Multiagent Game of Intelligent Building Detection and Its Harm Rumor Analysis

Yang, Mingjian; She, Dandan; Guo, Yangming

doi:https://doi.org/10.1155/2023/6639335

Mathematical Problems in Engineering

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Abstract Introduction Conclusion Data Availability Conflicts of Interest Authors’ Contributions Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 6639335 | https://doi.org/10.1155/2023/6639335

Multiagent Game of Intelligent Building Detection and Its Harm Rumor Analysis

Mingjian Yang,¹Dandan She,¹and Yangming Guo¹

Academic Editor: Chiara Bedon

Received03 Feb 2023

Revised03 Apr 2023

Accepted15 Apr 2023

Published05 May 2023

Abstract

The “14th Five-Year” development plan of the construction industry of the Chinese government makes it clear that intelligent buildings are the general direction of future construction development. However, the occurrence of construction accidents in recent years has brought huge casualties. With the rapid development of third-party inspection institutions, their judgment has become an important threshold for the access to smart buildings. The failure of inspection institutions to detect the renewal of leases may lead to the failure of intelligent systems, leading to the failure of construction equipment and causing major safety accidents such as the uncontrolled fall of construction elevators and the fall of tower crane items. As the supervisor of third-party inspection institutions, government functional departments are responsible for the failure of intelligent systems. All of them undertake the important role of intelligent building security. This paper builds an evolutionary game model with government regulatory authorities, third-party testing institutions, and intelligent construction enterprises as the three game parties, based on variables that affect the factors of the players, and discusses the possible scenarios of the stabilization strategy, which draws the following points: (1) the increase of incentives and penalties by the government is conducive to promoting the construction of high-quality intelligent buildings and the normative behavior of the third party without intention to seek rent, but the increase of incentives will not be conducive to the government fulfilling its regulatory responsibilities. (2) The reasonable reward and punishment mechanism set by the government must meet the condition that the sum of rewards and punishments for all parties is greater than their speculative returns so as to ensure the safety of intelligent buildings in the evolving and stable market environment. (3) The accountability of the superior government for the dereliction of duty of the regulatory authorities is of great significance to enhancing the stability of enterprises in building high-quality intelligent buildings. (4) It is also an effective way to avoid the construction of low-quality smart buildings by improving the listed sales income of enterprises and increasing the rent-seeking cost of enterprises. Combined with the improved SIR model, it is calculated that after the occurrence of a construction accident, when the rumor first appears, the rumor will quickly spread out of control without timely management and supervision. The conclusion of the game model provides a great reference value for the government’s regulatory behavior. The quality of the government’s regulatory behavior is directly related to the future of high-quality development of intelligent construction and also expands the application field of evolutionary game theory and SIR theory. The government should actively manage third-party testing institutions and intelligent building enterprises before construction accidents happen. After the accident, strict management and supervision should be carried out on well-known bloggers before the emergence of rumors so as to reduce the possibility of standardizing individuals’ reprinting of rumors and avoid the uncontrollable negative impact in the later period, thus seriously affecting the credibility of government supervision.

