Evolutionary Game Analysis of Governmental Intervention in the Sustainable Mechanism of China’s Blue Finance

Abstract

This article is a case study of the blue finance mechanism (BFM) in China and makes use of evolutionary game theory and numerical simulation to show how the BFM plays a critical role in promoting the sustainable development of China’s marine economy, society, and environment. To ensure the perpetuation of the BFM, it is necessary for the Chinese government to attract private sector investment in the marine sector (PSIMS). By intervening in the BFM, the government can create a more favorable investment environment, which can then lead to greater private sector investment and contribute to the overall sustainability of the ocean. The goal of this article is to create an analytical model based on public finance and government management to examine the efficiency of Chinese governmental involvement in the BFM in order to boost the maritime industry by attracting private sector investment for funding the BFM. The results revealed the following: First, governmental involvement can have significant positive effects in promoting the sustainable development of the BFM in China. Second, the timeliness of governmental intervention in China can affect the private sector’s incentive to invest in the marine sector. Third, the Chinese government’s intervention in subsidizing costs can have significant impacts in engaging the private sectors to expand capital injection into marine investments. The minimization of potential risks of investment in the marine sector is critical to enhancing investor confidence and trust. The early intervention of the Chinese government is therefore crucial. Additionally, to further incentivize PSIMS, the Chinese government must make a concerted effort to increase subsidies and provide non-monetary rewards. This will help achieve sustainable development in the country’s economy, society, and environment.

1. Introduction

The significance of the marine system in fostering sustainable development is widely acknowledged. This is reflected in SDG14, “Life Below Water,” which aims to conserve and sustainably utilize ocean, sea, and marine resources to promote sustainable development. With the establishment of SDG14, the ocean is viewed as a vital component for promoting both economic and social sustainability while also ensuring the preservation of the marine environment in a sustainable manner [1]. The achievement of sustainable development in the ocean is greatly dependent on the implementation of sustainable practices within the ocean economy. As commercial exploitation of the ocean increases, the ocean economy is growing at a rapid pace [2,3]. The future of the global ocean economy is anticipated to be a sustainable economy, characterized by marine industries that are economically viable, socially equitable, and environmentally sustainable [4,5]. It is crucial to note that the expansion of the ocean economy is imperative for the survival of humanity. In 2017, the ocean economy accounted for 3.3% of the world’s GDP, making it the seventh largest economy globally [6]. The ocean economy plays a crucial role in society, with most of its contributions being non-substitutable and some being completely irreplaceable. Moreover, the growth of the ocean economy is closely tied to the development of the marine industry, which has undergone evolution over time and has given rise to new businesses, such as undersea mineral mining, marine medicine and biological products, and marine renewable energy, among others [7]. Tirumala and Tiwari [8] have posited that the provision of financial assistance to the marine sector has the potential to result in increased productivity within the marine industry, improved operational efficiency, and attractive returns for investors. As a result of these promising benefits, both governmental and non-governmental entities have demonstrated a keen interest in expanding the marine sector, recognizing its potential as a driving force for sustainable economic growth. However, subsequent network analysis has indicated that the impact and significance of non-government organizations in the sustainable development of the ocean economy is relatively limited compared to that of the government [8]. Hence, this paper will primarily focus on the government’s role.

The blue economy was first mentioned in the Blueprint for Sustainable Ocean and Coastal Development, published by the United Nations in 2011. It was defined as a general term for all activities related to the development of marine and coastal zone economies based on the sustainable use of marine space and resources around coordinated economic, social, and ecological development, following an ecosystem approach, and carried out through technological innovation [9]. Shiiba et al. [10] proposed a regulatory-driven blue finance mechanism (BFM) as a framework for sustainable ocean development by highlighting the importance of converting the blue economy concept into an operational principle. The blue economy has given birth to blue finance, and the goal of blue finance is also to support the adjustment of marine industries to meet the needs of the blue economy, and to guide social capital investment to support the establishment of a sustainable marine industrial system and marine ecological protection and restoration, thus realizing the synergistic development of environmental, economic, and social benefits [11].

Blue finance is a funding mechanism that was established by the European Union in 2007 [12,13,14]. The mechanism is based on a model of sustainable financing, which involves using revenues generated from the use of natural resources to finance their conservation and sustainable management. This model aims to create a sustainable funding stream for marine conservation and management, which can be used to support the development of the marine economy and ensure the long-term sustainability of marine resources. As the times have changed, the notion of blue finance has been innovated. For example, the Seychelles government issued the world’s first blue sovereign bond in October 2018 with the aim of preserving and maintaining the coral ecology around the Seychelles islands and expanding marine protected areas. Countries subsequently followed suit and began issuing blue bonds to finance marine development.

Among other things, the issuance of blue bonds and the implementation of blue financial mechanisms have been strongly promoted by the Chinese government in China. The reason for this is that China’s waters are vast, and the development of the marine industry requires significant financial support. Therefore, the Chinese government has tried to help the marine sector raise funds by introducing the BFM. With the support of the Chinese government, a total of 14 blue bonds has been issued in China as of December 2022 (see Appendix A). The use of blue financial instruments as a fundraising tool has been promoted in coastal cities in China, such as Ningbo [15], Qingdao [16], and Hainan [17]. The BFM is significant in that it recognizes the critical role of financing in achieving sustainable ocean management and development. It highlights the need for innovative financing mechanisms and partnerships between governments, the marine sector, and the private sector to achieve a sustainable ocean economy.

The growing popularity of blue finance has also elicited concerns from the Chinese government. For starters, blue financing initiatives may have a substantial environmental impact, notably on marine ecosystems and biodiversity [18]. Second, blue finance efforts may be more risky than traditional financial operations [19], so the Chinese government is worried about how to control these risks while guaranteeing the financial system’s safety and stability. Finally, the Chinese government is concerned about the long-term profitability and sustainability of blue financing initiatives, as well as their potential to contribute to the attainment of sustainable development goals. In light of these concerns, the Chinese government has sought to address them through intervention in the realm of the BFM.

The involvement of the Chinese government in the BFM has provided some degree of stability in its operations. However, the limited allocation of financial capital by the Chinese government is constraining the sustainable growth of the ocean economy [20]. This shortage of investment can have a detrimental effect on the ocean, as it reduces the resources available for efforts aimed at preserving and sustainably utilizing marine resources, thus hampering the promotion of the ocean’s economic, social, and environmental sustainability. Considering the aforementioned challenges, the marine sector has sought to employ financial instruments for the private sector’s financing to overcome the constraints of insufficient size and limited finance sources [21]. This is because financial instruments may be utilized to secure financing and address the hindrances posed by limited financial capital in the sustainable growth of the ocean economy [22]. The categorization of financial instruments utilized for financing in the marine industry is based on the presence or absence of intermediary involvement in the financing process. The two distinct categories are direct financing and indirect financing. Currently, direct financing is more widely utilized for several reasons. Firstly, the fees imposed by intermediaries in indirect financing raise the investment cost for investors, making direct financing a more cost-efficient option. Additionally, direct financing affords the financier with a longer period of use for the funds, which is deemed more suitable for the marine industry due to its requirement for a significant amount of capital.

The role of the BFM role is to seek private sector investment in the marine sector (PSIMS), which requires the engagement of the Chinese government. Compared to other industries, marine industry investment possesses three distinct characteristics: significant upfront costs, a prolonged period to recoup investments, and a high level of risk. Given these difficulties, investment enterprises are often hesitant to enter the marine sector, making governmental intervention and incentives crucial to ensure the sustainable operation of the BFM. The absence of governmental support in the BFM could hinder its effective functioning, thereby making it difficult for the marine sector to attract investment despite the adoption of financial instruments. This scenario would render the government’s objective of using blue finance to promote sustainable ocean development unachievable. Therefore, it is imperative for the Chinese government to actively participate in the BFM in order to realize its desired sustainable outcome.

The utilization of financial instruments for financing in the marine sector alone does not ensure the perpetual functioning of the BFM. Its effective functioning requires the intervention of external forces, namely, the government. To attract PSIMS, the Chinese government is diversifying its intervention in BFM. Subsidies and tax breaks are the most common types of incentives [23]. The provision of subsidies and tax incentives can serve to reduce both the costs and risks associated with investments in the maritime sector and can also mitigate instances of market failure [24,25,26]. The Chinese government has also recognized the importance of developing a sustainable ocean economy and has taken steps to promote this through various policy measures. For example, in 2020, China’s Ministry of Finance announced a pilot program for blue finance in five coastal provinces, including Guangdong, Fujian, Shandong, Liaoning, and Hebei. The pilot program is aimed at facilitating investment in sustainable marine projects, such as marine renewable energy, sustainable fisheries, and marine tourism. The program offers financial incentives and support for private investors who want to invest in these sectors, including subsidies, tax breaks, and low-interest loans. In addition to subsidies and tax breaks, incentives for the marine sector may also take the form of legislative measures and non-monetary rewards offered by the Chinese government and have the potential to further attract PSIMS. The BFM is deemed more suitable for China than other marine policies, such as donation initiatives facilitated through foundations. There are several reasons to support this claim. Firstly, the BFM provides a financial instrument that can generate sustainable funding for the marine sector, whereas donations by organizations can only meet temporary funding needs and fail to address the fundamental funding problem. Secondly, the BFM is a government-supported mechanism that the Chinese government can efficiently intervene in. As a result, the BFM can be trusted more by the public than social organizations, thus ensuring its proper functioning. Finally, the BFM is a flexible financing mechanism that allows for funds to be allocated based on the specific needs of each region or sector. This enables targeted and impactful funding that can be tailored to the unique needs of a particular region or sector. Nevertheless, it is worth mentioning that the blue financial mechanism is not applicable to all countries, and its effectiveness is limited by certain conditions, such as the authority of the government and the willingness of the private sector to support it.

However, there is no denying that government involvement in the BFM has the potential to bring harm to the environment. For example, subsidies for fishing provided by the government may lead to overfishing, which can cause irreparable damage to marine ecosystems and biodiversity. Such subsidies can create incentives that promote overfishing, leading to depletion of fish populations and harm to other marine species. Similarly, subsidies for marine transportation and shipping can cause harm to marine ecosystems due to the increase in carbon emissions. These emissions result in ocean acidification and warming, thus contributing to climate change, which poses significant threats to marine biodiversity and ecosystems. Therefore, it is crucial for governments to carefully consider the potential environmental impacts of subsidies and design policies that promote sustainable practices and innovation in BFM.

The BFM encompasses three key participants: the marine sector, the private sector, and the Chinese government. Of these, the private sector is the direct recipient of governmental subsidies, creating a dynamic between the Chinese government and the private sector in which subsidies serve as a means of interaction. The Chinese government aims to minimize the provision of subsidies and tax exemptions in order to achieve PSIMS, while the private sector strives to maximize the availability of subsidies and tax concessions in order to minimize the investment costs incurred. Each participant strives to optimize their individual benefits. Accordingly, a game between the Chinese government and the private sector is formed. Furthermore, the interplay between the Chinese government and the private sector is a longstanding issue, and during the course of this interaction, both parties may take into consideration their respective interests and adjust their strategies accordingly. Consequently, the two participants in the BFM exhibit a level of sustainability and adaptability, rather than being static entities. Through a process of trial and error, they continually modify their strategies in response to evolving circumstances, striving to achieve optimal results and ultimately attain a state of dynamic equilibrium [27,28]. As a result, this paper utilizes dynamic game theory to investigate and analyze the optimal strategies in the game played between the Chinese government and the private sector, which is consistent with the principles of dynamic game theory. Understanding the evolution sheds light on the dynamics and sustainability of the BFM. In evolutionary games, the assumption of complete rationality is abandoned in favor of analyzing the dynamic adjustment process, which compensates for the lack of a rational and static perspective [29] and is more in line with real-life human decision-making situations in which game parties can choose to cooperate or not cooperate based on the analysis of realistic factors, their own cognition, and the continuous trial and error process [30].

