Influence of trust networks on the cooperation efficiency of PPP projects: moderating effect of opportunistic behavior

ABSTRACT Current studies on trust relationships and their impact on project cooperation efficiency tends to start from a binary perspective of project owners and contractors; however, this viewpoint is problematized with the concept of network-level trust. This study attempted to reveal the relationship between trust networks, opportunistic behaviours, and cooperation efficiency among all participants of public–private partnership (PPP) projects and to fill in the research gaps. PLS-SEM was used to analyze 189 valid questionnaires from PPP projects of China urban rail transit. Data analysis found that opportunistic behavior is negatively correlated with project cooperation efficiency, and its moderating effect on the relationship between trust network density and project benefits efficiency is supported by data. Trust network density is positively correlated with cooperation efficiency, and negative correlation with opportunistic behavior is supported by data. There is a positive correlation between trust network centralization and opportunistic behavior, and a negative correlation between trust network centralization and cost efficiency is supported by data. The relationship between network centralization and benefits efficiency has not been supported. These conclusions can help optimize cooperation efficiency from the perspective of stakeholder management and trust networks governance. GRAPHICAL ABSTRACT


Introduction
The public-private partnership (PPP) mode in utilities and infrastructure projects requires all participants to make full use of their own advantages to promote sustainable development of the projects. Relevant studies have shown that the PPP mode is a long-term social network activity from a certain perspective (Chowdhury, Chen, and Tiong 2011). Therefore, each participant of the PPP project has the possibility of implementing opportunistic behaviours, and affect the efficiency of cooperation and the sustainability of the project. The risk events caused by these opportunistic behaviours spread rapidly along the social networks on which the project is embedded and affect each stakeholder, thus affecting project cooperation efficiency (Liu et al. 2015). However, studies have indicated that the traditional dual subject perspective is inadequate to effectively explain and govern the multilateral opportunist behaviours or network-level risks in social network situations (Goh and Sandhu 2014).
In practice, not everyone involved in the project has a contractual relationship, they contact each other and form co-operative relationships through relational contracts. In fact, there is a general working interaction between the various parties involved in PPP projects. For example, project demonstration and financing, quality appraisal, cost certification, performance evaluation and other processes require multiparty participation. However, engineering supervision, cost management, engineering design, financing and other enterprises, as the main participants of PPP project, maintain a direct contractual relationship with the project owner, while there is only a noncontractual cooperative relationship between these participants. This extensive cooperative relationship is mainly affected by the internal management rules or relationship governance measures of the project (Wang, Fang, and Fu 2019b). In practice, there is basically no process that only needs two parties to complete, because the implementation of any engineering task rely on the joint efforts and mutual supervision of various parties. Considering that the direct contractual relationship between multiple parties may be missing, relationship governance becomes more important. Therefore, it is more common for PPP projects to strengthen project cooperation efficiency through relationship governance among various participants (Sun, Liang, and Wang 2019). Therefore, the relationship networks of stakeholders, in which trust relationship plays a fundamental role, must be explored (Marques and Rui,2018). Additionally, the Chinese society is relationship-oriented and has a special preference for trust and mutual benefit (Zhu et al, 2006). Therefore, this study adopted the concept of opportunistic behaviour based on trust, that is, the stakeholders with a low degree of trust are prone to induce opportunistic behaviours (Capaldo and Giannoccaro 2015a;Gianno and Iftikhar, 2019). This view is consistent with classic studies, that is, participants trading in a low-trust environment are highly likely to engage in opportunistic behaviours (Williamson 2017).
For regions where the PPP model is not well understood, participants of PPP project have different experiences and habits, and the situation of information asymmetry is obvious (Paul, Simon, and Savas 2001). Therefore, opportunistic behaviours within the scope of the project have a greater impact on cooperation efficiency (Rashidibajgan et al. 2021). Traditional studies have focused on the dual relationship between government and private investment companies, ignoring the complex network of stakeholders, who may form alliances and seek rent, in the PPP project. This leads to moral hazard and adverse selection, and thus, affects PPP project cooperation efficiency. Classical social network theory has pointed out that trust relationship has inhibitory effect on opportunistic behaviour in social network, but it does not clearly distinguish the density or centralization of trust network . In fact, these two aspects respectively represent the universality and concentration of trust relationship in the social network structure. Along with the basic view of social network theory and trust relationship, existing research on supply chain or engineering project management has obtained some interesting findings, they focus on the networked level trust structure and its influence on opportunistic behavior or project performance (Capaldo and Giannoccaro 2015a;Wang et al. 2021). However, these studies lack extensive empirical tests and do not distinguish overall indicators such as network density and centralization. Therefore, this study considered the trust network among stakeholders of PPP projects as the core perspective Li et al., 2018a). In fact, the trust network, opportunistic behaviours and cooperative efficiency in this study are all carried out from the perspective of the whole project, focusing on the analysis of the overall performance and sustainability of PPP project. Specifically, it considered the density and centralisation of the network structure as the analysis objects and judged the influence of the trust networks on the opportunistic behaviours of stakeholders and PPP project cooperation efficiency through an empirical analysis. The findings of this study are helpful to improve the internal management rules of PPP projects in practice and optimize the relationship governance scheme of each participant. At the same time, this study analyses the influence of trust networks density and centralization on opportunistic behaviours and cooperation efficiency, and puts forward corresponding countermeasures and suggestions. It provides a networklevel governance perspective and inspiration for overall improvement of cooperation efficiency and suppression of opportunistic behaviours tendencies of all participants.
The rest of the present research is organized as follows. Section 2 reviews the theoretical background related to this study. Then, Section 3 establishes the research model and proposes several hypotheses. Section 4 introduces the research method of a questionnaire survey. Section 5 shows the results, while Section 6 gives the discussion. This study is ended up with Section 7, consisting of result summary, limitations and recommendations.

