Research on the Competitive and Cooperative Relationships of Urban Agglomerations Based on the Lotka–Volterra Model: A Case Study of the Guangdong–Hong Kong–Macao Greater Bay Area

Abstract

This study investigates the competitive and cooperative relationships within urban agglomerations, specifically focusing on the Guangdong–Hong Kong–Macao Greater Bay Area (GBA). Using the Lotka–Volterra model from ecology, the research aims to analyse and predict the dynamic relationships among cities in this area. The purpose is to understand how competition and cooperation influence regional integration, and their complex economic connections. This paper employs both qualitative and quantitative methods, including time-series analysis and the application of the Lotka–Volterra model, to evaluate economic interactions and the roles of various cities or regions within the GBA. The study reveals that mutualistic, competitive, predatory, commensal, and parasitic relationships coexist among them, with core cities such as Shenzhen, Guangzhou, Hong Kong, and Macao assuming pivotal roles in shaping the overall dynamics. The findings highlight the importance of functional division, regional cooperation, and innovative collaboration to enhance sustainable development. Policy recommendations are provided to foster a balanced and integrated growth model, emphasizing inter-city cooperation, resource sharing, and avoidance of industrial homogeneity.

1. Introduction

The Guangdong–Hong Kong–Macao Greater Bay Area (GBA) serves as a pivotal engine for Chinese economic development strategy [1], tasked with the crucial mission of promoting regional economic integration and high-quality growth [2]. It plays a significant role as a regional growth pole, particularly in advancing the “Belt and Road Initiative” (The Belt and Road Initiative, proposed by China in 2013, is a significant international cooperation initiative aimed at promoting global economic collaboration and development by enhancing policy coordination, infrastructure connectivity, unimpeded trade, financial integration, and people-to-people bonds among participating countries. The name of the initiative derives from two core concepts: the “Silk Road Economic Belt” and the “21st Century Maritime Silk Road”, which represent land-based and maritime economic cooperation corridors, respectively) and fostering deeper cooperation between Hong Kong, Macao, and Mainland China [3]. The area encompasses nine cities in Guangdong Province along with the two Special Administrative Regions of Hong Kong and Macao, making it the largest and most populous world-class urban agglomeration to date.

In sectors such as finance, technology, and manufacturing, the GBA exhibits robust growth momentum. Economic connections among cities within the region are becoming increasingly tight, with industrial synergies gradually taking shape [4]. However, the area also faces numerous challenges, including uneven regional development, resource and environmental constraints, industrial upgrading and transformation, and ecological and environmental protection issues [5]. For instance, economic disparities between the core Pearl River Delta areas and peripheral regions are becoming more pronounced, with mounting pressure on resource consumption.

Further exploration and analysis of the competitive and cooperative relationships among cities within this region are of significant theoretical and practical importance for advancing regional integration processes, optimizing resource allocation, enhancing overall regional competitiveness, and achieving high-quality development.

In the context of globalization and regional integration, the competitive and cooperative relationships within urban agglomerations have become increasingly complex. Especially for diverse and intricate urban agglomerations like the GBA, balancing competition and cooperation to achieve resource sharing and complementary advantages has become crucial [6]. On one hand, competition among cities for attracting capital, talent, and technology has intensified, leading to industrial structural convergence and resource waste. On the other hand, regional economic integration requires stronger cooperation among cities, resource sharing, formation of complementary advantages, and joint responses to global economic competition [7]. How to balance competition and cooperation among cities to achieve mutual benefit and win–win results has become an important topic in regional development [8]. By utilizing the Lotka–Volterra model from ecology to analyse and predict competitive and cooperative relationships among cities, identifying key nodal cities within the urban agglomeration and their impact on overall development, we can optimize regional layouts and coordinate urban development strategies.

The urban agglomerations constitute a highly intricate and expansive network encompassing numerous subsystems and feedback mechanisms. However, the Lotka–Volterra model can only focus on a limited number of pivotal variables and their interrelationships. This simplification process inevitably results in a degree of abstraction and may overlook certain aspects of the actual scenario. Despite certain limitations in urban research, this model possesses distinct advantages in capturing dynamic interactions, simplifying complex relationships, and providing visualization, prediction, and simulation capabilities. By acknowledging the model’s limitations and making appropriate adjustments and enhancements based on specific research contexts and challenges, the model can serve as a valuable analytical tool for studying inter-city competition and cooperation.

Therefore, exploring the competitive and cooperative relationships within urban agglomerations based on the Lotka–Volterra model is not only a frontier exploration in theoretical research but also provides theoretical basis and practical guidance for addressing issues such as unbalanced development, industrial homogeneity, and inefficient resource allocation in the Guangdong–Hong Kong–Macao Greater Bay Area, thereby advancing regional sustainable development strategies.

