, in order to establish an evolutionary game model. The reason is that universities & research institutions have the talent, knowledge, and technology necessary for innovation, and can continuously provide new products, technologies, materials, and processes. Agriculture-related enterprises can provide material resources and locations for research and development, and can connect with the market, accurately grasp the market demand, in order to carry out effective and relevant industry–university–research innovation activities. The government can play a leading role in guiding industry, universities & research institutes to establish innovation cooperation based on market demand, so as to effectively promote agricultural innovation and development. All three can independently choose to participate or not to participate under the premise of limited rationality. Therefore, whether agriculture-related enterprises, universities & scientific research institutions choose collaborative innovation behaviors, and whether the government chooses to regulate collaborative innovation behaviors are in line with the dynamic process of evolutionary game, and are formed through multiple evolutionary games of various subjects. The reason why financial institutions and intermediaries are not selected is that they only provide funds, technology promotion and other services for agricultural innovation activities, play auxiliary service functions, and directly participate in the collaborative innovation of industry, university and research, and can not lead the success or failure of synergistic innovation. Therefore, this paper explores and analyzes the evolutionary game of collaborative innovation behaviors of government, agribusiness, universities and research institutions using the evolutionary game model in order to reveal the evolutionary process of agricultural innovation ecosystem.

3.2 Basic assumptions

This paper explores the evolution process of collaborative innovation behaviors of government, agriculture-related enterprises, universities & research institutions, and makes the following assumptions:

1. Game players
   Assuming that there are three game players, namely, the government, denoted as G, agriculture-related enterprises, denoted as A, and universities & research institutions, denoted as U. All three players carry out collaborative innovation on the basis of limited rationality, so they can not know the collaborative innovation behavior choices of the other two parties in advance. In order to explore the most favorable choice for themselves, they have to constantly adjust their collaborative innovation behaviors through practice [51].
2. Strategy selection.
   In the collaborative innovation strategy selection, each of the three game parties has two strategy choices [52]. On the one hand, the government can choose the strategy of regulation or non-regulation, i.e., the government’s game strategy set is (regulation, non-regulation). Regulation can be understood as the government supervising and regulating the collaborative innovation behaviors of agriculture-related enterprises, universities & research institutions through the formulation of policies and regulations, and providing subsidies and incentives to agriculture-related enterprises, universities & research institutions that actively participate in synergistic innovation. Assuming that the probability of the government adopting a strategy of regulation is x, the probability of adopting a strategy of no regulation is (1−x). On the other hand, agriculture-related enterprises, universities and research institutions can choose collaborative innovation or non-collaboration strategy according to their own interests, i.e. the set of game strategies of agriculture-related enterprises, universities & research institutions is (collaborative, non-collaborative). Assuming that the probability of agriculture-related enterprises, universities & research institutions participating in collaborative innovation is y and z respectively, the probability of not participating in collaborative innovation is (1−y) and (1−z) respectively. Among them, x,y,z∈[0,1]. In the game process, no matter the government or agriculture-related enterprises or universities & research institutions, any player is randomly paired to play the game.
3. Cooperation cost
   The government encourages agriculture-related enterprises, universities and research institutes to participate in collaborative innovation through policies, and regulates the process of synergistic innovation [53]. Assuming that the incentive cost generated is K and the cost of implementing regulation is C_g. Among them, the proportion of government incentive funds received by agriculture-related enterprises participating in collaborative innovation is γ, and the proportion of government incentive funds received by universities & research institutes participating in collaborative innovation is (1−γ), γ∈[0,1]. When agricultural-related enterprises, universities & research institutions carry out synergistic innovation, both parties need to invest in human, material and financial resources. Assuming that the costs invested by agricultural-related enterprises and universities in adopting collaborative innovation strategies are C_a and C_u respectively. When the government imposes regulation and incentives on collaborative innovation activities, it will reduce the cost of collaborative innovation for agriculture-related enterprises, universities & research institutions. Assuming that when the government adopts the regulatory strategy, the cost reduction factor of collaborative innovation of agricultural-related enterprises is ϕ₁, and the cost reduction factor of collaborative innovation of universities & research institutions is ϕ₂. When the government adopts the regulatory strategy, the cost reduction of collaborative innovation of agriculture-related enterprises is ϕ₁C_a, and the cost reduction of collaborative innovation of universities and research institutions is ϕ₂C_u.
4. Cooperation benefits
   Government regulation and incentives can improve the efficiency of collaborative innovation between industry, academia and research, accelerate the speed of agricultural technology diffusion, and promote the transformation of regional agriculture to high-quality growth, allowing the government to reap the benefits. Assuming that M_g is the benefit obtained when the government adopts a regulatory strategy, and N is the benefit obtained when the government adopts a non-regulatory strategy. Agricultural-related enterprises, universities & scientific research institutions will generate basic income when they do not carry out synergistic innovation. Assuming that the base benefit of agriculture-related enterprises without collaborative innovation strategy is I_a; the base benefit of universities & research institutions without collaborative innovation strategy is I_u. In the case of synergistic innovation, both parties will gain additional collaborative innovation benefits. Assuming that the revenue generated by collaborative innovationof agriculture-related enterprises, universities and research institutions is S. Among them, the distribution ratio of collaborative innovation revenue of agriculture-related enterprises is δ respectively, and the distribution ratio of innovation revenue of universities and research institutions is (1−δ), δ∈[0,1]
5. Liquidated damages
   The prerequisite for collaborative innovation by agriculture-related enterprises, universities and research institutions is the signing of a contract and the payment of a deposit in advance.Under the guarantee of the contract, if any player betrays the contract involving agriculture-related enterprises, universities & scientific research institutions, it will pay the corresponding liquidated damages to the other player [54, 55]. Assuming that when the agriculture-related enterprises, universities & research institutions betray the synergistic innovation, the liquidated damages to be paid to the other player are W_a and W_u respectively.

