A Determining Method of the Project Quality Guarantee Deposit under the Condition of Asymmetric Information with the Contractor’s Credit Level into Consideration

On the basis of analyzing the relationship between a contractor’s credit, project quality assurance, owner’s monitoring level, and the quality guarantee deposit, the quality expected benefit model of the owner and the contractor was constructed under the conditions of symmetric information and asymmetric information, in which the owner assumed the primary responsibility for the project quality, the project characteristics were incorporated, the credit level was taken as the contractor’s decision variable, and the project quality monitoring level and detention of the quality guarantee deposit were taken as the owner’s decision variables. In light of the maximum value principle, an optimal solution to the owner’s quality monitoring decision and the quality deposit detention strategy was derived; through the simulation calculation, the decision-making results under different information conditions were analyzed.


Introduction
Project quality is one of the elementary objectives of a construction project. Under the market economy, a contractor, as the undertaker and the subject of liability of implementing the construction project, plays a fundamentally decisive role in the construction quality based on the quality assurance system under its credit level. As the guarantee mode of the project quality and a means of contract restraint of propelling contractors to improve their quality assurance credit levels, quality guarantee deposits have been widely adopted in the project contracting community over a long time. e amount of a quality guarantee deposit is usually determined in accordance with the relevant regulations or with reference to the experience in projects or market practices.
is relatively onefold approach leads to an unreasonable quality guarantee deposit of varying degrees. Sometimes, the quality guarantee deposit for a contractor with a high credit level is high, which causes the contractor's capital e ciency loss and further increases the contract price at large if things continue this way; but sometimes, the quality guarantee deposit for a contractor with a low credit level is insu cient, which evidently increases the quality risk and the quality monitoring burden of the owner. ere is still a lack of research on the mode to reasonably determine quality guarantee deposits [1].
Many scholars have begun to study the problem of quality control under asymmetric information [2][3][4][5][6][7]. e paper systematically studied the quality control in the supply chain of a water conservancy construction project [6,7]. e owner and the contractor's quality bene t model in the supply chain was established, and an optimal solution to the owner's quality monitoring decision under the condition of asymmetric information was concluded. For the construction and implementation of the project, this paper helped the owner make an effective detention strategy for the quality guarantee deposit from the owner's standpoint with the impact of the contractor's credit level into consideration, which led to a more reasonable, more scientific, and more comprehensive detention of the quality guarantee deposit [8]. It was concluded that an optimal credit level would bring a win-win result for the owner and the contractor.

Expected Benefit of the Owner and the Contractor
is section is built on a two-level supply chain system of a construction project composed of an owner and a contractor who both had a neutral risk preference [8]. e owner was the dominant and the contractor was the follower, but they both pursued a maximized personal expected benefit. e owner was able to learn of the contractor's credit level based on which the detention proportion of project quality guarantee deposit and the monitoring level for the contractor were determined [9][10][11][12]. e expected benefit obtained by the owner in the construction project is (1) In the equation, E(A) refers to the owner's expected benefit; A 1 refers to the benefit when there is a qualified project; A 2 refers to the benefit when there is an unqualified project; R b refers to the contractor's credit level; I a refers to the monitoring level of the owner for the contractor; S(R b ) refers to the quality guarantee deposit; B a (I a ) refers to the owner's quality monitoring cost; and V refers to the total contract price paid by the owner to the contractor at the project settlement. e expected benefit received by the contractor in the construction project is (2) In the equation, E(B) refers to the contractor's expected benefit, B r (R b ) refers to the contractor's credit level, and P refers to the cost of project reworking (or maintenance) when the owner finds quality problems by the contractor.

The Detention Strategy of the Quality Guarantee Deposit with Symmetric Information
With symmetric information, the owner is able to observe the contractor's credit level R b by the credit rating system and results, so the owner's quality monitoring decision is an optimization problem [13][14][15]; i.e., At the same time, the contractor participation constraint is In the equation, M is a normal number, and from (4), Substituting (5) into (3), we have e first-order partial derivative of the owner's quality monitoring level I a is evaluated in (6) and made it 0.
e owner's loss due to quality defects caused by the contractor is bigger than the contractor's reworking expenses, so (A1-A2-P) (1 − Rb) ≥ 0, and therefore, there is an extreme value in the above equation. e owner's quality monitoring cost consists of two parts [16]: one is the direct monitoring cost of the owner C 1 and the other is the indirect monitoring cost. e indirect cost coefficient is k a , so we can assume that the owner's control cost is as follows [17]: B a * (I a ) � k a * I a 2 + C 1 * . e contractor's credit cost consists of two parts: one is the direct cost of safeguarding credit C 2 and the other is the indirect cost. e indirect cost coefficient is k r , so we can assume that contractor's credit cost is B r * (R b ) � k r * R b 2 + C 2 * . e second-order partial derivative in (3) with respect to I a is d 2 E(A)/dI 2 a � −B a ″ (I a ) < 0, so there is a maximum value for (3); at the same time, the owner's quality monitoring decision is I a I * a in (7). After putting equation (7) and the owner's monitoring cost together, I a * is obtained: e detention strategy of the quality guarantee deposit is e detention of quality guarantee deposit S * * with symmetric information is

