# Game Analysis of Container Ports Co-Competition and Coordinated Development in Guangdong-Hong Kong-Macao Greater Bay Area

Authors: Shan Liang; Xuanfei Wang; Zhenjie Liao
Journal: Mathematical Problems in Engineering
 (2023)

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## Abstract

The port groups of the Guangdong-Hong Kong-Macao Greater Bay Area faces a new competitive and cooperative game structure concerning global competition, making it is necessary to build a comprehensive port coordination and development mechanism. In this study, we apply the logistics model to conduct parameter estimation and evolution trend analysis on the development of the port group and highlight that the current container throughput of the Guangdong-Hong Kong-Macao Greater Bay Area port group will reach the maximum and the new impetus is needed to push it into the next round of development and evolution. Combined with the theory of ecological population, the Lotka–Volterra model of multiple groups is introduced to study competition and cooperation game, explore their interaction, and provide quantitative support for the formation of different central port groups in the Guangdong-Hong Kong-Macao Greater Bay Area. The study provides references for strengthening the construction of complementary resources and coordinated mechanism within the port group, realizing the differential development between ports in the Guangdong-Hong Kong-Macao Greater Bay Area.


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## Body

## 1. Introduction

Bay area economy is a new field in current economic and social development; it leads regional economic development [1–3]. Currently, the Guangdong-Hong Kong-Macao Greater Bay Area (henceforth, Greater Bay Area) construction is steadily progressing. As the core node of the commodity market supply chain in the Greater Bay Area [4], competition between ports is particularly fierce, reflected in both coastline natural resources and market supply. Owing to economic hinterland overlap, this competitive relationship is becoming increasingly prominent in the Greater Bay Area port group’s current development process. Because of influences from the social system, capital environment, and other factors, the Greater Bay Area ports have formed a multicenter port group development model with the Hong Kong, Shenzhen, and Guangzhou ports as the center and the surrounding feeder ports choosing to embrace the central port. The competition and cooperation among regional ports are primarily manifested in greater competition between ports of the same level and mutually beneficial symbiosis or predator-prey relations between ports of different levels. The ports’ coordinated development has become a major strategic choice for the Greater Bay Area in the new era. Therefore, to better guide development requires analyzing the game behavior of the port groups in the area and quantifying the interaction between the central ports and central ports and branch ports, as well as among branch ports.Currently, the pace of China’s economic structure adjustment is increasing, and the requirements for coordinated port development are increasing [5]. This is manifested in ports changing from simple competition, based on their own development and social resource optimization, to a degree of cooperation, which gives full play to cooperative advantages to achieve the synergy of maximizing benefits [6, 7].In the literature, Jiang et al. introduced an analysis framework for port connectivity from a global container liner shipping network perspective [8]. Marasco and Romano proposed an integrable nonautonomous Lotka–Volterra model in conducting a quantitative study of the interaction among container ports located in the Le Havre–Hamburg range [9]. Hintjens showed how the port authority can be advantageous for cooperation with adjacent port authorities [10]. Yang et al. employed Landsat images from 1987, 1997, 2007, and 2017 to derive the urban bay area’s using the object-oriented support vector machine (O-SVM) classification method; a multiscale spatial analysis method detected the landscape characteristics and types of growth in the urban expansions [11]. Park and Kim conducted an importance-performance analysis (IPA) on the importance of consideration factors before entering the port hinterland and satisfaction of consideration factors after moving to Busan and Gwangyang ports [12]. Twrdy and Zanne addressed the problem of sustainability of ports logistics and presented current conditions in the Port of Koper, the Mediterranean port located in the North Adriatic [13]. Fan et al. combined the dual competition of market demand competition and shoreline resources faced by China’s ports and established a game model to analyze port competition and cooperation in the Yellow Sea [14]. Zhao et al. conducted quantitative research on the port system’s competition and cooperation relationships against the background of constructing China’s 21st century Maritime Silk Road [15].Through systematic research and analysis, Kuang et al. highlighted that port city separation constitutes a breakthrough in China’s port supply side reform [16]. Guo and Yang studied the integration of ports in Northeast China from the perspective of maximizing the internal transportation social welfare of the outward transportation system [17]. Lai et al. discussed the revenue of the port competition and cooperation game and the coordination mechanism of the port supply chain [18]. Yu and Xu researched the income status of adjacent inland ports under different types of competition strategies based on the Hotelling model [19].Presently, many provinces in China have established provincial port groups through provincial government investment or have relied on existing provincial state-owned enterprises. As the core platform for ports’ coordinated development, this path has distinct top-down authority and easily becomes large scale in a short time. However, the coordinated development of ports in the Greater Bay Area goes beyond the scope of provinces and systems and involves stakeholders at different levels. The construction of a port coordinated development mechanism is more difficult. Most existing studies on the Greater Bay Area ports are qualitative analyses with a few quantitative studies based on the results of the relevant Pearl River Delta ports.For example, Luo et al. took the terminal price competition and scale expansion between Hong Kong and Shenzhen ports as the research object and established a two-stage game model to launch [20]. Wang et al. outlined the importance of the Regional Port Alliance based on an analysis of the game model established by the Pearl River Delta ports [21]. Cheng et al. took the Hong Kong and Shenzhen ports as the research objects to provide a quantitative discussion on port trade facilitation [22]. Yu and Shan established a quantitative model to study the competition and cooperation game relationship between ports from the perspectives of local governments and container terminals [23]. Xia established a container port alliance model based on a game theory and analyzed the income distribution and functional solution of a cooperative game [24]. Wang et al. compared the competition between the Shenzhen port and the Guangzhou and Hong Kong ports using the factor analysis method [25]. In sum, quantitative research on the game analysis of ports’ coordinated development in the Greater Bay Area is limited, and a development mechanism for reference and promotion is absent. Considering the important significance of ports in the construction of the Greater Bay Area, we explore the port interaction mechanism of the Greater Bay Area from the perspective of the competition and cooperation game to provide reference for the coordinated development of area ports.


