Exploring Coordinative Mechanisms for Environmental Governance in Guangdong-Hong Kong-Macao Greater Bay Area: An Ecology of Games Framework

To solve regional environmental problems, there is a trend of establishing urban agglomerations and formulating cooperative policy institutions in China. The extant studies on policy institutions largely focus on the coordinative mechanisms of multiple actors within one single institution. Only a few studies have tried to understand how different policy institutions are interlinked and mutually affected to influence actors’ decisions and problem resolutions. This article applies a network-based analytical approach and adopts the Ecology of Games Framework to explore how regional environmental governance is coordinated in the Guangdong-Hong Kong-Macao Greater Bay Area. It was found that coordinative mechanisms in regional environmental governance can happen around three elements: policy institutions, policy actors, and policy issues. Policy institutions tend to serve as an umbrella for many diverse and interdependent activities and actors within individual institutions. Additionally, positive externalities emerging between different policy institutions perform as coordinators across institutions. For actors, state-level actors usually play as facilitators of policy institutions while they are not active in participating in policy games in later phases; it is regional actors, particularly from Guangdong, that are active in the operation of policy institutions. For policy issues, they emerge because they are often tied with each other, and some of them play as the common ground for seemly separating policy institutions.


Introduction
With numerous overlapping jurisdictions across two semi-autonomous and highly developed cities (Hong Kong and Macao) and one economically dynamic province (Guangdong) that contains 21 prefecture-level cities, the Greater Bay Area (GBA) is an institutionally complex setting for environmental governance [1]. The GBA is a highly urbanized city cluster, with an average inter-city distance shorter than 10 km, which makes the prevention and control of transboundary air pollution a severe challenge [2]. Water quality is also a pressing concern [3]: the region's rivers serve the water needs of nearly 60 million inhabitants and 1.3 trillion USD economic activities every year. Moreover, the two cities, Hong Kong and Macao, rely primarily on the Dongjiang River in Guangdong for water supply based on the long-term contract with the mainland. Given this situation, there is an increasing risk that environmental pollution originating from any of the cities in the GBA, if it remains uncontrolled, will converge and turn into a significant region-wide problem [4].
By recognizing the transboundary nature of environmental pollution in the GBA, the environmental authorities in Hong Kong and Guangdong started to contact with each other in 1983 and have developed several regionally based policy institutions for coordinated environmental planning and decision-making. For instance, the first policy institution is the Guangdong-Hong Kong Environmental Protection Liaison Group, which was established in 1990 and upgraded to the Guangdong-Hong Kong Joint Working Group on Sustainable Development and Environmental Protection in 2000. However, this liaison group is not the only cooperative institution. In fact, our empirical study discovers 12 policy institutions that were established during 1985-2018 in the GBA, directly or indirectly aiming for regional environmental governance. In these policy institutions, actors with different or even competing interests come together, discuss, negotiate and make policy decisions on environmental issues.
The extant studies on policy institution largely focus on the coordinative mechanisms of multiple actors within one single institution or the pattern of actor interactions within a specific regional project [5][6][7][8][9]. Only a few studies have tried to understand how different policy institutions are interlinked and mutually affected to influence policy outcomes [10][11][12]. In this article, we follow in the opinion that the policy institutions that exist at a particular time and place may generate interdependent effects and combine to define the complex institutional system of environmental governance. Instead of focusing on one policy institution at a time, the regional environmental governance is the function of decisions made in multiple concurrent policy institutions. Therefore, the article answers the question: how regional environmental governance in the Guangdong-Hong Kong-Macao GBA is coordinated across multiple interdependent collaborative policy institutions?
To answer the question, we rely on the Ecology of Games Framework (EGF), which was first proposed by a sociologist Norton Long [13] who depicts urban systems as "ecology of games" that consist of multiple games played simultaneously by actors intending to achieve their individual goals and interests. The EGF is useful for our purpose because: (1) it specifically aims at analyzing sustainability issues, including ecological and environmental protection problems, which fits our research field of environmental governance, and (2) it draws explicit attention to interdependence of policy institutions at different geographic scales ranging from local to global, which is an important starting point for exploring and interpreting coordinative mechanisms among multiple actors that address a myriad of interconnected issues [14].
The article is structured as follows. Section 2 presents the EGF in detail, including its main conceptual elements and potential theoretical arguments. Section 3 introduces the case area, the methods we used to operationalize the EGF and our data collection and processing strategies. Section 4 displays the empirical findings. Section 5 discusses our findings and concludes the article and points out future research agenda.

