Green innovation ecosystem evolution: Diffusion of positive green innovation game strategies on complex networks

Zhang, Ren-Jie; Tai, Hsing-Wei; Cao, Zheng-Xu; Wei, Chia-Chen; Cheng, Kuo-Tai Article Green innovation ecosystem evolution: Diffusion of positive green innovation game strategies on complex networks Journal of Innovation & Knowledge (JIK) Provided in Cooperation with: Elsevier Suggested Citation: Zhang, Ren-Jie; Tai, Hsing-Wei; Cao, Zheng-Xu; Wei, Chia-Chen; Cheng, KuoTai (2024) : Green innovation ecosystem evolution: Diffusion of positive green innovation game strategies on complex networks, Journal of Innovation & Knowledge (JIK), ISSN 2444-569X, Elsevier, Amsterdam, Vol. 9, Iss. 3, pp. 1-17, https://doi.org/10.1016/j.jik.2024.100500 This Version is available at: https://hdl.handle.net/10419/327403 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ Green innovation ecosystem evolution: Diffusion of positive green innovation game strategies on complex networks Ren-Jie Zhang a , Hsing-Wei Tai b,c, *, Zheng-Xu Cao d , Chia-Chen Wei e , Kuo-Tai Cheng f a Weifang University of Science and Technology, Weifang, 262700, China b Professor, School of Civil and Architectural Engineering, Weifang University of Science and Technology, Weifang, 262700, China c Professor, Department of Engineering and Management, International College Krirk University, Bangkok 10220 Thailand d Management college, Ocean University of China, Qingdao 266100, China e Associate Professor, Department of Civil Engineering, Pingtung University of Science and Technology, Pingtung 912301, Taiwan f Professor, Department of Environmental and Cultural Resources, National Tsing Hua University, Hsinchu, 300044, Taiwan ARTICLE INFO Article History: Received 25 October 2022 Accepted 9 May 2024 Available online 27 May 2024 ABSTRACT The essence of the evolution of the green innovation ecosystem is the process by which the positive strategy of green innovation spreads in a complex network. In this study, the "Object-Technology-Environment-Management-Culture (OETMC)" structure paradigm of innovation ecosystems is presented, and a causal analysis framework of green innovation ecosystem evolution based on green innovation behavior strategy, supported by green innovation efficiency and focused on green innovation ecosystems is developed. Based on this framework, the structure of the green innovation ecosystem and the diffusion process of positive green innovation in the network are discussed. The results reveal the following. (1) The complexity of the green innovation ecological network has visibly improved, but numerous blank connections remain. These are the key constraints that hinder structural evolution. (2) The appearance of a large number of long-range connections weakens the constraint of geographical distance but also hinders edge nodes from joining the network. (3) The existence of preference attachment and power law distribution of the green innovation ecological network leads to the incomplete convergence of positive green innovation strategy at any initial strategy ratio. (4) Default cost and pollution tax rate ensure the enthusiasm of green innovation actors to seek innovation cooperation by increasing opportunity costs, thus accelerating the formation and reconstruction of the green innovation ecological network. These conclusions provide a decision-making reference for governments to encourage green innovation subjects to formulate targeted policies. © 2024 The Author(s). Published by Elsevier España, S.L.U. on behalf of Journal of Innovation & Knowledge. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Keywords: Innovative ecosystem Green innovation Complex network Evolutionary game Temporal and spatial distribution pattern JEL classification: O31 O35 Q55 Q56 Introduction Green innovation provides a feasible scheme for reducing the negative externalities resulting from traditional economic growth and the additional costs of environmental pollution and has become an important means for countries worldwide to pursue sustainable development (Zhang et al., 2023;Satrovic et al., 2024). Green innovation, also known as ecological innovation, environmental innovation, and sustainable innovation, expands and supplements the concept of innovation adding the influence of economic, social, ecological, and other factors, and has richer theoretical connotations and practical significance (Fan et al., 2022;Zhao et al., 2021). In essence, it is an innovative activity aimed at reducing pollution outputs of production processes and enhancing the ecological environment’s carrying capacity and sustainability. These goals embody the organic integration of social value, economic value, humanistic value, and technical value (Huang et al., 2022). Green innovation has become a key measure of how developing countries deal with international sustainable governance trends such as carbon taxes on trade and carbon trading. How to build and improve a green innovation system and lead in gaining core technological advantages in global sustainable development governance has also become a focus of attention around the world (Zhang et al., 2022a). The wide application of next-generation information technologies such as 5 G and AI in various fields not only provides strong support for the transformation of the green innovation paradigm but also intensifies the reshaping of international green technology competition patterns. As the largest developing country, China faces greater challenges in green innovation (Zhang et al., 2022b;Xu et al., 2021). On the one hand, the spatial imbalance of the allocation of innovative * Corresponding author at: School of Civil and Architectural Engineering, Weifang University of Science and Technology, Weifang, 262700, China. E-mail address: [email protected] (H.-W. Tai). https://doi.org/10.1016/j.jik.2024.100500 2444-569X/© 2024 The Author(s). Published by Elsevier España, S.L.U. on behalf of Journal of Innovation & Knowledge. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Journal of Innovation & Knowledge 9 (2024) 100500 Journal of Innovation &Knowledge https://www.journals.elsevier.com/journal-of-innovation-and-knowledge elements leads to significant gaps between regions. Compared with China’s eastern coastal areas, the central and western regions have weaker innovation foundations and insufficient supplies of innovative elements, which results in them being marginal regions in the overall green innovation spatial layout (Han et al., 2022;Ye et al., 2020;Zhang et al., 2022a); On the other hand, China has yet to form a complete green innovation system. Although the innovation agglomeration mode with provincial capital cities (or central cities) as the core plays a vital role in improving the efficiency of cooperative innovation, some problems remain, such as inaccurate policies, weak initiatives related to innovation subjects, and an imperfect innovation environment (Han et al., 2024). Targeting these problems, how to promote the transformation of China’s linear green innovation to nonlinear, from innovation organization to innovation network, and from innovation cluster to innovation ecosystem has become unavoidable and realistic problems within the current international competition for green technology innovation (Jin et al., 2024). A similar concept of innovation ecosystems can be traced to the commercial ecosystem described by James Morre in 1993, which was first formally presented in the research report of the American Competitiveness Council in 2004. It was not until 2013, when the European Union proposed the "Innovation 3.000 paradigm, with the innovation ecosystem at its core, that this concept gained widespread attention in all social sectors (Lian et al., 2022). With increased research, the definition of an innovation ecosystem has tended to diversify. It is generally believed that