PPP project cooperation efficiency
Since the new public management movement, the public-private partnership mode has become the mainstream of the utilities and infrastructure projects (Otrusinová and Pastuszková 2013). This model attaches importance to the cooperative relationship between government and private investors, and to give full play to the advantages of all parties involved in the project and make the project achieve better performance (Jing and Jian 2014). Therefore, there have been abundant findings about the consolidation of cooperative relationship and the improvement of cooperation efficiency (Zheng, Jia-Xin, and School 2019b). From the perspective of the whole life cycle of PPP project, the improvement of cooperation efficiency is particularly important, which directly affects the performance and sustainability of public utilities and infrastructure (Andrews and Steven 2013).
In fact, the research on PPP project cooperation efficiency has been widely concerned. Studies have shown that once the PPP project can improve the service efficiency and reduce the operating cost, it means the improvement of the cooperation efficiency; otherwise, it means that the PPP project efficiency is decreasing (Oliver 2003). The maximization of resource utilization efficiency and the lowest comprehensive cost are the main contents of PPP project cooperation efficiency. According to the development of transaction cost theory, there are three main forms of rational allocation of resources (Morallos et al. 2018). Among them, hierarchical management is the focus of enterprise resource allocation, contractual relationship is the basis of market resource allocation, and long-term and efficient cooperative relationship is the premise of market and enterprise to jointly play the role of resource allocation (Alston 2006). Then, according to the transaction cost theory, the cooperation efficiency of PPP projects can be measured by increasing cooperation benefits and reducing transaction costs (Minogue 2018). At the same time, the influence of PPP project control right, risk management, partnership and other perspectives on PPP project cooperation efficiency has also attracted the attention of relevant research. For example, the cooperative relationship is divided into demand, political and legal environment, communication and other aspects, and then the influence of each factor on the cooperation efficiency of PPP projects is analysed (Eugenijus, Alvydas, and Ba Rtkus 2008;Kim 2017). The same research also evaluates the efficiency of PPP project cooperation through the evaluation of project effectiveness (Trynov 2016). Similarly, interesting conclusions are also drawn about the influence of customer experience, management structure and other factors on the cooperation efficiency of PPP projects (Tang and Shen 2013). On this basis, there are also studies to discuss the impact of performance guarantee and subsidy policies implemented by the government on the efficiency of PPP project cooperation (Shi et al. 2018).
However, the current research on PPP project cooperation efficiency mostly focuses on the dual perspective of government and private investors, ignoring the complex social network environment among project participants Li et al., 2018a). In fact, all trading behaviours are rooted in the social networks, and each participant in the networks will have an impact on trading results, and even a chain reaction. Therefore, the study of PPP project cooperation efficiency should consider the perspective of the relationship network structure of each participant, which is also an important entry point of this study.

Trust networks
Numerous studies on trust have been performed, and the definitions, conclusions, and related inferences have been discussed in depth in the fields of psychology, sociology, management, and computer science (Connelly, Miller, and Devers 2012;Bergh, Thorgren, and Wincent 2011). This study focused on the trust network structure among the stakeholders of PPP projects, belonging to civil project management. However, existing studies in this aspect have mainly focused on the dual trust relationship perspective of developer-contractor (Capaldo and Gianno, 2015b). In other words, studies have overlooked numerous project stakeholders and the complex social networks embedded by stakeholders. China's social environment has a strong relationship-oriented feature, that is, there is an obvious preference for reciprocity, mutual benefit, trust, and multilateral win-win situation Li et al., 2018a). These factors should be studied among stakeholders, rather than the binary relationship model of developer-contractor. In fact, many researchers have supported that the trust networks should be further explored (Molin and Masella 2016;Nunkoo and Ramkissoon 2012). Studies have defined the trust networks as a network of relationships, in which people are willing to put valuable, important, long-term resources, or businesses at risk of other people's bad behaviour (Tilly 2004). On this basis, some researchers have analysed the trust networks from the perspective of public governance and informal system (Goodfellow et al. 2020). Additionally, some studies have focused on the impact of trust networks on higher education management and have reported some interesting results (Posselt 2018). A few results in the supply chain field have shown interactions between trust networks and opportunistic behaviours by characterising a complex adaptive system (Capaldo and Giannoccaro 2015a; Gianno Cc Aro and Iftikhar 2019). However, the interpretation and analysis of trust networks mainly focus on cryptography, computer science, and other fields and on the optimization of trust algorithms or the decentralization of trust networks (Sabatini and Sarracino 2015). PPP project involves many participants, who do not all have contractual relationship, but cooperate for the same project. In fact, there is a relational contract among them, and trust relationship plays an important role in it. It provides a governance idea for the project participants in the absence of contractual relationship. Therefore, it is of practical significance and academic value to analyze the trust relationship networks formed by project participants Li et al., 2018a).
In practice, not all parties in a PPP project have direct contractual relations, but they need to cooperate with each other to complete specific task. For example, in China's project cost management process, contractor shall submit to the project owner a report containing the completed quantities and price information, then the project supervisor needs to review the quantity of the project, cost consulting company reviews the price in the bill of quantities, engineering designer shall review the engineering drawings of variations, and the government departments may also make selective checks on project quality. In this process, the project participants have frequent cooperation and communication, and the slack or inaction of any party may lead to project delay, and more serious quality or safety accidents may occur. To avoid this situation, existing studies are mostly analysed from the perspective of relationship governance, mainly focusing on the analysis of the governance mode among project participants, the relationship network structure and its impact on project performance (Li et al., 2018a;Wang et al. 2021). This study pays attention to the fundamental role of trust in relationship governance, so it focuses on the networked structure composed of trust or distrust relationships among project participants. Therefore, based on the basic concepts of nodes and connections in social network theory, the network-level trust structure formed among all participants is defined as trust networks. Some studies have also used this definition and come to some interesting conclusions (Capaldo and Giannoccaro 2015a;Li et al., 2018a;Wang et al. 2021). Based on this definition, following the basic concepts of density and centralization in social network theory, this study will analyze these two aspects of trust networks in PPP project.

