Quality reward and punishment strategy selection method and system based on cumulative foreground theory and tripartite evolutionary game

Abstract

The invention provides a quality reward and punishment strategy selection method based on a cumulative foreground theory and a tripartite evolutionary game. The method comprises the following steps: step 1, determining a tripartite game theoretical model; 2, setting a strategy set and parameter composition: setting game model parameters based on game subject strategy behaviors and cost and income factors; 3, constructing a payment matrix and a revenue function considering the cumulative foreground; step 4, solving and discussing equilibrium points of the game model: calculating and copying a dynamic equation, discussing possible equilibrium points of the game model, and further obtaining an equilibrium strategy of each game main body; and 5, the data input system finds and draws a reward and punishment scheme: setting parameter assignment, and proposing the reward and punishment scheme and example reference verified by the model system by adjusting the reward and punishment of the production enterprise on employee behaviors. According to the method, the quality supervision data is used as input of quality reward and punishment scheme formulation, the bounded rationality of people is considered, and scientific and effective method guidance can be provided for enterprises to select quality reward and punishment strategies.

Description

Technical field

[0001] The present invention relates to the field of quality management and is a method for selecting quality reward and punishment strategies based on cumulative prospect theory and three-party evolutionary game. It is used to guide enterprises in formulating quality reward and punishment strategies, which helps to improve employees' quality awareness, standardize their scientific research and production behaviors, and thus enhance the quality efficiency of enterprises. [Background Technology]

[0002] Employee production behavior is strongly correlated with product quality, and the degree to which employees prioritize quality is strongly correlated with the company's quality assessment system. Therefore, strong institutional constraints are necessary to help companies achieve the goal of "rewarding with excitement and punishing with pain." For companies, comprehensively utilizing various incentive methods and formulating quality reward and punishment strategies can effectively intervene in employee quality behavior, thereby improving product quality and achieving the goal of high-quality and reliable products. This not only enhances industry competitiveness but also promotes high-quality, healthy development of the industry. Current research on reward and punishment strategies focuses solely on the company itself, neglecting the comprehensive role of supervisory departments and employees as co-participants. Furthermore, it overlooks the important characteristic of humans being bounded rational. Research on quality reward and punishment strategies that consider human psychological factors is urgently needed. [Summary of the invention]

[0003] The purpose of this invention is to provide a method and system for selecting quality reward and punishment strategies based on cumulative prospect theory and three-party evolutionary game. This method addresses the problems of existing enterprise quality reward and punishment strategies, such as poor applicability, insufficient effectiveness, neglect of participants' bounded rationality, and incomplete consideration of the main subjects. By constructing a three-party game model involving relevant authorities, enterprises, and employees, this method clarifies the quality supervision working mechanism, hierarchical relationships, and value flows, and depicts the behavioral decisions and psychological changes of each subject during the quality supervision process, providing decision-making support for enterprises in selecting quality reward and punishment strategies.

[0004] The present invention is a method for selecting quality reward and punishment strategies based on cumulative prospect theory and three-party evolutionary game, and its specific steps are as follows:

[0005] Step 1: Define the three-party game model. Based on the quality supervision work mechanism, restore the management logic relationship between the various entities and determine the flow of resources and information.

[0006] Step 2: Set the strategy set and parameter composition. Based on the strategic behavior of the game players, cost and benefit factors, set the game model parameters.

[0007] Step 3: Construct a payoff matrix and benefit function that considers cumulative prospects. Based on the cumulative prospect theory, analyze the player's value perception and decision-making changes, adjust and optimize the game model parameters, and construct the payoff matrix and function.

[0008] Step 4: Solve and discuss the equilibrium point of the game model. Calculate and replicate the dynamic equations, discuss the possible equilibrium points of the game model, and then derive the equilibrium strategies of each player.

[0009] Step 5: Input data into the system to develop reward and punishment plans and examples. Parameters are assigned based on actual data. By adjusting the manufacturer's rewards and penalties for employee behavior, a reward and punishment plan validated by the game model system is proposed.

[0010] Among them, the establishment of the three-party game model in step 1 is based on sufficient research. By restoring the quality supervision mechanism, the parties involved in quality supervision are determined, namely the relevant competent departments, production enterprises and employees.

[0011] The specific implementation process of the policy set and parameter settings in step 2 is as follows:

[0012] (1) Set the strategy sets of relevant authorities, production enterprises and employees. The strategy set of relevant authorities is (strict supervision, not strict supervision); the strategy set of production enterprises is (positive reward, negative reward); the strategy set of employees is (strict compliance with quality requirements, not strict compliance with quality requirements). The probability of strategy selection of all participants is in the interval [0,1].

[0013] (2) Set the game model parameters. The parameters are divided into benefit type, loss (cost) type and coefficient type, as follows:

[0014] ① Income: The social reputation benefit R obtained by the competent department due to no quality problems g ; When the competent authorities strictly supervise, the rewards for strict supervision of production enterprises R c ; Rewards for employees who strictly comply with quality requirements when the production enterprise strictly supervises e .

[0015] ② Loss (cost) category: Regulatory costs of the competent authorities C g ; Supervision cost of production enterprises C c ; Internal and external losses of the production enterprise L c When the competent authorities are strict in supervision, the production enterprises are not strict in supervision; the penalties for c ; Labor cost of employees C e ; Perceived labor cost saved by employees due to not strictly complying with quality requirements C es ; When the production enterprise strictly supervises, the penalty for employees who do not strictly comply with the quality requirements e ; Employee salary reduction due to quality issues e .

[0016] ③ Coefficient category: the loss coefficient Q of the social reputation benefits of the competent department due to quality problems; the loss coefficients β and γ of the rewards / penalties imposed on the production enterprises by the competent department due to its failure to strictly supervise; the loss coefficient δ of the defective rate when employees strictly comply with quality requirements; the probability of quality problems occurring α.