The theoretical contributions of this paper are threefold: (1) The first is the enhancement of public finance and development finance through Chinese governmental intervention in the long-term blue finance system. (2) The utilization of financial instruments in the maritime industry expands the scope of the modified Modigliani–Miller (MM) theory, contributing to the optimization of the capital structure of the marine sector. (3) The structure and methodology of analysis presented in this work serve as a guide for future research in marine investment and government management.

The practical contribution of this study is primarily focused on providing policy recommendations to the government, the private sector, and marine sector. (1) It provides guidance to the Chinese government on their involvement in the BFM, the implementation of incentives, and the development of ocean-related legislation. This can contribute to the sustainable growth of the ocean economy, the promotion of maritime infrastructure, and the preservation of marine life. (2) Recommendations are provided to the private sector for investment in the maritime sector based on the outcomes of the evolutionary game, reducing their investment risk and maximizing their investment income, while also promoting corporate social responsibility. (3) It contributes to the optimization of finance and capital within the marine sector.

This study uses evolutionary game theory and numerical simulation analysis to examine the impact of China’s governmental involvement on the behavior and growth of the parties involved in the BFM. The purpose of this paper is to promote the advancement of a high-quality BFM, stimulate private sector investment in the maritime sector, and enhance the confidence of the Chinese government‘s participation in BFM. Furthermore, it seeks to contribute to the sustainable development of the ocean from both the government’s and the private sector’s perspectives. As a result, this paper is structured as follows: After the introduction, the second section provides a comprehensive review of the relevant literature and outlines the model assumptions. The third section presents the evolutionary game model, including a stability analysis, while the fourth section carries out numerical simulation analysis based on the evolutionary model. The final section comprises a discussion of the results, followed by the conclusion and suggestions for future research.

2. The Literature Review and Hypotheses

Currently, academic research on the BFM focuses mostly on the qualitative level. At the qualitative level, scholars at home and abroad have described the background of the BFM and affirmed the importance of government in the BFM [10,31]. Such studies can be cited by governments in their decision-making processes for intervening in a BFM while ignoring the use of empirical evidence for argumentation. As a result, there is a lack of conviction. In addition, existing research on China’s BFM has focused mostly on business economics, health care sciences, environmental sciences ecology, biodiversity conservation, and psychology. Such studies, representing a hotspot in a multi-disciplinary subject, address most elements of BFMs but lack systematic and dynamic research methodologies. The BFM as a continuous mechanism is pertinent to the sustainable development of the ocean and should be analyzed from a dynamic perspective.

Blue finance is gaining popularity, and relevant research is developing. Figure 1a shows that studies on blue finance were rare prior to 2006 but grew after 2007. On 31 January 2023, this research discovered only 492 articles with the keywords “blue finance” in the Web of Science (WOS) core collection database. Similarly, as shown in Figure 1b, this work discovered only 56 articles with the keywords “blue finance” on the China National Knowledge Infrastructure (CNKI) website on 31 January 2023. Furthermore, as shown in Figure 1c, only 95 publications with the keywords “blue finance” were found on Citation Information by Japan’s National Institute of Informatics (CINii), and they were all released after 2017.

2.1. Literature Review on the Background of BFM

China’s BFM has undergone three significant stages of development. During the first stage, the Chinese government released the “Outline of the 12th Five-Year Plan for the Development of the National Ocean Economy” (2012) and “Outline of the 13th Five-Year Plan for the Development of the National Ocean Economy” (2017), which proposed national strategies for promoting the diversified development of marine finance and accelerating the reform of the investment and financing system of the marine economy. During the second stage, in January 2018, the People’s Bank of China collaborated with eight other departments to issue the “Guidance on Improving and Strengthening Financial Services for the Development of the Marine Economy”. This guidance focused on coordinating and optimizing financial resources to improve and strengthen financial services for the development of the marine economy. Specific measures were proposed, including increasing bank credit support, optimizing equity and bond financing, enhancing insurance services, and improving the investment and financing system. The third stage began in January 2020, when the China Banking and Insurance Regulatory Commission issued the “Guidance on Promoting the High-Quality Development of the Banking and Insurance Industry”. This guidance included blue bonds in innovative green financial products, reflecting China’s commitment to promoting sustainable development in the marine economy [32].

The development of BFMs is of great importance to China. China’s marine industry is large and diverse, and with a high percentage of GDP, its sustainable development cannot be achieved without the support of financial products and services [33]. For example, Industrial Bank actively promotes the “blue-green integration” model and has built a diversified blue financial product service system such as marine industrial park financing, marine ecosystem supply chain financing, pledge of sea area use rights, and blue bonds (see Figure 2). Moreover, it can provide much-needed financing to support China’s development of sustainable marine economic activities, such as renewable energy projects and sustainable fishing practices. This support can drive job creation [34].

The historical evolution of the ocean economy highlights the fact that the revitalization of the marine sector necessitates long-term financial support [35]. The financial burden of supporting the marine sector is primarily borne by the government [36]. According to the data of the “2022 China Ocean Economic Development Index Report” released by China’s Ministry of Land and Resources, China’s gross marine product exceeded 9 trillion in 2021, accounting for 9% of GDP. Despite the significant contribution of the ocean to GDP, capital investment in the ocean remains inadequate in China [37,38]. The majority of this investment capital has been provided by the government [39]. This limited investment can be attributed to the limited understanding of the oceans, with 60% of them located outside of state borders, resulting in a significant shortfall of funding for sustainable development initiatives [40].

BFMs were formed to encourage PSIMS and to improve the ocean economy’s long-term sustainability [30]. Since the introduction of BFMs, there has been a gradual diversification of finance channels for marine industry-related enterprises [41], contributing to the expansion of the ocean economy and ecosystem. Furthermore, the marine sector’s financial instruments, known as “blue financial instruments (BFIs)”(see Figure 2), are intimately linked to the expansion of the marine sector [42]. According to the modified MM theory, the cost of debt is lower than the cost of equity in the event of bankruptcy [43]. As a result, debt-based financial instruments, such as blue bonds and blue loans, are more commonly used in the BFM compared to equity-based instruments. This is because in the event of bankruptcy, creditor claims are fulfilled prior to shareholder claims. To boost investor trust in the private sector and increase financing efficiency, the marine sector is also utilizing technologies such as block chain and digital platforms(see Figure 2) to improve the transparency and disclosure of financial activities [44]. Historically, governments and their agencies have played a crucial role in providing financial, policy, and institutional support in the blue finance landscape [8]. Moreover, the Chinese government is also providing technical assistance by offering training programs to educate stakeholders on how to effectively utilize emerging technologies, including blockchain and other digital tools, in maritime management [45].

Aside from technical aid, the Chinese government also contributes equipment and talent [46]. The marine sector also helps the Chinese government in a multitude of ways. It creates jobs for individuals living near coastal regions, which boosts local economies and generates tax money [47]. Furthermore, the operation of the maritime sector has hastened the development of marine infrastructure. According to Sha et al. [48], the marine industry may encourage marine ecological conservation by applying sustainable practices such as minimizing their carbon footprint or investing in research initiatives to better understand how human activities affect ocean ecosystems.

2.2. Governmental Intervention in BFM

The characteristics of a considerable investment cost input, a protracted period for capital to be locked up, and significant risk, combined with the favorable externalities of marine investment, result in the costs and benefits to the private sector being out of balance [49]. There are currently no defined criteria or adherence standards in place for blue finance schemes [50]. This makes ensuring uniformity across multiple projects challenging and can cause difficulties when attempting to attract private capital investment towards the marine sector. Furthermore, blue financial investment initiatives are more focused on environmental, social, and governance imperatives, but investors do not prioritize these.

The private sector is hesitant to invest based on these factor. Unmet financing puts maritime investment markets at a danger of collapse. As a result, relying on government forces outside the market to manage this risk is necessary [51]. The objective of the BFM is driven by Chinese government action as a primary factor in addressing positive externalities. To encourage the private sector to participate in the maritime industry, the Chinese government has reduced investment costs through particular funding and financial aid [52]. Furthermore, the Chinese government has stepped in with the creation of a blue financial framework and rules governing maritime investments. Tirumala and Tiwari [8] agree on the need for a framework to enhance ocean economy investments and project delivery.

The BFM serves as a platform to promote the sustainable growth of the ocean-based economy and maintain the balance between economic development and environmental protection. In this mechanism, the Chinese government has a fundamental obligation to promote the public’s welfare by providing resources, incentives, and regulations that encourage sustainable development in the marine sector. Furthermore, it can regulate private sector investments in the ocean economy to ensure that they align with the public’s values, such as environmental and social standards. By performing its role effectively, the Chinese government can contribute to the creation of an ocean economy that balances economic growth and environmental preservation, thereby benefiting both the public and the environment.

However, the timing of governmental intervention is not inconsequential. It has been widely acknowledged that the appropriateness of the timing of governmental intervention can play a crucial role in determining the level of PSIMS. If the Chinese government intervenes in a timely manner to provide fiscal incentives [23] and other financial mechanisms for blue finance initiatives, it can help attract private sector investment. A timely governmental intervention can demonstrate the government’s commitment to the development of blue finance and build confidence among private sector investors. This can lead to increased investments in marine and coastal resource management projects, which can help to preserve these important ecosystems and support sustainable development. On the other hand, if the Chinese government does not intervene in a timely manner, or if its intervention is inadequate, it can discourage private sector investment. In such cases, private sector investors may view the lack of governmental support as a signal that the development of blue finance initiatives is not a priority, and they may be less likely to invest in these projects. In conclusion, the timeliness of governmental intervention is critical in attracting PSIMS. A timely and effective governmental intervention can help to create a supportive environment for private sector investment, which is essential for the successful development and implementation of blue finance initiatives.

In the BFM, both the Chinese government and the private sector have concerns regarding advantages and costs, which influence their relationship of conflict and collaboration. The problem of Chinese government interference, in particular, has an impact on the game model’s steady state. The outcome of this consideration influences the strategy choice. Moreover, the BFM endeavors to advance sustainable development in the domains of the ocean economy, society, and environment. Thus, it is perceived as a long-term, dynamic mechanism that is adaptable to changing circumstances. In this sustainable mechanism, the Chinese government and the private sector will continually adjust their strategies in response to the behavior of each other during the strategy selection process until a stable strategy is reached [53].

This research focuses on the BFM game model with governmental involvement, assuming only two types of players: the Chinese government, and the private sector. The private sector has the choice of investing or not investing in the marine sector. The private sector is frequently hesitant to invest due to the characteristics of the marine industry. The Chinese government, on the other hand, recognizes the potential for private sector investment to advance the sustainable development of the ocean economy, and thus it encourages the private sector to make investments in this industry. To achieve this goal, the Chinese government intervenes in the BFM by providing the private sector with subsidies, tax breaks, and other incentives to invest. The government of Shandong, China, has introduced tax exemptions and financial subsidies for the Blue Economic Zone on the Shandong Peninsula, and has achieved initial success [54]. As a result, a dynamic interaction is established between the decisions of companies to invest in the marine sector and the Chinese government‘s level of intervention.

2.3. Game Model and Hypothesis

Participants in the game model, according to rational economic participant theory, are rational and self-interested, with the primary goal of insuring and promoting their own interests to the greatest extent feasible [55]. Assuming two parties are involved, the Chinese government as incentive implementer and the private sector as BFM player are both finitely rational in the game’s process [56]. The participants’ end strategy options are more likely to be optimal if they are continually altering and learning during the game.

2.3.1. Model Hypothesis

In this study, the evolutionary game approach is utilized to dynamically investigate the activities of the Chinese government and the investment corporations in BFM. The model’s assumptions are as follows:

(1)

In order to fulfil its goal of luring investors to the maritime industry, the Chinese government mostly intervenes in the BFM through incentives. Therefore, $\left\{\mathrm{interfere}, \mathrm{not} \mathrm{intervene}\right\}$ is the Chinese government’s set of game strategies. The set of gaming tactics for the private sector is $\left\{\mathrm{invest}, \mathrm{not} \mathrm{invest}\right\}$ based on its strategic requirements.

