The Cooperative Game Study of Chinese Overseas Direct Investment in the Construction of Green Ports

Abstract

With the development of Chinese overseas direct investment (ODI) in green ports, a series of conflicts and contradictions among the participating parties have emerged, which in turn affect and hinder the process of project construction. This paper analyzes the current situation of Chinese ODI in green ports, constructs a cooperative game model between Chinese port investment enterprises and the host government with introduces the effort level, and selects three actual green port projects for calculation and analysis to show that Chinese ODI in green ports can bring economic and environmental benefits to both parties. It is found that the expected revenues and effort levels of both the Chinese port enterprises and the host government are positively correlated with each other’s effort levels, and there exists an optimal effort level and an optimal investment amount of the Chinese port enterprises to maximize the benefits obtained by both parties in the green port project. At the same time, the cases studied find that the benefits obtained by the host government are higher; Therefore, Chinese port investment enterprises can promote green ports projects by finding their own optimal effort level. Additionally, active cooperation is the optimal choice of the host government.

1. Introduction

As an important node in the development of transportation, trade and logistics, the port is an important urban facility to promote the economic development of a region or even a country, and a green port is an important window to promote the development of a green economy and realize environmental sustainability. Over the past 20 years, China has seen an unprecedented surge of investment in overseas transportation and logistics infrastructure projects. As of 2019, more than 100 overseas ports have been partially or fully built, invested in, or managed by Chinese companies [1,2]. Among them, a total of 16 port projects take green measures or achieve green results. For example, COSCO Shipping holds 100% of the shares of Piraeus Port in Greece, and has been insisting on investing in the construction with the concept of green and sustainable development.

In 2001, COSCO Shipping and the China Shipping Group invested in the ports of Long Beach and Los Angeles in the U.S., respectively, marking the beginning of Chinese overseas direct investment (ODI) in port construction. After 2001, Chinese ODI in port construction projects showed explosive growth, and according to The Statistical Collection of 40 Years of Overseas Port Projects in Chinese Ports, the number of port projects built by Chinese ODI from 2001 to 2019 reached 100, which include: 37 in Asia, 32 in Africa, 11 in Europe, 9 in South America, 6 in North America, and 5 in Oceania. 2009 saw a surge in Chinese ODI in port project construction under the steady promotion of the quadrillion investment plan. In 2013, the “Belt and Road” initiative was an important driving force for Chinese ODI in port construction, with its more active performance and more mature cooperation mechanism, and after its launch, the number of Chinese port ODI exploded: the number of ports constructed increased by 70%, and the scale of construction also increased significantly. Based on these time points, this paper divides the evolution of Chinese ODI in port construction into three time periods: 2001 to 2008, 2009 to 2012, and 2013 to the present. From 2001 to 2008, the number of Chinese ODI for port construction gradually increased. At this time, it was in the initial stage, lacking comprehensive understanding of the political and economic environment of each country and insufficient experience in investment and construction. Secondly, the proximity layout can form a link between domestic and foreign ports and build Chinese global shipping service network. From 2009 to 2012, development was rapid, showing the spreading trend of expanding the layout, especially to South America and the Korean Peninsula. This is mainly due to the close diplomatic relations between China and other countries and the easing of the international political environment during this period, as well as the consideration of Chinese port investors for their own overseas development and the need to improve Chinese global port layout network. From 2013 to the present shows explosive growth and the layout tends to be perfected. During this period, China has strengthened its investment in strategic maritime corridors, and the layout of overseas port projects has shown a clear trend of aggregation, with the global network route basically perfected. In this paper, the number of investment ports in different regions in each stage is described in Figure 1.

Asia, Africa, and Europe are the key investment areas for Chinese ODI port construction, while ports in the Indian Ocean, Mediterranean Sea and other seas are the main nodes. Asia is the core region for China’s ODI construction: southeast Asia has a mature port operation system, forming a port network with Singapore as the core; five of the eight countries in south Asia border with China’s western border of Tibet and Xinjiang, which is the gateway to Chinese western external development, but also an important node connecting China to Africa; west Asia has been the main route between the East and the West since ancient times, including the Suez Canal connecting the Mediterranean Sea and the Red Sea; the Persian Gulf in the south is a major shipping route for the world’s oil. The ports based in these regions provide opportunities for Chinese direct investment in green ports there. There are many ports in coastal areas of Africa and most of them are located in important nodes of international shipping networks, so it is another key area for Chinese ODI in building green ports. Africa’s good natural resources provide conditions for the development of its port economy, but the region has a low level of economic development, weak technical capacity, lack of construction of ports and basic transportation hubs, and underdeveloped maintenance and operation capabilities. The region is in urgent need of port development and construction, and most countries continue to introduce preferential policies to attract foreign investment in order to promote the development of the local port economy. The overall economy of the European region is in a high level, and most countries have a developed shipping industry and transportation infrastructure, with early development and high modernization level of ports, and a large number of international ports with perfect construction, green operation concepts and advanced technology have been formed long ago. However, there is fierce competition among the European shipping industry, and the outbreak of European debt crisis in the early 21st century led to the recession of European economy. The ports fell into serious debt, and the signs of recession of port development were obvious. This provides realistic conditions for Chinese ODI in the region to build green ports.

The Chinese unprecedented overseas port infrastructure investment boom has sparked widespread interpretations and contradictions in academic and business media, mainly focusing on investment objectives, models, benefits and risks [3,4,5]. Based on the existing studies, this paper classifies the main construction modes into four categories: new construction investment mode, joint venture cooperation mode, M&A mode and franchising mode, and lists the corresponding ports built by the Chinese port investment enterprises using the corresponding modes (See Appendix A). In the port sector, the new construction investment mode is for Chinese investors to undertake the construction of a brand-new port through ODI, or to expand an existing terminal. Currently, Chinese investors use the BOT (build–operate–transfer) mode of operation for new or expanded ports overseas. Specifically, the Chinese investor signs an agreement with the host government that owns the port or a port enterprise. Under its own leadership to form a project company to undertake a new or expanded green port project and be responsible for the development, construction and operation of the port; the project company has the right to operate and manage the green port project and earn revenue for a certain period of time; upon expiration of the period, the Chinese investor delivers the project to the host government and withdraws from the project. The BOT model can clarify the profit return rate, reduce disputes between the investing company and the host government, and improve efficiency. Second, joint venture cooperation refers to two or more enterprises jointly funding a new enterprise to develop the international market and operate the enterprise with shared benefits and risks. This is one of the most common ways of ODI in Chinese port construction. For Chinese port investment enterprises, establishing a joint venture can expand investment channels, can take advantage of the status of local partners, quickly integrate into the economic, political, cultural and legal environment of the host country, reduce capital, time and labor costs, and a series of risks. Thirdly, M&A mode refers to the acquisition of overseas operating port enterprises by Chinese port investors, the acquisition of all or part of the shares of the existing operator, or the operating rights of the port enterprise. For Chinese port investors, M&A can avoid the high costs and complicated procedures required to obtain overseas green port concessions in other ways, and it has become one of the main directions of development for Chinese green port ODI. The M&A mode is more applicable to Eurasian ports with green development experience, which helps them to more easily obtain market channels, technical experience, resources and experience in green port construction in host countries and reduce green operation costs. Forth, the franchising mode refers to the Chinese port investor signing a franchise agreement with the host country, paying it a franchise fee and gaining the right to build, operate and manage the port in the host country. Franchising is usually applicable to ports with more mature development; it can make use of the franchisee’s existing corporate logo, know-how and other port construction and operation resources to reduce investment costs and promote the development of green ports.

In contrast, in order to maintain national security, promote national economic development, and ensure control and supervision of major infrastructure projects, the host government will be involved in various forms in the implementation of specific projects, and play multiple roles in each project [6]. On the one hand, host government can participate as key players in green ports. It may participate as the subject of the project concession award. In this case, the concession agreement signed between the two parties gives the host government the right control over the port project, and it may introduce foreign investment in the form of a concession that requires the concessionee to assume responsibility for the construction and operation of the port project. Then, the host government may participate in the project equity investment. It often participates in a project in the form of dry shares, land use rights, equity in national enterprises or other in-kind contributions, either directly or indirectly; the purpose of the government is to obtain profit returns and enhance the regulatory control of the project. Additionally, it will also support the green port project by providing land, infrastructure, etc. through its own state-owned enterprises [6]. When the host government participates as a project participant, the conflict of economic interests will become the main conflict between the two sides, including the conflict of profit distribution and the national economic interests of the host country and the Chinese port investment enterprises. On the other hand, the host government will be involved in the whole project as a legislator and law enforcer, and thus may influence the implementation of the project by introducing and enforcing strict laws, or even hinder the project process. This paper argues that the main reason for the host government to enact strict laws and regulations for foreign investors is the protection of the public interest of the host country. It includes public safety, public environment, public health and labor rights and other needs of various aspects of society. For example, in terms of public security, the host government is more concerned about the impact of ODI in green port projects on their domestic ecology and national public health. For example, the Colombo Port City project invested in by China in Sri Lanka was halted in 2015 because the host government believed that the project violated the environmental protection laws and damaged the ecological environment [7]. In the construction of green ports in Chinese ODI, regardless of its role, the host government will adopt a strict investment access system and a series of laws and regulations for Chinese investors, which will affect the process of the construction of green ports locally.

