Results of the study of managerial negligence and its loss bearing in project management system based on game theory (https://doi.org/10.63386/610695)

Author information ：Yicheng Wang*

Teesside University, UK

Advanced Business Bachelor

Funding：NO

Email address list：wangyicheng_2024@163.com 

Author’s Profile：Yicheng Wang was born in Beijing, China, in 2000. From 2015 to 2018, he studied in Huairen No. 11 Middle School and received his high school diploma in 2018. From 2018 to 2020, he studied in Shanghai Jiao Tong University International University Pathway courses. In 2023, he completed the Doctor of Business Administration course in Game Theory at EU Business School under the guidance of Professor Junlin Li. From 2024, he studied in Amity Global Institute, Singapore and Teesside University, UK. Currently, he is engaged in entrepreneurial ventures and philanthropic activities while pursuing further business education.

Abstract: In the rapid development of social economy, the construction industry, as an important pillar of the national economy, not only provides a material and technical basis for economic reform and innovation, but also relies on economic development to provide important needs for itself. Especially after entering the era of big data, the construction field of engineering management project requirements are more and more high, but there is an information disconnect phenomenon in each link, information asymmetry between the participants, as well as conflict in the distribution of interests, so how to use the game theory to optimize the project management system, based on the synergistic management thinking to build a mathematical model of multi-party game clear mechanism of the whole process of engineering project management is the mechanism of the new period of scientific research scholars to explore the It is the main topic for research scholars to discuss in the new period. In this paper, after understanding the game theory and the current status of project management research in the field of construction, according to the situation of managerial dereliction of duty and the loss caused by the four different types of project internal loss and external loss of the distribution of research, and finally combined with the case study to explore the project management model based on the game theory in the field of construction and the results of empirical analyses, in order to provide a strong support for the new era of construction engineering.

Keywords: game theory; project management; managers; negligence; loss bearing

1. Introduction

In the continuous reform and improvement of China’s socialist market economic system, the industrial scale of the construction field is getting bigger and bigger, and has shown a steady growth trend in recent years, with the industrial scale hitting a record high year by year. With China’s construction field overall output growth rate rising, China’s urbanisation and construction industrialisation development pace accelerated significantly, prompting the upstream and downstream industries to flourish, and thus giving rise to a series of practical problems. In the face of the increasingly competitive market environment, the construction field gradually recognised the dereliction of duty of the project management personnel during the management and their important responsibilities, and through the analysis of the model constructed by the game theory, the process engineering management mode is proposed in line with the common interests, and the development of a collaborative management mechanism conducive to the participation of the overall goal of the project based on the optimal cost can be achieved. Therefore, scholars at home and abroad to strengthen the game theory as the core of the project management system research, and mastered the influence of the synergistic process of the game parties to achieve win-win factors, so as to provide effective management measures for the project engineering construction.

Nowadays, China’s construction field is developing faster and faster, and production safety and quality accidents occur frequently, especially in the traditional construction industry, because the engineering project involves a large property fund, the overall construction cycle is too long, and the project construction links are relatively complex, so the project construction usually ignores the balanced relationship between interests and responsibilities, resulting in frequent quality and safety, cost claims and other problems in the construction management link. Therefore, combining advanced theories to explore the problems in the construction project management system, and gradually improve the economic benefits of project management, is the main topic explored by scholars in the field of construction engineering at present. As the core theory and main method of modern microeconomics, the core idea of game theory lies in the fact that the people in the bureau choose their own maximum utility based on the probability of behaviour, which is of great significance to the whole process of construction cost management. For example, some scholars use game theory to systematically study the behaviour of owners involved in large-scale complex projects to find strategic partners. The study points out that under certain conditions, based on the game method to study the strategic interaction between the project bidders, it can be found that the provision of accurate bidding price can encourage the bidders to obtain effective compensation in the early stage; There are also scholars based on the period of delay conflict between the owner and the contractor, selecting the practice of case study which contains the main factors affecting the restoration of the project’s original schedule needs to be increased by the contractor to increase the extra The main factors are that restoring the original schedule of the project requires the contractor to increase additional expenditures, and the continuation of the previous procedures and the delayed completion of the project will cause the owner to lose. On this basis, the use of mathematical game models to analyse the behaviour and strategy of the moderator to participate in the delayed project to determine the bargaining, can help owners and contractors to comprehensively consider the delay caused by the actual project. At present, domestic and foreign experts and scholars have applied the game theory ideas to project management, but the game theory of engineering project managers dereliction of duty and their losses bear less research, so this paper mainly combines the practice of case studies to explore the model changes in which, and then put forward effective project management measures, with a view to provide strong support for the new era of construction engineering project management.