Stakeholder opportunistic behaviours
Trust can inhibit opportunistic behaviours, which has been confirmed by many studies (Fink and Kessler 2010). Therefore, considering the uncertainties abound in PPP projects, trust is often used as an incentive approach to the contractor to reduce opportunistic behaviour and to improve project performance (Xu et al. 2018). Based on previous findings, opportunistic behaviour can be divided into two forms according to stages: ex-ante and ex-post. Adverse selection is generally considered the main manifestation of ex ante opportunistic behaviour, and moral hazard and rip-off are considered the ex post opportunistic behaviour (Das and Rahman 2010). From the relational contract perspective, strong and weak forms of opportunism behaviours exist. The strong form explicitly violates the agreement of formal contract, and the weak form violates the relational contract; however, it does not violate the formal agreement (Wang et al. 2015;Tang et al. 2020). From the perspective of implementation motivation, opportunistic behaviours can be divided into active and passive (Seggie, Griffith, and Jap 2013). In this respect, the deliberate distortion of facts, deliberate misdirection, and active breach of a contract are classified as active opportunism, and the indolence, omission, and evasion of obligations are classified as passive opportunism (Steinle, Schiele, and Bohnenkamp 2019;Williamson and Ghani 2012). In the PPP project management field, many studies have considered the inhibitory effect of trust on opportunistic behaviour as a known condition (Williamson 2017). However, most studies have not distinguished opportunistic behaviours according to active or passive opportunistic behaviours . Relatively more objective reality is that stakeholders consider the decisions and information of other project participants to decide whether to implement opportunistic behaviours. Therefore, the analysis of behavioural motivation should be paid more attention. This requires relevant investigations in the project management field to upgrade from a binary to network-level relationship (Capaldo and Giannoccaro 2015a;Wang et al. 2021). Therefore, exploring the influence of network-level trust on opportunistic behaviour is one of the core goals of this study.

Model development and hypotheses
We proposed a conceptual model that includes trust networks, opportunistic behaviour, and PPP project cooperation efficiency ( Figure 1). According to social network analysis (SNA) theory, the trust networks is divided into two aspects: density and centralisation (Capaldo and Giannoccaro 2015a;Wang et al. 2021). The opportunistic behaviour and PPP project cooperation efficiency use a mature classification system and scale. Specifically, the opportunistic behaviour can be divided into active or passive opportunism according to its trigger factors (Jing and Jian 2014;Zheng et al. 2019a). From the whole-life-cycle perspective of PPP project cooperation efficiency, it can be divided into two aspects: benefits and costs efficiency (Shao, Wei, and Chu 2019;Wang, Xu, and Zhao 2013).