3.3 Evolution model construction

Based on the above basic assumptions, the game payment matrix of the three parties in the agricultural innovation ecosystem when the government, agriculture-related enterprises, universities and research institutions adopt different strategies can be derived, as shown in Table 1.

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Table 1. Payment matrix of three players in the collaborative innovation game.

https://doi.org/10.1371/journal.pone.0289408.t001

Based on the basic assumptions of the evolutionary game model and the payment matrix, an evolutionary game model of the agricultural innovation ecosystem can be constructed for the expected benefits of three parties: government (G), agriculture-related enterprises (A), universities & research institutions (U), as follows:

Assuming that the expected return when the government adopts a "regulation" strategy is E_g1, the expected return when it adopts a "non-regulation" strategy is E_g2, and the average expected return is , then: (1) (2) (3)

Assuming that the expected return of an agribusiness firm adopting a "collaboration" strategy is E_a1, and the expected return of a "non-collaboration" strategy is E_a2, the average expected return is , then: (4) (5) (6)

Assuming that the expected return when universities & research institutions adopt the "Collaboration" strategy is E_u1, and the expected return when adopting the "Non-collaboration" strategy is E_u2, the average expected return is , then.

(7)

(8)

(9)

From (1) and (3), the government’s replication dynamic equation can be constructed as follows: (10)

Based on (4) and (6), the replication dynamic equation of agriculture-related enterprises can be constructed as follows: (11)

From (7) and (9), the replication dynamics equations for universities and research institutions can be constructed as follows: (12)

Simultaneous (10), (11) and (12), a replicated dynamic equation system for governments, agriculture-related enterprises, universities & research institutions can be established as follows: (13)

The three replication dynamic equations in system (13) reflect the direction and speed of strategic adjustment of government, agriculture-related enterprises, universities & scientific research institutions respectively [56].

3.4 Stability analysis of evolutionary game

According to the stability theory, when satisfying F(x) = 0, and ; F(y) = 0, and ; F(z) = 0, and , the government, agriculture-related enterprises, universities & research institutions strategy adjustment will be regionally stable.

1. (1) Stability analysis of government

When F(x) = 0, then there are two equilibrium points x = 0 or x = 1.

