# Integration, Game, and Sustainable Development of Shenzhen Port Based on Governmental Regulations

Authors: Xuanfei Wang; Shan Liang; Zhenjie Liao
Journal: Journal of Mathematics
 (2022)

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## Abstract

The internal integration, game, and sustainable development of Shenzhen Port play key roles in developing a synergy mechanism among Guangdong-Hong Kong-Macau Greater Bay Area (GBA) ports. Using a logistics model, a parameter estimation and evolutionary analysis of Shenzhen Port were performed, revealing that it requires a new impetus to promote growth in its container throughput. Based on the population ecology theory, a two-population Lotka-Volterra model was used to discuss the activity and mutual effect between the western and eastern port areas of Shenzhen Port, quantitatively measuring the varying degrees of the hindering effects between them. To reduce competition and strengthen cooperation, a port game matrix with a punishment mechanism of governmental regulations was created to discuss the internal integration of Shenzhen Port. The results show that, along with the promoting effect of port cooperation on the increase in container throughput, there is a gradual increase in the punishment of speculative behaviours. Government-dominated port cooperation prevents the prisoner’s dilemma in the port activity process. The findings of this study provide quantitative data support and decision-making references for achieving resource complementarity, developing synergy mechanisms, and attaining sustainable development in Shenzhen Port.


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## Body

## 1. Introduction

As the gateway to foreign trade, ports play an important role in national economies. Historically, Shenzhen Port has developed a coastal trade pattern centered on the eastern and western port areas, presenting a world-oriented development trend. The container throughput of Shenzhen Port steadily ranks among the top four worldwide [1–3]. Owing to the decline in the global shipping market in the postcrisis era, Shenzhen Port has faced various emerging problems in recent years. While the construction of a synergy mechanism between the ports in the GBA has recently accelerated, the requirements for port integration have become increasingly high. Shenzhen Port, as the core of the ports in the GBA, faces the development of a new activity pattern. Therefore, the eastern and western ports of Shenzhen must not only boost competitiveness through efficient management and operation but also need to think about the cooperation among each other to develop a transportation junction while competing against ports outside of the GBA. Moreover, the eastern and western port areas should cooperate on a competitive basis, strengthen the mutual complementarity of their port resources, and build a synergy mechanism among different ports to develop the ports in Shenzhen sustainably [4]. Through integration and alliance, ports in major countries and regions worldwide have achieved a good balance between partial interest and overall interest, significantly facilitating the healthy development of the local port industry [3, 5–7]. In Shenzhen, port integration is ongoing, but is far from sufficient. This is primarily due to the activity and inadequate synergy mechanism between different ports, in addition to the capital environment facing the ports in Shenzhen. No mature empirical theory is available for reference, necessitating a constant exploration on a matter-of-fact basis. Therefore, this study discusses the port integration and game of Shenzhen Port in the context of developing a synergy mechanism between the ports in the GBA. The findings of this study are of great significance for the sustainable development of Shenzhen Port.


### 1.1. Literature Review

The existing literature on ports mainly includes longitudinal and cross-sectional studies. Among longitudinal studies of ports, Álvarez-SanJaime et al. [8] discussed the impact on port competition of the integration of port and inland transport services. Donselaar et al. [9] examined the societal costs and benefits of cooperation between port authorities. Based on Stackelberg’s cooperative game theory (Stackelberg [10], Li et al. [11]), Lai et al. [12, 13] built a modified model with optimal Shapley values (Shapley [14], Casajus and Huettner [15], and Nan et al. [16]) to discuss the supply chain coordination mechanism of ports. Among cross-sectional studies of ports, Zhao et al. [17] analyzed the evolution of the port system along “maritime silk road.” Hotelling model (Yu and Xu [18], Wang et al. [19]) has been widely applied due to the special spatial characteristics of port competition [20, 21]. Fan et al. [22] examined the competition and cooperation in a port cluster based on a game model. Kaselimi et al. [23] established a terminal duopoly game model based on the Hotelling demand structure selected by customers to study the impact of exclusive terminals on competition among port groups. With the economic recession, the process of port integration has accelerated in China. Kuang et al. [24] examined the supply-side reform of Chinese ports based on port-city separation. Guo and Yang [25] quantitatively analyzed the port integration in multiport areas.In the above research, different scholars have combined the research objects and methods to carry out quantitative analysis, providing references for subsequent scholars to conduct related research. With the construction in the GBA, research on building a port cooperation mechanism has gradually become popular in academia, and this needs to be further promoted on the basis of the abovementioned scholars’ research. At present, domestic scholars combine the methods and ideas in existing research and take the port integration of the GBA as the research object to carry out quantitative and qualitative research. For example, Li [26] examined the evolution of cocompetition between the main ports in the GBA to provide a reference for the construction and development of ports there. Building a cocompetition relationship model, Huang [27] empirically investigated the development of port clusters in the GBA. Wang et al. [28] analyzed governance models of port clusters in the GBA, proposing the strategic idea of developing an international shipping center through appropriate measures (e.g. innovative top-level design). Focusing on the port clusters in the GBA, Liu et al. [29] investigated the green and coordinated development of ports, offering several suggestions.Existing studies on port outcomes in the GBA are based on the vertical and horizontal research dimensions of ports. The analysis of the key points and difficulties of port collaborative development shows that the construction of an internal synergy mechanism of Shenzhen Port is the core point in the port integration due to its development of capital environment and other reasons in the GBA. Therefore, Shenzhen Port plays a key role in developing a synergy mechanism among the ports in the GBA such that its internal integration is of vital importance. However, prior to the proposed GBA construction strategy, existing quantitative studies were mainly conducted from the perspective of the pearl river delta [30, 31]. Yu and Shan [32] quantitatively analyzed the cocompetition game in a port cluster. Luo et al. [33] used a two-stage game model to investigate the postentry container port capacity expansion. Wang et al. [34] used the game theory model to analyse the factors and conditions affecting regional port governance in southern China. Cheng et al. [35] examined the convenience of port trade, as exemplified by the Shenzhen Port and Hong Kong Port. Since the proposal of the GBA construction strategy, existing studies on Shenzhen Port have been scarce and most are qualitative in nature. From the GBA construction perspective, Zhang et al. [36] investigated the synergetic development of Shenzhen Port and other ports in the GBA, discussing port synergy at different levels based on an analysis of port development status. Zhong et al. [37] examined the construction of combined ports in terms of regional synergy to provide a reference for the construction of combined ports in Shenzhen.In summary, existing studies [30–33, 35, 38] on Shenzhen Port have mostly discussed cooperation and competition between the overall Shenzhen Port and other ports but have not analyzed the development of Shenzhen Port itself nor have they quantitatively measured the internal integration and game of Shenzhen Port. To develop a synergy mechanism among the ports in the GBA, this study models and analyses the internal integration and game of Shenzhen Port to explore its development trends as well as the mutual effects among its port areas. As a result, this study explores the synergy mechanism among the ports in Shenzhen to provide quantitative data support and decision reference for the sustainable development of Shenzhen Port.