[0017] The payment benefit matrix and function construction considering the cumulative prospect in step 3 are specifically implemented as follows:

[0018] (1) Adjustment of perceived benefits based on the cumulative prospect theory. According to the cumulative prospect theory, the perceived value of a parameter is calculated as follows: V = ∑ i π(P i )v(Δx i ),in:

[0019]

[0020] Where V is the perceived value, v(Δx i ) is the value function, θ, is the risk preference coefficient, Δx i is the difference between the actual game income and the reference point, λ is the loss aversion coefficient of the behavior subject, reflecting its sensitivity to loss. Compared with the prospect theory, the parameter ξ (0≤ξ≤1) is introduced to indicate the sensitivity of the behavior subject to relative benefits; π(P i ) is the weight function, P i is the probability of loss, and σ represents the estimated coefficient and trend attitude of the individual towards gain / loss.

[0021] (2) Construction of the payment benefit matrix. First, it is clear that the three parties (N=3) have a total of 2 N =8 strategy sets, setting the strategy selection probabilities of relevant competent departments, production enterprises, and front-line employees, and then combining the parameters to establish a payment benefit matrix.

[0022] (3) Derivation of the replication dynamic equation. Based on the payoff matrix, the expected returns of the three game players under each strategy are calculated, and the replication dynamic equations for the supervisory department, the production enterprise, and the employees are derived separately.

[0023] The specific implementation process of the discussion on solving the equilibrium point of the game model in step 4 is as follows:

[0024] (1) The stability of the equilibrium point of the dynamic system described by the differential equation is obtained from the local stability analysis of the Jacobian matrix.

[0025] (2) By introducing the equilibrium points of the replicated dynamic equation system into the Jacobian matrix calculated above, the Jacobian matrix corresponding to each equilibrium point can be obtained, and the eigenvalues ​​corresponding to each equilibrium point can be obtained respectively.

[0026] (3) According to Lyapunov's system stability theory, an unstable point is one whose eigenvalue is greater than zero. Parameter constraints are added to the stable point to perform stability analysis.

[0027] Among them, the game model simulation in step 5 proposes a reward and punishment plan, analyzes the impact of parameter variable changes on the main strategy selection, and provides opinions and suggestions for the company to formulate a quality reward and punishment plan.

[0028] The advantages and beneficial effects of the present invention are:

[0029] (1) By establishing a "psychological-mathematical" game model to restore the strategic game of each participant in the quality supervision work mechanism, it has more novel theoretical support than the previous quality reward and punishment strategy formulation method, and can objectively reflect the implementation effect of the company's quality reward and punishment strategy.

[0030] (2) Different from the traditional game theory which is based on the assumption of complete rationality, the important characteristics of cumulative prospect theory, such as loss aversion and probability distortion, can better reflect the psychological characteristics of decision makers and provide a more accurate basis for analyzing decision-making under different quality reward and punishment strategies.

Brief Description of the Drawings

[0031] Figure 1 It is a process for selecting quality reward and punishment strategies based on cumulative prospect theory and evolutionary game.

[0032] Figure 2 It is the game relationship between each participating entity.

[0033] Figure 3 It is a three-party game tree structure.

[0034] Figure 4a 、 Figure 4b 、 Figure 4c 、 Figure 4d 、 Figure 4e and Figure 4f The impact of different reward and punishment schemes on system evolution. [Specific implementation method]

[0035] The present invention provides a quality reward and punishment strategy selection method and system based on cumulative prospect theory and three-party evolutionary game, and further explains the specific implementation steps, such as Figure 1 As shown:

[0036] Step 1: Clarify the three-party game model. Through sufficient investigation and research, starting from the quality supervision mechanism involving relevant competent departments, production enterprises, and front-line employees, analyze the payment and benefits of each party from the perspective of the supervision relationship between the subjects, and clarify the game relationship between the various participants in the quality formation process, such as Figure 2 shown.

[0037] Step 2: Set the strategy set and parameter composition. Based on the strategic behavior of the game subject, cost and benefit factors, set the game model parameters. The implementation steps are as follows:

[0038] (1) Assume that the employee's strategic choice space is V1 = {strictly comply with quality requirements, not strictly comply with quality requirements}; the production enterprise's strategic choice space is V2 = {positive rewards, negative rewards}; and the relevant regulatory authorities' strategic choice space is V3 = {strict supervision, not strict supervision}. If the probability that an employee strictly complies with quality requirements is x, then the probability that they do not strictly comply with quality requirements is 1-x; the probability that the production unit actively rewards is y, and the probability that they passively reward is 1-y; the probability that the relevant regulatory authorities choose strict supervision is z; then the probability that they choose not to strictly supervise is 1-z, and x, y, z∈(0,1).

[0039] Among them, "employees strictly abide by quality requirements" means that the behavior of employees complies with the requirements of quality work regulations, and quality problems will not occur in the production process. "Employees do not strictly abide by quality requirements" means that employees violate quality work regulations during production, which may lead to quality problems. Once quality problems occur, it will cause economic losses to the production enterprise and reputation loss to the government. "Active rewards for production enterprises" means two-way incentives (rewards and punishments) for employees. Employees are rewarded when they strictly abide by quality requirements, and punished when they do not strictly abide by quality requirements. "Passive rewards for production enterprises" means that employees are not rewarded when they strictly abide by quality requirements, and are only punished for not strictly abiding by quality requirements. "Strict supervision by competent authorities" means rewards and punishments for production enterprises based on their implementation of superior requirements. "Not strict supervision by competent authorities" means that the intensity of rewards and punishments for production enterprises is somewhat weakened compared to "strict supervision".

[0040] (2) Set the corresponding parameters of different strategies for each subject, as shown in the table:

[0041]

[0042]

[0043] Note: The range of the depreciation coefficient is (0,1)

[0044] Step 3: Construct a payoff matrix and profit function that considers cumulative prospect. Based on the cumulative prospect theory, analyze the player's value perception and decision-making changes, and adjust and optimize the game model parameters.