In this context, the core question addressed in this paper is: through this paper, how to seize the development opportunities and overcome the challenges and risks that exist in the construction of green ports by Chinese ODI, so as to guarantee the economic, social and environmental benefits of the participating subjects and enhance their cooperative behavior, then promote stable cooperation and sustainable development among the participating countries.

2. Literature Review

At present, the existing research in this area has been relatively mature and mainly focused on three aspects: green port research, port ODI research and the application of game theory in port ODI. However, there are still some imperfections, most of the literature separates ODI from green ports, and only a small amount of literature studied the benefits of ODI in green ports by qualitative analysis. The research on the combination of ODI and green ports is still in its initial stage. Meanwhile, many scholars have applied the game theory approach to the study of green ports, mainly focusing on the application of evolutionary games, but there are fewer studies based on cooperative games to analyze the cooperation of participating subjects. This paper concentrates on the cooperation game between Chinese port investment enterprises and the host government and introduces the influence of effort level on the cooperation game model to further fit the application scenario of overseas direct investment. In addition, the papers on overseas direct investment in research on sustainable development are relatively abundant, but there are few studies on the construction of green ports, and this paper enriches the theoretical base research in the field. Additionally, the research in green ports has been abundant, but the quantitative research is still in the development stage.

Among them, the research on green port mainly focuses on the development status of the green port in China, the construction of the green port, and the evaluation system of green port. In the study of the development status, the development ideas and strategies of Chinese green ports are mainly proposed by summarizing the green development experiences of ports at home and abroad. For example, He [8], Nie [9], Xu [10] and Wang [11] respectively analyzed the green development of ports in Tianjin, Shenzhen, the Yangtze River Economic Belt, and Hainan and put forward countermeasures to promote the construction of green ports. Luo [12], Xu [10] and Nie [9] propose strategies for the development of green ports in China by drawing on the experiences of smart port construction in Singapore, port construction in Dubai, and port construction in Shenzhen, respectively, and taking into account the development of Chinese ports and future trends. The research on green port construction is mainly focused on the influencing factors and green technologies for building green ports. Among them, green technologies mainly include three key elements of shore power equipment, automated container terminal system, and green and clean energy. Kotrikla et al. [13] explored the potential of shore power in reducing emissions for sustainable development of ports. Compared to traditional terminals, automated container terminals have greater advantages in cargo handling, energy saving and emission reduction, and environmental protection [14]. Zhu [15] studied the synergistic emission reduction effect of sulfur dioxide and carbon dioxide in container terminals after replacing fuel oil with clean energy and proved that clean energy is effective in energy saving and emission reduction of containers. With the increasingly strict environmental protection policies, green investment has become an important way of green development in ports. Zheng et al. [16] analyzed the factors limiting the green development of the container port economy and proposed the best green investment decision scheme by constructing a system dynamics model for port green economy development. Liu et al. [17] studied the impact of green technology investment efficiency on the green port supply chain and proposed suggestions to promote the development of green ports from the perspective of green investment. In terms of the research on the evaluation system of green ports, Zhu [18] used hierarchical analysis to determine the evaluation index system of green ports and the rules for the classification of green port levels and constructed four indicators such as green concept as the vertical evaluation content. Zhao [19] constructed a hierarchical fuzzy comprehensive evaluation model to analyze four indicators such as port-related intensity to determine the green development level of ports. Some scholars have also studied the competitiveness level of ports, such as Huang et al. [20], who proposed five major competitiveness evaluation indicators of green ports and determined the weights of various indicators through the ANP method to provide reference for evaluating the performance level of green ports. Han and Xu [21] evaluated the competitiveness of green ports from five perspectives, including environmental development, based on the gray cloud clustering model, and compared the greening competitiveness of three ports, including Dalian Port, Tianjin Port, and Qingdao Port. Wang et al. [22] from a quantitative perspective, the green efficiency of 18 ports in China’s five port groups are compared from 2012 to 2016 using the game cross-efficiency and the competition and cooperation cross-efficiency models in a data envelopment analysis (DEA). Deng et al. [23] study the influence mechanism of environmental regulation on green port construction by constructing a three-way evolutionary game model of government, port enterprises and transportation enterprises. In summary, existing studies focus on the environmental impacts, evaluation, and construction of green ports. Recent trends indicate that researchers have become increasingly focused on reducing emissions, optimizing operations, evaluating policies, and identifying post-pandemic health issues associated with green ports [24].

In terms of ODI in ports, the expansion of investment cooperation areas among countries and the promotion of MSR initiatives have promoted the development of ODI in building ports, and the existing models of ODI in building ports include joint venture cooperation, mergers and acquisitions, BOT, and port alliances [19,25,26]. Port ODI is mainly analyzed from a quantitative perspective. Song and van Geenhuizen [27], using panel data analysis from 1999–2010, investigated that port infrastructure investment in China also contributes to a large extent to the economic growth of the region concerned, mainly through direct and indirect relationships. Yang and He et al. [5] provide a quantitative and comprehensive analysis of Chinese investments and operations in African port infrastructure, describing the specialization of major Chinese SOEs in their investment approach and the reasons behind the geographical distribution. Yang and Li et al. [2] focus on the level of Chinese overseas investment in building container terminals performance, examines the role of Chinese investor attributes in achieving higher port competitiveness, and analyzes panel data on 68 overseas container terminals of China’s three major international port operators from 2008–2019. It also finds that for SOEs, investing in regions with political instability and fewer regional ports is more likely to gain greater market share. At present, the research on the risk of ODI in ports are more mature, but there are less research on ODI in the construction of green ports. Yang [28] believes that the construction and development of green ports is an important part of promoting the “Belt and Road” initiative and should increase the investment in green ports. Yao et al. [29] focuses on the environmental risks in ODI in Chinese ports and proposes that ODI in the construction of ports should focus on the sustainable development of ports. Cai and Yu [30] compares the trends and experiences of international green port development and propose that China should promote green port technology in the process of “One Belt, One Road” construction.

To a certain extent, ODI is a process of continuous game between the investing country and the host country. The equilibrium of game theory provides the research basis for the decision-making behavior of each participant, and it is also the main method to study the behavior of the participating subjects. For example, Rao [31] use game to search equilibrium with unobservable investment. Meng et al. [32] established an evolutionary game theory model of “government–port–third-party organization” regarding the development of green intelligent ports to find the most suitable evolutionary path for the development of green intelligent ports. Tian [33] uses game to study a new model of two-way international direct investment in China, which provides a reference for securing Chinese ODI and maintaining the interests of both sides of the game. Ge [34] establishes a Stackelberg game model for investment decisions in dual-hub ports to study the development model of dual-hub ports existing in Asia and to explore how to reasonably allocate investments to both infrastructure and value-added supply chain areas of ports. Feng et al. [26] uses game theory to study the multi-win cooperation of ODI in ports along the MSR. Game theory is often used on the study of ODI, and the research results are relatively comprehensive, but there is less literature on the use of game theory to study ODI in port construction. Most researchers use game theory to study the cooperation and competition between ports, and even less literature on the use of cooperative game to study ODI in ports.

There are both common and conflicting interests on Chinese ODI green ports in the host country. Chinese port investment enterprises may hold different ideas and requirements from the host government in terms of investment access methods, ecological and environmental issues, tariffs, labor protection and dispute settlement mechanisms, and the differences in interest claims, laws and regulations stipulated by the host government for investors investing in their own countries, so the differences of cultural between the two countries may affect the project process to a certain extent. Therefore, analyzing these hindering factors is the key to the success of ODI in building green ports. In the context of green investment and sustainable development becoming the trend of port construction, it is particularly important to promote Chinese ODI in building green ports, meet the interests of both sides, promote the green and sustainable development of the invested ports, better promote the sustainable development of China and the host country in economy, society and environment, and realize the long-term interests of both countries.