1. Introduction

The development of smart buildings is directly related to the implementation efficiency of high-quality intelligent and digital transformation and upgrading of the construction industry, and it also relates to the life, health, and property safety of the residents. It has always been a hot issue concerned by the government. The importance of smart architecture is clearly defined in the “14th Five-Year Plan” for construction industry development of the Chinese government and the “14th Five-Year Plan” for construction industry development in megacities such as Beijing and Shanghai. However, in recent years, safety accidents of smart buildings occur frequently. These accidents fully exposed the lack of government management, building detection mechanism not being perfect, intelligent building digital system information transmission not being smooth, and grassroots staff practice as not being standard problems. The government’s credibility is inevitably challenged by the impact of the government’s performance view, such as infrastructure tax and the protection of local enterprises supported by local protectionism, resulting in the harm of rumors expanding credibility. As an independent third party, intelligent building testing institutions provide quality testing services for government functional departments and building subjects, which can supplement government supervision, eliminate social doubts on government credibility, and reduce the harm of rumors. With the rapid development of third-party testing institutions, their judgment has become an important threshold for the access of smart buildings, and they play an important role in the safety of smart buildings together with government quality supervision departments. Therefore, it is of great practical significance to study the supervision strategy for the third party quality inspection institutions. Relevant game research studies on rent-seeking behavior include game influence, technical measures, evolutionary strategies, and stability studies. The application of a three-way game is especially extensive in game theory. Okuguchi and Yamazaki [1] studied rent-seeking behavior in oligopoly game, indicating that tripartite evolutionary game is applicable to the study of rent-seeking behavior. Chen [2], Kou et al. [3], Liu et al. [4] Wu et al. [5], and Huang [6] analyzed the regulation rent-seeking mechanism of coal industry, international environmental protection cases, e-commerce platform, prefabricated housing, and other aspects based on the three-party game model. They also put forward proposals to raise the level of supervision in government departments. However, in the existing research studies on the three-party game strategy, there is no research on the regulation strategy of intelligent building detection rent-seeking behavior under the government reward and punishment mechanism. Lyapunov’s first method is a basic method for analyzing the stability of differential equations in modern cybernetics, which is widely used in system stability analysis. For example, Lu et al. [7] analyzed the stability of mechanical operating system. Lilong [8] combined Lyapunov’s first method to analyze and verify the stability of equilibrium points of game systems by simulation. At present, Lyapunov’s first method is rarely used in the stability analysis of three-party game, and most of the analysis is limited to the stability of pure strategy points, lacking the equilibrium analysis of mixed strategy points. The academic research on the transformation and upgrading of the construction industry and the supervision mechanism provides a lot of meaningful suggestions for the benign development of the construction industry. Ghaffarian Hoseini [9], Salvado [10], Pokhrel [11], Eini [12], and Rodrigues [13], respectively, researched on BIM application (BIM-IkBMs), full life cycle management, carbon capture device real-time management system monitoring, web application management system, etc., to provide recommendations for promoting the successful implementation of sustainable building performance. However, the current research mainly starts from the intelligent management and technology of the building industry. The rent-seeking behavior of the detection unit is less concerned. However, there have been a large number of cases in the research of other product and service quality regulation strategies, including the construction of mixed game strategies and regulation strategies under different conditions, which provide a wealth of cases and suggestions for the government. For example, Tanner [14], Konefal and Hatanaka [15], Junna [16], Du et al. [17], Celso and Alejandro [18], and Liu et al. [19] are all concerned about food safety. Evolutionary game studies have been carried out in such fields as product introduction, multipayment, energy enterprises, DSGE method, and illegal mining enterprises, but there are few research studies on the quality safety strategy of intelligent buildings. The public opinion communication and governance that affect the government’s credibility are also current research hotspots. Li et al. [20] studied the temporal and spatial evolution of online public sentiment in emergencies by using the SIR model and concluded that when public opinion occurs at the initial stage of an event, the government’s control of public opinion is both cheap and effective. Yin [21] proposed an emotion-based E-SFI transmission dynamic model and a dynamic multiple negative emotion-based MNE-SFI model [22], which considered the categories of positive, neutral, and negative emotions as well as the emotional choices of the user community. We investigate the information dissemination process of public emotions and examine how negative emotions spread on social media and the impact of emotional mutations. As can be seen from above, in the aspect of online public opinion, most of them focus on the research of the propagation mechanism of negative public opinion and lack of damage to the propagation and management of public opinion caused by the loss of government credibility, which, in turn, is caused by intelligent building safety accidents. This paper explores the rent-seeking phenomenon of intelligent building inspection agencies, explores how to guarantee the quality of intelligent buildings and the government supervision mechanism, and grasps the propagation mechanism of corresponding negative public opinions by combining the improved SIR model.

To sum up, this study mainly has the following four questions:

Firstly, considering the rent-seeking behavior between intelligent building enterprises and third-party testing institutions, this paper constructs a tripartite evolutionary game model of intelligent building enterprises, third-party intelligent building testing institutions, and government regulators and analyzes the related stability and optimal strategies. Secondly, Lyapunov’s first rule is used to find out the strategic equilibrium point of complex dynamic systems for stability analysis, and different strategy combinations and trends are evolved in combination with different conditions. Thirdly, the improved SIR (S for susceptible, I for infected, and R for removed) model is used to analyze the government’s negative public opinion caused by smart building safety accidents and explore the evolution trend under different conditions. Finally, MATLAB software is used for simulation analysis to verify the effectiveness of model analysis under different initial conditions, and based on the analysis conclusion, countermeasures and suggestions are proposed for the government to improve the quality supervision mechanism of smart buildings and control dangerous public opinion.

2. Hypothesis and Construction of the Evolutionary Game Model

The construction engineering and quality inspection of intelligent buildings are the key factors to ensure the quality of intelligent buildings. The logical relationship of the three-party evolutionary game players constructed in this paper is shown in Figure 1.

2.1. Model Assumptions

The construction quality and quality detection of intelligent buildings are the key factors to ensure the quality of intelligent buildings, and the government supervision also plays a decisive role. As shown in Figure 1, the three parties in the game are assumed. All three parties in the game are involved in two strategies to choose, and different strategies have different selection probabilities. Combining different income equations, construct different income matrix, so that each choice has different choice income. This study makes the following assumptions:

Assumption 1. When construction enterprises build high-quality smart buildings, smart buildings pass the test. When an enterprise builds a low-quality smart building, it will obtain the listing permit by quality testing through rent-seeking from a third-party testing agency, which has rent-seeking costs. Moreover, speculation in building a low-quality smart building requires speculative costs, which mainly include management expenses such as falsified construction records, false packaging, and false publicity. The construction of a smart building by an enterprise has speculative costs.

