# Analysis on the Types and Characteristics of Collusion Behavior of Government Investment Project Tenderees

Authors: Sirui Nie; Yun Chen; Jingjing Li; Wenxi Zhu; Chongsen Ma
Journal: Complexity
 (2022)

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## Abstract

The classification of collusion behaviors of government-invested project tenderers is one of the important methods to describe the characteristics and laws of collusion behaviors and strengthen the governance of collusion. Firstly, the variables that affect the type of collusion behavior are selected and cluster analysis is carried out on the cases of collusion in government investment project bidding. Then use the social network to mine the types and characteristics of the collusion behavior of the tenderee. Finally, a BP neural network automatic identification model is established to quickly discriminate the types of collusion, which can effectively overcome the subjectivity of traditional methods. As a result, three typical types of collusion of tenderees can be obtained: intervention type, opportunity type, and cooperation type. The study found that the three types of collusion behavior have their own characteristics and laws, and the relationship between the variables that affect the type of collusion behavior is complex and affects each other.


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## Body

## 1. Introduction

Since the issuance of the Bidding and Tendering Law, The bidding market in China has accumulated rich practical experience [1] and the most serious, widespread and frequent corruption in government investment projects is bidding collusion, which takes the form of Manipulation Tendering, bid rigging, bid collusion, bid evaluation expert collusion, splitting of projects and avoidance of bidding.Existing research on the characteristics and patterns of collusion, On the one hand, the patterns of collusion occurrence are detected by detecting abnormal behavior in the bidding process. Reeves-Latour and Morselli [2] found patterns of collusion evolution in manipulation networks based on core peripheral social network analysis. Wachs and Kertesz [3] proposed a network-based framework to detect collusion through the behavioral characteristics of bid-rigging organizations in the bidding market. Conley and Decarolis [4] detected the existence of bidder groups by statistical testing of aggregate collusion law. Chen and Hou [5] developed a robust and effective collusion identification mechanism based on the law of collusion from the perspectives of rigid failure, tracking feedback and trial-and-error locking. On the other hand, relevant scholars have found laws by summarizing the characteristics of the collusion behaviors that have occurred. Signoret et al. [6] summarized the laws of 187 maximum price auctions and found collusion by comparing with the expected behavior of noncolluding bidders. Kwasnica and Sherstyuk [7] discussed the behavioral rules in multiunit auctions, Imhof et al. [8] detected collusion based on the systematic correlation between bids, and David [9] compared the behavioral characteristics of bidding with noncolluding bidders. If there is an abnormal behavior, it can be determined that the behavior of these bidders is suspicious, so as to discover the collusion law. These studies provide a theoretical basis for discovering the characteristics of collusive behavior and the law of general collusiveness.Most of the current research methods on the characteristics and laws of tender conspiracy are discussed from the perspective of the actors, using network analysis, mathematical reasoning, big data and other methods, mainly to explore the laws between the subjects of the conspiracy acts and between the subjects and their attributes. However, there is a lack of in-depth systematic analysis of the subjects involved in the whole process of collusion, the links and ways of occurrence and the characteristics of the case itself, which is the basis and key issue for the exploration of the characteristics and laws of collusion as a whole. Based on this, from the perspective of the overall bidding process, this paper sorts out and analyzes various attribute variables that may affect the law of collusion in government investment projects, hoping to obtain the characteristics and laws of collusion behavior of government investment project tenderees.This paper mainly uses cluster analysis to classify the collected cases of collusion through systematic clustering from the perspective of exploring the characteristics of the conspiracy behavior of the tenderee. And on the basis of classification, the social network analysis is carried out on the relevant cases of each category, and the characteristics and laws of the types of collusive behaviors of tenderers are explored. Finally, the BP neural network [10] is used to construct an automatic identification model of the type of collusion behavior of government investment project tenderees, and the type of collusion in bidding and tendering is judged. This paper systematically analyzes the types of collusion behaviors of tenderers, and explores the law of collusion, in order to provide new ideas for the governance of collusion behaviors in bidding.


## 2. Types of Conspiracy Behaviors in Project Bidding

### 2.1. Selection of Variables

There are many variables related to bidding collusion, and the interaction mechanism between the variables is very complicated. A certain number of case studies are helpful to discover the behavioral characteristics and internal laws of bidding collusion, and provide a basis for the governance of bidding collusion. According to the theory of behavioral economics, individual characteristics will affect individual behavior [11], and the individual characteristics of tenderers will have an impact on behavior selection. The whole process of bidding is a process of signing a contract. The behaviors of bidding conspiracy are diverse and involve a wide range of links [12]. The characteristics of each link are different, the degree of difficulty of collusion and the frequency of collusion are also different. Due to the differences in the formulation of laws and the level of supervision in various regions and fields, and the economic forms in different regions of our country, there are structural differences in the form of corruption [13], and the situation of collusion is related to regional differences; The characteristics and laws that affect collusion [14]. Therefore, in the process of describing the collusion behavior of bidding, it is necessary to consider the influence of the region and field of bidding on the collusion behavior of bidding. Therefore, this paper selects the characteristics of individual rights of the tenderee, the depth of involvement in the conspiracy, the links and methods of the conspiracy, and the regions and fields of the conspiracy cases from the micro and macro, internal and external perspectives as the variables analyzed in this paper.


#### 2.1.1. Selection of Personal Characteristic Variables of the Tenderee

The personal characteristics of tenderees in government investment project bidding will have certain influence on the results of collusive behavior [15]. To analyze the characteristics and laws of the type of conspiracy of the tenderee, the variable of the tenderee's personal characteristics occupies a very important position.Among them, tenderees are divided according to their power characteristics and the depth of involvement in collusion, which can be divided into: Staff, Head of Department, Key Position, Deputy, Hand; Direct action, Influence, Meddling, Decision making.


#### 2.1.2. Selection of Links and Variables of Collusion

The links and methods of conspiracy in bidding contain a lot of information, which can provide data support for the analysis of the types and characteristics of the collusion behavior of tenderees. The links of collusion in bidding involve: Prebidding, Establishment of project bidding team, Engagement of consultancy,Determination of project technical requirements and bidding programme, Preparation of prequalification documents (including announcement), Preparation of bidding documents, Issue tender notice or invitation for award, Offer of prequalification documents, Qualification evaluation, Issuance of prequalification result notice or invitation to bid, Offer of bidding documents, Site survey, issuance of clarifications and addenda, opening of tenders, evaluation of tenders and determination of successful candidates, and Internal designation of the winning bidder, forcing other bidders to withdraw, signing of contracts. The manifestations of collusion include vertical collusion, horizontal collusion, and mixed bid-rigging [16]. Based on the existing research [17], the concept of collusion behavior in bidding is summarized, and the concept with exclusive juxtaposition and superiority is selected. The results are as follows: pendant and pendant monopoly, accompanying or rotating bids, price alliance, market segmentation, bid rigging, avoidance of bidding, false bidding and open solicitation, disclosure of information, failure to sign contracts in accordance with bidding documents, compensation after the fact, conspiracy with bid evaluation experts, conspiracy with bidding agencies, internal designation of successful bidders, organization of bid rigging, winning bidder and forcing other bidders to withdraw, multiparty collusion.