This paper will apply the cooperative game to study Chinese ODI in building green ports, analyze that current situation, and establish a cooperative game model between Chinese port investment enterprises and the government of the port host country, study the economic and environmental benefits that each side can obtain when building green ports under the condition of reaching cooperation, and explain from the profit perspective that Chinese ODI in Green ports can promote the sustainable development of the host country’s economy and environment, and propose countermeasures to promote Chinese ODI in green ports.

3. Model Analysis

Based on above, this paper selects Chinese port investment enterprises and the host government as the main players in the cooperative game. Both parties have the same interests in ODI in green ports, and they hope to build green ports and gain benefits from them. However, there are certain conflicts of interest due to the differences in demands in the process of the cooperative game. Different behavioral strategies are adopted for different profit objectives, and different effort costs are paid, which affect their own profit income. Therefore, this paper will construct a cooperative game model to calculate the respective benefits of both parties under the condition of a binding cooperation agreement and fair reciprocity to show that the construction of green ports by Chinese ODI is beneficial to the sustainable development of economy, environment and society on both sides. In order to clarify the respective benefits of both parties in the cooperative game, this paper will analyze the behavior of both parties in the construction of green ports by Chinese ODI.

First of all, Chinese port investment enterprises are the main investor and promoter of ODI in building green ports. In the process of green port construction, they do not only pursue the maximization of economic benefits, but also take the responsibility of a large country to promote the green development of the ports and promote the increase of the triple benefits of port economy, environment and society. They not only bear the most basic costs of investment and construction, but also make the greatest efforts in the cooperative game with the host government to promote the construction of green ports and take the initiative to bear the corresponding green costs, such as the costs of green energy, green materials, automation equipment and other green technologies, and even take the initiative to bear the social welfare required by the host government. Besides, this paper argues that the host government will also make certain efforts to promote the construction of green port projects, such as actively improving the domestic investment environment, attracting Chinese port investment enterprises, providing financial support for the construction of green ports, and reducing taxes. However, in practice, even if the host government and Chinese port investors reach a cooperation agreement, the host government may implement initiatives that hinder the green port project process. For example, it is concerned about the impact of foreign investment on its domestic economy, ecological environment, labor rights and social stability, and implements a strict investment access system and various laws and regulations. In the distribution of economic benefits, in order to allocate higher profits, it may also raise taxes and require Chinese port investment enterprises to pay additional social benefits, etc.

3.1. Model Assumptions

In order to make the game model constructed more realistic, the following hypothesis are made in the cooperative game process.

Hypothesis 1. 

Chinese port investment enterprises and the host government must reach a cooperation agreement and sign binding contract terms on the investment of green ports. At this time, the benefits obtained by each party involved in the investment of the green port must be greater than the benefits of each party working alone, and the overall benefits will be greater than the overall benefits of working alone.

Hypothesis 2. 

Chinese port investment enterprises and the host government are equal in power, and both are fair and reciprocal.

Hypothesis 3. 

Chinese port investment enterprises and the host government are both finite and rational and have incomplete information.

Hypothesis 4. 

In the construction of green ports by Chinese ODI, there are only two subjects, the Chinese port investment enterprise and the host government, and there is no cost of attracting investment in the host country and no third party participation, i.e., the set of stakeholders in the game is, 1 represents the Chinese port investment enterprise, and 2 represents the host government.

Hypothesis 5. 

Chinese port investors agree with the host government to bear additional social responsibility costs in addition to the basic investment.

Hypothesis 6. 

In the construction of green ports by Chinese ODI, the goal of Chinese port investment enterprises is not only to obtain maximum economic benefits, but also to promote the green development of the constructed ports and contribute to the host country’s economy and ecological environment; the goal of the host government is to maintain its own economic interests and public interests, and this paper argues that Chinese port investment enterprises will put in more efforts.

Hypothesis 7. 

In order to reduce the risk of ODI and improve the flexibility of investment, Chinese port investment enterprises make ODI in different countries to build green ports, corresponding to different levels of investment cooperation according to the economic development of the host country.

Hypothesis 8. 

Chinese port enterprises are risk-neutral and host governments are risk-averse.

Chinese port investment enterprises carry out a series of activities such as investment, planning, construction and operation of green ports in the host countries and need to negotiate and play with different host governments at different stages, and both parties are stakeholders in the green port projects and have a certain correlation of interests. In the actual investment activities, Chinese port investment enterprises have to consider the possible risks while pursuing the benefits, so they will neither be adventurous nor willing to simply adopt a conservative strategy. ODI in the construction of green ports itself has the characteristics of risk-compatible and long return cycle, and investors choose to enter uncertain foreign markets with risks that do not meet the risk-averse characteristics, so this paper considers Chinese port investment enterprises as risk-neutral. No matter what role the host government plays in the construction of the project, it will give priority to its own economic interests and public interests from being harmed. In the cooperation process, the host government needs to consider not only the economic and environmental benefits, but also the market environment, labor rights and ecological protection of the country, etc. Based on this, the host government will often implement relevant policies, systems and laws and regulations to protect the rights and interests of the country. Therefore, this paper assumes that the host government is risk-averse.

Based on the hypothesis of the game model and the research content, this section specifies the parameter symbol settings used in the game. They are shown in

Table 1. Parameter settings of the cooperative game model for Chinese ODI in building green ports.

Game Subjects	Parameters	Symbolic Meaning
Chinese Port Investment Enterprise	a	Effort level of Chinese port investment enterprises invest in building green ports
	p	Effort cost factor for ODI in building green ports
	$\alpha$	Environmental and social benefit coefficients of Chinese port investment enterprises from green ports
	I	The amount of green investment in Chinese port investment enterprises (including the use of various types of green equipment and green energy)
	$\zeta$	Investment coefficient of Chinese port investment enterprises
	e	Investment conversion factor of Chinese port investment enterprises
	A	Social responsibilities required of Chinese port investment enterprises by the host government
	$\partial$	Fixed income charged by the host government to Chinese port investment enterprises
	$\theta$	Exogenous variables
	m	Effort level coefficient of Chinese port investment enterprises
Host Government	b	Effort level of host government to build green ports
	p	Effort cost factor for ODI in building green ports
	$\beta$	Coefficient of environmental and social benefits to the host government from green ports
	f	Investment conversion factor of host government
	r	Tax rates charged to investors by the host country
	$\rho$	Host Government risk aversion factor
	1 − m	Host government effort level factor
	$\theta$	Exogenous variables

.

The main parameters of the cooperative game model are explained and specified.

1

Effort level a, b and effort level coefficient$m,1-m$;

The concept of effort level is widely used in the research of supply chain, and some scholars have extended it to the field of investment to study the relationship between the effort level and the investment profit; scholars such as Bai [35], Tai et al. [36], and Huang et al. [37] have applied it to the study of the game between multinational enterprises and the host government. In the process of Chinese ODI in building green ports, Chinese port investment enterprises will pay negotiation efforts to promote the process of project in addition to the basic investment costs, and for the technical, personnel, and management efforts, the host government will provide efforts in opening up the market, tax incentives, etc. Therefore, this paper considers that the effort level has an impact on the normal promotion of the project and the respective benefits of both parties, so the effort level of Chinese port investment enterprises and the host government are set as a and b, respectively, a and b belong to [0, 1], while this paper defines the respective effort level of both parties as a game variable. The coefficients of the effort levels of Chinese port investment enterprises and host government are $\mathrm{m},1-\mathrm{m}$, that is, the degree of influence of the effort of them on the final profit gain, and its importance mainly reflected by the efficiency and effectiveness of their respective work in the project construction. It sets $\mathrm{m}\subset \left(0,1\right)$, When $0<\mathrm{m}<\frac{1}{2}$, the effort level of Chinese port investment enterprises is more important; $\mathrm{When}\mathrm{m}=\frac{1}{2}$, then it means that the host government and the Chinese port investment enterprise are of equal importance. The value of $\frac{1}{2}<\mathrm{m}<1$ means that the host government’s effort level is more important [38]. Chinese port investment enterprises and the host government will both gain economic, environmental and social benefits from their efforts in the construction of green ports, and at this time there is a benefit function $\mathrm{Q}={\mathrm{a}}^{\mathrm{m}}{\mathrm{b}}^{1-\mathrm{m}}+\mathsf{\theta }$, that θ is the exogenous variables of the mean value of 0 and variance of ${\mathsf{\sigma }}^2$, and the expected revenues are $\mathrm{E}\left(\mathrm{Q}\right)={\mathrm{a}}^{\mathrm{m}}{\mathrm{b}}^{1-\mathrm{m}}$.