the innovation ecosystem is a network structure formed by a series of stakeholders participating in value-creation activities around core enterprises. There is a strong technical dependence among stakeholders, and they can capture, integrate, innovate, diffuse, and increase the value of complementary knowledge with and among other stakeholders by exerting their unique advantages. This definition emphasizes the relationship between innovation subjects but ignores the guiding role of the external environment in the formation and evolution of innovation ecosystems. (Li et al., 2022a,2022b).Therefore, innovation ecosystems are also described as a functional complex with a specific scale and structure formed by the interdependence of innovation subjects and environments through knowledge, technology, culture, etc., within a certain time and space, or as an industrial cluster "innovation habitat" with diversified cooperation and unified action standards (Zhou et al., 2022). Furthermore, from the perspective of composition and system structure, the innovation ecosystem is also an organizational community that includes several layers, including core, extension, outer, and derivative layers. Each layer is connected by the value chain, industrial chain, knowledge chain, and trust relationship, which form an internal mechanism to promote the evolution of an innovation ecosystem (Liu & Liang, 2024). Similar to natural ecosystems, the driving force of self-organization evolution in innovation ecosystems primarily comes from the interaction and transformation of information, knowledge, and resources among internal populations and the external environment (Irfan et al., 2022; Bohn & Rogge, 2022;Abid et al., 2022). Thus, the strategic selection of an innovative population in response to external environmental changes is a direct inducement for the evolution of innovation ecosystems. This is because the nonlinear effect of an innovation ecosystem will lead to some strategic behavior of the innovation subject not being locally limited, but spreading to other species or populations unpredictably. Additionally, the evolutionary direction of innovation ecosystems will be determined by the law of natural selection. In summary, prior research has primarily focused on examining the concepts of discrimination, structural characteristics, and evolutionary mechanisms of innovation ecosystems, which have certain supplementary effects on enriching and perfecting the theory of innovation ecosystems. However, there the following problems still deserve further consideration. (1) The deconstruction of the innovation ecosystem from a comprehensive perspective. Previously, evolutionary economic geography was used to explain the structural composition, community characteristics, and evolutionary trends of innovation ecosystems. Although effective, this is insufficient to fully explain the ecological and systematic characteristics of innovation ecosystems. (2) Innovate the complexity of ecological network topology. Innovation ecological networks play key roles in promoting the formation and evolution of innovation ecosystems. Their structural complexity reflects the flow state of elements among innovation subjects and also provides a search path for the diffusion of game strategies among innovation subjects. Nevertheless, the morphological evolution and structural characteristics of innovation ecological networks still have attracted insufficient attention. (3) The essential law and underlying logic of innovation ecosystem evolution, a logical population growth model, and a Lotka-Volterra competition analysis model are often used to examine interactions between innovation groups and to explain the evolutionary choices of innovation ecosystems, but these methods cannot explain strategic choice mechanisms of innovation subjects and their influence on the whole ecosystem (Zhou et al., 2022;Zhang et al., 2022a). The evolution law of the innovation ecosystem discussed in this study is based on the strategic choice of the innovation subject. Compared with prior studies, the main contributions of this study are as follows. (1) It explains the characteristics and formation mechanism of a green innovation ecosystem from the comprehensive perspectives of ecology, innovation, and system, and attempts to summarize the basic paradigm structure of an innovation ecosystem based on comparing different types of green innovation ecosystems with different spatial scales to provide theoretical support for the discussion of operation mechanisms. (2) It uses cities as the basic communities in innovative ecosystems to construct a green innovation ecological network based on the efficiency of urban green innovation, examines the morphological evolution and structural characteristics of the innovation ecological network in geographical space, and identifies the diversified ecological network structure formed locally by the innovation community. (3) It establishes a causal analysis framework for green innovation ecosystem evolution based on the behavior of green innovation agents, supported by green innovation efficiency, and focused on green innovation ecological networks. Based on this framework, the complex network evolution game model is used to simulate the diffusion mechanism of a green innovation agent strategy within an ecological network and its sensitivity to external factors. The marginal contributions of this study lie in presenting a causal analysis framework that spans micro (the primary strategy of green innovation) to macro (innovation ecological network), expounding the underlying logical law of the evolution of green innovation ecosystem, and considering the influence of geographic space on the evolution and strategic diffusion of innovation ecological networks. This presents a new research paradigm for related research which not only highlights the ecological and systematic nature of green innovation activities, but is also generalizable to other countries or regions, and can provide a decision-making reference for promoting the construction of a green innovation ecosystem. R.-J. Zhang, H.-W. Tai, Z.-X. Cao et al. Journal of Innovation & Knowledge 9 (2024) 100500 2 Mechanisms and characteristics of green ecosystem formation Paradigm structure of green innovation ecosystem According to various research scales, innovation ecosystems can be divided into five levels: industrial innovation ecosystems, urban innovation ecosystems, regional innovation ecosystems, national innovation ecosystems, and global innovation ecosystems (Yang et al., 2022;Xu et al., 2022;Ramkumar et al., 2022). Despite the concept of enterprise innovation ecosystems presented in some studies, we believe that enterprise innovation activities do not meet the basic characteristics of innovation ecosystems. On the one hand, it is usually difficult for enterprises to possess all the resources necessary for innovation activities, which requires cooperation with other innovation subjects and access to their superior resources. Additionally, the innovation ecosystem should have all the elements that can meet the innovation needs of internal communities. On the other hand, the internal relationship of an enterprise is simple, it cannot form standardized industrial technical standards, and the degree of external influence is far greater than the degree of transformation of the external environment; thus, it lacks ecological characteristics. The innovation activities of enterprises belong to an innovation system, not an innovation ecosystem. Therefore, it is necessary to discuss the basic structure of innovation ecosystems using different research scales. Innovatively, we summarize the paradigm structure of an innovative ecosystem, which includes objects, environment, technology, management, and culture (the OETMC paradigm). Governments, enterprises, universities, research