# Analysis on the Evolution Mechanism of Open Environmental Protection Innovation among Equipment Manufacturing Oligopolistic Enterprises Based on Data Simulation

Authors: Yang Wang; Liyou Fu
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The global economic environment is becoming increasingly complex with the variable change in the competition regulation and the merging of technological innovation. A single equipment manufacturing enterprise cannot achieve the realization of an intelligent strategy. With the help of open innovation, the enterprise can build an intelligent manufacturing innovation ecosystem based on promoting internal re-engineering of enterprises and mutual opening of internal innovation resource processes among enterprises to strengthen cooperation. However, since open innovation is a complex collaborative innovation of multiorganizational cooperation, this paper analyzes and discusses the green open innovation cooperation strategy among oligopolistic enterprises in the equipment manufacturing industry under the influence of environmental regulation by using relevant models and theories of evolutionary game theory. In addition, the optimal combination under the existing situation is selected by using the model to simulate and analyze the selection trends and results of oligopolistic enterprises several times. The study shows that the probability of choosing an open green innovation strategy among oligopolistic equipment manufacturing firms is positively proportional to the excess benefit of open green innovation and government subsidies and inversely proportional to the excess benefit of knowledge spillover, government penalties, and the cost of open collaborative innovation and knowledge spillover between two firms.


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## Body

## 1. Introduction

With rapid industrialization and urbanization, China has achieved high growth in socio-economic development. After 40 years of reform and opening-up, China's economic construction has made worldwide achievements. From 1979 to 2022, China’s economy maintained 35 years of growth at an average annual rate of more than 7%. 2022 is the second year of the “Fourteenth Five-Year Plan,” and the primary steady and positive economic operation trend remains unchanged. However, behind the rapid economic growth, the sloppy growth model of high investment, high energy consumption, and high emission has made China pay a heavy price in resources and the environment. Environmental problems, such as resource shortage and air pollution, have seriously affected people's quality of life and health. China has paid a high environmental cost for the high economic growth. The increasingly severe resource and environmental problems are not only a development dilemma for China but also a common concern for all countries in the world.Since environmental problems have negative externalities and their public goods nature makes it challenging to define property rights, it is difficult to solve environmental problems by market forces alone, so the government needs to make up for the “market failure” by formulating and implementing active and effective environmental regulation policies. In order to achieve sustainable economic growth, quality, and upgrading, the Chinese government has been committed to the development of a green economy with the times. Since the Ninth Five-Year Plan, the government has emphasized the need for sustainable development and has implemented a series of pollutant control and environmental protection policies. The Fifth Plenary Session of the 18th Central Committee proposed “green development” as one of the five significant concepts to guide China’s future economic and social development, reflecting China’s determination to achieve green development.The manufacturing industry is the main body of the national economy, the country’s foundation, the instrument of the country’s prosperity, and the foundation of the country’s strength. Building a manufacturing industry with international competitiveness is the way to enhance comprehensive national strength, guarantee national security, and build a world power. Since the reform and opening-up, China's manufacturing industry clusters have sprung up and thrived, showing a high-speed growth trend, contributing significantly to the regional economy, and becoming a significant driving force and the cornerstone of national economic growth.However, with the outbreak of the financial crisis and changes in the external environment, such as the rapid changes in Internet technology, China’s manufacturing clusters are facing unprecedented transformation pressure. On the one hand, the rapid rise of China’s labor costs has weakened the cheap advantage and the flow of low-end manufacturing to Southeast Asia and South Asia. The original industrial chain has been interrupted, the production and operation of manufacturing small enterprises are not optimistic, and the United States has returned to manufacturing after the financial crisis, making Chinese manufacturing under the back and forth. On the other hand, the emergence of Germany’s Industry 4.0 model has led to the mature development of a new generation of information technology such as cloud computing, big data, and the Internet of Things. China also puts forward the “Internet+” support model for the development of manufacturing services, the global manufacturing industry is facing the pressure of comprehensive transformation, and the combination of productive services and manufacturing has become the main trend of manufacturing value creation. Under the dual pressure of declining industrial endowment advantage and lagging technology in China’s manufacturing industry, the innovation-led development model has become the key to transforming and upgrading manufacturing industry clusters.Innovation refers to the creation and innovation at all levels of business management to produce and operate products that match the market demand, making full use of and continuously optimizing the allocation of its resources and social resources according to the development trend of market demand. However, the limited production resources in modern society and the specialization brought by the division of labor make it difficult for enterprises to grasp all the knowledge required for technological development. Collaborative knowledge innovation refers to the cooperation mode of knowledge innovation and diffusion realized by bringing together innovation resources through the joint participation of knowledge creation and technology innovation subjects from universities, enterprises, government, intermediary organizations, and financial institutions and the full release of production factors such as talents, information, capital, and technology.Compared with “involuntary diffusion of knowledge spillover for innovation,” the efficiency and quality of knowledge collaboration-driven innovation are higher. Knowledge synergy can quickly gather the knowledge advantages of different subjects, fill the knowledge gap, and promote the emergence of knowledge innovation through the optimization and integration of tacit knowledge. Besides, it can also help clarify each subject’s rights, responsibilities, and benefit distribution in new knowledge creation and avoid cluster innovation from falling into the deadlock of “prisoner’s dilemma.” On the other hand, it helps to clarify the power, responsibility, and benefit distribution among the subjects in the process of new knowledge creation and avoid the deadlock of the “prisoner’s dilemma” for cluster innovation.Due to the complexity of the knowledge collaboration system, it is difficult to compare multiple participants simultaneously. In this paper, we take the green innovation of equipment manufacturing enterprises implemented by green policy as the background and explore the process of transformation from the traditional closed knowledge innovation mode of relying on their resources to the collaborative knowledge innovation mode of effectively integrating internal and external resources in order to reduce costs, avoid risks, and accelerate knowledge innovation efficiency of equipment manufacturing oligarchic enterprises. In order to reduce costs, avoid risks, and accelerate knowledge innovation efficiency, equipment manufacturing oligopolies began to change from the traditional closed knowledge innovation mode relying on their resources to the collaborative knowledge innovation mode.


## 2. Literature Review

### 2.1. Environmental Regulation and Green Innovation in Manufacturing

The traditional economist argues that while beneficial to society’s overall welfare, implementation of environmental regulations comes at manufacturers’ expense. Environmental regulations can increase firms’ costs and reduce their ability to innovate, but “well-designed” environmental regulations may improve the environmental quality and output through technological compensation and learning effects [1]. Besides, appropriate environmental regulations can stimulate firms’ technological innovation improve production efficiency and industrial concentration [2], and appropriate environmental regulations can offset the production costs that environmental regulations may bring and influence industrial restructuring and upgrading through intermediate variables such as barriers to entry, consumer demand, technological innovation, and FDI [3]. Environmental regulation can also promote firms’ green innovation [4] and help its diffusion. However, most green technology advances are highly dependent on government policy interventions, and technological innovation acts as a connecting bridge between environmental regulation and green economic growth [5]. Government can guide manufacturers to make rational decisions and maximize social welfare through appropriate tax and subsidy policies [6]. Other economists insist that environmental regulation and technological innovation are uncertain, and environmental regulation promotes and inhibits industrial productivity. There is a “U”-shaped relationship between government environmental regulation and the efficiency of green technological innovation that “inhibits first and then promotes.” Local governments can innovatively guide the transfer and innovation of polluting industries by appropriately adjusting the strength of environmental regulation according to the needs of economic development, environmental protection, and other policy purposes [7].Factors such as establishment time, firm size, regional differences, and industry heterogeneity also affect the innovation effect of environmental regulations on equipment manufacturing firms. Usually, equipment manufacturing firms with more extensive tend to be more likely to engage in green innovation than smaller firms [8], and the shorter the firm’s establishment time, the more likely it is to innovate. Furthermore, China’s central and western regions are more likely to transform and upgrade their manufacturing industries through green innovation than the eastern regions [9]. The effects on the performance of firms in heavy pollution industries and state-owned enterprises are more significant [10], formal environmental regulations have a positive effect on the advanced manufacturing industry structure, and informal environmental regulations have a positive effect on the rationalization and advanced manufacturing industry structure [11].In the era of underdeveloped information technology, manufacturing enterprises have little scope and space to purchase technical services from similar production enterprises. Simultaneously, the competition-oriented market structure also determines that manufacturing enterprises cannot rely on other manufacturing enterprises’ technology for a long time to develop, and it is not easy to achieve a high degree of sharing of manufacturing technology. However, in intelligent manufacturing, the first consideration of enterprises may be how to rapidly expand the application of technology to bring the advantages of technology into play in the shortest possible time. Because technological progress is so fast, it is not easy to maintain the technological advantage for a long time. Therefore, the subjective motivation for the high sharing of manufacturing technology is sufficient.The main findings of the relevant literature above are summarized in Table1.Table 1
Literature on the relationship between environmental regulation and green innovation in manufacturing.
No.Research perspectiveAuthorsMain content1Negative correlationDension [12];Environmental regulations increase the cost of firms and inhibit technological innovation.Gollop and Robert [13];2Positive correlationDu and Chen [2];A “well-designed” environmental regulation may improve the environmental quality and output through technological compensation and learning effects.Jin [3];3Positive correlationSun et al. [4];Government can not only guide manufacturers to make rational decisions but also maximize social welfare through appropriate tax and subsidy policies.Xu [5];Ma et al. [6];4Positive correlationMarcel et al. [8];Factors such as establishment time, firm size, regional differences, and industry heterogeneity also affect the innovation effect of environmental regulations on equipment manufacturing firms.Yuan and Chen [9];Peng [10];5Uncertain relationshipJiang and Liu [7];There is a “U”-shaped relationship between government environmental regulation and the efficiency of green technological innovation.Porter [1];


