Low-carbon technology innovation (LCTI) plays a crucial role in reducing carbon emissions (Shi et al., 2021; Gu et al., 2024; Wei et al., 2024b). LCTI serves as a crucial component in advancing sustainable and environmentally responsible business practices (Xu and Liu, 2024; Li Y. et al., 2024). LCTI optimizes energy use and improves resource allocation to lower carbon emissions. This eases the burden of green transformation for enterprises, addresses energy and environmental challenges, and supports sustainable economic growth (Qi et al., 2021; Chi et al., 2022).

Prior research has indicated that government interventions at the policy level, including financial incentives, regulatory sanctions, and carbon trading schemes, are essential for driving corporate innovation in low-carbon technologies (Wang and Chen, 2024). The literature focuses primarily on the influence of individual enterprises’ positioning, low-end enterprises within the supply chain, and financial institutions on their inclination toward green financial services. Concurrently, scholars should focus more on the crucial role played by financial institutions. To address this disparity, some scholars have explored factors pertaining to financial institutions, such as banking competition and credit financing (Liu and Zhao, 2024). Kong et al. (2024) emphasized that financial development fosters corporate green technology innovation. However, most studies rely on linear regression to analyze enterprise behavior in low-carbon technology innovation (Zhao et al., 2024).

Several scholars have examined the regulation of governments, financial institutions, and third parties from both static and dynamic perspectives. Wang W. et al. (2024) examined the strategic behaviors and interactions of governments, construction enterprises, and financial institutions in advancing carbon emission reduction (CER) by integrating regulatory and market-driven mechanisms. By formulating an evolutionary game model involving the government, cold chain logistics enterprises, and financial institutions, Wu R. et al. (2024) explored how environmental regulatory policies and green credit influence the improvement of low-carbon operational efficiency in cold chain logistics enterprises. A study by Guo et al. (2022) used various recycling structural models to assess how government regulations influence corporate efforts to reduce carbon emissions. Additionally, Zhang et al. (2023) proposed a tripartite evolutionary game model that includes the government, enterprises, and energy regulatory service centers (ESCs). They examined the influence of government subsidies on promoting independent innovation within photovoltaic enterprises. Similarly, Cui et al. (2020) and Xu J. et al. (2023) developed an evolutionary game model that incorporates four key stakeholders: the government, financial institutions, enterprises, and consumers. Their study demonstrated that the robustness of the green financial system positively influences sustainable development and clean production. Chen et al. (2021) explored the influence of government oversight on enterprise behavior via a two-party evolutionary game theory framework. Li Q. et al. (2024) explored the impact of government incentives and constraint mechanisms on carbon offset and carbon neutrality through an evolutionary game model incorporating local governments, tourism enterprises, and tourists. Although numerous scholars have utilized evolutionary game models to explore the effects of regulatory mechanisms imposed by governments and financial institutions on enterprises or consumers, there exists a limited body of research that specifically examines the impact of collaborative governance between these entities on enterprises’ low-carbon technological innovation. This is particularly true regarding the behaviors exhibited during the financing process for low-carbon production.

Several researchers have increasingly employed tripartite evolutionary game theory to depict and simulate stakeholder decision-making processes as well as conflict resolution strategies. Evolutionary games underscore dynamic equilibrium, rendering them more realistic. In the field of low-carbon technology innovation, Shi et al. (2023) and Zhou W. et al. (2024) applied tripartite evolutionary game theory to analyze the dynamic evolution process. The interactions among governments, financial institutions, and businesses are influenced by both internal and external factors. These stakeholders can ascertain an optimal strategy only through prolonged engagement; however, it remains unclear how their interactions will unfold or what implications they may hold for curtailing corporate innovation in low-carbon technologies.