#### 2.1.3. Selection of Collusion Region and Field Variables

Bidding has different characteristics in various regions and fields, so it is essential to consider regions and fields when exploring the characteristics of the collusive behavior of tenderees. The division of the regions where collusion occurs into East, Central and West based on the overall level of economic development of the country; the areas where collusion occurs are divided into local government investment projects according to the book “Public Financial Management of Local Government Investment Projects-Centralized Payment and Accounting”: Agriculture, forestry and water conservancy, Energy, Transport, Information industry, Raw materials, Machinery manufacturing, Light industry and tobacco, High technology, Urban construction, Social undertakings, Finance, Foreign investment, overseas investment.Therefore, the variable names and definitions analyzed in this paper are shown in Table1.Table 1
Variable names and definitions.
Variable nameVariable definitionsRights features =AStaff = 1, head of department = 2, key position = 3, deputy = 4, hand = 5Depth of involvement =BDirect action = 1, influence = 2, meddling = 3, decision making = 4Behavioural links =CPrebidding = 0. Establishment of project bidding team = 1. Engagement of consultancy = 2. Determination of project technical requirements and bidding programme = 3. Preparation of prequalification documents (including announcement) = 4. Preparation of bidding documents = 5. Issue tender notice or invitation for award = 6. Offer of prequalification documents = 7. Qualification evaluation = 8. Issuance of prequalification result notice or invitation to bid = 9. Offer of bidding documents = 10. Site survey = 11, issuance of clarifications and addenda = 12, opening of tenders = 13, evaluation of tenders and determination of successful candidates = 14, internal designation of the winning bidder, forcing other bidders to withdraw = 15, signing of contracts = 16Behaviour =DPendant and pendant monopoly = 1. Accompanying or rotating bids = 2. Price alliance = 3. Market segmentation = 4. Bid rigging = 5. Avoidance of bidding = 6. False bidding and open solicitation = 7. Disclosure of information = 8. Failure to sign contracts in accordance with bidding documents = 9. Compensation after the fact = 10. Conspiracy with bid evaluation experts = 11. Conspiracy with bidding agencies = 12. Internal designation of successful bidders = 13. Organization of bid-rigging = 14. Winning bidder and forcing other bidders to withdraw = 15. Multiparty collusion = 16.Region =EEast = 1, central = 2, west = 3Fields =GAgriculture, forestry and water conservancy = 1, energy = 2, transport = 3, information industry = 4, raw materials = 5, machinery manufacturing = 6, light industry and tobacco = 7, high technology = 8, urban construction = 9, social undertakings = 10, finance = 11, foreign investment = 12, overseas investment = 13


### 2.2. Clustering Results of Collusive Behaviors

This paper takes the cases of collusion in bidding for government-invested engineering projects announced from 2000 to 2020 as the sample, and the data source of the sample is the supervision website sponsored by China Discipline Inspection and Supervision Newspaper and the justice website sponsored by Inspection Daily. “bidding crime,” “bidding bribery,” and so on, yielded a total of 109 cases. The cases were summarized to explore the characteristics and laws of tenderee collusion. Hierarchical cluster can be used to classify the cases according to the nature of the research object, which is conducive to making classification decisions [18].In this study, 109 cases were systematically clustered using the variables in Table1 as clustering variables, and the Euclidean distance measurement interval was applied to obtain a clustering spectrum of bidding collusion cases as shown in Figure 1.Figure 1
Cluster spectrum of bidding collusion cases.From Figure1, it can be seen that there are three categories of cases of collusion in bidding for government investment projects, representing three types of collusion in bidding. The heat map representation of the results for each variable is shown in Figure 2.Figure 2
Statistical heat map of cases under each variable definition.The correspondence of the specific values in Figure2 is shown in Table 1, and Figure 2 represents the number of cases included in each collusion type under the definition of the variable corresponding to the current value. From it can be seen that.The first type of collusion is the intervention type, with a total of 14 cases. That is, tenderees of this type have decision-making and supervisory powers in their hands and can, through their own rights, conspire with acquaintances, relatives, or tenderees with whom they have a long-standing relationship before the bidding process has been completed. In the central region, more than 70% of these cases occur in the transport sector, followed by the agriculture, forestry and water conservancy sector, accounting for more than 80% of the total; the collusion mainly occurs in the prebidding stage, accounting for 57% of the total, mostly through avoidance of bidding and false bidding, open bidding and secret bidding, etc. To achieve the purpose of collusion, or direct operation, meddling and decision-making to influence the bidding results. The majority of tenderees involved in collusion were a handful, followed by department heads, both of whom accounted for over 70%, and those in key positions were also higher than the other two types.The second type of collusion is opportunistic, with 68 cases. In other words, the occurrence of this type of conspiracy is somewhat random, with conspirators seeking various opportunities to conspire with tenderees, which can take the form of bribes, acquaintances, kickbacks and other forms of conspiracy at various stages. The incidence of collusion is highest in the urban construction field and the social utility field, with both reaching over 40%; the geographical distribution is relatively even, with the largest number in the eastern region, followed by the central and western regions, each accounting for over 40%, 30% and 20%; it mostly occurs in the prebidding and bid evaluation stages, but the probability of collusion occurring in the preparation of bidding documents stage is significantly higher than the other two, and the other links accounting for over 10% of the total amount of Four, collusion mostly takes the form of avoidance of bidding and false bidding, open invitation and secret determination, etc., accounting for 40% and over 30% respectively; more ways of involvement are direct operation and influence; a handful of colluding tenderees and department heads are not very different from each other in the forefront, and a handful of tenderees is less compared to the other two categories, with a more even distribution of power characteristics.The third type of collusion is the cooperative type, with a total of 27 cases. In other words, the conspirators maintained close contact with the tenderees for a long period of time, and once there was a government investment project requiring bidding, the conspiracy occurred through the conspirators establishing contact with the bidders, bidding agencies and bid evaluation experts. This type of collusion occurs in the bid evaluation stage, with more than 85% of the bids being evaluated; collusion mainly occurs in the form of multiparty collusion and collusion with bid evaluation experts, with the two accounting for more than 70% of the total; among them, the combined proportion of a hand and a deputy involved in collusion is up to more than 85%, with a hand accounting for the highest proportion of the three types, with more than 60%, mainly through meddling to achieve the purpose of collusion; among them, collusion occurs in the central region The highest probability of collusion occurs in the social services sector, at over 30%.


## 2.1. Selection of Variables

There are many variables related to bidding collusion, and the interaction mechanism between the variables is very complicated. A certain number of case studies are helpful to discover the behavioral characteristics and internal laws of bidding collusion, and provide a basis for the governance of bidding collusion. According to the theory of behavioral economics, individual characteristics will affect individual behavior [11], and the individual characteristics of tenderers will have an impact on behavior selection. The whole process of bidding is a process of signing a contract. The behaviors of bidding conspiracy are diverse and involve a wide range of links [12]. The characteristics of each link are different, the degree of difficulty of collusion and the frequency of collusion are also different. Due to the differences in the formulation of laws and the level of supervision in various regions and fields, and the economic forms in different regions of our country, there are structural differences in the form of corruption [13], and the situation of collusion is related to regional differences; The characteristics and laws that affect collusion [14]. Therefore, in the process of describing the collusion behavior of bidding, it is necessary to consider the influence of the region and field of bidding on the collusion behavior of bidding. Therefore, this paper selects the characteristics of individual rights of the tenderee, the depth of involvement in the conspiracy, the links and methods of the conspiracy, and the regions and fields of the conspiracy cases from the micro and macro, internal and external perspectives as the variables analyzed in this paper.


