CN112200409A - Multi-party game based engineering quality management analysis method - Google Patents
Multi-party game based engineering quality management analysis method Download PDFInfo
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Abstract
The invention relates to an engineering quality management analysis method based on a multiparty game, which comprises the steps of constructing a construction unit and construction unit complete information static game model and a construction unit and supervision unit complete information static mixed strategy game model according to the distribution of construction units and game factors between the construction units and the supervision units; and solving Nash equilibrium solutions of the construction unit and construction unit complete information static game model and the construction unit and supervision unit complete information static mixed strategy game model, and solving the income expectation and analysis result of each participant in the Nash equilibrium state. The invention analyzes the functions and behaviors of all participants in engineering construction, determines the necessity of playing games for the participants in engineering construction and operation stages, establishes a corresponding game model, finds out Nash equilibrium points through research and analysis, and analyzes the economic benefits of the Nash equilibrium points, so that the pareto is optimal, namely the total social benefits are maximized.
Description
Technical Field
The invention relates to the technical field of engineering construction, in particular to a process quality management analysis method based on a multi-party game.
Background
When the building industry in China just starts, because the novel industry is introduced from abroad at that time, the practical construction experience is lack and the profit is huge, and in addition, the novel industry is not restricted by corresponding perfect laws and regulations, the phenomena of work stealing and material reduction in the whole engineering construction industry are very serious, a plurality of bean curd residue engineering and important construction safety accidents occur, the serious damage is caused to the economic development in China and the health and safety of people in society, so that the problem is considered to be the oriented thinking that the construction unit is extremely unfair as long as the engineering accidents occur at present.
The multiple parties in engineering quality management comprise a construction unit, a general contract unit, an investigation and design unit, a supervision unit, a construction unit, a government quality supervision organization, an engineering material equipment supplier and the like, and because the functions and the benefit targets of the engineering quality management are different, the influence of the engineering quality management on each stage of the engineering construction is greatly different, and the engineering quality management is closely related and interacted. The project quality is a result of the joint action of each participating subject on the basis of the unified management policy and the target, but each participating subject can not necessarily do some behaviors of violating morals or even laws and regulations under the drive of benefits under various practical conditions, so each participating subject needs to play games.
In the prior art, Liu super and Xia nan station analyze the reasons of the problem of the engineering quality in three aspects of project positioning, system constraint and daily on-site management and control at the angle of a construction unit, and propose quality management and control measures from the aspects of investment, construction period and construction unit selection contract agreement patrol system and on-site management and control so as to achieve the aim of improving the quality of the construction engineering.
The beam nation and the beam connection consider that the effective measure for engineering quality management is to manage the quality in the construction process, analyze and discuss the problems in the construction process and the engineering quality management measures, and consider that the beam connection also controls the engineering quality of the road and the bridge from the technical aspect.
Research in its published civil engineering quality evaluation from building safety indicators shows that the inspection efficiency of building construction is low and serious defects in the construction process are the main causes of building and construction accidents, so that a comprehensive civil engineering quality evaluation method is proposed, which includes quality system level indicators, defect loss, engineering program stability and construction safety indicators-quality systems are widely considered from the aspects of project organization potential, building material suppliers and construction companies, etc., and shows that the implementation of civil engineering quality and safety management mechanisms (technical regulations, certification, insurance, implementation of quality systems) should establish scientific-based engineering quality evaluation standards and structural safety.
Turgut Acikara et al thinks that because construction projects have complexity and many project risks, many small and medium-sized enterprises easily ignore the importance of project quality management, companies managing project quality can reduce risks caused by project period control and cost dependence, participants who are also lack of quality management can have negative effects on project management and enterprise competitiveness, and investigate, analyze and analyze the attitude of Turkish construction project participants on the quality management.
Although the existing research and analysis on the influence elements of engineering quality management is relatively comprehensive, the research on the participating subjects in the engineering quality management is relatively less, the participating subjects in the engineering quality management are operators of the whole engineering construction and play different roles in the engineering quality management, the relationship among the participating subjects is complex, and the participating subjects are likely to perform actions of damaging the engineering quality under the drive of benefits, so that how to reasonably research and analyze the engineering quality management is a problem to be solved at the present stage.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides an engineering quality management analysis method based on a multi-party game, and solves the problem that the existing engineering quality analysis lacks of participating subject analysis.