[0045] (1) Adjust the parameters according to the cumulative prospect theory: the probability that an enterprise chooses a passive strategy and is discovered by the competent authorities is P1, but there is a possibility that it will not be discovered and the enterprise will be able to escape punishment. The cumulative prospect perceived value corresponding to the punishment received by the enterprise is:

[0046] V(Pc )=π(1-P1)v(0)+π(P1)v(p c )=π(P1)v(p c )

[0047] The probability that an employee chooses not to strictly comply with quality requirements and is discovered by the company is P2. There is also a possibility that the employee will not be discovered and will escape punishment. The cumulative perceived value of the employee's punishment is:

[0048] V(P e )=π(1-P2)v(0)+π(P2)v(p e )=π(P2)v(p e )

[0049] (2) Construct the payoff matrix of the game model and calculate the benefits of the three game entities under the eight strategies. For example: "The competent authority chooses a strict supervision strategy, the production enterprise chooses a positive reward strategy, and the employees choose to strictly comply with quality requirements." In this case, the competent authority pays the supervision cost and obtains social reputation benefits. In addition, it will pay a bonus to the production enterprise for its positive strategy. The competent authority's benefits are -C g +R g -R c In addition to paying the regulatory costs, the manufacturer will receive rewards from the competent authorities and will also receive certain rewards for employees who strictly abide by quality requirements. The manufacturer's profit is -C c -R e +R c Employees will pay labor costs and receive bonuses from the company. In addition, they may be punished by salary demotion due to quality problems. The employee benefit is -C e +R e -αδV(L e The payoff matrices corresponding to other strategy sets are solved in the same way as above, and the results are as follows. The game tree is as follows Figure 3 As shown:

[0050]

[0051]

[0052] Step 4: Solve and discuss the equilibrium point of the game model. Calculate and replicate the dynamic equations, discuss the possible equilibrium points of the game model, and then derive the equilibrium strategies of each player. Combined with the cumulative prospect theory, discuss the game outcomes.

[0053] (1) According to the payoff matrix of the game model, assuming that the expected benefit of employees choosing the strategy of “strictly complying with quality requirements” during the game is π 11 , the expected return of choosing the strategy of “not strictly adhering to quality requirements” is π 12, the average return is π1, and the replication dynamic equation is F(x), which is as follows:

[0054] π 11 =-C e +yR e -αδV(L e )

[0055] π 12 =-C e -V(P e )-αV(L e )+C es

[0056] F(x)=x(π 11 -π1)=x(1-x)(π 11 -π 12 )=x(1-x)(yR e +V(P e )+α(1-δ)V(L e )-C es )

[0057] Assume that the expected profit of the enterprise choosing the "positive reward" strategy in the game is π 21 , the expected return of choosing the "negative reward" strategy is π 22 , the average return is π2, and the replication dynamic equation is F(y), which is calculated as follows:

[0058] π 21 =-C c +(1-x)V(P e )-xR e -αδxV(L c )-α(1-x)V(L c )+zR c +(1-z)βR c

[0059] π 22 =-C c +(1-x)V(P e )-zP c -(1-z)γV(P c )-αδxV(L c )-α(1-x)V(L c )

[0060] F(y)=y(1-y)(-xR e +(z+β-zβ)R c +(z+γ-zγ)V(P c ))

[0061] Assume that the expected benefit of the relevant competent authorities choosing the "strict supervision" strategy in the game process is π 31 , the expected return of choosing the “non-strict regulation” strategy is π 32 , the average benefit of employees is π3, and the replication dynamic equation is F(z), which is as follows:

[0062] π 31 =-C g +R g -yR c +(1-y)V(P c )

[0063] π 32 =-C g +QR g -yβR c +(1-y)γV(P c )

[0064] F(z)=z(1-z)((1-Q)R g -y(1-β)R c +(1-y)(1-γ)V(P c ))

[0065] By combining the replication dynamic equations of employees, enterprises, and relevant authorities, we can obtain the replication dynamic equation system:

[0066]

[0067] (2) According to the method proposed by Friedman, the stability of the equilibrium point of the dynamic system described by the differential equation can be obtained from the local stability analysis of the Jacobian matrix. The Jacobian matrix can be expressed as:

[0068]

[0069] Introducing the equilibrium point of the replicated dynamic equation system into the Jacobian matrix calculated above can obtain the Jacobian matrix corresponding to each equilibrium point. First, analyze the stability of the equilibrium point E1(0,0,0). The Jacobian matrix at this time is:

[0070]

[0071] According to Lyapunov system stability theory, when all eigenvalues ​​of J have negative real parts at a certain equilibrium point, that point is the ESS of the game. From the Jacobian matrix J1, we can see that the three eigenvalues ​​of the matrix are:

[0072] λ1=V(P e )+α(1-δ)V(L e )-C es

[0073] λ2=βR c +γV(P c )

[0074] λ3=(1-Q)R g +(1-γ)V(P c )

[0075] Therefore, it can be judged that E1(0,0,0) is an unstable point. By analogy, the eight equilibrium points of the game model are substituted into the Jacobian matrix one by one, and the eigenvalues ​​corresponding to each equilibrium point can be obtained, as shown in the table.

[0076]

[0077]

[0078] (3) Equilibrium situation analysis. According to Lyapunov’s system stability theory, an eigenvalue greater than zero is an unstable point. Therefore, E1(0,0,0), E2(0,0,1), and E5(1,0,0) are unstable points. E3(0,1,0), E4(0,1,1), E6(1,0,1), E7(1,1,0), and E8(1,1,1) can be analyzed for stability by adding parameter constraints.

[0079] Case 1: When R e +V(P e )+α(1-δ)V(L e )-C es <0 and (1-Q)R g -(1-β)R c <0 holds, the rewards employees receive for strictly adhering to quality requirements are lower than the difference between the labor saved and the penalties and salary deductions incurred for not strictly adhering. Consequently, employees will choose the "lax compliance" strategy. The benefits of strict supervision by regulatory authorities are lower than the rewards they pay to enterprises, leading regulatory authorities to favor the "lax supervision" strategy. In this case, the stable point of the game model, E3(0,1,0), is not the optimal solution. Product quality cannot be guaranteed, and the long-term interests of all three parties in the game cannot be met.

[0080] Case 2: When R e +V(P e )+α(1-δ)V(L e )-C es <0 and -(1-Q)R g +(1-β)R c<0 holds true, the rewards employees receive for strictly adhering to quality requirements are lower than the difference between the labor saved and the penalties and salary deductions incurred for not strictly adhering. Therefore, employees will choose the "not strictly adhering to quality requirements" strategy. The benefits of strict supervision by the competent authority are higher than the rewards paid to the company, so the competent authority tends to choose the "strict supervision" strategy. In this case, the stable point of the game model is E4(0,1,1). Employee violations directly affect product quality, and this stable point is not the optimal solution.

