Tripartite Evolutionary Game Analysis of Participants’ Behaviors in Technological Innovation of Mega Construction Projects under Risk Orientation

Abstract

Technological innovation of mega construction projects (MCPs) plays a crucial role in promoting upgrades to the construction industry. However, MCPs are complex and the transformation ratio of technological innovation achievements is generally low. To achieve the goal of technological innovation of MCPs which requires organizations from multiple fields to participate, it is critical to find the factors that influence cooperation and subsequently reduce the risk of technological innovation. Therefore, taking the risk as the guide of participants’ behaviors, this study constructs an evolutionary game model by tripartite participation: the owners or the representatives of the users who rely on the MCPs with technological innovation (the Users), the construction production enterprises (the CPEs), and the universities and the research institutes (the URIs). We derive the evolutionary stable strategy and apply matlab2020a for simulation analysis. The findings are as follows: (1) The strategy choice of the participant will be influenced by the strategy choices of other participants. (2) Collaborative cooperation for all parties is the evolutionary stable strategy. (3) The sensitivity of the participants to different parameters is different, and they are more sensitive to the perceived loss of technological innovation risk, risk-taking ratio, technological innovation investment, and cost compression coefficient. Based on the research results, the study provides effective suggestions for the Users and the government. The Users can quantify risk loss, refine risk management and establish collaborative cooperation evaluation indexes, and it is necessary for the government to encourage technological innovation of MCPs.

1. Introduction

The development of society will take construction innovation as the main battlefield [1]. Moreover, the transformation and upgrading of the construction industry will take the technological innovation of MCPs as the starting point [2]. However, MCPs characterized by a large investment scale, complex technology, and many stakeholders, as well as the uncertainty of technological innovation leads to the complexity of technological innovation in MCPs [3]. Although the current construction scale is gradually expanding and the innovation capacity is gradually improving, the development of construction management level lags, and the successful completion of technology innovation in MCPs faces a large number of obstacles [4]. At present, the failure rate of technological innovation is high, and failure due to failed cooperation is common [5]. Technological innovation partnership faces a “rocky road” [6,7]. How to improve management capability, promote collaborative innovation, and successfully complete technological innovation in MCPs are problems that need to be solved.

The technological innovation of MCPs requires the participation of many participants with professional backgrounds to complete together through multiple stages of research and application [8,9]. At present, the transformation ratio of technological innovation achievements is generally low, and the success and failure of technological innovation are closely related to the participants’ behaviors [10]. The starting point and interest demand among the cooperating participants determine their behaviors [11], and collaborative cooperation is manifested by the importance attached to relations, which is a closer relationship compared to simple cooperation [12]. In simple cooperation, there is a lack of effective communication and resource coordination between participants, neglecting simultaneous optimization of behavior and low system matching [13]. Simple cooperation will bring technological innovation risk, leading to the failure of technology innovation in MCPs [14,15]. The risk-related parameters are introduced to explore both cooperation and conflict in multiple games to derive the key factors of collaborative cooperation in the technological innovation of MCPs [16].

Technological innovation in MCPs is more complex than most technological innovation projects and compared with the research on technological innovation in enterprises and high-tech industries, there is less research on technological innovation in MCPs [17,18]. Under risk orientation, how to effectively promote the participants in technological innovation of MCPs to carry out collaborative cooperation? To answer the above questions, the participants in the technological innovation of MCPs: the Users, the CPEs, and the URIs are simultaneously included in the same analysis framework for research. Based on six model assumptions, the study obtains the possible stable equilibrium states and corresponding preconditions of the technological innovation system in MCPs as well as the subjects’ strategy choices and related internal and external factors affecting the evolution of the system equilibrium. The technological innovation of MCPs should be coordinated and managed by the Users, and the URIs and the CPEs should participate together. Only by fully combining theory and practice can technological innovation achievements meet the needs of MCPs. However, technological innovation in different MCPs has its particularity, and this paper will not be able to include all factors of collaborative cooperation.