institutes, financial institutions, intermediaries, and users are the most active elements in innovation ecosystems. The enterprise is a key part directly involved in green innovation activities and is also an important carrier in promoting the marketization and industrialization of green innovation achievements. Its advantage is its high sensitivity to market demand. Rich R&D investment provides more trial and error costs for the enterprise’s green innovation activities and also provides guarantees for improving the efficiency of green innovation and shortening the innovation cycle (Pushapananthan & Elmquist, 2022; Nylund et al., 2021). Universities and research institutes are primarily responsible for exploring the frontier of green innovation technology and knowledge, and promoting it while providing corresponding talent support for green innovation activities. As the "adhesive" to ensure the coordinated and efficient operation of all innovation subjects, the government intends to develop incentives such as reducing the risks associated with green innovation, building an innovation platform to provide a harmonious innovation environment for innovators, and guiding or cultivating the independent innovation ability of participants through management system innovation. Thus, the government can also be considered among the direct participants in green innovation. Financial institutions fund R&D for innovative subjects and green finance and innovation subsidies lower the risk of green innovation, increasing participation and enthusiasm in innovative green innovation subjects (Wu et al., 2022). Intermediary service organizations include public organizations and professional organizations. The former primarily provides consultation, legal protection, and technology trading services for innovation actors, while the latter is composed of clusters that provide professional support services such as industrial alliances and trade associations. Users are both the source of green innovation demand and the users of green innovation products or services. Their green demand and information feedback somewhat guide the research and development direction of innovation. The market, technical, institutional, financial, and ecological environments all provide carrier support for green innovation activities. The market environment reflects the needs of current users and niche market space and can provide research and development direction for green innovation subjects. Technology environments can help innovation subjects quickly locate their technology niche within a green innovation ecosystem and formulate appropriate innovation strategies based on the state of their own technology (Min et al., 2020;Melander & Arvidsson, 2022). Institutional and financial environments are usually the focus of a series of measures taken by the government to promote green innovation. For small and mediumsized enterprises or start-ups, they can quickly improve their innovation capability and reduce innovation risks and costs. The natural environment is the fundamental source of various elements in green innovation activities and is also the basic space where the green innovation ecosystem is located. Technology is the initial driving force for the formation of the relationship between innovation subjects. The diversity of green technology stock, standardization of green technology norms, and trading volume of the green technology market reflect the activity of the green innovation ecosystem. In this ecosystem, management is represented by heteronomy management and self-organization management. Heteronomy management refers to the macro-control mechanism with the government as its core and is the external factor that determines the evolutionary direction of the green innovation ecosystem. Self-organization refers to the system evolution mechanism formed by a long-term strategy game with the relationships among innovation subjects as the main line. This includes the internal factors that affect the evolutionary direction of a green innovation ecosystem (Wang et al., 2022a;Liu et al., 2021). The culture is primarily reflected in that the main body of green innovation has the same or similar value orientation. Additionally, religious beliefs, behavioral habits, aesthetic concepts, and corporate cultures will also affect the formation of a green innovation ecosystem. With the guidance of the OETMC paradigm and considering the following advantages, we chose to investigate the characteristics and evolutionary mechanisms of green innovation ecosystems at the city scale. (1) As an independent and complete administrative unit, a city’s internal elements should be based on the overall city’s goals regarding strategic planning and scheme implementation. Additionally, (2) a city contains all the elements of the OTEMC paradigm and can be regarded as a community or subsystem in the innovation ecosystem. Furthermore, (3) the urban green innovation ecosystem not only includes the micro-scale industrial green innovation ecosystem but also belongs to the regional green innovation ecosystem as a green innovation community. Therefore, the city scale will become a bridge to realize the unity of opposites from micro (strategic choice) to macro (system evolution). Formation mechanism of the green innovation ecosystem As described earlier, the evolution of a green innovation ecosystem is the result of the strategic game between green innovation subjects relying on the green innovation ecological network. Here, we present a causal analysis framework from micro to macro to explain this perspective (Fig. 1). Research institutes, universities, and innovative enterprises have become the backbone of green innovation. Although they differ greatly in organizational structures, technology preferences, and management systems, they are very complementary in resource endowment, knowledge structure, and platform carrier, which makes their deep coupling constitute the core kinetic energy of green innovation (Zhang et al., 2021;Li et al., 2022c). The innovation subject invests in green innovation elements such as human resources, infrastructure, and R&D funding, and produces academic papers, technical patents, and new theoretical knowledge through cooperation or competition with others. The relative value of input and output reflects the green innovation performance of the participants. Therefore, the input and output of all innovation subjects reflect the comprehensive level of urban green innovation—that is, the efficiency of green innovation. However, the spatial distribution of urban green R.-J. Zhang, H.-W. Tai, Z.-X. Cao et al. Journal of Innovation & Knowledge 9 (2024) 100500 3 innovation efficiency is usually unbalanced. The combined actions of the spillover effect and the siphon effect result in the formation of a hierarchical nested spatial pattern with administrative divisions as the boundary which evolves into diverse agglomeration areas (Li et al., 2022d; Satrovic et al., 2024). The elements of green innovation in the surrounding areas of the agglomeration rely on value, industrial, innovation, and element chains to flow to high-efficiency areas, thus promoting the formation of a green innovation ecological chain among cities, and forming a green innovation ecological network with complex structure and diverse forms in certain areas (Li & Sun, 2021;Fang et al., 2022). A green innovation ecological network is an abstract expression of the internal relationships within a green innovation ecosystem. It provides a search path for innovation subjects to choose game objects and also provides carrier support for the strategy diffusion of green innovation subjects (Jin et al., 2022;Javanmardi, 2022). Therefore, we will utilize the morphological characteristics and structural complexity of a green innovation ecological network as the