Structural Elements in the EGF
The EGF is built upon five structural elements: policy institutions, policy actors, policy issues, policy games, and policy systems. The rest of this section describes these conceptual terms in more detail, using Figure 1 as an illustration.
Given resource interdependency, policy actors need to participate in one or more policy institutions. Policy institutions are sort of "platforms", "venues", or "arenas" that provide opportunities for different actors to get together, interact, and make collective decisions. Policy  [15,16]).
Actors may be any kind of meaningful social unit, including individuals, collective entities, firms, government and non-government organizations, and divisions within organizations, as well as nonhuman agents, such as knowledge repositories [17]. Policy actors refer to those actors that are involved in policy processes and whose choices and actions will ultimately affect policy outcomes [18].
Policy actors are characterized by specific capacities. Capacities refer to all resources available to a policy actor that allow the policy actor to influence the policy process and finally the policy outcome in a certain way and to a certain degree. The resources may include monetary resources, political power such as authority and discursive legitimacy, accessibility to information, and ownership of advanced technologies [19]. Policy actors are further characterized by their explicit perceptions on the substance of a policy issue and clear preferences (and preference ranking) towards solutions for the issue. These perceptions and preferences, according to the rational choice theories, may be relatively stable [20], while they may also be altered through learning and persuasion [21].
Understanding policy actors' capacities, perceptions, and preferences would allow us to infer the course of action that is likely to be chosen and thereby predict the possible policy outcomes. However, it is often the case that an actor cannot determine policy outcomes according to its perception and preference by using its own resources. It is a fact that policy actors depend on each other for resources [22]. Resource dependency theory stresses that each policy actor has to interact with others in order to acquire the necessary resources for goal achievement and survival since no actor can generate all necessary resources on its own [23].
Given resource interdependency, policy actors need to participate in one or more policy institutions. Policy institutions are sort of "platforms", "venues", or "arenas" that provide opportunities for different actors to get together, interact, and make collective decisions. Policy institutions have formal rules and informal norms that structure how policy actors make collective decisions [24]. The foremost rules of a policy institution concern about agenda-setting, because successful negotiation and cooperation requires actors to agree on a mutually attractive agenda. In determining the agenda, actors distinguish

Coordinative Functions in the EGF
EGF's coordinative functions originate from its structural elements of policy institutions, policy issues, and policy actors. Policy institutions play a coordinating role because the existence of multiple policy institutions in a policy system creates the potential for institutional externalities or spillovers, where actors' decisions and strategies in one institution could affect what happens in other institutions. In the EGF, two kinds of institutional externalities are distinguished: payoff externalities [15] and strategy externalities [29].
Payoff externalities occur when a decision outcome in one policy institution impacts a collective action problem in another policy institution, either in a positive or negative way. It is called a direct payoff externality if two or more policy institutions share the same policy issue; and an indirect payoff externality takes place when two policy institutions do not have overlapping jurisdiction over the same policy issue, but the decision in one institution may convey its influence to the other institution via some kind of mechanism or process [15].
Strategy externalities may occur when an actor participates in multiple policy institutions, since the behavioral strategies that an actor adopts for maximizing its utility may positively or negatively affect its achievement of utilization in other policy institutions. Scholars argue that actors participating in multiple policy institutions may generate positive strategy externalities because multiple participations may reinforce actors' reputational influence and give actors more information accessibility. Therefore, one might predict that an actor's capability and experience (through the use of strategies) to draw Sustainability 2019, 11, 3119 5 of 33 resources in one policy institution may positively affect its capability to benefit from other institutions. However, there are also scholars who claim that an actor's strategies in one institution may block the actor to benefit from other institutions. The reason is that, because of bounded rationality and cognitive load constraint, actors will design strategies according to the incentive structure of an institution that may maximize its utility. However, these well-designed strategies may not match with incentive structures of other policy institutions. In other words, the "best" strategies in one policy institution might be ineffective in other policy institutions [29,30].
Apart from policy institutions that perform coordinative functions, shared policy issues under the jurisdictions of multiple policy institutions may also play a coordinating role. In the literature on collaborative governance or interorganizational relations, it is often assumed that coordination is done by direct actor interaction [31]. At the same time, it is undeniable that coordination can take place in a context where actors do not have direct interactions beforehand [32]. Particularly, Boons and Berends [33] suggest that, in the coordination of interorganizational arrangements, a lack of tight coupling between the organizations can be compensated by shared issues. In the EGF, we see a similar role for common policy issues that exist if multiple policy institutions happen to address similar problems and pay attention to similar problems (without intention). We see this emergent overlap as an important coordination mechanism between actors that are otherwise independent.
The existence of common policy issues by itself is not sufficient for multiple actors to cooperate effectively. It is also required that some actors involved in policy institutions become aware of the common issues. According to the literature on social network analysis, the recognition of the common issue is most likely to happen if there are actors that participate in more than one policy institutions. These actors usually have a bridging position in the actor network and thus play a coordinating role with information obtained from multiple institutions.
Therefore, in the EFG, coordinative functions can be performed by policy institutions, policy issues, and policy actors. Policy institutions coordinate through institutional externalities; policy issues coordinate through common ground; and policy actors coordinate through their bridging positions and more accessibility to information.