### 2.2. Collaborative Knowledge Innovation and Equipment Manufacturing Industry

With the continuous development of science and technology, the difficulty of the knowledge and technology involved in the enterprise’s field is increasing, and the scope of coverage is becoming more comprehensive. Cross-disciplinary and cross-disciplinary product development is becoming more common, which makes integrating technical knowledge and complementary resources between enterprises an inevitable choice. Since only a few large enterprises can independently complete the knowledge innovation and production of complex products, it is difficult for public enterprises to rely on their resources (capital, human resources, technology) to achieve product innovation.Henry Chesbrough, a professor at Harvard Business School, was the first to propose the concept of “open innovation” at the firm level, stating that firms should be able to use external research capabilities as well as their channels and external channels when they wish to develop technologies and products. The wide dispersion of innovation resources allows companies to develop technologies and products using external research capabilities [14–16]. The widely dispersed nature of innovation resources makes it difficult for any one organization to take on the role of innovation alone. The need to open up internal innovation resources and processes to each other and strengthen cooperation has become an inevitable requirement for corporate innovation activities [17].Collaborative knowledge innovation among enterprises is a process of identifying, acquiring, sharing, integrating, and creating knowledge across disciplines and organizations. Scholars at home and abroad have conducted much research on the motivation of collaborative knowledge innovation. They have reached a considerable consensus that the primary motivations for collaborative knowledge innovation include integrating complementary resources, sharing knowledge innovation costs, reducing knowledge innovation risks, and improving the dynamic resilience of organizations. Collaborative knowledge innovation cooperation between firms provides more efficient and convenient access to resources than traditional market transactions. When complementary resources are shared and integrated, synergistic effects can be created, helping members of a collaborative knowledge innovation alliance achieve a tremendous technological advantage [18]. Collaborative knowledge innovation and information exchange and sharing among firms can increase the probability of success in new product development [19]. Through effective communication of knowledge innovation projects, strategies, and goals, alliance members can choose more appropriate knowledge innovation paths, thus improving knowledge innovation efficiency and reducing costs. In addition, in collaborative knowledge innovation, adequate division of labor can be carried out to give full play to each member’s technical advantages. Such specialized division of labor will undoubtedly increase the success rate and reduce capital consumption. Besides, modern management scientists believe that organizations are now in an era of rapid changes in the external environment. The speed of technological change increases daily, demanding the organization’s ability to innovate and adapt. New knowledge is often generated in constantly changing and innovating organizations, leading to opportunistic behavior due to the spillover effect of knowledge. Therefore, a perfect knowledge and technology trading market has not yet been formed, and various factors constrain rapid knowledge trading and dissemination. By promoting mutual technology information exchange through collaborative knowledge innovation between organizations, enterprises can make dynamic adjustments according to changes in market demand and technological development to have sufficient resilience in the rapidly changing external environment [20–23].In the era of underdeveloped information technology, manufacturing enterprises have little scope and space to purchase technical services from similar production enterprises. Simultaneously, the competition-oriented market structure also determines that manufacturing enterprises cannot rely on other manufacturing enterprises’ technology for a long time to develop, and it is not easy to achieve a high degree of sharing of manufacturing technology. However, in intelligent manufacturing, the first consideration of enterprises may be how to rapidly expand the application of technology to bring the advantages of technology into play in the shortest possible time. Because technological progress is so fast, it is not easy to maintain the technological advantage for a long time. Therefore, the subjective motivation for the high sharing of manufacturing technology is sufficient.Open innovation integrates the enterprise’s internal and external resources [20] and emphasizes the importance of external knowledge resources for the innovation process, requiring firms to accelerate enterprise technology development and commercialization of internal and external channels. Equipment manufacturing innovation enterprises improve their technology in knowledge inflow and outflow, improve green innovation efficiency, avoid business risks, and avoid wasting social resources [24]. Building an open innovation platform can crack innovation problems and enhance innovation capability for multiple innovation subjects such as enterprises, universities, and research institutes. It can also form the gathering effect of resources to realize the full integration of innovation resources and promote the transformation and upgrading of the traditional manufacturing industry.The open innovation model has received increasing attention [25]. Achieving open and cooperative innovation, extending the innovation work to the middle and lower reaches of enterprises, and establishing an innovation cooperation model with different partners can effectively integrate and utilize social resources [26]. It is necessary to promote enhanced cooperation among enterprises, universities, and research institutions to decentralize innovation activities and open up new technologies and products using complementary resources. It is necessary to establish and provide an equal and open information platform for employees to fully exchange innovation results and inspire each other, collide ideas, and stimulate creativity. Every effort should be made to online cooperative research centers to realize the contribution of talents, information, equipment, and other resources to improve the overall knowledge innovation power and level.The main findings of the relevant literature above are summarized in Table2.Table 2
Literature on the motivation of collaborative knowledge innovation for equipment manufacturing.
No.Research perspectiveAuthorsMain content1Integrating complementary resourcesJiang et al. [11];Collaborative knowledge innovation cooperation between firms provides more efficient and convenient access to resources than traditional market transactions.Chesbrough and Euchner [14];Chesbrough [15];Bez and Chesbrough [16];2Sharing knowledge innovation costsWang and Xu [17];Collaborative knowledge innovation and information exchange and sharing among firms can increase the probability of success in new product development.Marabelli and Newell [18];3Reducing knowledge innovation risksWilliamson [19];Equipment manufacturing innovation enterprises improve their technology in knowledge inflow and outflow, improve green innovation efficiency, avoid business risks, and avoid wasting social resources.Gong and Yang [23];4Improving the dynamic resilience of organizationsBoger set al. [20];Enterprises can make dynamic adjustments according to changes in market demand and technological development to have sufficient resilience through collaborative knowledge innovation between organizations.Wang et al. [21];Eduardo and Gabriela [22];5Integrating social resourcesNeeraj [24];Extending the innovation work to the middle and lower reaches of enterprises and establishing an innovation cooperation model with different partners can effectively integrate and utilize social resourcesChen [25];


### 2.3. Evolutionary Game Theory and Open Innovation Strategy

Since the open collaborative innovation in the equipment manufacturing industry emphasizes the rational behavioral choice of participating enterprises according to the external environment, choosing a particular strategy depends on their own strategy choice and other enterprises’ strategy choice. The result of a strategy chosen by the enterprise depends not only on its own strategy choice but also on other enterprises’ strategy choices. This paper chooses the dynamic replication model based on differential equations, commonly used in evolutionary game theory, to conduct the study. Fisher and Hamilton first originated the evolutionary game theory from genetic ecologists’ analysis of animals and plants’ conflict and cooperation behavior. Scholars later used it to analyze human beings’ competitive cooperation behavior because of the similarity between human behavior and other organisms’ behavior. Taylor and Jonker first proposed the replication dynamics model in 1978 [27] and later studied it in depth in Maynard monographs [28]. This model describes a deterministic evolutionary model of the evolution of group strategies in differential systems [29]. Because of differential systems’ beneficial mathematical analytic properties, the replica dynamic model is one of the most commonly used population evolutionary dynamic models in evolutionary games [30, 31].In addition, evolutionary games have been widely used in strategic decision processes among different individuals nowadays. Economists have also studied the strategic decision process between government and firms and found that firms adjust their short-and long-term game behaviors in the supply chain by considering government subsidies [6, 32, 33]. The same situation also occurs between manufacturers and retailers [34, 35], firms and financial institutions [35–38], and university and industry partnerships [39–41]. Therefore, the green collaborative innovation development strategy of Chinese equipment manufacturing enterprises is studied, taking horizontal cooperative enterprises as the game subject, and the limited rational behavior of different sizes and types, game participants in decision making due to incomplete information, by constructing the basic model and introducing the model of reward and punishment mechanism, investigating the phenomenon of repeated game cooperation in environmental innovation by the double oligarchic equipment manufacturing enterprises without and with government participation.The main findings of the relevant literature above are summarized in Table3.Table 3
Literature on the use of the evolutionary game theory.
No.Research perspectiveAuthorsMain content1Population evolution strategyTaylor and Jonker [27];The replica dynamic model is one of the most commonly used population evolutionary dynamic models in evolutionary games.Maynard [28]; Weibull [29]; Hofbauer [30];Sigmund et al. [31];2Strategy between government and firmsMa et al. [6];Firms adjust their short-and long-term game behaviors in the supply chain by considering government subsidies.Bao et al. [32];Geng and Zhang [33];3Strategy between manufacturer and retailerXie et al. [34];Manufacturer and retailer adjust their strategy to present the optimal orders to maximize profits.Wang and Cheng [35];4Strategy between firms and financial institutionsBerz [38];Firms and financial institutions adjust their strategy reducing the innovation cost, share customer resources, expand incremental revenue, and seek long-term cooperation.Wang and Shu [17];Yu and Zhang [37];5Strategy between university and industry partnershipsZhou et al. [41];The integration of industry, university, and research promotes the integration and development of enterprises, universities, research institutes, and financial institutions to interact and cooperate and promote the transformation of scientific and technological achievements.Gaskill et al. [40];