2. Literature Review

Urban competition and cooperation within urban agglomerations are intricate phenomena [9] that have garnered significant attention in academic research. The application of ecological theory in comprehending these dynamics adds a nuanced perspective to the interactions between cities within these agglomerations [10]. By delving into various themes related to urban competition and cooperation, researchers have illuminated the challenges and opportunities inherent in these environments [11].

2.1. The Formation and Evolution of Urban Agglomerations

Extensive research has been conducted on the formation and evolution of urban agglomerations, focusing specifically on the developmental stages transitioning from single-center to multi-center structures [12]. Understanding these stages is essential for predicting future growth patterns and identifying potential areas of conflict or synergy between cities. By recognizing the dynamics of competition and cooperation at each stage of development, policymakers can formulate strategies to foster sustainable growth and the equitable distribution of resources.

One key aspect that has been explored is the expansion of urban areas within agglomerations [13]. Studies have emphasized the necessity for a comprehensive understanding of urban expansion, particularly in the wake of natural disasters and environmental challenges [14]. The growth of cities within agglomerations can have profound implications for the environment, infrastructure, and quality of life for residents. Therefore, comprehending the patterns and drivers of urban expansion is crucial for effective urban planning and sustainable development [15]. Moreover, research on urban agglomerations has focused on examining the role of cooperation and competition between government entities and technology service platforms [16]. Analyzing strategies employed by these stakeholders in a competitive environment can provide insights into how collaboration can lead to mutual benefits [17]. By exploring different models of cooperation, researchers aim to optimize decision-making processes and enhance the overall efficiency of urban governance within agglomerations [18]. Understanding the formation and evolution of urban agglomerations is essential for addressing their challenges. To examine the urban expansion, governance strategies, and developmental transitions, researchers can provide valuable insights into how cities can navigate competition and cooperation in a balanced manner.

2.2. Economic Disparities and Shared Interests in Urban Agglomerations

Contrasting the development modes of various agglomerations illuminates the significance of inter-city cooperation in fostering balanced growth and integration [19]. The promotion of collaboration among cities and the mitigation of economic disparities can facilitate sustainable development and bolster global competitiveness for urban agglomerations [20]. Furthermore, the interaction between urbanization and the eco-environment in mega-urban agglomerations has been a pivotal area of study, underscoring the imperative for integrated planning and sustainable practices [21].

Furthermore, the impact of urban agglomeration on regional inequality has garnered significant attention, as research emphasizes both the favorable and unfavorable consequences of agglomeration on economic disparities [22]. Effective management of urban agglomerations is crucial in order to harness their potential for stimulating economic growth and innovation, while also addressing the potential exacerbation of inequalities. It is essential to identify mechanisms that facilitate the sharing of benefits and promote healthy competition, thereby mitigating regional disparities and fostering inclusive development within these agglomerations. Moreover, the spatial connection and economic disparities among various urban agglomerations have been a focal point of research [23]. Addressing economic disparities within urban agglomerations is crucial for establishing long-term sustainable and mutually beneficial cooperative relationships. Coordinated planning and policy interventions are imperative to ensure that growth equitably benefits all cities within an urban cluster, rather than exacerbating existing inequalities.

2.3. Synergistic Growth and Sustainable Development in Urban Agglomerations

By analyzing the collaboration patterns among cities [24] and identification of pivotal factors driving innovation [25], researchers aim to enrich the knowledge economy within agglomerations. Reinforcing knowledge innovation networks has the potential to enhance competitiveness and cultivate a culture characterized by perpetual learning and growth. Moreover, the importance of regional cooperation and coordination within urban agglomerations has been emphasized in research, highlighting the necessity for integrated approaches to resource management and infrastructure development [26]. By aligning population growth with land use planning and industrial development [27], urban agglomerations can optimize the allocation of resources and enhance their overall competitiveness. Promoting coordinated coordination between sectors can lead to more sustainable and resilient urban environments [28].

The sustainable development of urban agglomerations relies on effectively balancing urban growth and environmental protection. By prioritizing areas such as environmental protection [29], infrastructure development [30], and social services [31], policymakers can create resilient and eco-friendly urban environments. Additionally, the knowledge innovation networks within urban agglomerations have been examined to understand the dynamics of knowledge sharing and diffusion of innovation [32]. Furthermore, the investigation of climatic risks on urban agglomerations has underscored the imperative for proactive measures to address environmental challenges [33]. By considering the interactive influence of climatic factors within and beyond urban agglomerations, policymakers can formulate effective strategies for air pollution control and ecological conservation [34]. Establishing inter-regional cooperation mechanisms and strengthening environmental legislation are indispensable steps in mitigating climatic risks and promoting sustainable development [35].