Case Introduction
The Guangdong-Hong Kong-Macao GBA is a national strategy of China to promote cooperation among Guangdong Province, and Hong Kong and Macao special administrative regions in various aspects such as public services, infrastructure construction, economic development, and environmental protection [34]. The GBA consists of eleven (9 + 2) cities, that is, nine mainland cities (Guangzhou, Shenzhen, Zhuhai, Foshan, Huizhou, Dongguan, Zhongshan, Jiangmen, and Zhaoqing) of the Pearl River Delta (PRD) and the two special administrative regions, Hong Kong and Macao ( Figure 2). It covers a total area of 560,000 km 2 , and had a population of approximately 70 million at the end of 2017. The total economic size and population of the nine mainland cities account for 85% and 52% of those in Guangdong Province, respectively (see Table 1 for a summary of city facts in the GBA).
world's largest bay area in terms of economic scale [35].
The GBA is an excellent example where officials with various backgrounds are striving very hard for regional cooperation through comprehensive and strategic planning, economic measures, environmental intervention, and institutional and legal systems of governance [36]. Nevertheless, the cities in the GBA have different levels of economic development and different economic structures and political systems, which makes the regional cooperation a challenging task [37].    As one of the most open and economically vibrant regions in China, the GBA plays a significant strategic role in the overall development of the country. The development of the GBA is not only a new attempt to break new ground in pursuing opening on all fronts in a new era, but also a further step in taking forward the practice of "one country, two systems". According to the estimates by the China Center for International Economic Exchanges, the total economic output of the GBA will be comparable to that of the Tokyo Bay Area by 2020; and the GBA's GDP in 2030 is expected to reach 30 trillion RMB, which will then surpass the economic size of the New York Bay Area, to become the world's largest bay area in terms of economic scale [35].
The GBA is an excellent example where officials with various backgrounds are striving very hard for regional cooperation through comprehensive and strategic planning, economic measures, environmental intervention, and institutional and legal systems of governance [36]. Nevertheless, the Sustainability 2019, 11, 3119 7 of 33 cities in the GBA have different levels of economic development and different economic structures and political systems, which makes the regional cooperation a challenging task [37].

Research Design and Methods
Our study used network-based approaches and the graph theory to visualize and analyze the coordinative mechanisms for environmental governance in the GBA [38]. Based on the conceptual framework in Section 2, our analysis focused on five major questions: (1) Which actors participate in which policy institutions? (2) Which policy institutions deal with what issues? (3) What is the pattern of actor interactions, and how are they interdependent? (4) What are the direct payoff and strategy externalities between policy institutions? (5) What are the indirect payoff externalities between policy issues.
Given these questions, this study adopted two types of graph. The first type is called "two-mode network graph", which is further distinguished into "policy institution-actor network" and "policy institution-issue network". In the former network, the nodes represent either policy institutions or actors of environmental governance in the GBA (distinguished by different colors and shapes), and the edges represent which actors are involved in which policy institutions (see Figure 3a for an example). Similarly, in the latter network, the nodes represent either policy institutions or policy issues, and the edges represent which policy issues are addressed by which policy institutions (see Figure 3b for an illustration). The second type of graph is called "one-mode network graph", in which the nodes represent policy institutions (Figure 4a), actors (Figure 4b), or issues (Figure 4c), and the edges represent direct payoff and strategy externalities between policy institutions, interdependent relationships between actors, and indirect payoff externalities between policy issues correspondingly.