## 2.1. Environmental Regulation and Green Innovation in Manufacturing

The traditional economist argues that while beneficial to society’s overall welfare, implementation of environmental regulations comes at manufacturers’ expense. Environmental regulations can increase firms’ costs and reduce their ability to innovate, but “well-designed” environmental regulations may improve the environmental quality and output through technological compensation and learning effects [1]. Besides, appropriate environmental regulations can stimulate firms’ technological innovation improve production efficiency and industrial concentration [2], and appropriate environmental regulations can offset the production costs that environmental regulations may bring and influence industrial restructuring and upgrading through intermediate variables such as barriers to entry, consumer demand, technological innovation, and FDI [3]. Environmental regulation can also promote firms’ green innovation [4] and help its diffusion. However, most green technology advances are highly dependent on government policy interventions, and technological innovation acts as a connecting bridge between environmental regulation and green economic growth [5]. Government can guide manufacturers to make rational decisions and maximize social welfare through appropriate tax and subsidy policies [6]. Other economists insist that environmental regulation and technological innovation are uncertain, and environmental regulation promotes and inhibits industrial productivity. There is a “U”-shaped relationship between government environmental regulation and the efficiency of green technological innovation that “inhibits first and then promotes.” Local governments can innovatively guide the transfer and innovation of polluting industries by appropriately adjusting the strength of environmental regulation according to the needs of economic development, environmental protection, and other policy purposes [7].Factors such as establishment time, firm size, regional differences, and industry heterogeneity also affect the innovation effect of environmental regulations on equipment manufacturing firms. Usually, equipment manufacturing firms with more extensive tend to be more likely to engage in green innovation than smaller firms [8], and the shorter the firm’s establishment time, the more likely it is to innovate. Furthermore, China’s central and western regions are more likely to transform and upgrade their manufacturing industries through green innovation than the eastern regions [9]. The effects on the performance of firms in heavy pollution industries and state-owned enterprises are more significant [10], formal environmental regulations have a positive effect on the advanced manufacturing industry structure, and informal environmental regulations have a positive effect on the rationalization and advanced manufacturing industry structure [11].In the era of underdeveloped information technology, manufacturing enterprises have little scope and space to purchase technical services from similar production enterprises. Simultaneously, the competition-oriented market structure also determines that manufacturing enterprises cannot rely on other manufacturing enterprises’ technology for a long time to develop, and it is not easy to achieve a high degree of sharing of manufacturing technology. However, in intelligent manufacturing, the first consideration of enterprises may be how to rapidly expand the application of technology to bring the advantages of technology into play in the shortest possible time. Because technological progress is so fast, it is not easy to maintain the technological advantage for a long time. Therefore, the subjective motivation for the high sharing of manufacturing technology is sufficient.The main findings of the relevant literature above are summarized in Table1.Table 1
Literature on the relationship between environmental regulation and green innovation in manufacturing.
No.Research perspectiveAuthorsMain content1Negative correlationDension [12];Environmental regulations increase the cost of firms and inhibit technological innovation.Gollop and Robert [13];2Positive correlationDu and Chen [2];A “well-designed” environmental regulation may improve the environmental quality and output through technological compensation and learning effects.Jin [3];3Positive correlationSun et al. [4];Government can not only guide manufacturers to make rational decisions but also maximize social welfare through appropriate tax and subsidy policies.Xu [5];Ma et al. [6];4Positive correlationMarcel et al. [8];Factors such as establishment time, firm size, regional differences, and industry heterogeneity also affect the innovation effect of environmental regulations on equipment manufacturing firms.Yuan and Chen [9];Peng [10];5Uncertain relationshipJiang and Liu [7];There is a “U”-shaped relationship between government environmental regulation and the efficiency of green technological innovation.Porter [1];


## 2.2. Collaborative Knowledge Innovation and Equipment Manufacturing Industry

With the continuous development of science and technology, the difficulty of the knowledge and technology involved in the enterprise’s field is increasing, and the scope of coverage is becoming more comprehensive. Cross-disciplinary and cross-disciplinary product development is becoming more common, which makes integrating technical knowledge and complementary resources between enterprises an inevitable choice. Since only a few large enterprises can independently complete the knowledge innovation and production of complex products, it is difficult for public enterprises to rely on their resources (capital, human resources, technology) to achieve product innovation.Henry Chesbrough, a professor at Harvard Business School, was the first to propose the concept of “open innovation” at the firm level, stating that firms should be able to use external research capabilities as well as their channels and external channels when they wish to develop technologies and products. The wide dispersion of innovation resources allows companies to develop technologies and products using external research capabilities [14–16]. The widely dispersed nature of innovation resources makes it difficult for any one organization to take on the role of innovation alone. The need to open up internal innovation resources and processes to each other and strengthen cooperation has become an inevitable requirement for corporate innovation activities [17].Collaborative knowledge innovation among enterprises is a process of identifying, acquiring, sharing, integrating, and creating knowledge across disciplines and organizations. Scholars at home and abroad have conducted much research on the motivation of collaborative knowledge innovation. They have reached a considerable consensus that the primary motivations for collaborative knowledge innovation include integrating complementary resources, sharing knowledge innovation costs, reducing knowledge innovation risks, and improving the dynamic resilience of organizations. Collaborative knowledge innovation cooperation between firms provides more efficient and convenient access to resources than traditional market transactions. When complementary resources are shared and integrated, synergistic effects can be created, helping members of a collaborative knowledge innovation alliance achieve a tremendous technological advantage [18]. Collaborative knowledge innovation and information exchange and sharing among firms can increase the probability of success in new product development [19]. Through effective communication of knowledge innovation projects, strategies, and goals, alliance members can choose more appropriate knowledge innovation paths, thus improving knowledge innovation efficiency and reducing costs. In addition, in collaborative knowledge innovation, adequate division of labor can be carried out to give full play to each member’s technical advantages. Such specialized division of labor will undoubtedly increase the success rate and reduce capital consumption. Besides, modern management scientists believe that organizations are now in an era of rapid changes in the external environment. The speed of technological change increases daily, demanding the organization’s ability to innovate and adapt. New knowledge is often generated in constantly changing and innovating organizations, leading to opportunistic behavior due to the spillover effect of knowledge. Therefore, a perfect knowledge and technology trading market has not yet been formed, and various factors constrain rapid knowledge trading and dissemination. By promoting mutual technology information exchange through collaborative knowledge innovation between organizations, enterprises can make dynamic adjustments according to changes in market demand and technological development to have sufficient resilience in the rapidly changing external environment [20–23].In the era of underdeveloped information technology, manufacturing enterprises have little scope and space to purchase technical services from similar production enterprises. Simultaneously, the competition-oriented market structure also determines that manufacturing enterprises cannot rely on other manufacturing enterprises’ technology for a long time to develop, and it is not easy to achieve a high degree of sharing of manufacturing technology. However, in intelligent manufacturing, the first consideration of enterprises may be how to rapidly expand the application of technology to bring the advantages of technology into play in the shortest possible time. Because technological progress is so fast, it is not easy to maintain the technological advantage for a long time. Therefore, the subjective motivation for the high sharing of manufacturing technology is sufficient.Open innovation integrates the enterprise’s internal and external resources [20] and emphasizes the importance of external knowledge resources for the innovation process, requiring firms to accelerate enterprise technology development and commercialization of internal and external channels. Equipment manufacturing innovation enterprises improve their technology in knowledge inflow and outflow, improve green innovation efficiency, avoid business risks, and avoid wasting social resources [24]. Building an open innovation platform can crack innovation problems and enhance innovation capability for multiple innovation subjects such as enterprises, universities, and research institutes. It can also form the gathering effect of resources to realize the full integration of innovation resources and promote the transformation and upgrading of the traditional manufacturing industry.The open innovation model has received increasing attention [25]. Achieving open and cooperative innovation, extending the innovation work to the middle and lower reaches of enterprises, and establishing an innovation cooperation model with different partners can effectively integrate and utilize social resources [26]. It is necessary to promote enhanced cooperation among enterprises, universities, and research institutions to decentralize innovation activities and open up new technologies and products using complementary resources. It is necessary to establish and provide an equal and open information platform for employees to fully exchange innovation results and inspire each other, collide ideas, and stimulate creativity. Every effort should be made to online cooperative research centers to realize the contribution of talents, information, equipment, and other resources to improve the overall knowledge innovation power and level.The main findings of the relevant literature above are summarized in Table2.Table 2
Literature on the motivation of collaborative knowledge innovation for equipment manufacturing.
No.Research perspectiveAuthorsMain content1Integrating complementary resourcesJiang et al. [11];Collaborative knowledge innovation cooperation between firms provides more efficient and convenient access to resources than traditional market transactions.Chesbrough and Euchner [14];Chesbrough [15];Bez and Chesbrough [16];2Sharing knowledge innovation costsWang and Xu [17];Collaborative knowledge innovation and information exchange and sharing among firms can increase the probability of success in new product development.Marabelli and Newell [18];3Reducing knowledge innovation risksWilliamson [19];Equipment manufacturing innovation enterprises improve their technology in knowledge inflow and outflow, improve green innovation efficiency, avoid business risks, and avoid wasting social resources.Gong and Yang [23];4Improving the dynamic resilience of organizationsBoger set al. [20];Enterprises can make dynamic adjustments according to changes in market demand and technological development to have sufficient resilience through collaborative knowledge innovation between organizations.Wang et al. [21];Eduardo and Gabriela [22];5Integrating social resourcesNeeraj [24];Extending the innovation work to the middle and lower reaches of enterprises and establishing an innovation cooperation model with different partners can effectively integrate and utilize social resourcesChen [25];


## 2.3. Evolutionary Game Theory and Open Innovation Strategy

Since the open collaborative innovation in the equipment manufacturing industry emphasizes the rational behavioral choice of participating enterprises according to the external environment, choosing a particular strategy depends on their own strategy choice and other enterprises’ strategy choice. The result of a strategy chosen by the enterprise depends not only on its own strategy choice but also on other enterprises’ strategy choices. This paper chooses the dynamic replication model based on differential equations, commonly used in evolutionary game theory, to conduct the study. Fisher and Hamilton first originated the evolutionary game theory from genetic ecologists’ analysis of animals and plants’ conflict and cooperation behavior. Scholars later used it to analyze human beings’ competitive cooperation behavior because of the similarity between human behavior and other organisms’ behavior. Taylor and Jonker first proposed the replication dynamics model in 1978 [27] and later studied it in depth in Maynard monographs [28]. This model describes a deterministic evolutionary model of the evolution of group strategies in differential systems [29]. Because of differential systems’ beneficial mathematical analytic properties, the replica dynamic model is one of the most commonly used population evolutionary dynamic models in evolutionary games [30, 31].In addition, evolutionary games have been widely used in strategic decision processes among different individuals nowadays. Economists have also studied the strategic decision process between government and firms and found that firms adjust their short-and long-term game behaviors in the supply chain by considering government subsidies [6, 32, 33]. The same situation also occurs between manufacturers and retailers [34, 35], firms and financial institutions [35–38], and university and industry partnerships [39–41]. Therefore, the green collaborative innovation development strategy of Chinese equipment manufacturing enterprises is studied, taking horizontal cooperative enterprises as the game subject, and the limited rational behavior of different sizes and types, game participants in decision making due to incomplete information, by constructing the basic model and introducing the model of reward and punishment mechanism, investigating the phenomenon of repeated game cooperation in environmental innovation by the double oligarchic equipment manufacturing enterprises without and with government participation.The main findings of the relevant literature above are summarized in Table3.Table 3
Literature on the use of the evolutionary game theory.
No.Research perspectiveAuthorsMain content1Population evolution strategyTaylor and Jonker [27];The replica dynamic model is one of the most commonly used population evolutionary dynamic models in evolutionary games.Maynard [28]; Weibull [29]; Hofbauer [30];Sigmund et al. [31];2Strategy between government and firmsMa et al. [6];Firms adjust their short-and long-term game behaviors in the supply chain by considering government subsidies.Bao et al. [32];Geng and Zhang [33];3Strategy between manufacturer and retailerXie et al. [34];Manufacturer and retailer adjust their strategy to present the optimal orders to maximize profits.Wang and Cheng [35];4Strategy between firms and financial institutionsBerz [38];Firms and financial institutions adjust their strategy reducing the innovation cost, share customer resources, expand incremental revenue, and seek long-term cooperation.Wang and Shu [17];Yu and Zhang [37];5Strategy between university and industry partnershipsZhou et al. [41];The integration of industry, university, and research promotes the integration and development of enterprises, universities, research institutes, and financial institutions to interact and cooperate and promote the transformation of scientific and technological achievements.Gaskill et al. [40];