(14)

The strategic choices of the government during the evolutionary game of collaborative innovation in agricultural innovation ecosystems are as follows:

1. ① When , then is constant, i.e., regardless of whether the government chooses to regulation or non-regulation, the benefits obtained by the same, x is in a steady state for any value within the interval of [0,1]. The replicated dynamic bitmap is plotted as shown in Fig 2(A).
2. ② When , then , . At this time, x = 0 is the final equilibrium point, i.e., when the net benefits obtained by the government by choosing the regulation strategy is greater than the benefits obtained by choosing non-regulation strategy. The government will eventually tend to choose regulation. The replication dynamic phase diagram is drawn as shown in the Fig 2(B).
3. ③ When , then , . At this time, x = 1 is the final equilibrium point, i.e., when the net benefits obtained by the government by choosing the regulation strategy is less than the benefits obtained by choosing non-regulation strategy. The government will eventually tend to choose regulation. The replication dynamic phase diagram is drawn as shown in the Fig 2(C).

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Fig 2. Dynamic phase diagram of the government.

. . .

https://doi.org/10.1371/journal.pone.0289408.g002

1. (2) Stability analysis of agriculture-related enterprises

When F(y) = 0, then there are two equilibrium points y = 0 or y = 1.

(15)

The strategic choices of agriculture-related enterprises during the evolutionary game of collaborative innovation in agricultural innovation ecosystems are as follows:

1. ① When , then is constant, i.e, regardless of whether agriculture-related enterprises choose to collaboration or non-collaboration, y is in a stable state for any value in the interval of [0,1]. The replicated dynamic bitmap is plotted as shown in Fig 3(A).
2. ② When , , . At this time, y = 0 is the final equilibrium point, i.e., when the net benefits obtained by agriculture-related enterprises by choosing collaboration strategy is greater than the benefits obtained by choosing non-collaboration strategy. Agriculture-related enterprises will eventually tend to choose collaborative innovation and draw the replication dynamic phase diagram, as shown in Fig 3(B).
3. ③ When , , . At this time, y = 1 is the final equilibrium point, i.e., when the net benefits obtained by agriculture-related enterprises by choosing collaboration strategy is less than the benefits obtained by choosing non-collaboration strategy. Agriculture-related enterprises will eventually tend to choose not to participate in collaborative innovation, and the replication dynamic phase diagram will be drawn, as shown in Fig 3(C).

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Fig 3. Dynamic phase diagram of agriculture-related enterprises.

. . .

https://doi.org/10.1371/journal.pone.0289408.g003

1. (3) Stability analysis of universities & research institutions

When F(z) = 0, then there are two equilibrium points z = 0 or z = 1.

(16)

The strategic choices of universities & research institutions during the evolutionary game of collaborative innovation in agricultural innovation ecosystems are as follows:

1. ① When , then is constant, i.e, regardless of whether universities & research institutions choose to collaboration or non-collaboration, z is in a stable state for any value in the interval of [0,1]. The replicated dynamic bitmap is plotted as shown in Fig 4(A).
2. ② When , , . At this time, z =0 is the final equilibrium point, i.e., when the net benefits obtained by universities & research institutions by choosing collaboration strategy is greater than the benefits obtained by choosing non-collaboration strategy. Universities & research institutions will eventually tend to choose collaborative innovation and draw the replication dynamic phase diagram, as shown in Fig 4(B).
3. ③ When , , . At this time, y = 1 is the final equilibrium point, i.e., when the net benefits obtained by universities & research institutions by choosing collaboration strategy is less than the benefits obtained by choosing non-collaboration strategy. Universities & research institutions will eventually tend to choose not to participate in collaborative innovation, and the replication dynamic phase diagram will be drawn, as shown in Fig 4(C).

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Fig 4. Dynamic phase diagram of universities & research institutions.

. . .

https://doi.org/10.1371/journal.pone.0289408.g004

1. (4) Stability point analysis of tripartite evolutionary game

According to the research method of Friedman (1991), the stability analysis of the evolutionary equilibrium points of the three parties in the game can be carried out by establishing the Jacobi matrix of the replicated dynamic group [57].