Trust networks and PPP project cooperation efficiency
Previous studies have pointed out that trust can improve the cooperation efficiency of PPP projects (Carbonara and Pellegrino 2018). Some studies have used the structural equation model for analysis, and some have described the relationship between trust and economic performance as an inverted U-shaped function, and this conclusion is also applicable to PPP project management (Niazi and Hassan 2016; Jayasuriya, Zhang, and Yang 2020). However, relevant studies analyzing project cooperation efficiency from the perspective of network-level trust are rare, so this study takes network-level trust as the starting point. In this study, network-level trust mainly uses the research method of social network analysis and divides it into two aspects: trust network density and centralization. Specifically, the relationship between the stakeholders of PPP projects includes factors such as trust and reciprocity, which have been the core concerns of social network research (Granovetter and Mark, 1985;Wang et al. 2021). In this regard, some studies have proposed a representative approach of stakeholders relationship connection strength analysis (Friedkin 1980;Yuksek 2017). Based on this approach, trust can be separated from relationship connection separately and refined to judge the network structure of trust relationship (Alhajj and Rokne 2018). At the same time, relevant studies in computer science have shown that the trust network structure quantified through social network analysis can calculate the network density, structure hole, centralization and other specific data (Kim and Sang 2013). Among them, the density of trust network reflects the close or sparse trust relationship among stakeholders. If the trust network density is large, it can indicate that the networks has a high level of stakeholder trust intensity (Guersakal, Aydm, and Tuezuentuerk 2011). In addition, the investigation of the centralization of trust network can reflect the concentration degree of trust relationship among stakeholders from the overall perspective (Bournemouth, University, of, Messina, et al. 2017). The higher centralization index indicates that the trust relationship in the network is unbalanced, that is, there are both trust concentrated and trust sparse groups (Dulaimi, Nepal, and Park 2005).
In fact, the density of trust network reflects the universality of trust, while the network centralization reflects the density imbalance of trust relationships in the network (Li et al., 2018a;Wang et al. 2021). Based on this, researches related to social capital theory have pointed out that trust relationship, as an important social capital, can promote cooperation efficiency (Gelderblom and Derik, 2018). To be specific, the higher the amount of social capital with trust as the main measurement index, the better the corresponding performance (Ekemen and Een 2020;Bouchillon 2021). Trust relationship in this perspective refers to the universal factors that widely exist in the social environment, rather than the trust relationship between the specific dualistic subjects (He et al. 2021). This is exactly the aspect of trust network density. Similarly, conclusions can be found in studies related to the theory of interorganizational trust. If the inter-organizational trust relationship is strong, the inter-organizational cooperation efficiency is better (Li et al., 2018b;Santos, 2021). The inter-organizational trust here mostly emphasizes the trust atmosphere created by stakeholders, rather than the specific trust relationship between dualistic subjects (Li et al. 2019;Li and Wang 2017). Therefore, the density index, which reflects the prevalence of trust relationship in the networks, can be considered to have a positive correlation with the cooperation efficiency (Li et al., 2018a;Wang et al. 2021).
However, the relationship between centralization of trust network and cooperation efficiency is more likely to be negatively correlated. In fact, there are three forms of network centralization in the theory of social network analysis, but all of them indicate the unbalanced distribution of relations or connections (Li et al., 2018b). Existing studies have shown that PPP projects often show a high centralization in the social network, which forms structural holes . This situation will lead to a negative development of project performance, which will also affect the cooperation efficiency of the project (Wu et al. 2020). Studies on supply chain, computer network and other aspects have drawn similar views, that is, a higher centralization index in social network will make the relationship imbalance obvious, which will lead to opportunistic behaviors and network vulnerabilities, and then affect the performance of supply chain or social networks (Kim and Sang 2013;Zhu and Lai 2019). Therefore, it is reasonable to believe that the relationship imbalance represented by the trust network centrality potential is negatively correlated with the project cooperation efficiency (Capaldo and Giannoccaro 2015a). Thus, we proposed the following hypotheses: H1a. The correlation between trust networks density and benefits efficiency is positive.
H1b. The correlation between trust networks density and costs efficiency is positive.
H1c. The correlation between trust networks centralisation and benefits efficiency is negative.
H1d. The correlation between trust networks centralisation and costs efficiency is negative.

Trust networks and opportunistic behavior
Trust is the foundation of co-operation, which can be transferred among stakeholders, and its role in project management is verified (Osei-Kyei, Chan, and Ameyaw 2017; Payan and Tan 2015). From the perspective of social network analysis theory, each stakeholder who trusts other is willing to believe that the partner will not take advantage of others. This is consistent with the basic concept of trust, that is, one party in the binary relationship believes that the other party will not take actions harmful to them even if the other party can do so (Mcevily and Tortoriello 2011). In fact, empirical studies have reported that binary trust relationship and opportunism are mainly negatively correlated (Barney and Hansen 1994;Capaldo and Giannoccaro 2015a). There are many stakeholders in the PPP project, and they play an important role in each stage or the whole process of the PPP project (Chowdhury, Chen, and Tiong 2011). However, opportunism occurs when one or more of PPP stakeholders take advantage of the weaknesses of others and seek their own unilateral interests and/or the whole at the expense of others. In this regard, studies have focused on the important role of trust in reducing the opportunist behaviour of PPP project stakeholders and have found that trust can reduce trade friction and promote PPP project performance (Consoli 2006). By contrast, by analysing the behaviours of stakeholders in PPP projects, some researchers have found that one of the causes of disputes and frictions is the lack of trust in co-operation. Therefore, positive measures should be taken for relationship governance (Smyth and Edkins 2007).
However, most existing studies have focused on the binary trust relationship perspective, which ignores the social relationship background rooted in the project, and the lack of investigation diversity in this aspect has attracted the attention of some researchers (Capaldo and Giannoccaro 2015a;Gianno Cc Aro and Iftikhar 2019). Meanwhile, the current research findings are mostly based on the different aspects of trust relationship, such as calculating trust, competence trust, goodwill trust, etc. These aspects emphasize the existence of the trust relationship, equivalent to the existence of the density of trust networks. Therefore, it can be concluded that the density of trust network is negatively correlated with opportunistic behaviour (Li et al., 2018a;Wang et al. 2021). However, from the perspective of the relationship imbalance of trust network, there may be inconsistent assumptions. In fact, PPP projects have many participants, among which some participants gain more trust relationships, that is, most participants trust, while some participants gain less or no trust. In this case, the trust network shows a high centralization index . Relevant studies on social capital theory have found that when there are great differences in the amount of social capital, opportunistic behaviours are likely to be induced (Ekemen and Een 2020;He et al. 2021). And trust relationship is the most important component of social capital. This finding is consistent with the practical experience of project management, that is, when there are absolutely trusted and untrusted participants, opportunistic behaviors frequently occur in projects. Therefore, it can be concluded that there is a positive correlation between trust network centrality and opportunistic behaviour.
To sum up, PPP project stakeholders are in a common social network, and they make behavioural decisions based on mutual observation and contact. This interactive behaviour rooted in social network has a long history in economic society (White 1981). In this process, different forms of trust can have different effects on opportunistic behaviours (Aa and Ik, 2020). Therefore, the social network perspective is required in the PPP project to identify all the stakeholders of trust relationships and to conclude the influence on opportunistic behaviour among stakeholders. Thus, we proposed the following hypotheses: H2a. The correlation between trust networks density and active opportunistic behaviour is negative.
H2b. The correlation between trust networks density and passive opportunistic behaviour is negative.
H2c. The correlation between trust networks centralisation and active opportunistic behaviour is positive.
H2d. The correlation between trust networks centralisation and passive opportunistic behaviour is positive.