Numerous scholars have extensively engaged in theoretical studies on the tripartite evolutionary game, yielding a plethora of valuable findings across various research domains. Furthermore, tripartite evolutionary game theory is applicable to emergency supply chains (Zhang and Kong, 2022), as are green building supply chains and other contexts (Wan et al., 2021). A tripartite evolutionary game model encompassing governmental entities, blue carbon trading platforms, and news media is proposed. They suggested that news media could exert positive regulatory control over the platform. Pan et al. (2023) conducted an innovative study recognizing the role of third-party media in shaping local governments’ environmental regulations. They developed a four-party evolutionary game model involving the central government, local authorities, enterprises, and the public to improve environmental governance in China. Zhou et al. (2022) developed a tripartite evolutionary game model involving sewage enterprises, the government, and the public, incorporating spatial analysis into strategy evolution. Their findings emphasize the importance of a reward and punishment mechanism in pollution control, resulting in the creation of an effective framework (Fan et al., 2024).

The tripartite evolutionary game, involving the government, financial institutions, and enterprises as stakeholders, has been applied primarily to sectors such as agriculture (Luo et al., 2023), traditional manufacturing (Liu et al., 2024), and the green supply chain (Huo et al., 2024).

Governments, enterprises, and financial institutions are working together to advance carbon emission reduction efforts. Enterprises reduce their emissions to increase their corporate reputation but must strengthen their capacity for emission reduction by developing low-carbon technologies. However, the high costs of such efforts can dampen financial institutions’ enthusiasm, leading to reduced investment in low-carbon innovations. By implementing permanent policies, governments can incentivize positive behavior from enterprises and financial institutions. Given the high cost of regulation, governments may also opt for negative regulation. The production of low-carbon products by enterprises generates positive societal benefits. This study, therefore, assumes that the government’s strategic scope is to “encourage low-carbon production” and “let conventional production go unchecked.” Similarly, enterprises have the option to choose between “innovating in low-carbon technologies” or “not pursuing innovation in low-carbon technologies”. The strategic options for financial institutions are “green finance” and “conventional finance.”

Figure 1 illustrates the logical relationships among the participating entities within the tripartite evolutionary game model of low-carbon production in enterprises.

Hypothesis 1

The game involves the government, enterprises, and financial institutions as stakeholders; it is characterized by bounded rationality and operates under conditions of asymmetric information.

Hypothesis 2

The strategy space α = (α₁,α₂) = (innovating in low-carbon technologies, not pursuing innovation in low-carbon technologies), with α₁ chosen with probability x and α₂ chosen with probability (1-x), where x ϵ [0,1]; the strategy space of the financial institution is β = (β₁,β₂) = (green financial service, conventional financial service), with the probability of choosing β₁ being y and the probability of choosing β₂ being 1-y, where y ϵ [0,1]. The government department’s policy space is θ = (θ₁,θ₂) = (incentive policy, loose policy), with θ₁ selected with a probability of z and θ₂ selected with a probability of 1-z.

Hypothesis 3

The government regulates financial institutions and enterprise sectors through a variety of measures, including incentives and subsidies, to generate fiscal revenue and promote social welfare. Financial institutions provide financing to the enterprise sector and benefit from financing income as well as government subsidies. The enterprise sector pursues different strategies to achieve the benefits of innovation or noninnovation while also facing constraints from regulations and transformation costs.

Hypothesis 4

The government department income and loss variables W ₁ represent the social welfare obtained by the government from economic growth, employment, resource allocation, etc. a represents the positive outcomes of reputation enhancement and sustainable economic growth achieved by the government through encouraging financial institutions and the enterprise sector to actively engage in green financial activities, thereby facilitating the green and low-carbon transformation of the economic structure. b argues that insufficient government support for green production drives enterprises to opt for traditional methods, negatively affecting the government. m represents the feedback coefficient of the influence of low-carbon technology innovation on social welfare. K ₁ denotes government subsidies to low-carbon innovation enterprises. G ₁ refers to a tax imposed by the government on non-low-carbon technology innovative enterprises. K ₂ represents government subsidies provided to financial institutions offering green financial services. G ₂ represents the institutional constraint values imposed by the government on the “effectiveness” and potential “green-washing behavior” of financial institutions’ services, as evaluated through the “transparency of green credit assessments.” C ₀ stands for governmental regulation costs.