### 2.1.1. Selection of Personal Characteristic Variables of the Tenderee

The personal characteristics of tenderees in government investment project bidding will have certain influence on the results of collusive behavior [15]. To analyze the characteristics and laws of the type of conspiracy of the tenderee, the variable of the tenderee's personal characteristics occupies a very important position.Among them, tenderees are divided according to their power characteristics and the depth of involvement in collusion, which can be divided into: Staff, Head of Department, Key Position, Deputy, Hand; Direct action, Influence, Meddling, Decision making.


### 2.1.2. Selection of Links and Variables of Collusion

The links and methods of conspiracy in bidding contain a lot of information, which can provide data support for the analysis of the types and characteristics of the collusion behavior of tenderees. The links of collusion in bidding involve: Prebidding, Establishment of project bidding team, Engagement of consultancy,Determination of project technical requirements and bidding programme, Preparation of prequalification documents (including announcement), Preparation of bidding documents, Issue tender notice or invitation for award, Offer of prequalification documents, Qualification evaluation, Issuance of prequalification result notice or invitation to bid, Offer of bidding documents, Site survey, issuance of clarifications and addenda, opening of tenders, evaluation of tenders and determination of successful candidates, and Internal designation of the winning bidder, forcing other bidders to withdraw, signing of contracts. The manifestations of collusion include vertical collusion, horizontal collusion, and mixed bid-rigging [16]. Based on the existing research [17], the concept of collusion behavior in bidding is summarized, and the concept with exclusive juxtaposition and superiority is selected. The results are as follows: pendant and pendant monopoly, accompanying or rotating bids, price alliance, market segmentation, bid rigging, avoidance of bidding, false bidding and open solicitation, disclosure of information, failure to sign contracts in accordance with bidding documents, compensation after the fact, conspiracy with bid evaluation experts, conspiracy with bidding agencies, internal designation of successful bidders, organization of bid rigging, winning bidder and forcing other bidders to withdraw, multiparty collusion.


### 2.1.3. Selection of Collusion Region and Field Variables

Bidding has different characteristics in various regions and fields, so it is essential to consider regions and fields when exploring the characteristics of the collusive behavior of tenderees. The division of the regions where collusion occurs into East, Central and West based on the overall level of economic development of the country; the areas where collusion occurs are divided into local government investment projects according to the book “Public Financial Management of Local Government Investment Projects-Centralized Payment and Accounting”: Agriculture, forestry and water conservancy, Energy, Transport, Information industry, Raw materials, Machinery manufacturing, Light industry and tobacco, High technology, Urban construction, Social undertakings, Finance, Foreign investment, overseas investment.Therefore, the variable names and definitions analyzed in this paper are shown in Table1.Table 1
Variable names and definitions.
Variable nameVariable definitionsRights features =AStaff = 1, head of department = 2, key position = 3, deputy = 4, hand = 5Depth of involvement =BDirect action = 1, influence = 2, meddling = 3, decision making = 4Behavioural links =CPrebidding = 0. Establishment of project bidding team = 1. Engagement of consultancy = 2. Determination of project technical requirements and bidding programme = 3. Preparation of prequalification documents (including announcement) = 4. Preparation of bidding documents = 5. Issue tender notice or invitation for award = 6. Offer of prequalification documents = 7. Qualification evaluation = 8. Issuance of prequalification result notice or invitation to bid = 9. Offer of bidding documents = 10. Site survey = 11, issuance of clarifications and addenda = 12, opening of tenders = 13, evaluation of tenders and determination of successful candidates = 14, internal designation of the winning bidder, forcing other bidders to withdraw = 15, signing of contracts = 16Behaviour =DPendant and pendant monopoly = 1. Accompanying or rotating bids = 2. Price alliance = 3. Market segmentation = 4. Bid rigging = 5. Avoidance of bidding = 6. False bidding and open solicitation = 7. Disclosure of information = 8. Failure to sign contracts in accordance with bidding documents = 9. Compensation after the fact = 10. Conspiracy with bid evaluation experts = 11. Conspiracy with bidding agencies = 12. Internal designation of successful bidders = 13. Organization of bid-rigging = 14. Winning bidder and forcing other bidders to withdraw = 15. Multiparty collusion = 16.Region =EEast = 1, central = 2, west = 3Fields =GAgriculture, forestry and water conservancy = 1, energy = 2, transport = 3, information industry = 4, raw materials = 5, machinery manufacturing = 6, light industry and tobacco = 7, high technology = 8, urban construction = 9, social undertakings = 10, finance = 11, foreign investment = 12, overseas investment = 13


## 2.1.1. Selection of Personal Characteristic Variables of the Tenderee

The personal characteristics of tenderees in government investment project bidding will have certain influence on the results of collusive behavior [15]. To analyze the characteristics and laws of the type of conspiracy of the tenderee, the variable of the tenderee's personal characteristics occupies a very important position.Among them, tenderees are divided according to their power characteristics and the depth of involvement in collusion, which can be divided into: Staff, Head of Department, Key Position, Deputy, Hand; Direct action, Influence, Meddling, Decision making.


## 2.1.2. Selection of Links and Variables of Collusion

The links and methods of conspiracy in bidding contain a lot of information, which can provide data support for the analysis of the types and characteristics of the collusion behavior of tenderees. The links of collusion in bidding involve: Prebidding, Establishment of project bidding team, Engagement of consultancy,Determination of project technical requirements and bidding programme, Preparation of prequalification documents (including announcement), Preparation of bidding documents, Issue tender notice or invitation for award, Offer of prequalification documents, Qualification evaluation, Issuance of prequalification result notice or invitation to bid, Offer of bidding documents, Site survey, issuance of clarifications and addenda, opening of tenders, evaluation of tenders and determination of successful candidates, and Internal designation of the winning bidder, forcing other bidders to withdraw, signing of contracts. The manifestations of collusion include vertical collusion, horizontal collusion, and mixed bid-rigging [16]. Based on the existing research [17], the concept of collusion behavior in bidding is summarized, and the concept with exclusive juxtaposition and superiority is selected. The results are as follows: pendant and pendant monopoly, accompanying or rotating bids, price alliance, market segmentation, bid rigging, avoidance of bidding, false bidding and open solicitation, disclosure of information, failure to sign contracts in accordance with bidding documents, compensation after the fact, conspiracy with bid evaluation experts, conspiracy with bidding agencies, internal designation of successful bidders, organization of bid rigging, winning bidder and forcing other bidders to withdraw, multiparty collusion.