Opportunistic behavior and PPP project cooperation efficiency
Many empirical studies have found that the opportunistic behaviour can have several negative effects on project performance (Tang et al. 2020). Some valuable deals may not go ahead because of concerns about the high-cost risks of the opportunistic behaviour (Yeonsung et al., 2016). The relationships formed between PPP project participants are usually unique and one-off, and due to the project's environmental uncertainty and complexity, the information between participants is likely to be asymmetric. In this case, opportunistic behaviours often occur (Saeed et al. 2021). There are many manifestations of opportunistic behaviours, which exist in all stages of the entire life of a project and can have a negative impact on project performance (Wang et al. 2016). Thus, we proposed the following hypothesis: H3a. The correlation between active opportunistic behaviour and benefits efficiency is negative.
H3b. The correlation between active opportunistic behaviour and costs efficiency is negative.
H3c. The correlation between passive opportunistic behaviour and benefits efficiency is negative.
H3d. The correlation between passive opportunistic behaviour and costs efficiency is negative.

Questionnaire design
We adopted a questionnaire survey to collect data and test the hypotheses. First, based on the theoretical and empirical literature, initial measurements were developed. Each item used in this study is derived from maturity scale, and is appropriately adapted according to the actual manifestation of trust relationship, opportunism, and cooperative efficiency in PPP projects. Specifically, this study uses the multi-item maturity scale to measure the network density (Ye, Shen, and García Guirao 2020;Nyuur, Brecic, and Debrah 2018;Frazier 2001) and centralization (Nyuur, Brecic, and Debrah 2018;Frazier 2001;Tsai 2001), forming items D1 to D3 and C1 to C3 in the scale. At the same time, there are mature scales of opportunistic behaviours (Kang et al. 2015;Seggie, Griffith, and Jap 2013) and cooperation efficiency (Shao, Wei, and Chu 2019;Wang, Xu, and Zhao 2013;Xu, Xi, and Tao 2011), which are adjusted in this study based on the actual situation of PPP projects in China. Subsequently, we held discussions with five experts to further refine measurement items. The five experts were called together at the end of 2020 when they jointly participated in the review and evaluation of a new rail transit PPP project in a municipality in China. They represent the government, academia, engineering consulting and design companies respectively. All of them have a master's degree or above, and have participated in many PPP projects with many years of work experience. In addition, these experts have all joined the expert database of PPP project center of Ministry of Finance of China (CPPPC), and they have enough experience in project evaluation and academic discussion. According to the feedback from the experts, we revised the initial measurement to improve the readability and validity of the questionnaire. In addition, a clear explanation and definition of trust relationship were added to the scale for respondents to understand (Xu et al. 2018). All the measurement items were measured on the 5-point Likert scale (1 = strongly disagree; 5 = strongly agree) and Table  1 presents the items.

Sampling and procedure
Snowball sampling method was adopted in this study (Jr 2013). By the beginning of 2021, Shanghai, Beijing, Guangzhou, Chengdu, Shenzhen, Nanjing and Wuhan had more than half of China's total urban rail transit traffic mileage. At the same time, through the official release of information shows that most of the subway projects in the above cities adopt BOT or BT modes. This can represent the specific application of PPP model in urban rail transit projects in China. In addition, relevant studies show that the core stakeholders of China's urban rail transit PPP projects mainly include various government departments, engineering design  and management consulting enterprises, financial enterprises, private investment and construction enterprises, etc. ). Based on the above reasons, 27 project managers or government directors from the above cities who have participated in rail transit PPP projects were selected to conduct an investigation, and they were asked to recommend specific staff from the core stakeholder enterprises familiar with urban rail transit PPP projects to participate in the questionnaire survey (Jr 2013). This aspect is specifically explained in the questionnaire, that is, if do not understand the rail transit PPP project, you do not need to fill in the questionnaire. In fact, 311 questionnaires were collected from January to April 2021. Respondents need to confirm that they have participated in the development, construction or operation process of urban rail transit PPP project, so as to ensure that they can understand the meaning of each item in the scale and give an exact answer. Questionnaire forms include electronic and paper versions, so the questionnaires with incomplete answers, obvious regularity of answer arrangement or contradictions in the answers are eliminated to obtain valid questionnaires. A total of 189 valid questionnaires were collected, with an effective response rate of 60.77%. Table 2 presents the characteristics of the respondents.