In conclusion, the study of urban competition and cooperation within urban agglomerations, enriched by the application of ecological theory, offers valuable insights into the complex dynamics of urban development [36]. Researchers have deepened our understanding of challenges and opportunities in urban environments by exploring themes such as urban expansion [37], stages of agglomeration formation [38], and regional inequalities [39]. Addressing the shortcomings in existing research, such as the need for more comprehensive models of cooperation [40] and integrating ecological considerations into urban planning [41], can pave the way for a more sustainable and resilient future for urban agglomerations. Achieving synergistic cooperation in urban agglomerations necessitates a comprehensive strategy that integrates knowledge innovation, regional collaboration, and environmental sustainability. The interplay among these elements fosters long-term economic resilience and promotes balanced development within urban clusters.

3. Theoretical Development and Methodology

3.1. Theoretical Analysis of Competitive and Cooperative Relationships Within Urban Agglomerations

In ecology, a population typically refers to the collective assembly of all individuals of the same species [42]. These individuals engage in competitive and cooperative interactions, which influence their survival and reproduction. In the analysis of urban agglomerations, each city can be regarded as a population that not only exchanges energy, information, and materials but also competes for limited resources and engages in resource sharing and complementary cooperative behaviors.

In the analytical methods of population ecology, the Lotka–Volterra model was initially designed to describe the dynamic relationships between predators and prey, but its principles are also applicable to analyzing competition and cooperation among cities [43]. The Lotka–Volterra model has been extended beyond its ecological origins to diverse fields within social science research. For instance, in analyzing the development of innovation within metropolitan areas, researchers developed a city-based Lotka–Volterra symbiosis model to investigate urban innovation levels under various symbiotic relationships [44]. This application demonstrates that the Lotka–Volterra model can effectively capture the dynamic interactions between various entities, offering a distinctive perspective and analytical tool for social science research. Competition among cities is primarily manifested in the acquisition and possession of resources, while cooperation may involve information sharing, technological exchange, and infrastructure development, among other aspects. These competitive and cooperative relationships are dynamic and change over time and with varying conditions.

When a city has a significant advantage in a particular domain, it may attract more resources and talent, thereby further enhancing its competitiveness. At the same time, cooperation among cities can achieve mutual benefits and win–win outcomes through resource sharing and joint development. This is not only beneficial for the development of individual cities but also helps to improve the competitiveness of the entire urban agglomeration [45]. For instance, cities within the Guangdong–Hong Kong–Macao Greater Bay Area have positively impacted both their own competitiveness and that of the entire urban cluster by establishing good complementary cooperation [46].

Based on the Lotka–Volterra model, competition and cooperation within urban agglomerations are regarded as a dynamic equilibrium relationship. Each city is seeking the optimal development path and establishing cooperative relationships with other cities to achieve common development [47]. This dynamic equilibrium requires continuous interaction between cities, involving both cooperation and competition [48]. Against the backdrop of globalization, the interconnections between cities have become more intertwined, expanding the scope of both rivalry and partnership. Therefore, by re-examining the competitive and cooperative relationships between cities, new opportunities for cooperation and competitive advantages can be discovered, ultimately achieving the goal of sustainable development [49].

The acquisition and possession of resources among cities significantly influence their competitive and cooperative relationships. This is because urban competitiveness is not only determined by its relative position in external markets but also relies on the productivity and efficiency of local resources [50]. Through resource management and optimized allocation, cities can enhance their attractiveness to resources and establish competitive and cooperative relationships with other cities [51].

In summary, cities within urban agglomerations, through strategies of resource acquisition and market occupancy, can not only shape their own competitiveness and market position but also contribute to optimizing resource allocation and enhancing overall efficiency. This is crucial for supporting the sustainable development of urban agglomerations [52].

3.2. The Mechanism of Competitive and Cooperative Relationships Based on the Lotka–Volterra Model

From historical and international perspectives, the economic growth of cities generally conforms to the logistic “S”-shaped growth curve [53]. This paper will employ the Lotka–Volterra model from ecology to analyse the complex interactions between different cities within urban agglomerations, aiming to reveal the competitive and cooperative relationships among them. It is assumed that cities i and j within the same urban cluster have intrinsic logical relationships in economic, social, and environmental domains, which can be characterized by the following equations:

$${\displaystyle \frac{d{C}_i}{dt}}=r_i{C}_i(1-{\displaystyle \frac{C_i+{\alpha }_{ji}{C}_j}{K_i}})$$

(1)

$${\displaystyle \frac{d{C}_{\mathrm{j}}}{dt}}=r_j{C}_j(1-{\displaystyle \frac{C_j+{\alpha }_{ij}{C}_i}{K_j}})$$

(2)

In Equations (1) and (2), C_i and C_j represent the socioeconomic scales of city i and city j at time t; r_i and r_j denote the economic growth rates of city i and city j, respectively; K_i and K_j indicate the maximum carrying capacities or total resource volumes of city i and city j; α represents the competitive coefficient between cities, which indicates the degree of impact that economic growth in one city has on the economies of other cities. Different combinations of positive and negative values of the competition coefficient between two cities can reflect the competitive and cooperative relationships between them, as indicated in

Table 1. Competitive and cooperative patterns of urban agglomerations.