## 3. Theoretical Modeling and Analysis

### 3.1. Basic Assumptions of the Model

Under the new environmental regulatory constraints, the equipment manufacturing industry is abstracted as two oligopolies A and B to facilitate the analysis. The game is played between these two firms. Furthermore, the model is constructed with the following assumptions.Traditional equipment manufacturing enterprises need to innovate green technology to cope with new environmental regulations. There are two mutually exclusive green technology innovation strategies: the open green innovation strategy and the exclusive green innovation strategy. An open green innovation strategy means that companies share the risk by using the research of external companies while building on their internal research capabilities. Companies with an exclusive green innovation strategy focus only on internal research and refuse to cooperate with external companies.Hypothesis 1.
Assume that the knowledge innovation benefits of the exclusive green innovation strategy of A and B arePA and PB. When A and B adopt the open green innovation strategy, the sharing and improving heterogeneous innovation knowledge between enterprises can optimize the production efficiency, reduce the cost of green innovation, and improve enterprises’ final benefit. Assume that excess benefits of open green innovation adopted by two firms, A and B, is PAB. Two firms share the benefits, where firm A accounts for a0≤a≤1, and firm B accounts for 1−a.Hypothesis 2.
The total cost of traditional equipment manufacturing enterprises A and B for open green innovation strategy isCAB, and firms A and B will share the total cost of innovation CAB. Firm A accounts for b0≤b≤1, and then, firm B accounts for 1−b.Hypothesis 3.
If one of the traditional equipment manufacturing enterprises A and B choose the open green innovation strategy, the other party adopts the exclusive green innovation strategy. Under the poor intellectual property and patent protection system, the enterprise that chooses the open green innovation strategy has zero excess returns because others imitate its core knowledge. And the enterprise that chooses the exclusive green innovation strategy obtains the excess benefit brought by the knowledge spillover ast;Hypothesis 4.
If the probabilities of traditional equipment manufacturing enterprises A and B choosing shared green innovation strategies arex0≤x≤1 and y0≤y≤1, respectively, then the probabilities of firms A and B choosing exclusive green innovation strategies are 1 − x and 1 − y.Hypothesis 5.
The government introduces incentive and penalty mechanisms to encourage collaborative innovation in equipment manufacturing enterprises in order to improve labor productivity and social benefits: assume that traditional equipment manufacturing enterprises A and B carry out an open green innovation strategy at the same time, the government gives subsidymm≥0; if only one party complies with the new environmental regulation for open green innovation strategy, while the other party takes exclusive innovation strategy, the party takes shared strategy no reward and no penalty, and the penalty amount of the exclusive strategy is nn≥0.
The main parameters and descriptions above are summarized in Table4.Table 4
Parameters and descriptions.
ParametersDescriptionsNotesPAKnowledge innovation benefits of exclusive green innovation of firm APA≥0PBKnowledge innovation benefits of exclusive green innovation of firm BPB≥0PABExcess benefits of open green innovation adopted by firms A and BPAB≥0CABTotal cost of firm A and B for open green innovation strategyCAB≥0aPercentage of excess benefits of open green innovation by firm A0≤a≤1bPercentage of the total cost of open green innovation by firm A0≤b≤1XProbability that firm A chooses an open green innovation strategy0≤x≤1YProbability that firm B chooses an open green innovation strategy0≤y≤1TExclusive innovation firms reap the excess benefits of knowledge spilloverst≥0mGovernment subsidies when firms A and B simultaneously engage in open green innovationm≥0NGovernment penalty for the exclusive strategy side when one side adopts the open green innovation strategyn≥0


### 3.2. Construction and Analysis of an Innovative Model of a Duopoly Firm without Reward and Punishment System

Based on the assumptions, the game payment matrix of traditional equipment manufacturing enterprises A and B is summarized in Table5.Table 5
Payoff matrix between the firms.
Firm BOpen green innovation strategyExclusive green innovation strategyFirm AOpen green innovation strategyPA+aPAB−bCAB,PB+1−aPAB−1−bCABPA−bCAB,PB+tExclusive green innovation strategyPA+t,PB−1−bCABPA,PB


#### 3.2.1. Step 1

The expected benefits of adopting the open green innovation strategy of firm A are as follows:(1)UA1=yPA+aPAB−bCAB+1−yPA−bCAB=ayPAB+PA−bCAB.The expected benefits of adopting the exclusive green innovation strategy of firm A are as follows:(2)UA2=yPA+t+1−yPA=PA+ty.The average expected return for firm A is(3)U¯A=xUA1+1−xUA2=xyaPAB−t−bCAB+PA+ty.The dynamic replication equation for firm A is(4)Fx=dxdt=xUA1−U¯A=x1−xyaPAB−t−bCAB.


#### 3.2.2. Step 2

The expected benefits of adopting the open green innovation strategy of firm B are as follows:(5)UB1=xPB+1−aPAB−1−bCAB+1−xPB−1−bCAB=x1−aPAB+PB−1−bCAB.The expected benefits of adopting the exclusive green innovation strategy of firm B are as follows:(6)UB2=xPB+t+1−xPB=PB+tx.The average expected return for firm B is(7)U¯B=yUB1+1−yUB2=yx1−aPAB−t−1−bCAB+PB+tx.The dynamic replication equation for firm B is(8)Fy=dydt=yUB1−U¯B=y1−yx1−aPAB−t−1−bCAB.


#### 3.2.3. Step 3

LetFx′=0, Fy′=0, the five equilibria of the game can be derived as O0,0, P0,1, R1,0, Q1,1, Sx∗,y∗, and(9)x∗=1−bCAB1−aPAB−t,y∗=bCABaPAB−t.By the definition of stable evolutionary strategy, a stable state must be stable and invariant to small perturbations to become a stable evolutionary strategy (ESS). By the conclusion of the differential equation that if (x, y) is the evolutionary stable strategy of the game, then (x, y) needs to satisfy the following conditions.The type of strategy and the replication dynamics process of the above firms are described in the plane withx, y as axes; that is, the replication dynamics phase diagram is as follows. Figure 1 shows the replication dynamics phase diagram between the firms.①
When located at pointO (0, 0), firms A and B will choose the exclusive green innovation strategy together, and(10)Fx′=−bCAB<0,Fy′=−b1−bCAB<0.Thus, pointO (0, 0) is an evolutionary stable strategy.②
When located at pointQ (1, 1), firms A and B will choose the open green innovation strategy, and Fx=0,Fy=0. Thus, point Q (1, 1) is an evolutionarily stable strategy.③
When located at the pointP (0, 1), firm A chooses the exclusive green innovation strategy while firm B chooses the open green innovation strategy.(11)Fx′=aPAB−t−bCAB,Fy′=1−bCAB>0.Therefore, pointP (0, 1) is not an evolutionary stable strategy.④
When located at the pointR (1, 0), firm A chooses an open green innovation strategy, and firm B chooses an exclusive green innovation strategy.(12)Fx′=bCAB>0,Fy′=1−bCAB>0.Thus, pointR (1, 0) is not an evolutionary stable strategy.⑤
When located at the pointQx∗,y∗,(13)Fx′=0,Fy′=0.Thus, pointSx∗,y∗ is a saddle point.Figure 1
Replication dynamics phase diagram between the firms.


#### 3.2.4. Step 4

From the above analysis, we can conclude that x=x∧∗ and y=y∧∗ divide the graph into four parts. O (0, 0) and Q (1, 1) are the evolutionary stabilization strategies of traditional equipment manufacturing enterprises A and B.The figure determines the firms’ strategic choice and the final chosen equilibrium result by the area of the quadrilateral OPSR and QPSR.And, whenSOPSR<SQPSR, both firms’ probability of adopting an open green innovation strategy is more significant than those adopting an exclusive green innovation strategy.WhenSOPSR>SPQPSR, the system eventually evolves to a stable equilibrium state where both firms adopt open-ended green innovation strategies.WhenSOPSR=SQPSR, the system evolves to two stable states with equal probability, and(14)SOPSR=121−bCAB1−aPAB−t+bCABaPAB−t.Figure2 shows the replication dynamics phase diagram between the firms.Figure 2
The firms’ strategic choice and the final chosen equilibrium result.Conclusion 1.
The probability of traditional equipment manufacturing enterprises A and B choosing an open green innovation strategy is directly proportional to the excess benefits of open green innovation adopted by firmsPAB.Proof.
The above equation shows thatSOPSR is inversely proportional to PAB, the larger PAB is, the smaller SOPSR is. Furthermore, both firms’ probability of adopting an open green innovation strategy is more significant than adopting an exclusive green innovation strategy, and the probability that the system evolves to Q (1, 1) increases.Conclusion 2.
The probability of traditional equipment manufacturing enterprises A and B adopting an open green innovation strategy is inversely proportional to the excess benefitt brought by knowledge spillover to the enterprise that chooses an exclusive green innovation strategy.Proof.
The above equation shows thatSOPSR is proportional to t. The more extensive t is, the larger SOPSR is. The probability that both parties adopt an open green innovation strategy is more significant than that both adopt an exclusive green innovation strategy, and the probability that the system evolves to O (0, 0) increases.Conclusion 3.
The probability of traditional equipment manufacturing enterprises A and B adopting an open green innovation strategy is inversely proportional to the total costCAB of traditional equipment manufacturing enterprises A and B complying with the new environmental regulations for open green innovation strategy at the same time.Proof.
The above equation shows thatSOPSR is proportional to CAB, the larger CAB is, the larger SOPSR is. Moreover, both firms’ probability of adopting an open green innovation strategy is more negligible than that both adopt an exclusive green innovation strategy, and the probability that the system evolves to O (0, 0) increases.