2. Analysis of how internal and external losses are allocated to different projects based on game theory

2.1 Problem assumptions

In the project management system, the use of game theory research, need to clarify its model components, including participants, action, information, continuity, strategy, support, results and equilibrium, in which participants, action, information, continuity is the composition of the game model of the rules of the game. The classification of specific games and the corresponding equilibrium concepts are shown in Table 1 below:

Table 1 Categorical analysis of game models

Information	Timing of Actions	Timing of Actions
Information	Static	Dynamic
Complete Information	Complete Information Static Game: Nash Equilibrium; Representative Figure: Nash (1950, 1951)	Complete Information Dynamic Game: Subgame Perfect Nash Equilibrium; Representative Figure: Selten (1965)
Incomplete Information	Incomplete Information Static Game: Bayesian Nash Equilibrium; Representative Figure: Harsanyi (1967, 1968)

In the case of construction project management personnel dereliction of duty, based on the game relationship between managers and shareholders, respectively, to construct a reasonable and optimal project global and members of the revenue model, and thus to analyse the corresponding loss bearing mechanism, to ensure that each member can fully demonstrate their responsibilities and capabilities, and to truly achieve the members of the maximum revenue and project global revenue maximization of the management objectives. Therefore, this study assumes that the losses of construction projects are caused by managers’ negligence without sufficient effort, after grasping the actual situation and compilation cost theory, the managers’ effort level is P_M and meets this condition, 1-P_M as the managers’ negligence, and the supervision level is P_S and meets this condition, and the cost spent by the managers under the level of effort C _M (P_M) and the cost spent by shareholders at the level of supervision C_S (P_S) as increasing functions and satisfying the following conditions:

Internal losses can be compensated for, external losses cannot, so the external losses of the project far outweigh the internal losses. Before signing the contract, managers and shareholders have symmetric information, whether C_M (P_M) or C_S (P_S) are observable, but after signing the contract, the information is asymmetric, so it is necessary to fully assess the benefit function of the project members before the contract, and thus to determine the mechanism of assuming the loss after it occurs, so as to better constrain the management project managers and shareholders. In the model study, θ_M represents the expected ideal state of the managers to obtain the benefits; θ_S represents the expected ideal state of the project shareholders to obtain the benefits; R represents the internal losses caused by the managers’ negligence, T represents the external losses caused by the managers’ negligence, α represents the allocation coefficient of the internal losses, which belongs to the proportion of the internal losses that the managers need to bear, β represents the allocation coefficient of the external losses that belongs to the proportion of external losses borne by managers.

2.2 Project global revenue maximisation model

Based on the above assumptions, the project global revenue maximisation is considered as an important issue for management and the project revenue function shown below is constructed:

In the above formula, (1-P_S)P_SR represents the internal losses incurred by managers who have been derelict in their duties during the operation of the project and this has been detected by the shareholders, and as a result of this; and (1-P_M)(1-P_S)T represents the external losses incurred by managers who have been derelict in their duties during the operation of the project but their behaviour has not been detected by the shareholders, and as a result of this.

Based on the analysis of the binary function and law enforcement calculations, U is made to complete the following partial derivatives:

Assuming that .

It is required to meet the binary function extremum condition of in Hessen’s determinant, then the global optimal solution of the project can be obtained with the following equations:

2.3 Model for maximising benefits to project members

In the case of shareholders to maintain the global optimal solution does not change, the level of effort of the project management personnel to rise or fall, it is possible to make their own earnings rise; as the optimal solution to maximize the total return of the project, the change in the level of effort of the project management personnel will make the project’s overall income decrease; and vice versa for shareholders. In this type of research, according to the actual operation of the project and the responsibility of bearing the corresponding losses, the comprehensive analysis of the project members’ earnings, to determine the behaviour of the project members to maximize earnings, whether it is in line with the conditions of the project’s overall earnings maximization, which is divided into the following cases:

First, managers bear internal losses and shareholders bear external losses. Under this condition, the project shareholders have supervised the managers’ dereliction of duty in all aspects, which can stimulate the managers’ own level of effort; and if they have not supervised the dereliction of duty, then they can improve the shareholders’ own supervisory ability. Assuming that U_M (P_M, P_S) refers to the utility function of project managers and U_S (P_M, P_S) refers to the utility function of project shareholders, then it can be obtained:

Before signing the contract, whether shareholders or managers in the P_M and P_S choice belongs to the static game behaviour, the corresponding Nash equilibrium solution is the solution of the maximum value problem ), , then it can be obtained:

Eligible:

Then the Nash equilibrium solution for the corresponding strategy can be obtained and the following conditions are met:

Combined with the equations, this way of assuming responsibility is reasonable, but it is difficult to reach the maximisation of the global benefits of the project, and the individual benefits of the project members cannot exceed the individual benefits under the globally optimal solution.