[0081] Case 3: When -V(P e )-α(1-δ)V(L e )+C es <0 and -R e +R c +V(P c ) < 0, the labor savings from employees' non-compliance with quality requirements is lower than the penalties and salary reductions incurred for non-compliance, leading employees to choose the "strict compliance" strategy. If the company's reward for strict compliance is higher than the sum of the absolute value of the rewards and penalties received from the competent authorities, the company will tend to choose the "passive reward" strategy. In this case, the stable point of the game model is E6(1,0,1). The company's passive reward strategy will affect employee attitudes and be detrimental to long-term product quality assurance, making this stable point suboptimal.

[0082] Case 4: When R e +V(P e )+α(1-δ)V(L e )-C es >0, R e -βR c -γV(P c )<0,(1-Q)R g -(1-β)R c <0, the labor savings from employees' non-compliance with quality requirements is lower than the sum of the penalties and salary deductions received for non-compliance and the rewards received for strict compliance. Therefore, employees will choose the "strict compliance" strategy. If the rewards paid by the enterprise for strict compliance are lower than the sum of the absolute values ​​of the rewards and penalties received from the competent authorities, the enterprise will tend to choose the "active reward" strategy. If the benefits of strict supervision by the competent authorities are lower than the rewards paid, the competent authorities will tend to choose the "lax supervision" strategy. In this case, the stable point of the game model is E7(1,1,0). Lax supervision by the competent authorities is detrimental to the enterprise's quality work, and this stable point is not the optimal solution.

[0083] Case 5: When R e >C es -V(P e )-α(1-δ)V(Le ), R e < R c +V(P c ), (1 - β)R c < (1 - Q)R g When all of the above hold simultaneously, the rewards received by employees for strict compliance are higher than the sum of the penalties and salary downgrade penalties due to non - strict compliance and the labor saved; the rewards paid by the enterprise to employees for strict compliance with quality requirements are lower than the sum of the rewards and the absolute value of the penalties given by the competent department to the enterprise; the benefits of strict supervision by the competent department are higher than the rewards paid by it to the enterprise. In this case, the stable point of the game model is E8(1, 1, 1), reaching the optimal solution of the game model. The simulation effects of the strategy evolutions of each subject in the above 5 cases are as Figure 4a-4f shown.

[0084] (5) Result discussion. From the above analysis, when the 3 conditions are simultaneously met, that is, the competent department strictly supervises, the enterprise actively rewards, and employees strictly comply with quality requirements, the system reaches the optimal level.

[0085]

[0086] However, in reality, the system converging to the optimal point (1, 1, 1) is also interfered by people's psychological factors. The analysis is as follows:

[0087] ① Due to the enterprise's fluke mentality, it underestimates P1. The enterprise takes not being inspected as a reference point and regards inspection as a "loss". Since the enterprise is more sensitive to losses than to gains (the loss aversion coefficient λ > 1), and underestimates medium or high - probability events and overestimates low - probability events, the psychological expectation of the enterprise is affected by the non - linear distortion of the probability weight function. Considering the actual situation of quality inspection work, P1 is not a low - probability event. Therefore, the enterprise has a fluke mentality of avoiding punishment and underestimates the actual probability of inspection by the competent department, that is, π(P1) < P1. With the optimization of the quality supervision system and mechanism, the progress of technical means, the popularization of big data detection and the Internet of Things platform, P1 is directly increased, which further leads to the enterprise underestimating the marginal cost of negative strategies and choosing wrong strategies.

[0088] ② Due to the employees' fluke mentality, they underestimate P2. Employees save labor cost C es by not strictly complying with quality requirements. Employees take not being discovered for their违规行为 as a reference point and regard being discovered as a "loss". Similarly, due to the employees' higher sensitivity to losses than to gains, underestimating medium or high - probability events and overestimating low - probability events, etc., employees will underestimate P2, that is, π(P2) < P2.

[0089] ③ The impact of cognitive overload and cognitive inertia. The cognitive overload effect is manifested in the limited information processing capabilities of employees. Quality systems and rules are complex and distributed across multiple documents, making it difficult for employees to fully understand relatively complex rules. Employees may be faced with a large amount of work-related information (such as task instructions, performance goals, etc.) at the same time, resulting in an inability to focus on assessing their own violation risks, i.e., information overload. Cognitive inertia is manifested in the fact that employees may rely on outdated information (previous corporate inspection frequency and penalty intensity) to judge the probability of violation risks. Even if the company has increased the frequency of inspections, employees may still maintain their original psychological expectations π (P2). At the same time, cognitive overload will aggravate cognitive inertia. When employees are overloaded, they are more inclined to rely on existing cognitive frameworks and are unable to actively learn, understand, and implement new regulatory requirements.

[0090] Step 5: Data input system to develop reward and punishment schemes and sample references. The user inputs their actual operating data into the quality reward and punishment strategy selection system. The system is as follows:

[0091] The quality reward and punishment strategy selection method and system proposed in this paper based on cumulative prospect theory and three-party evolutionary game are implemented using Matlab 2017b software. The specific steps are as follows:

[0092] (1) Assign values ​​to the replication dynamic equation parameters of the three parties in the game, setting R e1 ,P e1 , build the f1 file:

[0093] %Define f(t,y) function;

[0094] function dy=f(t,y);

[0095] %Set parameter values;

[0096] Re=2, Pe=0.5, Rg=12.5, Rc=2.5, Pc=2.5, Ces=3, Le=1, α=0.1, δ=0.8, β=0.5, γ=0.5, Q=0.8;

[0097] % Let y(1)=x, y(2)=y, y(3)=z; use parameters to represent dy(1), dy(2), dy(3);

[0098] dy(1)=y(1)*(1-y(1))*(y(2)*Re+Pe+α*(1-δ)*Le-Ces);

[0099] dy(2)=y(2)*(1-y(2))*(-y(1)*Re+(y(3)+β-y(3)*β)*Rc+(y(3)+γ-y(3)*γ)*Pc);

[0100] dy(3)=y(3)*(1-y(3))*((1-Q)*Rg-y(2)*(1-β)*Rc+(1-y(2))*(1-γ)*Pc);

[0101] dy=[dy(1);dy(2);dy(3)];