## 1.1. Literature Review

The existing literature on ports mainly includes longitudinal and cross-sectional studies. Among longitudinal studies of ports, Álvarez-SanJaime et al. [8] discussed the impact on port competition of the integration of port and inland transport services. Donselaar et al. [9] examined the societal costs and benefits of cooperation between port authorities. Based on Stackelberg’s cooperative game theory (Stackelberg [10], Li et al. [11]), Lai et al. [12, 13] built a modified model with optimal Shapley values (Shapley [14], Casajus and Huettner [15], and Nan et al. [16]) to discuss the supply chain coordination mechanism of ports. Among cross-sectional studies of ports, Zhao et al. [17] analyzed the evolution of the port system along “maritime silk road.” Hotelling model (Yu and Xu [18], Wang et al. [19]) has been widely applied due to the special spatial characteristics of port competition [20, 21]. Fan et al. [22] examined the competition and cooperation in a port cluster based on a game model. Kaselimi et al. [23] established a terminal duopoly game model based on the Hotelling demand structure selected by customers to study the impact of exclusive terminals on competition among port groups. With the economic recession, the process of port integration has accelerated in China. Kuang et al. [24] examined the supply-side reform of Chinese ports based on port-city separation. Guo and Yang [25] quantitatively analyzed the port integration in multiport areas.In the above research, different scholars have combined the research objects and methods to carry out quantitative analysis, providing references for subsequent scholars to conduct related research. With the construction in the GBA, research on building a port cooperation mechanism has gradually become popular in academia, and this needs to be further promoted on the basis of the abovementioned scholars’ research. At present, domestic scholars combine the methods and ideas in existing research and take the port integration of the GBA as the research object to carry out quantitative and qualitative research. For example, Li [26] examined the evolution of cocompetition between the main ports in the GBA to provide a reference for the construction and development of ports there. Building a cocompetition relationship model, Huang [27] empirically investigated the development of port clusters in the GBA. Wang et al. [28] analyzed governance models of port clusters in the GBA, proposing the strategic idea of developing an international shipping center through appropriate measures (e.g. innovative top-level design). Focusing on the port clusters in the GBA, Liu et al. [29] investigated the green and coordinated development of ports, offering several suggestions.Existing studies on port outcomes in the GBA are based on the vertical and horizontal research dimensions of ports. The analysis of the key points and difficulties of port collaborative development shows that the construction of an internal synergy mechanism of Shenzhen Port is the core point in the port integration due to its development of capital environment and other reasons in the GBA. Therefore, Shenzhen Port plays a key role in developing a synergy mechanism among the ports in the GBA such that its internal integration is of vital importance. However, prior to the proposed GBA construction strategy, existing quantitative studies were mainly conducted from the perspective of the pearl river delta [30, 31]. Yu and Shan [32] quantitatively analyzed the cocompetition game in a port cluster. Luo et al. [33] used a two-stage game model to investigate the postentry container port capacity expansion. Wang et al. [34] used the game theory model to analyse the factors and conditions affecting regional port governance in southern China. Cheng et al. [35] examined the convenience of port trade, as exemplified by the Shenzhen Port and Hong Kong Port. Since the proposal of the GBA construction strategy, existing studies on Shenzhen Port have been scarce and most are qualitative in nature. From the GBA construction perspective, Zhang et al. [36] investigated the synergetic development of Shenzhen Port and other ports in the GBA, discussing port synergy at different levels based on an analysis of port development status. Zhong et al. [37] examined the construction of combined ports in terms of regional synergy to provide a reference for the construction of combined ports in Shenzhen.In summary, existing studies [30–33, 35, 38] on Shenzhen Port have mostly discussed cooperation and competition between the overall Shenzhen Port and other ports but have not analyzed the development of Shenzhen Port itself nor have they quantitatively measured the internal integration and game of Shenzhen Port. To develop a synergy mechanism among the ports in the GBA, this study models and analyses the internal integration and game of Shenzhen Port to explore its development trends as well as the mutual effects among its port areas. As a result, this study explores the synergy mechanism among the ports in Shenzhen to provide quantitative data support and decision reference for the sustainable development of Shenzhen Port.