### 3.3. Construction and Analysis of an Innovative Model of a Duopoly Firm with the Introduction of a Reward and Punishment System

After the introduction of the reward and punishment system, the innovation strategy options of the duopoly firms are summarized in Table6.Table 6
New payoff matrix between the firms.
Firm BOpen green innovation strategyExclusive green innovation strategyFirm AOpen green innovation strategyPA+aPAB+m−bCAB,PB+1−aPAB+m−1−bCABPA−bCAB,PB+t−nExclusive green innovation strategyPA+t−n,PB−1−bCABPA,PB


#### 3.3.1. Step 5

New expected benefits of adopting the open green innovation strategy of firm A are as follows:(15)UA1′=yPA+aPAB−bCAB+1−yPAB−1−bPA−bCAB=ayPAB+PA+my−bCAB.New expected benefits of adopting the exclusive green innovation strategy of firm A are as follows:(16)UA2′=yPA+t+1−yPA=PA+ty−ny.The average new expected return for firm A is(17)U¯A′=xUA1′+1−xUA2′=xyaPAB+m+n−t−bCAB+PA+ty−ny.The new dynamic replication equation for firm A is(18)Fx′=dxdt=xUA1′−U¯A′=x1−xyaPAB−t+m+n−bCAB.


#### 3.3.2. Step 6

New expected benefits of adopting the open green innovation strategy of firm B are as follows:(19)UB1′=xPB+1−aPAB−1−bCAB+1−xPB−1−bCAB=x1−aPAB+PB−1−bCAB+mx.New expected benefits of adopting the exclusive green innovation strategy of firm B are as follows:(20)UB2′=xPB+t+1−xPB=PB+tx−nx.The new average expected return for firm B is(21)U¯B′=yUB1′+1−yUB2′=yx1−aPAB−t+m+n−1−bCAB+PB+tx−nx.The dynamic replication equation for firm B is(22)Fy′=dydt=yUB1′−U¯B′=y1−yx1−aPAB−t+m+n−1−bCAB.IfFX′=0, Fy′=0S′x∗′,y∗′, the five equilibria of the game can be derived as O′0,0, P′0,1, R′1,0, Q′1,1, S′x∗′,y∗′, and(23)x∗′=1−bCAB1−aPAB−t+m+n,y∗′=bCABaPAB−t+m+n.Then, whenSO'P'S'R'<SQ′P′S′R′ Both firms’ probability of adopting an open green innovation strategy is more significant than both parties’ adoption of an exclusive green innovation strategy.WhenSO′P′S′R′>SQ′P′S′R′, the system eventually evolves to a stable equilibrium state where both parties adopt open-ended green innovation strategies.WhenSO′P′S′R′=SQ′P′S′R′, the system evolves to two stable states with equal probability and(24)SO′P′S′R′=121−bCAB1−aPAB−t+m+n+bCABaPAB−t+m+n.Figure3 shows the firms’ new strategic choice and the final chosen equilibrium result.Figure 3
The firms’ new strategic choice and the final chosen equilibrium result.Conclusion 4.
The probability that traditional equipment manufacturing enterprises A and B adopt an open green innovation strategy is proportional to the subsidym given by the government when firms A and B conduct an open green innovation strategy at the same time.Proof.
The above equation shows thatSO′P′S′R′ is inversely proportional to m. The larger m is, the smaller SO′P′S′R′ is. Furthermore, both firms’ probability of adopting an open green innovation strategy is more significant than that both adopt an exclusive green innovation strategy, and the probability that the system evolves to Q′ (1, 1) increases.Conclusion 5.
The probability of traditional equipment manufacturing enterprises A and B adopting an open green innovation strategy is proportional to the penalty amountn on choosing an exclusive strategy.Proof.
The above equation shows thatSOPSR is inversely proportional to n. The larger n is, the smaller SOPSR. The probability that both sides adopt an open green innovation strategy is more significant than that both adopt an exclusive green innovation strategy, and the probability that the system evolves to Q′ (1, 1) increases.


## 3.1. Basic Assumptions of the Model

Under the new environmental regulatory constraints, the equipment manufacturing industry is abstracted as two oligopolies A and B to facilitate the analysis. The game is played between these two firms. Furthermore, the model is constructed with the following assumptions.Traditional equipment manufacturing enterprises need to innovate green technology to cope with new environmental regulations. There are two mutually exclusive green technology innovation strategies: the open green innovation strategy and the exclusive green innovation strategy. An open green innovation strategy means that companies share the risk by using the research of external companies while building on their internal research capabilities. Companies with an exclusive green innovation strategy focus only on internal research and refuse to cooperate with external companies.Hypothesis 1.
Assume that the knowledge innovation benefits of the exclusive green innovation strategy of A and B arePA and PB. When A and B adopt the open green innovation strategy, the sharing and improving heterogeneous innovation knowledge between enterprises can optimize the production efficiency, reduce the cost of green innovation, and improve enterprises’ final benefit. Assume that excess benefits of open green innovation adopted by two firms, A and B, is PAB. Two firms share the benefits, where firm A accounts for a0≤a≤1, and firm B accounts for 1−a.Hypothesis 2.
The total cost of traditional equipment manufacturing enterprises A and B for open green innovation strategy isCAB, and firms A and B will share the total cost of innovation CAB. Firm A accounts for b0≤b≤1, and then, firm B accounts for 1−b.Hypothesis 3.
If one of the traditional equipment manufacturing enterprises A and B choose the open green innovation strategy, the other party adopts the exclusive green innovation strategy. Under the poor intellectual property and patent protection system, the enterprise that chooses the open green innovation strategy has zero excess returns because others imitate its core knowledge. And the enterprise that chooses the exclusive green innovation strategy obtains the excess benefit brought by the knowledge spillover ast;Hypothesis 4.
If the probabilities of traditional equipment manufacturing enterprises A and B choosing shared green innovation strategies arex0≤x≤1 and y0≤y≤1, respectively, then the probabilities of firms A and B choosing exclusive green innovation strategies are 1 − x and 1 − y.Hypothesis 5.
The government introduces incentive and penalty mechanisms to encourage collaborative innovation in equipment manufacturing enterprises in order to improve labor productivity and social benefits: assume that traditional equipment manufacturing enterprises A and B carry out an open green innovation strategy at the same time, the government gives subsidymm≥0; if only one party complies with the new environmental regulation for open green innovation strategy, while the other party takes exclusive innovation strategy, the party takes shared strategy no reward and no penalty, and the penalty amount of the exclusive strategy is nn≥0.
The main parameters and descriptions above are summarized in Table4.Table 4
Parameters and descriptions.
ParametersDescriptionsNotesPAKnowledge innovation benefits of exclusive green innovation of firm APA≥0PBKnowledge innovation benefits of exclusive green innovation of firm BPB≥0PABExcess benefits of open green innovation adopted by firms A and BPAB≥0CABTotal cost of firm A and B for open green innovation strategyCAB≥0aPercentage of excess benefits of open green innovation by firm A0≤a≤1bPercentage of the total cost of open green innovation by firm A0≤b≤1XProbability that firm A chooses an open green innovation strategy0≤x≤1YProbability that firm B chooses an open green innovation strategy0≤y≤1TExclusive innovation firms reap the excess benefits of knowledge spilloverst≥0mGovernment subsidies when firms A and B simultaneously engage in open green innovationm≥0NGovernment penalty for the exclusive strategy side when one side adopts the open green innovation strategyn≥0


## 3.2. Construction and Analysis of an Innovative Model of a Duopoly Firm without Reward and Punishment System

Based on the assumptions, the game payment matrix of traditional equipment manufacturing enterprises A and B is summarized in Table5.Table 5
Payoff matrix between the firms.
Firm BOpen green innovation strategyExclusive green innovation strategyFirm AOpen green innovation strategyPA+aPAB−bCAB,PB+1−aPAB−1−bCABPA−bCAB,PB+tExclusive green innovation strategyPA+t,PB−1−bCABPA,PB


### 3.2.1. Step 1

The expected benefits of adopting the open green innovation strategy of firm A are as follows:(1)UA1=yPA+aPAB−bCAB+1−yPA−bCAB=ayPAB+PA−bCAB.The expected benefits of adopting the exclusive green innovation strategy of firm A are as follows:(2)UA2=yPA+t+1−yPA=PA+ty.The average expected return for firm A is(3)U¯A=xUA1+1−xUA2=xyaPAB−t−bCAB+PA+ty.The dynamic replication equation for firm A is(4)Fx=dxdt=xUA1−U¯A=x1−xyaPAB−t−bCAB.


### 3.2.2. Step 2

The expected benefits of adopting the open green innovation strategy of firm B are as follows:(5)UB1=xPB+1−aPAB−1−bCAB+1−xPB−1−bCAB=x1−aPAB+PB−1−bCAB.The expected benefits of adopting the exclusive green innovation strategy of firm B are as follows:(6)UB2=xPB+t+1−xPB=PB+tx.The average expected return for firm B is(7)U¯B=yUB1+1−yUB2=yx1−aPAB−t−1−bCAB+PB+tx.The dynamic replication equation for firm B is(8)Fy=dydt=yUB1−U¯B=y1−yx1−aPAB−t−1−bCAB.


### 3.2.3. Step 3

LetFx′=0, Fy′=0, the five equilibria of the game can be derived as O0,0, P0,1, R1,0, Q1,1, Sx∗,y∗, and(9)x∗=1−bCAB1−aPAB−t,y∗=bCABaPAB−t.By the definition of stable evolutionary strategy, a stable state must be stable and invariant to small perturbations to become a stable evolutionary strategy (ESS). By the conclusion of the differential equation that if (x, y) is the evolutionary stable strategy of the game, then (x, y) needs to satisfy the following conditions.The type of strategy and the replication dynamics process of the above firms are described in the plane withx, y as axes; that is, the replication dynamics phase diagram is as follows. Figure 1 shows the replication dynamics phase diagram between the firms.①
When located at pointO (0, 0), firms A and B will choose the exclusive green innovation strategy together, and(10)Fx′=−bCAB<0,Fy′=−b1−bCAB<0.Thus, pointO (0, 0) is an evolutionary stable strategy.②
When located at pointQ (1, 1), firms A and B will choose the open green innovation strategy, and Fx=0,Fy=0. Thus, point Q (1, 1) is an evolutionarily stable strategy.③
When located at the pointP (0, 1), firm A chooses the exclusive green innovation strategy while firm B chooses the open green innovation strategy.(11)Fx′=aPAB−t−bCAB,Fy′=1−bCAB>0.Therefore, pointP (0, 1) is not an evolutionary stable strategy.④
When located at the pointR (1, 0), firm A chooses an open green innovation strategy, and firm B chooses an exclusive green innovation strategy.(12)Fx′=bCAB>0,Fy′=1−bCAB>0.Thus, pointR (1, 0) is not an evolutionary stable strategy.⑤
When located at the pointQx∗,y∗,(13)Fx′=0,Fy′=0.Thus, pointSx∗,y∗ is a saddle point.Figure 1
Replication dynamics phase diagram between the firms.