The remainder of this paper is structured as follows. Section 2 reviews the relevant literature to identify research gaps and previous work that can be built on. Section 3 builds the evolutionary game model for the technological innovation system of MCPs. Section 4 analyzes the replicator dynamics equations, asymptotic stability, and strategic stability. Section 5 represents the sensitivity analysis of different factors impacting the evolutionary results. Section 6 presents the discussion, and conclusions and applications are given in Section 7.

2. Literature Review

2.1. Technological Innovation of MCPs

The Oxford handbook of megaproject management considered that the megaproject typically costs 1 billion or more, and they have the characteristics of a long construction cycle, large investment scale, many participants in construction, severe technical difficulty, and innovation requirements [19]. Typical MCPs include the Qinghai-Tibet Railway, Hong Kong-Zhuhai-Macao Bridge, Great Seto Bridge, etc., and technological innovation can facilitate overcoming the difficulties encountered during the construction of MCPs, such as collaborative virtual reality and the Building Information Model [20,21]. In MCPs, demand, risk, and culture are found to be the motivations behind the technological innovation of MCPs, and converting a creative idea into reality requires projects and some form of project management [22,23].

The technological innovation of MCPs is complex and has many stakeholders. Wang and Zhang built a basic framework of the collaborative innovation network of MCPs and analyzed the roles played by different participants at different stages [24]. Zhao and An established a simulation model to study the collaborative management of MCPs, revealing the collaborative elements in the complex supply chain of the management system [25]. To complete the technological innovation of MCPs, participants usually have their strengths and basic technology innovation capabilities, and Zhang et al. pointed out that alliance-specific capabilities and knowledge-based capabilities are two key capabilities that drive technology alliance collaborative innovation [9]. However, a large number of challenges can hinder the successful completion of technological innovation of MCPs, and Guo et al. explored the influencing factors leading to the network vulnerability of technological innovation in MCPs under dual governance conditions of formal contracts and relational constraints [26]. Obviously, the technological innovation of MCPs has both internal and external factors.

2.2. Evolutionary Game Theory

Evolutionary game theory is based on the theory of biological evolution and genetic theory [27]. The evolutionary mechanism of genetic heredity, variation, and adaptive competition determines that biological evolution is based on populations rather than individuals and that biological evolution can only be manifested by an increase in the number or proportion of superior genes and a decrease in the number or proportion of inferior genes [28]. Evolutionary game theory was originally proposed by SMITH and PRICE in the study of biological phenomena, introducing the idea of evolutionary game theory and the concept of evolutionary stable strategy (ESS) for the first time [29], and the replicated dynamic equation proposed by Taylor and Jonker explains the essential features of the evolutionary game [30]. The game player tries different behavioral strategies and undergoes partial mutations each time, and in the process of continuous choice modification, the game player learns to imitate the successful choices of other individuals through choice to achieve a better strategy. When the external environment changes, the group takes time to adapt, so there may be a temporary instability state, but once the strategy that maximizes benefits is identified, the whole group will choose the strategy, and natural selection will eliminate other strategies and eventually evolve to form the ESS [31].

The evolutionary game theory takes the group as the research object and reveals the complexity and dynamic evolution path of the behavior from the perspective of finite rationality, which is widely used in the analysis of network cooperation, enterprise cooperative innovation, the stability of strategic alliances, etc. [32,33,34].

2.3. Cooperative Behavior

In general, cooperative behavior belongs to the psychological category and is expressed as mutual help, mutual encouragement, and mutual support [35]. When technological innovation can benefit all participating subjects, different subjects have a common interest orientation and can easily form collaborative cooperation, but the increase in one participant’s interest will lead to damage to other participants’ interests, and a conflict of interest among technological innovation subjects often affects cooperation [36]. Chen et al. defined the innovation behaviors of participants as “collaborative innovation”, “simple cooperation”, and “non-cooperation” [37]. Liu et al. classified the cooperation behavior among the government, the platform, and the enterprise as “active cooperation” and “negative cooperation” [38]. Some researchers identified “cooperation” and “non-cooperation” as the innovation strategies of industry-university research [39,40].