## 2. Materials and Methods

### 2.1. Logistic Model of the Scale Change of Shenzhen Port

The development of a port is usually characterized by slow growth in the initial stage, rapid development in the intermediate stage, and slow changes in the later stage [17]. This is consistent with the development of biotic populations. Therefore, a logistics model, for the development of a biotic population, can be applied to analyses the scale change of Shenzhen Port. Following previous studies [20, 21], the general form of logistics model can be written as(1)dptdt=rpt1−ptK,where pt denotes the scale of Shenzhen Port in year t, r denotes the growth rate of Shenzhen Port, and K denotes the maximum scale of Shenzhen Port. Solving the differential equation of the above formula leads to(2)pt=K1+eε−rtK>0,r>0,where ε=LnK/p0−1, p0 denotes the port scale at the initial time, and ε/r,K/2 denotes the turning point of port development. Considering that container throughput has become an important index for Shenzhen Port, it was used in this study to represent its scale. The container throughput data for Shenzhen Port from 1999 to 2018 are described in Table 1.Table 1
Container throughput of Shenzhen Port from 1999 to 2018.
YearThroughput (10,000 TEUs)YearThroughput (10,000 TEUs)199929920091,825200040020102,251200150820112,257200276220122,29420031,06520132,32820041,36620142,40420051,62020152,42020061,84720162,39820072,11020172,52120082,14220182,574


## 2.1. Logistic Model of the Scale Change of Shenzhen Port

The development of a port is usually characterized by slow growth in the initial stage, rapid development in the intermediate stage, and slow changes in the later stage [17]. This is consistent with the development of biotic populations. Therefore, a logistics model, for the development of a biotic population, can be applied to analyses the scale change of Shenzhen Port. Following previous studies [20, 21], the general form of logistics model can be written as(1)dptdt=rpt1−ptK,where pt denotes the scale of Shenzhen Port in year t, r denotes the growth rate of Shenzhen Port, and K denotes the maximum scale of Shenzhen Port. Solving the differential equation of the above formula leads to(2)pt=K1+eε−rtK>0,r>0,where ε=LnK/p0−1, p0 denotes the port scale at the initial time, and ε/r,K/2 denotes the turning point of port development. Considering that container throughput has become an important index for Shenzhen Port, it was used in this study to represent its scale. The container throughput data for Shenzhen Port from 1999 to 2018 are described in Table 1.Table 1
Container throughput of Shenzhen Port from 1999 to 2018.
YearThroughput (10,000 TEUs)YearThroughput (10,000 TEUs)199929920091,825200040020102,251200150820112,257200276220122,29420031,06520132,32820041,36620142,40420051,62020152,42020061,84720162,39820072,11020172,52120082,14220182,574


## 3. Lotka–Volterra Model

According to related studies [39–41], the mutual effect between ports within a region shares similar characteristics with the ‘population’ concept in ecology. Specifically, the number of individuals in a population will eventually reach the level allowed by the environmental capacity. The population may then develop a predator-prey relationship or competitive relationship as a result of resource conflict [42, 43]. Similarly, port scale and competitiveness are subject to dynamic changes under the combined effect of diverse factors (e.g., geographical location, natural conditions, and governmental regulations). Recently, Lotka–Volterra models, which analyses the population relationship, have been widely applied in management studies [44–48]. Based on related studies, this study used the concept of port game as an entry point, analogized the relationship between ports to the development relationship between biotic populations, and discussed the internal integration and game of Shenzhen Port in terms of developing a synergy mechanism among the ports in the GBA.There is a limit on the number of containers in Shenzhen Port. When port groups in the region with relatively equal strength contend for hinterland resources, they will produce a block effect to each other’s development. To facilitate the subsequent analysis, Port 1 (China Merchants Port) and Port 2 (Yantian International Container Terminals (YICT)), both subordinate to Shenzhen Port, were modeled and analyzed in this study. China Merchants Port and YICT face the same market, where their products or services can be completely substituted by each other. The game results between them show that they each gain a certain market share. The development of China Merchants Port and YICT are consistent with the logistics law of growth, making them eligible for the use of Lotka–Volterra models. Therefore, the following model was developed:(3)dp1tdt=r1p1t1−p1tK1+η12p2tK2,dp2tdt=r2p2t1−p2tK2+η21p1tK1.The Lotka–Volterra model is a direct extension of the logistics equation for single population growth. In equation (3), p1t and p2t, respectively, denote the container throughput of China Merchants Port and YICT in year t; K1 and K2 denote the maximum container throughput of China Merchants Port and YICT, respectively; r1 and r2 denote the growth rate of container throughput of China Merchants Port and YICT, respectively; η12 denotes the influence coefficient that YICT has on China Merchants Port; and η21 denotes that China Merchants Port has on YICT. The results of the game model depend on K and η, whereas r determines the rate at which a competition pattern is established. According to the population ecology theory, three factors determine the process of mutual competition between two types of creatures in the same environment: the inherent growth rate (r), the environmental constraint on biological reproduction (K), and the mutual effect between the participants in the game process (η).To calculate the coefficients of influence between China Merchants Port and YICT, by the transformation of the formulaα10=r1, α11=−r1/K1, α12=r1η12/K2, α20=r2, α21=r2η21/K1, and α22=−r2/K2, equation (3) was converted into equation (4) using the grey estimation method as follows:(4)dp1tdt=α10p1t+α11p12t+α12p1tp2t,dp2tdt=α20p2t+α22p22t+α21p1tp2t.Based on the mapping relationship between grey derivative and even logarithm, equation (5) can be obtained as follows:(5)p1t+1−p1t=α10p1t+1+p1t2+α11p1t+1+p1t22+α12p1t+1+p1t2p2t+1+p2t2,p2t+1−p2t=α20p2t+1+p2t2+α21p1t+1+p1t2p2t+1+p2t2+α22p2t+1+p2t22.When substituting the parameterst=1,2,…,n, we can get the matrix equation R1n=β1α1∧ and R2n=β2α2∧, as follows:(6)β1=p11+p122p11+p1222p11+p122p21+p222p12+p132p12+p1322p12+p132p22+p232⋯⋯⋯p1n−1+p1n2p1n−1+p1n22p1n−1+p1n2p2n−1+p2n2,(7)β2=p21+p222p11+p122p21+p222p21+p2222p22+p232p12+p132p22+p232p22+p2322⋯⋯⋯p2n−1+p2n2p1n−1+p1n2p2n−1+p2n2p2n−1+p2n22,(8)R1n=p12−p11,p13−p12,…,p1n−p1n−1T,α1∧=α10,α11,α12,α2∧=α20,α22,α21,R2n=p22−p21,p23−p22,…,p2n−p2n−1T.Using the nonlinear least squares method, we obtain the following:(9)α1∧=β1Tβ1−1β1TR1n,α2∧=β2Tβ2−1β2TR2n.Port game matrix creation: existing studies [49–53] have shown that stable cooperation between ports on a competitive basis plays a crucial role in significantly increasing their competitiveness, promoting increases in market demand, and strengthening the effect of mutualistic symbiosis. Therefore, cooperation on a competitive basis will play a dominant role in the game of Shenzhen Port. When the external environment is relatively mature, the container throughput of the two ports will vary stably and reach equilibrium. If we let equation (3) equal to 0, dp1t/dt=0 and dp2t/dt=0, then the four equilibrium points are E1K1,0, E20,K2, E30,0, and E4K11+η12/1−η12η21,K21+η21/1−η12η21, respectively, according to literature [54], where E1 and E2 are the results of a zero-sum game and E3 is the result of excessive competition. The first three equilibrium points reveal that disordered competition in Shenzhen Port restricts the growth of the port scale, thus hindering the healthy development of the western and eastern port areas and opposing the harmonious coexistence of ports. Therefore, this study mainly analyzed the port game in the E4 state. A game matrix was created to analyse the relationship between China Merchants Port and YICT. Both participants in the port game have two choices: cooperation or noncooperation. We assumed that the cooperation strategy for China Merchants Port yields a proportion of δ to YICT, while the cooperation strategy for YICT yields a proportion of λ to China Merchants Port. Table 2 presents the game matrix for the two ports.Table 2
Port game matrix.
YICT CmpCooperationNon-cooperationCooperationK11+η12+λ/1−η12+λη21+δ,K21+η21+δ/1−η12+λη21+δK11+η12/1−η12η21+δ,K21+η21+δ/1−η12η21+δNon-cooperationK11+η12+λ/1−η21η12+λ,K21+η21/1−η21η12+λK11+η12/1−η12η21,K21+η21/1−η12η21