The purpose of the invention is realized by the following technical scheme: a project quality management analysis method based on multiparty gaming comprises the following steps:
a model construction step: constructing a construction unit and construction unit complete information static game model and a construction unit and supervision unit complete information static mixed strategy game model according to the game factors between the construction unit distribution and the construction unit and supervision unit;
and (3) economic benefit analysis step: and solving Nash equilibrium solutions of the construction unit and construction unit complete information static game model and the construction unit and supervision unit complete information static mixed strategy game model, and solving the income expectation and analysis of each participant in the Nash equilibrium solution.
Further, the gaming factors include participants, actions, information and payments of the various participants.
Further, the static game model for constructing the complete information of the construction units and the construction units comprises:
setting a construction unit and the construction unit as participants, and assuming that the construction unit has professional detection equipment and personnel, has accurate rechecking work check on the construction unit, and receives a check result provided by the construction unit;
by YnRepresenting a particular action of participant I in a game strategy model, BⅠ＝{YnRepresents a combination of all actions available for selection of I; is prepared from radix Aconiti PratidisnRepresenting a specific action of participant II in the game strategy model, BnRepresenting a specific action of participant II in the game strategy model, BⅡ＝{ХnRepresents the combination of all actions available for selection by II;
assuming that a participant accurately knows the information of the other participant, the game countermeasure model is clarified into a complete information static game model;
let WnAnd paying for the nth participant, wherein n is I and II. Assuming that the detection cost of a construction unit is c, the cost saved by the construction unit due to providing unqualified data is m, if the construction unit detects the quality problem, the saved cost m is not collected, meanwhile, the construction unit is risk compensated, and the compensation coefficient is i, namely the loss of the construction unit is im.
Further, the solving of the nash equilibrium solution of the complete information static game model of the construction unit and the construction unit includes:
setting alpha and beta as the qualification probability and the inspection probability of a construction unit and a construction unit respectively, and further obtaining the income expectation of the construction unit and the income expectation of the construction unit according to the payment matrix;
obtaining Nash equilibrium solution alpha by carrying out bias derivation on the construction unit income expectation and the construction unit income expectation*,β*。
Further, the solving for revenue expectations of the participants at the Nash equilibrium solution and the analyzing includes:
in the construction unit and construction unit complete information static game model, Nash equilibrium solution alpha of the construction unit and the construction unit is solved*,β*Bringing the income expectation of the construction unit and the income expectation of the construction unit into the income expectation of the construction unit to obtain the income expectation of the construction unit and the income expectation of the construction unit at the Nash equilibrium solution;
and analyzing the income expectation of each participant at the Nash equilibrium point in the model to judge whether the quality behavior of each participant is qualified.
Further, the constructing of the construction unit and supervision unit complete information static mixing strategy game model comprises:
setting supervision units and construction units as model participants and using VnRepresenting a particular action of participant x in the game strategy model, Ex＝{VnRepresents a combination of all actions from which x can be selected; likewise, with UnRepresenting a particular action of participant y in the game strategy model, Ey＝{UnRepresents the combination of all actions available for y to select;
assuming that the participant supervision unit and the construction unit know the action strategy information of the two parties, the game model is clarified into a complete information static mixed strategy game model;
let O benAnd paying for the nth participant, wherein n is x and y. The profit of the advanced construction process that the construction unit makes the quality qualified is m, the cost obtained by making the quality unqualified by saving the cost is w, and therefore the quality unqualified in the construction unit is not detectedThe hourly profit is w + m; the inspection cost of the supervision unit is d, the reward coefficient is l, and the proctor unit gains ld-d when inspecting the quality problem. The penalty coefficient is gamma, and the loss is w-gammam when the quality of the construction unit is unqualified and is detected.
Further, the solving of the nash equilibrium solution of the construction unit and supervision unit complete information static mixed strategy game model includes:
setting lambda and eta as the probability of supervision unit inspection and the probability of construction unit engineering qualification respectively, and further obtaining the income expectation of supervision units and the income expectation of construction units according to the payment matrix;
and obtaining Nash equilibrium solution eta by carrying out bias derivation on the income expectation of the supervision unit and the income expectation of the construction unit*,λ*。
Further, the solving for revenue expectations of the participants at the Nash equilibrium solution and the analyzing includes:
in the construction unit and supervision unit complete information static mixed strategy game model, Nash equilibrium solution eta of supervision unit and construction unit is obtained*,λ*Bringing the income expectation of the construction unit and the supervision unit into the income expectation of the construction unit and the supervision unit to obtain the income expectation of the construction unit and the income expectation of the construction unit at the Nash equilibrium solution;
and analyzing the income expectation of each participant at the Nash equilibrium point in the model to judge whether the quality behavior of each participant is qualified.