fundamental starting point to examine the evolution of a green innovation ecological system (Jin et al., 2024). The evolution of green innovation ecosystems is primarily reflected in four aspects: system structure, subsystem behavior, system state, and environmental adaptability. The purpose of its evolution is to improve the green innovation ability of innovation subjects and gradually clarify their niche within the entire system. Especially for new enterprises, this can help them quickly develop various resources and accelerate their embedding into the entire ecosystem. Therefore, system evolution is the process of differentiation and optimization in the green innovation ecosystem. Multidimensional mapping of the green innovation ecosystem Evolutionary economic geography theory has difficulty effectively explaining the complexity of the green innovation ecosystem. This motivates us to try to analyze the mapping characteristics of the green innovation ecosystem from the comprehensive perspectives of innovation, systematics, and ecology (Fig.2). Fig. 2 shows the structural mapping and feature mapping of the green innovation ecosystem in different dimensions. Structural mapping explains the green innovation ecosystem according to the OTEMC structural paradigm and thus obtains its innovation view as an innovation network composed of the value chain, factor chain, and industrial chain. Similarly, the system view presents a loose subject-relationship network with characteristics including the socialized division of labor, and an Fig. 1. Causal analysis framework of green innovation ecosystem evolution. R.-J. Zhang, H.-W. Tai, Z.-X. Cao et al. Journal of Innovation & Knowledge 9 (2024) 100500 4 ecological view, and reveals an ecological network formed by the interaction of the competition and cooperation chains. Therefore, we believe that the green innovation ecosystem can be understood as a composite network formed by the superposition and coupling of the innovation network, the subject-relationship network, and the ecological network, which is the key carrier of the operation and evolution of the innovation ecosystem. Feature mapping not only sums up all types of mapping network features but also includes new features emerging from the interaction between networks, as shown in Fig. 2. In the context of innovation, green innovation activities are profitoriented, and to maintain their core competitiveness, enterprises will give priority to green technology development and green product production, and obtain surplus profits in niche markets (Yao et al., 2020;Farooq et al., 2024). Due to the constraints of enterprise scale and superior resources, a linear cooperation model has been formed among enterprises and has evolved into a green innovation cooperation network with core enterprises forming the mainstay and supplemented by non-core enterprises. Research institutions focus on national strategic needs and key funding projects to conduct strategic integrated innovation and focus more on improving original innovation ability and frontier theory breakthroughs. Universities serve as green innovation knowledge transmitters while also producing elements of green innovative talent (Wang et al., 2022a). From a systematic perspective, the green innovation ecosystem is a subsystem embedded in the economic-social-ecological system and has a typical dissipative structure (Yang et al., 2021). That is, the green innovation ecosystem must continuously input outside materials and energy to ensure normal system operations. If inputs cease, the system will no longer exist. This feature reflects the dynamic and stable nature of the green innovation ecosystem. Furthermore, it also meets the characteristics of synergy, hierarchy, and nonlinearity. However, we believe that the emergent properties of the green innovation ecosystem are the most noteworthy, as they describe characteristics that individual elements of the ecosystem lack. Generally, the structure of a green innovation ecological network is considered the emergence of the complexity of a green innovation ecosystem and reflects the sum of complex relationships among green innovation subjects (Xu et al., 2018;Wang & Yang, 2022b). Ecological features are important distinctions between the green innovation system and the green innovation ecosystem. The ecology of the green innovation ecosystem is primarily reflected in the close cooperation and well-defined competition and cooperation relationships among innovation subjects, which are win-win and can be adaptively adjusted according to external environment changes to maintain the system’s stability. From the ecological perspective, various types of green innovation subjects represent species in the ecosystem, and each green innovation species is in specific technical, social, and economic niches. Its cooperation scope with other green innovation subjects constitutes the niche space of this species. All the innovative species and innovative environments in a given spacetime range constitute an innovative community (the urban community is the research object in this study), and the innovative community belongs to a larger green innovation ecosystem (Lian et al., 2022). The innovation ecosystem also follows the evolutionary law of "natural selection." Its genetic mechanism is reflected in the green innovation subject’s imitation behavior. For the innovation subject, this can directly obtain the existing innovation results through Fig. 2. Multidimensional mapping model of green innovation ecosystem. R.-J. Zhang, H.-W. Tai, Z.-X. Cao et al. Journal of Innovation & Knowledge 9 (2024) 100500 5 "genetic factors." Genetic factors include a mature green innovation management system, green innovation technology, theoretical knowledge, etc., which strongly support the promotion of green innovation ability in new innovative subjects. However, to maintain the core competitiveness of its own products or services, the imitated innovation subject will launch new innovations in combination with market demand, that is, the variation mechanism of green innovation (Wang et al., 2021;Walrave et al., 2018). Nevertheless, not all green innovation achievements can adapt to changing innovation environments and the selection mechanism of the green innovation ecosystem will eliminate ineffective innovations. Combined with the above analysis, we define the concept of a "green innovation ecosystem" as occurring within a certain time and space and where all types of innovation actors both compete and cooperate to develop, produce, or provide after-sales green technologies, green products, or services, and form complex network relationships through strategic games. The green innovation ecosystem is an ecological, systematic, self-organizing, and adaptive green innovation function complex based on this complex network relationship. Methods and materials Construction of the green innovative ecological network The green innovation network, which is based on attribute data such as cooperative patent data, property right relationships, value chains, and talent flow, can somewhat describe the strength of the green innovation ecological chain among regions. However, due to data source singleness and preferences, calculation results are onesided and it is difficult to describe the formation and evolution complexity of the green innovation ecological network in a panoramic way (Zhang et al., 2022a;Teng et al., 2021;Russell & Smorodinskaya, 2018). Additionally, this network construction type usually ignores the flow of physical production factors such as human capital, R&D funds, and infrastructure investment among green innovation subjects, especially the non-physical influences such as knowledge transfer, experience sharing, and spillover effects among green innovation subjects. This unilaterally separates the logical relationship between