## 4. Results and Discussion

### 4.1. Development and Evaluation Trends in Shenzhen Port

We performed the parameter estimation using the nonlinear least squares method (as described in Table3), according to the data of Shenzhen Port and using statistical software StataSE 15 to analyse the model. The results for Shenzhen Port pass the parameter estimation tests, with high fitting accuracy. We also fitted the development trends of Shenzhen Port based on the logistics model (as described in Figure 1). The analysis shows that the inflection point of the development of Shenzhen Port occurred in 2005 (1988 + 7.1773/0.4313 = 2004.6). The container throughput of Shenzhen Port grew rapidly before 2005, peaked, and then declined in subsequent years. In particular, the container throughput grew slowly, characterized by undulations, after 2010 (as shown in Figure 2).Table 3
Nonlinear least square parameter estimation results.
ParameterCoefficientStd. errtP valueμ2432.311034.8069.89≤0.001ε7.17720.4516.09≤0.001θ0.43130.0315.54≤0.001Figure 1
Container throughput (blue line) and fitted values (red line) of Shenzhen Port.Figure 2
Growth rate per year (red line) of the container throughput of Shenzhen Port from 2011 to 2019.In the past 10 years, the container throughput growth rate per year was relatively low, except in 2014 (3.2%) and 2017 (5.1%) (Figure2). The container throughput of Shenzhen Port was 25 770 000 TEUs in 2019, with a growth rate of only 0.1% compared with 2018.The analysis in Figure2 shows that the container throughput of Shenzhen Port has entered a slow growth stage; Shenzhen Port requires a new impetus to promote its next stage of development. The analysis results of this study are consistent with the actual trend of the container throughput of Shenzhen Port. While the construction of a synergy mechanism has recently accelerated among the ports in the GBA, the requirements for port integration are increasingly high. Shenzhen Port, as the core of the GBA, faces a new cocompetition game pattern as it participates in global competition. To attain sustainable development, strengthening mutual complementarity and building a synergy mechanism among the ports in Shenzhen are necessary.


### 4.2. Analysis of Port Interaction Relationship

The container throughput data for the two ports from 1999 to 2019 are shown in Table4:Table 4
Container throughput of YICT and China Merchants Port of Shenzhen from 1999 to 2019 (unit: ten thousand TEU).
YearsYICTChina merchants port19991591372000215181200127522320024183262003526494200462670920057588352006887955200710021103200896811582009858943201010131169201110261149201210671158201310801139201411671103201512171075201611701097201712701118201813161135201913071142According to the data in Table4 and (5)–(9), using the matrix calculation function of MATLAB software,(10)α1∧=0.571388468,−0.000478507,−2.4446×10−5,α2∧=0.422445633,−0.000338144,−1.39879×10−5.The coefficients of influence were restored in equations (3) and (4), yielding η12=−0.0554 and η21=−0.0395. Hence, China Merchants Port and YICT have a hindering effect on the development of each other, but the hindering effect of YICT on China Merchants Port is more significant than that of China Merchants Port on YICT. The findings of this study are consistent with the actual historical development of Shenzhen Port. YICT in the east and YICT in the west are two major ports in Shenzhen. Based on superior natural conditions (e.g. harbour water depth), YICT has recently implemented specific measures such as green and smart development, resulting in a relatively rapid growth trend in its container throughput. To fight for a large market share, the competition between ports is increasingly fierce. China Merchants Port in western Shenzhen has recently faced sluggish container throughput growth (specifically, container throughput has approached its limit). Therefore, the addition of a new impetus to the growth of its container throughput should be a matter of urgency, with the adoption of appropriate measures [55–59]. This explains why China Merchants Port has built a partnership with Shenzhen Chiwan, recently developing a combined port with Shunde Port. At the same time, due to the existence of η12=−0.0554<α11=−0.000478507 and η21=−0.0395<α22−0.000338144, it indicates that the effect of “interspecific” competition is much smaller than the “intraspecific” competition effect. It means that the blocking effect brought by the competition between populations is greater than the adverse effect of the competition within populations on their own development. In addition, compared with the limits of the respective container throughput of YICT and China Merchants Port, their limits for combined container throughput show different characteristics (1129<K1=1194 and 1294>K2=1233). Disordered competition between the two ports will inhibit the growth of their container throughput. By contrast, YICT, which is relatively young and vibrant, can actively adjust itself to address port competition. Because the hindering effect of YICT on China Merchants Port is more significant than that of China Merchants Port on YICT as well as the sluggish container throughput growth faced by the relatively old China Merchants Port, there is a lag in how fast the port scale reaches its limit. Next, this paper will analyse the game and development of the east and west ports in Shenzhen.