The analysis of factors influencing technological innovation behavior will facilitate the formulation of management recommendations. The evolutionary game is a suitable method to discuss the key factors of cooperative innovation, and Zan et al. considered the impact of the gent coupling degree, group size, and government policies on the stable evolution of collaborative innovation in industry-university research [41]. Huang et al. pointed out that the stability of inter-organizational alliances among asymmetric enterprises will be affected by trust, knowledge complementarity, government rewards and technology coercive transfer coefficient, technology absorptive capacity, and risk coefficient [42]. In recent years, a large number of scholars have introduced the government to construct a tripartite evolutionary game model. Hu Jun et al. concluded that government subsidies and cooperation income distribution coefficients are the key factors affecting technological cooperation through a tripartite evolutionary game [39]. Li and Zhou studied the mechanism of green technology innovation and pointed out that equitable distribution of income from collaborative innovation and penalties for non-compliance can consolidate the cooperative relationship among government, enterprises, and academic research [40].

2.4. Technological Innovation Risk

“Risk-leading audit” is an audit term; risk-leading audit refers to the risk identification of the audited unit as the basis for a comprehensive analysis of various factors for the achievement of the management objectives of the audited unit [43]. Bogoda, L., applied a risk-oriented system engineering approach to conducting a study on CNSiATM and avionics collaborative network security [44]. Katanaeva et al. built risk-oriented thinking models in the quality management system [45]. It can be found that scholars in various countries are gradually paying attention to risk and conducting risk-oriented research, but the connotation of risk orientation varies in different studies.

MCPs require a lot of technological innovation and scientific research, which require organizations from multiple industries and fields to participate in the work of technological innovation, and due to the complexity of construction technology and construction equipment of MCPs, there are a variety of risks in the process of technological innovation [22,46]. Technological innovation risks may significantly reduce technological innovation performance and lead to the interruption or even failure of technological innovation of MCPs [47]. To integrate ethical, legal, and social implications into the daily work of R&I practitioners, Brandl, C., et al., proposed to prioritize the innovation-based problems in dependence of potential risks [48]. Qu et al. empirically examined the impact of risk-taking on green technology innovation in high-tech enterprises and pointed out that risk-taking on high-tech enterprises’ green technology innovation has significant attribute heterogeneity and regional heterogeneity [49]. There is a lot of research on the risk of technological innovation, and it is necessary to start from the source to reduce the risk of technological innovation of MCPs.

2.5. Summary

In summary, scholars have analyzed the participants in the technological innovation of MCPs, their strategies, and influencing factors, and through the analysis of technological innovation risks, it is very obvious that the reduction of technological innovation risks of MCPs is necessary. Compared with the currently existing research, there are three main differences in the following aspects: (1) Taking the behaviors of participants in technological innovation of MCPs as the research objects. By establishing an evolutionary game model, the stability analysis of the equilibrium solution is carried out and the key factors of strategy selection are derived by using matlab2020a simulation analysis. (2) In the selection of participants in the technological innovation of MCPs, they will go through strict bidding review and competitive bidding, therefore this paper is based on the basic cooperative innovation ability of each participant. (3) Risk-related parameters are introduced to quantify the consequences of the participants’ behavioral choices, which are more in line with the actual construction situation.

3. Model Building

In the process of MCPs, technological innovation is an important means to break through technical problems. To find out the key factors of cooperation, a tripartite evolutionary game model for the technological innovation of MCPs under the risk orientation is established. The methodology involves three steps:

• Analyze literature to find out the participants in the technological innovation of MCPs and their relationship.
• Make model assumptions and establish the payment matrix, then get the replicated dynamic equations, and we can analyze the asymptotic stabilities and ESS through the Jacobi matrix.
• Assign parameters based on ESS, then carry out simulations by matlab2020a.

The following flowchart describes these steps, as summarized in Figure 1.

3.1. Moder Assumption

Hypothesis 1.

Participants. Without considering other constraints, the Users, the construction production enterprises, the universities, and the research institutes constitute a complete system, and all participants are finite rational individuals, who have their behavioral selection criteria and power. The Users refer to the owners or the representative of the users who rely on the MCPs with technological innovation. The construction production enterprises refer to survey, design, construction, and other production enterprises, which are at the core of technological innovation activities. Universities and research institutes are important output participants in technological innovation achievements.