(2)

Tirumala and Tiwari [8] noted that the final beneficiary of most blue finance projects is a private sector developer. ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ are documented as the income that the private sector can make by investing in the maritime sector with and without governmental assistance, and ${\mathrm{R}}_1$ > ${\mathrm{R}}_2$ > 0. By intervening in the BFM, the Chinese government encourages the private sector to invest through incentives and uses the “visible hand” to macro-regulate the growth of the maritime sector, increasing its economic efficiency [57]. The private sector gains from the marine industry’s improved economic efficiency and greater income.

(3)

The revenue that the private sector may generate by investing in non-marine industries is thus designated as ${\mathrm{R}}_3$, and ${\mathrm{R}}_3$ >${ \mathrm{R}}_2$. Humankind’s grasp of the seas is less than that of land [48], which, along with the significant uncertainty of marine investments, leads the private sector to prefer more developed non-marine industries [58]. The marine sector focuses on the peaceful cohabitation of marine economic society and the environment in the process of establishing the BFM, fostering the creation of marine ecosystems [47]. As a result, by investing in the development of the marine sector and the management of marine ecosystems, the private sector is assuming corporate social responsibility, acquiring social repute and increasing its visibility [59].

(4)

Government policies can allocate funding to support research on and development of market-based instruments, reduce perverse subsidies, and create positive subsidies that fund the transition to more sustainable industries [60]. Regulations introduced by the Chinese government have decreased the uncertainty of investment in the maritime sector, and the intangible advantages achieved by enterprises are recorded as ${\mathrm{IR}}_0$ [61,62]. Governments have important roles to play in enabling businesses to reduce their environmental damages and produce positive marine impacts [63]. Sustainable growth of the ocean economy also provides the Chinese government with intangible benefits such as public acclaim, which is denoted as ${\mathrm{ER}}_0$. Such a return will not always be measured by standard performance measures but will sometimes include a range of social and ecological benefits, and these need to be included [64]. Similarly, when PSIMS is adopted, the Chinese government earns money through taxes. The Chinese government hopes to achieve the twin goals of safeguarding seas and coastlines while also expanding its potential contribution to sustainable development, including promoting human well-being and lowering environmental dangers and ecological scarcity through creative approaches [26]. The measurement of intangible benefits is inherently difficult; therefore, there is no relationship between the size of ${\mathrm{IR}}_0$ and ${\mathrm{ER}}_0$.

(5)

If the Chinese government intervenes, it receives revenue as ${\mathrm{GR}}_1$, but if the Chinese government does not intervene, it receives revenue as ${\mathrm{GR}}_2$, and so it may be stated that ${\mathrm{GR}}_1$ > ${\mathrm{GR}}_2$ > 0. Furthermore, the private sector chooses to invest in non-marine businesses, and the Chinese government obtains money recorded as ${\mathrm{GR}}_3$. Xu et al. [57] demonstrated through empirical study that interfering in the assumption of the BFM allows the Chinese government to obtain more economic benefits than not intervening. Non-marine (land-based) industries are more established and profitable than maritime industries. Therefore, the Chinese government gains ${\mathrm{GR}}_2$ from the development of marine industries are lower than the gains ${\mathrm{GR}}_{3 }$ harvested from non-marine industries. However, there is no strict limit on the size of ${\mathrm{GR}}_1$ and ${\mathrm{GR}}_2$.

(6)

To encourage the private sector to participate in the maritime sector, the Chinese government gives subsidies to invest in the private sector, the cost of which is recorded as ${\mathrm{C}}_0$. Subsidies are offered by the Chinese government to reduce the cost of private sector investment while simultaneously reducing the pressure to invest [65]. Subsidies, tax breaks, and other incentives, on the other hand, raise the Chinese government’s financial spending and burden the Chinese government [66]. A cost–benefit analysis is similar to how the Chinese government assesses costs and consequences [67,68,69]. According to some studies, investment firms have been discouraged from participating in the marine sector due to the high risks and unpredictability of investment income [70]. Chinese government subsidies have a significant role in encouraging the private sector to invest in the marine sector.

As a result, Chinese governmental involvement is essential to develop incentive measures to alleviate the scarcity of marine investment funds, as well as to play a role in directing and encouraging investment enterprises [71]. The Chinese government makes grants to foster and aid the creation of innovative enterprises. By obtaining governmental subsidies, the private sector can lessen its capital investment demands, lower its expenditures, and increase profits [72,73,74,75]. Furthermore, Zhao and Yang [76] established empirically that there is a substantial positive association between governmental subsidies and the business success of ocean-related firms; moreover, the larger the governmental subsidy, the better the enterprise’s business performance.

Some studies claim that governmental intervention to provide subsidies, although having a catalytic effect on firm performance, is just transitory. Subsidies are less effective since marine investment is frequently long-term [77]. Moreover, Zhen et al. [78] observed that Chinese government subsidies increase the private sector’s financial reliance, have a limited long-term impact on BFM growth, and increase the Chinese government’s financial burden.

2.3.2. Basic Hypothesis

Assuming the marine sector chooses to request BFI to raise financing, a game model between the private sector and the Chinese government is developed, as depicted by the dynamic game tree in Figure 3. The game model participants’ actions are as follows: The first phase involves the private sector deciding whether to invest in the marine industry, and the second involves the Chinese government deciding whether to intervene in the BFM.

The game model participants’ tactics may be summarized as follows: ${\mathrm{P}}_1$ (invest, intervene), ${\mathrm{P}}_2$ (invest, not intervene), ${\mathrm{P}}_3$ (not invest, intervene), ${\mathrm{P}}_4$ (not invest, not intervene).

2.3.3. Pure Strategy Nash Equilibrium Analysis

Reverse-engineering the game model uses the order of the players’ activities as a guide. The second issue of contention is whether the Chinese government will intervene in the BFM. The most effective way for the Chinese government to intervene is when the private sector’s activity is to invest. When the private sector does not invest, the Chinese government’s best approach is non-intervention. Continuing with the tree diagram study, the equilibrium strategy in this game associated with the sub game refined Nash equilibrium is ${\mathrm{P}}_1$ (invest, intervene), which means the private sector invests in the marine industry, and the Chinese government intervenes in BFM.

Based on the pure strategy Nash equilibrium analysis, the PSIMS can be considered as an equilibrium strategy when the Chinese government intervenes in a static game. The intervention of the Chinese government can take different forms, such as monetary incentives, which involve providing subsidies and tax breaks to reduce the investment costs of private enterprises. Alternatively, non-monetary incentives can also be used, including official recognition, media publicity, and other forms of commendation to acknowledge the contributions made by private sector entities (

Table 1. Chinese government intervention methods.

Government Intervention Methods	Monetary Incentives	Non-Monetary Incentives
	Subsidies	Official Recognition
	Tax Breaks	Media Publicity
	…	…

).

3. Model Analysis

3.1. Evolutionary Game Replication Dynamic Equation

The relationship between the Chinese government and the private sector in the BFM is best understood through the lens of public finance theory [79] and government management [80]. According to public finance theory, the Chinese government plays a crucial role in allocating resources and managing risks in the economy [81]. In the context of blue finance, the Chinese government can use various policies, such as tax incentives, subsidies, and guarantees, to encourage PSIMS. On the other hand, the private sector must balance its desire for financial returns with its obligation to consider the social and environmental impacts of its investment decisions. This interplay between government management and private sector investment decisions is an ongoing game [82] in which the ultimate goal is to promote sustainable marine and coastal resource management while ensuring financial stability and economic growth. Therefore, the relationship between the private sector and the Chinese government can be analyzed within the framework of an evolutionary game.

According to evolutionary game theory, if the fitness of a single strategy is larger than the population’s average fitness, the proportion of selections among such strategies will continuously increase [83]. The growth rate is determined by the differential equation of replicator dynamics, and the greater the value of replicator dynamics, the quicker the proportion of strategy selection increases [78]. The sustainability of BFM relies on the dynamics of the choice of the Chinese government and the private sector’s strategies. A cooperative alliance network can enhance the benefits of the entire mechanism [84]. Understanding the relationship between cooperation behaviors and the underlying network dynamics is essential for better policy making [85].

The private sector and the Chinese government make strategic decisions based on their preferences. The likelihood that the private sector will choose the “invest” strategy is $\mathsf{\alpha }$, while the probability that the private sector will choose the “not invest” approach is $1-\mathsf{\alpha }$. The chance that the Chinese government will choose the “intervene” approach is $\mathsf{\beta }$, while the probability that the Chinese government will choose the “not intervene” strategy is $1-\mathsf{\beta }, \mathsf{\alpha },\mathsf{\beta }\in \left[0,1\right]$. When combined with the model hypothesis in

Table 2. Game payoff matrix for the private sector and the Chinese government.

	Game Players
	Private Sector	Chinese Government
${\mathrm{P}}_1$	${\mathrm{R}}_1+{\mathrm{IR}}_0+{\mathrm{C}}_0$	${\mathrm{GR}}_1+{\mathrm{ER}}_0+{\mathrm{C}}_0$
${\mathrm{P}}_2$	${\mathrm{R}}_2+{\mathrm{IR}}_0$	${\mathrm{GR}}_2+{\mathrm{ER}}_0$
${\mathrm{P}}_3$	${\mathrm{R}}_3$	${\mathrm{GR}}_3-{\mathrm{C}}_0$
${\mathrm{P}}_4$	${\mathrm{R}}_3$	${\mathrm{GR}}_3$

, the anticipated revenues of the private sector using the “invest” and “not invest” strategies and its average revenue are ${\mathrm{E}}_{1,1}$, ${\mathrm{E}}_{1,2}$, and ${\mathrm{E}}_{1,0}$, as determined below.

$${\mathrm{E}}_{1,1}=\mathsf{\beta }\left({\mathrm{R}}_1+{\mathrm{IR}}_0+{\mathrm{C}}_0\right)+\left(1-\mathsf{\beta }\right)\left({\mathrm{R}}_2+{\mathrm{IR}}_0\right)$$

(1)

$${\mathrm{E}}_{1,2}={\mathrm{R}}_3$$

(2)

$${\mathrm{E}}_{1,0}={\mathsf{\alpha }\mathrm{E}}_{1,1}+\left(1-\mathsf{\alpha }\right){\mathrm{E}}_{1,2}={\mathsf{\alpha }\mathsf{\beta }\mathrm{R}}_1+\alpha {\mathrm{IR}}_0+{\mathsf{\alpha }\mathsf{\beta }\mathrm{C}}_0+\mathsf{\alpha }\left(1-\mathsf{\beta }\right){\mathrm{R}}_2+\left(1-\mathsf{\alpha }\right){\mathrm{R}}_3$$

(3)

For the probability of the private sector choosing the “invest” strategy, the evolutionary game replication dynamic equation is:

$$\begin{array}{c}\mathrm{F}\left(\mathsf{\alpha }\right)=\mathrm{d}\mathsf{\alpha }/\mathrm{dt}=\mathsf{\alpha }\left(1-\mathsf{\alpha }\right)\left({\mathrm{E}}_{1,1}-{\mathrm{E}}_{1,2}\right)=-\mathsf{\alpha }\left(\mathsf{\alpha }-1\right)({\mathsf{\beta }\mathrm{R}}_1+{\mathrm{IR}}_0+{\mathsf{\beta }\mathrm{C}}_0+\\ \left(1-\mathsf{\beta }\right){\mathrm{R}}_2-{\mathrm{R}}_3)\end{array}$$

(4)

The predicted revenues for the Chinese government’s “intervene” and “do not intervene” strategies and its average revenues are ${\mathrm{E}}_{2,1}$, ${\mathrm{E}}_{2,2}$, and ${\mathrm{E}}_{2,0}$, respectively, as computed below.

$${\mathrm{E}}_{2,1}={\mathsf{\alpha }\mathrm{GR}}_1+{\mathsf{\alpha }\mathrm{ER}}_0+\left(1-\mathsf{\alpha }\right){\mathrm{GR}}_3-{\mathrm{C}}_0$$