2

Effort cost factor $p_i$

Both Chinese port investment enterprises and the host government will make efforts to the construction of green ports when they reach cooperation, and at this time, effort cost will be incurred, and the effort cost factor is ${\mathrm{p}}_{\mathrm{i}}$(i = 1,2; 1 represents the Chinese port investment enterprise and 2 represents the host government). According to the above analysis, the effort cost function of Chinese port investment enterprises is $\frac{1}{2}{\mathrm{p}}_1{\mathrm{a}}^2$, and the effort cost function of the host government is $\frac{1}{2}{\mathrm{p}}_2{\mathrm{b}}^2$, and the effort cost of both parties is greater than 0.

3

Benefit sharing factor$\alpha ,\beta$

The environmental and social benefits obtained from Chinese ODI in the construction of green ports are allocated proportionally, and the benefit sharing coefficients are $\mathsf{\alpha },\mathsf{\beta }$, 0 $<$ $\mathsf{\alpha }+\mathsf{\beta }\le 1$. In this paper, we assume that both parties are fair and reciprocal, and for the sake of simplicity in the later calculation, we set $\mathsf{\alpha }=\mathsf{\beta }=\frac{1}{2}$.

4

Green investment amount of Chinese port investment enterprises I

Chinese port investment enterprises will invest more investment amount, which is not only for the basic investment, but also for the green technology in the process of port planning, construction and operation, the use of various types of clean energy, etc. Therefore, this paper defines the ideal amount of green investment of Chinese port investment enterprises as I.

5

Investment coefficient$\zeta$and the conversion coefficient of Chinese port investment enterprises e

In practice, Chinese ODI in building green ports will encounter various risks such as economic, political, cultural and international security, etc. In order to reduce the economic losses brought by various risks, Chinese port investment enterprises often adopt different investment levels according to the host country’s economic development. In this paper, in order to make the cooperative game model more realistic, the investment coefficient is set $\mathsf{\zeta }$, and use $\mathsf{\zeta }\mathrm{I}$ denotes the different investment cooperation levels between Chinese port investment enterprises and the host government; 0 $<$ $\mathsf{\zeta }<1$, $\mathrm{I}$ is the ideal green investment amount. The value of ζ, in this paper, we adopt the concept in the Dictionary of Finance and Economics that the investment coefficient is the ratio of investment amount to national income growth in a certain period. A small coefficient indicates that it takes less investment to increase the same national income and the investment is more efficient. This paper focuses on the investment in the construction of green ports, which is a capital construction investment, so the calculation of the investment coefficient adopts this method: When the investment coefficient reflects the comparative relationship between capital construction investment and the amount of national income growth. Additionally, the conversion coefficient of Chinese port investment enterprises e refers to the research results of Feng et al. [39]. It is considered that the value of this parameter is the part of the investment amount that actually converts port development, and the value is taken as the ratio of the host country’s port infrastructure quality index to its optimal index value, and the port is very developed and efficient according to the international standard port infrastructure quality of 7, which is the optimal index.

6

Social responsibility A and fixed benefits$\partial$required of Chinese port investment enterprises by the host government

In order to protect their own economic interests and public interests, the host government will ask the Chinese port investor to take on more social welfare and fixed benefits when negotiating with the Chinese port investor, such as employing local laborers to promote local employment and protecting the host country’s ecological environment, etc. The fixed benefits may include income tax levied by the host government. In order to promote the success of green port projects, Chinese port investment enterprises will choose to accept the host country’s request to assume social responsibility and pay fixed benefits to the host country, so this paper sets A and ∂ to make the model more realistic.

3.2. Model Construction

3.2.1. Cooperative Game Model Construction

The sources of benefits for the host government in participating in Chinese ODI in building green ports include environmental and social benefits, the amount of investment by Chinese port investment enterprises, and the additional social benefits and fixed benefits required of Chinese port investment enterprises. The costs are mainly the costs of the host government’s efforts to attract Chinese port investment enterprises and build green ports, so the benefits for the host country $\mathrm{S}\left(\mathsf{\pi }\right)$ are

$$\mathrm{S}\mathsf{\pi }={\mathsf{\beta }\mathrm{a}}^{\mathrm{m}}{\mathrm{b}}^{1-\mathrm{m}}+\mathrm{r}\mathsf{\zeta }\mathrm{I}+\mathrm{f}\mathsf{\zeta }\left(\mathrm{I}+\mathsf{\theta }\right)+\mathrm{A}+\partial -\frac{1}{2}{\mathrm{P}}_2{\mathrm{b}}^2$$

(1)

According to Hypothesis 8, known ODI in the construction of green ports in the host government is a risk-averse subject, there is a risk cost. Assume that the host government’s benefit function is $(\mathrm{Eu}(\mathrm{s}(\mathsf{\pi }))=\mathrm{k}-{\mathrm{e}}^{-\mathsf{\rho }\mathrm{S}(\mathsf{\pi })}$, where ρ is the host country risk aversion coefficient, an $\mathsf{\rho }=-\frac{{\mathrm{u}}^{″}}{{\mathrm{u}}^{\prime }}$ d, $\mathrm{S}\left(\mathsf{\pi }\right)$ is the host government benefit. The host government expected revenue is

$$\begin{gathered} \mathrm{E}\left(\mathrm{u}\left(\mathrm{s}\left(\mathsf{\pi }\right)\right)\right)=\underset{-\infty }{\overset{+\infty }{{\displaystyle \int }}}\left(\mathrm{K}-{\mathrm{e}}^{-\mathsf{\rho }\mathrm{s}\left(\mathsf{\pi }\right)}\right)\frac{1}{\sqrt{2\mathsf{\pi }}\mathsf{\sigma }}{\mathrm{e}}^{-\frac{{\mathsf{\theta }}^2}{2{\mathsf{\sigma }}^2}}\mathrm{d}\mathsf{\theta } \\ =\mathrm{K}-{\mathrm{e}}^{-\mathsf{\rho }({\mathsf{\beta }\mathrm{a}}^{\mathrm{m}}{\mathrm{b}}^{1-\mathrm{m}}+\mathrm{r}\mathsf{\zeta }\mathrm{I}+\mathrm{f}\mathsf{\zeta }\mathrm{I}+\mathrm{A}+\partial -\frac{1}{2}{\mathrm{P}}_2{\mathrm{b}}^2-\frac{{\mathsf{\rho }\mathrm{f}}^2{\mathsf{\sigma }}^2}{2})} \end{gathered}$$

Since the investment amount of Chinese port investment enterprises depends on various factors such as the scale of the project and the expected outcome, the environmental and social benefits that can be created after the completion of the green ports are also random, so the benefits of the host government are random. Additionally, the host government pursues not only economic benefits, but also maximizes the benefits of various aspects such as the ecological environment and society brought by the green port, so this paper will introduce the deterministic equivalent utility CI to replace the random benefits of the host country, then there are:

$$\mathrm{E}\left(\mathrm{u}\left(\mathrm{s}\left(\mathsf{\pi }\right)\right)\right)=\mathrm{E}\left(\mathrm{CI}\right)=\mathrm{K}-{\mathrm{e}}^{-\mathsf{\rho }\left(\mathrm{CI}\right)}$$

Obtain the determination of equivalent utility:

$$\mathrm{CI}={\mathsf{\beta }\mathrm{a}}^{\mathrm{m}}{\mathrm{b}}^{1-\mathrm{m}}+\mathrm{r}\mathsf{\zeta }\mathrm{I}+\mathrm{f}\mathsf{\zeta }\mathrm{I}+\mathrm{A}+\partial -\frac{1}{2}{\mathrm{P}}_2{\mathrm{b}}^2-\frac{{\mathsf{\rho }\mathrm{f}}^2{\mathsf{\sigma }}^2}{2}$$

The equivalent expected utility function of the host government at this point is

$$E\mathrm{u}={\mathsf{\beta }\mathrm{a}}^{\mathrm{m}}{\mathrm{b}}^{1-\mathrm{m}}+\mathrm{r}\mathsf{\zeta }\mathrm{I}+\mathrm{f}\mathsf{\zeta }\mathrm{I}+\mathrm{A}+\partial -\frac{1}{2}{\mathrm{P}}_2{\mathrm{b}}^2-\frac{{\mathsf{\rho }\mathrm{f}}^2{\mathsf{\sigma }}^2}{2}$$

(2)