### 3.2.4. Step 4

From the above analysis, we can conclude that x=x∧∗ and y=y∧∗ divide the graph into four parts. O (0, 0) and Q (1, 1) are the evolutionary stabilization strategies of traditional equipment manufacturing enterprises A and B.The figure determines the firms’ strategic choice and the final chosen equilibrium result by the area of the quadrilateral OPSR and QPSR.And, whenSOPSR<SQPSR, both firms’ probability of adopting an open green innovation strategy is more significant than those adopting an exclusive green innovation strategy.WhenSOPSR>SPQPSR, the system eventually evolves to a stable equilibrium state where both firms adopt open-ended green innovation strategies.WhenSOPSR=SQPSR, the system evolves to two stable states with equal probability, and(14)SOPSR=121−bCAB1−aPAB−t+bCABaPAB−t.Figure2 shows the replication dynamics phase diagram between the firms.Figure 2
The firms’ strategic choice and the final chosen equilibrium result.Conclusion 1.
The probability of traditional equipment manufacturing enterprises A and B choosing an open green innovation strategy is directly proportional to the excess benefits of open green innovation adopted by firmsPAB.Proof.
The above equation shows thatSOPSR is inversely proportional to PAB, the larger PAB is, the smaller SOPSR is. Furthermore, both firms’ probability of adopting an open green innovation strategy is more significant than adopting an exclusive green innovation strategy, and the probability that the system evolves to Q (1, 1) increases.Conclusion 2.
The probability of traditional equipment manufacturing enterprises A and B adopting an open green innovation strategy is inversely proportional to the excess benefitt brought by knowledge spillover to the enterprise that chooses an exclusive green innovation strategy.Proof.
The above equation shows thatSOPSR is proportional to t. The more extensive t is, the larger SOPSR is. The probability that both parties adopt an open green innovation strategy is more significant than that both adopt an exclusive green innovation strategy, and the probability that the system evolves to O (0, 0) increases.Conclusion 3.
The probability of traditional equipment manufacturing enterprises A and B adopting an open green innovation strategy is inversely proportional to the total costCAB of traditional equipment manufacturing enterprises A and B complying with the new environmental regulations for open green innovation strategy at the same time.Proof.
The above equation shows thatSOPSR is proportional to CAB, the larger CAB is, the larger SOPSR is. Moreover, both firms’ probability of adopting an open green innovation strategy is more negligible than that both adopt an exclusive green innovation strategy, and the probability that the system evolves to O (0, 0) increases.


## 3.2.1. Step 1

The expected benefits of adopting the open green innovation strategy of firm A are as follows:(1)UA1=yPA+aPAB−bCAB+1−yPA−bCAB=ayPAB+PA−bCAB.The expected benefits of adopting the exclusive green innovation strategy of firm A are as follows:(2)UA2=yPA+t+1−yPA=PA+ty.The average expected return for firm A is(3)U¯A=xUA1+1−xUA2=xyaPAB−t−bCAB+PA+ty.The dynamic replication equation for firm A is(4)Fx=dxdt=xUA1−U¯A=x1−xyaPAB−t−bCAB.


## 3.2.2. Step 2

The expected benefits of adopting the open green innovation strategy of firm B are as follows:(5)UB1=xPB+1−aPAB−1−bCAB+1−xPB−1−bCAB=x1−aPAB+PB−1−bCAB.The expected benefits of adopting the exclusive green innovation strategy of firm B are as follows:(6)UB2=xPB+t+1−xPB=PB+tx.The average expected return for firm B is(7)U¯B=yUB1+1−yUB2=yx1−aPAB−t−1−bCAB+PB+tx.The dynamic replication equation for firm B is(8)Fy=dydt=yUB1−U¯B=y1−yx1−aPAB−t−1−bCAB.


## 3.2.3. Step 3

LetFx′=0, Fy′=0, the five equilibria of the game can be derived as O0,0, P0,1, R1,0, Q1,1, Sx∗,y∗, and(9)x∗=1−bCAB1−aPAB−t,y∗=bCABaPAB−t.By the definition of stable evolutionary strategy, a stable state must be stable and invariant to small perturbations to become a stable evolutionary strategy (ESS). By the conclusion of the differential equation that if (x, y) is the evolutionary stable strategy of the game, then (x, y) needs to satisfy the following conditions.The type of strategy and the replication dynamics process of the above firms are described in the plane withx, y as axes; that is, the replication dynamics phase diagram is as follows. Figure 1 shows the replication dynamics phase diagram between the firms.①
When located at pointO (0, 0), firms A and B will choose the exclusive green innovation strategy together, and(10)Fx′=−bCAB<0,Fy′=−b1−bCAB<0.Thus, pointO (0, 0) is an evolutionary stable strategy.②
When located at pointQ (1, 1), firms A and B will choose the open green innovation strategy, and Fx=0,Fy=0. Thus, point Q (1, 1) is an evolutionarily stable strategy.③
When located at the pointP (0, 1), firm A chooses the exclusive green innovation strategy while firm B chooses the open green innovation strategy.(11)Fx′=aPAB−t−bCAB,Fy′=1−bCAB>0.Therefore, pointP (0, 1) is not an evolutionary stable strategy.④
When located at the pointR (1, 0), firm A chooses an open green innovation strategy, and firm B chooses an exclusive green innovation strategy.(12)Fx′=bCAB>0,Fy′=1−bCAB>0.Thus, pointR (1, 0) is not an evolutionary stable strategy.⑤
When located at the pointQx∗,y∗,(13)Fx′=0,Fy′=0.Thus, pointSx∗,y∗ is a saddle point.Figure 1
Replication dynamics phase diagram between the firms.


## 3.2.4. Step 4

From the above analysis, we can conclude that x=x∧∗ and y=y∧∗ divide the graph into four parts. O (0, 0) and Q (1, 1) are the evolutionary stabilization strategies of traditional equipment manufacturing enterprises A and B.The figure determines the firms’ strategic choice and the final chosen equilibrium result by the area of the quadrilateral OPSR and QPSR.And, whenSOPSR<SQPSR, both firms’ probability of adopting an open green innovation strategy is more significant than those adopting an exclusive green innovation strategy.WhenSOPSR>SPQPSR, the system eventually evolves to a stable equilibrium state where both firms adopt open-ended green innovation strategies.WhenSOPSR=SQPSR, the system evolves to two stable states with equal probability, and(14)SOPSR=121−bCAB1−aPAB−t+bCABaPAB−t.Figure2 shows the replication dynamics phase diagram between the firms.Figure 2
The firms’ strategic choice and the final chosen equilibrium result.Conclusion 1.
The probability of traditional equipment manufacturing enterprises A and B choosing an open green innovation strategy is directly proportional to the excess benefits of open green innovation adopted by firmsPAB.Proof.
The above equation shows thatSOPSR is inversely proportional to PAB, the larger PAB is, the smaller SOPSR is. Furthermore, both firms’ probability of adopting an open green innovation strategy is more significant than adopting an exclusive green innovation strategy, and the probability that the system evolves to Q (1, 1) increases.Conclusion 2.
The probability of traditional equipment manufacturing enterprises A and B adopting an open green innovation strategy is inversely proportional to the excess benefitt brought by knowledge spillover to the enterprise that chooses an exclusive green innovation strategy.Proof.
The above equation shows thatSOPSR is proportional to t. The more extensive t is, the larger SOPSR is. The probability that both parties adopt an open green innovation strategy is more significant than that both adopt an exclusive green innovation strategy, and the probability that the system evolves to O (0, 0) increases.Conclusion 3.
The probability of traditional equipment manufacturing enterprises A and B adopting an open green innovation strategy is inversely proportional to the total costCAB of traditional equipment manufacturing enterprises A and B complying with the new environmental regulations for open green innovation strategy at the same time.Proof.
The above equation shows thatSOPSR is proportional to CAB, the larger CAB is, the larger SOPSR is. Moreover, both firms’ probability of adopting an open green innovation strategy is more negligible than that both adopt an exclusive green innovation strategy, and the probability that the system evolves to O (0, 0) increases.


## 3.3. Construction and Analysis of an Innovative Model of a Duopoly Firm with the Introduction of a Reward and Punishment System

After the introduction of the reward and punishment system, the innovation strategy options of the duopoly firms are summarized in Table6.Table 6
New payoff matrix between the firms.
Firm BOpen green innovation strategyExclusive green innovation strategyFirm AOpen green innovation strategyPA+aPAB+m−bCAB,PB+1−aPAB+m−1−bCABPA−bCAB,PB+t−nExclusive green innovation strategyPA+t−n,PB−1−bCABPA,PB


### 3.3.1. Step 5

New expected benefits of adopting the open green innovation strategy of firm A are as follows:(15)UA1′=yPA+aPAB−bCAB+1−yPAB−1−bPA−bCAB=ayPAB+PA+my−bCAB.New expected benefits of adopting the exclusive green innovation strategy of firm A are as follows:(16)UA2′=yPA+t+1−yPA=PA+ty−ny.The average new expected return for firm A is(17)U¯A′=xUA1′+1−xUA2′=xyaPAB+m+n−t−bCAB+PA+ty−ny.The new dynamic replication equation for firm A is(18)Fx′=dxdt=xUA1′−U¯A′=x1−xyaPAB−t+m+n−bCAB.