## 2.1.3. Selection of Collusion Region and Field Variables

Bidding has different characteristics in various regions and fields, so it is essential to consider regions and fields when exploring the characteristics of the collusive behavior of tenderees. The division of the regions where collusion occurs into East, Central and West based on the overall level of economic development of the country; the areas where collusion occurs are divided into local government investment projects according to the book “Public Financial Management of Local Government Investment Projects-Centralized Payment and Accounting”: Agriculture, forestry and water conservancy, Energy, Transport, Information industry, Raw materials, Machinery manufacturing, Light industry and tobacco, High technology, Urban construction, Social undertakings, Finance, Foreign investment, overseas investment.Therefore, the variable names and definitions analyzed in this paper are shown in Table1.Table 1
Variable names and definitions.
Variable nameVariable definitionsRights features =AStaff = 1, head of department = 2, key position = 3, deputy = 4, hand = 5Depth of involvement =BDirect action = 1, influence = 2, meddling = 3, decision making = 4Behavioural links =CPrebidding = 0. Establishment of project bidding team = 1. Engagement of consultancy = 2. Determination of project technical requirements and bidding programme = 3. Preparation of prequalification documents (including announcement) = 4. Preparation of bidding documents = 5. Issue tender notice or invitation for award = 6. Offer of prequalification documents = 7. Qualification evaluation = 8. Issuance of prequalification result notice or invitation to bid = 9. Offer of bidding documents = 10. Site survey = 11, issuance of clarifications and addenda = 12, opening of tenders = 13, evaluation of tenders and determination of successful candidates = 14, internal designation of the winning bidder, forcing other bidders to withdraw = 15, signing of contracts = 16Behaviour =DPendant and pendant monopoly = 1. Accompanying or rotating bids = 2. Price alliance = 3. Market segmentation = 4. Bid rigging = 5. Avoidance of bidding = 6. False bidding and open solicitation = 7. Disclosure of information = 8. Failure to sign contracts in accordance with bidding documents = 9. Compensation after the fact = 10. Conspiracy with bid evaluation experts = 11. Conspiracy with bidding agencies = 12. Internal designation of successful bidders = 13. Organization of bid-rigging = 14. Winning bidder and forcing other bidders to withdraw = 15. Multiparty collusion = 16.Region =EEast = 1, central = 2, west = 3Fields =GAgriculture, forestry and water conservancy = 1, energy = 2, transport = 3, information industry = 4, raw materials = 5, machinery manufacturing = 6, light industry and tobacco = 7, high technology = 8, urban construction = 9, social undertakings = 10, finance = 11, foreign investment = 12, overseas investment = 13


## 2.2. Clustering Results of Collusive Behaviors

This paper takes the cases of collusion in bidding for government-invested engineering projects announced from 2000 to 2020 as the sample, and the data source of the sample is the supervision website sponsored by China Discipline Inspection and Supervision Newspaper and the justice website sponsored by Inspection Daily. “bidding crime,” “bidding bribery,” and so on, yielded a total of 109 cases. The cases were summarized to explore the characteristics and laws of tenderee collusion. Hierarchical cluster can be used to classify the cases according to the nature of the research object, which is conducive to making classification decisions [18].In this study, 109 cases were systematically clustered using the variables in Table1 as clustering variables, and the Euclidean distance measurement interval was applied to obtain a clustering spectrum of bidding collusion cases as shown in Figure 1.Figure 1
Cluster spectrum of bidding collusion cases.From Figure1, it can be seen that there are three categories of cases of collusion in bidding for government investment projects, representing three types of collusion in bidding. The heat map representation of the results for each variable is shown in Figure 2.Figure 2
Statistical heat map of cases under each variable definition.The correspondence of the specific values in Figure2 is shown in Table 1, and Figure 2 represents the number of cases included in each collusion type under the definition of the variable corresponding to the current value. From it can be seen that.The first type of collusion is the intervention type, with a total of 14 cases. That is, tenderees of this type have decision-making and supervisory powers in their hands and can, through their own rights, conspire with acquaintances, relatives, or tenderees with whom they have a long-standing relationship before the bidding process has been completed. In the central region, more than 70% of these cases occur in the transport sector, followed by the agriculture, forestry and water conservancy sector, accounting for more than 80% of the total; the collusion mainly occurs in the prebidding stage, accounting for 57% of the total, mostly through avoidance of bidding and false bidding, open bidding and secret bidding, etc. To achieve the purpose of collusion, or direct operation, meddling and decision-making to influence the bidding results. The majority of tenderees involved in collusion were a handful, followed by department heads, both of whom accounted for over 70%, and those in key positions were also higher than the other two types.The second type of collusion is opportunistic, with 68 cases. In other words, the occurrence of this type of conspiracy is somewhat random, with conspirators seeking various opportunities to conspire with tenderees, which can take the form of bribes, acquaintances, kickbacks and other forms of conspiracy at various stages. The incidence of collusion is highest in the urban construction field and the social utility field, with both reaching over 40%; the geographical distribution is relatively even, with the largest number in the eastern region, followed by the central and western regions, each accounting for over 40%, 30% and 20%; it mostly occurs in the prebidding and bid evaluation stages, but the probability of collusion occurring in the preparation of bidding documents stage is significantly higher than the other two, and the other links accounting for over 10% of the total amount of Four, collusion mostly takes the form of avoidance of bidding and false bidding, open invitation and secret determination, etc., accounting for 40% and over 30% respectively; more ways of involvement are direct operation and influence; a handful of colluding tenderees and department heads are not very different from each other in the forefront, and a handful of tenderees is less compared to the other two categories, with a more even distribution of power characteristics.The third type of collusion is the cooperative type, with a total of 27 cases. In other words, the conspirators maintained close contact with the tenderees for a long period of time, and once there was a government investment project requiring bidding, the conspiracy occurred through the conspirators establishing contact with the bidders, bidding agencies and bid evaluation experts. This type of collusion occurs in the bid evaluation stage, with more than 85% of the bids being evaluated; collusion mainly occurs in the form of multiparty collusion and collusion with bid evaluation experts, with the two accounting for more than 70% of the total; among them, the combined proportion of a hand and a deputy involved in collusion is up to more than 85%, with a hand accounting for the highest proportion of the three types, with more than 60%, mainly through meddling to achieve the purpose of collusion; among them, collusion occurs in the central region The highest probability of collusion occurs in the social services sector, at over 30%.


## 3. Characteristics and Analysis of the Types of Conspiracy Behavior of the Tenderee

This paper uses co-occurrence network analysis to explore the internal structure and collusion type characteristics between the variables, with co-occurrence representing the case where two variables appear in the same case at the same time. The co-occurrence network between the variables is shown in Figure3, where the size of the nodes indicates the centrality of the point degree; the larger the value, the larger the node and the more important the variable; the thickness of the connecting line represents the number of co-occurrence; the thicker the line, the more times the two variables appear together and the closer the link.Figure 3
Analysis of co-occurrence network of each variable.From Figure3, it can be seen that the point degree centrality of a handful, central, agriculture, forestry and water conservancy is higher and occupies a more important position in the co-occurrence network; the proximity centrality of several variables in the field is higher and is closely connected to other variables; the intermediary centrality of central and eastern regions, false bidding, and explicit bidding is higher, indicating a stronger ability to connect other variables. However, the network is specific to all types of variables and does not show the characteristics of each type of collusion well. This paper intends to analyze the characteristics of each collusion type through co-occurrence network and centrality of nodes.