### 4.3. Port Game Matrix Analysis

For the game matrix in Table2, China Merchants Port and YICT are found to be prone to evolve towards the prisoner’s dilemma. Specifically, for each participant, the best result is K11+η12+λ/1−η21η12+λ or K21+η21+δ/1−η12η21+δ when the other participant chooses to cooperate, but not itself. The second best result is K11+η12+λ/1−η12+λη21+δ or K21+η21+δ/1−η12+λη21+δ when both participants choose to cooperate. The third best result is K11+η12/1−η12η21 or K21+η21/1−η12η21 when neither participant chooses to cooperate. The worst result is K11+η12/1−η12η21+δ or K21+η21/1−η21η12+λ when one participant chooses to cooperate, but the other participant chooses not to. Therefore, the following conditions exist for the prisoner’s dilemma:(11)K11+η12+λ1−η21η12+λ>K11+η12+λ1−η12+λη21+δ>K11+η121−η12η21>K11+η121−η12η21+δ,K21+η21+δ1−η12η21+δ>K21+η21+δ1−η12+λη21+δ>K21+η211−η12η21>K21+η211−η21η12+λ.Furthermore, we assume the following:(12)K11+η12+λ1−η12+λη21+δ+K21+η21+δ1−η12+λη21+δ>K11+η121−η12η21+δ+K21+η21+δ1−η12η21+δ,K11+η12+λ1−η12+λη21+δ+K21+η21+δ1−η12+λη21+δ>K11+η12+λ1−η21η12+λ+K21+η211−η21η12+λ.As long as the above two conditions are met, the individual rationality of the participants is not consistent with the collective rationality. Through further analysis of equation (11), it can be found that 0<δ<0.0395 and 0<λ<0.0554, and equation (12) is guaranteed to be established. In fact, the range value of δ and λ has realistic meaning. It shows that, under the background of port integration in the GBA, the cooperation between eastern and western ports in Shenzhen has less positive effect on each other than blocking effect. This is also the reason why the port cooperation among the ports in this region is not active and the integration work is lagging behind under the background of vigorously promoting port integration by the state. Therefore, it is necessary to introduce the punishment mechanism when the incentive measures fail. The prisoner’s dilemma is a primary problem faced by society when it chooses a cooperation strategy during socioeconomic development. At all times and globally, numerous institutional arrangements in society (including laws and social norms) are designed to address the prisoner’s dilemma, using the punishment mechanism as a feasible solution. Governmental regulations were introduced in this study [60–62]; punitive measures were taken to address the prisoner’s dilemma in the port cooperation process. In the current stage, the internal integration of Shenzhen Port involves different levels of competent authorities, necessitating the implementation of government-dominated reform. We assumed that, in the port integration process, the uncooperative party is punished with a fine of Xi, where both parties believe that punitive measures can be carried out effectively.While rewards and punishments promote port cooperation, we assumed that China Merchants Port chooses to cooperate, but YICT chooses not to. The revenue obtained by China Merchants Port is thenK11+η12/1−η12η21+δ, while the revenue obtained by YICT is K21+η21+δ/1−η12η21+δ−X2. As long as the fine is sufficiently high to ensure that K21+η21+δ/1−η12η21+δ−X2<K21+η21+δ/1−η12+λη21+δ, the best choice for YICT is to implement a cooperative strategy. Likewise, when K11+η12+λ/1−η21η12+λ−X1<K11+η12+λ/1−η12+λη21+δ, the best choice for China Merchants Port is also to implement a cooperative strategy. When both parties choose to cooperate, a balanced state is attained, thus overcoming the contradiction between individual rationality and collective rationality. This explains the necessity for the introduction of governmental regulations. The following section analyses the maximum likelihood of port cooperation, i.e., the minimum value of Xi:(13)K11+η12+λ1−η21η12+λ−X1<K11+η12+λ1−η12+λη21+δ,K21+η21+δ1−η12η21+δ−X2<K21+η21+δ1−η12+λη21+δ.We solved equation (13) to obtain the following equation:(14)X1>K11+η12+λδ1−η21η12+λη21+δ,X2>K21+η21+δλ1−η12η12+λη21+δ.When governmental regulations act on the strategies of China Merchants Port and YICT (i.e., ensuring mutual cooperation), the minimum fine for their speculative behaviours is, respectively,K11+η12+λδ/1−η21η12+λη21+δ,K21+η21+δλ/1−η12η12+λη21+δ.If we letfλ=K11+η12+λδ/1−η21η12+λη21+δfδ=K21+η21+δλ/1−η12η12+λη21+δλ∈0,1,δ∈0,1 and calculate the minimum values of fλ and fδ, we can then obtain f′λ=K1δ1+η21η21+δ/1−η21η12+λη21+δ2f′δ=K2λ1+η12η12+λ/1−η12η12+λη21+δ2.Bothλ∈0,1,δ∈0,1, fλ, and fδ are increasing functions, that is, the minimum value of punishment for the uncooperative party under governmental regulations when one party chooses to cooperate, but the other party chooses not to. If the two parties do not believe that punitive measures can be carried out effectively or if the punishment for speculative behaviours is not sufficiently severe (i.e., X1<K11+η12+λ/1−η21η12+λ−K11+η12+λ/1−η12+λη21+δ or X2<K21+η21+δ/1−η12η21+δ−K21+η21+δ/1−η12+λη21+δ), the port game returns to the prisoner’s dilemma, resulting in port cooperation failure.The above analysis shows that, under governmental regulations, the punishment mechanism for speculative behaviours enacted by the uncooperative port serves to better maintain the cooperation between the two parties and reduce their speculative behaviours. Given that existing market shares remain unchanged, the promoting effect of port cooperation must meet the following condition:(15)K11+η12K21+η21=K11+η12+λK21+η21+δ.Specifically, under the action of governmental regulations, both ports implement a cooperative strategy, resulting in container throughput growth. Additionally, they can still maintain their original market shares, while extra revenue arises as a result of the promoting effect on each other. Briefly, the two ports achieve a win-win result. Substituting equation (15) into the equation for the ratio of the minimum punishment between China Merchants Port and YICT under governmental regulations on their strategies (i.e. mutual cooperation), we obtain the following:(16)f=X1X2=K11+η12+λδ1−η21η12+λη21+δ×1−η12η12+λη21+δK21+η21+δλ=K11+η12+λK21+η21+δ×δλ×1−η12η12+λη21+δ1−η21η12+λη21+δ=K11+η12K21+η21×1−η12η12+λη21+δ1−η21η12+λη21+δ×δλ.If we substitute the calculated values ofK1, K2, η12, and η21 into equation (16), the ratio of the fines for speculative behaviours between the two ports is as follows:(17)f=1127.851184.3×1+0.0554λ−0.0554δ−0.03951+0.0395λ−0.0554δ−0.0395×δλ.Respectively, taking the values ofδ and λ at equal intervals on [0,1], Figure 3 shows the three-dimensional surface of the simulation results described in equation (17).Figure 3
Three-dimensional surface of the speculation penalty ratio.According to Figure3, the ratio of the fine (f) is an increasing function with respect to δ, that is, f increases gradually with an increase in δ. Evidently, significant container throughput growth will occur if YICT chooses to cooperate with China Merchants Port. In the process of government-dominated port integration, when YICT cooperates with China Merchants Port, the fine for speculative behaviours enacted by China Merchants Port will gradually increase with an increase in the promoting effect of China Merchants Port on container throughput growth in YICT. Likewise, the ratio of fines (f) is a decreasing function with respect to λ, that is, f decreases gradually with an increase in λ. Evidently, significant container throughput growth will occur if China Merchants Port chooses to cooperate with YICT. In the process of government-dominated port integration, when China Merchants Port cooperates with YICT, the fine for speculative behaviours enacted by YICT will gradually increase with an increase in the promoting effect of YICT on container throughput growth in China Merchants Port.