(5)

$${\mathrm{E}}_{2,2}=\mathsf{\alpha }\left({\mathrm{GR}}_2+{\mathrm{ER}}_0\right)+\left(1-\mathsf{\alpha }\right){\mathrm{GR}}_3$$

(6)

$$\begin{array}{cc}{\mathrm{E}}_{2,0}={\mathsf{\beta }\mathrm{E}}_{2,1}+(1& -\mathsf{\beta }){\mathrm{E}}_{2,2}\\ & =\mathsf{\beta }\left(\left({\mathrm{C}}_0-{\mathrm{GR}}_3\right)\left(\mathsf{\alpha }-1\right)+\mathsf{\alpha }\left({\mathrm{ER}}_0-{\mathrm{C}}_0+{\mathrm{GR}}_1\right)\right)-\mathsf{\alpha }({\mathrm{ER}}_0\\ & +{ \mathrm{GR}}_2)-{\mathrm{GR}}_3\left(\mathsf{\alpha }-1\right)\left(\mathsf{\beta }-1\right)\end{array}$$

(7)

For the probability of the Chinese government to choose the “intervene” option, the evolutionary game replication dynamic equation is:

$$\mathrm{F}\left(\mathsf{\beta }\right)=\mathrm{d}\mathsf{\beta }/\mathrm{dt}=\mathsf{\beta }\left(1-\mathsf{\beta }\right)\left({\mathrm{E}}_{2,1}-{\mathrm{E}}_{2,2}\right)=\mathsf{\beta }\left(\mathsf{\beta }-1\right)\left({\mathrm{C}}_0-{\mathrm{GR}}_1\mathsf{\alpha }+{\mathrm{GR}}_2\mathsf{\alpha }\right)$$

(8)

Equations (9) and (10) comprise a system of repeated dynamic equations made up of Equations (4) and (8).

$$\begin{array}{cc}\mathrm{F}\left(\mathsf{\alpha }\right)=\mathrm{d}\mathsf{\alpha }/\mathrm{dt}=& \mathsf{\alpha }\left(1-\mathsf{\alpha }\right)\left({\mathrm{E}}_{1,1}-{\mathrm{E}}_{1,2}\right)\\ & =-\mathsf{\alpha }\left(\mathsf{\alpha }-1\right)\left({\mathrm{IR}}_0+{\mathrm{R}}_2-{\mathrm{R}}_3+\mathrm{C}\mathsf{\beta }+{\mathrm{R}}_1\mathsf{\beta }-{\mathrm{R}}_2\mathsf{\beta }\right)\end{array}$$

(9)

$$\mathrm{F}\left(\mathsf{\beta }\right)=\mathrm{d}\mathsf{\beta }/\mathrm{dt}=\mathsf{\beta }\left(1-\mathsf{\beta }\right)\left({\mathrm{E}}_{2.1}-{\mathrm{E}}_{2,2}\right)=\mathsf{\beta }\left(\mathsf{\beta }-1\right)\left({\mathrm{C}}_0-{\mathrm{GR}}_1\mathsf{\alpha }+{\mathrm{GR}}_2\mathsf{\alpha }\right)$$

(10)

3.2. Equilibrium Point and Stability Analysis

The local stability of the Jacobi matrix and the interest matrix, as stated in Friedman [86], may be used to assess if the strategy combinations generated by the two sides of the game are stable strategies, i.e., ESS [87,88,89]. It also investigates which factors influence both sides’ strategic decisions.

Such that the equations $\mathrm{F}\left(\mathsf{\alpha }\right)=\mathrm{d}\mathsf{\alpha }/\mathrm{dt}=0$ and $\mathrm{F}\left(\mathsf{\beta }\right)=\mathrm{d}\mathsf{\beta }/\mathrm{dt}=0$ of the replicated dynamic equation (Equation (8)), the five equilibrium points are obtained as

$$\mathrm{A}\left(0,0\right),\mathrm{B}\left(0,1\right),\mathrm{C}\left(1,0\right),\mathrm{D}\left(1,1\right),\mathrm{E}\left(x^{*},y^{*}\right)$$

where ${\mathrm{x}}^{*}={\mathrm{C}}_0/\left({\mathrm{GR}}_1-{\mathrm{GR}}_2\right),{ \mathrm{and} \mathrm{y}}^{*}=\left({\mathrm{IR}}_0+{\mathrm{R}}_2-{\mathrm{R}}_3\right)/({\mathrm{C}}_0+{\mathrm{R}}_1-{\mathrm{R}}_2)$, which also satisfy $0\le {\mathrm{x}}^{*}\le 1,0\le {\mathrm{y}}^{*}\le 1.$

The evolution of the private sector and Chinese government selection strategies may be described as a system by system (9). The Jacobi matrix [90,91,92,93] is

$$\mathrm{J} =\left[\begin{array}{cc}\frac{\partial \mathrm{F}\left(\mathsf{\alpha }\right)}{\partial \mathsf{\alpha }}& \frac{\partial \mathrm{F}\left(\mathsf{\alpha }\right)}{\partial \mathsf{\beta }}\\ \frac{\partial \mathrm{F}\left(\mathsf{\beta }\right)}{\partial \mathsf{\alpha }}& \frac{\partial \mathrm{F}\left(\mathsf{\beta }\right)}{\partial \mathsf{\beta }}\end{array}\right]$$

where

$$\frac{\partial \mathrm{F}\left(\mathsf{\alpha }\right)}{\partial \mathsf{\alpha }}=\left(1-2\mathsf{\alpha }\right)\left({\mathrm{IR}}_0+{\mathrm{R}}_2-{\mathrm{R}}_3+{\mathrm{C}}_0\mathsf{\beta }+{\mathrm{R}}_1\mathsf{\beta }-{\mathrm{R}}_2\mathsf{\beta }\right)$$

(11)

$$\frac{\partial \mathrm{F}\left(\mathsf{\alpha }\right)}{\partial \mathsf{\beta }}=-\mathsf{\alpha }\left(\mathsf{\alpha }-1\right)\left({\mathrm{C}}_0+{\mathrm{R}}_1-{\mathrm{R}}_2\right)$$

(12)

$$\frac{\partial \mathrm{F}\left(\mathsf{\beta }\right)}{\partial \mathsf{\alpha }}=-\mathsf{\beta }\left({\mathrm{GR}}_1-{\mathrm{GR}}_2\right)\left(\mathsf{\beta }-1\right)$$

(13)

$$\frac{\partial \mathrm{F}\left(\mathsf{\beta }\right)}{\partial \mathsf{\beta }}=\mathsf{\beta }\left({\mathrm{C}}_0-{\mathrm{GR}}_1\mathsf{\alpha }+{\mathrm{GR}}_2\mathsf{\alpha }\right)+\left(\mathsf{\beta }-1\right)\left({\mathrm{C}}_0-{\mathrm{GR}}_1\mathsf{\alpha }+{\mathrm{GR}}_2\mathsf{\alpha }\right)$$

(14)

When a local equilibrium fulfills the Jacobi matrix’s determinant $\det \left(\mathrm{J}\right)>0$ and trace $\mathrm{tr}\left(\mathrm{J}\right)<0$, it is a stable evolutionary strategy [86].

The determinant and trace of the Jacobi matrix are obtained by combining the aforementioned analyses; $\det \left(\mathrm{J}\right)>0$ and $\mathrm{tr}\left(\mathrm{J}\right)$ are:

$$\det \left(\mathrm{J}\right)=\frac{\partial \mathrm{F}\left(\mathsf{\alpha }\right)}{\partial \mathsf{\alpha }}\times \frac{\partial \mathrm{F}\left(\mathsf{\beta }\right)}{\partial \mathsf{\beta }}-\frac{\partial \mathrm{F}\left(\mathsf{\alpha }\right)}{\partial \mathsf{\beta }}\times \frac{\partial \mathrm{F}\left(\mathsf{\beta }\right)}{\partial \mathsf{\alpha }}$$

(15)

$$\mathrm{tr}\left(\mathrm{J}\right)=\frac{\partial \mathrm{F}\left(\mathsf{\alpha }\right)}{\partial \mathsf{\alpha }}+\frac{\partial \mathrm{F}\left(\mathsf{\beta }\right)}{\partial \mathsf{\beta }}$$

(16)

The five equilibrium points, as given in

Table 3. The numerical expressions of the local stabilities of equilibrium points.

Equilibrium	$\mathbf{d}\mathbf{e}\mathbf{t}\left(\mathbf{J}\right)$	$\mathbf{t}\mathbf{r}\left(\mathbf{J}\right)$
$\mathrm{A}\left(0,0\right)$	${\mathrm{IR}}_0+{\mathrm{R}}_2-{\mathrm{R}}_3$	${\mathrm{IR}}_0+{\mathrm{R}}_2-{\mathrm{R}}_3-{\mathrm{C}}_0$
$\mathrm{B}\left(0,1\right)$	$\left({\mathrm{IR}}_0-{\mathrm{R}}_3+{\mathrm{C}}_0+{\mathrm{R}}_1\right){\mathrm{C}}_0$	${\mathrm{IR}}_0+{\mathrm{R}}_2-{\mathrm{R}}_3+{\mathrm{C}}_0+{\mathrm{R}}_1-{\mathrm{R}}_2+{\mathrm{C}}_0$
$\mathrm{C}\left(1,0\right)$	$({\mathrm{R}}_3-{\mathrm{R}}_2-{\mathrm{IR}}_0)\left({\mathrm{GR}}_1-{\mathrm{GR}}_2-{\mathrm{C}}_0\right)$	$\left({\mathrm{R}}_3-{\mathrm{R}}_2-{\mathrm{IR}}_0\right)\left({\mathrm{GR}}_1-{\mathrm{GR}}_2-{\mathrm{C}}_0\right)$
$\mathrm{D}\left(1,1\right)$	$\begin{array}{cc}({\mathrm{R}}_2-{\mathrm{R}}_1-{\mathrm{C}}_0+& {\mathrm{R}}_3-{\mathrm{R}}_2-{\mathrm{IR}}_0\left)\right({\mathrm{C}}_0\\ & -{\mathrm{GR}}_1+{\mathrm{GR}}_2)\end{array}$	$\begin{array}{cc}({\mathrm{R}}_2-{\mathrm{R}}_1-{\mathrm{C}}_0+& {\mathrm{R}}_3-{\mathrm{R}}_2-{\mathrm{IR}}_0\left)\right({\mathrm{C}}_0\\ & -{\mathrm{GR}}_1+{\mathrm{GR}}_2)\end{array}$
$\mathrm{E}\left(x^{*},y^{*}\right)$	$\begin{array}{cc}[{\mathrm{C}}_0/\left({\mathrm{GR}}_1-{\mathrm{GR}}_2\right)& \left(\right({\mathrm{C}}_0/\left({\mathrm{GR}}_1-{\mathrm{GR}}_2\right))\\ & -1\left)\right({\mathrm{C}}_0+{\mathrm{R}}_1\\ & -{\mathrm{R}}_2\left)\right]\left[\right({\mathrm{R}}_3-{\mathrm{R}}_2\\ & -{\mathrm{IR}}_0)/({\mathrm{C}}_0+{\mathrm{R}}_1\\ & -{\mathrm{R}}_2\left)\right(1+({\mathrm{IR}}_0+{\mathrm{R}}_2\\ & -{\mathrm{R}}_3)/({\mathrm{C}}_0+{\mathrm{R}}_1\\ & -{\mathrm{R}}_2\left)\right)\left({\mathrm{GR}}_1-{\mathrm{GR}}_2\right)]\end{array}$	$0$

Note: $x^{*}={\mathrm{C}}_0/\left({\mathrm{GR}}_1-{\mathrm{GR}}_2\right), \mathrm{and} y^{*}=\left({\mathrm{IR}}_0+{\mathrm{R}}_2-{\mathrm{R}}_3\right)/({\mathrm{C}}_0+{\mathrm{R}}_1-{\mathrm{R}}_2))$.

, were submitted to stability analysis.