Construct reliability and validity
The results of the exploratory factor analysis should be considered first. In order to ensure the credibility of the research data and results, this study invited industry experts to discuss and revise the scale items through focus groups. Then, SPSS Statistics 24.0 software was used to conduct exploratory factor analysis for each variable. Based on the criterion that Cronbach's α coefficient is greater than 0.7, as shown in Table 1 (Astrachan, Patel, and Wanzenried 2014). Based on the above results, confirmatory factor analysis was further considered, and the reliability of the scale was tested. Using SmartPLS 3.3.2 software, the effective data collected through the scale were analyzed. Specifically, partial least squares (PLS) algorithm is used to calculate the external model load and the reliability of the surface. In this study, the discriminant criteria pointed out by previous studies were adopted, that is, the factor loading of the measurement item should be greater than 0.5, and the combined reliability (CR) of all variables should be greater than 0.7 (Yan, Guo, and Ning 2020a). Therefore, all variables as shown in Table 1 passed verification. It can be judged that the scale used in this study has good reliability. In addition, the average extraction variance (AVE) of each factor is greater than 0.5, indicating that each factor in the scale has good convergence validity (Jr 2013). And as shown in Table 3, the average variance extracted (AVE) of each variable is higher than the highest squared correlation (HSC), indicating acceptable discriminant validity (Yan et al. 2020b). In other words, the data in the diagonal position is larger than the row and column data in Table 3 which it is located, indicating a good validity (Hair, Ringle, and Sarstedt 2011).
In fact, compared with the covariance structural equation method based on maximum likelihood estimation method, the calculation method based on PLS is more suitable for this research. The former method is more suitable for the relatively mature theory verification, while partial least squares structural equation model (PLS-SEM) is more suitable for the early theory development and testing (Astrachan, Patel, and Wanzenried 2014). In addition, this method can also be used to estimate the path model effectively when the sample size is small (Xu, Xi, and Tao 2011). Therefore, PLS-SEM method is more consistent with the exploratory research of trust networks, opportunism and cooperation efficiency.

Test of the structural model and hypotheses
The global goodness-of-fit (GoF ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ) is an important index to measure the goodness of fit of PLS-SEM (Ringle, Henseler, and Sarstedt 2011). After calculation, the GoF value in this study was 0.570, greater than the optimal standard value (GoF = 0.36) (Tenenhaus, Amato, and Vinzi 2004), indicating that the model has a good goodness of fit standard. After the goodness of fit test, SmartPLS 3.3.2 software was used to carry out the analysis of Bootstrapping method. The samples were 5000 times, recommended by previous research findings (Astrachan, Patel, and Wanzenried 2014). The results of testing are shown in Table 4, where P value represents the level of significance. In general, the smaller the P value, the better the significance (Li et al. 2019). Therefore, it can be judged that some hypotheses are not supported by data.

Relationship between trust networks and PPP project cooperation efficiency
According to the data analysis results of this research (Figure 2), the hypotheses H1a and H1b are supported. There is a positive correlation between trust network density and PPP project cooperation benefits efficiency, with a correlation coefficient of 0.353 and P value of 0.000. At the same time, there is a positive correlation between network density and PPP project cooperation costs efficiency, with a correlation coefficient of 0.111 and P value of 0.015. But hypothesis H1c has not been supported. In fact, the influence of the relationship imbalance represented by the trust network centralization on the benefits efficiency is not clear, and the relationship may be regulated by a variety of influencing factors, so the relationship between the two cannot be simply expressed linearly. Hypothesis H1d is supported by research date. There is a negative correlation between trust network centralization and PPP project cooperation costs efficiency, with a correlation coefficient of −0.33 and P value of 0.000. In fact, the hypothesis about trust network density and cooperation efficiency is supported by data, which is also in line with the practice of PPP projects. Research data in this study are mainly from urban rail transit projects, which have more uncertainties and risks than above-ground projects because they involve more underground construction and operation (Li, Yin, and Zhang 2020). Existing studies have shown that trust is correlated with risk suppression and performance improvement of engineering projects (Zheng et al. 2019a). This can also explain the positive correlation between trust network density and cooperation efficiency of PPP projects, that is, the ubiquitous trust  relationship can improve cooperation efficiency by suppressing risks and improving construction performance.
On the other hand, the findings of this study are interesting, especially the hypothesis H1c which is not supported by the data. The current data analysis results do not support the correlation between trust network centralization and benefits efficiency, but support the negative correlation between trust network centralization and costs efficiency. In fact, there are many participants in PPP projects at the same time, and the trust network centralization indicates the imbalance of relationship, that is, although there is a general trust relationship among project participants, some participants get most trust, while some participants only get a small amount of trust. For example, in the construction process of PPP projects, the government often sends third-party regulatory agencies to participate in project management, including engineering supervision, cost consulting, design management, BIM technology assistance and other enterprises. Research shows that these enterprises have information advantages in the construction process, so they are easy to obtain more trust and form trust alliance, and are more likely to form network structure holes . In this case, the behavior of these enterprises will directly affect the project costs, which is manifested as the false calculation of actual quantities and prices, and the increase of design margin. Therefore, the negative correlation between network centralization and costs efficiency is supported by data and engineering practice. However, the benefits efficiency of PPP projects is mainly manifested in information and knowledge sharing, risk resistance, output effect and other aspects. These factors are often stipulated by specific contract terms in practice, so the influence of relationship governance represented by trust is not clear, which is also illustrated by the data analysis results of this study.