## 2. Model Construction

### 2.1. Evolution Analysis of the Port Group in the Guangdong-Hong Kong-Macao Greater Bay Area

Biological population development and evolution in a certain area show that survival is inseparable from the ecological environment [26]. The population will multiply and die as per natural law, and its strength will dynamically change [27]. Simultaneously, the population evolves through adaptation and changing the environment [28]. Different populations in the same area may portray either predator-prey relations, competitive relations, or mutually beneficial symbiotic relations because of resource competition [29]. Similarly, in the case of ports, dynamic port economic developments relate closely to port location and comprehensive management changes. Owing to port economic structure and comprehensive environment changes, a port undergoes dynamic changes [30]. Port growth and evolution follow certain rules; that is, the speed is slow in the early and late stages, and it increases rapidly in the middle stages. The overall evolutionary process presents an S-shaped curve, which is consistent with a biological population’s growth and evolutionary law. Therefore, the logistics model, which was first used to study the evolutionary law of biological populations [31], is introduced into studying port evolution here. The formula is as follows:(1)dPtdt=αP1−PH,where Pt denotes the port group scale of the Greater Bay Area at time t, α denotes the throughput growth rate of the port group, and H denotes the maximum value of the port scale. By solving the differential equation with the abovementioned formula, we obtain the following:(2)Pt=H1+eε−αtH>0,α>0,where ε=LnH/P0−1, P0 denotes the port scale at the initial time, and ε/α,H/2 denotes the turning point of port evolution trend. Since container throughput has become an important indicator of the port group’s scale, we use the Greater Bay Area’s container throughput data to represent the port group scale (Table 1) and estimate the parameters of the group’s container throughput data from 1999 to 2018 in combination with the logistics model. The development and evolution trend of the port group is fitted.Table 1
Container throughput of the Guangdong-Hong Kong-Macao Greater Bay Area from 1999 to 2018.
YearsThroughputs (10000TEU)YearsThroughputs (10000TEU)1999211620095663200025582010659720012715201168992002323220126896200337632013699220044403201473522005484620157325200654882016747320076032201780352008630420188117According to the parameter estimation results (Table2) and evolution trend (Figure 1) of the Greater Bay Area port group logistics model, the inflection point of the bay’s evolution appeared in 2005 (1999 + 1.2377/0.2315 = 2005). Before that, the port group’s container scale increased rapidly, and the growth rate peaked in 2005. Since then, the growth rate of the port group’s container scale has shown the characteristics of instability. The aforementioned phenomenon is mainly affected by changes in China’s port control mode. After entering the 21st century, China’s port control mode has gradually changed from the central government to the coexistence of local government and the market. After the decentralization of port management power, the enthusiasm of local governments to build ports was mobilized. Relying on its geographical advantages, Shenzhen port has introduced Hong Kong port enterprises, which has continuously participated in the operation and management of Shenzhen port through shares and therefore greatly promoted the growth of port scale [32, 33]. After 2017, the Greater Bay Area port group’s container throughput will reach its limit. The main reason is that the Chinese government has once again issued port management policies to encourage private capital to participate in port reform. The continuous construction of and vicious competition among ports are serious issues, and ports’ insufficient division, cooperation, and differentiated development lead to excess supply. Therefore, new impetus is needed to promote the Greater Bay Area port group’s entry into a new development and evolutionary process.Table 2
Estimation results of port group in Guangdong-Hong Kong-Macao Greater Bay Area.
CoefStd. err.tP >|t|95% conf.Intervals/betal18030.5450214.2237.490.0007578.5808482.511/betal21.23780.092413.390.0001.04271.4328/betal30.23150.020111.510.0000.18910.2739Figure 1
Fitting of evolution trend of the port group in the Guangdong-Hong Kong-Macao Greater Bay Area.Our analysis results are in good agreement with the current scale development of port clusters in the Greater Bay Area. In recent years, the Greater Bay Area port group confronted a new competition and cooperation game pattern regarding participation in the global competition. With the emergence of the sluggish global shipping market in the postcrisis period, the problems of the Greater Bay Area port group are gradually being exposed, which will affect the region’s long-term development. Presently, the pace of economic structure adjustment in the Greater Bay Area is accelerating, and the coordinated development requirements of port groups are becoming increasingly higher. This requires strengthening constructing the complementary and coordinated development mechanism of port groups in the Greater Bay Area to realize differentiated development.


### 2.2. Model Establishment

The Lotka–Volterra model was originally proposed by American ecologist Lotka and Italian mathematician Volterra [34, 35]. The model is used to study the interaction of different populations in the same environment. Within the same spatial and temporal range, different populations compete for limited resources and establish predator-prey relations and mutual-symbiosis relations. As an important theoretical method to study the evolution and development of ecological populations, the Lotka–Volterra model can intuitively reflect the relationship between different populations. It is widely used in logistics industry development [36, 37], industrial ecology [38, 39], and network innovation [40]. This model is currently often applied in the port field, primarily to explore the interaction relationship between two or three ports [41, 42]. However, there are often no less than three ports in the same region. Related studies on multiple ports in the same region are mainly discussed from the economics perspective, such as the research on port city development using the PSM-DID method [43], the comparative study on operation efficiency of port container terminals based on a DEA model [44], and the research on port throughput prediction based on a dynamic penalized support vector regression model [45]. The interaction relationship, however, between multiple ports is rarely quantified. In view of its wide application in the academic field, this study expands and introduces the Lotka–Volterra model into our research to examine the interaction relationship between ports, using the competition and cooperation game of the Greater Bay Area port groups as an example. The interaction between ports can be represented by the following mathematical symbols:(1)
Promoting Effect. Port i is positively correlated with the change of port j scale, which is recorded as i+⟶j(2)
Hindrance. Port i is negatively correlated with the change of port j scale, which is recorded as i−⟶jThus, three different port relationship modes are formed:(i)
Mutually Beneficial Symbiosis between Ports. Namely, i+⟶j and j+⟶i(ii)
Competition between Ports. Namely, i−⟶j, and j−⟶i(iii)
Predator-Prey Relationship between Ports. Namely, i−⟶j and j+⟶iConsidering the actual port development in the Greater Bay Area and the principle of port coordination from easy to difficult, we apply the multigroup Lotka–Volterra model to our research on the competition and cooperation game of its nine ports in mainland China and establish the multigroup Lotka–Volterra model as shown in the following formula:(3)dP1tdt=α1P11+β12P2H2+β13P3H3+⋯+β19P9H9,dP2tdt=α2P21+β21P1H1+β23P3H3+⋯+β29P9H9,⋮dP9tdt=α9P91+β91P1H1+β92P2H2+⋯+β98P8H8.Among them,Piti=1,2,…,9 are the container throughputs of the nine Greater Bay Area ports at t time, αii=1,2,…,9 is the growth rate of port i, βiji,j=1,2,…,9 is the influence coefficient of port j on port i, and Hii=1,2,…,9 is the maximum handling capacity of port i. We convert the abovementioned model into the following formula:(4)dP1tdt=λ11P1+λ12P1P2+λ13P1P3+⋯+λ19P1P9,dP2tdt=λ22P2+λ21P1P2+λ23P2P3+⋯+λ29P2P9,⋮dP9tdt=λ99P9+λ91P1P9+λ92P2P9+⋯+λ98P8P9.Based on the grey derivative and even logarithm mapping relationship, the following formula is obtained:(5)P1t+1−P1t=λ11P1t+1+P1t2+λ12P1t+1+P1t2P2t+1+P2t2+⋯+λ19P1t+1+P1t2P9t+1+P9t2,P2t+1−P2t=λ22P2t+1+P2t2+λ21P1t+1+P1t2P2t+1+P2t2+⋯+λ29P2t+1+P2t2P9t+1+P9t2,⋮P9t+1−P9t=λ99P9t+1+P9t2+λ91P1t+1+P1t2P9t+1+P9t2+⋯+λ98P8t+1+P8t2P9t+1+P9t2.We substitutet=1,2,3,⋯,n time data into the following formula and obtain the matrix equation Xin=κiλi∧i=1,2,…,9; taking Guangzhou port as an example, its matrix equation is X2n=κ2λ2∧, where(6)κ2=P21+P222P11+P122⋯P21+P222P91+P922P22+P232P12+P132P22+P232⋯P22+P232P92+P932⋮⋮⋮P2n−1+P2n2P1n−1+P1n2P2n−1+P2n2⋯P2n−1+P2n2P9n−1+P9n2.X2n=P22−P21,P23−P22,⋯,P2n−P2n−1T, λ2∧=λ22,λ21,λ23,⋯,λ29T. Using the least square rule, there are(7)λ2∧=κ2Tκ2−1κ2TX2n.