αij αji	Patterns	Conception
0, 0	None	Relatively independent development, with no mutual impact
+, +	Mutualism	Both parties benefit from the development process
−, −	Competition	The development of one party affects the development of the other
+, −	Predation	The development of one party requires support from the other
−, 0	Commensalism	One party positively promotes the development of the other
+, 0	Parasitism	One party hinders the development of the other

.

Based on the equations of the Lotka–Volterra model, the evolutionary state and equilibrium point of the competition and cooperation relationship between two cities represent the stable maximum output state in their development. The final evolutionary state depends on the magnitude of the model parameters.

If ${\displaystyle \frac{d{C}_i}{dt}}=0$, ${\displaystyle \frac{d{C}_j}{dt}}=0$, then the economic growth rates of city i and city j are zero at the equilibrium state, thereby obtaining the balance value of the competitive and cooperative relationship between the cities.

And C_i = 0 or C_i = K_i − α_jiC_j; C_j = 0 or C_j = K − α_ijC_i.

According to the equations, four possible steady-state solutions and their corresponding competition and cooperation evolution outcomes are calculated, as shown in

Table 2. Steady-state solutions and competition-cooperation evolution outcomes.

Steady-State	Competition and Cooperation Evolution Outcomes
E (0, 0)	Neither of the two cities can survive within the urban agglomeration
E (K1, 0)	The development of City 1 crowds out the existence of City 2
E (0, K2)	The development of City 2 crowds out the existence of City 1
E (C*1, C*2) 1	Under the condition that α21·α12 < 1, both cities can achieve a stable coexistence state

^1. When two cities have achieved a state of stable coexistence, the specific numerical values of the stable solutions for both cities are as follows: $C_i^{*}={\displaystyle \frac{K_i-{\alpha }_{ji}{K}_j}{1-{\alpha }_{ij}{\alpha }_{ji}}},C_j^{*}={\displaystyle \frac{K_j-{\alpha }_{ij}{K}_i}{1-{\alpha }_{ij}{\alpha }_{ji}}}$.

.

The competition and cooperation relationships among cities allow for the possibility of collaboration, thus eliminating the scenario where one city completely disappears. Instead, the competitive and cooperative dynamics between cities tend to form a stable coexistence state, where both cities share resources to some extent and develop together. This implies that within the urban agglomeration, two cities can reach an equilibrium point C*_i and C*_j, with both values being greater than zero. To verify the stability of the equilibrium point, the steady-state solution E (C*₁, C*₂) needs to be substituted into the determinant Det (J) and trace Tr (J) of the Jacobian matrix, and their signs should be used to determine stability. Specifically, if Det (J) > 0 and Tr (J) < 0, then the equilibrium point is locally asymptotically stable.

Additionally, during the competitive process among cities, if there are sufficient resources within the urban agglomeration to support them and the mutual influence in competition is not strong, i.e., (α_ij·α_ji) < 1, then these two cities will form a stable coexistence state. Under such circumstances, K_i and K_j will represent the maximum carrying capacity or the upper limit of resource allocation for each city within the urban agglomeration.

4. Empirical Analysis of the Competition and Cooperation Relationships in the GBA

4.1. Model Variables and Model Processing

After discretizing the Lotka–Volterra competition model using the forward Euler method, this study constructs a corresponding econometric model based on the resulting discrete of Equations (3) and (4). To accurately estimate the model parameter α_ij and α_ji, this paper also employs the ordinary least squares (OLS) method to fit and analyse the time-series data.

$$\Delta {\mathrm{C}}_{\mathrm{i}}=r_i{C}_i(1-{\displaystyle \frac{C_i}{K_i}})-{\alpha }_{\mathrm{ji}}{\displaystyle \frac{r_i{C}_i{C}_j}{K_i}}+{\epsilon }_{\mathrm{i}}$$

(3)

$$\Delta {\mathrm{C}}_{\mathrm{j}}=r_j{C}_j(1-{\displaystyle \frac{C_j}{K_j}})-{\alpha }_{ij}{\displaystyle \frac{r_j{C}_j{C}_i}{K_j}}+{\epsilon }_j$$

(4)

In the analysis of urban agglomerations, indicators such as population and land area reflect the quantitative scale of different cities, while indicators of urban economic development efficiency or the intensity of resource utilization better reflect the quality of regional economic development. This paper uses economic output efficiency to characterize the scale of urban development (C_i), which is the ratio of the regional economic total to the urban built-up area and can intuitively reflect the intensity of urban economic activities. To express the development speed of different cities in terms of time and space, the GDP growth rate reflects the urban economy growth speed, which corresponds well to the economic output efficiency as a representation of development scale. Therefore, the GDP growth rate is chosen as the intrinsic growth rate (r_i) of the city. GDP reflects the economic activities and output capacity of a city and is one of the core indicators for measuring the comprehensive strength of a city. Based on the GDP data of various cities and regions over the years, a time-series model is used to predict the GDP data for each city and region in 2030 as the maximum carrying capacity indicator (K_i).