Relationship between trust networks and opportunistic behavior
The results of this research show that there is a negative correlation between the density of trust networks and opportunistic behavior. The results are like those of previous researches (Shao, Wei, and Chu 2019). However, the difference between this research and the past is that opportunistic behavior is divided into two forms: active and passive. This focuses on reflecting the triggering reasons of opportunistic behaviors of all stakeholders, and is a holistic perspective of the motivation of opportunistic behaviors (Wang, Fang, and Li 2019a). Specifically, there is a negative correlation between trust network density and active opportunistic behavior, with a correlation coefficient of −0.368 and P value of 0.000. Meanwhile, the density of trust relationship is also negatively correlated with passive opportunistic behavior, with a correlation coefficient of −0.232 and P value of 0.000. However, there is a positive correlation between trust networks centralization and opportunistic behavior. Specifically, there is a positive correlation between trust network centralization and active opportunistic behavior, with a correlation coefficient of 0.54 and P value of 0.000. And there is a positive correlation between trust network centralization and passive opportunistic behavior, with a correlation coefficient of 0.641 and P value of 0.000.
In fact, the research on trust and opportunistic behavior in PPP projects is quite common. However, it is regrettable that previous similar researches did not consider the social network perspective in the classification and measurement of trust relationship or opportunistic behavior (Capaldo and Giannoccaro 2015a;Gianno Cc Aro and Iftikhar 2019). This research attempts to reveal the network-level structure of trust relationships and its influence on opportunistic behavior. This involves not only the trust relationship from the perspective of duality, but also the integration of many trust relationships between duality subjects into a unified social network (Li et al., 2018a;Wang et al. 2021). Under this premise, opportunism does not represent the behaviors of specific individuals, but carries out a comprehensive analysis of the active or passive factors that induce opportunistic behaviors in the whole networks. The results of this research show that the density of trust networks is negatively correlated with opportunistic behavior. This indicates that in the social network composed of multiple stakeholders in PPP projects, the ubiquitous and stable trust relationship can inhibit opportunistic behaviors. Previous researches on social capital theory and interorganizational trust have also found similar conclusions (Andrews and Steven 2013;Osei-Kyei, Chan, and Ameyaw 2017).
However, the data of this research indicate that there is a positive correlation between trust networks centralization and opportunistic behavior. In SNA theory, networks centralization represents the imbalance of the density of trust relationship.In practice, if a participant or interest group in PPP project is overtrusted by other participants, it will also lead to the spread of opportunistic behavior, which reflects that there may be a U-shaped correlation between opportunistic behavior and trust. Previous similar studies also have exploratory conclusions in this regard (Niazi and Hassan 2016;Jayasuriya, Zhang, and Yang 2020). In fact, the centralization, a network-level indicator, shows an imbalance, which emphasizes that both the aggregation and sparsity of trust relationships exist in the networks structure. In this perspective, the assumption that there is a purely linear relation between trust and opportunistic behavior may be contrary to practice, which will be one of the key directions of the next research.

Moderating effect based on opportunistic behavior
The data analysis results of this research support hypotheses H3a-d. This indicates that there is an obvious negative correlation between opportunistic behavior and PPP project cooperation efficiency from the perspective of trust networks. This result is consistent with similar findings from previous researches (Dulaimi, Nepal, and Park 2005). At the same time, opportunistic behavior has a moderating effect on the relationship between trust network density and PPP project benefits efficiency. The SmartPLS 3.3.2 software was used to calculate the path coefficients and test their significance. The number of bootstrap samples is 6,000, recommended by previous research conclusions (Smyth and Edkins 2007). The specific data analysis results of the moderating effect are shown in Table 5. In the relationship path between trust network density, passive opportunistic behavior and PPP project benefits efficiency, P value is 0.028. This indicates that the moderating effect is significant. The moderating effect of opportunistic behavior on other pathways was not significant.
In fact, there are many stakeholders in every stage of PPP project, so the moderating effect of passive opportunistic behavior on the relationship between trust network density and cooperation benefits efficiency is consistent with engineering practice experience. This is because the passive opportunistic behaviors mainly refer to laziness, omission and evasion of obligations, it is not easy to detect the behaviors of PPP project participants, so the impact time of these behaviors is more lasting and the impact scope is larger Li et al., 2018a). For example, if there is a stable trust network density in a PPP project, although there is a positive correlation between it and benefits efficiency, passive opportunistic behaviors may be transmitted along the trust network because they are not easily detected. In this case, the lack of information and incomplete contract terms caused by laziness and inaction will spread to the whole project cycle, and ultimately profoundly affect the project performance (Capaldo and Giannoccaro 2015a; Gianno Cc Aro and Iftikhar 2019) Such practice cases often occur, and the most common example is the poor quality of the results of consulting or design companies, which affects the project construction and operation. In fact, the moderating role of passive opportunism in this study is supported by data as well as engineering practice.

Conclusions and implications
This study revealed the influence of trust network density and centralization on the cooperation efficiency of PPP projects, and explored the relationship between trust network and opportunistic behavior. Partial least squares structural equation modeling was used to analyze 189 sample data. The results show that trust network density is negatively correlated with opportunistic behavior and positively correlated with cooperation efficiency, and there is a partial moderating effect of passive opportunistic behavior. Trust network centralization is positively correlated with opportunistic behavior and negatively correlated with cost efficiency. In addition, opportunistic behavior is negatively correlated with PPP project cooperation efficiency. To sum up, a series of measures should be taken to strengthen the density of trust network of PPP projects and reduce the centralization, to improve the cooperation efficiency and promote the sustainable development of projects.