## 2.1. Evolution Analysis of the Port Group in the Guangdong-Hong Kong-Macao Greater Bay Area

Biological population development and evolution in a certain area show that survival is inseparable from the ecological environment [26]. The population will multiply and die as per natural law, and its strength will dynamically change [27]. Simultaneously, the population evolves through adaptation and changing the environment [28]. Different populations in the same area may portray either predator-prey relations, competitive relations, or mutually beneficial symbiotic relations because of resource competition [29]. Similarly, in the case of ports, dynamic port economic developments relate closely to port location and comprehensive management changes. Owing to port economic structure and comprehensive environment changes, a port undergoes dynamic changes [30]. Port growth and evolution follow certain rules; that is, the speed is slow in the early and late stages, and it increases rapidly in the middle stages. The overall evolutionary process presents an S-shaped curve, which is consistent with a biological population’s growth and evolutionary law. Therefore, the logistics model, which was first used to study the evolutionary law of biological populations [31], is introduced into studying port evolution here. The formula is as follows:(1)dPtdt=αP1−PH,where Pt denotes the port group scale of the Greater Bay Area at time t, α denotes the throughput growth rate of the port group, and H denotes the maximum value of the port scale. By solving the differential equation with the abovementioned formula, we obtain the following:(2)Pt=H1+eε−αtH>0,α>0,where ε=LnH/P0−1, P0 denotes the port scale at the initial time, and ε/α,H/2 denotes the turning point of port evolution trend. Since container throughput has become an important indicator of the port group’s scale, we use the Greater Bay Area’s container throughput data to represent the port group scale (Table 1) and estimate the parameters of the group’s container throughput data from 1999 to 2018 in combination with the logistics model. The development and evolution trend of the port group is fitted.Table 1
Container throughput of the Guangdong-Hong Kong-Macao Greater Bay Area from 1999 to 2018.
YearsThroughputs (10000TEU)YearsThroughputs (10000TEU)1999211620095663200025582010659720012715201168992002323220126896200337632013699220044403201473522005484620157325200654882016747320076032201780352008630420188117According to the parameter estimation results (Table2) and evolution trend (Figure 1) of the Greater Bay Area port group logistics model, the inflection point of the bay’s evolution appeared in 2005 (1999 + 1.2377/0.2315 = 2005). Before that, the port group’s container scale increased rapidly, and the growth rate peaked in 2005. Since then, the growth rate of the port group’s container scale has shown the characteristics of instability. The aforementioned phenomenon is mainly affected by changes in China’s port control mode. After entering the 21st century, China’s port control mode has gradually changed from the central government to the coexistence of local government and the market. After the decentralization of port management power, the enthusiasm of local governments to build ports was mobilized. Relying on its geographical advantages, Shenzhen port has introduced Hong Kong port enterprises, which has continuously participated in the operation and management of Shenzhen port through shares and therefore greatly promoted the growth of port scale [32, 33]. After 2017, the Greater Bay Area port group’s container throughput will reach its limit. The main reason is that the Chinese government has once again issued port management policies to encourage private capital to participate in port reform. The continuous construction of and vicious competition among ports are serious issues, and ports’ insufficient division, cooperation, and differentiated development lead to excess supply. Therefore, new impetus is needed to promote the Greater Bay Area port group’s entry into a new development and evolutionary process.Table 2
Estimation results of port group in Guangdong-Hong Kong-Macao Greater Bay Area.
CoefStd. err.tP >|t|95% conf.Intervals/betal18030.5450214.2237.490.0007578.5808482.511/betal21.23780.092413.390.0001.04271.4328/betal30.23150.020111.510.0000.18910.2739Figure 1
Fitting of evolution trend of the port group in the Guangdong-Hong Kong-Macao Greater Bay Area.Our analysis results are in good agreement with the current scale development of port clusters in the Greater Bay Area. In recent years, the Greater Bay Area port group confronted a new competition and cooperation game pattern regarding participation in the global competition. With the emergence of the sluggish global shipping market in the postcrisis period, the problems of the Greater Bay Area port group are gradually being exposed, which will affect the region’s long-term development. Presently, the pace of economic structure adjustment in the Greater Bay Area is accelerating, and the coordinated development requirements of port groups are becoming increasingly higher. This requires strengthening constructing the complementary and coordinated development mechanism of port groups in the Greater Bay Area to realize differentiated development.