The invention has the following advantages: a project quality management analysis method based on a multi-party game determines the necessity of game playing on participants in the engineering construction and operation stages by analyzing the functions and behaviors of the participants in each stage, establishes corresponding game models for construction units, supervision units and construction units respectively, finds Nash equilibrium points through research and analysis, and analyzes economic benefits of the Nash equilibrium points to optimize the pareto, namely maximize the total social welfare.
Detailed Description
The invention relates to an engineering quality management method based on a multi-party game, which comprises the following steps:
1. game of construction unit and construction unit
The following model assumptions are made from relevant knowledge of game theory for engineering projects:
(1) the participators: in a game countermeasure model for engineering quality management, a main body in a game assumes two participants, namely a construction unit (participant I) and a construction unit (participant II). Here, the problem study requires the following assumptions: firstly, construction units have professional detection equipment and personnel, and recheck work of the construction units is accurate; and receiving the inspection result provided by the construction unit.
(2) And (4) action: by YnRepresenting a particular action of participant I in a game strategy model, BⅠ＝{YnRepresents a combination of all actions available for selection of I; also by using PIKHznRepresenting a specific action of participant II in the game strategy model, BnRepresenting a specific action of participant II in the game strategy model, BⅡ＝{ХnRepresents the combination of all actions available for II to choose from. Therefore, there are: y is1: quality of acceptance behavior, Y2: an unqualified quality behavior; pivot piece1Checking construction Unit Mass behavior2-not checking the construction unit quality behaviour; b isⅠ＝{Y1,Y2}，BⅡ＝{Х1,Х2}。
The corresponding action combination of the model comprises: (Y)1,Х1),(Y1,Х2),(Y2,Х1),(Y2,Х2)。
The construction unit pays the detection cost to carry out quality behavior inspection on the construction unit, and can obtain certain compensation after detecting the quality problem, so the construction unit can select one behavior of obtaining unqualified compensation of the construction unit quality through inspection and not checking the construction unit quality to ensure the maximum benefit of the construction unit. The construction entity obtains one of the gains by selecting to provide the qualified quality behavior to avoid checking for loss of the quality behavior and risking that the unqualified quality behavior is not checked to ensure the maximum gain of the construction entity.
(3) Information: the information is the primary basis for the game of the construction unit and the construction unit. The characteristics and the behaviors of the game main body are combined with the information to be analyzed, and the decision which is most beneficial to the game main body can be made. For research reasons, it is assumed that each participant in the gaming model has an accurate knowledge of the slaving strategy of the other participants, i.e., the model assumes that the participant's information is complete. Based on the assumptions, the game strategy model is clarified into a complete information static game model.
(4) And (4) payment: let WnAnd paying for the nth participant, wherein n is I and II. Assuming that the detection cost of a construction unit is c, the cost saved by the construction unit due to providing unqualified data is m, if the construction unit detects the quality problem, the saved cost m is not collected, meanwhile, the construction unit is risk compensated, and the compensation coefficient is i, namely the loss of the construction unit is im. The construction unit does not check the quality problem of the construction unit, but if the construction unit has the quality problem, the construction unit bears the cost m saved by the construction unit and bears the loss im caused by the quality problem, so the loss of the construction unit for processing the unqualified quality behavior of the construction unit is m + im.
