Evolutionary Game and Simulation of Collaborative Green Innovation in Supply Chain under Digital Enablement

: The deep integration of digital technologies has given rise to the development of new industries and models in various sectors, as well as new opportunities and challenges. Whether digital transformation can drive collaborative green innovation in the supply chain has also become an important topic of great interest, which has not yet been resolved. In this paper, we study the impact of digital enablement on collaborative green innovation in supply chain enterprises in order to assist in reasonable strategic decision making. An evolutionary game model is constructed for both upstream and downstream supply chain companies under digital enablement, following which the model is solved and systematically simulated. Our main ﬁndings are as follows: The inﬂuencing factors of collaborative green innovation in the supply chain can be divided into driving factors, blocking factors, and regulating factors. After digital enablement, the effect of the drivers of collaborative green innovation is more obvious, the side-effects of the deterrents are weakened, and the threshold of the positive effect of the moderators is expanded. Overall, digital enablement helps to promote collaborative green innovation in the supply chain, and companies should apply digital technology to enable collaborative green innovation.


Introduction
Since the Industrial Revolution, the mode of production that aims to maximize economic benefits has led to serious ecological and environmental issues, threatening the sustainable development of human society [1].Promoting environmental protection and sustainable development has become a key focus for countries around the world, as well as an important factor affecting the development of companies in various sectors.Under the multiple pressures of government, society, and competitors, companies must shoulder the responsibility of protecting the environment while pursuing economic benefits [2].Green innovation, also known as ecological innovation, aims to reduce environmental risks, emphasizing that companies must improve their awareness of environmental protection in the process of innovation and gradually realize the ecologicalization of production processes and products [3].Due to its attributes of taking into account economic, social, and environmental effects, green innovation has become an important way for companies to effectively reduce environmental risks while achieving economic growth [4].
With the development of economic globalization, green innovation is difficult for a single company to achieve, requiring all companies in the supply chain to cooperate to improve the efficiency and share the risks of green innovation [5].Fontoura et al. [6] have stated that supply chain collaboration contributes to green technology innovation and improves green innovation performance.Companies in the chain cooperate in the form of an alliance in order to complete a series of activities from design to production of new products, involving the integration of knowledge, technology, organization, and systems among companies, effectively optimizing resource allocation, reducing economic costs [7], giving full play to systematicness [8], achieving the overall effect that a single subject cannot achieve and, finally, promoting the efficient operation of the supply chain and the win-win of economic benefits [9].The higher the degree of collaboration, the easier it is for companies to carry out green innovation [10].Thus, promoting collaborative green innovation in the supply chain is an inevitable requirement and urgent task for sustainable economic and social development [11].
In order to maximize their own interests, the companies in the supply chain will constantly adjust their coordination strategies, such that there are evolving game behaviors in the coordination process.Collaborative green innovation in the supply chain often fails due to poor information communication between companies, the mismatch between the synchronous R&D capabilities of suppliers and the needs of manufacturers, the high cost of green collaborative innovation, and the lack of motivation of collaborative innovation, which seriously hinders the green innovation of companies [12].
In the digital age, promoting green technology innovation among the companies in a supply chain requires not only innovation in terms of the system and mechanism, but also the enablement of digital technology.Digitalization indicates that an organization, (or industry, country, and so on) adopts or uses digital technology to create new value, having a transformative impact on the organization [13].Companies use digital technology to acquire corresponding skills and abilities [14], as well as higher autonomy, independence, and free development space [15], thus realizing the individual leap toward development [16].
Based on the theory of ecological modernization, digital enablement can combine digital technology with green innovation activities [17], effectively reducing the fuzziness of green innovation activities [18], improving company innovation efficiency [19], and reducing company energy consumption and R&D costs, consequently improving the technological innovation capability, core competitiveness, and sustainable green innovation of a company [20].Digital enablement has changed the original production mode, organizational form, business model, and innovation theory [21], endowing companies with higher productivity and more intellectual capital, improving the ability of companies to use data for innovation, and expanding the connotation of product and service innovation [22].Digitalization can break the limitations of time and space, enhance connectivity among innovation participants, promote information exchange and integration between companies [23], improve communication and information exchange efficiency [24], effectively expand the scope of communication, and help to promote cooperation among different members [25].By greatly improving resource allocation efficiency, it can reduce the cost of collaborative innovation and improve company connectivity, intelligence, and analysis capacity [26].
Digitalization can be seen as conducive to overcoming multiple obstacles, such as poor information communication between companies in the supply chain and the mismatch between the input of the production factor and the terminal demand, while effectively empowering green innovation [27].For example, as a partner to many car companies, the power battery supplier CATL makes full use of digital technology to enable collaborative green innovation in the supply chain.Using digital technology, CATL connects upstream and downstream data in the supply chain, effectively solving information communication and resource allocation problems to achieve integration of R&D and manufacturing, the manufacturing supply chain, and manufacturing services, resulting in good results such as a 50% reduction in development cycles, a 21% reduction in operating costs, a 75% reduction in product defect rates, a 24% increase in overall resource utilization, and a 56% increase in production efficiency [28].Therefore, it is of great practical significance to deeply study the collaborative green innovation of supply chain enterprises against the background of digital enablement.