## 2.2. Model Establishment

The Lotka–Volterra model was originally proposed by American ecologist Lotka and Italian mathematician Volterra [34, 35]. The model is used to study the interaction of different populations in the same environment. Within the same spatial and temporal range, different populations compete for limited resources and establish predator-prey relations and mutual-symbiosis relations. As an important theoretical method to study the evolution and development of ecological populations, the Lotka–Volterra model can intuitively reflect the relationship between different populations. It is widely used in logistics industry development [36, 37], industrial ecology [38, 39], and network innovation [40]. This model is currently often applied in the port field, primarily to explore the interaction relationship between two or three ports [41, 42]. However, there are often no less than three ports in the same region. Related studies on multiple ports in the same region are mainly discussed from the economics perspective, such as the research on port city development using the PSM-DID method [43], the comparative study on operation efficiency of port container terminals based on a DEA model [44], and the research on port throughput prediction based on a dynamic penalized support vector regression model [45]. The interaction relationship, however, between multiple ports is rarely quantified. In view of its wide application in the academic field, this study expands and introduces the Lotka–Volterra model into our research to examine the interaction relationship between ports, using the competition and cooperation game of the Greater Bay Area port groups as an example. The interaction between ports can be represented by the following mathematical symbols:(1)
Promoting Effect. Port i is positively correlated with the change of port j scale, which is recorded as i+⟶j(2)
Hindrance. Port i is negatively correlated with the change of port j scale, which is recorded as i−⟶jThus, three different port relationship modes are formed:(i)
Mutually Beneficial Symbiosis between Ports. Namely, i+⟶j and j+⟶i(ii)
Competition between Ports. Namely, i−⟶j, and j−⟶i(iii)
Predator-Prey Relationship between Ports. Namely, i−⟶j and j+⟶iConsidering the actual port development in the Greater Bay Area and the principle of port coordination from easy to difficult, we apply the multigroup Lotka–Volterra model to our research on the competition and cooperation game of its nine ports in mainland China and establish the multigroup Lotka–Volterra model as shown in the following formula:(3)dP1tdt=α1P11+β12P2H2+β13P3H3+⋯+β19P9H9,dP2tdt=α2P21+β21P1H1+β23P3H3+⋯+β29P9H9,⋮dP9tdt=α9P91+β91P1H1+β92P2H2+⋯+β98P8H8.Among them,Piti=1,2,…,9 are the container throughputs of the nine Greater Bay Area ports at t time, αii=1,2,…,9 is the growth rate of port i, βiji,j=1,2,…,9 is the influence coefficient of port j on port i, and Hii=1,2,…,9 is the maximum handling capacity of port i. We convert the abovementioned model into the following formula:(4)dP1tdt=λ11P1+λ12P1P2+λ13P1P3+⋯+λ19P1P9,dP2tdt=λ22P2+λ21P1P2+λ23P2P3+⋯+λ29P2P9,⋮dP9tdt=λ99P9+λ91P1P9+λ92P2P9+⋯+λ98P8P9.Based on the grey derivative and even logarithm mapping relationship, the following formula is obtained:(5)P1t+1−P1t=λ11P1t+1+P1t2+λ12P1t+1+P1t2P2t+1+P2t2+⋯+λ19P1t+1+P1t2P9t+1+P9t2,P2t+1−P2t=λ22P2t+1+P2t2+λ21P1t+1+P1t2P2t+1+P2t2+⋯+λ29P2t+1+P2t2P9t+1+P9t2,⋮P9t+1−P9t=λ99P9t+1+P9t2+λ91P1t+1+P1t2P9t+1+P9t2+⋯+λ98P8t+1+P8t2P9t+1+P9t2.We substitutet=1,2,3,⋯,n time data into the following formula and obtain the matrix equation Xin=κiλi∧i=1,2,…,9; taking Guangzhou port as an example, its matrix equation is X2n=κ2λ2∧, where(6)κ2=P21+P222P11+P122⋯P21+P222P91+P922P22+P232P12+P132P22+P232⋯P22+P232P92+P932⋮⋮⋮P2n−1+P2n2P1n−1+P1n2P2n−1+P2n2⋯P2n−1+P2n2P9n−1+P9n2.X2n=P22−P21,P23−P22,⋯,P2n−P2n−1T, λ2∧=λ22,λ21,λ23,⋯,λ29T. Using the least square rule, there are(7)λ2∧=κ2Tκ2−1κ2TX2n.


## 3. Empirical Research

### 3.1. Quantification of Port Parameters

In the Greater Bay Area, according to the degree of administrative subordination, most of the leading ports in various cities belong to local governments; other ports in the same city are also under their control. Therefore, this paper regards the ports in the Greater Bay Area as an area of interest to analyze the interaction between ports. These independent individuals represent the whole of the ports in the Greater Bay Area. Based on the division of administrative regions and the interests of local governments in China, this analysis basically represents the interrelationship between various cities and ports within the Greater Bay Area. Therefore, we substitute the container throughput data of the nine ports from 1999 to 2018 and repeat this step to obtain the matrix equation parametersλi∧=i=1,2,…,9, as shown in Table 3.Table 3
Ports parameter value of the matrix equation.
Shenzhen (j = 1)Guangzhou (j = 2)Dongguan (j = 3)Foshan (j = 4)Huizhou (j = 5)Jiangmen (j = 6)Zhaoqing (j = 7)Zhongshan (j = 8)Zhuhai (j = 9)Shenzhen (i = 1)−0.00160.006470.031020.004150.00840.04896−0.0556−0.0293Guangzhou (i = 2)0.000380.000060.00098−0.0024−0.0081−0.0030.014170.00016Dongguan (i = 3)−0.01114−0.00050.002360.027890.023780.054350.07361−0.0043Foshan (i = 4)−0.0011−0.00080.00087−0.0046−0.01570.011740.028070.00592Huizhou (i = 5)−0.01680.01074−0.0133−0.04030.0114−0.10730.343060.00332Jiangmen (i = 6)0.00018−0.00170.00220.01332−0.00560.021830.00099−0.0086Zhaoqing (i = 7)−0.0009−0.00180.001810.007810.01191−0.01950.012450.0573Zhongshan (i = 8)0.00061−0.00080.001560.0082−0.0054−0.0110.01472−0.0038Zhuhai (i = 9)−0.0021−0.00020.001930.00605−0.0071−0.04340.014450.0997