[0102] end

[0103] (2) Adjust the company's quality reward and punishment parameters for employees (R e2 ,P e2 ), keep other parameters unchanged, and build the f2 file:

[0104] %Define f(t,y) function;

[0105] function dy=f(t,y);

[0106] %Reset parameter values;

[0107] Re=3, Pe=1, Rg=12.5, Rc=2.5, Pc=2.5, Ces=3, Le=1, α=0.1, δ=0.8, β=0.5, γ=0.5, Q=0.8;

[0108] % Let y(1)=x, y(2)=y, y(3)=z; use parameters to represent dy(1), dy(2), dy(3);

[0109] dy(1)=y(1)*(1-y(1))*(y(2)*Re+Pe+α*(1-δ)*Le-Ces);

[0110] dy(2)=y(2)*(1-y(2))*(-y(1)*Re+(y(3)+β-y(3)*β)*Rc+(y(3)+γ-y(3)*γ)*Pc);

[0111] dy(3)=y(3)*(1-y(3))*((1-Q)*Rg-y(2)*(1-β)*Rc+(1-y(2))*(1-γ)*Pc);

[0112] dy=[dy(1);dy(2);dy(3)];

[0113] end

[0114] (3) Adjust the company's quality reward and punishment parameters for employees (R e3 ,P e3 ), keep other parameters unchanged, and build the f3 file:

[0115] %Define f(t,y) function;

[0116] function dy=f(t,y);

[0117] %Reset parameter values;

[0118] Re=4, Pe=2, Rg=12.5, Rc=2.5, Pc=2.5, Ces=3, Le=1, α=0.1, δ=0.8, β=0.5, γ=0.5, Q=0.8;

[0119] % Let y(1)=x, y(2)=y, y(3)=z; use parameters to represent dy(1), dy(2), dy(3);

[0120] dy(1)=y(1)*(1-y(1))*(y(2)*Re+Pe+α*(1-δ)*Le-Ces);

[0121] dy(2)=y(2)*(1-y(2))*(-y(1)*Re+(y(3)+β-y(3)*β)*Rc+(y(3)+γ-y(3)*γ)*Pc);

[0122] dy(3)=y(3)*(1-y(3))*((1-Q)*Rg-y(2)*(1-β)*Rc+(1-y(2))*(1-γ)*Pc);

[0123] dy=[dy(1);dy(2);dy(3)];

[0124] end

[0125] (4) Construct the f_main file, calculate and replicate the dynamic function, draw the three-party game selection images under three situations, and realize the visualization of the evolutionary game results.

[0126] First, the three-party strategy starts from 0.5, and the ode45 function is used to calculate the system equilibrium solution and draw a graph. The red curve represents the change of employee decision-making, the blue curve represents the change of production enterprise decision-making, the green curve represents the change of department decision-making, and the solid line represents R e1 ,P e1 When setting the initial value,

[0127] %Solve f1;

[0128] % Set the iteration to 20 times;

[0129] tspan = [0, 20];

[0130] %Set the three-party strategy to start from 0.5;

[0131] y0=[0.5; 0.5; 0.5];

[0132] %Use ode45 function to calculate the system equilibrium solution;

[0133] [t,y]=ode45('f1',tspan,y0);

[0134] data = [t,y];

[0135] save f.txt data–ascii;

[0136] % plot R e1 ,P e1 The image is set to the initial value, where the red curve represents the change in employee decision-making, the blue curve represents the change in production enterprise decision-making, and the green curve represents the change in the decision-making of the competent department, represented by the solid line:

[0137] plot(t,y(:,1),'r-',t,y(:,2),'b-',t,y(:,3),'g-');

[0138] xlim=get(gca,'xlim');

[0139] ylim=get(gca,'ylim');

[0140] set(gca,'xtick',(0:5:20));

[0141] grid on

[0142] hold on

[0143] %Solve f2;

[0144] tspan = [0, 20];

[0145] y0=[0.5; 0.5; 0.5];

[0146] [t,y]=ode45('f2',tspan,y0);

[0147] data = [t,y];

[0148] save f2.txt data–ascii;

[0149] % plot R e2 ,P e2 The corresponding image of the situation is represented by the solid line:

[0150] plot(t,y(:,1),'r-*',t,y(:,2),'b-*',t,y(:,3),'g-*');

[0151] xlim=get(gca,'xlim');

[0152] ylim=get(gca,'ylim');

[0153] set(gca,'xtick',(0:5:20));

[0154] grid on

[0155] hold on

[0156] %Solve f3;

[0157] tspan = [0, 20];

[0158] y0=[0.5; 0.5; 0.5];

[0159] [t,y]=ode45('f3',tspan,y0);

[0160] data = [t,y];

[0161] save f3.txt data–ascii;

[0162] % plot R e3 ,P e3 The corresponding image of the situation is represented by the dotted line:

[0163] plot(t,y(:,1),'r-.',t,y(:,2),'b-.',t,y(:,3),'g-.');

[0164] xlim=get(gca,'xlim');

[0165] ylim=get(gca,'ylim');

[0166] set(gca,'xtick',(0:5:20));

[0167] grid on

[0168] hold on

[0169] Users can judge whether the system is in the optimal strategy based on the visual calculation results. If it is not optimal, they can adjust the reward and punishment parameters to optimize the system to the optimal level and obtain an effective reward and punishment plan.

[0170] To guide users in using the quality reward and punishment strategy selection method and system proposed in the present invention, the present invention provides examples for reference, as follows:

[0171] (1) Taking the energy enterprises in City K as an example, we conducted on-site investigations on relevant enterprises in conjunction with the Energy Department of the Development and Reform Commission of City K to collect actual operation data. We also need to ensure sufficient data support and use statistical methods for pre-processing.