In terms of theoretical research, the existing literature has mainly focused on green supply chain management [29], the impact of subsidies and policies on green innovation in supply chain [30], supply chain green innovation performance [31], customer's influence on green innovation in the supply chain [32], supply chain resilience and safety [33], supply chain green innovation partner selection, and so on [34].Although some schol-ars have conducted detailed analyses on the factors that influence collaborative green innovation in the supply chain [35], few studies have thoroughly discussed the mechanism and effect of digitalization on collaborative green innovation in the supply chain.Feng et al. [36] have stated that, in the era of Industry 4.0, supply chain companies should integrate digital technology into supply chain green innovation management activities.Zhang et al. [37] have stated that the ability of supply chain enterprises to quickly organize and cope with changes (i.e., their agility) has a significant positive impact on green product and process innovation and is conducive to promoting the company's green innovation performance.Digitization is an important means for improving the agility of the supply chain [38].Therefore, digital technology can improve the green innovation performance of and promote green innovation in the supply chain [39].
With the increasingly urgent need for companies in the supply chain to carry out green innovation collaboratively and the increase in digital enablement, the practice of green collaborative innovation in the supply chain urgently requires relevant theoretical guidance.However, the existing literature has not yet answered how companies in the supply chain can achieve green innovation through cooperation in the context of digital enablement.Considering the previous studies, this paper integrates the mechanism of digital enablement with collaborative green innovation in the supply chain, and deeply analyzes its influence and mechanism on collaborative green innovation in the supply chain using game theory, which improves upon and supplements relevant theories.
In this paper, an evolutionary game model of collaborative green innovation in the supply chain is proposed, which includes downstream manufacturers and upstream suppliers.First, we discuss the influence of digital enablement on the strategies of companies in the supply chain regarding collaborative green innovation.After that, by comparing and analyzing the effects of other factors influencing collaborative green innovation with and without digital enablement, we further analyze how digitalization can empower the companies in the supply chain according to these factors, thus affecting collaborative green innovation.The main findings of this study are as follows: (1) Digitalization promotes collaborative green innovation by reducing the cost of collaborative innovation and improving the income from collaborative innovation.With the increasing intensity of digital enablement, the willingness of companies in the supply chain to participate in collaborative green innovation is continuously strengthened.(2) The factors affecting collaborative green innovation in the supply chain can be summarized as driving factors, blocking factors, and regulating factors.After digital enablement, the effect of driving factors becomes more obvious, the negative effect of blocking factors is weakened, and the regulating factors play a role in a larger threshold range.
In summary, this study considers the problem of collaborative green innovation in the supply chain under the background of digital enablement, which can help companies in the supply chain to better realize collaborative operations through the help of digital technology-a concept in line with sustainable development.Based on previous studies, we use evolutionary game theory to build an evolutionary game model of collaborative supply chain innovation, discuss the choice of collaborative innovation strategies by companies under different circumstances, use the MATLAB R2020b software to simulate the model, and discuss the mechanism and function of digital enabling collaborative green innovation in the supply chain, as well as the driving factors, blocking factors, and regulating factors associated with collaborative supply chain green innovation.This study provides theoretical support for the collaborative green innovation decision making of companies, while also contributing to the sustainable development of the manufacturing industry.

Problem Description and Basic Hypothesis
Evolutionary game theory is based on bounded rationality, in which individuals with limited information constantly adjust their strategies at the margin, according to their vested interests, to pursue improvement of their own interests [40].With the development of evolutionary game theory, many scholars have used it to discuss collaborative innovation from the perspectives of the innovation ecosystem and the innovation alliance [41].Some scholars have used evolutionary game theory to study collaborative innovation in the supply chain [42].
Green technology innovation requires cooperation among the companies in the supply chain, where the upstream and downstream companies are the main players of collaborative green innovation in the supply chain.For different interest motives, upstream and downstream companies in the supply chain present a game relationship in the collaborative green innovation process, with both having incomplete rational characteristics.Whether the two sides choose collaborative innovation is a process of multiple choices and adjustments, aiming at maximizing their own interests and constantly adjusting and improving strategies.
Therefore, we assumed that a supply chain with digital enablement is composed of upstream and downstream companies, and the decision-making choices of each company included "participation" and "non-participation".An evolutionary game model between the downstream green innovation demander and the upstream green innovation collaborator of the supply chain collaboration was constructed to study the influence of the behavioral interaction between the two parties and the system stability under different circumstances, as well as to analyze the influence of digital enablement and other influencing factors on the evolutionary results of the system.
Based on the above conditions, we present the following hypotheses.
Hypothesis 1. Downstream manufacturing company A is the demand side of collaborative green innovation in the supply chain.A can quickly and accurately obtain market information and personalized needs of users, put forward collaborative innovation needs, and choose collaborative innovation partners.Upstream supply company B is the collaborative green innovation partner of the supply chain, and B can obtain multiple collaborative innovations demand information, and make the best strategy choice according to the actual situation.