4.2. Study Area and Data Sources

The research scope of this paper is centered around the analysis and discussion of the competitive and cooperative relationships among cities and regions within a specific spatial domain. This urban agglomeration comprises Shenzhen, Guangzhou, Dongguan, Huizhou, Zhuhai, Foshan, Zhongshan, Jiangmen, and Zhaoqing in Guangdong Province along with the Hong Kong Special Administrative Region and Macao Special Administrative Region. The geographic boundaries of this region are visually illustrated in Figure 1.

This study selects the period from 2008 to 2022 as the time range for data analysis and conducts time-series analysis on various data indicators mentioned previously. The majority of the data used in the study mainly comes from the “China City Statistical Yearbook”, “Guangdong Statistical Yearbook” and statistical bulletins published by various cities. For data on Hong Kong and Macao, this paper primarily relies on official statistical data published by government departments of the two regions and conducts necessary calculations and processing based on them. Additionally, for some missing data, this paper employs the exponential smoothing method to make reasonable predictions.

4.3. Estimation and Analysis of Model Parameters

Using Eviews software (version 11) and applying the discretized Lotka–Volterra competition model, the urban competition coefficients were estimated, which are shown in

Table 3. The positive or negative values matrix of competition and cooperation coefficients based on the Lotka–Volterra model.

CITY	Shenzhen	Guangzhou	Dongguan	Huizhou	Zhuhai	Foshan	Zhongshan	Jiangmen	Zhaoqing	Hong Kong	Macao
Shenzhen		++	0	+−	0	0	++	0	0	++	++
Guangzhou			0	−−	0	0	−+	0	0	−+	−+
Dongguan				0−	0	0	0+	0	0	0+	0+
Huizhou					0	0	++	0	0	−+	−+
Zhuhai						0	0+	0	0	0+	0+
Foshan							0+	0	0	0+	0+
Zhongshan								0	0	++	++
Jiangmen									0	0+	0+
Zhaoqing										0+	0+
Hong Kong											++
Macao

.

In regression analysis, the R², also known as the coefficient of determination, is an important indicator that measures the proportion of variation in the dependent variable that can be explained by the independent variables through the regression relationship. In this study, it is assumed that when the regression coefficient R² is greater than 0.6, the error between the predicted values and the actual values is within a reasonable range, indicating that the degree of explanation of the independent variables to the dependent variable is acceptable. Based on the process mentioned above, it further infers that the positive or negative values of α can characterize the competitive and cooperative relationship between cities. Conversely, if R² is less than 0.6, it indicates that there is no significant competitive or cooperative relationship between the independent variables and the dependent variable. In this case, it assumes the competition coefficient α to be zero.

Combining Table 1, regarding the competition and cooperation patterns of urban agglomerations and Table 3 showing the competition and cooperation coefficients between various cities and regions within the GBA, it can analyse the competitive and cooperative relationships in the economy among different cities and regions, as shown in

Table 4. The matrix of competition and cooperation relationships between cities or regions within GBA.

CITY	Shenzhen	Guangzhou	Dongguan	Huizhou	Zhuhai	Foshan	Zhongshan	Jiangmen	Zhaoqing	Hong Kong	Macao
Shenzhen		Mutualism	Parasitism	Predation	Parasitism	Parasitism	Mutualism	Parasitism	Parasitism	Mutualism	Mutualism
Guangzhou			Commensalism	Competition	Parasitism	Commensalism	Predation	Commensalism	Commensalism	Predation	Predation
Dongguan				Commensalism	None	None	Parasitism	None	None	Parasitism	Parasitism
Huizhou					Commensalism	Commensalism	Mutualism	Commensalism	Commensalism	Predation	Predation
Zhuhai						None	Parasitism	Parasitism	None	Parasitism	Parasitism
Foshan							Parasitism	None	None	Parasitism	Parasitism
Zhongshan								Parasitism	Parasitism	Mutualism	Mutualism
Jiangmen									None	Parasitism	Parasitism
Zhaoqing										Parasitism	Parasitism
Hong Kong											Mutualism
Macao

.

4.4. Research Results

As a dynamic analytical framework, the Lotka–Volterra model effectively captures the intricate dynamics between urban entities, encompassing symbiotic relationships, competitive interactions, predatory behaviors, and other complex patterns. The strength of this model resides in its versatility and adaptability, allowing for adjustments based on regional characteristics such as city size, resource availability, and industrial composition. This study employs the Lotka–Volterra model to analyze competition and cooperation among cities within the GBA. Below are our research findings.