[0172] (2) The Energy Department conducted quality inspections on 11 energy companies in City K. The department gained social reputation benefits of RMB 1.5 million due to no quality problems throughout the year. g = 12.5 (converted into months, the same below). Since the company had no quality problems throughout the year and its quality performance was excellent, it received a reward or penalty of RMB 300,000 from the competent department. c =2.5,P c = 2.5. The labor cost of employees is wages and salaries. The cost saved by not strictly complying with quality requirements is 20% of daily work. Let C e =15, C es =0.2×C e =3. Assuming that the social reputation benefit and the quality problem loss coefficient are 0.8, then Q = δ = 0.8, the reward / penalty loss coefficient is 0.5, then β = γ = 0.5, and the probability of a component having a quality problem is α = 0.05. Due to the accountability for quality problems, the annual performance salary is reduced according to the company's system (the case is 10%), and L e =0.1×C e = 1. By changing the company's quality reward and punishment parameters for employees (R e ,P e ), studying the effectiveness of reward and punishment schemes.

[0173] (3) Keep Re unchanged, change the value of Pe, and study the changes in the game evolution results.

[0174] Set Pe = 0.5 and vary the Re value. When Re = 2, x converges to x = 0, and employees do not strictly adhere to quality requirements. When Re = 6, the decisions of both employees and the company fluctuate, and the system becomes unstable. When Re = 4, x converges to x = 1, and employees strictly adhere to quality requirements. The supervisory department will adopt a strict supervision strategy, and the company will choose an active reward strategy. The solution with Re = 4 and Pe = 0.5 is feasible.

[0175] Set Pe = 1 and change the Re value. When Re = 2, convergence is not obvious, and employee strategies are between 0.4 and 0.5, which is not a proactive strategy. When Re = 6, employee decisions fluctuate unstably between 0.6 and 1.0, and enterprise decisions fluctuate between 0.1 and 0.65, making the system unstable. When Re = 4, x converges to x = 1. Employees will strictly adhere to quality requirements, the competent department will choose a strict supervision strategy, and the enterprise will choose a proactive reward strategy. The solution of Re = 4 and Pe = 1 is feasible.

[0176] Set Pe = 2 and change the value of Re. When Re = 2, x converges to x = 1, and employees strictly comply with quality requirements. When Re = 6, the decisions of employees fluctuate unstably between 0.5 and 1.0, and the decisions of the enterprise fluctuate between 0.1 and 0.6, and the system is in an unstable state. When Re = 4, x converges to x = 1 and the convergence speed accelerates. Employees will strictly comply with quality requirements, the competent department will choose a strict supervision strategy, and the enterprise will choose an active reward strategy. The plan with Re = 4 and Pe = 2 is feasible.

[0177] From the above analysis, it can be seen that the three plans of ① Re = 4, Pe = 0.5, ② Re = 4, Pe = 1, and ③ Re = 4, Pe = 2 are feasible. It is analyzed that too low rewards and punishments are not conducive to intervening in employees' positive decisions, and appropriately raising the reward standard can make the result of the three-party game tend to the optimal solution.

[0178] (4) Keep Pe unchanged and change the value of Re to study the change of the game evolution result.

[0179] Set Re = 3 and change the value of Pe. When Pe = 0.5, Pe = 1, and Pe = 2, all three parties choose active strategies, and the system evolves to a stable state. The larger the value of Pe, the faster the strategy evolution speed of each subject, that is, the greater the punishment intensity for employees, the higher the enthusiasm for strictly complying with quality requirements.

[0180] Set Re = 4 and change the value of Pe. This situation is similar to Re = 3. When Pe = 0.5, Pe = 1, and Pe = 2, all three parties choose active strategies, and the system evolves to a stable state. The larger Pe is, the faster the evolution speed. Through comparative analysis, it can be seen that under the same punishment intensity for employees, the higher the reward amount, the higher the enthusiasm for strictly complying with quality requirements.

[0181] Set Re = 5 and change the value of Pe. When Pe = 0.5, Pe = 1, and Pe = 2, the enterprise's strategy choices cannot evolve to an active reward strategy, and the system is in an unstable state. The evolution result does not meet the execution expectation of quality incentive work.

[0182] The results show that too high reward and punishment standards will increase the cost burden of the enterprise, and the plan is not suitable for long-term implementation. Since V(Pe) < Pe, the enterprise also has to solve the problems of "the punishment is not painful" and employees having a fluke mentality. Two solutions are proposed. One is to directly increase the punishment intensity. Although it can solve practical problems, too high punishment does not meet the psychological expectations of employees. The other is to strengthen institutional design, introduce supervision technologies, and make the inspection intensity public and transparent through carrying out quality education activities. Compared with the two, the second plan is more scientific, conforms to the values of most people, can improve employees' cognitive overload and cognitive inertia problems, is conducive to the long-term development of quality incentive work, and has a relatively positive effect on ensuring quality and efficiency.

[0183] In summary, the Re value should be between 3 and 4, and the Pe value should be between 1 and 2. Re should be between 0.25 and 0.33 times the employee's salary, and Pe should be between 0.083 and 0.167 times the employee's salary. Companies can employ a guiding strategy of "appropriate rewards and light punishments" to influence employees' positive decision-making, such as Re = 4 and Pe = 2. Companies should also strengthen the promotion of quality education activities, increase the frequency of quality inspections, and optimize inspection plans to further address employee complacency and cognitive issues.

Claims

1. A quality reward and punishment strategy selection method based on cumulative prospect theory and three-party evolutionary game, characterized by: The steps include: Step 1: Clarify the three-party game model; based on the quality supervision work mechanism, restore the management logic relationship between each subject and determine the flow of resources and information; Step 2: Set the strategy set and parameter composition; set the game model parameters based on the strategic behavior, cost and benefit factors of the game players; Step 3: Construct a payoff matrix and benefit function that considers cumulative prospects. Based on the cumulative prospect theory, analyze the value perception and decision-making changes of the players, adjust and optimize the game model parameters, and construct the payoff matrix and function. Step 4: Solve and discuss the equilibrium point of the game model; calculate and replicate the dynamic equation, discuss the possible equilibrium points of the game model, and then derive the equilibrium strategy of each game player; Step 5: Input data into the system to develop a reward and punishment plan; set parameter values ​​based on actual data, and by adjusting the production company's rewards and penalties for employee behavior, propose a reward and punishment plan that has been verified by the game model system.