Hypothesis 2.
Companies A and B can choose two strategies.Their decision making is not disturbed by external factors.The probability that A chooses the cooperation strategy is x(0 ≤ x ≤ 1), and the probability that A chooses the non-cooperation strategy is 1 − x.The probability that B chooses the cooperation strategy is y (0 ≤ y ≤ 1), and the probability that B chooses the noncooperation strategy is 1 − y.

Defining Relevant Variables
Digital technology can promote change in factors such as the efficiency of collaborative innovation in the supply chain, partner selection of the innovation subject, and cost of collaborative innovation.These factors ultimately affect the strategic choice of the collaborative innovation subject [25].On one hand, digital enablement can improve the efficiency of collaborative innovation, reduce the cost of collaborative innovation, and thus promote both parties to choose collaborative strategies.On the other hand, due to digital enablement, game players can obtain more information and opportunities for partner selection, which has a negative impact on collaborative strategy selection.In this paper, the digital enablement coefficient (α) is used to reflect the degree of digital enablement: "1 + α" reflects positive enablement, while "1 − α" represents negative enablement.
In addition, collaborative green innovation in the supply chain is affected by many factors [43].Among them, government subsidies [44], collaborative innovation benefits and costs [45], benefit distribution mechanisms [46], reward and punishment mechanisms [47], and policy support are considered the main factors affecting the game strategy of collaborative innovation in the supply chain [48].Under the background of digital enablement, the influence of these factors on collaborative green innovation in the supply chain is worth further discussion.Therefore, we mainly selected these variables to build the model.They can be divided into two categories.
The first category mainly involves variables related to the benefits of collaborative green innovation.First, when players in games choose not to participate in synergy, the net benefits of independent innovation are S 1 and S 2 .Second, it is assumed that, when the companies choose to participate in collaborative innovation, there will be excess returns of collaborative innovation (M) which will not only be affected by the digital enablement coefficient (α), but also by the success probability of collaborative innovation (p) and the profit distribution ratio (l and 1 − l).When game players choose not to cooperate, they have the opportunity to cooperate with other players, which leads to opportunity income (E A and E B ).In addition, to support green innovation, the government will provide green innovation subsidies (G) to companies participating in collaboration; the proportion of subsidies is consistent with the profit distribution ratio.
The second category mainly involves variables related to the cost of collaborative green innovation.When choosing collaborative innovation, the players in the game must pay the cost of collaborative innovation (C), which should be shared by both parties, and the proportion of the cost is consistent with the distribution ratio of benefits.In order to realize digital innovation, both parties also need to pay the cost of digital transformation (C D 1 and C D 2 ).Furthermore, it is assumed that the game between the two parties is a strategic adjustment, made based on the fact that the party that agrees to cooperate has paid the cost of collaborative innovation.To limit the infringement of benefits caused by a breach of contract, when one party makes a choice of uncoordinated strategy, it will be regarded as a breach of contract and liquidated damages must be paid to the other party, which is indicated by the liquidated damages coefficient (k).
The relevant symbols and meanings of the variables used in the model are listed in the following Table 1.
Opportunity benefits of A obtained by not participating in collaborative innovation E 2 Opportunity benefits of B obtained by not participating in collaborative innovation

Evolutionary Game Modeling
According to the above assumptions, both the demander, A, and the collaborator, B, in collaborative innovation can take two states: Participating in collaboration and not participating in collaboration.Therefore, there are four combinations of collaborative green innovation strategy in the supply chain: {x,y}, {x,1 − y}, {1 − x,y}, {1 − x,1 − y}.The corresponding payoff matrix for the game is shown in Table 2.