Research Design and Methods
Our study used network-based approaches and the graph theory to visualize and analyze the coordinative mechanisms for environmental governance in the GBA [38]. Based on the conceptual framework in Section 2, our analysis focused on five major questions: (1) Which actors participate in which policy institutions? (2) Which policy institutions deal with what issues? (3) What is the pattern of actor interactions, and how are they interdependent? (4) What are the direct payoff and strategy externalities between policy institutions? (5) What are the indirect payoff externalities between policy issues.
Given these questions, this study adopted two types of graph. The first type is called "two-mode network graph", which is further distinguished into "policy institution-actor network" and "policy institution-issue network". In the former network, the nodes represent either policy institutions or actors of environmental governance in the GBA (distinguished by different colors and shapes), and the edges represent which actors are involved in which policy institutions (see Figure  3a for an example). Similarly, in the latter network, the nodes represent either policy institutions or policy issues, and the edges represent which policy issues are addressed by which policy institutions (see Figure 3b for an illustration). The second type of graph is called "one-mode network graph", in which the nodes represent policy institutions (  We visualized the graphs by using the Ucinet software, which can help us to perform a series of analyses on the graphs. In this study, we used five indicators to reveal the coordinative mechanisms for environmental governance in the GBA (cf. [39,40]): (1) directed edge, which indicates an affiliation relationship. For example, a directed edge linking an actor to a policy institution implies that the actor participates in the policy institution; a directed edge connecting a policy institution to an issue indicates that the policy institution addresses the issue; (2) (undirected) edge, which indicates a mutual relationship between two elements. For instance, an edge between two actors indicates mutual dependence between the two actors; (3) weight of an edge, which indicates the frequency of affiliated relationship. If the weight of an edge between an actor and a policy institution is 10, that means the actor participates in 10 policy games under the policy institution; (4) two-mode betweenness centrality, which indicates the importance of a node in one mode in bridging nodes in another mode; (5) (one-mode) betweenness centrality, which indicates the central position of the node in bridging other nodes in the network. Table 2 provides a summary of our sub-questions and the approaches and indicators that are used to answer the questions.  We visualized the graphs by using the Ucinet software, which can help us to perform a series of analyses on the graphs. In this study, we used five indicators to reveal the coordinative mechanisms for environmental governance in the GBA (cf. [39,40]): (1) directed edge, which indicates an affiliation relationship. For example, a directed edge linking an actor to a policy institution implies that the actor participates in the policy institution; a directed edge connecting a policy institution to an issue indicates that the policy institution addresses the issue; (2) (undirected) edge, which indicates a mutual relationship between two elements. For instance, an edge between two actors indicates mutual dependence between the two actors; (3) weight of an edge, which indicates the frequency of affiliated relationship. If the weight of an edge between an actor and a policy institution is 10, that means the actor participates in 10 policy games under the policy institution; (4) two-mode betweenness centrality, which indicates the importance of a node in one mode in bridging nodes in another mode; (5) (one-mode) betweenness centrality, which indicates the central position of the node in bridging other nodes in the network. Table 2 provides a summary of our sub-questions and the approaches and indicators that are used to answer the questions. Table 2. A summary of research questions, analytical approaches, and measurement indicators.

Research Questions Analytical Approaches Measurement Indicators
(1) Which actors participate in which policy institutions?
Two-mode network: policy institution-actor network Directed edge; weight of an edge; two-mode betweenness centrality.
(2) Which policy institutions deal with what issues?
Two-mode network: policy institution-issue network Directed edge; weight of an edge; two-mode betweenness centrality.
(3) What is the pattern of actor interactions, and how are they interdependent?
(4) What are the direct payoff and strategy externalities between policy institutions?
One-mode network: policy institution network Directed edge; betweenness centrality.
(5) What are the indirect payoff externalities between policy issues?
One-mode network: issue network Undirected edge; betweenness centrality.