the allocation of green innovation factors and the formation of spatial topological networks (Shaw & Allen, 2018). Therefore, we chose the ecological efficiency of green innovation as the basic data for constructing the green innovation ecological network and attempted to optimize the original network construction method. The following aspects generally reflect the feasibility of constructing a green innovation ecological network with green innovation efficiency: (1) Green innovation efficiency quantifies the rationalization degree of allocation of green innovation elements on an urban scale from the perspective of input and output, thereby avoiding the malpractice of "output-only theory" that attaches importance to outputs and neglects inputs, and enhances the differentiation of green innovation efficiency in different cities while considering the characteristics of comprehensiveness and comprehensiveness. (2) The evaluation index system of green innovation efficiency is highly consistent with the formation mechanism of the green innovation ecological network shown in Fig. 1. Therefore, the capital investment and human capital in the index system are the mapping of capital flow, factor flow, and knowledge flow in the green innovation network. This fundamentally eliminates the one-sidedness of calculation results caused by a single data source and reflects the feasibility and applicability of building a green innovation ecological network based on efficiency. (3) This index realizes the unity of the strategic choices of the green innovation subject and the evolution of the green innovation ecological network structure. The efficiency of urban green innovation reflects the ability of green innovation subjects to play games and produce results under various influencing factors, and also possesses the key power to promote the evolution of the green innovation ecological network and becomes a bridge connecting micro and macro. As green innovation efficiency must consider unexpected outputs in production processes, services, and development, we chose the SBM model considering unexpected output as the green innovation efficiency measurement model as it can incorporate the slack variables into the objective function and weaken the influence of radial and angle on the accuracy of measurements in traditional models (Zhang et al., 2022a). The specific formula is as follows: r¼ 11 KX K k¼1 Sk xk0 1þ1 IþJX I i¼1 Sd i yd i0 þX J i¼1 Su i yu i0 ! s:t xk0¼X M m¼1 mmxkm þs k;k¼1;2¢¢¢;K yd i0¼X M m¼1 mmyd im sd i;i¼1;2;¢¢¢;I yu i0¼X M m¼1 mmyu im þsu i;i¼1;2;¢¢¢;J 1¼X M m¼1 mm mm0;s k0;sd i0;su i0 8 > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > : ð1Þ Whererrepresents the efficiency of urban green innovation, the value range is [0,1]. K,I,Jrepresent the quantity of input, output, and unexpected output, respectively. s k,sd i,su irepresent slack variables of input, output, and unexpected output, respectively. xk0,yd i0,yu i0represent input, output, and unexpected output respectively, andmmis the correction coefficient. Setting the characteristic index of green innovation ecological network Fig. 1 shows that the formation of a green innovation ecological network depends on the spatial imbalance of green innovation efficiency. This indicates that the influence of geographical space distance must be considered when constructing green innovation ecological network relationships. This is consistent with the description of economic diffusion theory by new economic geography. Therefore, we chose the gravity model as the basic model to describe the correlation of green innovation among cities. Since the efficiency of green innovation emphasizes the rationalization degree of factor allocation, there may be a problem of "pseudo-efficiency" in the results, that is, the high or low input and output results that suggest falsely high efficiencies for green innovation. Pseudo-efficiency nodes will generate redundant connections in the ecological network for green innovation. Economic distance is introduced to weaken the influence of such nodes. Economic distance reflects the economic scale gap between cities and simultaneously reflects the preference and attachment characteristics of a green innovation network. The optimized gravity model is as follows: Fij ¼PiPj D2 ijE2 ij Kð2Þ WhereFijrepresents the green innovation attraction of city ito city j, that is, the strength of the green innovation ecological chain; PiandPjrepresent the green innovation efficiency of cityito cityjrespectively; DijandEijrepresent the geographical distance and economic distance between cityito cityj, respectively; Kis the correction coefficient and is used to adjust the data magnitude and enhance contrast. R.-J. Zhang, H.-W. Tai, Z.-X. Cao et al. Journal of Innovation & Knowledge 9 (2024) 100500 6 Considering the complexity of the green innovation ecological network structure, we defined the network density, hierarchy, network structure entropy, centrality, and average distance to describe its characteristics (Table 1). Specifically, the network density reflects the ratio of the existing number of connections in a green innovation ecological network to the theoretical maximum number of connections. The greater the value, the stronger the ecological innovation chain between cities. Network structure entropy describes the order of the evolution of a green innovation ecological network, and is the quantitative expression of its self-organization effect. The greater its value, the greater the ecological network’s chaos degree, and vice versa, the stronger the ecological network’s order. Hierarchy reflects the connectivity gap between nodes in the green innovation ecological network and indirectly describes nodes’degrees of control of the green innovation resources in the ecological network. The larger the fitting coefficient, the more serious the differentiation of the ecological network for green innovation is. Centrality describes the connectivity of urban nodes in the green innovation ecosystem, with the average distance reflecting the flow rate of green innovation elements within the ecological network. The greater the value, the more nodes the elements pass through, and the worse the transmission speed and fluency of an ecological network for green innovation. Construction of complex network evolution game model An evolutionary model can predict the direction of group evolution by simulating the competition and cooperation among different biological populations in nature, and it is widely used in social and economic fields, especially in analyzing the behavior of enterprises in the market (Zhang et al., 2022a; Benitez et al., 2022; Barile et al., 2022). This study chooses an evolutionary game model to discuss the diffusion process of green innovation behavior. Compared with the particle swarm optimization algorithm and genetic algorithm, its advantages primarily involve dealing with dynamic interaction and strategy evolution, especially the bounded rationality of players, which is very important to understanding the evolution of green innovation ecosystems. Therefore, due to incomplete information and cognitive biases among participants, they cannot obtain the best choice through one decision, but must combine the strategies of other decision makers and the changes in the external environment, and then gradually approach the satisfactory strategy through constant "trial and error." This "trial and error" process is macroscopically manifested as the diffusion of game strategies on the green innovation ecological network and microscopically interpreted as the learning or imitation of game strategies among green innovation subjects. The evolution game model remains a "black-box test" analysis process, which divides the participants into different game groups according to the game strategy, and judges the final evolution