### 3.1. Characteristics of Interventional Collusion

The analysis of the co-occurrence network for each variable of intervention-based collusion is shown in Figure4, and the centrality ranking of the nodes is shown in Table 2.Figure 4
Interventional collusion variable co-occurrence network.Table 2
Centrality of intervening collusion variables.
GlossaryPoint degree centralityProximity centralityIntermediate centralityCentral27.1746.2506.769Circumventing bidding21.7397.6160.494Transportation21.73919.3280.000First-in-command21.7394.1670.000Before bidding21.7397.0770.494Direct operation16.3045.0001.630Meddling10.8704.5450.626Agriculture, forestry, and water conservancy10.87010.8490.000Head of department8.1524.1670.000Decision-making8.1524.3480.000Fraudulent bidding, open and secret bidding8.1529.0201.334Qualification evaluation8.1527.0551.845Eastern region5.4354.7620.247Affiliation and affiliation monopoly5.4357.5160.000Key positions5.4354.1670.000West5.4354.9890.000Preparation of tender documents2.7174.9890.000Issuing prequalification documents2.7176.5530.000Deputy2.7174.1670.000Energy2.7179.6230.000Evaluate bids, determine winning candidates2.7176.5530.000Bid-rigging2.7177.4430.000Influence2.7174.3480.000Raw materials2.7178.1270.000As can be seen from Figure4 and Table 2, (1) in terms of point centrality, the point centrality of “central,” “transportation,” “bidding avoidance,” “a handful of people,” and “before bidding” is higher. It means that before the bidding is carried out, a handful of people with a lot of power and information can easily interfere with the bidding behavior and circumvent the bidding by various means to achieve the purpose of direct designation of the project, followed by the proposal of “three bases and one hub” in the central region and the continuous improvement of the comprehensive transportation infrastructure network system, which requires The number of projects to be tendered has increased, and the transport sector is prone to collusion in tendering due to its large volume of works, profits and strong professionalism. (2) From the perspective of closeness centrality, the central position of “transportation,” “agriculture, forestry and water conservancy,” and “energy” can be related to other variables, and they are closely related to other variables. A description of the types of collusion that the tenderee established in these areas. (3) From the point of view of betweenness centrality, “middle,” “qualification assessment,” and “direct operation” are the “intermediaries” associated with each factor, and by connecting other variables to conduct collusion, they have a certain control effect on other variables.This type of collusion is mostly carried out before the bidding process, which is more covert and can effectively avoid risks and reduce the risk of investigation and punishment of the conspirators. This type of collusion indicates that the central region's transport sector has more information at their disposal, and under the influence of the “human interest” society, tenderees can take advantage of information asymmetry to establish relationships with family members, acquaintances or circles of interest around power through direct operations, and collusion can occur. This type of tendereeer has discretionary power to do special things in the bidding process, circumventing or violating bidding procedures [19]. In response to such collusion governance, ideological education on clean government should be done well for tenderees, and the daily life style of tenderees should be standardized and restrained. Strengthen the supervision and management mechanism, standardize the power operation mechanism, and strictly investigate the interest circle around the tenderee.


### 3.2. Characteristics of Opportunistic Collusion

The analysis of the co-occurrence network for each variable of opportunistic collusion is shown in Figure5, and the centrality ranking of the nodes is shown in Table 3.Figure 5
Copresence network of opportunistic collusion variables.Table 3
Centrality of opportunistic collusion variables.
GlossaryPoint degree centralityProximity centralityIntermediate centralityCity construction19.64312.4480.000East17.8574.3481.859Agriculture, forestry, and water conservancy17.26216.3930.000Prebidding17.2625.0000.341Bidding avoidance16.6675.2630.327First-in-command15.4763.2260.000Direct operation14.8813.7040.562Central region14.2864.3482.040False bidding, explicit bidding and secret bidding13.6907.1261.572Head of department12.5003.2260.000Influence10.7143.7040.479Decision-making9.5243.7040.427Deputy8.9293.2260.000Western region8.3334.3420.227Evaluation of bids, determination of successful candidates7.1435.0001.280Preparation of bidding documents6.5484.9920.308Bid-rigging5.9525.8710.125Qualification evaluation5.9524.9920.322Meddling5.3573.5710.105Key positions3.5713.2260.000Dependency and dependency monopoly2.3815.2260.083High technology1.7868.1080.000Issue tender notice or award invitation1.1904.7170.000Machinery manufacturing1.1908.7720.000Hire consulting agency1.1904.5110.057Issuing prequalification result notice or invitation to bid0.5954.5050.000Bid opening0.5954.5050.000Light industry and tobacco0.5955.4740.000Revealing information0.5955.1900.000Conspire with bid evaluation experts0.5955.1900.000Conspiracy with bidding agency0.5954.7170.000From Figure5 and Table 3, we can see that, (1) from the point of view of centrality, “urban construction,” “east,” “before bidding” and “agriculture, forestry and water conservancy” are ranked relatively high, indicating that this type of collusion mostly occurs in the field of urban construction and agriculture, forestry and water conservancy in the eastern region, and has a higher probability of occurring before bidding. (2) From the perspective of closeness centrality, “agriculture, forestry and water conservancy,” “urban construction” and “machinery manufacturing” are in the center, more closely related to other variables and more independent. (3) In terms of intermediary centrality, “central,” “eastern” and “sham bidding and hidden bidding” are ranked relatively high, indicating a good performance in linking other variables. In addition, there are fewer variables with a mediated centrality of 0, indicating a wide range of variables and complex co-occurrence.Although the actual power and room for rent-seeking of colluding tenderees are smaller than those of the other two types, they are able to participate in various economic activities extensively and specifically because they are on the front line and have greater administrative discretion [20], so there are more opportunities for collusion to occur. The opportunity type of collusion involves the most stages and accordingly involves the most forms of collusion, and the depth of involvement of tenderees in collusion is more evenly distributed; the variables are closely linked, complex and varied, and this type of collusion can be operated directly at the front line with greater randomness, occurring in a more dispersed manner and in relatively complex circumstances, and the occurrence of collusion is more diverse. In response to such collusion, it is necessary to make the bidding process transparent, improve the level of bidding information, and continuously improve the bidding system.


### 3.3. Cooperative Collusion Characteristics

The analysis of the co-occurrence network for each variable of cooperative collusion is shown in Figure6, and the centrality ranking of the nodes is shown in Table 4.Figure 6
Co-occurrence network of cooperative collusion variables.Table 4
Centrality of cooperative collusion variables.
GlossaryPoint degree centralityProximity centralityIntermediate centralityEvaluate bids, determine winning candidates31.5936.2502.399First-in-Command23.3523.7040.000Central19.2315.2532.719Agriculture, forestry, and water conservation16.48412.3810.000Meddling15.1104.3482.885Multiparty collusion13.7366.6330.168Conspiracy with bid evaluation experts12.3636.6670.830Urban construction10.98912.2070.000East9.6154.9901.732Deputy9.6153.7040.000Decision-making8.2423.8460.000Western region8.2424.9711.13Influence6.8684.0000.231Direct operation6.8684.0000.038Fraudulent bidding, explicit solicitation5.4957.0270.176Machinery manufacturing4.1217.0650.000Transportation4.1218.9350.000Key positions2.7473.7040.000Internal designation of the winning bidder, forcing other bidders to withdraw2.7476.5820.308Issue tender notice or invitation for award1.3745.4850.000Prepare bidding documents1.3745.4850.000Head of department1.3743.7040.000Set up project bidding team1.3745.2000.000High technology1.3746.9890.000Failure to sign a contract in accordance with the bidding documents1.3745.8040.000Conspiring with bidding agency1.3746.5330.000Qualification evaluation1.3745.1790.000From Figure6 and Table 4, it can be seen that (1) from the point of view of centrality, the centrality of “evaluation of bids and determination of successful candidates,” “a handful of people” and “central region” occupies a relatively high position. This indicates that this type of collusion mostly occurs in the central region and the possibility of the involvement of a handful of people is higher. The tenderees have too many contacts with all parties in the bidding process, and long-term cooperative relationships have been established between the parties, so that they can operate at the stage of bid evaluation and determination of the winning candidate to achieve the purpose of collusion. (2) In terms of proximity to the center, “agriculture, forestry and water conservancy,” “urban construction” and “transportation” are ranked relatively high and are more closely linked to other variables in the center. (3) In terms of intermediary centrality, “intervention,” “central” and “evaluation of bids and determination of the winning candidate” ranked high, and were able to link other variables better, and had relatively greater control and influence over other variables.In cooperative collusion, the conspirators maintain long-term cooperation and have good cooperative mutual trust [21] and can quickly and tacitly engage in conspiracy during the tenderee evaluation stage. This type of collusion tenderees hold the leadership and can establish long-term collusion with other stakeholders through taking kickbacks, commission and demanding bribes, with a strong continuity [22]. Once a tenderee occurs these colluders gather to engage in conspiracy, in which case there may be multiple winning situations for the same tenderee. Therefore, in response to such conspiracy, it is necessary to focus on the situation where the bid winning rate is too high, as well as the review of tenderees' bid-rigging and affiliation, and improve and fully utilize the credit evaluation mechanism.