B Participation y
No Participation 1−y

Revenue Function Construction
According to Table 2, when company A participates in or does not participate in collaborative green innovation, the expected benefits and average benefits are A x , A 1−x , and A, respectively, as described by the following formulae: The expected returns and the average returns of the companies participating and not participating in collaborative green innovation are B y , B 1−y , and B, respectively, as shown in the following equations:

Stable Solution of Replicator Dynamics Equation
According to the above revenue expectation function, the organizational dynamics equation for the evolutionary game of the collaborative green innovation demander A is shown in Equation (7), while the organizational dynamics equation for the evolutionary game of the collaborative green innovation collaborator B is shown in Equation (8).On this basis, according to the method proposed by Frideman, the Jacobian matrix can be constructed, as shown in Equation (9).

Analysis of Strategic Stability
The equilibrium point at P 1 (1,1) indicates that both sides of the game choose to participate in collaborative innovation.To judge the stability of this point, it is brought into the Jacobian matrix of the system, and the matrix becomes: with eigenvalues Similarly, by bringing the other three equilibrium points into the Jacobian matrix in Equation ( 9), the eigenvalues of each equilibrium point can be obtained, as shown in Table 3.According to the stability condition of the evolutionary game (detJ > 0 and trJ < 0), when all eigenvalues of the following equilibrium point are negative, the equilibrium point indicates an evolutionarily stable strategy (ESS).
Table 3. Eigenvalues corresponding to equilibrium points of the system.

Equilibrium Points
Eigenvalues U A1 and U B1 represent the innovation costs of company A and company B in the case of collaborative green innovation, respectively; U A2 and U B2 are the benefits after successful collaborative green innovation; U A3 and U B3 are the benefits from other opportunities obtained by not participating in collaborative green innovation; U A4 and U B4 represent the government subsidies obtained from participating in collaborative green innovation; and U 5 represents the liquidated damages paid by both parties due to withdrawing from the collaboration.In the following Table 4, we discuss the stable strategies of the evolutionary game under different scenarios.
Situation 1: ) is the only evolutionary stable equilibrium point, and both companies A and B choose to participate in collaborative green innovation.
This situation shows that, for both downstream company A and upstream company B, the collaborative green innovation income minus cost, plus the government green subsidy, is still greater than the sum of other opportunity income and possible liquidated damages, such that both parties are more inclined to choose to participate in the collaborative innovation strategy.It can be seen that, in practice, if we want to promote collaborative green innovation in the supply chain, we can improve collaborative innovation income and save innovation costs.Digital enablement plays an important role in this respect.Furthermore, from the government's perspective, improving subsidies for collaborative green innovation companies also has important and notable effects.
This situation describes that collaborative green innovation is difficult to achieve because the cost of collaborative green innovation is too high, the default cost required to quit the collaboration is too low, or the government green subsidy is not high enough to compensate for the default cost.If we want to break this deadlock, on one hand, we should increase the number of liquidated damages.However, more importantly, we should effectively reduce the cost of collaborative innovation and improve profits after successful collaborative innovation in order to promote collaborative green innovation.
Situation 3: < 0, the point P 3 (0,1) is the only evolutionary stable equilibrium point.While company A leaves the collaboration, company B is willing to continue to participate in collaborative green innovation.
This situation shows that, even with government subsidies, the net income obtained by company A choosing collaborative green innovation is still less than the sum of its opportunity income and liquidated damages; that is, it will abandon the intra-chain collaborative innovation in the period of strong external opportunity income.However, due to the relatively few external opportunities of company B, it is more willing to choose to continue cooperation.At this time, if we want to effectively promote collaborative green innovation in the supply chain, we can refer to the methods applicable to condition 1 and use digital and other technical means to further improve the benefits of collaborative innovation, save innovation costs, or increase government subsidies and other measures to promote collaborative innovation.
Situation 4: the point P 4 (1,0) is the unique evolutionary stable equilibrium point.Here, company A is willing to continue to participate in collaborative green innovation, while company B tends to quit the collaboration.
This situation is symmetric with situation 3, and its internal reasons and treatment measures are similar; as such, they will not be repeated in this paper.
Analysis of the above four situations indicates that the profitability of companies in collaborative innovation is the fundamental factor affecting collaborative green innovation in the supply chain.The main influencing factors of U A1 , U A2 , U A3 , U A4 , U B1 , U B2 , U B3 , U B4 , and U 5 include the digital enablement coefficient (α), the excess returns of collaborative green innovation (M), government green innovation subsidy (G), cost of collaborative green innovation (C), liquidated damages coefficient (k), profit distribution ratio (l), and other factors.In the following, we analyze the impacts of changes in these parameters on the strategic evolution of both companies.