Hypothesis 5

Financial sector income and loss variables: N ₁ denotes the revenue generated by financial institutions from providing innovative green financial services, green products, intermediary fees, and other enterprise services. n represents the increase in the credit risk ratio due to the innovation of green financial services by financial institutions. U ₁ represents the revenue generated by the financial institution from providing traditional financial products (including credit risk). C ₁ encompasses costs associated with financial institutions’ innovation in green financial services, staff training, green product development, promotion, ancillary expenses, asset transfer losses, and related expenditures. f ₁ indicates that the provision of green financial services to support low-carbon technology innovators can result in indirect benefits such as increased market share, enhanced competitiveness, and greater social recognition.

Hypothesis 6

Profit and loss variables of enterprises: U ₂ represents the profits of enterprises engaged in low-carbon technology innovation. N ₂ represents the additional income gained from higher product sales and lower energy consumption and waste disposal costs achieved through low-carbon production. L denotes the probability of loss due to the enterprise’s failure to achieve the anticipated outcomes from low-carbon technology innovation. f ₂ signifies that enterprises opt for low-carbon technology innovation to obtain development prospects, improve social reputation, and obtain other indirect benefits. C ₂ represents the total expenses for technology development, equipment upgrades, and personnel involved in low-carbon technology innovation. F ₁ denotes the financial expenses incurred by enterprises while utilizing green financial services. F ₂ refers to the associated financial costs that enterprises are required to pay when accessing traditional financial services. S denotes the cost associated with rent-seeking behavior by companies not opting for low-carbon technology innovation to access green financial services.

We set some relevant parameters and defined their meanings, as shown in Table 1.

Table 2 presents the tripartite payoff matrix derived from the symbolic assumption outlined above. The analysis further explores the evolutionary stable strategies and various equilibria arising from the interactions among the three stakeholders.

The Jacobi matrix for the tripartite evolutionary game system is expressed as (Equations 13‐22) follows: J = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 (13) a 11 = 2 x − 1 F 2 + C 2 − N 2 − f 2 + L N 2 + U 2 + y F 1 − S − F 2 − z G 1 + K 1 (14) a 12 = x x − 1 F 1 − F 2 − S (15) a 13 = − x x − 1 G 1 + K 1 (16) a 21 = − y y − 1 N 1 (17) a 22 = 2 y − 1 C 1 − f 1 − z K 2 + G 2 − x N 1 (18) a 23 = − y y − z K 2 + G 2 (19) a 31 = z z − 1 G 1 + b + K 1 − a (20) a 32 = z z − 1 K 2 + G 2 (21) a 33 = 2 z − 1 C 0 − G 2 − G 1 + W 1 + x G 1 + b + K 1 − a + y K 2 + G 2 − m W 1 (22)

The replicator dynamic equations for the government, enterprises, and financial institutions are as (Equations 23‐25) follows: F x = d x d t = x x − 1 F 2 + C 2 − N 2 − f 2 + L N 2 + U 2 + y F 1 − S − F 2 − z G 1 + K 1 (23) F y = d y d t = y y − 1 C 1 − f 1 − z K 2 + G 2 − x N 1 (24) F z = d z d t = z z − 1 C 0 − G 2 − G 1 + W 1 + x G 1 + b + K 1 − a + y K 2 + G 2 − m W 1 (25)

When the above equation satisfies F(x) = 0, F(y) = 0, and F(z) = 0, eight valid local equilibria are determined. At each equilibrium point, the three stakeholders adopt pure strategies to establish the domain boundary. E₉ may also emerge as an equilibrium point within the domain but is ultimately excluded as it falls outside the domain. The stability of each of the eight equilibrium points is subsequently assessed via the Jacobi matrix. The evolutionary game model yields eight equilibrium points and eight potential ESSs. Table 3 illustrates the relationship between costs and benefits for each stakeholder, which largely influences the selection of an evolutionary stabilization strategy.