Assumption 2. Intelligent buildings can only be listed and sold for people to live in after passing the test of the third-party testing institution. If they fail to pass the test, they cannot be listed. When an enterprise builds a low-quality smart building, if the third-party testing institution refuses to seek rent, the test will fail. If the third-party testing institution intends to seek rent and conducts rent-seeking behavior with the construction enterprise, it will help the low-quality smart building obtain the listing license. The rent-seeking costs of third-party testing institutions mainly include the expenses of forging test records and issuing false reports.

Assumption 3. The construction of high-quality intelligent buildings by enterprises is conducive to the health of residents and social stability, and it brings social benefits to the government. When enterprises build low-quality smart buildings and reach rent-seeking agreements with third-party testing agencies, low-quality smart buildings will be sold on the market, which will increase the uncertainty of building safety and affect residents’ life and property safety and social and economic development, and cost the government to maintain social stability and regulate the construction industry in the later period. Due to the loose supervision strategy of the government quality supervision department that leads to the sale of low-quality smart buildings on the market, the supervision department will be punished by the superior subjective department, which will set up the administrative penalty limit. On the basis of the above analysis, the following variables were set to describe all the benefits and costs for the participants: α₁—Build high-quality intelligent buildings; α₂—Build low-quality smart buildings; x—The probability of choosing to build high-quality smart buildings; 1 − x—The probability of choosing to build low-quality smart buildings; β₁—Third-party testing institutions have no intention of seeking rent; β₂—Third-party testing institutions have intention of seeking rent; y—Probability of unintentional rent-seeking by a third-party testing agency; 1 − y—Probability of intentional rent-seeking by a third-party testing agency; γ₁—Government quality and safety supervision departments strictly supervise; γ₂—Government quality and safety supervision departments tax supervision; z—The probability of strict supervision by government quality and safety supervision departments; 1 − z—The probability of tax supervision by government quality and safety supervision departments; R_s—Income after the market sale of smart buildings; C_sh—The cost for enterprises to build high-quality smart buildings; C_sl—The cost for enterprises to build low-quality smart buildings, C_sh > C_sl; ^B_t—Third-party testing institutions obtain marketing authorization through quality testing through rent-seeking, rent-seeking cost, B_t < (C_sh − C_sl); C_s—The speculative cost of building smart buildings V_t—The testing income of the third-party testing institution; C_t—Intended rent-seeking costs of third-party testing institutions; F_s—Smart building companies that build low-quality smart buildings will be fined; F_t—Third-party testing agencies that intend to seek rent can be fined; M_s—Enterprises are rewarded for building high-quality smart buildings; M_t—Reject the reward of rent-seeking third-party testing agencies; —The cost of strict government regulation; —Government brings social benefits; —Late government maintenance of social stability and regulation of the construction industry cost; —The supervision department will be subject to the penalties of the superior subjective department, > .

2.2. Model Construction

According to the above assumptions, the intelligent building construction enterprise, the third-party testing agency, and the government department construct a mixed strategy game matrix, as shown in Table 1.

3. Model Analysis

3.1. Stability Strategy Analysis of Intelligent Building Construction Enterprises

The expected return and average expected return () of intelligent building construction enterprises to build high-quality or low-quality intelligent buildings are

The dynamic equation of selection strategy of intelligent building construction enterprise is as follows:

The first derivative of x and the setting G(y) are

According to the stability analysis of the differential equation, the probability that the construction enterprise chooses to build a high-quality intelligent building is in a stable state and needs to meet the following requirements:

Because , so G(y) is a minus function with respect to y. Thus, when , G(y) = 0, . Intelligent building enterprises cannot be sure of stable strategy. When y < , G(y) > 0, and , x = 0. It is an evolutionary game stability strategy (ESS) of intelligent building construction enterprises. On the contrary, x = 1 is ESS.

The probability of the construction enterprise to produce low-quality intelligent buildings is A₁ volume V_A1, and the probability of stable construction of high-quality intelligent buildings is A₂ volume V_A2.

Conclusion 1. The probability of intelligent building enterprises to build high-quality intelligent buildings is positively related to the sales revenue, rent-seeking cost, speculative cost, and government incentive mechanism of intelligent buildings and negatively related to the cost saved by intelligent building enterprises to build low-quality intelligent buildings. It is proven as follows: according to the expression of the probability V_A2 of high-quality construction of intelligent construction enterprises, the first-order partial derivative is solved, andTherefore, the increase in R_s, B_t, and (F_s + M_s) or the decrease in (C_sh − C_sl) can increase the probability of construction enterprises producing high-quality smart buildings.
Conclusion 1 shows that ensuring the sales revenue of intelligent buildings of construction enterprises can effectively prevent enterprises from building low-quality intelligent buildings. The government can effectively curb the emergence of low-quality smart buildings by increasing the amount of rewards and punishments and can increase the speculative cost of enterprises by increasing publicity and media influence so as to urge construction enterprises to build high-quality smart buildings.