### 3.2. Port Competition and Cooperation Analysis

According to the conversion relationship between parameterλij∧=i,j=1,2,…,9 and the influence coefficient βij between ports, the positive and negative parameters λij∧ and βij are consistent and can be used to analyze the interaction relationship of the nine ports (Table 4):(1)
For Shenzhen port and Guangzhou port,λ12∧<0, indicating that Guangzhou port negatively affects Shenzhen port, and λ21∧>0, indicating that Shenzhen port positively affects Guangzhou port. That is, the two ports have a predator-prey relationship, where Shenzhen port is the predator and Guangzhou port is the predator. (The analysis here is on the interaction between the nine ports in the Guangdong-Hong Kong-Macao Greater Bay Area, which may be different from the analysis of the interaction between the central ports in the Greater Bay Area alone, because Guangzhou port and Shenzhen port have formed two different management and control modes. During the analysis within the Greater Bay Area, this makes Guangzhou port’s advantage in integrating other neighboring ports by administrative means more prominent, which demonstrates that the same population affects the results in different ecological environments and further verifies the rationality of introducing the Lotka–Volterra model based on the ecological population theory discussed in Section 2.2.) Regarding its relationship with Dongguan port, Shenzhen port is the predator and Dongguan port is the predator. With Foshan port, Shenzhen port is the predator and Foshan port is the prey. With Huizhou port, Shenzhen port is the predator and Huizhou Port is the predator. With Zhaoqing port, Shenzhen port is the predator and Zhaoqing port is the predator. With Zhongshan port, Shenzhen port is the predator and Zhongshan port is the predator. In contrast, Shenzhen port has a mutually beneficial symbiotic relationship with Jiangmen port and a competitive relationship with Zhuhai port.(2)
For Guangzhou port and Dongguan port,λ23∧>0, indicating that Dongguan port positively affects Guangzhou port, and λ32∧<0, indicating that Guangzhou port negatively affects Dongguan port. That is, the two ports have a predator-prey relationship, where Guangzhou port is the predator and Dongguan port is the prey. As for its relationship with Foshan port, Guangzhou port is the predator and Foshan port is the predator. With Huizhou port, Guangzhou port is the predator and Huizhou port is predator. With Zhongshan port, Guangzhou port is the predator and Zhongshan port is the predator. With Zhuhai port, Guangzhou port is the predator and Zhuhai port is the predator. In contrast, Guangzhou has a competitive relationship with Jiangmen port and Zhaoqing port.(3)
For Dongguan port and Foshan port,λ34∧>0, indicating that Foshan port has a positive effect on Dongguan port, and λ43∧>0, indicating that Dongguan port has a positive effect on Foshan port. That is, the two have a mutually beneficial and symbiotic relationship. Similarly, it has a mutually beneficial symbiotic relationship with Jiangmen port, Zhaoqing port, and Zhongshan port, predator-prey relationship with Huizhou Port, Dongguan port, Huizhou port, Zhuhai port, predator relationship with Zhuhai port, and predator relationship with Dongguan port.(4)
For Foshan port and Huizhou port,λ45∧<0, indicating that Huizhou port negatively affects Foshan port, and λ65∧<0, indicating that Foshan port negatively effects Huizhou port. That is, the two have a competitive relationship. It has a predator-prey relationship with Jiangmen port. Between Foshan port and Jiangmen port, both are predators. It has a mutually beneficial symbiotic relationship with Zhaoqing, Zhongshan, and Zhuhai ports.(5)
For Huizhou port and Jiangmen port,λ56∧>0, indicating that Jiangmen port has a positive effect on Huizhou port, and λ65∧<0, indicating that Huizhou port negatively affects Jiangmen port. That is, the two have a predator-prey relationship, where Huizhou port is the predator and Jiangmen port is the predator. With Zhaoqing port, Huizhou port is the predator and Zhaoqing port is the predator. With Zhongshan port and Zhuhai port, Huizhou port is the predator and Zhongshan port and Zhuhai port are the predators.(6)
For Jiangmen port and Zhaoqing port,λ67∧>0, indicating that Zhaoqing port has a positive effect on Jiangmen port, and λ76∧<0, indicating that Jiangmen port negatively affects Zhaoqing port. That is, the two have a predator-prey relationship, where Jiangmen port is the predator and Zhaoqing port is the predator. In the relationship between Zhongshan port and Jiangmen port, both are predators. In contrast, Jiangmen has a competitive relationship with Zhuhai port.(7)
For Zhaoqing port and Zhongshan port,λ78∧>0, indicating that Zhongshan port acts positively on Zhaoqing port, and λ87∧>0, indicating that Zhaoqing port positively affects Zhongshan port. That is, the two have a mutually beneficial and symbiotic relationship. Similarly, it also has a mutually beneficial symbiotic relationship with Zhuhai port.(8)
For Zhongshan port and Zhuhai port,λ89∧<0, indicating that Zhuhai port negatively affects Zhongshan port, and λ98∧>0, indicating that the two have a predator-prey relationship, where Zhongshan port is the predator and Zhuhai port is the predator.Table 4
Ports co-competition analysis.
ShenzhenGuangzhouDongguanFoshanHuizhouJiangmenZhaoqingZhongshanZhuhaiShenzhenPredator-preyPredator-preyPredator-preyPredator-preyMutually beneficial symbiosisPredator-preyPrey-predatorCompetitive relationshipGuangzhouPredator-preyPredator-preyPrey-predatorCompetitive relations’Competitive relationshipPredator-preyPredator-preyDongguanMutually beneficial symbiosisPredator-preyMutually beneficial symbiosisMutually beneficial symbiosisMutually beneficial symbiosisPrey-predatorFoshanCompetitive relations’Prey-predatorMutually beneficial symbiosisMutually beneficial symbiosisMutually beneficial symbiosisHuizhouPredator-preyPrey-predatorPredator-preyPredator-preyJiangmenPredator-preyPredator-preyCompetitive relationshipZhaoqingMutually beneficial symbiosisMutually beneficial symbiosisZhongshanPrey-predator