Chinese port investment enterprises and the host government have contradictory interests based on different objectives in the joint construction of green port projects, but both pursue the maximization of their own utility. Assume that the expected revenue functions of two parties are continuous and derivable. The benefit function of the Chinese port investor is complete information known by both parties, but the benefit function of the host government is incomplete information. Because the host government requires the Chinese port investment enterprise to bear the social welfare A and fixed income ∂, whether the host government stipulates the lowest tax and its investment conversion coefficient are only known by the host government itself, and there is information inequality between the two parties. In addition to considering the size of the project and the infrastructure development of the host government, Chinese port investment enterprises will also determine the investment amount based on maximizing the benefits, so they hope that the host government will provide an investment conversion coefficient that maintains the normal benefits, while the host government aims to maximize its own economic, environmental and social benefits to enhance the investment conversion factor. Therefore, there is a certain dispute between the two sides on the host government’s investment conversion factor. However, Chinese port investment enterprises must follow a constraint when investing in the construction of green ports in the host country: that is, the benefits provided by Chinese port investment enterprises to the host government should exceed the retained benefits W of the host government, that is, there is

$${\mathsf{\beta }\mathrm{a}}^{\mathrm{m}}{\mathrm{b}}^{1-\mathrm{m}}+\mathrm{r}\mathsf{\zeta }\mathrm{I}+\mathrm{f}\mathsf{\zeta }\mathrm{I}+\mathrm{A}+\partial -\frac{1}{2}{\mathrm{P}}_2{\mathrm{b}}^2-\frac{{\mathsf{\rho }\mathrm{f}}^2{\mathsf{\sigma }}^2}{2}\ge \mathrm{W}$$

(3)

Only if this constraint holds, the host government will cooperate with the Chinese port investor and allow them to invest green ports in their own country. In order to maximize its own benefits, the host government will take various measures to enhance the investment conversion factor f, so as to increase the amount of investment into actual benefits. Additionally, it will choose an optimal investment conversion factor to maximize the equivalent expected revenue function, i.e., the partial derivative of Equation (2) with respect to f, and obtain the incentive constraint as: $-{\mathrm{f}\mathsf{\rho }\mathsf{\sigma }}^2=0$; then we have.

$$\mathrm{f}=\frac{\mathsf{\zeta }\mathrm{I}}{{\mathsf{\rho }\mathsf{\sigma }}^2}$$

(4)

According to Equation (4), there is a negative relationship between the investment conversion coefficient f and the host country risk aversion coefficient $\mathsf{\rho }$, the higher $\mathsf{\rho }$, the more difficult for the host government’s investment conversion factor to work, i.e., the more difficult for the host government’s investment to be converted into the revenue.

Chinese port investment enterprises have to pay more costs, including the basic green investment amount, the cost of human, technical and management efforts for the construction of green ports, additional social benefits agreed with the host government, fixed income, etc.; the main benefits are the conversion of the investment amount, the environmental and social benefits brought about by the operation of green ports, so China port investment enterprises in ODI in the construction of green ports benefits $\mathrm{C}\left(\mathsf{\pi }\right)$ are:

$$\mathrm{C}\mathsf{\pi }={\mathsf{\alpha }\mathrm{a}}^{\mathrm{m}}{\mathrm{b}}^{1-\mathrm{m}}+\mathrm{e}\mathsf{\zeta }\mathrm{I}-\mathrm{r}\mathsf{\zeta }\mathrm{I}-\frac{1}{2}{\mathrm{p}}_1{\mathrm{a}}^2-\frac{1}{2}{\mathrm{p}}_1{(\mathsf{\zeta }\mathrm{I})}^2-\mathrm{A}-\partial$$

According to Hypothesis 8, Chinese port investment enterprises are risk neutral, and there is no risk cost, so the expected revenue of Chinese port investment enterprises is Ev.

$$\mathrm{Ev}={\mathsf{\alpha }\mathrm{a}}^{\mathrm{m}}{\mathrm{b}}^{1-\mathrm{m}}+\mathrm{e}\mathsf{\zeta }\mathrm{I}-\mathrm{r}\mathsf{\zeta }\mathrm{I}-\frac{1}{2}{\mathrm{p}}_1{\mathrm{a}}^2-\frac{1}{2}{\mathrm{p}}_1{(\mathsf{\zeta }\mathrm{I})}^2-\mathrm{A}-\partial$$

(5)

During the negotiation game, Chinese port investment enterprises understand that if the utility brought to the host country by green ports is not lower than its reserved utility W, the host government will be willing to reach a cooperation agreement to allow Chinese port investment enterprises invest, i.e., as long as Equation (3) is made to hold, at this point we can obtain:

$$\mathrm{r}\mathsf{\zeta }\mathrm{I}+\mathrm{A}+\partial =\mathrm{W}-({\mathsf{\beta }\mathrm{a}}^{\mathrm{m}}{\mathrm{b}}^{1-\mathrm{m}}+\mathrm{f}\mathsf{\zeta }\mathrm{I}-\frac{1}{2}{\mathrm{p}}_2{\mathrm{b}}^2-\frac{{\mathsf{\rho }\mathrm{f}}^2{\mathsf{\sigma }}^2}{2})$$

(6)

Bringing Equations (4) and (6) into Equation (5) for the expected revenue function of a Chinese port investment firm, we have

$$\mathrm{Ev}={\mathsf{\alpha }\mathrm{a}}^{\mathrm{m}}{\mathrm{b}}^{1-\mathrm{m}}+{\mathsf{\beta }\mathrm{a}}^{\mathrm{m}}{\mathrm{b}}^{1-\mathrm{m}}+\mathrm{e}\mathsf{\zeta }\mathrm{I}-\frac{1}{2}{\mathrm{p}}_2{\mathrm{b}}^2-\frac{1}{2}{\mathrm{p}}_1{\mathrm{a}}^2-\frac{1}{2}{\mathrm{p}}_1{(\mathsf{\zeta }\mathrm{I})}^2+\frac{{\mathsf{\zeta }}^2{\mathrm{I}}^2}{2{\mathsf{\rho }\mathsf{\sigma }}^2}-\mathrm{w}$$

(7)

In order to maximize the benefits brought by green ports, Chinese port investment enterprises will make optimal investment decisions, i.e., choose the optimal investment amount to maximize the economic, environmental and social benefits, and this optimal investment amount can also meet the requirements of building green ports, and derive (7) with respect to I and let it be zero, resulting in

$$\mathrm{I}=\frac{{\mathsf{\rho }\mathsf{\sigma }}^2\mathrm{e}}{{\mathsf{\rho }\mathsf{\sigma }}^2{\mathrm{p}}_1-\mathsf{\zeta }}$$

(8)

Then, Equation (8) is the optimal investment amount of Chinese port investment enterprises, and Equation (8) is brought into Equations (2) and (5) to obtain the expected revenue functions of the two subjects in the equilibrium situation of the game, respectively.

The host government expects the benefit function to be:

$$\mathrm{Eu}={\mathsf{\beta }\mathrm{a}}^{\mathrm{m}}{\mathrm{b}}^{1-\mathrm{m}}+\frac{2{\mathrm{r}\mathsf{\zeta }\mathrm{e}\mathsf{\rho }\mathsf{\sigma }}^2[({\mathrm{p}}_1{\mathsf{\rho }\mathsf{\sigma }}^2-\mathsf{\zeta })+{\mathrm{e}}^2{\mathsf{\zeta }}^2{\mathsf{\rho }\mathsf{\sigma }}^2]}{2{({\mathsf{\rho }\mathsf{\sigma }}^2{\mathrm{p}}_1-\mathsf{\zeta })}^2}+\mathrm{A}+\partial -\frac{1}{2}{\mathrm{p}}_2{\mathrm{b}}^2$$

(9)

The expected revenue function for Chinese port investment firms is:

$$\mathrm{Ev}={\mathsf{\alpha }\mathrm{a}}^{\mathrm{m}}{\mathrm{b}}^{1-\mathrm{m}}+\frac{{\mathrm{e}\mathsf{\rho }\mathsf{\sigma }}^2[{\mathsf{\zeta }\mathrm{p}}_1{\mathsf{\rho }\mathsf{\sigma }}^2\left(2\mathrm{e}-2\mathrm{r}-\mathsf{\zeta }\mathrm{e}\right)-2{\mathsf{\zeta }}^2\left(\mathrm{e}-\mathrm{r}\right)]}{2{({\mathsf{\rho }\mathsf{\sigma }}^2{\mathrm{p}}_1-\mathsf{\zeta })}^2}-\mathrm{A}-\partial -\frac{1}{2}{\mathrm{p}}_1{\mathrm{a}}^2$$

(10)

3.2.2. Analysis of the Impact of Effort Level

According to the expected revenue functions, it is known that the efforts made by both parties will also affect the final expected revenue of each party. This paper will specifically study the relationship between the optimal effort level and the expected revenue of both parties, and calculate the optimal expected revenue function of both parties under the optimal effort level.