### 3.3.2. Step 6

New expected benefits of adopting the open green innovation strategy of firm B are as follows:(19)UB1′=xPB+1−aPAB−1−bCAB+1−xPB−1−bCAB=x1−aPAB+PB−1−bCAB+mx.New expected benefits of adopting the exclusive green innovation strategy of firm B are as follows:(20)UB2′=xPB+t+1−xPB=PB+tx−nx.The new average expected return for firm B is(21)U¯B′=yUB1′+1−yUB2′=yx1−aPAB−t+m+n−1−bCAB+PB+tx−nx.The dynamic replication equation for firm B is(22)Fy′=dydt=yUB1′−U¯B′=y1−yx1−aPAB−t+m+n−1−bCAB.IfFX′=0, Fy′=0S′x∗′,y∗′, the five equilibria of the game can be derived as O′0,0, P′0,1, R′1,0, Q′1,1, S′x∗′,y∗′, and(23)x∗′=1−bCAB1−aPAB−t+m+n,y∗′=bCABaPAB−t+m+n.Then, whenSO'P'S'R'<SQ′P′S′R′ Both firms’ probability of adopting an open green innovation strategy is more significant than both parties’ adoption of an exclusive green innovation strategy.WhenSO′P′S′R′>SQ′P′S′R′, the system eventually evolves to a stable equilibrium state where both parties adopt open-ended green innovation strategies.WhenSO′P′S′R′=SQ′P′S′R′, the system evolves to two stable states with equal probability and(24)SO′P′S′R′=121−bCAB1−aPAB−t+m+n+bCABaPAB−t+m+n.Figure3 shows the firms’ new strategic choice and the final chosen equilibrium result.Figure 3
The firms’ new strategic choice and the final chosen equilibrium result.Conclusion 4.
The probability that traditional equipment manufacturing enterprises A and B adopt an open green innovation strategy is proportional to the subsidym given by the government when firms A and B conduct an open green innovation strategy at the same time.Proof.
The above equation shows thatSO′P′S′R′ is inversely proportional to m. The larger m is, the smaller SO′P′S′R′ is. Furthermore, both firms’ probability of adopting an open green innovation strategy is more significant than that both adopt an exclusive green innovation strategy, and the probability that the system evolves to Q′ (1, 1) increases.Conclusion 5.
The probability of traditional equipment manufacturing enterprises A and B adopting an open green innovation strategy is proportional to the penalty amountn on choosing an exclusive strategy.Proof.
The above equation shows thatSOPSR is inversely proportional to n. The larger n is, the smaller SOPSR. The probability that both sides adopt an open green innovation strategy is more significant than that both adopt an exclusive green innovation strategy, and the probability that the system evolves to Q′ (1, 1) increases.


## 3.3.1. Step 5

New expected benefits of adopting the open green innovation strategy of firm A are as follows:(15)UA1′=yPA+aPAB−bCAB+1−yPAB−1−bPA−bCAB=ayPAB+PA+my−bCAB.New expected benefits of adopting the exclusive green innovation strategy of firm A are as follows:(16)UA2′=yPA+t+1−yPA=PA+ty−ny.The average new expected return for firm A is(17)U¯A′=xUA1′+1−xUA2′=xyaPAB+m+n−t−bCAB+PA+ty−ny.The new dynamic replication equation for firm A is(18)Fx′=dxdt=xUA1′−U¯A′=x1−xyaPAB−t+m+n−bCAB.


## 3.3.2. Step 6

New expected benefits of adopting the open green innovation strategy of firm B are as follows:(19)UB1′=xPB+1−aPAB−1−bCAB+1−xPB−1−bCAB=x1−aPAB+PB−1−bCAB+mx.New expected benefits of adopting the exclusive green innovation strategy of firm B are as follows:(20)UB2′=xPB+t+1−xPB=PB+tx−nx.The new average expected return for firm B is(21)U¯B′=yUB1′+1−yUB2′=yx1−aPAB−t+m+n−1−bCAB+PB+tx−nx.The dynamic replication equation for firm B is(22)Fy′=dydt=yUB1′−U¯B′=y1−yx1−aPAB−t+m+n−1−bCAB.IfFX′=0, Fy′=0S′x∗′,y∗′, the five equilibria of the game can be derived as O′0,0, P′0,1, R′1,0, Q′1,1, S′x∗′,y∗′, and(23)x∗′=1−bCAB1−aPAB−t+m+n,y∗′=bCABaPAB−t+m+n.Then, whenSO'P'S'R'<SQ′P′S′R′ Both firms’ probability of adopting an open green innovation strategy is more significant than both parties’ adoption of an exclusive green innovation strategy.WhenSO′P′S′R′>SQ′P′S′R′, the system eventually evolves to a stable equilibrium state where both parties adopt open-ended green innovation strategies.WhenSO′P′S′R′=SQ′P′S′R′, the system evolves to two stable states with equal probability and(24)SO′P′S′R′=121−bCAB1−aPAB−t+m+n+bCABaPAB−t+m+n.Figure3 shows the firms’ new strategic choice and the final chosen equilibrium result.Figure 3
The firms’ new strategic choice and the final chosen equilibrium result.Conclusion 4.
The probability that traditional equipment manufacturing enterprises A and B adopt an open green innovation strategy is proportional to the subsidym given by the government when firms A and B conduct an open green innovation strategy at the same time.Proof.
The above equation shows thatSO′P′S′R′ is inversely proportional to m. The larger m is, the smaller SO′P′S′R′ is. Furthermore, both firms’ probability of adopting an open green innovation strategy is more significant than that both adopt an exclusive green innovation strategy, and the probability that the system evolves to Q′ (1, 1) increases.Conclusion 5.
The probability of traditional equipment manufacturing enterprises A and B adopting an open green innovation strategy is proportional to the penalty amountn on choosing an exclusive strategy.Proof.
The above equation shows thatSOPSR is inversely proportional to n. The larger n is, the smaller SOPSR. The probability that both sides adopt an open green innovation strategy is more significant than that both adopt an exclusive green innovation strategy, and the probability that the system evolves to Q′ (1, 1) increases.