The following conclusions can be derived based on the ESS (

Table 4. Local stability of equilibrium points.

Equilibrium	$\mathbf{d}\mathbf{e}\mathbf{t}\left(\mathbf{J}\right)$	$\mathbf{t}\mathbf{r}\left(\mathbf{J}\right)$	Stability
$\mathrm{A}\left(0,0\right)$	$+$	$-$	$\mathrm{ESS}$
$\mathrm{B}\left(0,1\right)$	$+$	$+$	Unstable point
$\mathrm{C}\left(1,0\right)$	$+$	$+$	Unstable point
$\mathrm{D}\left(1,1\right)$	$+$	$-$	$\mathrm{ESS}$
$\mathrm{E}\left(x^{*},y^{*}\right)$	$+$	$\times$	Meaningless

) determination conditions: The stable strategies of the evolutionary game are $\left(0,0\right)$ and $\left(1,1\right)$, where $\left(1,1\right)$ is the cooperative strategy of the participating subjects, $\left(0,1\right)$ and $\left(1,0\right)$ are unstable positions, and $\mathrm{E}\left(x^{*},y^{*}\right)$ is the saddle point.

The evolutionary game’s steady state analysis allows for the following deductions (Figure 4):

(1)

When $\mathsf{\beta }={\mathrm{y}}^{*}\left(0\le {\mathrm{y}}^{*}\le 1\right)$, there is always $\mathrm{F}\left(\mathsf{\alpha }\right)=0$, meaning that the system will reach the evolutionary steady state regardless of the values in the definition domain; similarly, when the probability of Chinese government subsidies is ${\mathrm{y}}^{*}$, the revenue of the private sector choosing to invest or not in the marine industry is unaffected. When $\mathsf{\alpha }={\mathrm{x}}^{*}\left(0\le {\mathrm{x}}^{*}\le 1\right)$, there is always $\mathrm{F}\left(\mathsf{\beta }\right)=0$, which means the system will reach an evolutionary steady state regardless of the value taken in the definition domain; when the probability of the private sector investing in the marine industry is ${\mathrm{x}}^{*}$, it makes no difference whether the Chinese government chooses to subsidize or not.

(2)

When $\mathsf{\alpha }>{\mathrm{x}}^{*}$, the evolutionary game will achieve a stable state; $\mathsf{\beta }=0$ and $\mathsf{\beta }=1$ are two feasible stable points. Alternatively, when at $\mathsf{\beta }=1$, $\partial \mathrm{F}\left(\mathrm{y}\right)$/$\partial \mathrm{y}<0$, the evolutionary game will reach a stable state, and $\mathsf{\beta }=1$ is the only viable stable point. Therefore, Chinese government stability by intervention in BFM to fund the private sector is an evolutionary approach. Similar to this, governmental non-intervention for subsidies is the evolutionary stable strategy, where $\mathsf{\alpha }<{\mathrm{x}}^{*}$ and $\mathsf{\beta }=0$ is the only conceivable stable position.

(3)

When $\mathsf{\beta }>{\mathrm{y}}^{*}$, then $\mathsf{\alpha }=0$ and $\mathsf{\alpha }=1$ are two conceivable stable state points; however, at $\mathsf{\beta }=1$, $\partial \mathrm{F}\left(\mathsf{\alpha }\right)$/$\partial \mathsf{\alpha }<0$ will attain a stable state, and $\mathsf{\alpha }=1$ is the sole possible stable point, implying that investing in the marine sector is an evolutionary stable strategy for the private sector. Similarly, $\mathsf{\beta }<{\mathrm{y}}^{*}$ and $\mathsf{\alpha }=0$ is the only conceivable stable point, and avoiding engaging in the maritime business is a stable evolutionary strategy for the private sector.

(4)

The equilibrium point’s phase diagram may be obtained; when ($\mathsf{\alpha },\mathsf{\beta }$) falls in the BECD area, the system will converge to the ideal state in which the Chinese government decides to subsidize and the private sector opts to invest in the maritime sector. When ($\mathsf{\alpha },\mathsf{\beta }$) falls in the ABEC area, the evolutionary game results in an unfavorable state in which the Chinese government decides not to subsidize and the private sector opts not to invest in the maritime industry.

When comparing the areas ${\mathrm{S}}_1$ of ABEC and ${\mathrm{S}}_2$ of BECD, when ${\mathrm{S}}_2>{\mathrm{S}}_1$, the two sides of the game tend to evolve in the direction of cooperation (namely, the Chinese government chooses to subsidize, and the private sector chooses to invest); conversely, when ${\mathrm{S}}_2<{\mathrm{S}}_1$, the two sides of the game’s final strategy choice evolve in the direction of non-cooperation (namely, the Chinese government chooses not to subsidize, and the private sector chooses not to invest). In selecting a cooperative approach, analyzing which aspects can impact the stable condition of the two sides of the game must be conducted. The characteristics that influence the size of the ${\mathrm{S}}_2$ region must then be investigated. The formula for the ${\mathrm{S}}_2$ area is presented below.

$${\mathrm{S}}_2=1+1/2\left[\left({\mathrm{IR}}_0+{\mathrm{R}}_2-{\mathrm{R}}_3\right)/\left({\mathrm{C}}_0+{\mathrm{R}}_1-{\mathrm{R}}_2\right)-{\mathrm{C}}_0/\left({\mathrm{GR}}_1-{\mathrm{GR}}_2\right)\right]$$

(17)

According to ${\mathrm{S}}_2$, the factors influencing the size of the ${\mathrm{S}}_2$ region are ${\mathrm{IR}}_0,{ \mathrm{C}}_0,{ \mathrm{R}}_1,{ \mathrm{R}}_2,{ \mathrm{R}}_3,{ \mathrm{GR}}_1,{ \mathrm{and} \mathrm{GR}}_2$. The findings obtained by using ${\mathrm{S}}_2$ to calculate the partial derivatives of each of these parameters are provided in Table 3, with “$+$” indicating a positive correlation, “$-$” indicating a negative correlation, and “$/$” indicating no detectable association.

From

Table 5. Parameter impact analysis of strategy selection.

Parameter	Partial Derivatives	$\mathbf{Relationship} \mathbf{with} {\mathbf{S}}_2$
${\mathrm{IR}}_0$	$>0$	$+$
${\mathrm{C}}_0$	$/$	$/$
${\mathrm{R}}_1$	$/$	$/$
${\mathrm{R}}_2$	$/$	$/$
${\mathrm{R}}_3$	$<0$	$-$
${\mathrm{GR}}_1$	$>0$	$+$
${\mathrm{GR}}_2$	$<0$	$-$

, ${\mathrm{IR}}_0$ is favorably associated with ${\mathrm{S}}_2$. When ${\mathrm{IR}}_0$ rises, ${\mathrm{S}}_2$ rises as well. The more the intangible revenue generated to PSIMS, the more the private sector is likely to pick a strategy of investing in the maritime sector that benefits it. Simultaneously, the intangible revenue of investment in the marine sector to the private sector is often produced as a result of the private sector taking marine ecological conservation into account. When the ${\mathrm{IR}}_0$ is higher, it indicates that the marine environment is more protected and hence more useful to the Chinese government. Profit for both parties drive the private sector–government collaboration agenda.

${\mathrm{R}}_3$ is inversely linked to ${\mathrm{S}}_2$. ${\mathrm{S}}_2$ falls as ${\mathrm{R}}_3$ grows. When it comes to the private sector, the higher the revenue produced by not investing in the marine industry, the more it signifies that investing in non-marine industries is profitable for the private sector that does not choose to participate in the marine business. Instead, the Chinese government desires PSIMS. As a result, the private sector rebels against the administration, causing both parties to end their collaboration and pursue a non-cooperation approach.

${\mathrm{S}}_2$ and ${\mathrm{GR}}_1$ have a positive correlation. ${\mathrm{S}}_2$ rises when ${\mathrm{GR}}_1$ increases. The Chinese government decides to interfere in BFM to subsidize based on the premise that the larger the return to the Chinese government through PSIMS, the more the Chinese government prefers to subsidize. The Chinese government obtains more advantages than the cost of the subsidies given, which tends to subsidize the strategy. The fact that PSIMS provide a sizable return for the Chinese government concurrently suggests that private sector investment revenue is sizable. As a result, the private sector frequently invests in the marine industry. As a result, the Chinese government and the private sector both choose the collaboration method that maximizes gains.

${\mathrm{S}}_2$ is adversely connected to ${\mathrm{GR}}_2$. ${\mathrm{S}}_2$ falls as ${\mathrm{GR}}_2$ grows. The Chinese government decides not to subsidize on the grounds that the higher the return from PSIMS, the greater the likelihood that the Chinese government may obtain a large amount of income without subsidies. As a result, the Chinese government selects the more advantageous no-subsidy alternative. The lack of Chinese government subsidies will raise the burden of investment expenditures on the private sector. Because of the high investment cost over time, the private sector prefers to invest in non-marine industries where the investment cost is substantially lower. As a result, the private sector and the Chinese government opt for the non-cooperation policy.

The relationships among ${\mathrm{C}}_0$, ${\mathrm{R}}_1$, ${\mathrm{R}}_2$, ${\mathrm{R}}_3$, and ${\mathrm{S}}_2$ is unknown. Moreover, it is obvious from the formula of ${\mathrm{S}}_2$ that the combined relationship of ${\mathrm{R}}_1-{\mathrm{R}}_2$, ${\mathrm{R}}_2-{\mathrm{R}}_3$ on ${\mathrm{S}}_2$ influences ${\mathrm{R}}_1$, ${\mathrm{R}}_2$, and ${\mathrm{R}}_3$, and its relationship with ${\mathrm{S}}_2$ cannot be appropriately elaborated by partial derivatives alone. ${\mathrm{S}}_2$ is likewise affected by ${\mathrm{GR}}_1$ and ${\mathrm{GR}}_2$ by combining the differences, which are also compared in the form of parameter sets for the sake of observation. In summary, there are five kinds of factors and parameter combinations that might influence the strategy choice of participating individuals.

The meanings indicated by the parameters and parameter combinations are shown in

Table 6. Meaning of parameters and parameter combinations.

Parameters and Parameter Combinations	Player	Meaning
${\mathrm{C}}_0$	Chinese government	Government cost of subsiding PSIMS.
${\mathrm{GR}}_1-{\mathrm{GR}}_2$	Chinese government	The difference in governmental revenue from PSIMS with and without governmental involvement.
${\mathrm{IR}}_0$	Private sector	Regulations introduced by the Chinese government have decreased the uncertainty of investment in the maritime sector, and the intangible advantages achieved by enterprises are recorded.
${\mathrm{R}}_1-{\mathrm{R}}_2$	Private sector	The difference in private sector revenue with and without governmental involvement.
${\mathrm{R}}_2-{\mathrm{R}}_3$	Private sector	The difference between the revenue gained by enterprises investing in marine industry and non-marine industry without governmental intervention.

. ${\mathrm{C}}_0$ and ${\mathrm{GR}}_1-{\mathrm{GR}}_2$ are government-related, whereas the remaining ones are private sector-related. The cost of Chinese government subsidies to PSIMS is denoted by ${\mathrm{C}}_0$. ${\mathrm{GR}}_1-{\mathrm{GR}}_2$ is the difference in Chinese government revenue from PSIMS with and without Chinese government engagement. ${\mathrm{IR}}_0$ denotes the intangible advantages to the private sector from Chinese government engagement in BFM. ${\mathrm{R}}_1-{\mathrm{R}}_2$ and ${\mathrm{R}}_2-{\mathrm{R}}_3$ both exhibit the variance value in relation to private sector income. ${\mathrm{R}}_1-{\mathrm{R}}_2$ denotes the difference in the private sector’s revenue with and without Chinese government participation, while ${\mathrm{R}}_2-{\mathrm{R}}_3$ denotes the difference in income generated by firms investing in the marine industry against non-marine industries without Chinese governmental involvement.