The first and second order derivatives of Equation (2), with respect to the host government’s effort level b, are, respectively:

$$\frac{\partial \mathrm{Eu}}{\partial \mathrm{b}}=\left(1-\mathrm{m}\right){\mathsf{\beta }\mathrm{a}}^{\mathrm{m}}{\mathrm{b}}^{1-\mathrm{m}}-{\mathrm{p}}_2\mathrm{b};\frac{{\partial }^2\left(\mathrm{Eu}\right)}{\partial {\mathrm{b}}^2}=\left({\mathrm{m}}^2-\mathrm{m}\right){\mathsf{\beta }\mathrm{a}}^{\mathrm{m}}{\mathrm{b}}^{-\mathrm{m}-1}-{\mathrm{p}}_2$$

According to the description of the parameters of the cooperative game model, there are 0 < m < 1, 0 < p₂ < 1, and $\mathsf{\beta },\mathsf{\alpha }\in \left[0,1\right]$, so that $\frac{{\partial }^2\left(\mathrm{Eu}\right)}{\partial \mathrm{b}}<0$, the function is a concave function and has a great value, so that $\frac{\partial \mathrm{Eu}}{\partial \mathrm{b}}=0$. The optimal effort level that maximizes the expected revenue of the host government is obtained as:

$$\mathrm{b}={\mathrm{a}}^{\frac{\mathrm{m}}{1-\mathrm{m}}}{[\frac{\left(1-\mathrm{m}\right)\mathsf{\beta }}{{\mathrm{p}}_2}]}^{\frac{1}{1-\mathrm{m}}}$$

(11)

Similarly, the expected revenue function Equation (5) for Chinese port investment enterprises with respect to the effort level a is found to have the first and second order derivatives, respectively, with the second order derivative $\frac{{\partial }^2\left(\mathrm{Ev}\right)}{\partial {\mathrm{a}}^2}<0$, when $\frac{\partial \mathrm{Ev}}{\partial \mathrm{a}}=0$ the expected revenue function is maximized, i.e., the optimal effort level of Chinese port investment enterprises is:

$$\mathrm{a}={\mathrm{b}}^{\frac{1-\mathrm{m}}{2-\mathrm{m}}}{(\frac{\mathrm{m}\mathsf{\alpha }}{{\mathrm{p}}_1})}^{\frac{1}{2-\mathrm{m}}}$$

(12)

Proposition 1. 

According to Equations (11) and (12), since 0 < m < 1, we have$0<\frac{m}{1-m}<1$, that$0<\frac{1-m}{2-m}<\frac{1}{2}$, with other values determined, Chinese port investment enterprises and host government effort levels are positively correlated, i.e., both will increase their own effort levels due to the increase in the effort level exerted by the other party.

Coupling (11) and (12), the optimal effort level for the host government and the Chinese port investment firm can be derived as

$$\mathrm{b}={(\frac{\mathrm{m}\mathsf{\alpha }}{{\mathrm{p}}_1})}^{\frac{\mathrm{m}}{\left(2-2\mathrm{m}\right)\left(1-\mathrm{m}\right)}}{[\frac{\left(1-\mathrm{m}\right)\mathsf{\beta }}{{\mathrm{p}}_2}]}^{\frac{2-\mathrm{m}}{\left(1-\mathrm{m}\right)\left(2-2\mathrm{m}\right)}}$$

(13)

$$\mathrm{a}=[\frac{\left(1-\mathrm{m}\right)\mathsf{\beta }}{{\mathrm{p}}_2}]{(\frac{\mathrm{m}\mathsf{\alpha }}{{\mathrm{p}}_1})}^{\frac{1}{\left(2-2\mathrm{m}\right)}}$$

(14)

Proposition 2. 

According to Equations (13) and (14), the effort level b of the host government and the effort level a of the Chinese port investment enterprise are mainly affected by the effort cost coefficients of both partiesp₁andp₂,and a and b are related top₁andp₂and are negatively correlated, respectively. The specific analysis is as follows.

It is known that 0 < m < 1, and in the effort level of host government b, the $\frac{\mathrm{m}}{\left(2-2\mathrm{m}\right)\left(1-\mathrm{m}\right)}$ is constantly greater than 0, without considering the influence of cost of its own effort p₂, the effort level b and the effort cost coefficient of Chinese port investment enterprises p₁ is negatively correlated, i.e., an increase of p₁ leads to a decrease in the effort level of the host government. This is consistent with the conclusion above that the effort level of Chinese port investment enterprises is positively correlated with the host government. Because when p₁ rises, the effort level of it a decreases. Additionally, it also affecting the effort level input of the host government. When the impact of effort cost of Chinese port investment enterprises is not considered, and $\frac{2-\mathrm{m}}{\left(1-\mathrm{m}\right)\left(2-2\mathrm{m}\right)}$ is constantly greater than 0, then the effort level b of the host government and its own effort cost coefficient p₂ is also negatively correlated, i.e., the effort cost rises and the host government will put less effort into the project construction. Therefore, the effort level of the host government in the construction of green ports is negatively related to its own effort cost coefficient p₂ and the effort cost coefficient of Chinese port investment enterprises p₁. Similarly, the effort level of Chinese port investment enterprises is negatively related to the host government’s effort cost p₂ and its own effort cost p₁. That is, when the effort cost of Chinese port investment enterprises and the host government increase, the effort level of Chinese port investment enterprises will also decrease.

When the effort level b of the host government and the effort level a of the Chinese port investment enterprise reach the values shown in Equations (13) and (14), respectively, the expected revenues of both parties are maximized, and combined with the optimal investment amount (8), the expected revenues of both parties can be derived as:

Host Government Expected Revenues:

$$\begin{gathered} \mathrm{Eu}=\mathsf{\beta }{[\frac{\left(1-\mathrm{m}\right)\mathsf{\beta }}{{\mathrm{p}}_2}]}^{\frac{1}{1-\mathrm{m}}}{\left(\frac{\mathrm{m}\mathsf{\alpha }}{{\mathrm{p}}_1}\right)}^{\frac{\mathrm{m}}{1-\mathrm{m}}}-\frac{1}{2}{\mathrm{p}}_2[\frac{\left(1-\mathrm{m}\right)\mathsf{\beta }}{{\mathrm{p}}_2}{]}^{\frac{2-\mathrm{m}}{{\left(1-\mathrm{m}\right)}^2}}{\left(\frac{\mathrm{m}\mathsf{\alpha }}{{\mathrm{p}}_1}\right)}^{\frac{\mathrm{m}}{{\left(1-\mathrm{m}\right)}^2}}+ \\ \frac{2{\mathrm{r}\mathsf{\zeta }\mathrm{e}\mathsf{\rho }\mathsf{\sigma }}^2[({\mathrm{p}}_1{\mathsf{\rho }\mathsf{\sigma }}^2-\mathsf{\zeta })+{\mathrm{e}}^2{\mathsf{\zeta }}^2{\mathsf{\rho }\mathsf{\sigma }}^2]}{2{({\mathsf{\rho }\mathsf{\sigma }}^2{\mathrm{p}}_1-\mathsf{\zeta })}^2}+\mathrm{A}+\partial \end{gathered}$$

(15)

Expected Revenues of Chinese port investment enterprises:

$$\begin{gathered} \mathrm{Ev}=\mathsf{\alpha }\left[{[\frac{\left(1-\mathrm{m}\right)\mathsf{\beta }}{{\mathrm{p}}_2}]}^{\frac{1}{\left(1-\mathrm{m}\right)}}{\left(\frac{\mathrm{m}\mathsf{\alpha }}{{\mathrm{p}}_1}\right)}^{\frac{\mathrm{m}}{\left(1-\mathrm{m}\right)}}\right]-\frac{1}{2}{\mathrm{p}}_1{[\frac{\left(1-\mathrm{m}\right)\mathsf{\beta }}{{\mathrm{p}}_2}]}^2{(\frac{\mathrm{m}\mathsf{\alpha }}{{\mathrm{p}}_1})}^{\frac{1}{1-\mathrm{m}}}+ \\ \frac{{\mathrm{e}\mathsf{\rho }\mathsf{\sigma }}^2[{\mathsf{\zeta }\mathrm{p}}_1{\mathsf{\rho }\mathsf{\sigma }}^2\left(2\mathrm{e}-2\mathrm{r}-\mathsf{\zeta }\mathrm{e}\right)-2{\mathsf{\zeta }}^2\left(\mathrm{e}-\mathrm{r}\right)]}{2{({\mathsf{\rho }\mathsf{\sigma }}^2{\mathrm{p}}_1-\mathsf{\zeta })}^2}-\mathrm{A}-\partial \end{gathered}$$

(16)

Therefore, in the construction of green ports by Chinese ODI, the expected revenues of the host government and Chinese port investment enterprises are related to their respective effort level, and the best benefits will be obtained by both parties when the efforts invested by both parties reach a certain level.