To maintain the general applicability of the stability analysis for the game evolution system, it is assumed that the parameters follow a set of constraints, namely, S + G ₁-C ₂-F ₁+ K ₁ + N ₂ + f ₂-N ₂ *L-U ₂ *L, G ₂ + K ₂-C ₁ + N ₁ + f ₁ and a-C ₀-b-K ₁-K ₂-W ₁+m*W ₁. In the context of green financial service development, the benefits derived from government regulation strategies, enterprises’ low-carbon technology innovation strategies, and financial institutions’ green financial service strategies are greater than those derived without such strategies. Given the complexity of the parameters involved in this model, we discuss stability strategies for evolutionary game models in four specific cases.

Scenario I: When G ₁ - C ₂ - F ₂ +K ₁ + N ₂ + f ₂ - N ₂*L - U ₂*L < 0 and K ₂ + G ₂- C ₁ + f ₁ < 0, the equilibrium points E₂ (0, 0, 1) and E₁ (0, 0, 0) represent stable strategies for the evolution of the tripartite game system, in which financial institutions do not engage in green financial services owing to a smaller sum of subsidies, constraints, and value-added benefits than the cost of low-carbon production and transition income. Additionally, when enterprises do not carry out low-carbon technology innovation, the benefit of financial institutions carrying out green financial services under government regulation is smaller than the basic benefit of not carrying out such services.

Scenario II: When G ₁ - C ₂ - F ₂ +K ₁ + N ₂ + f ₂ - N ₂*L - U ₂*L < 0 and K ₂ + G ₂- C ₁ + f ₁ > 0, the financial institutions fail to provide green financial services, and the sum of government regulation subsidies, taxes and value-added benefits to enterprises is less than the difference between enterprise low-carbon innovation costs and transformation benefits. In addition, when enterprises do not engage in low-carbon technology innovation, the benefits of the green financial services provided by financial institutions under government supervision are greater than the basic benefits when enterprises do not use green financial services. E₈ is the equilibrium point, and {low-carbon technology innovation, green financial services, and incentives} represents the evolutionarily stable strategy of the tripartite game system.

Scenario III: When G ₁ - C ₂ - F ₂ +K ₁ + N ₂ + f ₂ - N ₂*L - U ₂*L > 0 and K ₂ + G ₂- C ₁ + f ₁ < 0, the financial institutions fail to provide green financial services and the total amount of subsidies and taxes and the value-added benefits from government regulations to enterprises surpass the gap between the cost of low-carbon innovation and their transition income. Furthermore, the benefit for financial institutions to offer green financial services when enterprises do not engage in low-carbon technology innovation is smaller than the basic benefit of not providing green financial services. E₈ is the equilibrium point, and {low-carbon technology innovation, green financial services, and incentives} represents the equilibrium point and serves as an evolutionary and stable strategy within the tripartite game system.

Scenario Ⅳ: When G ₁ - C ₂ - F ₂ +K ₁ + N ₂ + f ₂ - N ₂*L - U ₂*L > 0 and K ₂ + G ₂- C ₁ + f ₁ > 0, the sum of subsidies, taxes, and value-added benefits of government regulations to enterprises exceeds the difference between the cost of low-carbon innovation and the transition income of enterprises when financial institutions do not provide green financial services. Furthermore, the net benefit of financial institutions providing green financial services in comparison to no green financial services is greater than the basic benefit. E₈ is the equilibrium point, and {low-carbon technology innovation, green financial services, and incentives} represents the equilibrium point and evolutionarily stable strategy in the tripartite game system.

The X-axis in Figure 5 represents enterprises, the Y-axis represents financial institutions, and the Z-axis represents government departments. As the initial proportion increases, all enterprises eventually opt for the “low-carbon technology innovation” strategy. Similarly, as the number of evolutionary iterations increases, the strategic combinations of participants can be represented via three-dimensional stochastic graphs. Ultimately, the evolutionary path through which financial institutions select green financial services and governments promote green production decisions can be identified.