Thus, WⅠ(Y1,Х1)＝0，WⅡ(Y1,Х1)＝-c，WⅠ(Y1,Х2)＝0，WⅡ(Y1,Х2)＝0， WⅠ(Y2,Х1)＝-im，WⅡ(Y2,Х1)＝-c+im，WⅠ(Y2,Х2)＝m，WⅡ(Y2,Х2)＝ -m-im。
Assuming that alpha and beta are respectively the qualification probability and the inspection probability of a construction unit and a construction unit, a payment matrix under the following mixed strategy can be obtained, and the following table represents a game model for engineering quality management of the construction unit and the construction unit;
the revenue expectation for the building unit is:
HⅠ(α,β)＝α[(β×0)+(1-β)×0]+(1-α)[β(-im)+(1-β)m]
＝(1-α)(1-β-iβ)m
the revenue expectation for the construction unit is:
HⅡ(α,β)＝β[α(-c)+(1-α)(im-c)]+(1-β)
×[α×0+(1-α)(-m-im)]
＝β[2im-2αim+m-αm-c]-(1-α)(1+im)
is provided with (alpha)*,β*) For mixed Nash equilibrium solutions, where 0<α*,β*<1, respectively solving partial derivatives for the income expectation formula of a construction unit and the income expectation formula of the construction unit to obtain:
order to
I.e., (. beta.)*+iβ*-1)m＝0、2im-2α*im+m- α*The Nash equilibrium solution of the construction unit and the construction unit can be obtained when m-c is 0:
so that the construction units can be known
The probability of the construction is used for making qualified quality behaviors, and the construction units are
The probability of (2) checking the quality behavior of the construction unit. That is, the probability that the construction unit will make a qualified quality action
Then, the optimal selection of the construction unit is to check the quality behavior of the construction unit; when the construction unit checks the probability of the quality problem of the construction unit
Then it is most preferable that the construction unit make the quality-qualified action.
From the above analysis, it can be seen that the game mixing Nash balance among participants in the engineering quality management is related to the inspection cost c of the construction unit, the unqualified quality behavior of the construction unit is found out and related to the compensation coefficient i of the construction unit and the cost m saved by the unqualified quality behavior of the construction unit. The following conclusions were drawn from the hybrid nash equilibrium:
(1) only if the probability of the construction unit to the quality behavior check of the construction unit is higher than beta*In the process, the optimal selection of a construction unit is to make qualified quality behaviors, so that the construction unit can be fully ensured not to influence the engineering quality management due to other unit reasons in the construction stage, and important construction conditions such as construction conditions, materials and the like are fully ensured;
(2) when the construction unit increases the compensation coefficient i for the construction unit, the Nash equilibrium is solved*The inspection probability beta of a construction unit is slightly lower than that of the previous construction unit, and the optimal choice of the construction unit still makes qualified quality behaviors; nash equilibrium solution alpha when the compensation coefficient is increased*Will increase, which means that the construction unit is more willing to make a qualified quality behaviour than before, the optimal choice of construction unit is still to check its quality behaviour;
(3) when the inspection cost c of a construction unit is reduced or the cost m saved by the construction unit making unqualified quality behaviors is reduced, the probability alpha of the construction unit making qualified quality behaviors is slightly lower than that before, and the optimal choice of the construction unit still checks the quality behaviors.
Therefore, two ways for ensuring the engineering quality management are provided for a construction unit: firstly, the inspection cost of a construction unit is reduced; and secondly, the compensation coefficient of the construction unit to the unqualified quality behavior is improved. When the compensation coefficient is determined, the engineering practice is combined, all factors possibly causing unqualified quality behaviors of related subjects are comprehensively analyzed, and the compensation coefficient is reasonably determined.
From the pure theoretical point of view, the inspection probability beta of a construction unit*Is completely linearly related to its compensation factor i, but this is not the case in engineering practice. The compensation factor usually cannot exceed a certain range due to various laws, regulations and regulations in the engineering industry and the limitation of manpower and material resources of construction units. In mind, the larger the compensation coefficient i is, the stronger the warning effect on the construction unit is, and the psychological security of the construction unit is easily caused, which leads to the inspection probability beta*Extremely low and vice versa.
Since the construction units and the construction units are in different positions in engineering quality management, when the responsibility and obligation of a plurality of construction unit parties are not realized, the construction units are inspectors, but the construction units are inspectors serving the construction units for the whole engineering, so that the construction units and the construction units can be reasonably grasped in all dimensions when playing games, and the construction units are not difficult to report intentionally. Therefore, in most cases, the construction unit does not make a compensation mechanism, but carries out related work by reminding the construction unit to complete and modify.
Although the construction unit needs to complete the preparation work of supervision, coordination, management and construction conditions among units such as reconnaissance, design and material suppliers, the work cannot be used as a lost way for the construction unit because any push-off is pale and weak before the project quality management. Therefore, the practioner considers that a supervision and management system should be established for the relevant working conditions of the construction units to ensure that the construction units can fairly cooperate under the relatively weak condition and ensure the smooth progress of the engineering quality management.