Numerical Simulation
Based on the construction of the evolutionary game model and stability analysis of the equilibrium points, numerical simulation analysis was carried out using MATLAB software.According to the existing literature, data on collaborative green innovation in the supply chain under digital enablement are scarce, and it is difficult to obtain statistical data.According to the basic paradigm of simulation parameter research in the relevant literature [49], we consulted experts on simulation in fields related to the supply chain and carried out simulation in combination with the actual research scope.In view of the impact of green technology innovation by automotive supply chain companies on environmental sustainability, we investigated and visited 12 automotive supply chain companies in China, including FAW Jiefang, Chery, Sailun, Double Star, and so on, in order to understand their evolutionary game behavior in the process of collaborative green innovation in the supply chain.Through analysis, it was found that the following initial values were consistent with the actual situation of companies, and the specific settings are given in Table 5.First, the horizontal axis coordinate in the evolution result represents the time (t), while the vertical axis coordinate (P) is between 0 and 1, which represents the probability of selection by the game player.Second, in the initial state, the attitude of companies A and B toward cooperation should be neutral.Thus, the initial willingness to cooperate of both parties in the game was established as x = 0.5 and y = 0.5.Finally, in order to compare the influence of each parameter on the willingness to choose the collaborative green strategy before and after digital enablement, when simulating the situation without digital enablement, the values of relevant parameters (i.e., α, C D 1 , and C D 2 were all set as 0.

The Total Impact of Digital Enablement
The digital enablement coefficient (α) is a parameter reflecting digital enablement intensity.Figure 1 reflects the evolutionary simulation results of the strategic game between collaborative innovation parties with α set as 0.1, 0.3, and 0.5.With the increase in α, the effect of digital enablement appeared, and the rising rate of the probability curve accelerated.When α was 0.1, the probability curve representing the willingness of both parties to co-operate converged to 1 at a time of 1.5; meanwhile, when α was 0.3 or 0.5, the time for the probability curve to reach a value of P = 1 was shortened.
The simulation results show that α plays a positive role in promoting green innovation in supply collaboration.The greater the enablement strength, the greater the probability that both parties will choose to cooperate in collaborative green innovation, and the more stable the cooperative relationship.

Digital Enablement through Driving Factors
In Figure 2a, under digital enablement, with increased M, both parties gradually have a strong willingness to cooperate and finally reach collaborative cooperation.The probability of strategy selection converges to 1, approaching the equilibrium point (1,1).When M was 18, it took the shortest time for the intention to tend to 1.
the time for the probability curve to reach a value of P = 1 was shortened.
The simulation results show that  plays a positive role in promoting tion in supply collaboration.The greater the enablement strength, the grea bility that both parties will choose to cooperate in collaborative green innov more stable the cooperative relationship.

Digital Enablement through Driving Factors
In Figure 2a, under digital enablement, with increased , both par have a strong willingness to cooperate and finally reach collaborative coo probability of strategy selection converges to 1, approaching the equilibriu When  was 18, it took the shortest time for the intention to tend to 1.In Figure 2b, when there was no digital enablement, with the increase in , although it still promoted collaborative innovation, the willingness of collaborative innovation obviously decreased, the rate of intention achievement was slowed down, and the time required for the convergence to 1 was delayed.Thus, it can be seen that, without digital enablement, the effect of  is weakened.
Government green collaborative innovation subsidies also have a positive impact on collaborative green innovation.As shown in Figure 3, with the increase in , the willingness of both parties to choose to participate in the collaboration gradually increased.Under digital enablement, the time required for strategy convergence to 1 was in the range of 1-1.5, while it was 1.5-2 without digital enablement.Therefore, digitization has a sig- In Figure 2b, when there was no digital enablement, with the increase in M, although it still promoted collaborative innovation, the willingness of collaborative innovation obviously decreased, the rate of intention achievement was slowed down, and the time required for the convergence to 1 was delayed.Thus, it can be seen that, without digital enablement, the effect of M is weakened.
Government green collaborative innovation subsidies also have a positive impact on collaborative green innovation.As shown in Figure 3, with the increase in G, the willingness of both parties to choose to participate in the collaboration gradually increased.Under digital enablement, the time required for strategy convergence to 1 was in the range of 1-1.5, while it was 1.5-2 without digital enablement.Therefore, digitization has a significant effect on promoting collaborative green innovation.
viously decreased, the rate of intention achievement was slowed down, and the time required for the convergence to 1 was delayed.Thus, it can be seen that, without digital enablement, the effect of  is weakened.
Government green collaborative innovation subsidies also have a positive impact on collaborative green innovation.As shown in Figure 3, with the increase in , the willingness of both parties to choose to participate in the collaboration gradually increased.Under digital enablement, the time required for strategy convergence to 1 was in the range of 1-1.5, while it was 1.5-2 without digital enablement.Therefore, digitization has a significant effect on promoting collaborative green innovation.Similarly, we also simulated the impact of the liquidated damages coefficient () and the probability of success of collaborative innovation () with different values on the collaborative green innovation behavior of upstream and downstream companies with or without digital enablement.The simulation results indicated that these factors are also beneficial in promoting collaborative green innovation.Under digital enablement, the Similarly, we also simulated the impact of the liquidated damages coefficient (k) and the probability of success of collaborative innovation (p) with different values on the collaborative green innovation behavior of upstream and downstream companies with or without digital enablement.The simulation results indicated that these factors are also beneficial in promoting collaborative green innovation.Under digital enablement, the promotion effect of these factors on collaborative green innovation was obviously enhanced.In summary, the application of digital technology can act as a catalyst for driving factors, helping to promote collaborative green innovation in supply chains.