In order to verify Propositions 1 and 2 and to specifically analyze the impact of effort levels a and b on the revenue of the host government and Chinese port investment enterprises, this paper uses numerical simulation to conduct a study. Since there are many parameters involved in the cooperative game model, and the effort cost and other parameters are private information which is difficult to obtain through data collection and other methods, and there are few existing studies with questionnaires similar to this paper, so the simulation assignment of the relevant parameters, this paper complies with the above game parameter description and refers to the existing studies of scholars such as Huang et al. [38] and Feng et al. [39] to assign values to the relevant parameters involved in the game model. $\mathsf{\alpha }=\mathsf{\beta }=0.5$, ${\mathsf{\rho }\mathsf{\sigma }}^2=1, \mathrm{A}=0.03,\partial =0.03, {\mathrm{p}}_1,{\mathrm{p}}_2\in \left(0,1\right)$. The conversion coefficient of Chinese port investment enterprises, the investment coefficient of Chinese port investment enterprises and the tax rate set by the host government are calculated according to the parameter descriptions and taken as the average $\mathrm{\zeta }=0.25$, $\mathrm{e}=0.85$, $\mathrm{r}=0.25$, first take m as 0.25, 0.5, 0.75, respectively to verify Proposition 1 and Proposition 2 to obtain the following

Table 2. Changes in the effort level between Chinese port investment enterprises and the host government under fixed cost factor P2.

P1		a	b
m = 0.25	0.9	0.34	0.94
	0.7	0.39	0.98
	0.5	0.49	1.07
	0.3	0.69	1.19
m = 0.5	0.9	0.23	0.16
	0.7	0.29	0.21
	0.5	0.42	0.28
	0.3	0.69	0.48
m = 0.75	0.9	0.07	0.000011
	0.7	0.12	0.000052
	0.5	0.23	0.000388

and

Table 3. Changes of efforts of host country government and efforts of Chinese port investment enterprises under fixed cost coefficient P1.

P2		a	b
m = 0.25	0.9	0.21	0.31
	0.7	0.31	0.37
	0.5	0.53	0.46
	0.3	1.16	0.65
m = 0.5	0.9	0.02	0.23
	0.7	0.03	0.29
	0.5	0.10	0.42
	0.3	0.48	0.69
m = 0.75	0.9	0.00000001	0.03
	0.7	0.000000126	0.05
	0.5	0.00000036	0.09
	0.3	0.0000602	0.27

.

From Table 2 and Table 3, it can be seen that regardless of the value of m, the effort level of the Chinese port investor a and the host government b are positively correlated, and one side of the cooperative game will increase the effort level of the other side to motivate the other side to put in more effort, which verifies Proposition 1. This situation is mainly because the host government and Chinese port investment enterprises have the same goal—to obtain more economic, environmental and social benefits. In order to achieve the same goal, both sides will improve their effort levels in different ways. For example, the Chinese port investment enterprises is willing to bear the additional social welfare costs required by the host government, and the host government will respond to the efforts of the Chinese port investment enterprises by reducing taxes, i.e., both parties are mutually beneficial. The table also shows that as the effort cost coefficients P1 and P2 increase, the effort level of the Chinese port investor a and the effort level of the host government b decrease, which verifies Proposition 2. The increase of the effort cost coefficients will lead to the increase of the investment and construction costs of the Chinese port investment enterprises and the host government, which will compress the profit income of both parties in the construction of green ports by Chinese ODI. Therefore, when the coefficient of effort cost rises, both parties will react negatively and reduce the effort level to reduce the cost and maintain the revenue level.

According to the cooperative game model constructed above, it analyzes the relationship between the income of the host country government and Chinese port investment enterprises and the effort level a and b when the effort level coefficient m is $0.25,0.5,0.75$, respectively, i.e., the relationship between the Chinese port investment enterprise paying more important effort level, both parties paying equally important effort level, and the host government paying more important effort level in three cases, and the following results are obtained by using Matlab numerical simulation.

According to Figure 2a, Figure 3a and Figure 4a result plots, it can be seen that regardless of m what value is taken, the correlation between the host government revenue and Chinese port investment enterprises’ effort level a and its own effort level b is consistent. That is, the host government’s expected revenue Eu and its own effort level show an inverted U-shaped change trend, with the increase of its own effort level, the host government return Eu appears to rise first and then fall, and the existence of the optimal host government effort level b makes the host government return Eu maximum, while the reason for the decline of the host government profit Eu at the highest point of the inverted U-shaped is related to the effort cost. The increase of the host government effort level is accompanied by an increase in effort cost, and the excessive effort cost leads to an increase in its own profit that is lower than the cost spent; meanwhile, the host government revenue Eu increases with the increase in effort level a of Chinese port investment enterprises, which is mainly due to the fact that Chinese port investment enterprises invest more effort cost and put more effort to enhance the project profit, and the host country is enjoying the profits brought by Chinese port investment enterprises without any increase in cost.

Similarly, according to Figure 2b, Figure 3b and Figure 4b it can be seen that the expected revenue Ev of Chinese port investment enterprises remains consistent with the correlation between the host country effort level b and their own effort level a, and is affected by m less influenced. In other words, the expected revenue Ev of Chinese port investment enterprises also has an inverted U-shaped trend with their own effort level a. The existence of optimal effort cost a of Chinese port investment enterprises makes the expected revenue Ev obtain the optimal value. Similarly, the expected revenue of Chinese port investment enterprises is positively correlated with the effort level of the host government, because when the effort level of the host government increases, they will respond by reducing their own effort level, expecting to obtain more profit at lower cost, and at this time, Chinese port investment enterprises can still obtain the profit brought by the host government’s increased effort. Additionally, comparing with the result graph, it can be seen that the expected revenue of the host government in green ports is higher than Chinese port investment enterprises, that mainly because Chinese port investment enterprises as investors will bear extra costs to promote the cooperation agreement between the two sides, its cost is much larger than that of the host government, so in the actual situation Chinese port investment enterprises get less revenue from green ports than the host government.

4. Case Analysis

4.1. Formatting of Mathematical Components

In order to verify the results of the empirical study, this paper selects the Gwadar Port in Pakistan, the new container port in Ghana, Africa, and the Piraeus Port in Greece, Europe as samples for case studies. It calculates the respective revenues of Chinese port investment enterprises and the host government in the joint construction of the project, and proves the realism of the proposed model from the perspective of actual cases as well as shows that participation in Chinese ODI in the construction of green ports can bring profits to the participants.

According to the main research content of this paper, the sample cases have the following conditions: (see Appendix B for port details)

(1)

Port projects that have entered into cooperation agreements with Chinese port investment enterprises and have been completed or put into operation.

(2)

Port construction and operation of the port into green technology, green energy or has green results of the port project.

(3)

Green port projects invested and constructed by Chinese port investment enterprises in four modes: new investment, joint venture and merger, merger and acquisition or concession.

4.2. Analysis Results

Based on the proposed cooperative game model, the respective revenues of the host government and Chinese port investment enterprises in the Gwadar Port, the new container port of Ghana Terme, and the Piraeus Port projects are calculated. According to the parameter setting above, still take $\mathsf{\alpha }=\mathsf{\beta }=0.5,{\mathsf{\rho }\mathsf{\sigma }}^2=1,\mathrm{A}=0.03,\partial =0.03,{\mathrm{p}}_1,{\mathrm{p}}_2\in \left(0,1\right)$. The conversion coefficient $\mathrm{e}$, the investment coefficients $\mathsf{\zeta }$ of Chinese port investment enterprises in each project, calculated as specified in the description of the game parameters, the tax rate $\mathrm{r}$ set by each government taken from the Foreign Investment Guide-2019 for each country developed by the Ministry of Commerce, the parameters of each port shown in

Table 4. Basic data of each project.