Conclusion 2. This shows that in the process of game evolution, the probability of intelligent building construction enterprises to build high-quality intelligent buildings increases with the refusal of third-party inspection agencies to seek rent, and the strict supervision of the government also increases the corresponding probability. The proof is as follows: according to the stability analysis of intelligent building construction enterprises, whenthen x = 0 is an evolutionary equilibrium strategy; on the contrary, x = 1 is an evolutionary equilibrium strategy. With the gradual increase in y and z, the stability of intelligent building construction enterprises increases from x = 0 (building low-quality intelligent buildings) to x = 1 (building high-quality intelligent buildings).
Conclusion 2 shows that the increase in the probability of unintentional rent-seeking of third-party building testing institutions is determined by the strategy that is conducive to the construction of high-quality smart buildings by construction enterprises. The government quality inspection department can ensure the quality and safety of smart buildings by increasing the probability of strict supervision and ensuring the fairness and equity of third-party testing institutions. The government can also regulate the sense of social responsibility and enterprise credibility of third-party testing through media publicity and reward and punishment rules, build a social security assurance mechanism for smart buildings, and promote social residents to live and work in peace and contentment.

3.2. Stability Strategy Analysis of the Third-Party Building Inspection Agency

The expected income and average income of the third-party drug testing agency from unintentional rent-seeking and intentional rent-seeking are

According to the equation set (5), the replication dynamic equation and the first derivative of the third-party testing agency are

According to the stability of the differential equation, the probability of the third party building inspection agency choosing unintentional rent-seeking must meet the following requirements:

and J(z) are subtracting functions. Therefore, when . At this time, the third-party testing agency cannot determine the stability strategy; when z < , J(z) > 0, so y = 0 is ESS; and when z > , y = 1 is ESS.

V_B1 is the probability of stable selection of unintentional rent-seeking by the third-party building testing agency, and V_B2 is the probability of stable selection of intentional rent-seeking by the third-party building testing agency.

Conclusion 3. The probability of unintentional rent-seeking of third-party building detection agencies is negatively related to the rent-seeking income of the third party and positively related to the government’s reward amount for unintentional rent-seeking, the amount of punishment for intentional rent-seeking, and the speculative cost. It is proven that V_B1 calculates the first derivative of each element separately to obtain . Therefore, the decrease in B_t and the increase in M_t, F_t, and C_t can increase the probability of unintentional rent-seeking by the third party.
Conclusion 3 shows that the government should strictly supervise the third-party building testing institutions when the rent-seeking income of the third-party building testing institutions is large. At the same time, strengthening the continuing education and training of testing personnel and expanding media publicity to increase the rent-seeking opportunity cost of third-party testing institutions will help reduce speculations. High fines can also effectively protect the safety of smart buildings, and rewards can also effectively promote the fairness of testing institutions.

Conclusion 4. In the evolution process, the probability of unintentional rent-seeking of third-party building inspection institutions increases with the strict supervision of government quality inspection departments and the probability of construction enterprises building high-quality smart buildings.

Proof. According to the strategic stability analysis of the third-party testing agency, . y = 0 is ESS; z > , x > , and y = 1 are ESS. Therefore, with the increase in x and z, the probability of unintentional rent-seeking of third-party detection agencies increases from y = 0 to y = 1. Therefore, y increases with the increase in x and z.
Conclusion 4 shows that the regulatory strategies of intelligent building construction enterprises and government quality inspection departments will affect the selection of stable game strategies for third-party testing institutions. The increased probability of government quality inspection departments strengthening supervision and enterprises building high-quality wisdom will prompt third-party testing institutions to choose a stable strategy of unintentional rent-seeking. Therefore, to promote the healthy and rapid development of the smart building industry and ensure the impartiality and independence of the third-party testing institutions, strict supervision measures from the quality inspection and supervision department of the government are required. At the same time, enterprises that build high-quality smart buildings should be rewarded, and their employees should be trained to have high quality awareness and refuse to invest.

3.3. Stability Strategy of Government Quality Supervision Department

The expected return and final average return of strict and loose supervision by the government quality supervision department are , respectively,

The replication dynamic equation and the first derivative of z selected by the government quality inspection department strategy are set as H(y), which are, respectively,

The strict supervision of the government quality inspection department is in a stable state and needs to meet because H(y) is an increasing function with respect to y. So when , it is unable to determine stability strategy.

when y < , H(y) < 0, z = 1 is ESS; conversely, z = 0 is ESS.