### 3.3. Coordinated Development of Ports in the Greater Bay Area

According to the abovementioned analysis, Guangzhou, Dongguan, Foshan, Zhongshan, and Zhuhai ports play the role of predator and prey, wherein Guangzhou port is the predator and Dongguan, Foshan, Zhongshan, and Zhuhai ports are also predators. In contrast, Dongguan port and Foshan port, Dongguan port and Zhongshan port, Foshan port and Zhongshan port, and Foshan port and Zhuhai port have formed mutually beneficial symbiotic relationships. Similarly, Shenzhen, Huizhou, and Zhaoqing ports play the role of predator and prey, wherein Shenzhen port is a predator and Huizhou Port and Zhaoqing port are also predators. Shenzhen port and Jiangmen port have formed a mutually beneficial symbiotic relationship. Huizhou, Jiangmen, and Zhaoqing ports also have predator-prey relationship, as do Zhongshan port and Shenzhen port, wherein both are predators. Zhuhai port and Shenzhen port have a competitive relationship, while Huizhou port and Guangzhou port have a predator-prey relationship, wherein both are predators. For Jiangmen, Zhaoqing, and Guangzhou ports, Jiangmen port and Zhuhai port and Huizhou Port and Foshan port have competitive relationships, respectively. Therefore, a port group centered on Guangzhou port (including Guangzhou, Dongguan, Foshan, Zhongshan, and Zhuhai ports) and another centered on Shenzhen port (including Shenzhen, Huizhou, Jiangmen, and Zhaoqing ports) have been formed. Their coordinated development can be divided into coordinated development within the port group, coordinated development between central ports, and coordinated development of the two port groups. The abovementioned analysis is consistent with the current development status of the port group in the Greater Bay Area, because the port group in the Guangdong Province in the area differs from other regions in China. Against the background of the country’s efforts to promote port integration, two different types of control modes have been formed, namely, Shenzhen port on the east bank of the Pearl River as a center and Guangzhou port on the south bank of the Pearl River as a center. For example, Shenzhen port and Huizhou port have established a combined port and Guangzhou port has cooperated with Zhongshan port and Zhuhai port, all of which were verified by our analysis.Combined with the data quantification, history of development, and current situation of the Greater Bay Area ports, coordinated development within the port groups is mainly reflected between a central port and a branch port. For the internal coordination of the port group centered on Guangzhou port, it is necessary to break through the boundary of the administrative management system; overcome local protectionism and administrative constraints; integrate the branch port into the new port group by means of allocation or paid transfer; ensure that the funds invested in the port by the local government are reasonably compensated; strengthen the dislocated division of labor between the branch ports; and find a complex balance of interests. Through policy formulation, the layout of port spatial structure in the form of division of labor and cooperation should be consciously guided. The internal coordination of the port group centered on Shenzhen port must formulate the best operating combination according to its needs so as to approach the market fully, mobilize market enthusiasm to the greatest extent, expand the water transfer mode and the construction of combined ports, and overflow bulk cargo to a cooperative port in the Greater Bay Area.The coordination between the central ports is mainly reflected in Guangzhou and Shenzhen ports’ land and sea hinterlands. Land-based hinterland coordination should dislocate from the collection and distribution system, the destination of goods, and the types of goods. The sea-based hinterland coordination should appropriately adjust the highly competitive routes and cooperate to develop potential advantageous routes based on the degree of urban external contact and development characteristics. The synergy between the two port groups is mainly manifested in the dual progress of government and market leadership. In the port group centered on Guangzhou port, the government department is subject to coordinated development and can actively play a macrocontrol role; however, a risk may exist in terms of coordinated development failure because of ignoring market law. The port group centered on Shenzhen port adheres to a market orientation and forms a staggered community of interests through holdings, joint ventures, and equity replacements; however, this model can easily lead to the polarization of port development. Therefore, it is necessary for government- and market-led approaches to complement each other and their advantages to better promote the coordinated development of ports in the Greater Bay Area.


## 3.1. Quantification of Port Parameters

In the Greater Bay Area, according to the degree of administrative subordination, most of the leading ports in various cities belong to local governments; other ports in the same city are also under their control. Therefore, this paper regards the ports in the Greater Bay Area as an area of interest to analyze the interaction between ports. These independent individuals represent the whole of the ports in the Greater Bay Area. Based on the division of administrative regions and the interests of local governments in China, this analysis basically represents the interrelationship between various cities and ports within the Greater Bay Area. Therefore, we substitute the container throughput data of the nine ports from 1999 to 2018 and repeat this step to obtain the matrix equation parametersλi∧=i=1,2,…,9, as shown in Table 3.Table 3
Ports parameter value of the matrix equation.
Shenzhen (j = 1)Guangzhou (j = 2)Dongguan (j = 3)Foshan (j = 4)Huizhou (j = 5)Jiangmen (j = 6)Zhaoqing (j = 7)Zhongshan (j = 8)Zhuhai (j = 9)Shenzhen (i = 1)−0.00160.006470.031020.004150.00840.04896−0.0556−0.0293Guangzhou (i = 2)0.000380.000060.00098−0.0024−0.0081−0.0030.014170.00016Dongguan (i = 3)−0.01114−0.00050.002360.027890.023780.054350.07361−0.0043Foshan (i = 4)−0.0011−0.00080.00087−0.0046−0.01570.011740.028070.00592Huizhou (i = 5)−0.01680.01074−0.0133−0.04030.0114−0.10730.343060.00332Jiangmen (i = 6)0.00018−0.00170.00220.01332−0.00560.021830.00099−0.0086Zhaoqing (i = 7)−0.0009−0.00180.001810.007810.01191−0.01950.012450.0573Zhongshan (i = 8)0.00061−0.00080.001560.0082−0.0054−0.0110.01472−0.0038Zhuhai (i = 9)−0.0021−0.00020.001930.00605−0.0071−0.04340.014450.0997