Region	Country	Projects	e	$\mathit{\zeta }$	r
Asia	Pakistan	Gwadar Port	0.57	0.64	0.25
Africa	Ghana	Special Code New Container Port	0.51	0.07	0.25
Europe	Greece	Piraeus Port	0.64	0.05	0.29

Data source: calculated by the authors as specified in the parameter description above.

.

Let m be 0.25, 0.5 and 0.75, respectively, and calculate the expected revenue Eu of each host government and the expected revenue Ev of the Chinese port investment enterprise in the three projects when the effort cost coefficient P1 of the Chinese port investment enterprise is changed, and the results are obtained as shown in Figure 5 and Figure 6.

From Figure 5 and Figure 6, the expected revenue of host government is positive overall in the three projects, and only in m = 0.75, the cost coefficient of effort of Chinese port investment enterprises decreases to a negative value. This indicates that the host government can obtain economic, environmental and social benefits in the construction of green ports by Chinese ODI. Additionally, when m = 0.75, the effort cost coefficient of Chinese port investment enterprises decreases, the effort of the host government is more important, and the effort level of it is much lower than that of Chinese port investment enterprises, which leads to the decline and even negative value of their expected revenue. In addition, when the effort cost coefficient of Chinese port investment enterprises decreases, the host government’s expected revenue tends to decrease first and then increase, because the effort cost coefficient of Chinese port investment enterprises also affects the effort level of the host government and the optimal investment amount of itself, which leads to fluctuations in the expected revenue of the host government. Therefore, the host government should pay attention to its own effort level in order to increase its own expected revenue. Comparing Figure 5 and Figure 6, we can see that the expected revenue of Chinese port investment enterprises is smaller than the host government as a whole, and even the expected revenue is negative when their own effort cost coefficients are too large. With the reduction of effort cost coefficient of Chinese port investment enterprises, they begin to get benefits from the project, but the expected benefits of them do not increase continuously with the reduction of effort cost coefficient, because there is an optimal effort level to maximize their expected revenues.

Taking m to be 0.25, 0.5 and 0.75, and calculating the expected revenue Eu of the host government and the expected revenue Ev of the Chinese port investment enterprises in the three projects when the host government effort cost coefficient P2 changes, and the results are shown in Figure 7 and Figure 8.

According to Figure 7, it can be seen that the expected revenue of the host government is positive overall in the three projects, but since the effort level by the host government is much smaller than the Chinese port investment enterprises, even if the host government’s effort cost is reduced, it will cause the host government’s expected revenue to be negative when its own effort level is more important and both parties’ effort levels are equally important. Therefore, in general, the host government can still gain economic, environmental and social benefits from Chinese ODI in green ports, and the host government’s expected revenues increase as the host government’s effort cost coefficient decreases. However, when its effort level plays a more important role, the lower effort cost coefficient will instead reduce its own revenues. From Figure 8, the decrease of the host government effort cost coefficient will lead to the increase of the expected revenues of Chinese port investment enterprises, which is mainly because the decrease of the host government effort cost coefficient is accompanied by the increase of the host government effort level, which motivates Chinese port investment enterprises to respond positively and put more efforts to increase the expected revenues. Therefore, for Chinese port investment enterprises, encouraging the host country government to improve its efforts in the construction of green ports by ODI is conducive to Chinese port investment enterprises to reduce losses and finally obtain profits.

5. Conclusions

Through the current situation of Chinese ODI in building green ports, it can be seen that the contradictions in the distribution of port revenue, economic interests and public interests between the host government and Chinese port investment enterprises will bring greater risks to Chinese port investment enterprises and directly hinder the process of construction, and even lead to project failure. According to the constructed cooperative game model, the expected revenues and effort levels of Chinese port investment enterprises and the host government are positively related to each other’s effort levels, and there is an optimal effort level to maximize the expected revenues of both parties. Specifically, suggestions for countermeasures to promote Chinese ODI in building green ports are presented.

From the perspective of Chinese port investment enterprises, they should promote the construction of green ports from three aspects: adhering to the concept of green development, strengthening awareness of responsibility and identifying various types of risks. Additionally, actively seeking their own optimal effort level and inspiring the host government to increase the effort level to maximize the economic, environmental and social benefits of both sides. First, adhere to the concept of green, sustainable and low-carbon, motivate the host government to improve cooperation, make use of China’s experience in the construction of green ports, establish a green port information management system, supervise the pollution in the process of port construction and operation in real time, take the initiative to develop and introduce green port technology, green materials, energy and products, protect the local ecological environment, and ensure that the sustainable operation can bring social and environmental benefits. Secondly, they should strengthen the sense of responsibility, reduce the conflict of interest to stabilize the cooperation between the two sides, gain an in-depth understanding of the host government’s investment access system, taxation system, host government work habits and social international corporate social responsibility evaluation standards and other policy regulations formulated by foreign investment enterprises, and reduce the risk of contradictions in negotiations. They should comply with international labor standards and the host country’s labor system under the premise of increasing the proportion of local labor employed. Then, they should improve the disclosure of social responsibility information in the construction of green ports, enhance the transparency of information and broaden the channels of local social supervision to enhance the competitiveness of Chinese port investment enterprises in the region. When it comes to the risk identification and prevention mechanism, the Chinese port investment enterprises should innovate diversified financing models, strengthen cooperation with diversified financial institutions, and balance the income distribution between the two sides to reduce economic risk. They should pay attention to the relevant policies formulated by the host country for foreign investment enterprises and the investigation and research of the existing local laws and regulations, such as expropriation, requisition, nationalization and temporary changes in policies due to public interests, and clarify the investment laws, labor protection, environmental protection and other laws and regulations formulated for foreign investment, so as to reduce the policy and legal risks. The company will also adhere to the localization management strategy, strengthen the cooperation with the mainstream local media, and promote the concept of investing in green ports to avoid social and cultural risks. Additionally, they should pay attention to innovation on core technology, research and development, and application, and should realize automatic and intelligent green port construction, such as improving the allocation efficiency of production factors and reducing construction costs through the application of big data, artificial intelligence, cloud computing, etc. Additionally, they should pay attention to the training of international talents, improve core competitiveness in enterprise employees and reduce labor costs. Additionally, they can, through the integration of government, industry, academia and research, focus on the construction of their own financing channels to reduce investment costs and improve the efficiency of investment transformation so as to obtain better profits.

For the host government, active cooperation is the best choice for the host government to participate while it also can obtain benefits and satisfy its interests in the projects. The host government can improve its cooperation by actively widening the communication channels and understanding the interests of both sides to promote the construction and obtain its own optimal expected revenues. Firstly, it can establish a green port-related investment cooperation mechanism or working group to deal timely with various problems arising from cooperation with Chinese port investment enterprises and provide effective consultation support for green port projects. Secondly, it can actively accept Chinese friendly exchange of visits, and jointly negotiate with the Chinese government to deepen the cooperation path of ODI to build green ports to enhance political mutual trust between countries and reduce political risks. In addition, it can supplement and improve the relevant investment agreements, provide Chinese port investment enterprises with corresponding tax concessions and policy protection, attract Chinese port investment enterprises to invest and adhere to mutual benefits. Finally, it should take the initiative to understand and agree Chinese green concept and interest demands, reduce conflicts between two sides, and actively implement green measures to participate in the construction of green ports. It should take the initiative to establish a green resource information service platform supplemented by the ecological environmental protection laws and regulations of the country. It should strictly regulate the behavior of Chinese port investment enterprises, reduce the damage of port construction to the ecological environment of the country and the legal risk of Chinese port investment enterprises, and create a harmonious and green cooperation atmosphere.

In conclusion, this paper uses the cooperative game with the introduction of effort level to study the construction of green ports by Chinese ODI, and the research perspective is innovative to a certain extent. We verify the possible benefits and risks of ODI in building green ports for China and Chinese enterprises, as well as the multiple benefits that international cooperation and active cooperation may bring to the host country and its government. We hope to use the cooperative game to improve the study of Chinese ODI in building green ports, and to be able to provide guidance for Chinese port investment enterprises’ decision making and international cooperation in host governments. However, due to the complexity and dynamics of the process of Chinese ODI in building green ports, there are some shortcomings in the paper. Firstly, Chinese ODI in building green ports involves more economic interest subjects, and in constructing the cooperative game model, this paper tries to study the main issue: the cooperative game between Chinese port investment enterprises and the host government, so more interest subjects are not selected. Secondly, the cooperative game model constructed in this paper involves a large number of parameters, and some of the parameter data are private information which cannot be obtained through data collection and questionnaire survey methods, so the processing of these data adopt the method of simulation assignment by drawing on the research of existing scholars.