Figure 6 shows that x, y, and z tend toward 1, with the evolutionary equilibrium point approaching (1, 1, 1). When the three parties demonstrate minimal initial willingness, the rate at which z tends toward 1 is significantly higher than that of x and y. With a rise in the initial willingness of all three parties, the speed at which x and y approach 1 accelerates noticeably, whereas z’s convergence slows. The simulation results indicate that when the initial willingness of all three parties is weak, government regulation plays a crucial role in driving low-carbon technology innovation in enterprises and promoting green financial services provided by financial institutions. As the willingness of enterprises and financial institutions to participate increases, the government can appropriately reduce incentives and regulatory costs compared with previous measures, thereby promoting green enterprise transformation and fostering the development of green financial services.

To investigate the influence of variations in K₁ on the process and outcome of evolutionary games, the values of K₁ were set to 10, 20, 30, and 40, respectively. Through simulation, the results after 50 iterations of the replicated dynamic equation system were observed, as specifically illustrated in Figure 7. To analyze the impact of changes in G₁ on the game process and outcome, the values of G₁ were set to 20, 40, 60, and 80, respectively. The corresponding simulation results are presented in Figure 8.

As depicted in Figure 7, during the evolution of the system toward a stable equilibrium point, an increase in government-provided incentive subsidies to enterprises accelerates the convergence rate of enterprises’ low-carbon production stability. Similarly, as shown in Figure 8, an increase in the taxation intensity for traditional production practices by enterprises enhances the speed at which enterprises adopt low-carbon production strategies. Moreover, as K₁ and G₁ increase, the likelihood of enterprises engaging in low-carbon production rises, while the probability of the government adopting incentive-based strategies diminishes. Furthermore, by comparing Figures 7, 8, it is evident that the effectiveness of government taxation in promoting low-carbon production exceeds that of government subsidies. Consequently, while the government employs subsidies and tax policies to encourage low-carbon production in enterprises, it must also reinforce supervision over these entities. In particular, for enterprises lacking mature low-carbon production technologies, the subsidy period can be appropriately extended to ensure the quality of low-carbon production and effectively promote sustainable enterprise development.

Next, set K₂ = 10, 20, 30, 40 to investigate the impact of government subsidies on financial institutions. The results are presented in Figure 9. Additionally, set G₂ = 30, 40, 50, 60 to analyze the influence of government regulation on the “transparency of green credit services” constraint value for financial institutions. The simulation outcomes are illustrated in Figure 10.

Figure 9 demonstrates that as K₂ increases continuously, the likelihood of the government adopting incentive policies decreases, while the probability of financial institutions opting to implement green financial services increases. Similarly, as shown in Figure 10, with the rise of G₂, the regulatory constraint imposed by the government on financial institutions becomes stricter, leading to a decline in the “transparency of green credit services,” which in turn elevates financial risks. Consequently, the feasibility and effectiveness of government regulation over green financial services improve. Therefore, the government should prudently design supervision and subsidy policies for financial institutions, enhance the regulatory framework, and encourage financial institutions to collaborate with the government in promoting low-carbon production among enterprises.

To analyze how changes in S affect the dynamics and results of the evolutionary game, S values of 20, 40, 60, and 80 were assigned. Figure 11 illustrates the simulation outcomes of the dynamic equations across 50 iterations. Similarly, to assess the impact of changes in C₂ on the processes and outcomes of evolutionary games, C₂ values of 30, 45, 60, and 75 were assigned. The corresponding simulation results are depicted in Figure 12.

Figure 11 shows that during the evolutionary process, as S increases, enterprises become increasingly likely to choose low-carbon technology innovation, whereas the probability of financial institutions selecting green financial services decreases. To increase the propensity for low-carbon production, the government can implement market-oriented measures such as increasing media transparency regarding corporate information, amplifying the social reputation of enterprises, raising consumer awareness of low-carbon initiatives, and increasing the rent-seeking costs associated with enterprise operations.