## 4.1. Development and Evaluation Trends in Shenzhen Port

We performed the parameter estimation using the nonlinear least squares method (as described in Table3), according to the data of Shenzhen Port and using statistical software StataSE 15 to analyse the model. The results for Shenzhen Port pass the parameter estimation tests, with high fitting accuracy. We also fitted the development trends of Shenzhen Port based on the logistics model (as described in Figure 1). The analysis shows that the inflection point of the development of Shenzhen Port occurred in 2005 (1988 + 7.1773/0.4313 = 2004.6). The container throughput of Shenzhen Port grew rapidly before 2005, peaked, and then declined in subsequent years. In particular, the container throughput grew slowly, characterized by undulations, after 2010 (as shown in Figure 2).Table 3
Nonlinear least square parameter estimation results.
ParameterCoefficientStd. errtP valueμ2432.311034.8069.89≤0.001ε7.17720.4516.09≤0.001θ0.43130.0315.54≤0.001Figure 1
Container throughput (blue line) and fitted values (red line) of Shenzhen Port.Figure 2
Growth rate per year (red line) of the container throughput of Shenzhen Port from 2011 to 2019.In the past 10 years, the container throughput growth rate per year was relatively low, except in 2014 (3.2%) and 2017 (5.1%) (Figure2). The container throughput of Shenzhen Port was 25 770 000 TEUs in 2019, with a growth rate of only 0.1% compared with 2018.The analysis in Figure2 shows that the container throughput of Shenzhen Port has entered a slow growth stage; Shenzhen Port requires a new impetus to promote its next stage of development. The analysis results of this study are consistent with the actual trend of the container throughput of Shenzhen Port. While the construction of a synergy mechanism has recently accelerated among the ports in the GBA, the requirements for port integration are increasingly high. Shenzhen Port, as the core of the GBA, faces a new cocompetition game pattern as it participates in global competition. To attain sustainable development, strengthening mutual complementarity and building a synergy mechanism among the ports in Shenzhen are necessary.