Data Collection
To produce the network graphs, we need to collect and code data. The data that we used in this study are "event data". Events can be anything that occurs in a certain place during a particular interval of time. If events are launched by certain actors, the events usually carry particular purposes and are expected to arouse changes. In this study, the events we collected are collective actions that are taken by relevant actors in policy institutions to deal with regional environmental issues in the GBA. That is, an event is qualified as one piece of data in our study if the event: (1) is explicitly referred to a policy institution of the GBA; (2) involves actors from at least two cities in the GBA; and (3) aims to Sustainability 2019, 11, 3119 9 of 33 address some issues of environmental governance in the GBA. The time span of the events in this study is a period of more than three decades from 1983 to 2018. The events were recorded in event sequence datasets development by Poole et al. [41] and Spekkink and Boons [32]. Each event has a time stamp calculated from the time point it occurred, a brief qualitative description of actions and interactions, the pre-conditional events for its occurrence, the actors involved, and the policy issues it deals with. The data collection process started in July 2018 and ended in January 2019. Two researchers were collecting the event data at the same time, and then synthesized the data to cross-check any missing events in individual collection. Finally, we collected 195 events that belong to 12 policy institutions. Affiliated to these events, we identified 132 actors and 76 issues associated with regional environmental governance in the GBA. The full event data are available from the corresponding author when there is a request. In the article, we provided a summary description on the groups of events in Section 4.1. The coded actors and issues can be found in the appendixes of this article.
Our sources of data include web pages, media reports, academic papers, and various types of documents produced by the actors involved in regional environmental governance in the GBA. The main webpages we searched include government portals of Guangdong, Hong Kong, and Macao, as well as other open information platforms of the involved governmental organizations. In addition, we used "baidu.com" as the main search engine to find webpages outside the governmental organizations. For media reports and academic papers, we used "CNKI.net" to collect event data. China National Knowledge Infrastructure (CNKI) contains information generated from scientific research, newspapers, conferences, and statistics yearbooks.

Empirical Findings
In this section, we present our empirical observations. We start with a summary description of the policy institutions in the GBA, which is built upon our event data (Section 4.1). In Sections 4.2 and 4.3, we offer analyses of the participation of actors in the policy institutions and the affiliation of policy issues with the policy institutions. In Sections 4.4-4.6, we analyze the interdependency of actors, direct payoff and strategy externalities between policy institutions, and indirect payoff externalities between policy issues, through the visualization of one-mode networks.  Table 3. Table 3 has four columns: (1) policy institution which reports the name of the policy institution; (2) label of the policy institution; (3) initial occurrence time which reports the time point (date) of the first policy game occurring in this policy institution; (4) summary description which offers a summary of the games with chronological order that have occurred in the policy institution. The summary is in the form of a qualitative description.  This policy institution was set up to facilitate the formulation of the Guangdong-Hong Kong-Macao GBA Plan. This GBA plan has been regarded as a national strategic plan to develop a globally competitive urban agglomeration.