## 3.1. Characteristics of Interventional Collusion

The analysis of the co-occurrence network for each variable of intervention-based collusion is shown in Figure4, and the centrality ranking of the nodes is shown in Table 2.Figure 4
Interventional collusion variable co-occurrence network.Table 2
Centrality of intervening collusion variables.
GlossaryPoint degree centralityProximity centralityIntermediate centralityCentral27.1746.2506.769Circumventing bidding21.7397.6160.494Transportation21.73919.3280.000First-in-command21.7394.1670.000Before bidding21.7397.0770.494Direct operation16.3045.0001.630Meddling10.8704.5450.626Agriculture, forestry, and water conservancy10.87010.8490.000Head of department8.1524.1670.000Decision-making8.1524.3480.000Fraudulent bidding, open and secret bidding8.1529.0201.334Qualification evaluation8.1527.0551.845Eastern region5.4354.7620.247Affiliation and affiliation monopoly5.4357.5160.000Key positions5.4354.1670.000West5.4354.9890.000Preparation of tender documents2.7174.9890.000Issuing prequalification documents2.7176.5530.000Deputy2.7174.1670.000Energy2.7179.6230.000Evaluate bids, determine winning candidates2.7176.5530.000Bid-rigging2.7177.4430.000Influence2.7174.3480.000Raw materials2.7178.1270.000As can be seen from Figure4 and Table 2, (1) in terms of point centrality, the point centrality of “central,” “transportation,” “bidding avoidance,” “a handful of people,” and “before bidding” is higher. It means that before the bidding is carried out, a handful of people with a lot of power and information can easily interfere with the bidding behavior and circumvent the bidding by various means to achieve the purpose of direct designation of the project, followed by the proposal of “three bases and one hub” in the central region and the continuous improvement of the comprehensive transportation infrastructure network system, which requires The number of projects to be tendered has increased, and the transport sector is prone to collusion in tendering due to its large volume of works, profits and strong professionalism. (2) From the perspective of closeness centrality, the central position of “transportation,” “agriculture, forestry and water conservancy,” and “energy” can be related to other variables, and they are closely related to other variables. A description of the types of collusion that the tenderee established in these areas. (3) From the point of view of betweenness centrality, “middle,” “qualification assessment,” and “direct operation” are the “intermediaries” associated with each factor, and by connecting other variables to conduct collusion, they have a certain control effect on other variables.This type of collusion is mostly carried out before the bidding process, which is more covert and can effectively avoid risks and reduce the risk of investigation and punishment of the conspirators. This type of collusion indicates that the central region's transport sector has more information at their disposal, and under the influence of the “human interest” society, tenderees can take advantage of information asymmetry to establish relationships with family members, acquaintances or circles of interest around power through direct operations, and collusion can occur. This type of tendereeer has discretionary power to do special things in the bidding process, circumventing or violating bidding procedures [19]. In response to such collusion governance, ideological education on clean government should be done well for tenderees, and the daily life style of tenderees should be standardized and restrained. Strengthen the supervision and management mechanism, standardize the power operation mechanism, and strictly investigate the interest circle around the tenderee.


## 3.2. Characteristics of Opportunistic Collusion

The analysis of the co-occurrence network for each variable of opportunistic collusion is shown in Figure5, and the centrality ranking of the nodes is shown in Table 3.Figure 5
Copresence network of opportunistic collusion variables.Table 3
Centrality of opportunistic collusion variables.
GlossaryPoint degree centralityProximity centralityIntermediate centralityCity construction19.64312.4480.000East17.8574.3481.859Agriculture, forestry, and water conservancy17.26216.3930.000Prebidding17.2625.0000.341Bidding avoidance16.6675.2630.327First-in-command15.4763.2260.000Direct operation14.8813.7040.562Central region14.2864.3482.040False bidding, explicit bidding and secret bidding13.6907.1261.572Head of department12.5003.2260.000Influence10.7143.7040.479Decision-making9.5243.7040.427Deputy8.9293.2260.000Western region8.3334.3420.227Evaluation of bids, determination of successful candidates7.1435.0001.280Preparation of bidding documents6.5484.9920.308Bid-rigging5.9525.8710.125Qualification evaluation5.9524.9920.322Meddling5.3573.5710.105Key positions3.5713.2260.000Dependency and dependency monopoly2.3815.2260.083High technology1.7868.1080.000Issue tender notice or award invitation1.1904.7170.000Machinery manufacturing1.1908.7720.000Hire consulting agency1.1904.5110.057Issuing prequalification result notice or invitation to bid0.5954.5050.000Bid opening0.5954.5050.000Light industry and tobacco0.5955.4740.000Revealing information0.5955.1900.000Conspire with bid evaluation experts0.5955.1900.000Conspiracy with bidding agency0.5954.7170.000From Figure5 and Table 3, we can see that, (1) from the point of view of centrality, “urban construction,” “east,” “before bidding” and “agriculture, forestry and water conservancy” are ranked relatively high, indicating that this type of collusion mostly occurs in the field of urban construction and agriculture, forestry and water conservancy in the eastern region, and has a higher probability of occurring before bidding. (2) From the perspective of closeness centrality, “agriculture, forestry and water conservancy,” “urban construction” and “machinery manufacturing” are in the center, more closely related to other variables and more independent. (3) In terms of intermediary centrality, “central,” “eastern” and “sham bidding and hidden bidding” are ranked relatively high, indicating a good performance in linking other variables. In addition, there are fewer variables with a mediated centrality of 0, indicating a wide range of variables and complex co-occurrence.Although the actual power and room for rent-seeking of colluding tenderees are smaller than those of the other two types, they are able to participate in various economic activities extensively and specifically because they are on the front line and have greater administrative discretion [20], so there are more opportunities for collusion to occur. The opportunity type of collusion involves the most stages and accordingly involves the most forms of collusion, and the depth of involvement of tenderees in collusion is more evenly distributed; the variables are closely linked, complex and varied, and this type of collusion can be operated directly at the front line with greater randomness, occurring in a more dispersed manner and in relatively complex circumstances, and the occurrence of collusion is more diverse. In response to such collusion, it is necessary to make the bidding process transparent, improve the level of bidding information, and continuously improve the bidding system.