The probability of strict supervision by the quality inspection department of the government is V_C1, and the probability of loose supervision is V_C2, which can be calculated as follows:

Conclusion 5. The probability of strict supervision by the government quality inspection department is positively related to the punishment of the government quality inspection department on the smart building and the fine imposed by the superior for the poor supervision of the government quality inspection department, negatively related to the reward given by the government quality inspection department to the smart building construction enterprises and third-party testing institutions, and affected by multiple relationships with the amount of fines imposed by the government on third-party testing institutions. It is proven that, according to V_C, the first-order partial derivatives of each element are solved, respectively, asWhen F_t increases, V_C1 increases. In addition, the increase of F_s and _g or the decrease of M_s and M_t can increase the probability of strict supervision by the government quality inspection department.
Conclusion 5 shows that the higher the fine amount set by the quality inspection department of the government, the more strict supervision will be promoted. The higher the reward amount set, the lower the strict supervision rate of the government, and the heavier the punishment imposed by the superior government on the quality inspection supervision department, the more often the supervision department will be promoted to fulfill its supervision responsibility. In addition, the more strictly the quality inspection department of the government supervises, the less interested the third-party institutions are in rent-seeking, which is conducive to the high-quality development of smart buildings.

Conclusion 6. In the evolutionary game process, the strict supervision rate of the government quality inspection department decreases with the increase in the probability of the construction enterprise building high-quality intelligent buildings and the probability of the third-party detection agency unintentional rent-seeking.
It is proven that y < is obtained from the evolutionary stability analysis of the government quality inspection department’s strategy selection, which isz = 1 is the stability strategy of the evolutionary game. With the increase of y and x, the probability of the government quality inspection department decreases from z = 1 to z = 0. The probability of z is negatively correlated with the probability of x and y.
Conclusion 6 shows that the probability of strict supervision by the government quality inspection department is affected by the strategic choice of intelligent building construction enterprises and third-party testing enterprises. When the probability of unintentional rent-seeking by third-party testing institutions and the probability of building high-quality intelligent buildings by construction enterprises increase, the probability of strict supervision by the government quality inspection department will decrease, which is easy to increase the possibility of lack of regulatory vacuum.

3.4. Equilibrium Point and Stability Analysis of Tripartite Evolutionary Game

System F(x) = 0, F(y) = 0, F(z) = 0. The system equilibrium point is

x, y, z ∈ [0, 1], E₉∼E₁₃ is meaningful under certain conditions because , is meaningless. The Jacobian matrix of the three-party game is

Lyapunov’s first rule is used to know that if all the eigenvalues of the Jacobian matrix are negative real parts, then the equilibrium point is asymptotically stable. If the eigenvalue of the Jacobian matrix has at least one positive real part, then the equilibrium point is an unstable point. In addition to the eigenvalues whose real part is zero, the other eigenvalues of the Jacobian matrix have negative real parts, which means the equilibrium point is in a critical state and the stability cannot be determined by the sign of the eigenvalues. The balance points are analyzed as follows.

Conclusion 7. When ① C_sl − C_sh + C_s + B_t + F_s + M_s < 0, M_t + F_t + C_t − B_t < 0, the replication dynamic equation has two stable points E₄ (0, 0, 1) and E₅ (1, 1, 0).
It is proven that, according to Table 2, condition ① is satisfied at this time, so E₄ (0, 0, 1) and E₅ (1, 1, 0) are the stable asymptotic points of the system. If conditions ② and ③ are not met, the equilibrium points E₁₂ (x₂, y₂, 0) and E₁₃ (x₃, y₃, 1) are unstable points.
Conclusion 7 shows that when the government’s incentives and punishments are small or the enterprise’s speculative income from building low-quality intelligent buildings is very high and the rent-seeking income ratio of the third-party detection unit is also high, the evolution of the combination strategy is stable at two stable points (building low-quality intelligent buildings, intentionally seeking rent, and strict supervision) and (building high-quality intelligent buildings, unintentional rent-seeking, and loose supervision). At this time, the government regulatory authorities lack effective supervision and cannot effectively restrict the testing behavior of construction enterprises and third-party testing institutions. It is risky for low-quality smart buildings to be approved, which poses a serious threat to the life and health of consumers. In order to avoid the emergence of bad stability strategies (building low-quality intelligent buildings, intentionally rent-seeking, and strict supervision), the regulatory authorities must set a large enough reward and punishment quota to play the role of the reward and punishment mechanism.