2. Game of supervision unit and construction unit
On the premise that a construction unit selects an advanced construction process, according to the relevant knowledge of the game theory, the following assumptions are made for the game model:
(1) the participators: in the project quality management participant game model, participants have a supervision unit (participant x) and a construction unit (participant y). The construction unit is not qualified in terms of engineering quality even if the advanced construction technology is selected and used, and the quality problem of the construction unit can be detected when the supervision unit selects and checks.
(2) And (4) action: by VnRepresenting a particular action of participant x in the game strategy model, Ex＝{VnRepresents a combination of all actions from which x can be selected; likewise, with UnRepresenting a particular action of participant y in the game strategy model, Ey＝{UnRepresents the combination of all actions available for y to select.
Thus having a value of V1: qualified engineering quality, V2: unqualified engineering quality, U1: checking the quality of the project, U2: the engineering quality is not checked; wx＝{V1,V2}，Wy＝{U1,U2}。
Correspondingly, the action combination of the model comprises the following steps: (V)1,U1),(V1,U2),(V2,U1),(V2,U2)。
The action participants selected from their alternatives from the group that had been analyzed by the study to give the most favorable selection. In the game of engineering quality management, a supervision unit selects whether to check the engineering quality or not to obtain the maximum benefit of the supervision unit for the consideration of the benefit of the supervision unit; and after selecting an advanced construction process, a construction unit controls the engineering construction to enable the engineering quality to be qualified, or obtains the maximum benefit in a mode of saving cost and enabling the engineering quality to be unqualified.
(3) Information: the information is used for analyzing the characteristics and the behaviors of the game main body in a combined manner, so that the decision which is most beneficial to the game main body can be obtained. For the purpose of model research, it is assumed that the action strategies of the quality management participant supervision unit and the construction unit are accurately known to each other, i.e. the model assumes that the information of the participants is complete. Based on the assumptions, the game model is clarified into a complete information static hybrid strategy game model.
(4) Strategy: in this problem, the strategy is an action rule for the administrative unit and the construction unit to maximize their own benefits after performing research and analysis on given information.
(5) And (4) payment: the payment refers to the cost or expense paid by the supervision unit and the construction unit in the game after the supervision unit and the construction unit are selected and combined. Let O benAnd paying for the nth participant, wherein n is x and y. The profit of the advanced construction process that the construction unit makes the quality qualified is m, and the cost obtained by making the quality unqualified by saving the cost is w, so the profit w + m is obtained when the quality unqualified of the construction unit is not detected. The inspection cost of the supervision unit is d (d)>0) The reward coefficient is l, and the yield ld-d is obtained when the quality problem is checked by a supervision unit. The penalty coefficient is gamma, and the loss is w-gammam when the quality of the construction unit is unqualified and is detected.
Therefore, there are: o isx(V1,U1)＝-d，Oy(V1,U1)＝m，Ox(V1,U2)＝-d+ld， Oy(V1,U2)＝w-γm，Ox(V2,U1)＝d，Oy(V2,U1)＝m，Ox(V2,U2)＝d， Oy(V2,U2)＝m+w。
And the lambda and the eta are respectively the probability of supervision unit inspection and the probability of construction unit engineering qualification. According to the assumptions, a payment matrix under a hybrid strategic game model can be obtained, and the following table represents a game model of a supervision unit and a construction unit;
according to the payment matrix of the model, the expectation of the supervision unit and the construction unit can be obtained;
the revenue expectation for the construction unit is:
Zx(η,λ)＝η[(λm)+(1-λ)m]+(1-η)[λ(w-γm)+(1-λ)(m+w)]
＝η(λγm+λm-w)+w+m-λm(γ+1)
the revenue expectation of the proctoring unit is:
Zy(η,λ)＝λ[η(-d)+(1-η)(-d+ld)]+(1-λ)[ηd+(1-η)d]
＝λd(l-lη-2)+d
is provided with (eta)*,λ*) For mixed Nash equilibrium solutions, where 0<η*,λ*<1, respectively calculating the deviation of the income expectation formula of a construction unit and the income expectation formula of a supervision unit, and obtaining:
order to
I.e. lambda*γm+λ*m-w＝0，d(l-lη*-2)＝ 0(d>0) (ii) a Therefore, the mixed Nash equilibrium solution of the construction unit and the supervision unit can be obtained as follows:
the probability that the construction unit uses the advanced construction process to make qualified quality is known as
The supervision unit will be
The probability of (2) is used for checking the quality condition of the advanced construction process used by a construction unit. According to the Nash equilibrium solution of the hybrid game model, the following conclusions are obtained:
(1) the reward coefficient l of the supervision unit is a factor which uniquely determines whether the construction unit uses an advanced construction process to make qualified project quality, when the reward coefficient l is less than 2, the optimal selection of the construction unit is that the project quality is not qualified, only when the reward coefficient l is greater than 2, the optimal selection of the construction unit is that the project quality is qualified, the greater the reward coefficient l is, the higher the possibility that the construction unit makes qualified quality behaviors is, but when the reward coefficient l is 4, the probability eta that the construction unit construction quality is qualified is 1/2.