As a result, the dynamic evolution process will be carried out numerically in the next section to demonstrate more clearly how these five sets of parameters and parameter combinations affect the strategy choice of participating individuals.

4. Numerical Simulation Analysis

Numerical simulation analysis is used to investigate the influence of the elements and parameter combinations listed in

Table 7. Strategy selection and results.

Factor		Governmental Intervention	Strategy Selection
			The Private Sector	Chinese Government	{Invest, Intervene} Strategy
			“Intervene” Strategy	“Invest” Strategy
Different Initial Probabilities		Yes	Yes	Yes	Yes
Parameters	${\mathrm{C}}_0$	Yes	Yes	Yes	Yes
	${\mathrm{GR}}_1-{\mathrm{GR}}_2$	Yes	Yes	-	Yes
	${\mathrm{IR}}_0$	Yes	-	Yes	Yes
	${\mathrm{R}}_1-{\mathrm{R}}_2$	Yes	-	Yes	Yes
	${\mathrm{R}}_2-{\mathrm{R}}_3$	No	-	Yes	Yes
	${\mathrm{ER}}_0$	Yes	-	-	-
	${\mathrm{GR}}_3$	No	-	-	-

on player strategy selection and to depict strategy choices around dynamic development more simply and intuitively. In addition, simulations can be utilized to optimize the dynamic and ongoing game between the Chinese government and the private sector, leading to the timely implementation of effective strategies for both sides. In this section, MATLAB software was utilized to run numerical simulations of the created evolutionary game model.

According to the assumptions, Chinese government action in macroregulation would boost the economic advantages of the maritime sector [57], and therefore the investment return ${\mathrm{R}}_1$ achieved by the private sector would be greater than the investment return ${\mathrm{R}}_2$ acquired in the absence of governmental intervention. Because of the significant risk of the maritime business, investment returns are highly unclear [70]. Because of the high cost in comparison to non-marine industries (land-based industries), which tend to mature, the return on investment ${\mathrm{R}}_2$ is less than ${\mathrm{R}}_3$. Because the Chinese government intervenes to provide an incentive subsidy, the investment cost of PSIMS is lower and the payout is larger than in the non-marine business, and ${\mathrm{R}}_1$ is bigger than ${\mathrm{R}}_3$.

With the injection of funds into the marine industry, BFM has accelerated the construction of marine ecological infrastructure and maintained the marine ecosystem while promoting the development of the ocean economy [94]. As a supplier of funds, the private sector has contributed to marine ecological construction and marine economic development, received praise from Chinese government and society, and gained intangible revenue ${\mathrm{IR}}_0$ [95,96,97]. The Chinese government as the implementer of investment incentives receives praise ${\mathrm{ER}}_0$ from the public. ${\mathrm{ER}}_0$ is higher than ${\mathrm{IR}}_0$ because the influence of the Chinese government is significantly higher than the private sector, and the Chinese government can receive more policy incentives from the state sector as well. Similarly, the Chinese government must obtain a portion of the economic benefits of the marine industry in the form of taxes and so on. The bigger the economic benefits, the larger the governmental income [98].

Under governmental involvement, the revenue of marine industry businesses is large, and thus governmental revenue ${\mathrm{GR}}_1$ is bigger than ${\mathrm{GR}}_2$. Returns to marine industry without governmental intervention are lower than returns to mature non-marine industry (land-based industry); therefore, ${\mathrm{GR}}_2$ is less than ${\mathrm{GR}}_3$. The Chinese government expenses are incurred when incentives such as subsidies, tax refunds, and others are implemented, and the cost is at least equal to, if not greater than, the difference between the private sector’s return on investment in the marine industry and not without Chinese government aid. The private sector will only choose to invest in the marine business if the difference is more than or equal to this amount; otherwise, the hypothesis is invalid.

The values were scaled down evenly for observation, and the assignments were as follows: ${\mathrm{R}}_1=110$, ${\mathrm{R}}_2=70$, ${\mathrm{R}}_3=90$, ${\mathrm{IR}}_0=5$, ${\mathrm{GR}}_1=80$, ${\mathrm{GR}}_2=40$, ${\mathrm{GR}}_3=50$, ${\mathrm{C}}_0=20$, and ${\mathrm{ER}}_0=30$. According to Yang and Liang [99], the key characteristics are associated with the real growth of the maritime industry and the principle of balance. Simultaneously, the selected values of 5:35:60 were established to accurately capture the differences in strategic choices between the government and the private sector at varying levels, and to ensure consistency in the selection of values. This setting was intended to enhance the representativeness of the study outcomes.

The “Statistical Bulletin on China’s Ocean Economy in 2021” reported that China’s gross marine product exceeded CNY 9 trillion for the first time in 2021, reaching CNY 903.85 billion. It increased by 8.3% over the previous year and contributed 8.0% of the national economic growth. The primary, secondary, and tertiary sectors accounted for 5.0%, 33.4%, and 61.6% of the marine industry’s total value, respectively. Numerical simulations were run under these conditions. To simplify the math, the numerical ratio was lowered to 5:35:60.

This was followed by a simulated assessment of the stability of the evolutionary game system with varied starting probabilities for the private sector and the Chinese government. The effect of modifying the major parameters and parameter combinations on the stability of the system was investigated.

4.1. Effect of Different Initial Probabilities on the Stability of Evolving Game Systems

The effect of adjusting each participant’s beginning probability on the system’s stability was explored. When the starting time was zero and all other parameters remained constant, the chances of the Chinese government choosing the “subsidy” strategy and the private sector choosing the “invest” option were $\left(0.1, 0.1\right), \left(0.1, 0.9\right), \left(0.9, 0.1\right)$, and $\left(0.9, 0.9\right)$, respectively. The simulation results for various starting probabilities are shown in Figure 5. The private sector and the Chinese government will make various strategic decisions based on their initial probability. When the private sector’s readiness to invest and the governmental desire to intervene are both low, as illustrated in Figure 5a, the private sector and the Chinese government are less likely to collaborate.

As demonstrated in Figure 5b, when the private sector invests sooner in the maritime sector and the Chinese government is less likely to engage in BFM, the Chinese government and the private sector will adopt a cooperative approach at t = 0.3. When the Chinese government chooses to interfere in BFM early and the private sector is less likely to invest in the maritime industry, the Chinese government and the private sector will arrive at a cooperative approach at t = 0.35. By comparing Figure 5b and Figure 5c, it is clear that the desire of the private sector to invest is more essential in the BFM’s cooperation plan than the Chinese government’s readiness to act and can lead to an ideal strategy for both sides more rapidly.

However, there is no doubt that Chinese government engagement in BFM might entice the private sector to participate and achieve an “invest” strategic decision. When both the private sector and the Chinese government have a high initial likelihood of investing and intervening, both sides will agree on a cooperative approach at t = 0.12. It was demonstrated that both parties have the same willingness and may arrive at the best approach D (1, 1) as soon as feasible. The Chinese government’s participation is thus required to influence the private sector’s readiness to make investment decisions in the maritime industry. Furthermore, the Chinese government should become directly involved as soon as feasible. As a result, the aim of supporting BFM growth is achieved.

4.2. Effect of Chinese Government on the Stability of Evolutionary Game Systems

The impact of government-related factors and parameter combinations on the private sector’s strategy selection was tested. This section examined the impact of Chinese government subsidy programs, intangible benefits acquired, and underlying benefits (${\mathrm{GR}}_1$, ${\mathrm{GR}}_2$, and ${\mathrm{GR}}_3$) on the stability of the evolutionary game system under various assumptions. In order to conduct the comparison, the starting probabilities were assumed to be (0.4, 0.6).

(1) The effect of Chinese government subsidies (${\mathrm{C}}_0$): Keeping all other parameters constant, ${\mathrm{C}}_0$ was set to 5, 35, or 60, and the strategy evolution pathways of the Chinese government and businesses were compared; the results are illustrated in Figure 6. The model findings showed that varying the values of ${\mathrm{C}}_0$ has an effect on the stability of the evolutionary game system. When $\mathrm{t}<0.07$, if the amount of Chinese government subsidies (${\mathrm{C}}_0$ = 50) is the same at the same time node, the participating subjects will pick the investment and subsidy strategy as quickly as possible, and both sides will reach the steady state in the shortest time.

When $t=0.07$, the time it takes to reach the stable strategy varies considerably depending on the value of ${\mathrm{C}}_0$. The amount of Chinese government subsidy (${\mathrm{C}}_0=35$) is the fastest to reach a stable condition, but the amount of Chinese government subsidy (${\mathrm{C}}_0=50$) progressively prefers to invest rather than interfere. This indicates that within a limited range, the greater the Chinese government subsidies are, the greater the incentive for PSIMS, resulting in a positive effect. When ${\mathrm{C}}_0={\mathrm{Z}}_0$, ${\mathrm{Z}}_0$ is the lowest of the sum of ${\mathrm{GR}}_1$, ${\mathrm{ER}}_0$, and ${\mathrm{GR}}_3$, and the pace of stable strategy selection will be at its fastest. When the value surpasses the total of ${\mathrm{Z}}_0$, the Chinese government must choose between advantages and expenses.

The Chinese government finally adopts the “do not intervene” approach when the quantity of subsidies becomes smaller than the benefit achieved. There is no evolutionary stabilizing technique in place at the moment. To some extent, the amount of the subsidies may be considered as having a positive impact on the private sector’s decision to invest in the marine business. The larger the subsidy amount, however, the better; the Chinese government must carefully determine the most suitable value to maximize the incentive impact while protecting its own interests. As a result, the Chinese government offers a wide range of subsidies. Subsidies, being the most eloquent manifestation of incentives, play a crucial role in promoting BFM growth.

(2) The effect of the difference in governmental revenue (${\mathrm{GR}}_1-{\mathrm{GR}}_2$): The two parameters ${\mathrm{GR}}_1$ and ${\mathrm{GR}}_2$ clearly have an impact on the size of ${\mathrm{S}}_2$ in the form of a difference, as shown in the calculation for the area of ${\mathrm{S}}_2$. As a result, parameter combinations are explored in relation to ${\mathrm{GR}}_1$ and ${\mathrm{GR}}_2$. The discussion on ${\mathrm{GR}}_1$ with the influence of ${\mathrm{GR}}_2$ and ${\mathrm{GR}}_3$ is to ascertain how the underlying advantages to the Chinese government from private sector investment in various industries affect the evolutionary strategies of both parties.

Assume ${\mathrm{GR}}_1-{\mathrm{GR}}_2={\mathrm{GR}}_0$ from the preceding assumptions; then $0<{\mathrm{GR}}_2<{\mathrm{GR}}_1$, and so $0<{\mathrm{GR}}_0$, and set ${\mathrm{GR}}_0$ to 15, 105, and 180, respectively. The difference in governmental revenue from PSIMS with and without Chinese government engagement is shown by ${\mathrm{GR}}_0$. Figure 7 depicts the simulation findings. The larger the value of ${\mathrm{GR}}_0$, the faster the private sector can achieve the “invest” strategy. This demonstrates that the cheap cost and strong return on investment of the private sector under Chinese government subsidies encourages them to aggressively participate in the maritime sector. Simultaneously, the greater the value of ${\mathrm{GR}}_0$, the sooner the two parties engage to develop a steady strategy of $\left\{\mathrm{investment}, \mathrm{subsidy}\right\}$.

When ${\mathrm{GR}}_0$ is less than ${\mathrm{C}}_0$, the Chinese government selects the “not intervene” method since the benefits of investment in the maritime sector from both governmental involvement and non-intervention do not outweigh the costs of subsidies. However, when ${\mathrm{GR}}_0$ is smaller than ${\mathrm{C}}_0$, the Chinese government opts for the “not interfere” method since the advantages of investment in the maritime sector from both governmental involvement and non-intervention do not outweigh the costs of subsidies. Because the private sector may still earn money by investing in the maritime business, it opts for the “invest” method.

Finally, Chinese government engagement in the BFM and the private sector’s subsidies are critical to MIRE finance. As a result, the Chinese government should actively play the role of “visible hand” regulation, expanding social capital inflows, pushing blue finance growth, and encouraging long-term marine economic development.