## 3.3. Cooperative Collusion Characteristics

The analysis of the co-occurrence network for each variable of cooperative collusion is shown in Figure6, and the centrality ranking of the nodes is shown in Table 4.Figure 6
Co-occurrence network of cooperative collusion variables.Table 4
Centrality of cooperative collusion variables.
GlossaryPoint degree centralityProximity centralityIntermediate centralityEvaluate bids, determine winning candidates31.5936.2502.399First-in-Command23.3523.7040.000Central19.2315.2532.719Agriculture, forestry, and water conservation16.48412.3810.000Meddling15.1104.3482.885Multiparty collusion13.7366.6330.168Conspiracy with bid evaluation experts12.3636.6670.830Urban construction10.98912.2070.000East9.6154.9901.732Deputy9.6153.7040.000Decision-making8.2423.8460.000Western region8.2424.9711.13Influence6.8684.0000.231Direct operation6.8684.0000.038Fraudulent bidding, explicit solicitation5.4957.0270.176Machinery manufacturing4.1217.0650.000Transportation4.1218.9350.000Key positions2.7473.7040.000Internal designation of the winning bidder, forcing other bidders to withdraw2.7476.5820.308Issue tender notice or invitation for award1.3745.4850.000Prepare bidding documents1.3745.4850.000Head of department1.3743.7040.000Set up project bidding team1.3745.2000.000High technology1.3746.9890.000Failure to sign a contract in accordance with the bidding documents1.3745.8040.000Conspiring with bidding agency1.3746.5330.000Qualification evaluation1.3745.1790.000From Figure6 and Table 4, it can be seen that (1) from the point of view of centrality, the centrality of “evaluation of bids and determination of successful candidates,” “a handful of people” and “central region” occupies a relatively high position. This indicates that this type of collusion mostly occurs in the central region and the possibility of the involvement of a handful of people is higher. The tenderees have too many contacts with all parties in the bidding process, and long-term cooperative relationships have been established between the parties, so that they can operate at the stage of bid evaluation and determination of the winning candidate to achieve the purpose of collusion. (2) In terms of proximity to the center, “agriculture, forestry and water conservancy,” “urban construction” and “transportation” are ranked relatively high and are more closely linked to other variables in the center. (3) In terms of intermediary centrality, “intervention,” “central” and “evaluation of bids and determination of the winning candidate” ranked high, and were able to link other variables better, and had relatively greater control and influence over other variables.In cooperative collusion, the conspirators maintain long-term cooperation and have good cooperative mutual trust [21] and can quickly and tacitly engage in conspiracy during the tenderee evaluation stage. This type of collusion tenderees hold the leadership and can establish long-term collusion with other stakeholders through taking kickbacks, commission and demanding bribes, with a strong continuity [22]. Once a tenderee occurs these colluders gather to engage in conspiracy, in which case there may be multiple winning situations for the same tenderee. Therefore, in response to such conspiracy, it is necessary to focus on the situation where the bid winning rate is too high, as well as the review of tenderees' bid-rigging and affiliation, and improve and fully utilize the credit evaluation mechanism.


## 4. Construction of a Model to Discriminate between Types of Collusion

From the above, it can be seen that the types of tenderee collusion have obvious characteristics and patterns. Using the BP neural network automatic discrimination model to discriminate the types of tenderee collusion cases in a certain region or a certain period of time can present the collusion situation clearly and understand the current situation and development trend of collusion occurrence. Specific recommendations are made based on the different characteristics of the three different types of collusion to achieve more efficient management of collusion in tendering for government investment projects. In addition, at the initial stage of collusion discovery, the categorisation of the discriminatory model can be used to quickly lock the direction of the case search, providing assistance in the collection of evidence of bidding collusion and the cracking of the case.


### 4.1. Model for Discerning the Type of Collusion

The collusion of government investment project tenderees can be classified into three types through systematic clustering analysis, and then the types of tenderees’ collusion are automatically discriminated through BP neural network. The 109 empirical cases collated were grouped, trained and tested separately, and a model capable of quickly and accurately discerning the types of tendereeer collusion was constructed.The steps in the implementation of the BP neural network automatic discriminative model are as follows.Step 1.
Selection of data. In this paper, the aforementioned 109 empirical cases, each with six characteristic variables, are selected, as shown in Table1; based on the results of systematic cluster analysis, the aforementioned empirical cases can be classified into three types of categories, namely 14, 68 and 27 cases.Step 2.
Set up training data and test data. The 109 empirical cases were allocated according to the ratio of 8 : 2, and 87 and 22 training data and test data were obtained respectively. The number of nodes in the input layer was set to 6 according to the number of variables in the cases; the number of nodes in the output layer was set to 3, i.e. three types of collusion: interventional, opportunistic and cooperative. of whichni=10, When equal to 1 indicates that it belongs to that class of collusion, otherwise it does not; the number of nodes in the implicit layer is determined according to [25].(1)l<n−1,(2)l<m+n+a,(3)l=log2n,where is the number of nodes in the implicit layer; is the number of nodes in the input layer; is the number of nodes in the output layer. Is a constant between 0 and 10. The 3-layer structure of this paper is shown in Figure 7,Figure 7
3-layer BP neural network structure diagram.Step 3.
The sample data is normalized. In this paper, the maximum-minimum method is used, with the following formula.(4)xi∗=xi−xminxmax−xmin,where, xi. are the values of the variables defined in Table 1, xmax. and xmin. are the maximum and minimum values of the 109 cases.Step 4.
Construct BP neural network. This paper uses the newff function to build a BP neural network.Step 5.
The network parameter settings are shown in Table5.Table 5
Setting of BP neural network training parameters.
Parameter nameDesign valueAttributenet.trainParam.lr0.01Learning ratenet.trainParam.goal0.00001Training target errornet.trainParam.epochs1000Set the number of training stepsnet.trainParam.show25Interval parameters for displaying training resultsnet.trainParam.mc0.01Additional momentum factornet.trainParam.min_grad1e-6Minimum performance gradientnet.trainParam.max_fail6Maximum number of confirmation failuresStep 6.
BP neural network training.Step 7.
BP neural network prediction. The trained model is used to predict the test samples.
The above BP neural network discriminative process leads to the following results, as shown in Figure8 and Figure 9.
Figure10shows the training performance of the BP neural network, and we can see that the final network error is small and has a good training effect, and when the BP network is trained to the 10th generation, the training results obtained are the best; by comparing the test collusion category and the actual collusion category (Figure 11), we can see that the overlap rate between the two reaches 92.00%, and each empirical case gets a better discriminatory result with high accuracy; so it can be obtained that only two of the classification errors Figure 10 are not zero; from the histogram of the training set and the error distribution in Figure 11 we can, see that there is a small error in the training set, while the error in the test set is almost zero, which has a good effect. In Table 6, the correct rates of the three types of collusion types discriminated for 22 cases in the test set are shown, which shows that the model is objective and efficient for the automatic discrimination of the categories of collusion types.Figure 8
Error MSE drop line.Figure 9
Classification of predicted collusion categories and actual collusion categories.Figure 10
BP neural network classification error.Figure 11
Histogram of the error distribution of the training and test sets.Table 6
Classification correct rate of three types of collusion.
Type of collusionCorrect rateInterventional1.000Opportunistic0.941Cooperative0.800