Therefore, the Jacobi matrix of the above group of replicated dynamic system is as follows: (17)

In system (17), if F(x) = F(y) = F(z) = 0, 8 local equilibrium points of the collaborative innovation game can be obtained, which are: O₁(0,0,0), O₂(1,0,0), O₃(0,1,0), O₄(0,0,1), O₅(1,1,0), O₆(1,0,1), O₇(0,1,1), O₈(1,1,1). In an evolutionary game, the equilibrium point satisfying the Jacobi matrix when all eigenvalues are negative is the evolutionarily stable point of the game system [58]. Therefore, the corresponding Jacobi matrix of 8 equilibrium points are calculated respectively, and the eigenvalues of the matrix are obtained. In order to save space, only an example is shown.

When the equilibrium point is O₁(0,0,0), the corresponding Jacobi matrix is as follows: (18)

The eigenvalues of the Jacobi matrix can be obtained from (18) as λ₁ = M_g−G_g−N, λ₂ = W_u−C_a, λ₃ = W_a−C_u. Similarly, Jacobi matrix eigenvalues corresponding to other equilibrium points can be calculated, as shown in Table 2.

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Table 2. Eigenvalues of Jacobi matrix in evolutionary game.

https://doi.org/10.1371/journal.pone.0289408.t002

Through the analysis of Table 2, it is found that the positive and negative values of the three characteristic values corresponding to different strategy combinations are difficult to determine. This is because the evolutionary game process of the government, agriculture-related enterprises, universities & research institutions is affected by many factors, and the strategy selection of the three parties will be adjusted with the change of the influencing factors. In order to conform to the objective reality, suppose , , , i.e., the net benefits obtained by the government by choosing regulation is greater than the benefits obtained by choosing non-regulation, and the net benefits obtained by agriculture-related enterprises, universities & research institutions by choosing collaboration is greater than the benefits obtained by choosing non-collaboration. In judging the positive and negative values of the 3 characteristic values corresponding to different strategy combinations, it is also necessary to consider the magnitude of the default amount obtained from the betrayal of co-innovation by only one player involved in co-innovation by the other player and the cost incurred by its participation in co-innovation. The specific situation is analyzed as follows:

1. (1) When W_u>C_a, W_a>C_u, it means that only one player of the agriculture-related enterprises or universities & research institutions involved in collaborative innovation obtains the default amount of the other player’s betrayal of collaborative innovation greater than the cost incurred by their participation in collaborative innovation, then the results of the stability analysis of the tripartite evolutionary game are shown in Table 3.

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Table 3. Stability point analysis of tripartite evolutionary game for W_u>C_a, W_a>C_u.

https://doi.org/10.1371/journal.pone.0289408.t003

According to the analysis results in Table 3, it can be seen that when W_u>C_a, W_a>C_u, in the evolutionary game of agricultural innovation ecosystem, point O₁(0,0,0) is the saddle point, the stable behavior combination of the evolutionary game occurs at point O₈(1,1,1), and the rest are instability points. It shows that when W_u>C_a, W_a>C_u, the result of the long-term game among the three players is that the government will choose to impose regulation on collaborative innovation, and the agriculture-related enterprises, universities & research institutions will choose collaborative innovation, i.e., the strategy combination of the equilibrium point is (regulation, collaboration, collaboration).

1. (2) When W_u>C_a, W_a>C_u, it means that the cost generated by the participation of agriculture-related enterprises in collaborative innovation is smaller than the default payment made by universities & research institutions betraying collaborative innovation, meanwhile, the cost generated by the participation of universities & research institutions in collaborative innovation is smaller than the default payment made by agriculture-related enterprises betraying collaborative innovation. The discussion can be divided into two cases., and the stability analysis results of the tripartite evolutionary game are shown in Table 4.