Second, managers bear the internal losses and shareholders share the external losses. Compared to the first approach, managers bear a greater proportion of the liability, which can further increase the level of managerial effort and ensure that shareholders maintain a certain level of oversight It should be noted that if the external losses are too low, resulting in shareholders bearing too little or nothing, then this can result in project shareholders failing to observe the behaviour in the form of the following:

Under certain conditions, applying the same way of solving as above can result in what is shown below:

Combined with the analysis of the above equations, it can be seen that this approach still fails to achieve consistency between global revenue maximisation and member revenue maximisation.

Third, managers and shareholders share internal losses and shareholders alone bear external losses. Under conditions where project managers are stronger, shareholders will bear more losses due to the specificities of the project, in the form described below:

Under certain conditions, the following results can be obtained by applying the same way of solving as above:

Combined with the analysis of the above equations it can be seen that this approach still fails to achieve consistency in maximising returns.

Fourth, both internal and external losses are shared by managers and shareholders. From the point of view of the overall benefits of the project, each benefit is shared by all members, and then the overall loss is also shared by all members in the following form:

Applying the solution in the same way gives the following results:

Combined with the analysis of the above equations, it can be seen that it is able to maximise both member benefits and global benefits.

3. Case studies

3.1 Modelling

A regional transport station hub project construction, for example, the initial planning budget investment of 8.827 billion yuan, the planning of the overall area of 924,400 square metres, is expected to be completed after the completion of the daily per capita traffic can reach 530,000 ~ 690,000 passengers, the overall project is divided into three project groups, a total of 19 projects, including individual construction, construction of 11 segments, the specific design is shown in Figure 1 below:

Figure 1 Project engineering diagram

As the overall transport hub project needs to have modern functions, assume the synergistic relationship of integrating the surrounding railway traffic and urban rail traffic in passenger transport, and be in line with the local economic development and external traffic demand, the composition of the main body of interest of the project is shown in Figure 2 below:

Figure 2 Composition of the project’s participating stakeholders

From the perspective of the project decision-making stage, it mainly studies the synergistic management relationship between the government departments and investors during the approval period, in which the benefits after the project application is successful and the benefits after the application is unsuccessful are the goals that the owner cares about, which can be regarded as the internal benefits; the government departments pay attention to the economic environment as well as the social benefits that are realised after the approval and implementation of the project, which can be regarded as the external benefits. According to the game theory research to construct the model shown in Figure 3 below, X represents concern, Y represents no concern, L represents decision-making behaviour approval, M represents decision-making behaviour without review:

Fig. 3 Model diagram of the two sides of the game

Table 2 Model table of both sides of the game

proprietor	government	The payoff matrix of both
follow()	review()	()
	Not review()	()
Do not follow()	review()	(0,-)
	Not review()	(,0)

Combined with the analysis of the above figure shows the final benefit of the decision points of the participating subjects, and is able to systematically study the benefit matrix between the two, as shown in Table 3 below:

Fig.4  Payoff matrix for both sides of the game

Table 3  Revenue matrix for both sides of the game

proprietor	government	The payoff matrix of both
follow()	review()	()
	Not review()	()
Do not follow()	review()	(0,-)
	Not review()	(,0)

On this basis, using the comprehensive evaluation method, the evaluation of the tender control price of 90,772,394,480 yuan, a total of 11 valid tender offers received, evaluation relative to the evaluation benchmark is higher than a percentage point deduction of 2 points, lower than a percentage point deduction, out of one hundred points. Combined with the game thinking and the corresponding model can be obtained as shown in Table 4 below evaluation results:

Table 4 Results of experimental studies

No.	Bidder	Bid Price (10,000 Yuan)	Evaluation Score	Rank
1	A	7354.586571	88.41182034
2	B	7680.123921	92.14815549
3	C	7800.130999	93.52552944
4	D	7905.374958	94.73346058
5	E	8018.992783	96.03750226
6	F	8162.608511	97.68584305	2
7	G	8434.870820	98.37856570	1
8	H	8497.421718	96.94271744	3
9	I	8581.152624	95.02068467
10	J	8618.711672	94.15852129
11	K	8769.495937	90.69728681

Combined with the analysis of the above table can be seen, according to the bidding analysis issued by the owner, it can be seen that the optimal offer is not only in line with the score of the effective offer, but also to protect the bidder’s revenue to maximise. There is visible, the use of game model calculation and analysis to select the real bidding offer data, the actual bidding offer target value in the scoring has obvious offer advantage.