Digital Enablement through Blocking Factors
Figure 4a shows the evolutionary simulation results of strategy combination considering collaborative green innovation costs C of 6, 8, and 10 under the effect of digital enablement.The simulation curve converged to 1 in the time range of 1-1.5, approaching the strategic equilibrium point (1,1).With an increase in the cost value, the speed of choosing the collaborative innovation strategy gradually slowed down and the willingness to cooperate decreased obviously.
As shown in Figure 4b, in the absence of digital enablement, the convergence time of both strategies to 1 was longer than that in the enablement state, and the convergence speed obviously slowed down.When C was 10, the convergence time to 1 was the longest, and both parties finally realized cooperation at a time in the range of 2-2.5.
The simulation results indicated that an increase in the collaborative innovation cost C is not conducive to driving the innovation subject to participate in collaborative innovation strategy and, thus, has a blocking effect on collaborative green innovation.The application of digital technology can save the cost of collaborative innovation and increase the excess return of collaborative innovation, to a certain extent, such that the ability of companies to cope with the increase in collaborative cost can be enhanced, which is beneficial for both parties, in terms of choosing collaborative innovation strategies.
is not conducive to driving the innovation subject to participate in collaborative innovation strategy and, thus, has a blocking effect on collaborative green innovation.The application of digital technology can save the cost of collaborative innovation and increase the excess return of collaborative innovation, to a certain extent, such that the ability of companies to cope with the increase in collaborative cost can be enhanced, which is beneficial for both parties, in terms of choosing collaborative innovation strategies.In the same way, increases in the opportunity income of both parties ( and  ) and the digital costs ( and  ) also blocked the achievement of collaborative green innovation cooperation.With the help of digital technology, the opportunity benefits obtained by both parties without participating in collaborative innovation increased, to a certain extent.However, digitalization has obvious advantages in terms of saving costs and increasing benefits.After enablement, collaborative innovation subjects had a relatively strong willingness to participate in collaborative innovation, further proving that digita enablement plays a positive role in promoting collaborative green innovation in the supply chain as a whole.In the same way, increases in the opportunity income of both parties (E 1 and E 2 ) and the digital costs (C D 1 and C D 2 ) also blocked the achievement of collaborative green innovation cooperation.With the help of digital technology, the opportunity benefits obtained by both parties without participating in collaborative innovation increased, to a certain extent.However, digitalization has obvious advantages in terms of saving costs and increasing benefits.After enablement, collaborative innovation subjects had a relatively strong willingness to participate in collaborative innovation, further proving that digital enablement plays a positive role in promoting collaborative green innovation in the supply chain as a whole.

Digital Enablement through Regulatory Factors
Figure 5 shows the simulation results when the benefit distribution ratio (l) of company A is 0.3, 0.5, or 0.7, with and without digital enablement.An increase in l indicates that the proportion of benefits obtained by company B decreases.Therefore, whether there is digital enablement or not, with the increase in l, the willingness of company A to participate in collaborative innovation increases, while B's willingness to participate in collaborative innovation gradually weakens.
When l was 0.3, the willingness of company B to participate in collaboration was obviously higher than that of company A. When the value was 0.5, the willingness of company B to participate in the collaboration was weakened, while company A was more willing to participate in the collaboration.When it was 0.7, the distribution gap of the benefit ratio was large, and the willingness of company A to participate in collaborative green innovation was the strongest, while the strategy curve of company B increased slowly.
As shown in Figure 5a, under digital enablement, both parties finally chose collaborative innovation in the time interval of 1-1.5.In Figure 5b, without digital enablement, both parties cooperated within the time interval of 1.5-2.Similar phenomena were also observed when l was 0.3 or 0.5.After digital enablement, the cost of collaborative green innovation was reduced, but the excess income had increased.Within the same threshold range, both parties could achieve collaborative green innovation in a shorter time, and the threshold range for both parties to choose the benefit distribution ratio of collaborative innovation was expanded.
rative innovation in the time interval of 1-1.5.In Figure 5b, without digital enablement both parties cooperated within the time interval of 1.5-2.Similar phenomena were also observed when  was 0.3 or 0.5.After digital enablement, the cost of collaborative green innovation was reduced, but the excess income had increased.Within the same threshold range, both parties could achieve collaborative green innovation in a shorter time, and the threshold range for both parties to choose the benefit distribution ratio of collaborative innovation was expanded.The simulation results demonstrated that the proportion of benefit distribution has a moderating effect on collaborative innovation, and the appropriate proportion of benefit distribution helps to mobilize the enthusiasm of both sides to participate in collaborative innovation, thus promoting their cooperation.After digital enablement, the regulation of the benefit distribution ratio is enhanced, and collaborative green innovation of the supply chain can be realized within a larger threshold range.Therefore, digital enablement can promote collaborative green innovation by regulating factors.