Firstly, there is a mutualistic relationship. Shenzhen occupies a core position in the GBA and has formed a significant symbiotic relationship with multiple cities including Hong Kong, Guangzhou, and Foshan. Through these collaborations, Shenzhen can effectively compensate for its own deficiencies in resources and technology, promoting the enhancement of its competitiveness. As the administrative center of the Pearl River Delta in China, Guangzhou has also established a symbiotic relationship with multiple cities and regions (such as Hong Kong, Shenzhen, Foshan). Through mutually beneficial cooperation mechanisms, these cities have all obtained corresponding benefits in the process of enhancing their competitiveness.

Secondly, there is a competitive relationship. Although the overall competitive relationship within the Greater Bay Area urban agglomeration is relatively weak, there are still some notable competitive relationships. For instance, Shenzhen and Huizhou have formed a reverse competitive–cooperative relationship, mainly characterized by competition in resources and development positioning. Similarly, there is a certain competitive relationship between Foshan and Jiangmen.

Thirdly, there is a predation relationship, where one city achieves its own development through the resources and support of another city. The predator–prey relationship is relatively significant within the GBA, especially between some supply-and-demand cities, such as Shenzhen and Huizhou, as well as Guangzhou and Zhongshan.

Fourthly, there is a commensalistic relationship, where the development of one city positively promotes the development of another. In the GBA, Guangzhou has formed a significant commensal relationship with several surrounding cities.

Lastly, there is a parasitic relationship, where the development of one city hinders the development of another to some extent. This type of relationship is relatively rare in the GBA and only exists between Shenzhen and Dongguan.

Overall, the cities and regions within the GBA exhibit a diversified pattern of competition and cooperation, primarily characterized by symbiosis and collaboration with relatively mild competitive relationships. Shenzhen, Guangzhou, Hong Kong, and Macao, as core cities within the GBA, have played a leading role. While the identified competitive and cooperative relationships provide a structured overview of city interactions, it is essential to critically assess the implications of these dynamics. For instance, mutualistic relationships, while beneficial, may reinforce economic dependencies that limit long-term autonomous growth. Similarly, competition, though often framed as a challenge, can drive innovation and diversification if managed through strategic policy interventions. Cooperation among cities mainly focuses on technology, industry, and resource sharing. The formation of competitive relationships mainly stems from resource contention and conflicts in development positioning; these competitions have not had a negative impact on the overall collaborative development of the urban agglomeration. This study not only offers theoretical and practical guidance for the sustainable development of this region but also serves as a critical reference for investigating competition and cooperation among cities in other regions in China, like Yangtze River Delta urban agglomeration.

5. Conclusions and Policy Recommendations

5.1. Conclusions

Within the GBA, complex competitive and cooperative relationships have been formed among various cities and regions. Shenzhen, Guangzhou, Hong Kong, and Macao, as core cities or regions, have established close economic cooperation with other non-core places. However, it should be noted that the interpretation of these relationships is not absolute and may vary depending on factors such as changes in economic conditions, policy interventions, and shifts in resource allocation. The model’s assumptions of constant interaction coefficients and the exclusion of external factors may not adequately represent the intricacies of urban dynamics. Future research could further explore these dynamic factors to provide a more comprehensive understanding of urban interactions within the GBA. Based on the research methodology employed in this study, it can be concluded that the relationship between competition and cooperation within this area is characterized as follows:

Specifically, Shenzhen, one of the core cities of the Greater Bay Area, has formed different types of competitive and cooperative relationships with multiple cities. Its relationship with Hong Kong and Macao is characterized by a significant symbiotic relationship, where interactions among these cities promote mutual economic growth and resource sharing, creating a mutually beneficial symbiotic situation. At the same time, Shenzhen also maintains a symbiotic relationship with Guangzhou and Zhongshan, with the development of these cities complementing each other and jointly enhancing regional competitiveness. By contrast, the relationship between Shenzhen and Huizhou is predator–prey, where Shenzhen’s development requires support from Huizhou, particularly in terms of resource and industrial complementarity. Shenzhen’s relationship with cities such as Dongguan, Foshan, Zhuhai, and Jiangmen is characterized as amensalism, where Shenzhen’s strong development has somewhat inhibited the growth potential of these cities. As the administrative center of the Greater Bay Area, Guangzhou maintains a symbiotic relationship with Shenzhen, indicating a high level of synergistic effect between the two cities in the fields of technology and industry.