From the perspective of project construction, the construction phase, which has the longest construction production cycle, is the focus of overall project cost control and quality management concerns, and since project engineering issues directly determine the safety and investment efficiency of the construction project, which is closely related to the lives and properties of the residents of the society, the study systematically investigates the game of all parties based on the payoff matrices of the owner, the supervisor, the contractors, and the NPOs, as shown in Table 5 below Payment results:

Table 5 Benefits Matrix for Owners, Supervisors, Contractors, and NPOs

B and C	D	A	A, D
		A (Y), D (0)	(F₁+F₂-C-kP-M) R-F P-R-F₂ M-N
		A (Y), D (1-0)	(f₁+f₂-c-kp-m) r-f p-r-f₂ -n
	Supervise (β)	A (1-Y), D (0)	(F₁+F₂-C-kP-M) R-F P-R-F₂ M-N
Rent-seeking Supervise (α) (P=1)		a (1-y), d (1-0)	(-C-kP-M) R P-R-N
		A (1-Y), D (0)	(F₁+F₂-kP-M) R-F P-R-F₂ M-N
	Do not Supervise (1-β)	a (1-y), d (1-0)	(-kP-M, R, P-R, -N)
	Supervise β	Not Discovered	(-C,0,0,-N)
No Rent-seeking Supervise (1-α) (P=1)		Not Discovered	(0,0,0,-N)

Combined with the analysis of the above table, the owner’s expected revenue will follow the increase in the level of punishment and continue to decline as the loss expansion factor and supervision costs increase. Under the condition of specifying the probability of owner’s supervision, regardless of how the equilibrium return of the contractor will change with the level of income and the amount of punishment, the expected return of the supervisor at the equilibrium point at this point is zero. Under the same conditions, the contractor’s expected return is also zero, while the NPO’s equilibrium return will continue to rise following the increase in profitability. From the perspective of the supervisor and the contractor, both are selected by the owner to supervise based on their own interests and project quality requirements; from the owner’s perspective, the optimal equilibrium probability of actual supervision is positively correlated with the contractor’s returns, the cost of bribes to the supervisor, and the probability of rent-seeking detected by the NPO, and negatively correlated with the probability of the owner’s discovery of the rent-seeking behaviour, and the fines; from the NPO’s perspective, if the actual rent-seeking behaviour probability is greater than the specified value, then the net benefit to the non-profit organisation will exceed zero, and vice versa, it will be less than zero, and there will be no benefit under equal conditions.

3.2 Regulatory mechanisms

In terms of the bidding process of the project, the owner, after releasing the tender information, will call multiple bidders to choose a low contract price, which can control the investment cost and improve the project to obtain revenue. The key to whether the bidder is successful or not lies in determining the expected value of the bid price and accurately controlling the general production cost of the subject matter. It can be seen that, in combination with the basic principle of the lowest standard and based on the synergistic management mechanism shown in Figure 5 below, the bidding stage can be further safeguarded by the optimal equilibrium of the offers in accordance with the game analysis shown in Figure 6below.

Figure 5 Co-management mechanism

Figure 6 Synergistic management measures based on game analysis

In the process of multi-stage and multi-object collaborative management of the project, the phenomenon of contractors and supervisors colluding to defraud the project quality problems is inevitable. Starting from different participants, the rational use of game theory to study the results of project quality supervision, fundamentally safeguard the quality of the project, reduce rent-seeking behaviour, based on the construction requirements to form a collaborative management mechanism, increase the intensity of the project penalties, the establishment of a standardized supervision mechanism, the rational use of supervision channels, the formation of a positive feedback system, which will help the project management personnel to conscientiously carry out their own duties and reduce unnecessary economic losses. According to the interests of the participants, the organisation of the collective activities of the different subjects of the project team, the systematic assessment of the team organisational integration whether to achieve the desired goals, if not also need to re-identify the project interests of the main body of the game between the relationship between the interests of each other, a clear degree of interest associated with each other, and at the same time to understand the configuration of the relationship between the team members, to ensure that it can achieve, and even beyond the initial stage of the project objectives. In addition, the construction project management of all aspects of the project face many requirements, the practice of operation may occur more problems, the communication between the main body of interest in the complexity of the information exchange, so as long as the project management is not completely finished, it is necessary to systematically understand according to the implementation of the project to the main body of interest of the integration of the configuration of the relationship between the changes that occur, and in accordance with the actual situation to be improved, the implementation of the synergistic management of the measures in an orderly manner.

Conclusion

In summary, this study is based on the information sharing conditions, based on the game theory to construct a safe and reasonable loss bearing mechanism, for the construction project to achieve the goal of maximising the overall revenue and maximising the revenue of the members to provide a strong support. In the future, we should start from different directions, continue to construct the corresponding game model, explore the loss bearing method under the condition of information asymmetry, as well as the measures to deal with the problem, so as to provide strong support for the construction management of building projects in the new era.

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