Discussion
Collaborative green innovation in the supply chain provides an important measure to solve the problem of sustainable development, effectively promoting green innovation and alleviating various problems associated with the sustainable development of the economy, environment, and society.In order to achieve this goal, scholars have conducted extensive research.The simulation results demonstrated that the proportion of benefit distribution has a moderating effect on collaborative innovation, and the appropriate proportion of benefit distribution helps to mobilize the enthusiasm of both sides to participate in collaborative innovation, thus promoting their cooperation.After digital enablement, the regulation of the benefit distribution ratio is enhanced, and collaborative green innovation of the supply chain can be realized within a larger threshold range.Therefore, digital enablement can promote collaborative green innovation by regulating factors.

Discussion
Collaborative green innovation in the supply chain provides an important measure to solve the problem of sustainable development, effectively promoting green innovation and alleviating various problems associated with the sustainable development of the economy, environment, and society.In order to achieve this goal, scholars have conducted extensive research.
The first kind of research focuses on the promotion mechanism of collaborative green innovation in supply chains.For example, Zhang et al. [50] constructed a game model of green behavior of supply chain enterprises and conducted simulations.As a result, they found that enterprise green investment income and costs, co-benefits, spillover benefits, greenness and output of raw materials or products, and fines can influence collaborative green innovation behavior.
The second type of research focuses on the role of the government in collaborative green innovation.Yu et al. [43] discussed the role of government policies in promoting collaborative green innovation in a regional supply chain by constructing a tripartite collaborative innovation evolutionary game between the government and upstream and downstream enterprises.
The third kind of research discusses collaborative green innovation in the supply chain from the perspective of collaborative partner selection.For instance, Li [49] has focused on the mechanism of forming and operating green innovation partnerships between manufacturers and suppliers, and held that the value/profit sharing ratio between the partners, knowledge compliance of the partners, and product type for the green innovation are key factors affecting the partnership.
However, most of the existing research has ignored the impact of digital technology on collaborative green innovation in the supply chain.In order to make up for this deficiency, in this paper, we constructed an evolutionary game model between demanders and partners of collaborative green innovation in the supply chain.By solving and simulating the model, we could discuss the role of digital enablement and analyze the factors affecting the participation of supply chain companies in collaborative green innovation against the background of digital enablement.
On the basis of previous studies, we further summarized the factors affecting collaborative green innovation into driving factors, blocking factors, and regulatory factors.First of all, benefits from green innovation, probability of success, government green subsidies, and penalties for breach of contract are the driving factors affecting collaborative green innovation in the supply chain.Digital enablement further expands the chances of efficiency and success for collaborative green innovation, increases the benefits of collaborative green innovation, strengthens the role of drivers and, therefore, enables collaborative green innovation to be driven.
Second, the cost of green innovation, return of opportunity, and digital cost are blocking factors associated to collaborative green innovation in the supply chain.Digital enablement requires companies to pay a certain amount of digital construction costs and may result in losses due to increased opportunities for partners to choose other companies to work with.However, overall, digital enablement contributes more to effectively reducing the cost of collaborative green innovation, thus weakening the negative interference of the return of opportunity and facilitating collaborative green innovation.
Third, the proportion of benefit distribution has a regulatory effect on collaborative green innovation.Digital enablement promotes the sensitivity of the regulation of benefit distribution ratios and expands the threshold range of the positive role of regulation factors, which is conducive to collaborative green innovation of the supply chain.
In conclusion, digital enablement facilitates and promotes collaborative green innovation in the supply chain.Figure 6 shows the basic logic of digital empowerment.