Additionally, Guangzhou maintains a commensal relationship with cities such as Foshan and Zhaoqing, where its dominant industries can drive the development of surrounding cities. In its relationships with Zhongshan and Hong Kong, Guangzhou exhibits a predator–prey relationship, meaning its development relies on the resource supply from these cities. However, the relationship between Guangzhou and Dongguan is competitive, with conflicts in development orientation and competition for resources between the two cities. Both Hong Kong and Macao maintain a symbiotic relationship with major cities such as Shenzhen and Guangzhou, indicating that cooperation between them can drive each other’s economic growth. In their relationships with cities such as Zhuhai and Foshan, Hong Kong and Macao exhibit a predatory relationship, relying on these cities’ industries and resources for support.

Furthermore, Hong Kong and Macao maintain a symbiotic relationship with major cities such as Shenzhen and Guangzhou within the urban agglomeration of the GBA, indicating that cooperation between them can drive each other’s economic growth. In their relationships with cities like Zhuhai and Foshan, Hong Kong and Macao exhibit a predatory relationship, relying on the industries and resources of these cities for support. Additionally, the relationship between Hong Kong and cities such as Zhongshan and Jiangmen is characterized as amensalism, where the development of these smaller cities is inhibited by Hong Kong’s economic advantage.

In the analysis of competitive and cooperative relationships within the GBA, besides the four core cities and regions of Shenzhen, Guangzhou, Hong Kong, and Macao, other non-core cities also play an important role in regional development. They form distinctive competitive and cooperative relationships with core cities and other cities, exhibiting both cooperation and a dynamic balance of competition and interdependence. This is specifically manifested in the following aspects.

(1) Dongguan exhibits a certain degree of amensalistic symbiosis with Shenzhen. Due to the geographical proximity between the two cities, some of Dongguan’s resources (such as talent and capital) are attracted to Shenzhen, leading to a certain degree of suppression in Dongguan’s industrial development. However, Dongguan also benefits from Shenzhen’s industrial spillover, receiving a significant amount of manufacturing and technology transfers, making it an important part of Shenzhen’s industrial chain. The relationship between Dongguan and Guangzhou is more complex, characterized by competition. Both cities have similar goals in industrial upgrading and technological innovation, particularly in the manufacturing and high-tech sectors, leading to some contention over resources and markets. Dongguan and Huizhou exhibit a commensalism relationship, with Dongguan positively impacting Huizhou through its manufacturing strength. Huizhou has enhanced its economic development by taking over Dongguan’s low-end manufacturing industries and supply chains.

(2) As an important traditional manufacturing center in the Pearl River Delta region, Foshan has actively promoted industrial transformation and upgrading in recent years, striving to enhance its competitiveness within this area. Foshan and Guangzhou exhibit a significant commensalism relationship. As the regional administrative and economic center, Guangzhou provides policy support and technical resources to Foshan, driving Foshan’s industrial transformation and upgrading. As the regional administrative and economic center, Guangzhou provides policy support and technical resources to Foshan, driving Foshan’s industrial transformation and upgrading. The promotion of the Guangzhou–Foshan urban integration has also facilitated a high degree of integration between the two regions in terms of infrastructure construction and industrial chain cooperation. The relationship between Foshan and Shenzhen is characterized as amensalism, with Shenzhen’s robust development exerting a certain degree of suppression on Foshan’s economic growth. Shenzhen’s strong advantages in attracting high-end manufacturing and technical resources pose challenges for Foshan in the process of industrial upgrading. The relationship between Foshan and Jiangmen is competitive. Both cities are at a critical stage of transformation and upgrading in traditional manufacturing, forming competition in strategic investments, technical resources, and market share.

(3) Being an important hinterland for Shenzhen and Dongguan, Huizhou plays a crucial role in undertaking industrial transfers and developing low-end manufacturing. The predator–prey relationship between Huizhou and Shenzhen is particularly significant. Shenzhen’s development relies on the land and labor resources provided by Huizhou, especially when Shenzhen faces land constraints, Huizhou becomes an important destination for Shenzhen’s industrial spillover. Huizhou has benefited from the economic radiation effect of Shenzhen’s rapid development, but it also faces pressure from resources and development opportunities being attracted by Shenzhen to some extent. The relationship between Huizhou and Dongguan exhibits commensalism, with Dongguan’s industrial chain and manufacturing capabilities promoting Huizhou’s economic development. By undertaking Dongguan’s manufacturing resources, Huizhou has expanded its own industrial scale.

(4) Zhongshan is a manufacturing city, maintaining close cooperative relationships with multiple cities in the area’s competitive and collaborative network. The relationship between Zhongshan and Shenzhen is characterized as commensalism, with Zhongshan experiencing rapid development through industrial collaboration and technological cooperation with Shenzhen. Zhongshan exhibits a certain predator–prey relationship with Guangzhou. As the economic center of the region, Guangzhou relies on Zhongshan to provide low-cost manufacturing resources and labor, helping Guangzhou maintain its leading position in high-end industries. The relationship between Zhongshan and Foshan is characterized by weak competition. The two cities have certain similarities in their manufacturing industries and industrial structures, leading to some competition for resources for industrial upgrading and market share.