(2) The probability of the regulatory unit making a qualified quality is related to the profit m, the penalty factor r and the cost saved w. The probability lambda of the supervision unit for checking the quality problem is positively correlated with the profit m and the fine coefficient r, and inversely correlated with the cost w saved by unqualified engineering quality. When the cost w of the construction unit is equal to the profit m, the probability of the supervision unit performing quality inspection is
The fine coefficient is a main influence factor for determining whether the supervision unit checks the engineering quality, so the fine coefficient r should be reasonably determined.
Therefore, when using advanced construction technology for construction units, the quality management should be controlled from two aspects: on one hand, the reward coefficient l for inspecting the quality problem of the supervision unit is increased so as to improve the qualified quality probability eta of the construction unit. On the other hand, a valid and feasible penalty coefficient r is established for a construction unit so as to ensure the probability lambda of the supervision unit for checking the quality problem, and thus the construction unit is promoted to ensure that the engineering quality is qualified.
3. Analysis of economic benefits
3.1 economic benefit analysis of construction units and construction units
Nash equilibrium solution obtained by game model of mixed strategy with construction unit and construction unit
Bringing the Nash equilibrium solution into the revenue expectation formula, the expectation of each participant at the Nash equilibrium solution is obtained as follows:
revenue expectation for the building units:
revenue expectation for construction units:
i.e. the total payment at the nash equilibrium point is: hⅠ+HⅡ＝0；
The total payment under the strategic combination is respectively as follows: the term "pass" refers to "c", "pass" or "no-pass" refers to "0", "fail" or "no-pass" refers to "c", "fail" or "no-pass".
In conclusion, the expected analysis of the profits of all the participants at the Nash equilibrium point in the game model shows that the construction unit is qualified in the quality behavior, and the maximum social total welfare is achieved when the construction unit does not check the construction unit, otherwise, the total welfare is reduced, and therefore the pareto optimal is achieved. Usually not necessarily pareto optimal at the nash equalization point. As the zero-sum non-cooperative game is adopted between the construction units in the game model, the economic benefit of any one of the construction units and the construction units under the non-cooperative game condition is the highest at the Nash equilibrium point, and the consideration on the total social benefit is neglected, so that the optimal selection of each participant is deep communication and cooperation enhancement, the improvement is continuously improved and perfected, and the pareto optimal is achieved, so that the total social benefit is maximized.
3.2 economic benefits analysis of supervision units and construction units
Nash equilibrium solution obtained by construction unit and supervision unit mixed strategy game model is
Bringing the Nash equilibrium de-emphasis into the expectation formula, the expectation among the Nash equilibrium de-emphasis participants is as follows:
revenue expectation for construction units:
revenue expectation for proctorial units:
i.e. the total payment at the nash equilibrium point is: zx+Zy＝m+d；
The total payment under the strategic combination is respectively as follows: the term "pass" refers to "d + m", "fail" refers to "d (l-1) + w- γ m", and "fail" refers to "d + m + w".
In conclusion, the expected analysis of the profits of all the participants at the Nash equilibrium point in the game model shows that the construction unit is qualified in the engineering quality, and the supervision unit achieves the respective maximum profits of the participants on the premise of ensuring the qualified engineering quality when not checking the construction unit. A mixed strategy game model is arranged between the supervision unit and the construction unit, the game model belongs to a non-cooperative game, the economic benefit of any party of the supervision unit and the construction unit under the condition of the non-cooperative game is the highest at the Nash equilibrium point, and the total social benefit is not considered. When the social total welfare in the game model is analyzed, the social total welfare at the Nash equilibrium point does not reach the pareto optimal value, so the pareto optimization can be carried out on the social total welfare.