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Table 4. Stability point analysis of tripartite evolutionary game for W_u>C_a, W_a<C_u.

https://doi.org/10.1371/journal.pone.0289408.t004

According to the analysis results in Table 4, when W_u>C_a, W_a>C_u, two cases and should be considered to judge the positive and negative eigenvalues of different strategy combinations, i.e., the sum of the government incentive funds obtained and the liquidated damages paid by the other player and the cost of collaborative innovation under government regulation should be compared when universities & research institutions choose collaboration strategy separately. The analysis shows that although the positive and negative eigenvalues of different equilibrium points are different in both cases, the saddle point is O₄(0,0,1), the final stable point is O₈(1,1,1), and the rest are instability points. When W_u>C_a, W_a>C_u, the stable strategy combination of the tripartite long-term game is (regulation, collaboration, collaboration).

1. (3) When W_u<C_a, W_a>C_u, it means that the cost generated by the participation of agriculture-related enterprises in collaborative innovation is greater than the default paid by universities & research institutions betraying collaborative innovation, meanwhile, the cost generated by the participation of universities & research institutions in collaborative innovation is smaller than the default paid by agriculture-related enterprises betraying collaborative innovation, and the same can be discussed in two cases, and the stability analysis results of the tripartite evolutionary game are shown in Table 5.

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Table 5. Stability point analysis of tripartite evolutionary game for W_u<C_a, W_a>C_u.

https://doi.org/10.1371/journal.pone.0289408.t005

According to the analysis results in Table 5, when W_u<C_a, W_a>C_u, two cases and should be considered to judge the positive and negative eigenvalues of different strategy combinations, i.e., the sum of the government incentive funds obtained and the liquidated damages paid by the other player and the cost of collaborative innovation under government regulation when the agriculture-related enterprises choose the collaboration strategy separately. The analysis shows that although the positive and negative eigenvalues of different equilibrium points are different in both cases, the saddle point is O₃(0,1,0), the final stable point is O₈(1,1,1), and the rest are unstable points. When W_u<C_a, W_a>C_u, the stable strategy combination of the tripartite long-term game is (regulation, collaboration, collaboration).

1. (4) When W_u<C_a, W_a<C_u, it means that the cost of agriculture-related enterprises participating in collaborative innovation is greater than the liquidated damages paid by universities & research institutions for betraying collaborative innovation, meanwhile, the cost of universities & research institutions participating in collaborative innovation is also greater than the liquidated damages paid by agriculture-related enterprises for betraying collaborative innovation, which needs to be discussed in four cases. stability analysis results of the tripartite evolutionary game are shown in Table 6.

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Table 6. Stability point analysis of tripartite evolutionary game for W_u<C_a, W_a<C_u.

https://doi.org/10.1371/journal.pone.0289408.t006

According to the analysis results in Table 6, when W_u<C_a, W_a<C_u, in order to judge the merits of different strategy combinations, it is necessary to further compare the sum of the government incentive funds received and the liquidated damages paid by the other player and the cost of collaborative innovation under government regulation when one of the agriculture-related enterprises or universities & research institutions chooses collaboration strategy separately. Therefore, it can be divided into four cases: , ; , ; , ; , . The analysis shows that saddle points in all four cases were O₃(0,1,0) and O₄(0,0,1). Except for , , the stable point of the equilibrium point in the other three cases is O₈(1,1,1), i.e., the stable strategy combination of the tripartite long-term game is (regulation, collaboration, collaboration). In the case of , , the stable points of the equilibrium point are O₂(1,0,0) and O₈(1,1,1), i.e., the stable strategy combination of the tripartite long-term game is (regulation, non-collaboration, non-collaboration) or (regulation, collaboration, collaboration). In short, when W_u<C_a, W_a<C_u, as long as the sum of government incentive funds obtained by at least one of the agriculture-related enterprises or universities & research institutions for selecting synergy strategies separately and the liquidated damages paid by the other player is greater than the cost of collaborative innovation generated under government regulation, the three parties of the government, agriculture-related enterprises, universities & research institutions will choose (regulation, collaboration, collaboration); When the sum of government incentive funds obtained by agriculture-related enterprises or universities & research institutions and the liquidated damages paid by the other player are both less than the cost of collaborative innovation generated under government regulation, the three players of the government, agriculture-related enterprises, universities & research institutions may choose (regulation, non-collaboration, non-collaboration) or (regulation, collaboration, collaboration). The final result of the game depends on the reward and punishment mechanism among agriculture-related enterprises, universities & research institutions and the government’s regulation.