2. The method for selecting quality reward and punishment strategies based on cumulative prospect theory and three-party evolutionary game according to claim 1, characterized in that: The specific implementation process of the policy set and parameter settings in step 2 is as follows: (1) Set the strategy sets of relevant departments, production enterprises and employees. The strategy set of relevant departments is [strict supervision, not strict supervision]; the strategy set of production enterprises is [positive reward, negative reward]; the strategy set of employees is [strict compliance with quality requirements, not strict compliance with quality requirements], and the probability of strategy selection of all participants is in the interval [0,1]. (2) Set the game model parameters. The parameters are divided into profit type, loss type and coefficient type, as follows: ① Income: The social reputation benefit R obtained by the competent department due to no quality problems g ; When the competent authorities strictly supervise, the rewards for strict supervision of production enterprises R c ; Rewards for employees who strictly comply with quality requirements when the production enterprise strictly supervises e ; ② Loss: Regulatory costs of the competent authorities C g ; Supervision cost of production enterprises C c ; Internal and external losses of the production enterprise L c When the competent authorities are strict in supervision, the production enterprises are not strict in supervision; the penalties for c ; Labor cost of employees C e ; The perceived labor cost saved by employees due to not strictly complying with quality requirements C es ; When the production enterprise strictly supervises, the penalty for employees who do not strictly comply with the quality requirements e ; Employee salary reduction due to quality issues e ; ③ Coefficient category: the loss coefficient Q of the social reputation benefits of the competent department due to quality problems; the loss coefficients β and γ of the rewards / penalties imposed on the production enterprises by the competent department due to its failure to strictly supervise; the loss coefficient δ of the defective rate when employees strictly comply with quality requirements; the probability of quality problems occurring α.

3. The method for selecting quality reward and punishment strategies based on cumulative prospect theory and three-party evolutionary game according to claim 1, characterized in that: The payment benefit matrix and function construction considering the cumulative prospect in step 3 are implemented as follows: (1) Adjustment of perceived returns based on the cumulative prospect theory; According to the cumulative prospect theory, the perceived value of the parameter is calculated as follows: V = ∑ i π(P i )v(Δx i ),in: Where V is the perceived value, v(Δx i ) is the value function, θ, is the risk preference coefficient, Δx i is the difference between the actual game income and the reference point, λ is the loss aversion coefficient of the behavior subject, reflecting its sensitivity to loss. Compared with the prospect theory, the parameter ξ (0≤ξ≤1) is introduced to indicate the sensitivity of the behavior subject to relative benefits; π(P i ) is the weight function, P i is the probability of loss, σ represents the estimated coefficient and trend attitude of individuals towards gain / loss; (2) Construction of the payment benefit matrix: First, we need to clarify the three parties in the game, that is, N = 3, with a total of 2 N = A set of 8 strategies, setting the strategy selection probabilities of relevant departments, production enterprises, and front-line employees, and then combining the parameters to establish a payment benefit matrix; (3) Derivation of the replication dynamic equation: Based on the payoff matrix, the expected benefits of the three game players under each strategy are calculated, and the replication dynamic equations of the competent department, production enterprise, and employees are derived respectively.

4. The method for selecting quality reward and punishment strategies based on cumulative prospect theory and three-party evolutionary game according to claim 1 is characterized by: The discussion on solving the equilibrium point of the game model in step 4 is as follows: (1) Obtain the stability of the equilibrium point of the dynamic system described by the differential equation from the local stability analysis of the Jacobian matrix; (2) Introducing the equilibrium point of the replicated dynamic equation system into the calculated Jacobian matrix to obtain the Jacobian matrix corresponding to each equilibrium point, and respectively obtaining the eigenvalue corresponding to each equilibrium point; (3) According to Lyapunov's system stability theory, the eigenvalue is greater than zero and it is an unstable point. Parameter constraints are added to the stable point to perform stability analysis.

5. The method for selecting quality reward and punishment strategies based on cumulative prospect theory and three-party evolutionary game according to claim 1 or 3, characterized in that: In step 3, the parameters are adjusted according to the cumulative prospect theory: the probability that the enterprise chooses a passive strategy and is discovered by the competent authorities is P1, but there is a possibility that it will not be discovered and the enterprise will escape punishment. The cumulative prospect perceived value corresponding to the punishment received by the enterprise is: V(P c )=π(1-P1)v(0)+π(P1)v(p c )=π(P1)v(p c ) The probability that an employee chooses not to strictly comply with quality requirements and is discovered by the company is P2. There is also a possibility that the employee will not be discovered and will escape punishment. The cumulative perceived value of the employee's punishment is: V(P e )=π(1-P2)v(0)+π(P2)v(p e )=π(P2)v(p e )。 6. The method for selecting quality reward and punishment strategies based on cumulative prospect theory and three-party evolutionary game according to claim 5, characterized in that: When the competent department chooses a strict supervision strategy, the production enterprise chooses an active reward strategy, and the employees choose to strictly comply with quality requirements, the competent department pays the supervision cost and obtains social reputation benefits. In addition, it will pay a bonus to the production enterprise for its active strategy. The competent department's benefit is -C g +R g -R c In addition to paying the regulatory costs, the manufacturer will receive rewards from the competent authorities and will also be rewarded for employees who strictly abide by quality requirements. The manufacturer's profit is -C c -R e +R c Employees will pay labor costs and receive bonuses from the company. In addition, they may be punished by salary demotion due to quality problems. The employee benefit is -C e +R e -αδV(L e ).

7. The method for selecting quality reward and punishment strategies based on cumulative prospect theory and three-party evolutionary game according to claim 1 or 4, characterized in that: According to the payoff matrix of the game model, let the expected benefit of employees choosing the strategy of "strictly complying with quality requirements" during the game be π 11 , the expected return of choosing the strategy of "not strictly adhering to quality requirements" is π 12 , the average return is π1, and the replication dynamic equation is F(x), which is as follows: p 11 =-C e +yR e -adV(L e ) p 12 =-C e -V(P e )-αV(L e )+C es F(x)=x(π 11 -π1)=x(1-x)(π 11 -π 12 )=x(1-x)(yR e +V(P e )+α(1-δ)V(L e )-C es ) Assume that the expected profit of the enterprise choosing the "positive reward" strategy in the game process is π 21 , the expected return of choosing the "negative reward" strategy is π 22 , the average return is π2, and the replication dynamic equation is F(y), which is calculated as follows: p 21 =-C c +(1-x)V(P e )-xR e -adxV(L c )-α(1-x)V(L c )+zR c +(1-z)βR c π 22 =-C c +(1-x)V(P e )-zP c -(1-z)γV(P c )-αδxV(L c )-α(1-x)V(L c ) F(y)=y(1-y)(-xR e +(z+β-zβ)R c +(z+γ-zγ)V(P c )) Assume that the expected benefit of the relevant competent authorities choosing the "strict supervision" strategy in the game process is π 31 , the expected return of choosing the "non-strict supervision" strategy is π 32 , the average benefit of employees is π3, and the replication dynamic equation is F(z), which is as follows: π 31 =-C g +R g - the R c +(1-y)V(P c ) p 32 =-C g +QR g -yβR c +(1-y)γV(P c ) F(z)=z(1-z)((1-Q)R g -y(1-β)R c +(1-y)(1-γ)V(P c )) By combining the replication dynamic equations of employees, enterprises, and relevant departments, we obtain the replication dynamic equation system:

8. The method for selecting quality reward and punishment strategies based on cumulative prospect theory and three-party evolutionary game according to claim 7, characterized in that: According to the method proposed by Friedman, the stability of the equilibrium point of the dynamic system described by the differential equation is obtained from the local stability analysis of the Jacobian matrix; the Jacobian matrix is ​​expressed as: The equilibrium point of the replicated dynamic equation system is introduced into the Jacobian matrix to obtain the Jacobian matrix corresponding to each equilibrium point. First, the stability of the equilibrium point E1(0,0,0) is analyzed. The Jacobian matrix at this time is: According to Lyapunov system stability theory, when all eigenvalues ​​of J have negative real parts at a certain equilibrium point, this point is the ESS of the game; it is obtained from the Jacobian matrix J1, and the three eigenvalues ​​of the matrix are: λ1=V(P e )+α(1-δ)V(L e )-C es λ2=βR c +γV(P c ) λ3=(1-Q)R g +(1-γ)V(P c )。 9. The method for selecting quality reward and punishment strategies based on cumulative prospect theory and three-party evolutionary game according to claim 8, characterized in that: Equilibrium situation analysis; According to Lyapunov system stability theory, eigenvalues ​​greater than zero are unstable points, so E1(0,0,0), E2(0,0,1), and E5(1,0,0) are unstable points. E3(0,1,0), E4(0,1,1), E6(1,0,1), E7(1,1,0), and E8(1,1,1) are analyzed for stability by adding parameter constraints; Case 1: When R e +V(P e )+α(1-δ)V(L e )-C es <0 and (1-Q)R g -(1-β)R c <0, the rewards employees receive for strictly adhering to quality requirements are lower than the difference between the labor saved by not strictly adhering and the penalties and salary demotions incurred for not strictly adhering. Employees will choose the "not strictly adhering to quality requirements" strategy. The benefits of strict supervision by the competent authorities are lower than the rewards they pay to the enterprises. Therefore, the competent authorities tend to choose the "not strict supervision" strategy. In this case, the stable point of the game model is E3(0,1,0), which is not the optimal solution. Product quality cannot be guaranteed, and the long-term interests of the three parties in the game cannot be met. Case 2: When R e +V(P e )+α(1-δ)V(L e )-C es <0 and -(1-Q)R g +(1-β)R c When the value < 0 is true, the reward employees receive for strictly adhering to quality requirements is lower than the difference between the labor saved by not strictly adhering and the penalty and salary reduction they receive for not strictly adhering. Therefore, employees will choose the "not strictly adhering to quality requirements" strategy. The benefits of strict supervision by the competent authority are higher than the reward it pays to the company, so the competent authority tends to choose the "strict supervision" strategy. In this case, the stable point of the game model is E4(0,1,1). Employees' violations directly affect product quality, and this stable point is not the optimal solution. Case 3: When -V(P e )-α(1-δ)V(L e )+C es <0 and -R e +R c +V(P c )<0, the labor saved by employees not strictly adhering to quality requirements is lower than the penalties and salary reductions they receive for not strictly adhering to quality requirements, so employees will choose the "strict adherence to quality requirements" strategy. The rewards paid by the company for employees' strict adherence to quality requirements are higher than the sum of the absolute values ​​of the rewards and penalties received by the competent authorities, so the company tends to choose the "passive reward" strategy. In this case, the stable point of the game model is E6(1,0,1). The company's passive reward strategy will affect employee attitudes and is detrimental to long-term product quality assurance. This stable point is not the optimal solution. Case 4: When R e +V(P e )+α(1-δ)V(L e )-C es >0, R e -βR c -γV(P c )<0,(1-Q)R g -(1-β)R c <0 are both true, the labor saved by employees not strictly complying with quality requirements is lower than the sum of the penalties and salary demotions received for not strictly complying with them and the rewards received for strictly complying with them, so employees will choose the "strict compliance with quality requirements" strategy; the rewards paid by the enterprise for employees strictly complying with quality requirements are lower than the sum of the absolute values ​​of the rewards and penalties received by the competent authorities, so the enterprise tends to choose the "active reward" strategy; the benefits of strict supervision by the competent authorities are lower than the rewards they pay, so the competent authorities tend to choose the "lax supervision" strategy; in this case, the stable point of the game model is E7(1,1,0), and the lax supervision of the competent authorities is not conducive to the quality work of the enterprises, so this stable point is not the optimal solution; Case 5: When R e >C es -V(P e )-α(1-δ)V(L e ), R e <R c +V(P c ), (1-β)R c When <(1-Q)R is established at the same time, the rewards received by employees for strict compliance are higher than the sum of the penalties and salary demotions received for non-strict compliance and the labor saved; the rewards paid by enterprises for employees' strict compliance with quality requirements are lower than the sum of the absolute values ​​of the rewards and penalties given to the enterprises by the competent authorities; the benefits of strict supervision by the competent authorities are higher than the rewards they pay to the enterprises; in this case, the stable point of the game model is E8(1,1,1), which reaches the optimal solution of the game model.

10. The method for selecting quality reward and punishment strategies based on cumulative prospect theory and three-party evolutionary game according to claim 9, characterized in that: When the three conditions are met simultaneously, i.e., strict supervision by the competent authorities, active incentives from enterprises, and strict compliance of employees with quality requirements, the system reaches its optimal level;

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