Figure 12 shows that as the system advances toward a stable state, lowering low-carbon production costs for enterprises can accelerate their shift to low-carbon technology innovation and increase financial institutions’ willingness to offer green financial products. As production costs for low-carbon manufacturing (C₂) increase, enterprises become less likely to pursue low-carbon technology innovation. When C₂ reaches a critical threshold, high costs may deter enterprises entirely from low-carbon technology innovation. Furthermore, the evolution from C₂ = 30 to C₂ = 45 indicates a greater likelihood of financial institutions opting for green financial services. However, when C₂ increases to 60, due to the high costs of green production, financial institutions are no longer motivated to offer green financial services. Therefore, to encourage low-carbon production, the government must enforce strict oversight of enterprises’ green infrastructure development while simultaneously addressing prohibitively high low-carbon technology innovation costs that could undermine efficient green output. Additionally, financial institutions and enterprises adopting low-carbon practices should receive subsidies to support their transition. Relaxing price controls strategically could help reduce low-carbon production costs at the enterprise level and lower financing expenses from banks—thus shifting the motivation for low-carbon practices from compliance-driven (“having to do”) to initiative-driven (“wanting to do”).

Subsequently, the values of L were assigned values of 0, 0.25, 0.5, and 0.75, with the simulation results shown in Figure 13. The parameters m were set at 0.1, 0.25, 0.5, and 0.75, with the corresponding simulation outcomes displayed in Figure 14. Figure 13 shows that throughout the evolutionary process, an increase in L is associated with a reduced likelihood of enterprises pursuing low-carbon technology innovation, while it simultaneously increases the probability of financial institutions engaging in green financial services. Conversely, Figure 14 reveals that the feedback coefficient linking enterprises’ low-carbon technology innovation with social welfare increases significantly, accelerating their transition to low-carbon practices and prompting greater government adoption of incentive policies. Consequently, governments must prioritize monitoring business risks faced by enterprises to ensure supply chain security and stability through robust internal control systems, sound corporate governance structures, and transparent decision-making processes. Furthermore, governments should actively encourage and support enterprises in increasing investments in low-carbon technology research and development (R&D). Promoting collaboration within industrial chains can help build a green supply chain ecosystem that incentivizes suppliers and partners to adopt low-carbon production methods. This ecosystem approach can create cluster effects that enhance environmental performance across industries, improve social welfare, and ultimately strengthen the feedback coefficient between enterprise-level low-carbon technology innovation and societal benefits.

To analyze the impact of the benefits and costs associated with the green financial services offered by financial institutions on the dynamics and outcomes of the evolutionary game, we define the direct benefits of these services as N₁ = 100, 150, 200 and the indirect benefits as f₁ = 30, 40, 50. The simulation outcomes generated from iterating the dynamic equations with an initial probability allocation of (0.2, 0.2, 0.2) across fifty cycles are illustrated in Figures 15, 16.

When the other conditions remain constant and the N₁ values are set at 100, 150, and 200, the outcomes of the simulation are depicted in Figure 15. During the system’s evolution toward a stable state, increased direct revenue from green financial services increases the likelihood of financial institutions engaging in such services. As shown in Figure 16, the simulation outcomes for f₁ values of 30, 40, and 50 indicate that higher indirect revenue from green financial services accelerates the system’s evolution. Therefore, it is essential for financial institutions to prioritize both direct and indirect income streams. Direct benefits can be increased by creating a variety of green financial products, including green bonds, green funds, green insurance, and carbon financial derivatives, which cater to diverse investment and financing requirements. Indirect benefits can be strengthened by building a robust green ecosystem through employee or team capacity building and by reinforcing social responsibility initiatives. Increasing both direct and indirect income streams further incentivizes financial institutions to invest in low-carbon enterprises and promote sustainable practices within these organizations.

Subsequently, values of C₁ = 50, 60, and 70 were assigned, with the simulation outcomes presented in Figure 17. The findings in Figure 17 indicate that rising costs associated with green financial services tend to discourage financial institutions from adopting these services while increasing the likelihood of government adoption of incentive policies. Therefore, it is essential for government bodies to account for the costs that financial institutions incur in implementing green financial services. This can be achieved by improving processes such as credit approval, project evaluation, and risk management through digitalization and automation technologies to reduce labor and time costs. Additionally, standardizing product design and operations can streamline green financial products. Establishing a unified certification and rating system for green finance will further reduce redundant evaluations, lower the overall cost of green financial services, and promote low-carbon technology innovation among enterprises.