### 4.2. Case Validation

Taking a case of vertical collusion in bidding for a government investment project as an example, the BP neural network automatic discriminative model trained above was used to classify it. Firstly, the data input of the BP neural network automatic discrimination model is shown in Table7; secondly, the trained automatic discrimination model is used to discriminate the types of collusion cases, and the training parameters and function forms are set as shown in the previous section; finally, the collusion cases belong to the first category, i.e. the intervention category of collusion.Table 7
efinition of case variables.
Empirical casesVariable nameRights characteristicsDepth of involvementCollusion linksMethod of collusionFieldsAreaVariable valueFirst-in-commandMeddlingBefore biddingCircumventing biddingTransportationCentral regionVariable input530623


## 4.1. Model for Discerning the Type of Collusion

The collusion of government investment project tenderees can be classified into three types through systematic clustering analysis, and then the types of tenderees’ collusion are automatically discriminated through BP neural network. The 109 empirical cases collated were grouped, trained and tested separately, and a model capable of quickly and accurately discerning the types of tendereeer collusion was constructed.The steps in the implementation of the BP neural network automatic discriminative model are as follows.Step 1.
Selection of data. In this paper, the aforementioned 109 empirical cases, each with six characteristic variables, are selected, as shown in Table1; based on the results of systematic cluster analysis, the aforementioned empirical cases can be classified into three types of categories, namely 14, 68 and 27 cases.Step 2.
Set up training data and test data. The 109 empirical cases were allocated according to the ratio of 8 : 2, and 87 and 22 training data and test data were obtained respectively. The number of nodes in the input layer was set to 6 according to the number of variables in the cases; the number of nodes in the output layer was set to 3, i.e. three types of collusion: interventional, opportunistic and cooperative. of whichni=10, When equal to 1 indicates that it belongs to that class of collusion, otherwise it does not; the number of nodes in the implicit layer is determined according to [25].(1)l<n−1,(2)l<m+n+a,(3)l=log2n,where is the number of nodes in the implicit layer; is the number of nodes in the input layer; is the number of nodes in the output layer. Is a constant between 0 and 10. The 3-layer structure of this paper is shown in Figure 7,Figure 7
3-layer BP neural network structure diagram.Step 3.
The sample data is normalized. In this paper, the maximum-minimum method is used, with the following formula.(4)xi∗=xi−xminxmax−xmin,where, xi. are the values of the variables defined in Table 1, xmax. and xmin. are the maximum and minimum values of the 109 cases.Step 4.
Construct BP neural network. This paper uses the newff function to build a BP neural network.Step 5.
The network parameter settings are shown in Table5.Table 5
Setting of BP neural network training parameters.
Parameter nameDesign valueAttributenet.trainParam.lr0.01Learning ratenet.trainParam.goal0.00001Training target errornet.trainParam.epochs1000Set the number of training stepsnet.trainParam.show25Interval parameters for displaying training resultsnet.trainParam.mc0.01Additional momentum factornet.trainParam.min_grad1e-6Minimum performance gradientnet.trainParam.max_fail6Maximum number of confirmation failuresStep 6.
BP neural network training.Step 7.
BP neural network prediction. The trained model is used to predict the test samples.
The above BP neural network discriminative process leads to the following results, as shown in Figure8 and Figure 9.
Figure10shows the training performance of the BP neural network, and we can see that the final network error is small and has a good training effect, and when the BP network is trained to the 10th generation, the training results obtained are the best; by comparing the test collusion category and the actual collusion category (Figure 11), we can see that the overlap rate between the two reaches 92.00%, and each empirical case gets a better discriminatory result with high accuracy; so it can be obtained that only two of the classification errors Figure 10 are not zero; from the histogram of the training set and the error distribution in Figure 11 we can, see that there is a small error in the training set, while the error in the test set is almost zero, which has a good effect. In Table 6, the correct rates of the three types of collusion types discriminated for 22 cases in the test set are shown, which shows that the model is objective and efficient for the automatic discrimination of the categories of collusion types.Figure 8
Error MSE drop line.Figure 9
Classification of predicted collusion categories and actual collusion categories.Figure 10
BP neural network classification error.Figure 11
Histogram of the error distribution of the training and test sets.Table 6
Classification correct rate of three types of collusion.
Type of collusionCorrect rateInterventional1.000Opportunistic0.941Cooperative0.800


## 4.2. Case Validation

Taking a case of vertical collusion in bidding for a government investment project as an example, the BP neural network automatic discriminative model trained above was used to classify it. Firstly, the data input of the BP neural network automatic discrimination model is shown in Table7; secondly, the trained automatic discrimination model is used to discriminate the types of collusion cases, and the training parameters and function forms are set as shown in the previous section; finally, the collusion cases belong to the first category, i.e. the intervention category of collusion.Table 7
efinition of case variables.
Empirical casesVariable nameRights characteristicsDepth of involvementCollusion linksMethod of collusionFieldsAreaVariable valueFirst-in-commandMeddlingBefore biddingCircumventing biddingTransportationCentral regionVariable input530623


## 5. Concluding Remarks

This paper presents an empirical analysis of collusion in bidding for government investment projects. Firstly, it divides the types of collusion through systematic cluster analysis, discovers the laws and internal links of each characteristic variable, and summarizes the characteristic laws of collusion; and establishes an automatic discriminatory model of collusion types, which is conducive to the rapid categorisation and regular summary of collusion cases.The characteristics of the tenderees’ rights, the depth of involvement, the links of conduct, the manner of conduct, the region, the field and other attributes all have an impact on the law of collusion and the division of types, and have obvious characteristics. (1) The proportion of tenderees involved in collusion as a handful is the highest of all three types of collusion, influencing tenderees in various ways. This is mainly because the market system is not yet perfect, resulting in unclear boundaries of the tenderees' power. The government and relevant units should strengthen the supervision and restraint of the tenderees' power in the future bidding collusion governance process. (2) As the legal and regulatory system is not yet perfect and the management is not yet standardized, there is a great lack of supervision before the bidding process leading to the frequent occurrence of bidding avoidance; the collusion between the tenderees and the bid evaluation experts at the bid evaluation stage is highly concealed and has a high incidence. (3) The areas where tenderee collusion occurs are closely related to the level of the local economy and can be governed in a manner appropriate to the local context.The three types of conspiracy tenderees have different rights characteristics and depth of involvement, and the links and methods of occurrence are quite different, and the fields and regions of occurrence have their own distinct characteristics, in each type of bidding collusion, the correlation between each attribute is very strong, which is conducive to discovering the law of the collusion behavior of the tenderee. By analyzing the relationship between each characteristic variable in each type of conspiracy, the motivation and characteristic law of the conspiracy are generally combined; Relevant departments should formulate local governance suggestions for different positions and fields according to the different characteristics of the three types of collusion tenderees, links, methods, regions and fields, so as to reduce the behavior of collusion in bidding, and achieve comprehensive prevention and control, focusing on prevention. This paper provides a new perspective and idea for the governance of government investment project bidding collusion through the coupled analysis of the behavioral characteristics, laws and governance of bidding collusion.However, this paper still has the following shortcomings:(1)
The analysis and research in this paper are based on the existing data, but the occurrence of bidding behavior is dynamic, and its characteristics and laws will change with time. The effect of time factor should be considered in future studies.(2)
This paper only analyzes the types and characteristics of the collusion behavior of the tenderee, and does not consider the influence variables of other subjects in the bidding process. Future research should be more comprehensive and in-depth.



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*Source: 5159393-2022-03-10.xml*