## 3.2. Port Competition and Cooperation Analysis

According to the conversion relationship between parameterλij∧=i,j=1,2,…,9 and the influence coefficient βij between ports, the positive and negative parameters λij∧ and βij are consistent and can be used to analyze the interaction relationship of the nine ports (Table 4):(1)
For Shenzhen port and Guangzhou port,λ12∧<0, indicating that Guangzhou port negatively affects Shenzhen port, and λ21∧>0, indicating that Shenzhen port positively affects Guangzhou port. That is, the two ports have a predator-prey relationship, where Shenzhen port is the predator and Guangzhou port is the predator. (The analysis here is on the interaction between the nine ports in the Guangdong-Hong Kong-Macao Greater Bay Area, which may be different from the analysis of the interaction between the central ports in the Greater Bay Area alone, because Guangzhou port and Shenzhen port have formed two different management and control modes. During the analysis within the Greater Bay Area, this makes Guangzhou port’s advantage in integrating other neighboring ports by administrative means more prominent, which demonstrates that the same population affects the results in different ecological environments and further verifies the rationality of introducing the Lotka–Volterra model based on the ecological population theory discussed in Section 2.2.) Regarding its relationship with Dongguan port, Shenzhen port is the predator and Dongguan port is the predator. With Foshan port, Shenzhen port is the predator and Foshan port is the prey. With Huizhou port, Shenzhen port is the predator and Huizhou Port is the predator. With Zhaoqing port, Shenzhen port is the predator and Zhaoqing port is the predator. With Zhongshan port, Shenzhen port is the predator and Zhongshan port is the predator. In contrast, Shenzhen port has a mutually beneficial symbiotic relationship with Jiangmen port and a competitive relationship with Zhuhai port.(2)
For Guangzhou port and Dongguan port,λ23∧>0, indicating that Dongguan port positively affects Guangzhou port, and λ32∧<0, indicating that Guangzhou port negatively affects Dongguan port. That is, the two ports have a predator-prey relationship, where Guangzhou port is the predator and Dongguan port is the prey. As for its relationship with Foshan port, Guangzhou port is the predator and Foshan port is the predator. With Huizhou port, Guangzhou port is the predator and Huizhou port is predator. With Zhongshan port, Guangzhou port is the predator and Zhongshan port is the predator. With Zhuhai port, Guangzhou port is the predator and Zhuhai port is the predator. In contrast, Guangzhou has a competitive relationship with Jiangmen port and Zhaoqing port.(3)
For Dongguan port and Foshan port,λ34∧>0, indicating that Foshan port has a positive effect on Dongguan port, and λ43∧>0, indicating that Dongguan port has a positive effect on Foshan port. That is, the two have a mutually beneficial and symbiotic relationship. Similarly, it has a mutually beneficial symbiotic relationship with Jiangmen port, Zhaoqing port, and Zhongshan port, predator-prey relationship with Huizhou Port, Dongguan port, Huizhou port, Zhuhai port, predator relationship with Zhuhai port, and predator relationship with Dongguan port.(4)
For Foshan port and Huizhou port,λ45∧<0, indicating that Huizhou port negatively affects Foshan port, and λ65∧<0, indicating that Foshan port negatively effects Huizhou port. That is, the two have a competitive relationship. It has a predator-prey relationship with Jiangmen port. Between Foshan port and Jiangmen port, both are predators. It has a mutually beneficial symbiotic relationship with Zhaoqing, Zhongshan, and Zhuhai ports.(5)
For Huizhou port and Jiangmen port,λ56∧>0, indicating that Jiangmen port has a positive effect on Huizhou port, and λ65∧<0, indicating that Huizhou port negatively affects Jiangmen port. That is, the two have a predator-prey relationship, where Huizhou port is the predator and Jiangmen port is the predator. With Zhaoqing port, Huizhou port is the predator and Zhaoqing port is the predator. With Zhongshan port and Zhuhai port, Huizhou port is the predator and Zhongshan port and Zhuhai port are the predators.(6)
For Jiangmen port and Zhaoqing port,λ67∧>0, indicating that Zhaoqing port has a positive effect on Jiangmen port, and λ76∧<0, indicating that Jiangmen port negatively affects Zhaoqing port. That is, the two have a predator-prey relationship, where Jiangmen port is the predator and Zhaoqing port is the predator. In the relationship between Zhongshan port and Jiangmen port, both are predators. In contrast, Jiangmen has a competitive relationship with Zhuhai port.(7)
For Zhaoqing port and Zhongshan port,λ78∧>0, indicating that Zhongshan port acts positively on Zhaoqing port, and λ87∧>0, indicating that Zhaoqing port positively affects Zhongshan port. That is, the two have a mutually beneficial and symbiotic relationship. Similarly, it also has a mutually beneficial symbiotic relationship with Zhuhai port.(8)
For Zhongshan port and Zhuhai port,λ89∧<0, indicating that Zhuhai port negatively affects Zhongshan port, and λ98∧>0, indicating that the two have a predator-prey relationship, where Zhongshan port is the predator and Zhuhai port is the predator.Table 4
Ports co-competition analysis.
ShenzhenGuangzhouDongguanFoshanHuizhouJiangmenZhaoqingZhongshanZhuhaiShenzhenPredator-preyPredator-preyPredator-preyPredator-preyMutually beneficial symbiosisPredator-preyPrey-predatorCompetitive relationshipGuangzhouPredator-preyPredator-preyPrey-predatorCompetitive relations’Competitive relationshipPredator-preyPredator-preyDongguanMutually beneficial symbiosisPredator-preyMutually beneficial symbiosisMutually beneficial symbiosisMutually beneficial symbiosisPrey-predatorFoshanCompetitive relations’Prey-predatorMutually beneficial symbiosisMutually beneficial symbiosisMutually beneficial symbiosisHuizhouPredator-preyPrey-predatorPredator-preyPredator-preyJiangmenPredator-preyPredator-preyCompetitive relationshipZhaoqingMutually beneficial symbiosisMutually beneficial symbiosisZhongshanPrey-predator