direction through the change in the number of groups. Notably, the game behaviors among individual members in different groups are random, which is inconsistent with the basic law of green innovation subject’s preferential imitation and preference attachment. However, the preference attachment characteristics of green innovation ecological networks limit the game set of green innovation subjects, and simultaneously follow the causal relationship of ecosystem evolution in Fig. 1. Therefore, it is necessary to build an evolutionary game model based on a green innovation ecological network. Additionally, we optimize the evolutionary game model of complex networks. In prior research, random networks have usually been constructed by setting relevant parameters (centrality, network density, etc.) to replace real networks as the carriers of evolutionary game models. Although the vast majority of networks, in reality, have a power-law distribution and scale-free characteristics, random networks do not account for geographical space distance and cannot accurately describe changes in network characteristics. Therefore, its essence remains the analysis mode of the "black box test" (Bai et al., 2021; Dedehayir et al., 2018). Thus, the game model of complex network evolution is constructed based on the green innovation ecological network and the following assumptions are presented. Assumption 1: Green innovation subjects determine their behavioral strategies according to innovation ability, market environment, other players’strategies, and risk tolerance. This means that they can adopt the strategy of {active green innovation}, continuously increase investment in green innovation, and develop new markets. Similarly, they may also adopt the strategy of {negative green innovation} to avoid risks and reduce costs. The strategic space of each green innovation subject is {positive green innovation, negative green innovation}, and the proportion of innovation subjects adopting the {positive green innovation} strategy is d, and the proportion of innovation subjects adopting the {negative green innovation} strategy is 1 din the whole green innovation ecosystem. Assumption 2: In the absence of any competition or cooperation among green innovation subjects, basic profits can still be made. The basic profit of the innovation subject adopting the {positive green innovation} strategy isR1, while the basic profits of the innovation subject adopting {negative green innovation} strategy isR2. Assumption 3: Cooperation requires an additional cost C, and the proportion of innovation subjects adopting the two strategies is b and 1 b, respectively. The profits DRobtained from cooperative R&D will be distributed according to the ratios of aand 1 a. In the process of cooperative innovation, any party can gain additional profitB1and B2due to resource sharing after betraying their partners, but this behavior will also pay the default cost P. Assumption 4: The government will provide financial subsidy G to the innovation subject that adopts the strategy of {positive green innovation}, but will simultaneously also adopt a carbon tax, pollution tax, energy use rights, and other governance measures, which will be recorded as pollution tax rate T. The pollutant discharge of innovative subjects adopting {positive green innovation} and {negative green innovation} strategies is recorded as Q1and Q2, respectively. Assumption 5: After completing a round of the game, the players will compare their profitUiwith the average profitUave and judge Table 1 Characteristic indicators of green innovation ecological network. Index Calculation method Variable meaning Network structure entropy CðXÞ¼P m i¼1 pilnðpiÞCðXÞrepresents the entropy of network structure, pirepresents the proportion of green innovation ecological chain strength of cityiin the total sample, and mrepresents the number of samples, which is 286 here. Network density CR¼G0 GCRrepresents the density of the green innovation network, G0represents the actual number of connections of the green innovation network, and Grepresents the theoretical maximum number of connections. Mean distance L¼1 1=2mðmþ1ÞPijDij Lrepresents the average path of a green innovation network, and that other variables are consistent with its predecessor. Centrality CRB ¼Ui m1CRBrepresents the degree center of cityi, and Uirepresents the number of connections between cityiand other cities. Hierarchy Kt¼CðK rankÞqKirepresents the vector composed of the degree centers of all cities, K rank represents the order of Ktfrom largest to smallest, qis the hierarchical fitting coefficient, and Cis a constant. R.-J. Zhang, H.-W. Tai, Z.-X. Cao et al. Journal of Innovation & Knowledge 9 (2024) 100500 7 whether to change their strategies accordingly. If the profits are lower than the average profit of nodes, they will imitate other node strategies with a specific probability according to the profit gap. The specific probability calculation formula is as follows: pro ¼1 1þexp½ðUiUaveÞ=kð3Þ where kis external noise. When k!0, it means that bounded rationality and external environmental influence will hardly change the player’s strategy. When k!1, it shows that bounded rationality and the external environment greatly influence the players’strategic choices, so that they cannot make rational judgments. Assumption 6: Game participants will disconnect the least profitable node connected to themselves and randomly search for other nodes in the green innovation ecological network with which to establish connections. This disconnection and reconnection mechanism reflects the feedback effect of the strategic choices of the green innovation subject on the system’s evolution and also describes the preference and attachment characteristics of the green innovation ecological network. The above analysis and assumptions support the construction of the payment matrix for the evolution game of green innovation ecological networks (Table 2). The algorithm in Appendix A simulates the diffusion process of the {positive green innovation} strategy of green innovation subjects on a green innovation ecological network. Data exploration Green innovation efficiency index system The construction of a green innovation efficiency index system must follow the principles of comprehensiveness, systematicness, and hierarchy, and reflect the embeddedness of green innovation activities in societies, economies, and ecology (Table 3). From the input perspective, human beings, as the most basic elements in green innovation activities, have the characteristics of flexibility and initiative, and are both leaders and participants in the process of green innovation (Zhang et al., 2022a;Ba et al., 2021). The quality and quantity of human capital will directly affect the efficiency and profit of green innovation activities, especially the cultivation and available pool of high-quality talent. Notably, core technical talents play an important role in promoting and stimulating the green innovation potential of innovation subjects; therefore, the number of R&D personnel was chosen to represent human capital investment. R&D funds are the power guarantee of the entire green innovation process, function as catalysts in the smooth progress of the green innovation process, accelerate technological research, and also provide basic support for developing new projects. The R&D funds of innovative enterprises in China primarily come from self-financing and government subsidies, while scientific research institutions and institutions of higher learning primarily rely on government subsidies and state funding. R&D investment, government financial subsidy, number of new product development projects, and scientific and technological expenditure are used to characterize R&D investment. Yet, green innovation activities must also consider resource consumption. Due to data