4.3. Effect of the Private Sector Parameters on the Stability of the Evolutionary Game System

The private sectors are the developers who promote and completely use the marine sector’s resources. BFM cannot be implemented consistently unless PS provides financial support. This section focuses on the intangible and underlying benefits gained by marine firms, as well as how these traits affect the stability analysis of the evolutionary game system. For the sake of comparison, the initial probability is also taken to be (0.4, 0.6).

(1) The effect of PSIMS’s intangible returns (${\mathrm{IR}}_0$): PSIMS actively encourages local economic development and contributes to the development of marine resources. At the same time, marine investment emphasizes marine ecological conservation and promotes sustainable ocean development, earning the private sector’s accolades from the Chinese government and social organizations while also growing firm reputation. Furthermore, the Chinese government intervenes to build corresponding laws to oversee the marine investment market, lowering the risk of marine sector investment and providing an intangible benefit to the private sector.

The monetary value of intangible advantages obtained by the private sector are changed while holding all other factors unchanged. Let ${\mathrm{IR}}_0$ be 0.5, 3.5, or 6, and the simulation analysis results are displayed in Figure 8. When $t>0.17$, the private sector tends to stabilize its strategy faster than the Chinese government, as shown by Figure 8a–c. Furthermore, the magnitude of intangible advantages acquired by the private sector influences the private sector’s evolutionary stabilization method and influences the Chinese government’s evolutionary pace. When ${\mathrm{IR}}_0$ is larger, there is a stronger incentive for the private sector to engage in the maritime sector, and the model can converge to a steady state more quickly than can the benchmark model. As a result, the evolutionary stability time of the Chinese government is shortened. As a result, the Chinese government praises PSIMS’s investment behavior via news coverage, honorary certificates, and in other ways. Moreover, the Chinese government could create PSIMS-related regulations to encourage the private sector to participate in the BFM.

(2) The effect of the difference in PSIMS revenue (${\mathrm{R}}_1-{\mathrm{R}}_2$): To test how the gains delivered to the private sector by investing in adjacent industries impact both parties’ evolutionary strategies, while examining separately the implications of ${\mathrm{R}}_1$, ${\mathrm{R}}_2$, and ${\mathrm{R}}_3$. It is obvious from the formula for the area of ${\mathrm{S}}_2$ that three parameters, namely, ${\mathrm{R}}_1$, ${\mathrm{R}}_2$, and ${\mathrm{R}}_3$, influence the size of ${\mathrm{S}}_2$ in the form of the difference. As a result, ${\mathrm{R}}_1$, ${\mathrm{R}}_2$, and ${\mathrm{R}}_3$ are discussed as a set of parameters.

Based on the preceding assumptions, $0<{\mathrm{R}}_2<{\mathrm{R}}_3$, it is clear that the difference of ${\mathrm{R}}_1-{\mathrm{R}}_2$ is higher than 0. Assume ${\mathrm{R}}_1-{\mathrm{R}}_2={\mathrm{H}}_0$, and set ${\mathrm{H}}_0$ to 10, 70, and 120, respectively. Figure 9 depicts the findings of the simulation analysis. When ${\mathrm{H}}_0$ = 10, the private sector and the Chinese government choose to invest rather than interfere, as shown by Figure 9a–c. The reason for this is because the difference of ${\mathrm{R}}_1-{\mathrm{R}}_2$ is smaller than ${\mathrm{C}}_0$. Because the Chinese government is losing money on the cost–benefit trade-off, it chooses not to interfere in the BFM. For the private sector, investing in the maritime business is still a profitable option; hence, they prefer to invest in the marine industry.

When ${\mathrm{H}}_0=70$ and $120$, both the private sector and the Chinese government tend to invest and interfere. The rationale for this is because the option of investment and involvement allows them to benefit participants. Comparing Figure 9b and c demonstrates that the greater the value of ${\mathrm{H}}_0$, the better it is for the private sector. As a result, the rate of convergence to the cooperative approach increases. ${\mathrm{H}}_0$ denotes the difference in returns obtained by the private sector with and without governmental involvement. According to the private sector’s action plans, governmental intervention helps to encourage PSIMS. The Chinese government should play a role in diversifying intervention mechanisms in order to entice private sector more to join in the BFM and boost the growth of the ocean economy.

(3) The effect of the difference in income between the private sector investing in the marine and non-marine industries (${\mathrm{R}}_2-{\mathrm{R}}_3$): Without governmental involvement, varying returns to enterprises investing in the maritime industry versus those investing in non-marine industries while holding other factors constant. Let ${\mathrm{R}}_2-{\mathrm{R}}_3={\mathrm{K}}_0$. Based on the assumptions, ${\mathrm{R}}_3>{\mathrm{R}}_2$; hence, ${\mathrm{K}}_0$ is negative. Let ${\mathrm{K}}_0$ be −5, −35, or −60, as appropriate. Figure 10 depicts the findings of the simulation analysis. The greater the absolute value of ${\mathrm{K}}_0$, the greater the return of the private sector investing in non-marine industries over those investing in marine industries. The comparison of Figure 10a–c demonstrates that as the absolute value of K grows, the quicker the private sector and the stable strategy of the Chinese government would be $\left\{\mathrm{invest} \mathrm{intervene}\right\}$.

${\mathrm{R}}_1>{\mathrm{R}}_3$ are the assumptions that can be known. As a result, whatever the absolute value of ${\mathrm{K}}_0$ is, it has no impact on the eventual strategy of the private sector and the Chinese government. However, the greater the absolute value of ${\mathrm{K}}_0$, the sooner the private sector and the Chinese government are likely to use the collaborate strategy because the Chinese government would have a feeling of crisis when the private sector invests in non-marine industries with considerably better returns than the marine business. In order to support the growth of the ocean economy, the Chinese government will intervene in the BFM more swiftly and implement incentives to entice the private sector to invest. The private sector continues to choose the “invest” strategy because the non-marine sector returns are still lower than returns from investing in the marine industry with governmental involvement.

The assumptions that can be known are ${\mathrm{R}}_1>{\mathrm{R}}_3$. Consequently, regardless of the absolute value of ${\mathrm{K}}_0$, it does not affect the choice of the final strategy of the private sector and the Chinese government. However, the larger the absolute value of ${\mathrm{K}}_0$, the faster the private sector and Chinese government will tend to choose the cooperate strategy because the Chinese government will have a sense of crisis when the private sector invests in the non-marine industry with much higher returns than the marine industry. In view of the original intention to promote the development of the ocean economy, the Chinese government will intervene in the BFM more quickly and adopt incentives to attract the private sector to invest. Since returns of the non-marine industry are still lower than the returns of investing in the marine industry with governmental intervention, the private sector still chooses the “invest” strategy. Although the absolute value of ${\mathrm{K}}_0$ influences the speed of strategy choosing of participating participants, the effect is minor and nearly non-existent. As a result, the magnitude of ${\mathrm{K}}_0$ has no effect on the strategy chosen by the participating subjects and plays only a minimal role in the evolution of BFM.

4.4. Effects of Other Parameters ($E{R}_0$, $G{R}_3$)

To investigate if criteria other than those involved in the S2 area formula influence the strategy choice of participating participants, evolutionary simulations were run for the remaining parameters ${\mathrm{ER}}_0$ and ${\mathrm{GR}}_3$.

Keeping all other parameters constant, set ${\mathrm{ER}}_0=2, 14, 24$ and compare the strategy development pathways of the private sector and the Chinese government. Figure 11a–c depicts the findings. Without a doubt, players prefer to stabilize their strategies around t = 0.83, regardless of the value of ${\mathrm{ER}}_0$ used. This indicates that the private sector opts for the “invest” method, while the Chinese government opts for the “intervene” option. Nonetheless, the intangible benefits of PSIMS to the private sector have little effect on player strategy selection.

Furthermore, ${\mathrm{GR}}_3$ is set to 5, 35, and 60. Figure 12 shows that regardless of the value of ${\mathrm{GR}}_3$, the choice of the private sector and Chinese government tactics is unaffected. Both sides will try to keep their strategic choices stable.

4.5. Discussion of Results

Several findings are shown in Table 7. Differences in the initial probability of the private sector and Chinese government adoption can influence strategy choices for both parties. The influence of Chinese government engagement is reflected in the parameters ${\mathrm{C}}_0$,${ \mathrm{GR}}_1-{\mathrm{GR}}_2$, ${\mathrm{IR}}_0$, ${\mathrm{R}}_1-{\mathrm{R}}_2$, and ${\mathrm{ER}}_{0 }$. Except for ${\mathrm{ER}}_0$ and ${\mathrm{GR}}_3$, the magnitude of parameters can impact the selection of the private sector and Chinese government strategies: ${\mathrm{C}}_0$ impacts both the private sector and Chinese government; ${ \mathrm{GR}}_1-{\mathrm{GR}}_2$ influence solely the private sector; while ${\mathrm{IR}}_0$, ${\mathrm{R}}_1-{\mathrm{R}}_2$ and ${\mathrm{R}}_2-{\mathrm{R}}_3$ affect the Chinese government. Furthermore, to the degree that they affect either the private sector or the Chinese government, these characteristics will eventually have an impact on the choice of cooperation approach ({invest, intervene}).

Although ${\mathrm{ER}}_0$ considers Chinese government engagement, the evolutionary findings reveal that its value has no effect on the two parties’ choices of strategy. ${\mathrm{GR}}_3$ is likewise not a significant factor in strategy outcomes. Simulation trials with various parameters demonstrated that the Chinese government’s participation is critical in the two-party collaboration approach and encourages the growth of the BFM. To summarize, governmental involvement helps the BFM through subsidized costs, Chinese government money through PSIMI, the private sector’s intangible benefits, and the private sector’s revenue from maritime investment.

This paper conducted numerical simulation experiments with reference to the proportion of the marine industry structure in China in 2021, which intuitively reflects the game process between the private sector and the Chinese government and reveals the impact of different initial probabilities, main parameters, and parameter combinations on the strategy choices by both parties. The simulation results match the theoretical consequences of the evolutionary game model. According to previous simulation studies, the provided parameters and parameter combinations have varying effects on players. Based on evolutionary simulations with different starting probabilities, it is reasonable to conclude that the size of the initial probability value influences the rate at which the game system achieves a stable state. Furthermore, the closer the initial value is to the evolutionary steady state ratio, the sooner the steady state is reached. As a consequence, the greater the possibility is that the Chinese government will execute a subsidy program, the greater the likelihood is that it will stoke PSIMS enthusiasm and the faster it will lead to collaboration between the two sides. Early governmental involvement in the BFM will be more advantageous in getting the private sector to invest in the marine industry.

The characteristics impacting the private sector and the Chinese government were modeled independently of the parameter combinations. Among them, simulation experiment findings of the private sector-related parameters and parameter combinations (${\mathrm{IR}}_0$, ${\mathrm{R}}_1-{\mathrm{R}}_2,{ \mathrm{R}}_2-{\mathrm{R}}_3$) show that the bigger the ${\mathrm{IR}}_0$ gathered, the more motivation for PSIMS. It can also hasten the participants’ stable approach toward collaboration. Furthermore, when ${\mathrm{R}}_1-{\mathrm{R}}_2$ is smaller than ${\mathrm{C}}_0$, the Chinese government decides not to intervene in the BFM. Only when ${\mathrm{R}}_1-{\mathrm{R}}_2$ exceeds or equals ${\mathrm{C}}_0$ will both players tend to cooperate in a stable strategy. Furthermore, the wider the disparity, the faster the two parties will collaborate. The results of the ${\mathrm{R}}_2-{\mathrm{R}}_3$ evolutionary simulation, on the other hand, reveal that the size of the difference between ${\mathrm{R}}_2$ and ${\mathrm{R}}_3$ has little influence on the choice of strategy for players and has a minimal effect on the growth of the BFM.