## 4.2. Analysis of Port Interaction Relationship

The container throughput data for the two ports from 1999 to 2019 are shown in Table4:Table 4
Container throughput of YICT and China Merchants Port of Shenzhen from 1999 to 2019 (unit: ten thousand TEU).
YearsYICTChina merchants port19991591372000215181200127522320024183262003526494200462670920057588352006887955200710021103200896811582009858943201010131169201110261149201210671158201310801139201411671103201512171075201611701097201712701118201813161135201913071142According to the data in Table4 and (5)–(9), using the matrix calculation function of MATLAB software,(10)α1∧=0.571388468,−0.000478507,−2.4446×10−5,α2∧=0.422445633,−0.000338144,−1.39879×10−5.The coefficients of influence were restored in equations (3) and (4), yielding η12=−0.0554 and η21=−0.0395. Hence, China Merchants Port and YICT have a hindering effect on the development of each other, but the hindering effect of YICT on China Merchants Port is more significant than that of China Merchants Port on YICT. The findings of this study are consistent with the actual historical development of Shenzhen Port. YICT in the east and YICT in the west are two major ports in Shenzhen. Based on superior natural conditions (e.g. harbour water depth), YICT has recently implemented specific measures such as green and smart development, resulting in a relatively rapid growth trend in its container throughput. To fight for a large market share, the competition between ports is increasingly fierce. China Merchants Port in western Shenzhen has recently faced sluggish container throughput growth (specifically, container throughput has approached its limit). Therefore, the addition of a new impetus to the growth of its container throughput should be a matter of urgency, with the adoption of appropriate measures [55–59]. This explains why China Merchants Port has built a partnership with Shenzhen Chiwan, recently developing a combined port with Shunde Port. At the same time, due to the existence of η12=−0.0554<α11=−0.000478507 and η21=−0.0395<α22−0.000338144, it indicates that the effect of “interspecific” competition is much smaller than the “intraspecific” competition effect. It means that the blocking effect brought by the competition between populations is greater than the adverse effect of the competition within populations on their own development. In addition, compared with the limits of the respective container throughput of YICT and China Merchants Port, their limits for combined container throughput show different characteristics (1129<K1=1194 and 1294>K2=1233). Disordered competition between the two ports will inhibit the growth of their container throughput. By contrast, YICT, which is relatively young and vibrant, can actively adjust itself to address port competition. Because the hindering effect of YICT on China Merchants Port is more significant than that of China Merchants Port on YICT as well as the sluggish container throughput growth faced by the relatively old China Merchants Port, there is a lag in how fast the port scale reaches its limit. Next, this paper will analyse the game and development of the east and west ports in Shenzhen.


## 4.3. Port Game Matrix Analysis

For the game matrix in Table2, China Merchants Port and YICT are found to be prone to evolve towards the prisoner’s dilemma. Specifically, for each participant, the best result is K11+η12+λ/1−η21η12+λ or K21+η21+δ/1−η12η21+δ when the other participant chooses to cooperate, but not itself. The second best result is K11+η12+λ/1−η12+λη21+δ or K21+η21+δ/1−η12+λη21+δ when both participants choose to cooperate. The third best result is K11+η12/1−η12η21 or K21+η21/1−η12η21 when neither participant chooses to cooperate. The worst result is K11+η12/1−η12η21+δ or K21+η21/1−η21η12+λ when one participant chooses to cooperate, but the other participant chooses not to. Therefore, the following conditions exist for the prisoner’s dilemma:(11)K11+η12+λ1−η21η12+λ>K11+η12+λ1−η12+λη21+δ>K11+η121−η12η21>K11+η121−η12η21+δ,K21+η21+δ1−η12η21+δ>K21+η21+δ1−η12+λη21+δ>K21+η211−η12η21>K21+η211−η21η12+λ.Furthermore, we assume the following:(12)K11+η12+λ1−η12+λη21+δ+K21+η21+δ1−η12+λη21+δ>K11+η121−η12η21+δ+K21+η21+δ1−η12η21+δ,K11+η12+λ1−η12+λη21+δ+K21+η21+δ1−η12+λη21+δ>K11+η12+λ1−η21η12+λ+K21+η211−η21η12+λ.As long as the above two conditions are met, the individual rationality of the participants is not consistent with the collective rationality. Through further analysis of equation (11), it can be found that 0<δ<0.0395 and 0<λ<0.0554, and equation (12) is guaranteed to be established. In fact, the range value of δ and λ has realistic meaning. It shows that, under the background of port integration in the GBA, the cooperation between eastern and western ports in Shenzhen has less positive effect on each other than blocking effect. This is also the reason why the port cooperation among the ports in this region is not active and the integration work is lagging behind under the background of vigorously promoting port integration by the state. Therefore, it is necessary to introduce the punishment mechanism when the incentive measures fail. The prisoner’s dilemma is a primary problem faced by society when it chooses a cooperation strategy during socioeconomic development. At all times and globally, numerous institutional arrangements in society (including laws and social norms) are designed to address the prisoner’s dilemma, using the punishment mechanism as a feasible solution. Governmental regulations were introduced in this study [60–62]; punitive measures were taken to address the prisoner’s dilemma in the port cooperation process. In the current stage, the internal integration of Shenzhen Port involves different levels of competent authorities, necessitating the implementation of government-dominated reform. We assumed that, in the port integration process, the uncooperative party is punished with a fine of Xi, where both parties believe that punitive measures can be carried out effectively.While rewards and punishments promote port cooperation, we assumed that China Merchants Port chooses to cooperate, but YICT chooses not to. The revenue obtained by China Merchants Port is thenK11+η12/1−η12η21+δ, while the revenue obtained by YICT is K21+η21+δ/1−η12η21+δ−X2. As long as the fine is sufficiently high to ensure that K21+η21+δ/1−η12η21+δ−X2<K21+η21+δ/1−η12+λη21+δ, the best choice for YICT is to implement a cooperative strategy. Likewise, when K11+η12+λ/1−η21η12+λ−X1<K11+η12+λ/1−η12+λη21+δ, the best choice for China Merchants Port is also to implement a cooperative strategy. When both parties choose to cooperate, a balanced state is attained, thus overcoming the contradiction between individual rationality and collective rationality. This explains the necessity for the introduction of governmental regulations. The following section analyses the maximum likelihood of port cooperation, i.e., the minimum value of Xi:(13)K11+η12+λ1−η21η12+λ−X1<K11+η12+λ1−η12+λη21+δ,K21+η21+δ1−η12η21+δ−X2<K21+η21+δ1−η12+λη21+δ.We solved equation (13) to obtain the following equation:(14)X1>K11+η12+λδ1−η21η12+λη21+δ,X2>K21+η21+δλ1−η12η12+λη21+δ.When governmental regulations act on the strategies of China Merchants Port and YICT (i.e., ensuring mutual cooperation), the minimum fine for their speculative behaviours is, respectively,K11+η12+λδ/1−η21η12+λη21+δ,K21+η21+δλ/1−η12η12+λη21+δ.If we letfλ=K11+η12+λδ/1−η21η12+λη21+δfδ=K21+η21+δλ/1−η12η12+λη21+δλ∈0,1,δ∈0,1 and calculate the minimum values of fλ and fδ, we can then obtain f′λ=K1δ1+η21η21+δ/1−η21η12+λη21+δ2f′δ=K2λ1+η12η12+λ/1−η12η12+λη21+δ2.Bothλ∈0,1,δ∈0,1, fλ, and fδ are increasing functions, that is, the minimum value of punishment for the uncooperative party under governmental regulations when one party chooses to cooperate, but the other party chooses not to. If the two parties do not believe that punitive measures can be carried out effectively or if the punishment for speculative behaviours is not sufficiently severe (i.e., X1<K11+η12+λ/1−η21η12+λ−K11+η12+λ/1−η12+λη21+δ or X2<K21+η21+δ/1−η12η21+δ−K21+η21+δ/1−η12+λη21+δ), the port game returns to the prisoner’s dilemma, resulting in port cooperation failure.The above analysis shows that, under governmental regulations, the punishment mechanism for speculative behaviours enacted by the uncooperative port serves to better maintain the cooperation between the two parties and reduce their speculative behaviours. Given that existing market shares remain unchanged, the promoting effect of port cooperation must meet the following condition:(15)K11+η12K21+η21=K11+η12+λK21+η21+δ.Specifically, under the action of governmental regulations, both ports implement a cooperative strategy, resulting in container throughput growth. Additionally, they can still maintain their original market shares, while extra revenue arises as a result of the promoting effect on each other. Briefly, the two ports achieve a win-win result. Substituting equation (15) into the equation for the ratio of the minimum punishment between China Merchants Port and YICT under governmental regulations on their strategies (i.e. mutual cooperation), we obtain the following:(16)f=X1X2=K11+η12+λδ1−η21η12+λη21+δ×1−η12η12+λη21+δK21+η21+δλ=K11+η12+λK21+η21+δ×δλ×1−η12η12+λη21+δ1−η21η12+λη21+δ=K11+η12K21+η21×1−η12η12+λη21+δ1−η21η12+λη21+δ×δλ.If we substitute the calculated values ofK1, K2, η12, and η21 into equation (16), the ratio of the fines for speculative behaviours between the two ports is as follows:(17)f=1127.851184.3×1+0.0554λ−0.0554δ−0.03951+0.0395λ−0.0554δ−0.0395×δλ.Respectively, taking the values ofδ and λ at equal intervals on [0,1], Figure 3 shows the three-dimensional surface of the simulation results described in equation (17).Figure 3
Three-dimensional surface of the speculation penalty ratio.According to Figure3, the ratio of the fine (f) is an increasing function with respect to δ, that is, f increases gradually with an increase in δ. Evidently, significant container throughput growth will occur if YICT chooses to cooperate with China Merchants Port. In the process of government-dominated port integration, when YICT cooperates with China Merchants Port, the fine for speculative behaviours enacted by China Merchants Port will gradually increase with an increase in the promoting effect of China Merchants Port on container throughput growth in YICT. Likewise, the ratio of fines (f) is a decreasing function with respect to λ, that is, f decreases gradually with an increase in λ. Evidently, significant container throughput growth will occur if China Merchants Port chooses to cooperate with YICT. In the process of government-dominated port integration, when China Merchants Port cooperates with YICT, the fine for speculative behaviours enacted by YICT will gradually increase with an increase in the promoting effect of YICT on container throughput growth in China Merchants Port.