Actor Participation in Policy Institutions
The list of actors in the Guangdong-Hong Kong-Macao GBA is shown in Appendix A of this article. In this section, we visualize part of our conceptual framework in Figure 5 (actor participation in policy institutions) and explore four questions: (1) for the actors, how many policy institutions they are active in? (2)  Based on Figure 5, Tables 4-6 present the statistical data on actor and policy institution. We see that most actors (124 out of 132) participate in a few (1, 2, or 3) policy institutions, and only eight actors are active in four and more than four largely interdependent policy institutions (Table 4). Among the eight actors, three are from Guangdong, two are from Hong Kong, one is from Macao, and the other two are from the state. Specifically, the Guangdong Department of Ecology and Environment (G5) participates in seven policy institutions (P1, P2, P3, P4, P8, P9, and P12), and G5 is also the most active actor that plays 87 policy games under the above-mentioned policy institutions. In addition, G5 is the most central actor in linking different policy institutions (see Table 6; two-mode betweenness centrality ranks the first which is 0.248). The Guangdong Governor (G2; two-mode betweenness centrality ranks the third which is 0.081) participates in six policy institutions (P3, P4, P5, P6, P11, and P12) and plays 49 policy games in these institutions. The Macao Environmental Protection Bureau (M18, two-mode betweenness centrality ranks the third which is 0.072) participates in five policy institutions (P4, P8, P9, P10, and P12) and plays 52 games in these institutions. The Guangdong Development and Reform Commission (G7; two-mode betweenness centrality ranks the second which is 0.092) participates in four policy institutions (P1, P2, P3, and P4) and plays 55 policy games in these institutions. Particularly, the Hong Kong Environmental Protection Department (H6; two-mode betweenness centrality ranks the fifth which is 0.039) also participates in four policy institutions (P1, P8, P10, and P12), but is the second active actor after G5, playing 60 policy games. For state-level actors, the President (S1) and the National Development and Reform Commission (S6) participate in four policy institutions, but they are not active in playing Based on Figure 5, Tables 4-6 present the statistical data on actor and policy institution. We see that most actors (124 out of 132) participate in a few (1, 2, or 3) policy institutions, and only eight actors are active in four and more than four largely interdependent policy institutions (Table 4). Among the eight actors, three are from Guangdong, two are from Hong Kong, one is from Macao, and the other two are from the state. Specifically, the Guangdong Department of Ecology and Environment (G5) participates in seven policy institutions (P1, P2, P3, P4, P8, P9, and P12), and G5 is also the most active actor that plays 87 policy games under the above-mentioned policy institutions. In addition, G5 is the most central actor in linking different policy institutions (see Table 6; two-mode betweenness centrality ranks the first which is 0.248). The Guangdong Governor (G2; two-mode betweenness centrality ranks the third which is 0.081) participates in six policy institutions (P3, P4, P5, P6, P11, and P12) and plays 49 policy games in these institutions. The Macao Environmental Protection Bureau (M18, two-mode betweenness centrality ranks the third which is 0.072) participates in five policy institutions (P4, P8, P9, P10, and P12) and plays 52 games in these institutions. The Guangdong Development and Reform Commission (G7; two-mode betweenness centrality ranks the second which is 0.092) participates in four policy institutions (P1, P2, P3, and P4) and plays 55 policy games in these institutions. Particularly, the Hong Kong Environmental Protection Department (H6; two-mode betweenness centrality ranks the fifth which is 0.039) also participates in four policy institutions (P1, P8, P10, and P12), but is the second active actor after G5, playing 60 policy games. For state-level actors, the President (S1) and the National Development and Reform Commission (S6) participate in four policy institutions, but they are not active in playing policy games, thus not included in the top 10 most central actors. Guangdong Vice Governor (G3) 36 Table 5. Statistical data on policy institutions.  For the policy institutions (Table 5), we see that almost every policy institution (except P11) involves state-level actors, but these state actors play policy games relatively less often than the regional actors, usually taking a role of initiator of policy institutions or a role of mediator between various regional actors. Therefore, we conclude in this section that state-level actors usually play as facilitators to initiate policy institutions while they are not active in the policy games in later phases; it is regional actors, particularly from Guangdong, who are active in running policy institutions and bridging different policy institutions.

Issue Affiliation with Policy Institutions
The list of issues in the Guangdong-Hong Kong-Macao GBA is shown in Appendix B of this article. In this section, we visualize another part of our conceptual framework in Figure 6 Table 9. Two-mode (issue-policy institution) betweenness centralities. Top Table 9 that shows the two-mode centralities for issues and policy institutions, we see that these four policy institutions that address the most policy issues are simultaneously the most important institutions in linking policy issues. It implies that the connection of issues develops within policy institutions.
If we look further at Table 9, we can also find that all the most central issues in bridging policy institutions are also the issues that are affiliated with policy institutions most, that is, they are part of the common ground. In other words, the most central issues in bridging policy institutions are the issues that are typically included as central aims of the policy institutions. This includes the issues, CEPA, Environmental Protection, Industrial Upgrading, Economy and Trade, Organizational Coordination, Environmental Industry, Joint Monitory, Motor Vehicle Management, Information Technology, and Quality Life Circle. In addition, nine out of the ten most central issues in bridging policy institutions link 8, 6, or 5 policy institutions; only one issue connects four policy institutions.
Therefore, we conclude in this section that the shared issues may play as the common ground for actors to cooperate. This indicates that actors' cooperation in policy institutions builds on issues that are central to the common ground.

Actor Interdependencies
In this section, we reconstructed the one-mode actor network for the GBA (Figure 7). Figure 5 already reveals that most actors tend to be active in only one, two, or three policy institutions, but there are some actors that are involved in four and more than four institutions and can act as bridges between the institutions because of their positions. Table 10 reports the top ten most central actors. In our case, we found that a large part of the most central actors (6 out of 10) is from Guangdong Province, one is from Macao, one is from Hong Kong, and one is from the state.    In addition, we found that eight out of ten most central actors are also the actors that our data report as Therefore, the finding of this section confirms with the above-mentioned conclusion in Section 4.1, that is, a large part of the most central actors is from Guangdong province. This indicates that Guangdong plays a critical role in bridging different actors from Hong Kong and Macao. In addition, this section reveals that most of the central actors are the initiators of policy institutions.