availability, this study did not consider the consumption of natural resources, such as land and water, but chose coal, natural gas, electricity, and other resources to represent the resource input of green innovation activities. As described earlier, the interest demands of different green innovation subjects differ. Enterprises usually focus on developing new technologies to ensure their core competitiveness, seek niche markets, and gain profits through developing new technologies, processes, or products. In contrast, universities and scientific research institutions focus more on acquiring patents, publishing academic papers, and other achievements. Therefore, the number of authorized patents, technology market turnover, and the number of academic papers published are used as the expected output of green innovation efficiency. Additionally, the number of unauthorized patents and the comprehensive index of environmental pollution are used to express unexpected output (Zhang et al., 2022b). Data source and verification Since 2010, China has successively presented strategic measures such as "green development," "innovation-driven," and "new development concept," which are very similar to the United Nations’17 Sustainable Development Goals (SDGs). Studying the relationship between green innovation subjects’strategy of diffusion and the evolution of the green innovation ecological network during this period can provide a model template for the construction and optimization of a regional green innovation ecosystem. A total of 286 Chinese cities from 2010 to 2021 were selected as research samples, and the data Table 2 Payment Matrix of Green Innovation Evolutionary Game. Participant B Positive Green Innovation Passive Green Innovation Participant A Positive Green Innovation p1 a:R1bCþaDRþGTQ1 p1 b:R2ð1bÞCþð1aÞDRþGTQ1 p2 a:R1bCþPTQ1þG p2 b:R2PþB2TQ2þð1bÞC Passive Green Innovation p3 a:R1bCPþB1TQ2 p3 b:R2þPð1bÞCTQ1þG p4 a:R1TQ1 p4 b:R2TQ2 Table3 Index system of green innovation efficiency. Target layer Criteria layer Index layer Unit Invest human capital number of R&D personnel person R&D funds amount of R&D investment ten thousand yuan government subsidy in technology and finance ten thousand yuan science and technology expenditure ten thousand yuan number of new product development projects item resource consumption total energy consumption ten thousand tons standard coal Output expected output authorized amount of patent item technical market turnover ten thousand yuan number of papers published piece unexpected output patent unauthorized quantity item comprehensive index of environmental pollution % R.-J. Zhang, H.-W. Tai, Z.-X. Cao et al. Journal of Innovation & Knowledge 9 (2024) 100500 8 its promoting effect on network density is second only to the default cost and sewage tax rate. Here, the collaborative innovation profit increased by 45 %, the network density increased by 30.233 %, and the network hierarchy decreased by 15.928 %. Cooperative innovation cannot only enhance the flow of green innovation elements among regions and improve the efficiency of factor allocation but can also provide favorable conditions for narrowing the gap in green innovation among regions. (3) The initial strategy proportion and fiscal subsidy have limited influence on the green innovation ecological network. Although the initial strategy proportion will affect the diffusion of the {positive green innovation} strategy in the green innovation ecological network and the convergence of the diffusion curve, it lacks a strong influence on the overall network characteristics through the green innovation subject. Yet, the financial subsidy’s influence on the green innovation ecological network is primarily reflected in the minor change in network structure entropy. Policy implications Green innovation is no longer limited to organizations or individuals but is reflected in the interactions and couplings of innovation ecosystems. China has yet to fully establish a natural green innovation ecosystem but has an incomplete green innovation ecosystem guided by policies and plans. This study focuses on the evolution of green innovation ecosystems, summarizes the OTEMC structural paradigm, and presents a causal analysis framework for the evolution of green innovation ecosystems. It also constructs an evolutionary game algorithm based on the green innovation ecological network to discuss the diffusion law of green innovation behavior, which has certain theoretical significance for enriching the innovation management framework and related theoretical methods of system engineering. Additionally, the influence direction and degrees of pollution tax rate, cooperative innovation profit, and financial subsidy on the diffusion of innovation behavior in the network are examined through simulation, thereby providing decision support for management departments and innovative enterprises to adopt appropriate green innovation strategies. Based on the research findings, this paper presents the following targeted suggestions. (1) Considering the provincial capitals or central cities in the central and western regions of China as strategic support points, focusing on planning and the layout of green technology innovation bases, such as new functional materials, new energy, hydrogen storage technology, and carbon capture and storage, encourages talents, capital, and other green innovation elements to gather in the region and accelerate the cultivation of independent innovation capabilities of core technologies. Additionally, this provides full play to the innovation spillover effect of core cities such as Chongqing, Chengdu, and Wuhan, promotes the growth of green innovation networks in the central and western regions, and fills the "network structure depression" in Yunnan and Guizhou. (2) Provide full play to the complementary roles of different types of green innovation subjects to improve the overall regional green innovation efficiency, release the green independent innovation potential of innovation subjects, encourage large-scale scientific research institutions and universities to focus on breakthroughs in green innovation system, management system, and mechanism, and frontier basic fields. Additionally, fully recognize the sensitive advantages of enterprises related to market demand and improve the efficiency and profitability of technological transformation. Using China’s eastern coastal areas as a springboard, aim at the forefront of international green innovation, actively seek international cooperation and innovation, and promote China’s niche in the global green innovation ecosystem. (3) Strengthen the facilitating role and service awareness of local governments in building a green innovation ecosystem and reduce the risks associated with green innovation failure and integrity through government scientific and technological innovation subsidies, green finance, innovation funds, and other policy measures to enhance the enthusiasm of enterprises for green collaborative innovation. By strengthening the stimulation of carbon taxes, pollution taxes, and other environmental regulation measures for innovation subjects, a good green innovation environment will be created. Conclusions and discussion Conclusion induction The regional green innovation ecosystem is a giant, open, and complex system formed by green innovation cooperation among cities, and is deeply rooted in society, the economy, and the ecosystem. This study combines and summarizes the basic characteristics of various innovation ecosystems, the OETMC structural paradigm of innovation ecosystems, and under the guidance of this paradigm forms a causal analysis framework of green innovation ecosystem evolution. This is based on the behavior of green innovation subjects, supported by green innovation efficiency, and aimed at a green innovation ecological network. Based