The Owner's Quality Control and Detention Strategy of the Quality Guarantee Deposit with Asymmetric Information
Asymmetric information can be defined as information available about a risk category that cannot be observed by both parties to the transaction at the same time and for which neither party has complete information about the other. Asymmetric information as opposed to symmetric information means that under the condition of a given total amount of information that can be produced by the market economy, in the total amount of information market players do not have access to any information, do not have timely access to information, and have no knowledge of the accuracy of information [18,19]. With asymmetric information, the contractor's credit level is completely unobservable to the owner, and the problem between the owner and the contractor is still an optimization problem [20][21][22]. e owner maximizes its own expected benefit by selecting its corresponding monitoring level I * * a [6], namely, Suppose the contractor's credit level and R b follows the probability distribution of probability density f(R b ). Under the condition of asymmetric information, the owner, as the leader of the game, has the advantage of being one step ahead, but when it is pursuing its own expected benefit maximization, given that the contractor is the follower, the owner will be subject to corresponding constraints from the contractor [23][24][25][26], namely, e first-order partial derivative of the equation is evaluated with respect to R b : R b is used as the control variable, the classical control problem is solved by the maximum principle, and the Hamiltonian function of the problem is established, namely, Among them, λ is a covariate. e governing equation is e mimicry equation is From the above equation, we have where F(R b ) is the probability distribution function of the contractor's credit level and C is a constant. Since z 2 H/z 2 I a � −B a ″ (I a )f(R b ) < 0, the second-order partial derivative is less than zero, so there is a maximum value on the optimal control issue. According to the equation (13) and the contractor's control cost, Detention strategy for quality guarantee deposit can be obtained as Detention S * * of quality guarantee deposit with asymmetric information is When the owner's monitoring cost function and the contractor's credit cost function are quadratic functions, the owner's monitoring level is related to the contractor's credit level. Different values of I a are selected, and the square matrix results of the contractor's credit level and the detention strategy of quality guarantee deposit under different information conditions when I a takes different monitoring levels are shown in Figures 1-6.

Results
(1) Under the conditions of symmetric information and asymmetric information, for the owner's certain monitoring level I a, , detention of the owner's quality guarantee deposit decreased with the increase of the contractor's credit level R b ; for the contractor's certain credit level R b , detention of the owner's quality guarantee deposit increased with the increase of the contractor's credit level S(R b ); but under the condition of asymmetric information, for the owner's same monitoring level I a , detention of the quality guarantee deposit was relatively high.    expected benefit E(B) decreased with the increase of the owner's monitoring level I a .
(3) Under the condition of asymmetric information, the information of both parties was unobservable, and the contractor's detained quality guarantee deposit was relatively small when the owner's monitoring level was at a low level. With the improvement of the contractor's credit level, the amount of the detained quality guarantee deposit had a continuous decline until it reached a minimum amount. erefore, the amount of the detained quality guarantee deposit under the condition of asymmetric information was higher than that of symmetric information, indicating that the owner should keep a relatively high monitoring level to ensure the project quality. (4) e balance point between the owner's expected benefit and the contractor's expected benefit corresponded to the fact that the contractor's credit level R b decreased with the increase of the owner's monitoring level I a . With the increase of the contractor's credit level, the owner's expected benefit increased, while the contractor's expected benefit decreased; at the same time, at different quality monitoring levels from the owner, the contractor's credit levels at which both sides reached the desired benefit equilibrium point were also different.   Mathematical Problems in Engineering erefore, both the owner and the contractor should have an appropriate monitoring level and a proper credit level so that both sides can realize their own maximum expected benefit.

Conclusion
is paper studied the determination method of the quality guarantee deposit of construction under different information conditions with the contractor's credit level taken into account. By introducing the variable of the contractor's credit level, potential moral hazards for a contractor in a construction supply chain was improved, and the corresponding quality benefit model was established. With living cases, the owner's and the contractor's quality guarantee deposit detention strategies and quality benefits under different information conditions and at different credit levels of the contractor were analyzed, providing owners with the basis to make effective monitoring strategies. From the perspective of the final expected benefits of both parties, as the owner's quality monitoring level increases, the smaller the equilibrium point of the contractor's credit level where both parties seek maximum benefits, which indicates that the owner's strong supervision will reduce the requirement of the contractor's credit to a certain extent, so the owner should choose the appropriate quality monitoring level.   Data Availability e datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.