Because pareto optimality is the most favorable selection of all participating principals, and the supervision unit and the construction unit are the supervision manager and the operation manager of engineering quality in the game model, game principals are easy to select and cooperate with each other in order to achieve the pareto optimality. When the pareto optimum is reached, supervision does not check the engineering quality of a construction unit, the construction unit does not provide qualified engineering quality, and although the social welfare reaches the maximum, the engineering quality management is seriously affected, so that in the engineering construction, in order to ensure the management of the engineering quality, the supervision unit and the construction unit are prevented from cooperating, and a government supervision department and a construction unit are required to strengthen the work supervision, so as to prevent the pareto optimum from being reached, and promote the engineering quality management.
According to the invention, a game model is established among all participants in the construction project, Nash equilibrium points are found through research and analysis, influence factors of engineering quality management are summarized, and economic benefit analysis is carried out on the Nash equilibrium points, so that the maximum social overall welfare is realized, namely the best pareto is achieved; the following results were obtained:
(1) the game model about engineering quality management established between the construction units is a zero-sum game, and the participation parties are in full opposition in interests, so that the possibility of cooperation is avoided. However, in order to ensure the engineering quality and the income of the participants, the two parties should deeply communicate and strengthen cooperation to realize the maximum social overall welfare, namely pareto optimality.
(2) The game model of quality management between the construction unit and the construction unit is a non-zero sum game, so that the profit-and-loss relationship of the participants is not large, and the mutual cooperation is the most preferable for the participants. However, because the cooperation of the two parties can cause serious hidden danger of engineering quality, the construction unit and the government supervision department need to strengthen the supervision on the work of the two parties, and the damage to the social public interests caused by the cooperation condition is avoided.
The foregoing is illustrative of the preferred embodiments of this invention, and it is to be understood that the invention is not limited to the precise form disclosed herein and that various other combinations, modifications, and environments may be resorted to, falling within the scope of the concept as disclosed herein, either as described above or as apparent to those skilled in the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (8)
1. A project quality management analysis method based on multi-party game is characterized in that: the engineering quality management analysis method comprises the following steps:
a model construction step: constructing a construction unit and construction unit complete information static game model and a construction unit and supervision unit complete information static mixed strategy game model according to the game factors between the construction unit distribution and the construction unit and supervision unit;
and (3) economic benefit analysis step: and solving Nash equilibrium solutions of the construction unit and construction unit complete information static game model and the construction unit and supervision unit complete information static mixed strategy game model, and solving the income expectation and analysis result of each participant in the Nash equilibrium state.
2. The multiparty gaming based engineering quality management analysis method according to claim 1, wherein: the gaming factors include participants, actions, information, and payments of the various participants.
3. The multiparty gaming based engineering quality management analysis method according to claim 1, wherein: the construction unit and construction unit complete information static game model comprises the following steps:
setting a construction unit and the construction unit as participants, and assuming that the construction unit has professional detection equipment and personnel, has accurate rechecking work check on the construction unit, and receives a check result provided by the construction unit;
by YnRepresenting a particular action of participant I in a game strategy model, BⅠ＝{YnIndicating all actions available for selection of ICombining; is prepared from radix Aconiti PratidisnRepresenting a specific action of participant II in the game strategy model, BnRepresenting a specific action of participant II in the game strategy model, BⅡ＝{ХnRepresents the combination of all actions available for selection by II;
assuming that a participant accurately knows the information of the other participant, the game countermeasure model is clarified into a complete information static game model;
let WnAnd paying for the nth participant, wherein n is I and II. Assuming that the detection cost of a construction unit is c, the cost saved by the construction unit due to providing unqualified data is m, if the construction unit detects the quality problem, the saved cost m is not collected, meanwhile, the construction unit is risk compensated, and the compensation coefficient is i, namely the loss of the construction unit is im.