on the analysis framework, a green innovation ecological network with green innovation efficiency as the core index was constructed by selecting the relevant data of 286 Chinese cities from 2010 to 2021, and the diffusion process and sensitivity of a "positive green innovation" strategy in the green innovation ecological network were examined and discussed. The primary conclusions are as follows. (1) The maturity and complexity of the green innovation ecological network have been significantly improved, and the network Table 5 Comparison of characteristic indexes of green innovation ecological network after simulation. Network density Network structure entropy Mean distance Hierarchy Type A Type B Type C d¼0:1 0.0100 0.5287 2.0772 1.3695 580,214 156,236 40,125 d¼0:9 0.0104 0.5067 1.9493 1.2788 589,548 158,062 40,151 DR¼20 0.0086 0.5324 2.1155 1.2858 560,883 172,421 41,164 DR¼65 0.0112 0.4949 1.7480 1.0810 650,140 175,321 41,647 P¼10 0.0090 0.5460 2.1380 1.3587 608,372 162,342 51,241 P¼45 0.0115 0.4851 1.7242 1.2741 665,822 184,211 51,976 G¼20 0.0086 0.5622 2.0381 1.3491 647,153 164,216 48,532 G¼80 0.0123 0.5461 2.0286 1.2648 555,401 170,145 49,321 T¼0:15 0.0092 0.5376 2.0675 1.2965 604,819 163,515 50,421 T¼0:55 0.0135 0.4755 1.8787 1.1830 649,272 174,216 51,532 Note: A, B, and C represent , , respectively. R.-J. Zhang, H.-W. Tai, Z.-X. Cao et al. Journal of Innovation & Knowledge 9 (2024) 100500 15 density has been continuously improved. However, both M-density and S-density remain at low levels and there are always large numbers of blank connections. These are the key constraints hindering the evolution of the network structure and simultaneously lead to the double imbalance of the spatial-temporal distribution and hierarchical structure of the green innovation ecological network. Although the emergence of a large number of long-range connections means that the geospatial distance constraint is weakened, it also slows the embedding of edge nodes. Additionally, it is notable that this green innovation ecological network has formed a pattern of "Point-axis," "Radial," and "N-tuple" staggered and coexisting locally. (2) The initial strategy proportion determines the convergence position of the diffusion path of the {positive green innovation} strategy in the green innovation ecological network. However, due to the existence of network preference attachment, power law distribution characteristics, and the problem of "virtual proportion interval," regardless of what the initial strategy proportion takes, the complete diffusion of the {positive green innovation} strategy cannot be realized. With the increase of cooperation innovation profit, default cost, and financial subsidy, the diffusion path of the {positive green innovation} strategy moves upward, and the marginal utility decreases with the increase in simulation value. Pollution tax rates have "duality," meaning that while appropriate environmental regulations can encourage green innovation subjects to adopt a "positive green innovation" strategy, an excessive pollution tax rate will cost innovation subjects more. (3) The default cost and pollution tax rate have accelerated the formation and reconstruction of a green innovation ecological network, and its operational mode involves increasing the opportunity cost of green innovation subjects to maintain their enthusiasm for cooperation. The feedback effect of cooperative innovation profit on the green innovation ecosystem is primarily reflected in reducing the shortest average distance within the network, which provides conditions for narrowing the gap in green innovation among regions. Notably, the initial strategy proportion and financial subsidy have limited influence on the microstructure of the green innovation ecological network. Discussion and influence This study aims to reveal the diffusion law of green innovation subject behavior strategy in complex networks, simulate the diffusion process by constructing a complex network evolution game model based on green innovation ecological network, and obtain enlightening results. Including the local spatial pattern of "dot-axis," "radial," and "N-tuple," the strategy of "positive green innovation" cannot achieve complete convergence under any initial strategy proportion, and the influence of pollution tax rate on " positive green innovation" strategy is dual. These results provide a reference for management departments to formulate scientific control measures and also help innovative enterprises adopt appropriate development strategies to improve resource utilization efficiency and reduce innovation risks. Compared with the existing research, this study presents a new perspective on the evolution of the microstructure of the green innovation ecological network and reveals its stage characteristics from "Point-axis" to "N-tuple" and from simple structure to complex structure. This result supplements the research conclusions of Zhang et al. (2023) and Xu et al. (2022) on the evolution of green innovation ecological networks. However, the result that the strategy of "positive green innovation" has not achieved complete convergence is inconsistent with the findings of Ramkumar et al. (2022) due to different model settings. When we built this model, we chose to use the real green innovation ecological network instead of a randomly generated virtual network. Thus, more node characteristics and network attributes are included in the present model. Comparatively, the research results of this paper are closer to reality. The impact of the pollution tax rate on green innovation is usually verified using an econometric model in existing research. However, we use the game model of complex network evolution to test the influence of its pollution tax rate on green innovation behavior. This generated a result that is almost consistent with Teng et al. (2022) and provides a new method and tool for subsequent research. Although some enlightening conclusions have been made in this paper, the following limitations remain. Firstly, for the problem that the diffusion path of the {positive green innovation} strategy in the network cannot converge completely at any initial strategy ratio, we believe that this is an intuitive manifestation of the nonlinearity of complex systems, and therefore it is worth further examining its causes. Secondly, when establishing simulation parameters, all green innovation agents have the same attributes by default, but the model we built can completely simulate the game relationship between different types of green innovation agents by adjusting parameters. Thus, setting differentiated basic profit levels, for example, can simulate the game relationship between core enterprises and general enterprises. Finally, this study believes that future research should focus on the interaction between different types of innovation subjects and the linkage effects of the macro-evolution direction of green innovation ecology. This may be an effective way to combine complex network theory with an econometric model to further explore this issue. Declaration of competing interest The authors declare that they have no known competing financial interests or per-sonal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Ren-Jie Zhang: Writing −original draft, Visualization, Software, Methodology. Hsing-Wei Tai: Writing −review & editing, Supervision, Investigation. Zheng-Xu Cao: Writing −review & editing. ChiaChen Wei: Writing −review & editing, Resources. Kuo-Tai Cheng: Supervision, Formal analysis. Acknowledgments This work was partly supported by the National Social Science Foundation [grant numbers 19BJY085] and Shandong Science Foundation [grant numbers ZR2020MG015]. Any opinions, findings, conclusions, and recommendations expressed in this paper are those of the authors. 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