Direct Payoff and Strategy Externalities of Policy Institutions
In this section, we built the one-mode policy institution network to illustrate payoff and strategy externalities in the GBA (Figure 8). We calculated the one-mode betweenness centralities of the policy institutions (Table 11). As can be seen, the Pan Pearl River Delta Forum on Regional Cooperation and Development (P7, one-mode betweenness centrality = 22.152) is the most central institution in bridging other institutions. This also means that P7 has the greatest effect on creating externalities between institutions. What follows is the State-led Greater Bay Area Plan (P12, one-mode betweenness centrality     By summing the weight of edges of the network in Figure 8, we obtained the total amount of externalities (117) between policy institutions. For example, there was a policy game that occurred in 13 January 2014, under the Guangdong-Hong Kong Liaison Group on Sustainable Development and Environmental Protection (P1), in which Guangdong and Hong Kong planned to construct a joint monitoring network on air quality. This decision created an externality to Macao and triggered Macao to actively participate in the Guangdong and Hong Kong's plan. Later in 3 September 2014, an inter-local agreement was signed between Guangdong, Hong Kong, and Macao to jointly prevent air pollution, and Macao formally joined the construction of monitoring network for air quality. Another example occurred between the Guangdong-Hong Kong Liaison Group on Sustainable Development and Environmental Protection (P1) and the Joint Meeting System of Guangdong-Hong Kong Cooperation (P3), where P3 created 17 externalities to P1. Although P3 comes later than P1, P3 involves discussions on a wider range of cooperation fields between Guangdong and Hong Kong, not only on environmental protection, but also on port, infrastructure, economy, and trade. Therefore, the decisions on environmental sustainability under P1 were seriously influenced by the decisions on economic cooperation in P3 since its establishment in March 1998. Moreover, externalities also happened between the Closer Economic Partnership Arrangements between the Mainland and Hong Kong and Macao (P5 and P6) and the Pan Pearl River Delta Forum on Regional Cooperation and Development (P7), where the decisions in P5 and P6 were treated as inputs for decisions in P7. Our data (1983-2018) report that P5 created 11 externalities to P7 and P6 brought about 10 externalities to P7. These externalities happened because P7 involves substantial issues on economic cooperation within the PRD, which needs to consider and incorporate decisions and plans that have been already made on economic affairs between Guangdong and Hong Kong, as well as between Guangdong and Macao. Then, the decisions of P7 subsequently created 11 externalities to P11 (the Pan Pearl River Delta Joint Meeting System of Major Leaders), because the major leaders in P11 need to facilitate the implementation of the decisions of P7 and aid with prompt coordination and communication. Furthermore, P11 brought about 12 externalities to P4 (the Joint Meeting System of Guangdong-Macao Cooperation) and 7 externalities to P3 (the Joint Meeting System of Guangdong-Hong Kong Cooperation), because the decisions of P4 and P3 must consider the pre-conditions generated by P11, i.e., the policy signals from the major leaders in the Pan PRD. Finally, another major chain of externality happened among P9, P8, and P1, where environmental technologies exhibited in P9 (the Macao International Environmental Cooperation Forum) played as inputs for decisions in P8 (the Pan Pearl River Delta Joint Meeting System of Cooperation on Environmental Protection), which then influenced the decisions in P1 for the reason that Guangdong-Hong Kong's cooperation on environmental protection has to be integrated into a higher scale of the Pan PRD. Therefore, the above-mentioned evidence suggests that policy institutions tend to serve as an umbrella for many diverse and interdependent activities within individual institutions. Additionally, positive externalities that emerge between different policy institutions perform as important coordinators across different policy institutions.