## 4. Numerical Simulation Analysis

Founded in 1984, Haier is a leading global provider of solutions for a better life. In the process of serial entrepreneurship and innovation, Haier Group began to implement comprehensive innovation management based on the process of re-engineering organizational innovation as the forerunner, all-employee innovation, and all-time innovation as the main features, and practical and other comprehensive synergies such as strategy, culture, market, and technological innovation, which has achieved remarkable results and significantly improved Haier’s core competitiveness.On January 15th, 2016, Haier Group announced that Haier Group and the United States General Electric signed a memorandum of understanding on cooperation on the same day, and the two sides will cooperate on a global scale, while Qingdao Haier Co. will integrate General Electric's home appliance business. General Electric will receive $5.4 billion in cash consideration from Haier.In fact, before the final decision, Haier negotiated with several enterprises. With the help of evolutionary game theory, we restore the selection process of Haier's cooperation object through a simple numerical simulation. In the following numerical simulation, we assume that traditional equipment manufacturing enterprise A is Haier, and B is other traditional equipment manufacturing enterprises with different conditions, and the simulation process is as follows.Since the initial conditions of the game in which traditional equipment manufacturing enterprises A and B adopt open green innovation strategy or exclusive green innovation strategy determine the process of dynamic evolution and final results, the values ofa, b, CAB, t, x, and y in the game process will affect the final strategy results of the whole game from the initial state to the stable evolutionary equilibrium.Assume that traditional equipment manufacturing enterprises A and B adopt exclusive green innovation strategy for research and development and the benefits ofPA and PB are 0.When firms A and B adopt an open green innovation strategy, the excess benefits of A and B's shared green innovationPAB=600, and firms A and B will share the benefits. Among them, firm A’s share is a=0.5, and the share of firm B is 1−a=0.5.The total cost of the open green innovation strategy for both A and B to comply with the new environmental regulation isCAB=200. Firms A and B will share the total cost of innovation. Assuming that the share of enterprise A is b=0.5, the share of enterprise B is 1−b=0.5.If either firm A and B choose the open green innovation strategy alone, its excess return choosing the open green innovation strategy will be 0 since others imitate its core knowledge. The excess benefit from knowledge spillovers for firms choosing the exclusive green innovation strategy ist = 100.If we assume that the probability of firm A and B choosing an open green innovation strategy isx =0.2 and y =0.8, respectively, the probability of enterprises A and B choosing an exclusive green innovation strategy is 1−x=0.8 and 1−y=0.2.Figure4 shows the results of numerical simulation using Matlab software. The results show that both firms’ willingness to adopt the open green innovation strategy converges to 0.5 at T = 0.12 and finally reaches the equilibrium of (0.5, 0.5) when x = y = 0.5.Figure 4
Baseline state of the firms’ willingness of choosing an open green innovation strategy.It indicates that both firms will be influenced by each other’s cooperation intention after many times of cooperation and finally reach an equilibrium. To further verify whether the equilibrium applies to all probabilities, Figures5 to 10 will show further verification.Figure 5
The firms’ willingness to choose an open green innovation strategy with differentPAB. (a) PAB = 600. (b) PAB = 300. (c) PAB = 599. (d) PAB = 601. (e) PAB = 1200.
(a)(b)(c)(d)(e)Figure 6
The firms’ willingness of choosing an open gren innovation strategy with differentt. (a) t = 100. (b) t = 50. (c) t = 99. (d) t = 101. (e) t = 200.
(a)(b)(c)(d)(e)Figure 7
The firms’ willingness of choosing an open green innovation strategy with differentCAB. (a)CAB=200. (b)CAB=100. (c)CAB=199. (d)CAB=201. (e)CAB=400.
(a)(b)(c)(d)(e)Figure 8
The firms’ willingness to choose an open green innovation strategy with differentm. (a) m = n = 0, m = 200, n = 0. (b) m = 100, n = 0. (c) m = 199, n = 0. (d) m = 201, n = 0. (e) m = 400, n = 0.
(a)(b)(c)(d)(e)Figure 9
The firms’ willingness to choose an open green innovation strategy with differentn. (a) m = n = 0, m = 0, n = 200. (b) m = 0, n = 100. (c) m = 0, n = 199. (d) m = 0, n = 201. (e) m = 0, n = 400.
(a)(b)(c)(d)(e)Figure 10
The firms’ willingness to choose an open green innovation strategy with different (m + n). (a) m = n = 0, m + n = 200. (b) m + n = 100. (c) m + n = 199. (d) m + n = 201. (e) m + n = 400.
(a)(b)(c)(d)(e)If both firms A and B adopt the open green innovation strategy, keeping other values constant, the model converges as shown in Figure5 after varying the excess return PAB of shared green innovation of firms A and B.The results show that if the excess return risesPAB=601 (Figure 5(d)) and PAB=1200 (Figure 5(e)), the cooperation of enterprises A and B eventually converges to open innovation strategy together, and the larger the excess returns, the faster the convergence rate.Moreover, if the excess returns fallPAB=599 (Figure 5(b)) and PAB=300 (Figure 5(c)), the cooperation between firms A and B eventually converges to an exclusive innovation strategy together, and the smaller the excess returns, the faster the abandonment rate.Thus, it can be verified Conclusion 1-1: the excess benefits are positively correlated with the willingness to open green innovation and not only that, Conclusion 1-2: there is an excess benefits pointPAB∗, which makes the probability of adopting open innovation strategy and an exclusive innovation strategy equal for both firms: if PAB＞PAB∗, the probability of adopting open innovation strategy is more significant than adopting an exclusive innovation strategy for both firms. And if PAB＜PAB∗, the probability of adopting an exclusive strategy is greater than the probability of adopting an open innovation strategy for both firms, and the greater the excess returns, the stronger the willingness to open green innovation.The convergence of the model is shown in Figure6 after one of the firms A and B choose the open green innovation strategy, and the firm that chooses the exclusive green innovation strategy obtains the excess benefit t from the knowledge spillover.The results show that if the excess return risest=101 (Figure 6(d)) and t=200 (Figure 6(e)), the cooperation between firms A and B eventually converges to an exclusive innovation strategy, and the larger the excess return, the faster the convergence rate.If the excess returns fall byt =50 (Figure 6(b)) and t =99 (Figure 6(c)), enterprises A and B eventually converge to an open innovation strategy, and the smaller the excess returns are, the faster the convergence rate is.Thus, it can be verified Conclusion 2-1: the excess benefit from knowledge spillover has a negative relationship with the firms’ willingness to share green innovation. Not only that, Conclusion 2-2: there exists a knowledge spillover excess benefit pointt∗, which makes the probability of adopting open innovation strategy and an exclusive innovation strategy equal for both firms. If t＞t∗, the probability of adopting an exclusive innovation strategy is more significant than adopting an open innovation strategy for both firms. If t＜t∗, the probability of adopting open innovation strategy is more significant than adopting an exclusive innovation strategy for both firms. Furthermore, the smaller the excess benefit from knowledge spillover, the stronger the willingness to share green innovation.If firms A and B adopt the open green innovation strategy, the model converges after complying with the new environmental regulation for the total cost change of the open green innovation strategy simultaneously, as shown in Figure7.The results show that if the knowledge innovation cost risesCAB=201 (Figure 7(d)) and CAB=400 (Figure 7(e)), the cooperation between firms A and B eventually converges to an exclusive innovation strategy, and the higher the knowledge innovation cost, the faster the convergence rate.If the knowledge innovation cost decreases byCAB=100 (Figure 7(b)) and CAB=199 (Figure 7(c)), the cooperation between firms A and B eventually converges to an open innovation strategy, and the lower the knowledge innovation cost, the faster the convergence rate.Conclusion 6.
The total cost of innovation negatively correlates with the willingness to share green innovation.
Not only that, Conclusion 3-2: there exists a knowledge innovation cost pointCAB∗, which makes the probability of adopting open innovation strategy and an exclusive innovation strategy equal for both firms. If CAB＞CAB∗, the probability of adopting open innovation strategy is more significant than adopting an exclusive innovation strategy for both firms. If CAB＜CAB∗, the probability of adopting an exclusive innovation strategy is more significant than adopting an open innovation strategy for both firms. Furthermore, the smaller the total cost of innovation, the stronger the willingness to share green innovation.
After introducing the reward and punishment mechanism, keeping other values unchanged, traditional equipment manufacturing enterprises A and B simultaneously carry out open green innovation strategies as shown in Figure8, after the government changes subsidy amount m.
The results show that if the government subsidy risesm=201 (Figure 8(d)) and m=400 (Figure 8(e)), the cooperation of A and B enterprises eventually converge to an open innovation strategy, and the higher the government subsidy, the faster the convergence rate.
If the government subsidy decreases bym=100 (Figure 8(b)) and m=199 (Figure 8(c)), the cooperation of both enterprises A and B will eventually abandon the open innovation strategy, and the lower the government subsidy, the faster the abandonment rate.
This verifies Conclusion 4-1: that government subsidies have a positive relationship with the willingness to share green innovation, and not only that, Conclusion 4-2: there exists a government subsidy value m∗, which makes the probability of adopting open innovation strategy and an exclusive innovation strategy equal for both firms. If m＞m∗, the probability of adopting open innovation strategy is greater than the probability of adopting a monopoly for both enterprises, and if m＜m∗, the probability of adopting an exclusive innovation strategy is greater than the probability of adopting open innovation strategy for both enterprises; and the more government subsidies, the stronger the willingness to share green innovation.
After introducing the reward and punishment mechanism, keeping other values constant, if only one firm complies with the new environmental regulation for the open green innovation strategy, the government punishment on the other side of the exclusive innovation strategy is varied forn. The model converges as in Figure 9.
The results show that if the government punishment risesn=201 (Figure 9(d)) and n=400 (Figure 9(e)), the cooperation of A and B enterprises eventually converges to an open innovation strategy, and the higher the government punishment, the faster the convergence rate.
If the government punishment decreases byn=100 (Figure 9(b)) and n=199 (Figure 9(c)), the cooperation of both enterprises A and B will eventually abandon the open innovation strategy, and the lower the government punishment, the faster the abandonment rate.
This verifies Conclusion 5-1: that government punishment has a positive relationship with the willingness to open green innovation, and not only that, Conclusion 5-2: there exists a government punishment valuen∗, which makes the probability of adopting open innovation strategy and an exclusive innovation strategy equal for both firms. If n＞n∗, the probability of adopting open innovation strategy is greater than the probability of adopting a monopoly for both enterprises, and if n＜n∗, the probability of adopting an exclusive innovation strategy is greater than the probability of adopting open innovation strategy for both enterprises; the more government punishment, the stronger the willingness to share green innovation.
After introducing the reward and punishment mechanism, keeping other values constant, the model converges as shown in Figure10 if the sum of the government reward (m) and the government punishment (n) is changed.
The results show that if the sum of the two risesm + n = 201 (Figure 10(d)) and m + n = 400 (Figure 10(e)), the cooperation between enterprises A and B eventually converges to open innovation strategy, and the higher the sum of the two, the faster the convergence; if the sum of the two falls m + n = 100 (Figure 10(b)) and m + n = 199 (Figure 10(c)), the cooperation between enterprises A and B eventually give up open innovation strategy, and the less the sum of the two, the faster the giving up.
Thus, we can verify Conclusion 6-1: that the government subsidy amountm and the government penalty amount n converge as shown in Figure 10. The sum of government subsidies and government punishment has a positive relationship with the willingness to share open innovation strategy, and not only that, Conclusion 6-2: there exists a sum of government subsidies and government punishment m+n∗, which makes the probability of adopting open innovation strategy and an exclusive innovation strategy equal for both firms. If m+n＞m+n∗, the probability of adopting open innovation strategy is more significant than adopting an exclusive innovation strategy for both firms. If m+n＜m+n∗, the probability of adopting an exclusive innovation strategy is more significant than adopting an open innovation strategy for both firms. And the higher the sum of the two, the stronger the willingness of green sharing innovation.


## 5. Conclusion

The advent of a knowledge-based economy and globalization has made market competition increasingly hot and intensified the relative tension of resources. In this context, improving the efficiency of resource utilization and enhancing innovation capability have become an issue of great concern and importance to enterprises. Collaborative innovation is one of the effective ways, but both academia and enterprises do not pay enough attention to research on collaborative innovation in enterprises. It can be seen that the research on collaborative innovation at the enterprise level has not yet attracted enough attention from scholars. On the other hand, from the perspective of enterprises themselves, the focus of enterprise management and policymakers on innovation is still on the innovation elements themselves, such as high-quality scientific and technological talents, financial resources, and institutional and cultural support. Few enterprise managers recognize the importance of collaborative innovation. Few enterprise managers recognize the nonlinear synergistic innovation utility among various innovation factors of the enterprise. As a result, enterprises themselves also do not pay enough attention to collaborative innovation. Therefore, the study of collaborative enterprise innovation has great significance and necessity, both from the theoretical point of view and from the practical application point of view.In order to more clearly understand and grasp collaborative innovation for a more in-depth study, this paper analyzes and discusses the open cooperation strategies among oligopolistic enterprises in the equipment manufacturing industry based on scholars’ previous studies using models and tools related to big data and evolutionary game theory. In addition, the optimal combination in the existing situation is selected by simulating and analyzing the selection trends and results of oligopolistic enterprises with the model several times.The study shows that the probability of choosing an open innovation strategy between oligopolistic equipment manufacturing firms is positively proportional to the excess benefits of open green innovation and government subsidies and inversely proportional to the excess benefits of knowledge spillovers, government penalties, and the cost of open coinnovation and knowledge spillovers between the two firms. In addition, each case has a critical value that directly affects the choice strategy of the two firms.This thesis takes the equipment industry as the starting point and explores the game relationship among many stakeholders, such as enterprises, government, financial institutions, and research institutions, from technology innovation and environmental friendliness in the equipment industry. Adopting the relevant models and tools of evolutionary game theory, an ecosystem with “well-designed environmental regulation” is constructed to achieve stable evolutionary strategies for different subjects. On this basis, we build a simulation platform and use big data to simulate and analyze the trend and results of each subject's choice several times, analyze the optimal combination of existing situations, and find the “threshold” of the innovation inflection point. This research is essential for reducing the uncertainty risks associated with corporate innovation and formulating governmental regulatory policies.The main research directions for the future are as follows.(1) In the well-designed open innovation platform for equipment manufacturing enterprises, external synergy among horizontal enterprises and upstream and downstream enterprises and synergy among internal factors of enterprises are added to effectively improve enterprise performance and form a stable mechanism by integrating how internal collaborative innovation and external collaborative innovation are integrated; (2) through industrial and enterprise research as well as relevant cases and data of target enterprises, a feasible, simulable, and credible all-round dynamic simulation system is established; (3) the experience of the manufacturing industry is extended to other industries to establish a universally applicable open environmental collaborative innovation ecosystem among enterprises.



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*Source: 5508783-2022-05-05.xml*