Conclusion 8. When F_s + M_s > C_sh − C_sl − C_s − B_t > 0, M_t + F_t > B_t − C_t > 0, the system has a stable point E₅ (1, 1, 0), and when F_s − M_t > C_g and F_t − M_s > C_g are satisfied, the replication dynamic system only has a stable point E₅ (1, 1, 0).
It is proven that, when F_s + M_s > C_sh − C_sl − C_s − B_t > 0, M_t + F_t > B_t − C_t > 0, according to Table 2, conditions ① and ⑤ are not met, then E₄ (0, 0, 1) is an unstable point, and E₁₃ (x₃, y₃, 1) is meaningless. At this time, if condition ④ is met, E₁₂ (x₂, y₂, 0) is the unstable point. If conditions ② and ③ are satisfied, more elements are needed to be judged. At this time, the stability of E₉ (0, y₁, z₁) and E₁₀ (x₁, 0, z₂) cannot be judged. When the conditions F_s − M_t > C_g and F_t − M_s > C_g are added, the conditions ② and ③ are not satisfied. At this time, E₉ (0, y₁, z₁) and E₁₀ (x₁, 0, z₂) are meaningless, and there is only one stable point E₅ (1, 1, 0) in the replication dynamic system.
Conclusion 8 shows that the sum of fines and rewards imposed by government regulatory authorities on intelligent building construction enterprises and third-party quality inspection institutions should be higher than their respective speculative earnings so as to effectively prevent the emergence of a stable strategy combination of third-party game systems (building high-quality intelligent buildings, third-party rent-seeking, and strict supervision). In addition, the income from the listing and sales of smart buildings, the cost of strict government supervision, and the changes in the amount of administrative penalties suffered by the government’s weak supervision do not change the stability results of the evolutionary stability strategy. In addition, the government has set a reasonable reward and punishment mechanism to avoid the emergence of a mixed strategy equilibrium point. For example, the difference between the fine amount of the intelligent construction enterprise and the reward to the third-party institution is greater than the cost of strict supervision, and the difference between the penalty amount of the third party institution and the reward to the intelligent construction enterprise is greater than the cost of strict supervision. It can be seen that the reward and punishment mechanism designed by the government can reasonably guarantee the construction quality of smart buildings and promote the transformation and upgrading of smart buildings for high-quality development.
To sum up, based on the tripartite evolutionary game model, the analysis of the tripartite subjects and the relevant results are of great policy-guiding significance and effectively promote the high-quality development of smart buildings. The degree of supervision of the government subject to third-party testing institutions and smart building construction institutions is directly related to the selection of high-quality operations. Through policy incentives and punishments, the working process of the construction and testing parties is effectively regulated to avoid the occurrence of rent-seeking illegal behaviors. In the game balance, all three parties get the maximum benefits.

4. Simulation Analysis

In order to verify the effectiveness of evolutionary stability analysis, the model is given numerical values in combination with the reality, and MATLAB 2016 is used for simulation training. According to the cost-benefit ratio of actual smart building projects and relevant literature research of Junna [16], Du et al. [17], and Liu et al. [23], value 1 is determined: R_s = 160, C_sh − C_sl = 85, C_s = 10, B_t = 40, F_s = 40, M_s = 20, C_t = 10, F_t = 20, M_t = 15, C_g = 15, and = 40, which meets the conditions in Corollary 8. Based on array 1, analyze the impact of R_s, B_t, F_t, M_t, M_s, and T_g on the process and results of evolutionary games.

First, in order to analyze the impact of R_s change on the evolutionary game process and results, R_s = 80, 160, and 240 are assigned, respectively, and the simulation results of 60 times of evolution of the copied dynamic equations over time are shown in Figure 2. To analyze the impact of B_t change on the evolutionary game process and results, B_t = 30, 60, and 90 are assigned, respectively; the simulation results are shown in Figure 3.

It can be seen from Figure 2 that, in the process of system evolution to a stable point, the improvement of sales revenue of smart buildings listed on the market can accelerate the evolution speed of smart building construction enterprises to build high-quality smart buildings. With the increase of R_s, the probability of smart building construction enterprises to build high-quality smart buildings increases, and the probability of government supervision departments to strictly supervise decreases. Therefore, the government must strengthen its supervision over the construction quality while controlling the construction price of smart buildings. Especially for smart buildings with unstable construction quality, the price control can be appropriately relaxed to ensure the construction quality and effectively reduce the economic burden of the construction process and the burden of people’s housing purchases.

Figure 3 shows that, in the evolution process, with the increase of B_t, the probability of construction enterprises building high-quality smart buildings increases and the probability of third-party quality inspection institutions engaging in unintentional rent-seeking decreases. The government can increase the rent-seeking cost of smart building construction enterprises and increase the probability of building high-quality buildings by increasing media exposure, enhancing the reputational influence of enterprises, and cultivating consumers’ awareness of smart building safety.

Next, assign F_t = 0, 30, and 60, respectively, and the simulation results are shown in Figure 4. Assign M_t = 0, 20, and 40, respectively, and the simulation results are shown in Figure 5.

Figure 4 shows that before the probability of enterprises building high-quality intelligent buildings is stable and 1, the increase of F_t will increase the rate of strict government supervision. After the evolution of enterprises building high-quality intelligent buildings is stable and 1, the probability of strict government supervision will gradually decline and be stable and 0. Moreover, the increase of F_t will increase the probability of detection of institutions’ unintentional rent-seeking.