The results of simulation tests using government-related parameters and parameter groups (${\mathrm{C}}_0,{\mathrm{GR}}_1-{\mathrm{GR}}_2$) show that the cost of Chinese government subsidies (${\mathrm{C}}_0$) is a specific element that impacts strategic choices and plays a critical role in both parties’ behavioral decisions. ${\mathrm{C}}_0$ is greater when the total of ${\mathrm{GR}}_1,{ \mathrm{GR}}_2$, and ${\mathrm{GR}}_3$ is less. The private sector and the Chinese government will hasten the transition to a stable approach. Instead, the Chinese government will consider the costs and advantages and decide not to act. The evolution of the ${\mathrm{GR}}_1-{\mathrm{GR}}_2$ results also shows the relevance of Chinese government engagement in the BFM and the function of Chinese government macro-regulation. When ${\mathrm{GR}}_1-{\mathrm{GR}}_2$ is greater than ${\mathrm{C}}_0$, the faster the players converge on an investment and intervention strategy. When the difference is less than or equal to ${\mathrm{C}}_0$, however, governmental intervention in BFM is not advantageous. As a result, the Chinese government opts for a “do not intervene” policy.

In addition, outside of the parameters included in the ${\mathrm{S}}_2$ area equation, ${\mathrm{ER}}_0$ and ${\mathrm{GR}}_3$ were simulated for evolution. The results of evolutionary simulations are consistent with theoretical elaboration that the size of ${\mathrm{ER}}_0$ and ${\mathrm{GR}}_3$ values has no effect on the private sector and Chinese government strategic options in the BFM.

5. Conclusions

This research describes a dynamic evolutionary game model between the private sector and the Chinese government in BFM. All aspects of the dynamic evolution of game player behavior, strategic equilibrium, and affecting variables are fully investigated. To enhance the precision of predicting the effects of parameter adjustments on participant evolution and outcomes, we conducted supplementary numerical simulations in conjunction with the Chinese case. Furthermore, simulations were utilized to optimize the ongoing dynamic game between the Chinese government and the private sector by enabling the timely implementation of effective strategies for both parties. The dynamics of decision-making between the two sides of the game were investigated on the assumption that both the private sector and the Chinese government are finite rational agents. As a result, the following conclusions are drawn.

(1)

Governmental intervention can have a substantial impact on advancing the sustainable development of the BFM in China. The effectiveness of Chinese government intervention in blue finance is demonstrated by numerical simulations of the Chinese case. Moreover, public finance and development finance can be enhanced through governmental intervention in the long-term blue finance system. However, the Chinese case also illustrates that Chinese government intervention puts pressure on public finances, and thus the degree of Chinese government intervention needs to be balanced. In addition, the Chinese government’s participation in policy formulation can play a vital role in fostering the sustainable development of the BFM and balancing ocean economic growth with environmental preservation. This can contribute to the sustainable growth of the ocean economy, the promotion of maritime infrastructure, and the preservation of marine life. Additionally, the Chinese government plays a crucial role in facilitating access to capital for sustainable marine projects through the provision of funding. This support can overcome obstacles to investment, such as high perceived risks, and incentivize private investment in the marine sector. Hence, governmental involvement in the sustainable development of the BFM is crucial in ensuring its success.

(2)

The participation of the Chinese government’s intervention in the BFM can play a crucial role in fostering investor confidence and trust. Governmental involvement in policy formulation can create a stable and predictable investment climate that emphasizes transparency and accountability, which in turn can increase investor confidence in the BFM and incentivize private investment in sustainable marine projects. The Chinese government has also increased its intervention in the blue financial sector based on this. Additionally, the Chinese government’s role in facilitating access to capital for sustainable marine projects also contributes to the enhancement of investor confidence and trust in the BFM. By providing support to overcome barriers to investment and signaling its commitment to the ocean economy, the Chinese government can encourage private investment in the BFM and contribute to its success. In conclusion, governmental intervention is vital in enhancing investor confidence and trust in the blue financial mechanism. By fostering a stable investment environment, facilitating access to capital, and supporting sustainable marine projects, the Chinese government can play a key role in attracting private investment and promoting the sustainable development of the BFM. Moreover, the effectiveness of Chinese government intervention in the BFM also serves as a guide for future research in marine investment and government management.

(3)

The sooner the Chinese government intervenes in BFM, the more inclined the private sector is to invest in the marine industry. Timeliness is key in this regard, as prompt governmental intervention can influence the investment decisions made by the private sector. As a result, the Chinese government should make suitable decisions and play a macro-regulatory role as soon as possible.

(4)

Chinese government subsidies are crucial in having a cooperative attitude in the gaming process between the private sector and the Chinese government. This assures a modest rate of return, allays the private sector’s fears, and encourages investment. However, the amount of Chinese government subsidies that may be granted is limited, and exceeding these limits will result in the Chinese government taking a hands-off stance. Chinese government subsidies have increased the incentives for the private sector to participate in the marine industry. As a result, the Chinese government must accurately grasp the threshold of the amount of subsidies, calculating its own costs and benefits in order to optimize the use of subsidies to pique the private sector’s interest in the marine industry. Furthermore, subsidies can be used to reduce the private sectors’ investment risk and maximize investment income. In addition, activating private sector investment in the marine sector has enabled corporate social responsibility to be demonstrated. The Chinese government has used tax breaks and subsidies to help stimulate the private sector investment in the marine sector, particularly in areas such as aquaculture and offshore wind power. This approach has provided valuable lessons for other countries seeking to leverage financial mechanisms to support similar objectives.

(5)

Intangible benefits obtained by the private sector when investing in the marine industry in China, such as governmental honors and public praise, have had a significant effect in contributing to the decision to choose the “invest” strategy. When the advantages of investing in the marine sector are almost equivalent to those of investing in the non-marine industry, the private sector is more likely to choose the marine industry owing to intangible benefits.

In conclusion, China’s governmental involvement in the BFM is a crucial factor in promoting the growth and sustainability of the maritime industry. Through policy formulation, the Chinese government can establish a stable and predictable investment environment, which can improve investor confidence and encourage private investment in sustainable marine projects. Moreover, early governmental intervention and the provision of monetary and non-monetary support in China can enhance the efficiency of financing and investment in the marine sector and promote its sustainable development. Furthermore, the Chinese government has played a role in optimizing the capital structure of the marine sector through intervention, such as facilitating the purchase of blue bonds by the private sector and intervening in the BFM.

6. Recommendations

6.1. Limitations and Future Work

This study investigates the dynamic game equilibrium in the BFM between the private sector and the Chinese government using evolutionary game theory and quantitative cost–benefit analysis. Although this work made some theoretical and practical improvements, future research in the three areas listed below should be prioritized. For starters, the study focused solely on incentive systems, ignoring the impact of punishment mechanisms. Non-marine industries with high yields are frequently associated with high levels of pollution; hence, non-marine industries might be classified. Governments have the authority to impose fines on polluting investments. The private sector is more sensitive to losses than equal earnings because they are “economic agents” [100]. Second, the maritime industry is supported by blue bonds, blue loans, and other financial instruments [101]. This paper contains no discussion of the classification of various investment techniques in the game model. Consequently, the evolutionary game model may be investigated further using various investment approaches. Finally, due to the shortage of actual case data, the simulation analysis’s data selection and simulation are at random. More real-world data should be collected in the future to further empirically test whether government funding is more effective than private funding in delivering growth, and whether that growth is benign or malign.

6.2. Recommendations

Recommendations for the Chinese government and the private sector to promote sustainable development in the ocean economy, society, and environment are listed as follows:

(1)

To enhance investment in the marine sector, the Chinese government’s proactive involvement in the BFM is of utmost importance. The Chinese government’s early intervention in the BFM can have a significant and positive impact on the growth and development of the marine industry. By taking proactive measures, the Chinese government can also minimize the potential risks associated with investment in the marine sector, thereby increasing the trust and confidence of investors. This, in turn, can lead to the establishment of a more sustainable and profitable marine industry. Therefore, the Chinese government’s early engagement in BFM plays a critical role in promoting investment and fostering sustainable development in the ocean economy, society, and environment.

(2)

In order to foster and advance the development of the marine sector, the Chinese government must make a concerted effort to increase subsidies and diversify its incentive systems. As emphasized by Dencer-Brown et al. [26], the Chinese government must take on a leading role in the ocean economy and actively work to encourage investment in this important sector. One effective way to achieve this is by utilizing flexible economic instruments and incentives, which can provide financial support to the private sector and help reduce the cost of investment in the marine industry. The Chinese government can establish financial subsidies and implement preferential policies for companies that invest in sustainable and environmentally friendly practices. This will not only encourage the private sector’s participation, but also create a favorable investment environment that can lead to increased investment and economic growth in the marine sector. In addition, by providing necessary financial support, the Chinese government can help mitigate any potential risks associated with investment in the marine sector, thus increasing investor confidence and promoting a more sustainable and profitable industry [102]. This can be accomplished through targeted measures such as the development of new financial instruments, the introduction of tax breaks or subsidies, and the provision of technical assistance to private sector entities. In conclusion, the Chinese government has a vital role to play in promoting investment in the marine sector. By increasing subsidies, utilizing flexible economic instruments and incentives, and providing ongoing financial assistance to the private sector, the Chinese government can help create a sustainable and profitable marine industry that contributes to the overall sustainable development of the ocean economy, society, and environment.

(3)

To further incentivize private sector investment in the marine industry, the Chinese government should consider enhancing the form of rewards it provides. While monetary incentives such as tax breaks or subsidies are important, non-monetary rewards can also play a crucial role in encouraging the private sector’s participation. These rewards can include official recognition, media publicity, and various forms of commendation for the contributions made by private sector entities to the growth and expansion of the marine sector. These non-monetary incentives can help to create a positive perception of the private sector and the marine sector, increasing investment and growth. By providing a comprehensive set of rewards that includes both monetary and non-monetary incentives, the Chinese government can create a more appealing and attractive investment environment, encouraging the private sector’s involvement and promoting the sustainable development of the ocean economy, society, and environment.

(4)

The Chinese government should promote public awareness and education about the importance of marine conservation and sustainable practices. It is recommended that the private sector prioritize investments in sustainable marine projects that can bring about economic growth, job creation, and environmental protection. To further encourage responsible investment, it is crucial that the private sector adopts sustainable business practices and incorporates the standards of environmental, social, and governance into their operations. In addition, collaboration between the private sector and the Chinese government, as well as other stakeholders, is crucial for promoting sustainable development in the ocean economy, society, and environment.

(5)

Support the development of local, small-scale marine sectors that prioritize sustainability and environmental stewardship. These sectors often have a greater incentive to prioritize sustainability and environmental stewardship as they are more directly impacted by the health of the local marine ecosystem. Governments can invest in training programs and provide technical assistance to help small businesses adopt best practices and improve their sustainability.

The aforementioned recommendations highlight the significance of a cooperative approach between the Chinese government and the private sector in advancing sustainable development within the ocean economy, society, and environment. Through the harmonious utilization of the strengths of both sectors, a sustainable and thriving ocean economy that offers mutual benefits to both the environment and society can be realized.

6.3. Future Studies

From the above discussion, future studies could focus on the following:

(1)

Risk management in the blue finance mechanism in China: Future research could explore the risks associated with China’s blue finance, such as environmental risks, credit risks, and operational risks. It could also investigate the effectiveness of China’s current risk management practices and suggest improvements.

(2)

Innovative blue financing mechanisms for Chinese marine projects: Future research could explore innovative blue financing mechanisms for Chinese marine projects, such as impact investment, crowdfunding, the integration of emerging financing technologies (such as blockchain, artificial intelligence, and big data) with marine finance (such as marine insurance, shipping finance, and marine renewable energy finance), and then analyze the benefits and drawbacks of these mechanisms and their potential for promoting sustainable marine development.

(3)

Internationalization of China’s marine finance: Future research could explore the potential for China’s blue finance to expand internationally, analyze the current international marine finance market and identify opportunities for Chinese firms to enter this market, and examine the challenges that Chinese firms may face in competing internationally in this field.