Indirect Payoff Externalities Between Policy Issues
In this section, we reconstructed the one-mode issue network to illustrate indirect payoff externalities in the GBA (Figure 9). We calculated the one-mode betweenness centralities of the policy issues (Table 12). As can be seen, the top ten most central issues are Air, Information Sharing, Tourism, Transportation, Environmental Protection, Clean Production, Joint Monitoring, Water, Food Security, and Motor Vehicle Management. If we look back at Table 9 that shows two-mode betweenness centralities of policy issues, we will find that only Information Sharing among the top ten most central issues mentioned above shows up as one of the most important issue in linking policy institutions. This strongly indicates that many of the central issues in creating externalities are not the most central issues in bridging policy institutions. That means, indirect payoff between issues does not generate from the common ground of policy institutions. In other words, these issues do not arise because of an overarching plan, but they arise independently, as part of the plans that actors develop in different policy games. In all policy games of our data, multiple issues are connected to each other. For example, the Shenzhen Bay is often tied to the ambition of actors to control air pollution. Additionally, joint monitoring and monitoring networks often emerge with air governance. In addition, water is usually tied to different kinds of discussions, such as the Shenzhen Bay, Mirs Bay, information sharing, joint monitoring, and air. Moreover, marine resource nursing, forest wetland protection, and clean production are often tied with water and air governance. Regarding the issue of air, it is also strongly tied with motor vehicle management and total amount control. Finally, joint monitoring and environmental education often show up together.
governance. In addition, water is usually tied to different kinds of discussions, such as the Shenzhen Bay, Mirs Bay, information sharing, joint monitoring, and air. Moreover, marine resource nursing, forest wetland protection, and clean production are often tied with water and air governance. Regarding the issue of air, it is also strongly tied with motor vehicle management and total amount control. Finally, joint monitoring and environmental education often show up together. Therefore, we concluded from this section that, for policy issues, they emerge because they are often internally tied with each other, not because they constitute the common ground of the policy actors.
Note: "x" means that the issue is addressed in the policy institution.
Therefore, we concluded from this section that, for policy issues, they emerge because they are often internally tied with each other, not because they constitute the common ground of the policy actors.

Conclusions
In this article, we applied the EGF to explore how regional environmental governance is coordinated across multiple interdependent policy institutions, using the case of Guangdong-Hong Kong-Macao GBA as an illustration. Our main findings include the following points.
First, policy institutions in environmental governance tend to serve as an umbrella for many diverse and interdependent activities and actors. Thus, policy institutions promote cooperation by providing interfaces that make diverse actors working together in an interacting system. From this perspective, policy institutions can serve as boundary organizations, and facilitate, enable and regulate relations between internal actors. This finding is in accordance with many empirical studies using the EGF [10][11][12][13][14][15], which recognizes that policy institutions actually perform as coordinators in decision-making among multiple actors. Apart from internal actors' coordination, our empirical evidence shows positive externalities between policy institutions. This indicates that policy institutions, through their involved actors and affiliated issues, can coordinate each other in a positive way. This finding contrasts with the existing literature on the EGF, which claims that, not only positive externalities, but also negative externalities between policy institutions may exist, that is, the incentive structure of one policy institution may influence actor decisions in other institutions in a negative way [16].
Second, regarding actors, we found that state actors and regional actors behave differently. Almost every policy institution involves state-level actors, but these state actors play policy games much less often than the regional actors, usually taking a role of facilitator to establish policy institutions or a role of mediator when conflicts emerge between regional actors. It is largely the regional actors that are active in policy games of regional environmental governance. This finding is in line with the existing literature on collaborative governance, which emphasizes the important role of leadership or higher-level authorities in facilitating and pushing forward collaborations [42][43][44][45]. In our case, among the most central regional actors, we found that a large part is from Guangdong Province and only one is from Macao and one is from Hong Kong, indicating that Guangdong possesses a larger discursive power. In addition, we found that most central actors are the actors that our data report as the initiators of the policy institutions.
Third, regarding policy issues, we found that many of the central issues in creating externalities are not the most central issues in bridging policy institutions. That means indirect payoff between issues does not generate from the common ground of policy institutions. In other words, these issues do not arise because of an overarching plan, but they arise independently, as part of the plans that actors develop in different policy games. This finding can be linked with another finding from the one-mode issue network: indirect externalities between policy issues usually happen within individual policy institutions, not across different institutions.
In this article, we focused on environmental governance in the GBA in China. Further research is required to assess the extent, to which the conceptual arguments and empirical findings presented in this article are generalizable to other regions, in other policy fields instead of environmental governance. The environmental governance cases we investigated occur largely among governmental organizations in the GBA, whereas many other regional or inter-local cooperation projects also involve non-governmental actors. Thus, it is important to assess the extent to which our findings also hold in cases of cooperation between governmental and non-governmental/private sectors.

Conflicts of Interest:
The authors declare no conflicts of interest.