Theoretical implications
This research addresses an interesting research gap. Current research on trust relationships and their impact on project cooperation efficiency tend to take a binary perspective, mainly focuses on the trust relationship between the project owner and the contractor. But this perspective is problematized with the concept of trust networks. How trust is established in these networks is the focus of this research and how such trust impact project performance. In fact, trust in the project management of this area of research progress is quite substantial (Li et al., 2018b). However, the one-time and unilateral nature of engineering projects restricts the research perspective of trust relationship. Most of the researches believe that the trust relationship in engineering projects is mainly used to solve the problems of project owner and contractor. Fortunately, the widespread promotion of PPP projects in China at the present stage has provided a new research field for the diversified perspective of trust relationship (Capaldo and Giannoccaro 2015a; Gianno Cc Aro and Iftikhar 2019). In fact, PPP projects do require the concerted efforts of many stakeholders to achieve good project performance, and such diversified cooperation can last for decades from project planning to operation and even handover stage . Therefore, from the perspective of the research on trust relationship in the field of PPP project management, it is necessary and creative to introduce the network-level of trust and analyze its influence on the fundamental problem, namely opportunistic behavior and cooperation efficiency. In fact, researches on network-level trust have been widely carried out in the fields of supply chain research, socio-economic research, computer networks, etc., and some of the conclusions of this research are consistent with them (Musigmann, von der Gracht, and Hartmann 2020;Capaldo and Giannoccaro 2015a). In fact, the study of costs and benefits efficiency can promote the sustainable development of PPP projects. At the same time, the research on the trust network among various stakeholders is also an important way to emphasize sustainable development.
On the other hand, the Social Network Analysis theory is also combined with the trust relationship in the research of computer science, sociology, business administration and other fields, and the related research results have been substantial, creating variety of social network and e-commerce application cases in practice (Wan et al. 2020). In this theoretical background, network density and centralization can be quantitatively calculated and specific data results can be obtained. Similarly, from the perspective of engineering project management, quantitative formulas can be used to calculate indicators such as trust network density and centralization of a specific project Li et al., 2018a). On this basis, this research expands the perspective to more macro PPP projects of the same type and collects data in the form of a survey scale to analyze the specific indicators of trust networks structure of PPP projects like urban rail transit. This is an innovative practice for the application of Social Network Analysis theory in engineering projects management.

Managerial implications
Most of the hypotheses of this research are supported by the results of the data analysis. However, through the data analysis of the centralization of trust network, more interesting results are obtained. The findings of this research provide some help for the practice of PPP project management. First, trust network density emphasizes the degree to which trust relationships are prevalent among project participants. According to the findings of this research, improving trust network density is conducive to improving PPP project cooperation efficiency, which is demonstrated by two aspects, namely benefits and costs efficiency. It is noted that the enhancement of the trust network density is a continuous process, and the participants in the project already have some formal or informal relationships, which establish or promote the continuous maintenance of trust among various stakeholders. Therefore, strengthening the trust network density of PPP project mainly considers enhancing the relational trust of each project participant (Smith 2013). In this regard, regular working meetings and mutual review of work results can be used to increase the frequency of contact and interaction among project participants. At the same time, in the implementation process of PPP projects, the Integrated Product Development (IPD) mode can be imitated, and all participants of the project can work in a centralized way, to promote the trust network density among all stakeholders (Mesa, Molenaar, and Alarcon 2019). Second, attention should be paid to the stability of trust relationship among all parties involved in PPP projects. In fact, the maintenance of trust relationship or the repair after the damage of trust relationship are worth focusing on the field of research, is also an important factor affecting the density of trust relationship.Based on this, it is suggested that all kinds of contracts or agreements should adopt flexible expression of contract terms in practice, that is, fully inject the concept of trust into the formal contract. At the same time, an open attitude is adopted in the relationship contract, requiring project participants to share work results and key data immediately. In this regard, Building Information Model (BIM) technology and Cloud Computing technology can be used to update the project progress. At the same time, the key information of the project can be transmitted to the network database in real time, so that all parties of the project can grasp the progress of the project. Above measures strengthen the trust relationship among various stakeholders and thus enhance the density of the trust network.
In the implementation process of PPP projects, the contract relationship of dual subjects is widely existed in the aspects of financing, construction, project management, etc., but it is not the contract of binary relationship that can cover all project participants and work processes (Marques and Berg 2011). In fact, a series of internal project management systems and work plans can guide all aspects of project implementation and integrate the work and tasks of various participants. Therefore, besides paying attention to project contract management, a series of project management systems and programs should be revised and managed in detail. This requires project management consultative meetings or similar centralized working mechanisms to be held throughout each milestone phase of the project. In this process, information exchange and communication among all parties can be strengthened, thus enhancing the trust network density among all participants in the project. On the other hand, in the process of making project management system and program, it is suggested to attach the specific information, capabilities and qualifications of each participant as attachments, so as to enhance the degree of competency-based trust between the parties and reduce the centrality of trust network, that is, to reduce the imbalance of trust.
More importantly, project managers need to pay attention to the negative impact of trust networks centralization on cooperation costs efficiency. When the quantitative index value of network centralization is high, it indicates that there are interest groups or individuals that are over-trusted and over-ignored in the networks. From the perspective of Social Network Analysis theory, structural holes can be formed, and the over-trusted group or individual will have a greater impact when implementing opportunistic behaviors . Therefore, project participants with excessive trust need to be supervised by stricter achievement assessment or work review mechanisms, such as regular work achievement reporting and review meetings, hiring independent third-party supervision or review agencies, and the implementation of transparent public supervision and reporting mechanisms (Marques 2017).

Limitations and future research
There are still some limitations. First, the data were collected from one geographic area. Therefore, applying the research results to other countries should be taken with care. Future studies with wider data from other countries and regions can provide valuable information and enable researchers to expand the generalization of research results. Second, this study uses the classification method of social network analysis to divide the trust network structure into density and centralization, which are indicators reflecting the integrity of the network structure. According to the research paradigm of social network analysis, the structure of trust network can also be quantitatively analyzed, such as trust alliance, structure hole, faction, etc., which needs to be deeply combined with the research of trust network and the method of Social Network Analysis.