(5) Jiangmen, despite being outside the core economic circle, also plays an important role in regional collaborative development. There is a competitive relationship between Jiangmen and Foshan. These two cities have similar manufacturing bases and are both promoting industrial upgrading, thus forming competition for capital, technology, and market share. The cooperation between Jiangmen and Zhongshan is mainly reflected in industrial collaboration. To some extent, they exhibit a symbiotic relationship, with Zhongshan’s manufacturing upgrade and technological transformation complementing Jiangmen’s industrial base.

(6) Zhaoqing primarily relies on the economic driving force of other cities within the region to achieve its own development. The commensalism relationship between Zhaoqing and Guangzhou is very pronounced. The economic radiation effect of Guangzhou has promoted the infrastructure construction and industrial undertaking in Zhaoqing. In the process of undertaking Guangzhou’s industrial spillover, Zhaoqing has continuously enhanced its own economic strength.

In summary, the non-core cities play a role in undertaking industries and promoting balanced regional development within the competitive and cooperative network. Through cooperation with core cities, they have achieved economic growth and industrial upgrading. At the same time, there is also a certain degree of competition between some cities, mainly in the areas of resource contention and industrial transformation. This competitive and cooperative relationship provides diversified impetus for the overall coordinated development of the Greater Bay Area and lays the foundation for mutual benefit and win–win cooperation among cities. Additionally, while this study primarily employs the Lotka–Volterra model to analyze urban interactions, future research could be enhanced by comparing these results with those derived from alternative models, such as spatial econometric models or the Kolmogorov population model. This would further substantiate the empirical findings and offer a more comprehensive understanding of urban dynamics within the GBA.

5.2. Policy Recommendations

Firstly, within the GBA, cities and regions should avoid homogeneous competition in industrial positioning and encourage functional division of labor. This aligns with the goal proposed in the Outline Development Plan for the GBA to “build a modern industrial system with international competitiveness and promote the formation of an industrial landscape characterized by complementary advantages and collaborative development.” Shenzhen can continue to play its role as a center for technological innovation, while Dongguan and Foshan can further strengthen their positioning as manufacturing bases. Cities like Zhongshan and Huizhou can focus on undertaking industrial spillovers and technological achievements transformation from core cities. By establishing clear division of labor and cooperation, a multi-centered, complementary development pattern can be formed, reducing resource competition and cutthroat competition between core cities and surrounding cities. Non-core cities such as Zhongshan and Jiangmen must be supported in developing emerging industries, such as new energy, artificial intelligence, and biomedicine, enabling these cities to occupy important positions in the industrial division of the GBA. Through policy guidance and financial support, we must nurture these cities to become emerging forces in the industrial chain of the Greater Bay Area, thereby enhancing the overall vitality of the regional economy.

Secondly, in line with the guiding principles of the GBA Science and Technology Innovation Action Plan, it is recommended to establish a collaborative innovation platform to promote the cross-city flow of production factors and facilitate resource sharing and collaborative innovation within this area. Specifically, with Shenzhen and Hong Kong taking the lead, cities such as Huizhou and Dongguan can deepen cooperation in the field of technological innovation, undertake technological achievements from Shenzhen, and enhance the overall technological level of the region through coordinated development. Within the region, more joint research institutions and innovation and entrepreneurship bases can be encouraged to establish, in order to improve collaboration among cities and achieve joint progress in technology and economy. In the fields of finance, trade, and high technology, we must leverage the strengths of Hong Kong and Shenzhen to expand the influence of the Greater Bay Area in the global industrial chain. At the same time, by optimizing the international investment environment, we must attract global enterprises and talents to innovate and start businesses in the Greater Bay Area, and build a world-class city cluster with true global influence.

Thirdly, in accordance with the requirements of the GBA Infrastructure Connectivity Plan, it is essential to further improve the construction of the transportation network within the GBA, enhancing connectivity between cities and regions. Particular attention should be paid to improving the accessibility of cross-city transportation modes, such as the Guangzhou–Shenzhen–Hong Kong High-Speed Railway, the Hong Kong–Zhuhai–Macao Bridge, and the central axis corridor of the Pearl River Delta. This will help reduce the spatial and temporal distances between cities, facilitate the free flow of labor, technology, capital, and other production factors, and optimize resource allocation. Additionally, the construction of transportation hubs, such as ports and airports, should be strengthened to promote the formation of an efficient and convenient logistics network, thereby enhancing the region’s overall international competitiveness. Through the integrated development of transportation infrastructure, a solid hardware foundation can be established to support the coordinated development of the GBA, effectively contributing to the realization of the goal outlined in the Outline Development Plan for the GBA to “build an international first-class bay area and a world-class city cluster.”