To sum up, this paper attempts to explore the three parties’ evolutionary game strategy choices of government, agriculture-related enterprises, universities & research institutions under different conditions. It is found that under the premise that the net benefits of the government regulation are greater than those of non-regulation. At the same time, on the premise that the net benefits of agriculture-related enterprises, universities & research institutions choosing collaboration are greater than the benefits of choosing non-collaboration. As long as the sum of at least one player of agriculture-related enterprises or universities & research institutions choosing collaboration strategy independently to obtain government incentive funds and the other player paying liquidated damages is greater than the cost of collaborative innovation under government regulation, all three players will ultimately choose (regulation, collaboration, collaboration). Only when the sum of the government incentive funds and the liquidated damages paid by the other player is less than the cost of collaborative innovation under government regulation, the three players may choose (regulation, non-collaboration, non-collaboration) or (regulation, collaboration, collaboration). The game players of the agricultural innovation ecosystem all pursue the maximization of benefits, i.e., (regulation, collaboration, collaboration) is a combination of strategies beneficial to the government, agriculture-related enterprises, universities & research institutions. Through collaborative innovation, agriculture-related enterprises can transform new technologies into new products and improve social and economic benefits. Universities & research institutions can better realize technology transformation. At the same time, the social benefits generated by collaborative innovation can enhance the recognition of the government in the minds of the public, thus prompting the government to adopt active policies to support collaborative innovation activities. Therefore, the optimal combination of (regulation, collaboration, collaboration) strategy, i.e., the equilibrium point O₈(1,1,1) is the optimal state. In order to promote industry-university-research collaborative innovation, agriculture-related enterprises, universities & research institutions should establish a more perfect reward and punishment mechanism, reasonably control costs, and establish a perfect liquidated damages system for breach of contract. The government should strengthen regulation and actively guide the atmosphere of collaborative innovation.

5.1 Conclusions

Innovation is the primary driving force for agricultural development, and it is also a key element for the modernization of agriculture and rural areas and, ultimately, the revitalization of rural areas. With the promotion of rural collective property rights system reform, land system reform, and supply and marketing cooperative comprehensive reform, the agricultural innovation paradigm has undergone significant changes. Objectively, it is necessary to promote the transformation of the agricultural innovation mode from a more open perspective, break the disadvantages of single industrial chain development, build a diversified agricultural innovation ecosystem, promote multi-body synergistic innovation, and change the transformation from blood transfusion to hematopoietic. Based on the forefront of innovation theory—i.e, the innovation ecosystem research perspective—in this paper, we positioned agriculture as a weak industry. First, the concept of an agricultural innovation ecosystem was defined and its constituent elements and structure were deconstructed. Then, evolutionary game theory was used to construct an evolutionary game model of cooperative innovation involving agricultural-related enterprises, universities, and scientific research institutions under the effects of government rewards and punishment, and numerical simulation was carried out suing MATLAB. Our research conclusions are as follows:

1. The source of innovation in the agricultural innovation ecosystem mainly comes from industry–university–research cooperation, which is at the core of the agricultural innovation ecosystem. Through industry–university–research synergistic innovation, agriculture-related enterprises may acquire mature technologies, advanced knowledge, talents from universities and research institutions, and improved independent innovation capabilities [60]. Meanwhile, universities and research institutions have gained platforms and space for scientific research from agriculture-related enterprises, making scientific research more suitable to the market demand and promoting technological transformation and diffusion.
2. The government, agriculture-related enterprises, universities & research institutions have different degrees of influence on each other’s participation intention. On the one hand, the willingness of agriculture-related enterprises, universities & research institutions to participate in collaborative innovation is mutually promoting. The willingness of one party to participate in collaborative innovation will increase with the willingness of the other party to participate in collaborative innovation. Moreover, the willingness of agriculture-related enterprises to participate in collaborative innovation is more sensitive than that of universities & research institutions. This is because when the willingness of agricultural enterprises or universities & research institutions to collaborate on innovation increases, they will take the initiative to seek industry-university-research cooperation, so as to promote the willingness of the other party to participate in collaborative innovation. Meanwhile, since agricultural enterprises are the direct beneficiaries of innovation results, their willingness to participate is significantly higher than that of universities & research institutions. Therefore, the government should tilt the incentive funds to universities & research institutions, enhance the enthusiasm of universities & research institutions to participate in collaborative innovation, and give full play to the role of innovation. On the other hand, the government’s regulatory willingness will decrease with the increase of the willingness of agricultural enterprises, universities & research institutions to participate in collaborative innovation. This is because at the early stage of the evolution of the agricultural innovation ecosystem, agriculture-related enterprises, universities & research institutions are not willing to participate in collaborative innovation, so the government must play a more active role and encourage agriculture-related enterprises, universities & research institutions to participate in collaborative innovation through policy guidance.
3. The participation cost changes of government, agriculture-related enterprises, universities and research institutions affect the collaborative innovation evolution of agricultural innovation ecosystem. On the one hand, the higher the regulatory cost and incentive cost, the lower the regulatory meaning. When the regulatory cost and incentive cost are too high, the government will withdraw due to excessive financial burden. Meanwhile, changes in government supervision cost and incentive cost have opposite effects on the willingness of agriculture-related enterprises, universities & research institutions to participate in collaborative innovation. With the increase of government supervision cost, the willingness of agriculture-related enterprises, universities & research institutions will decline; with the increase of government incentive cost, the willingness of agriculture-related enterprises, universities & research institutions will also increase. This is because excessive government intervention will affect the normal operation of the market mechanism, and then affect the cooperation between enterprises, universities and research institutes. The increase of incentive cost will mobilize the enthusiasm of agriculture-related enterprises, universities & research institutions to participate in collaborative innovation. Therefore, the government should establish a reasonable range of regulatory costs and incentive costs to ensure the smooth development of collaborative innovation activities. On the other hand, the cost of agricultural enterprises, universities & research institutions participating in collaborative innovation will also affect each other’s willingness to participate. The higher the cost of collaborative innovation, the lower the willingness of agricultural enterprises, universities & research institutions to participate in collaborative innovation. Therefore, a more complete cost control mechanism should be established to maintain the operation of agricultural innovation ecosystem.
4. The changes of liquidated damages affect the willingness of agriculture-related enterprises, universities and scientific research institutions to participate in collaborative innovation. The higher the liquidated damages set, the more it can promote collaborative innovation, and the punishment of agriculture-related enterprises for betraying collaborative innovation is more sensitive than that of universities and scientific research institutions. However, when the liquidated damages are set too high, it may cause agriculture-related enterprises, universities and research institutions to fear high penalties and choose to conduct R&D alone. Therefore, an effective liquidated damages system and a reasonable amount of liquidated damages should be formulated to create a favorable environment for collaborative innovation.

5.2 Contribution

Based on the practice of Chinese agricultural industry development, this paper explores key issues related to agricultural innovation ecosystems and their evolutionary processes from an innovation ecosystem perspective, and the main research contributions are summarized as follows:

1. Early research on innovation ecosystems mostly involved high-tech industries, strategic emerging industries, cultural and creative industries and other industries with high technological content, and the scope of research was mostly in developed regions of developed countries. As the research progresses, the relevant theoretical research gradually begins to be refined, but the relevant research is still very limited for the low technology content industries in developing countries, especially the weak agriculture. Based on the current situation of China’s agricultural industry, this paper proposes the connotation of agricultural innovation ecosystem and constructs an integrated framework to deconstruct agricultural innovation ecosystem, which breaks through the traditional "point-to-point" linear innovation paradigm of agriculture and conducts a more systematic, ecological and organic research for the coordinated development of economy, society and ecology, which is an important contribution to enrich and expand the innovation ecosystem theory.
2. Although the theory of innovation ecosystem has been relatively mature and the number of related research results has increased year by year, the research on agricultural innovation ecosystem has just started, and it still remains on some superficial research of theoretical framework construction, and lacks the internal logic and mechanism analysis under the guidance of specific system thinking. Moreover, most existing studies analyze agricultural innovation ecosystems from a static perspective, and do not reveal the evolutionary relationship among innovation agents from a dynamic perspective. In addition, the existing research results on evolutionary game mainly focus on the two-party game between the core firm and the complementary firm, and the multi-party evolutionary game research is relatively rare. To break through the plight of agricultural independent innovation ability promotion, production, study and research, this paper establishes a tripartite collaborative innovation evolution game model of government, agriculture-related enterprises, universities and scientific research institutions, and reveals the dynamic evolution process of collaborative innovation in agricultural innovation ecosystem through numerical simulation. The relevant research in order to promote agricultural innovation ecosystem value to create a collaborative innovation provides a decision-making reference.
3. Considering the limitation of agricultural innovation resources in developing countries, this paper takes China, the largest developing country, as the research object to study the agricultural innovation ecosystem and its evolution. The relevant results can break through the dilemma of low-end locking of agricultural science and technology innovation in developing countries, and promote intra- and inter-regional synergistic and integrated innovation of multiple subjects from the perspective of open innovation, so as to realize a convergent development path of symbiosis, sharing and co-creation, and contribute to high-quality agricultural development and rural revitalization in developing countries.

5.3 Implications

This paper is oriented to developing countries, based on the research perspective of innovation ecosystem, locates agriculture as a weak industry, and studies the evolution process of agricultural innovation ecosystem and its collaborative innovation based on the development status of Chinese agricultural industry. The present research results explore and extend the theoretical and fundamental research on agricultural innovation ecosystems, providing a better exploration of innovation-driven development in agriculture. In order to better maintain the stability of the agricultural innovation ecosystem and promote the sustainable development of agriculture, we put forward the following suggestions:

1. The goal of cooperation should be unified and fully communicated, in order to ensure cooperation between the industry, universities, and research institutes has a common direction and sustainability, in order to avoid the failure of cooperation due to inconsistent goals.
2. A mechanism for sharing interests and risks should be established, in order to clarify the responsibilities of all parties and choose different modes of benefit distribution according to the different modes of cooperation. For example, risk and return may be linked to the investment proportion. Under the premise of clear property rights, a diversified profit distribution mechanism can be stimulated by way of joint construction, technological investment, and equity incentive. Furthermore, third-player institutions can be introduced, a multi-player conflict coordination mechanism can be established, and the formation of a risk-sharing mechanism can be promoted.
3. Give full play to the role of the government, in terms of establishing effective reward and punishment mechanisms, guiding and coordinating the members of all parties, establishing agricultural innovation projects, building platforms to attract agriculture-related enterprises and research institutions to participate in agricultural science and technology innovation activities, and the establishment of multiple financing channels, in order to provide favorable financial support for industry–university–research synergistic innovation.
4. The government should play a role in decision making, while reducing direct intervention in agricultural science and technology innovation activities, giving full play to the decisive role of the market, allocating more innovation resources to the dynamic and potential agriculture-related enterprises, and cultivation agriculture-related enterprises to become the core subject of the regional agricultural innovation ecosystem.

5.4 Deficiencies and future prospects

The main deficiency of this paper is that, when studying the collaborative innovation evolution process of agricultural innovation ecosystems, universities & research institutions were regarded as the parties for the analysis. In fact, there are partial differences between the functions of universities & research institutions in synergistic innovation, and this paper does not distinguish between them. In addition, in the numerical simulation of the collaborative innovation evolution of agricultural innovation ecosystem, the valuation technology was used for simulation without using actual research data, which is relatively lacking in guiding significant practices. Therefore, future research should continue to follow-up on these results and, on the basis of distinguishing the functions of universities and research institutions, further study the evolutionary game process of cooperative innovation in agricultural innovation ecosystems, as well as collecting research data for simulation, such that the analysis results may be more scientific.