## 3.3. Coordinated Development of Ports in the Greater Bay Area

According to the abovementioned analysis, Guangzhou, Dongguan, Foshan, Zhongshan, and Zhuhai ports play the role of predator and prey, wherein Guangzhou port is the predator and Dongguan, Foshan, Zhongshan, and Zhuhai ports are also predators. In contrast, Dongguan port and Foshan port, Dongguan port and Zhongshan port, Foshan port and Zhongshan port, and Foshan port and Zhuhai port have formed mutually beneficial symbiotic relationships. Similarly, Shenzhen, Huizhou, and Zhaoqing ports play the role of predator and prey, wherein Shenzhen port is a predator and Huizhou Port and Zhaoqing port are also predators. Shenzhen port and Jiangmen port have formed a mutually beneficial symbiotic relationship. Huizhou, Jiangmen, and Zhaoqing ports also have predator-prey relationship, as do Zhongshan port and Shenzhen port, wherein both are predators. Zhuhai port and Shenzhen port have a competitive relationship, while Huizhou port and Guangzhou port have a predator-prey relationship, wherein both are predators. For Jiangmen, Zhaoqing, and Guangzhou ports, Jiangmen port and Zhuhai port and Huizhou Port and Foshan port have competitive relationships, respectively. Therefore, a port group centered on Guangzhou port (including Guangzhou, Dongguan, Foshan, Zhongshan, and Zhuhai ports) and another centered on Shenzhen port (including Shenzhen, Huizhou, Jiangmen, and Zhaoqing ports) have been formed. Their coordinated development can be divided into coordinated development within the port group, coordinated development between central ports, and coordinated development of the two port groups. The abovementioned analysis is consistent with the current development status of the port group in the Greater Bay Area, because the port group in the Guangdong Province in the area differs from other regions in China. Against the background of the country’s efforts to promote port integration, two different types of control modes have been formed, namely, Shenzhen port on the east bank of the Pearl River as a center and Guangzhou port on the south bank of the Pearl River as a center. For example, Shenzhen port and Huizhou port have established a combined port and Guangzhou port has cooperated with Zhongshan port and Zhuhai port, all of which were verified by our analysis.Combined with the data quantification, history of development, and current situation of the Greater Bay Area ports, coordinated development within the port groups is mainly reflected between a central port and a branch port. For the internal coordination of the port group centered on Guangzhou port, it is necessary to break through the boundary of the administrative management system; overcome local protectionism and administrative constraints; integrate the branch port into the new port group by means of allocation or paid transfer; ensure that the funds invested in the port by the local government are reasonably compensated; strengthen the dislocated division of labor between the branch ports; and find a complex balance of interests. Through policy formulation, the layout of port spatial structure in the form of division of labor and cooperation should be consciously guided. The internal coordination of the port group centered on Shenzhen port must formulate the best operating combination according to its needs so as to approach the market fully, mobilize market enthusiasm to the greatest extent, expand the water transfer mode and the construction of combined ports, and overflow bulk cargo to a cooperative port in the Greater Bay Area.The coordination between the central ports is mainly reflected in Guangzhou and Shenzhen ports’ land and sea hinterlands. Land-based hinterland coordination should dislocate from the collection and distribution system, the destination of goods, and the types of goods. The sea-based hinterland coordination should appropriately adjust the highly competitive routes and cooperate to develop potential advantageous routes based on the degree of urban external contact and development characteristics. The synergy between the two port groups is mainly manifested in the dual progress of government and market leadership. In the port group centered on Guangzhou port, the government department is subject to coordinated development and can actively play a macrocontrol role; however, a risk may exist in terms of coordinated development failure because of ignoring market law. The port group centered on Shenzhen port adheres to a market orientation and forms a staggered community of interests through holdings, joint ventures, and equity replacements; however, this model can easily lead to the polarization of port development. Therefore, it is necessary for government- and market-led approaches to complement each other and their advantages to better promote the coordinated development of ports in the Greater Bay Area.


## 4. Conclusion

The collaborative development of ports in the Guangdong-Hong Kong-Macao Greater Bay Area is an operation form established for ports of different levels based on common goals to cope with uncertain environment in the new era. It has the characteristics of dynamic, multiple levels, and complexity and can produce optimization effect, complementary effect, and integration effect synergistically. Therefore, it has become an effective way to promote the current supply-side reform of ports.Based on the game perspective of the coordinated development of ports in the Guangdong-Hong Kong-Macao Greater Bay Area, this paper, first, introduces the logistics model to estimate parameters and analyze the evolution trend of the port cluster in the Guangdong-Hong Kong-Macao Greater Bay Area on the basis of analyzing the consistency between the evolutionary development of regional ports and the growth and evolution law of biological populations. It is pointed out that the container throughput scale of the port cluster in the Guangdong-Hong Kong-Macao Greater Bay Area will reach the limit. Therefore, new impetus is needed to promote the port cluster to enter the next round of development and evolution. Second, combined with the ecological population theory, this study innovatively introduced the expanded multipopulation Lotka–Volterra model into the analysis of the competition and cooperation game of mainland ports in the Guangdong-Hong Kong-Macao Greater Bay Area to explore the interaction between the ports. The research object is different from the existing academic achievements in that there are several central ports in the Guangdong-Hong Kong-Macao Greater Bay Area port cluster that belong to different management and control modes and the central ports have a higher discourse power in the development process and will form different types of port control modes in the future development, while the regional branch ports are limited by their own scale and regional barriers. We choose to cooperate with the central port according to the needs and then form different port cooperation alliances. The study provides a reference for strengthening the complementarity of resource advantages and the construction of collaborative mechanism within the port cluster of the Guangdong-Hong Kong-Macao Greater Bay Area and achieving differentiated development of ports. Third, on the basis of this quantitative analysis, this paper proposes that the ports in the Guangdong-Hong Kong-Macao Greater Bay Area should not only curb competition but also emphasize the stable and orderly cooperation mechanism construction among the ports. Scientific and reasonable top-level design and overall planning are the keys to the coordinated development of the ports in the Guangdong-Hong Kong-Macao Greater Bay Area. The government should formulate supportive policies according to local conditions and properly handle the relationship between the ports. Strengthen the institutional constraint mechanism of port cluster, promote the construction of trust mechanism and benefit distribution mechanism, avoid the moral hazard brought by opportunism, speed up the construction of regional comprehensive transportation hub centered on Guangzhou Port, explore the leading port model centered on Shenzhen Port, and guide the branch ports to actively embrace the central port. The Guangdong-Hong Kong-Macao Greater Bay Area port cluster will be formed into a port coordinated development mechanism with reasonable functional zoning and mutual benefit.Finally, the game analysis content of port co-competition and coordinated development in the Guangdong-Hong Kong-Macao Greater Bay Area in this paper, which studies and quantifies the interaction between ports, has important guiding significance for the current coordinated development of ports in the Guangdong-Hong Kong-Macao Greater Bay Area. Meanwhile, in order to more accurately grasp the port development dynamics and strive for improvement, factors such as local economic development and port investment should be considered in the study of port competition and cooperation game in the future. In addition, during the double cycle of new development period, the research on the network competition mechanism of the central port cluster in the Guangdong-Hong Kong-Macao Greater Bay Area under different types of management and control modes will also be the next research direction.



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*Source: 1659050-2023-01-03.xml*