Conclusions
Collaborative green innovation in the supply chain has become an important means to facilitate the sustainable development of the manufacturing industry.Whether the development of digital technology can promote collaborative green innovation is a key issue for relevant companies.In this study, we analyzed the influence of digital enablement on collaborative green innovation in the supply chain by constructing an evolutionary game model of supply chain collaborative green innovation, followed by solving and simulating the model.The results of this research show that digital enablement can effectively promote the collaborative green innovation of companies in the supply chain.
The conclusion of this paper has certain theoretical significance.The existing literature has carried out a relatively comprehensive study on the collaborative green innova-

Conclusions
Collaborative green innovation in the supply chain has become an important means to facilitate the sustainable development of the manufacturing industry.Whether the development of digital technology can promote collaborative green innovation is a key issue for relevant companies.In this study, we analyzed the influence of digital enablement on collaborative green innovation in the supply chain by constructing an evolutionary game model of supply chain collaborative green innovation, followed by solving and simulating the model.The results of this research show that digital enablement can effectively promote the collaborative green innovation of companies in the supply chain.
The conclusion of this paper has certain theoretical significance.The existing literature has carried out a relatively comprehensive study on the collaborative green innovation of supply chains.However, few studies have paid attention to the impact of digitalization on collaborative green innovation in the supply chain, as well as the changes in organizational structure, innovation mode, and innovation efficiency of collaborative green innovation in the supply chain against the background of digitalization.To some extent, the study of this paper has enriched the theories related to collaborative green innovation in the supply chain and provided a reference for scholars to carry out research in this field.
The preceding research also has some practical implications and sheds light on collaborative green supply chain management.First, the research conclusion shows that digitization contributes to collaborative green innovation.Companies within the supply chain should actively improve their own technology, make full use of digital technology, deepen their knowledge and information sharing, and improve the efficiency and chances of success of collaborative green innovation.Second, high digital costs will have a negative impact on collaborative green innovation.Companies should pay attention to maintaining the stability of collaborative relationships and make full use of safeguards (e.g., liquidated damages) to combat opportunism and "free-riding" behavior, as well as implementing cost-sharing mechanisms for collaborative innovation.Third, in the process of digitalization, companies should pay attention to cost control in order to avoid compromising collaborative green innovation due to high construction costs.Finally, the study found the positive effect of government subsidies on collaborative green innovation.The government can promote collaborative green innovation through policy and financial support for companies in the supply chain.
The research in this paper had some shortcomings, as follows.In the context of digitalization, this article discussed the game relationship of collaborative green innovation between upstream and downstream companies in the supply chain, based on a point-topoint bilateral relationship.Under the digital background, the innovation organization structure is network-like, and the collaborative green innovation system should be a multi-agent collaborative network system, with higher complexity in the number and functioning of its subjects.Therefore, in our follow-up study, we intend to focus on the collaborative innovation of multiple subjects in the green innovation ecosystem under a digital background.Specific research will involve considering how the government, companies, and other innovation organizations cooperate in the green innovation ecosystem while relying on the digital platform, as well as the role of the government and the platform in promoting collaborative green innovation.

Figure 1 .
Figure 1.Influence of α on collaborative green innovation.

Figure 2 .
Figure 2. Influence of  on collaborative green innovation: (a) Evolution results with digital enablement; and (b) evolution results without digital enablement.

Figure 2 .
Figure 2. Influence of M on collaborative green innovation: (a) Evolution results with digital enablement; and (b) evolution results without digital enablement.

Figure 3 .
Figure 3. Influence of  on collaborative green innovation: (a) Evolution results with digital enablement; and (b) evolution results without digital enablement.

Figure 3 .
Figure 3. Influence of G on collaborative green innovation: (a) Evolution results with digital enablement; and (b) evolution results without digital enablement.

Figure 4 .
Figure 4. Influence of  on collaborative green innovation: (a) Evolution results with digital ena blement; and (b) evolution results without digital enablement.

Figure 4 .
Figure 4. Influence of C on collaborative green innovation: (a) Evolution results with digital enablement; and (b) evolution results without digital enablement.

Figure 5 .
Figure 5. Influence of  on collaborative green innovation: (a) Evolution results with digital enable ment; and (b) evolution results without digital enablement.

Figure 5 .
Figure 5. Influence of l on collaborative green innovation: (a) Evolution results with digital enablement; and (b) evolution results without digital enablement.

Table 1 .
Model symbols and meanings.
x Probability of A choosing collaboration x ∈ [0, 1] y Probability of B choosing collaboration y ∈ [0, 1] S 1 Independent innovation benefits of A S 2 Independent innovation benefits of B M Excess returns of collaborative green innovation l Profit distribution ratio of collaborative innovation demanders l ∈ [0, 1] p Probability of success of collaborative innovation p

Table 2 .
Payoff matrix for both sides of the game.

Table 4 .
Analysis of equilibrium points and conditions of the system under different circumstances.

Table 5 .
Initial simulation parameter values.