As shown in Figure 5, increasing M_t will reduce the rate of strict government supervision during the evolution process. Therefore, the government should reasonably formulate a reward and punishment mechanism to replace the fixed payment of the third-party testing agency with bonus, so that the third-party building testing agency can share the responsibility of protecting public life and property with the government.

Furthermore, assign M_s = 0, 30, and 60, respectively, and copy the simulation results of 60 times of evolution of dynamic equations with time, as shown in Figure 6; assign T_g = 30, 60, and 80, respectively, and the simulation results are shown in Figure 7.

Figure 6 shows that, in the process of evolutionary stability, the probability of strict government regulation will decrease with the increase of M_s, and the probability of third-party quality inspection institutions refusing to seek rent will increase. Figure 7 shows that after the probability of intelligent building construction enterprises building high-quality intelligent buildings is stable at 1, the increase of T_g will increase the probability of strict government supervision. It can be seen that although the government’s incentive mechanism for smart building construction enterprises can promote their construction of high-quality smart buildings, it is not conducive to the performance of the regulatory authorities themselves. The higher penalty amount imposed by the superior government will enable the regulatory authorities to continue to exercise strict supervision, further increasing the robustness of building high-quality smart buildings.

Array 1 satisfies the conditions in Conclusion 8, and array 2 is assigned:

R_s = 160, C_sh−C_s = 105, C_s = 10, B_t = 50, F_s = 25, M_s = 15, C_t = 10, F_t = 18, M_t = 12, C_g = 15, and T_g = 40 meet the conditions in inference 7 and evolve the two groups of values 60 times over time from different initial strategy combinations, as shown in Figures 8 and 9.

It can be seen from Figure 8 that the simulation result, E₁₀ (x₁, 0, z₂), is an unstable point, and the system now has only one stable evolution strategy combination (building high-quality smart buildings, unintentional rent-seeking, and loose supervision), which is consistent with the conclusion of inference 8. Figure 9 shows that under condition 1, the system has two evolutionary stability points (0, 0, 1) and (1, 1, 0), which are the strategy combinations of drug manufacturers, third-party drug testing institutions, and government regulatory authorities (building low-quality intelligent buildings, intentionally rent-seeking, and strict supervision) and (building high-quality intelligent buildings, unintentionally rent-seeking, and loose supervision). Therefore, the regulatory authorities should strengthen information construction, investigate the interests of intelligent construction enterprises and third-party construction testing institutions in many aspects, ensure that the sum of fines and rewards for all parties is higher than the speculative profits of all parties, and avoid the phenomenon that low-quality intelligent construction harms consumers due to the rent-seeking behavior of third-party testing institutions. It can be seen that the conclusion of the simulation analysis and strategy stability analysis of all parties is consistent and effective, which has practical guiding significance for the construction quality supervision of smart buildings. Through numerical simulation and comparison of existing research results, it makes up for the gap in the current research field and puts forward reasonable suggestions and policy planning for the effective management and supervision of third-party testing institutions and construction units of intelligent buildings, which promotes the sustainable development of China’s intelligent buildings.

5. Rumor Analysis

Social media network communication has its own characteristics. In recent years, safety liability accidents caused by the poor quality of smart buildings have become common, many of which are caused by the negligence of construction enterprises and third-party testing institutions. However, more people listen to rumors, which challenge the credibility of the government. Therefore, the research on the spread of online rumors has great practical and theoretical significance. The SIR model is the most classic model of infectious disease, where S represents susceptible, I represents infected, and R represents displaced. Susceptible to susceptible infections, those who are susceptible to infectious diseases are classified into three categories: class S, those who are not susceptible to the disease but lack immune capacity and are susceptible to infection after coming into contact with susceptible persons; category I, active, refers to a person who has an infectious disease, which is transmitted to members of category S; class R, removal, refers to a person who is isolated or becomes immune to illness. This paper uses the improved SIR model to analyze the simulation data. The network pusher has great information dissemination ability, and its dissemination exists for the dissemination node in the social network. Let its contact rate be θ₁. For common nodes in the network that can transmit information, set the contact rate as θ₂. Different from the traditional SIR model, in social networks, the removed nodes are not necessarily transformed from the propagation points. After users know the message, they have a certain probability to stop forwarding and exit and also have a certain probability to continue forwarding. However, relatively few users continue to do so.

To sum up, the spread rules of rumor information on social networks including heat propagation nodes can be expressed as follows: (1) the contact rate of common nodes in social networks is θ₁. The effective contact rate with other nodes is θ₂. (2) After receiving the information, the node may be transformed into an ordinary information disseminator μ by making the change to move it out by 1 − μ. It turns into an ordinary node with a probability of 1 − μ. (3) Finally, rumors spread continuously on social networks and eventually become stable.