## 5. Conclusions

Based on the analysis and verification of its development, this study argues that Shenzhen Port requires a new impetus to promote its next stage of development. Using a two-population Lotka–Volterra model, this study quantitatively analyzed the mutual effect between China Merchants Port and YICT in Shenzhen, finding that each port can hinder the growth of each other’s container throughput. Before implementing port integration, the relevant authorities must fully consider the development of port game and the role of different ports. This should then be followed by coordinated port planning to maximise the benefits of the ports. Port cooperation has become a dominant trend in terms of developing a synergy mechanism among the ports in the GBA. Shenzhen Port plays a key role in the development of ports in the GBA and should not only moderately curb excessive competition among its internal ports but also develop a stable and orderly cooperation mechanism among the internal ports. After introducing a punishment mechanism (i.e., governmental regulations), the fines for speculative behaviours enacted by a participant will gradually increase with an increase in the promoting effect of port cooperation on the growth of the container throughput of each port, and this government-dominated port cooperation prevents the prisoner’s dilemma in the port game. On the other hand, relevant national departments and the local government of Shenzhen should make greater efforts to encourage the cooperation between the eastern and western ports of Shenzhen, so that the promoting effect of the cooperation between the two sides is greater than the blocking effect, so as to avoid the prisoner's dilemma in the cooperation between the two sides and then turn into stag hunt game or even snow drift game (Skyrms [63] and Fort [64]), which is more conducive to mutual cooperation. As a result, considering that different levels of competent authorities regulate the ports in Shenzhen, coordinated port planning in Shenzhen is necessary, as is building a consensus on port cooperation. In the port integration process, Shenzhen Port should consider the development of other ports in Shenzhen, adhere to the principles of market orientation and capital drive, and build a community of common interest among the ports in Shenzhen by different means (e.g., investments, share right replacements, and shareholdings). The objective should be to eliminate the adverse monopoly effect of port function division, develop a collaborative mechanism, credibility mechanism, and interest allocation mechanism between the ports, and achieve mutual benefits.



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*Source: 2583027-2022-09-15.xml*