4. The multiparty gaming based engineering quality management analysis method according to claim 1, wherein: the step of solving the Nash equilibrium solution of the complete information static game model of the construction unit and the construction unit comprises the following steps:
setting alpha and beta as the qualification probability and the inspection probability of a construction unit and a construction unit respectively, and further obtaining the income expectation of the construction unit and the income expectation of the construction unit according to the payment matrix;
obtaining Nash equilibrium solution alpha by carrying out bias derivation on the construction unit income expectation and the construction unit income expectation*,β*。
5. The multiparty gaming based engineering quality management analysis method of claim 4, wherein: solving the revenue expectation of each participant at the Nash equilibrium solution and analyzing comprises:
in the construction unit and construction unit complete information static game model, Nash equilibrium solution alpha of the construction unit and the construction unit is solved*,β*Bringing the income expectation of the construction unit and the income expectation of the construction unit into the income expectation of the construction unit to obtain the income expectation of the construction unit and the income expectation of the construction unit at the Nash equilibrium solution;
and analyzing the income expectation of each participant at the Nash equilibrium point in the model to judge whether the quality behavior of each participant is qualified.
6. The multiparty gaming based engineering quality management analysis method of claim 2, wherein: the construction unit and supervision unit complete information static mixing strategy game model is constructed by the following steps:
setting supervision units and construction units as model participants and using VnRepresenting a particular action of participant x in the game strategy model, Ex＝{VnRepresents a combination of all actions from which x can be selected; likewise, with UnRepresenting a particular action of participant y in the game strategy model, Ey＝{UnRepresents the combination of all actions available for y to select;
assuming that the participant supervision unit and the construction unit know the action strategy information of the two parties, the game model is clarified into a complete information static mixed strategy game model;
let O benAnd paying for the nth participant, wherein n is x and y. The profit of the advanced construction process with qualified quality is m by a construction unit, the cost obtained by unqualified quality is w by saving cost, and therefore the profit is w + m when the unqualified quality of the construction unit is not detected; the inspection cost of the supervision unit is d, the reward coefficient is l, and the proctor unit gains ld-d when inspecting the quality problem. The penalty coefficient is gamma, and the loss is w-gammam when the quality of the construction unit is unqualified and is detected.
7. The multiparty gaming based engineering quality management analysis method of claim 6, wherein: the step of solving the Nash equilibrium solution of the construction unit and supervision unit complete information static mixed strategy game model comprises the following steps:
setting lambda and eta as the probability of supervision unit inspection and the probability of construction unit engineering qualification respectively, and further obtaining the income expectation of supervision units and the income expectation of construction units according to the payment matrix;
and obtaining Nash equilibrium solution eta by carrying out bias derivation on the income expectation of the supervision unit and the income expectation of the construction unit*,λ*。
8. The multiparty gaming based engineering quality management analysis method of claim 7, wherein: solving the revenue expectation of each participant at the Nash equilibrium solution and analyzing comprises:
in the construction unit and supervision unit complete information static mixed strategy game model, Nash equilibrium solution eta of supervision unit and construction unit is obtained*,λ*Bringing the income expectation of the construction unit and the supervision unit into the income expectation of the construction unit and the supervision unit to obtain the income expectation of the construction unit and the income expectation of the construction unit at the Nash equilibrium solution;
and analyzing the income expectation of each participant at the Nash equilibrium point in the model to judge whether the quality behavior of each participant is qualified.
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| CN112965368A (en) * | 2021-01-19 | 2021-06-15 | 云南卫士盾科技有限公司 | Differential countermeasure model construction method for mine accident disaster emergency investment under stacklberg game |
| CN116151871A (en) * | 2023-04-23 | 2023-05-23 | 北京金准咨询有限责任公司 | Project evaluation management method and related equipment |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112965368A (en) * | 2021-01-19 | 2021-06-15 | 云南卫士盾科技有限公司 | Differential countermeasure model construction method for mine accident disaster emergency investment under stacklberg game |
| CN112965368B (en) * | 2021-01-19 | 2022-07-26 | 云南卫士盾科技有限公司 | Construction method of differential countermeasure model for mine accident disaster emergency investment under stacklberg game |
| CN116151871A (en) * | 2023-04-23 | 2023-05-23 | 北京金准咨询有限责任公司 | Project evaluation management method and related equipment |
| CN116151871B (en) * | 2023-04-23 | 2023-11-21 | 北京金准咨询有限责任公司 | Project evaluation management method and related equipment |
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