Its model is shown in Figure 10.

i₀ in the figure represents the proportion of heat propagation nodes in social network rumors, and its value is generally fixed; i(t) represents the proportion of common propagation nodes at time t, consisting of i₁(t) and i₂(t), where i₁(t) represents the common propagation nodes generated by the heat propagation nodes, and i₂(t) represents the new propagation nodes generated by the common propagation nodes; θ₁(t) is the contact rate of the heat propagation node; θ₂(t) is the contact rate of the common propagation node; R(t) represents the proportion of nodes removed; μ represents the immunity probability; and the total number of users in the social network is N.

The number of users of Microblog Live reached 200 million. On the 60th day, 98% of the nodes moved out, indicating that 98% of the users have been rumored. The number of the three types of nodes is basically stable, so the rumor-spreading process is over. It can be seen that the information spreads slowly in the first 0–20 days (the number of propagation nodes is limited), increases rapidly in the next 20–60 days (the number of propagation nodes also increases rapidly), and tends to be flat after 60 days. Then, the 60-day propagation efficiency is realistic. At present, the rumor propagation has been completed within 5 days. It is shown in Figure 11.

5.1. Reduce Immunity Probability

It can be seen from Figure 12 that when the immune probability drops to about 90%, the topic will be infected at 0 node within 6 days, so that the topic will be fully infected. In other words, 10% of users who have access to this information will actively convert it, which is also difficult in reality.

5.2. Improve the Daily Contact Rate of Heat Transmission Nodes

It can be seen from Figure 13 that if there are only 10 heat propagation nodes, each node must be a well-known blogger node that can effectively convey the “super heat” of 10 million users. For 200 million daily active users in the model, this is unrealistic.

5.3. Improve Daily Contact Rate of Common Nodes

It can be seen from Figure 14 that the daily contact rate of ordinary users must reach 300, that is, half of the heat transmission nodes can achieve the above effect.

In general, the rumor will be fully covered in the above 5–7 days, which will cause great difficulties in preventing the spread of rumors and recovering from their adverse effects. When rumors appear, we need to strictly manage and supervise well-known bloggers, reduce the possibility of regulating individual reprints of rumors, avoid uncontrollable negative effects in the later period, and seriously affect the credibility of government supervision.

6. Conclusion

Considering the possible rent-seeking behavior of intelligent building construction enterprises and third-party testing institutions, this paper analyzes the stability of each party’s strategy choice, the stability of game strategy balance, and the influence relationships of each element by building a three-way evolutionary game model between intelligent building construction enterprises, third-party testing institutions, and government regulators and verifies the effectiveness of the analysis conclusion through simulation analysis. The conditions for the rent-seeking behavior of smart buildings as a stable strategy combination are obtained, and the relevant countermeasures and suggestions for the quality supervision of smart buildings are put forward according to the relationship between various influencing factors and stable conditions. In addition, combined with the spread analysis of rumor information in Internet media, we put forward corresponding suggestions to stop rumors.

The main conclusions include the following:

(1) The government’s increase in rewards and punishments will help promote enterprises to build high-quality smart buildings and regulate the behavior of third parties who are not interested in rent-seeking, but it will not help the government perform its regulatory responsibilities; (2) the reasonable reward and punishment mechanism set by the government must meet the condition that the sum of rewards and punishments for all parties is greater than their speculative profits so as to ensure the safety of smart buildings in an evolutionary and stable market environment; (3) the accountability of the superior government for the dereliction of duty of the regulatory authorities is of great significance to enhancing the stability of enterprises in building high-quality smart buildings; (4) it is also an effective way to prevent enterprises from building low-quality smart buildings by improving the sales revenue of smart buildings listed on the market and increasing the rent-seeking cost of enterprises; and (5) when rumors appear, we need to strictly manage and supervise well-known bloggers, reduce the possibility of regulating individual reprints of rumors, avoid uncontrollable negative effects in the later period, and seriously affect the credibility of government supervision [24–31].

7. Research Limitations

This paper only considers the quality supervision of smart buildings in construction and testing under asymmetric information and bounded rationality without considering the adverse impact of smart buildings on the market and the influence of game order.

7.1. Future Work

It will be our next research direction to introduce consumer feedback and other factors, build a dynamic and repeated game model with consumer participation, study the influence mechanism of listing and use of smart buildings on the quality of smart buildings, and put forward innovative suggestions to improve the quality supervision of smart buildings.

Data Availability

The data is in the simulation of this paper.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Authors’ Contributions

Mingjian Yang conceptualized the study, performed formal analysis, and wrote the original draft. Dandan She wrote the original draft, edited the manuscript, and visualized the study. Yangming Guo typesetted the articles. All authors have read and approved the final manuscript.

Acknowledgments

This study was supported by The Jiujiang Vocational and Technical College-University-Level Science and Technology Project “Research and Development and Preparation of Key Technologies of Portable Cast-in-Place Concrete Thickness Intelligent Detector” (grant no. 2022008).

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Copyright © 2023 Mingjian Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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