Hypothesis 2.

Participation strategies. Bidding for the MCPs requires strict review and competitive bidding to ensure the competence of participants in cooperation [50], and it is assumed that all participants have a basic social responsibility and will not choose the non-cooperative strategy. The strategy ensemble of the Users: {collaborative cooperation, simple cooperation}, x is the probability of choosing collaborative cooperation for the Users; the strategy ensemble of the CPEs: {collaborative cooperation, simple cooperation}, y is the probability of choosing collaborative cooperation for the CPEs; the strategy ensemble of the URIs: {collaborative cooperation, simple cooperation}, z is the probability of choosing collaborative cooperation for the URIs. x, y, z take values between 0 and 1. The specific performance of each participant’s strategy choice is shown in

Table 1. Specific performance of the different strategies among the Users, the CPEs, and the URIs.

Participant	Strategies
	Collaborative Cooperation	Simple Cooperation
Users	1. Active feedback demand and innovative information. 2. Provide sufficient financial and institutional support.	1. The feedback on technological innovation demand is not enough. 2. The supervision is not enough.
CPEs	1. Work closely with other participants to share information and knowledge. 2. Promote the success of technological innovation while ensuring the best overall benefits of technological innovation.	1. The feedback on the actual situation of innovative technology in the application is not timely. 2. Technological innovation activities that have no benefits for itself is out of sight [36].
URIs	1. Make full use of research resources to complete the research tasks stipulated in the contract on time and with quality.	1. The completion of the research tasks is perfunctory. 2. The information feedback is not timely. 3. Technological innovation needs cannot be met [37].

.

Hypothesis 3.

The relationship between behavior, risk, and benefit. The relationship between behavior and risk is expressed as follows: the risk perceived loss coefficient is 0 if all participants choose the collaborative cooperation strategy. The risk perceived loss coefficient is 1 if all participants choose the simple cooperation strategy. The rest of the cases are described by setting discount coefficients of the risk perception loss [51]. Risk and benefit are inversely proportional, and the presence of risk will lead to the reduction of the participants’ benefits [52].

Hypothesis 4.

$r_1,r_2,r_3$are the benefits obtained by the Users, the CPEs, and the URIs to complete the technological innovation of MCPs.$c_1,c_2,c_3$are the costs of technological innovation of MCPs invested by the Users, the CPEs, and the URIs. If the participant chooses collaborative cooperation, the cost compression coefficient is 1. If the participant chooses simple cooperation, the behavior of the participant will likely lead to technological innovation risk, and the cost compression coefficient is m (0 < m < 1).

Hypothesis 5.

When the participants all choose the simple cooperation strategy,$L$is the perceived loss of technological innovation risk that needs to be shared, and perceived risk generally includes the chance of loss and magnitude of the loss [53].$p_1, p_2,p_3$are the proportions of the total risk borne by the Users, the CPEs, and the URIs$\left(p_1+p_2+p_3=1\right)$[54].$f_1$and$f_2$are respectively the discount coefficients of the risk perception loss for one participant or two choosing the collaborative cooperation strategy$(f_1>f_2)$, assuming that without considering the differences brought by different participants choosing the same strategy [55].

Hypothesis 6.

In the case that technological innovation in MCPs is completed well and achieves practical results,$g$is the reward from government authorities for the Users to complete MCP with high quality [56]. Under the premise that the Users choose the collaborative cooperation strategy,$w$denotes the reward of the Users to the CPEs or the URIs for choosing the collaborative cooperation strategy, and$k$denotes the penalty of the Users to the CPEs or the URIs for choosing the simple cooperation strategy [57].

The definitions of the main parameter symbols are summarized in

Table 2. Glossary of symbols and abbreviations.

Symbol	Description	Symbol	Description
$r_1$	Benefit obtained by the Users	$c_1$	Cost invested by the Users
$r_2$	Benefit obtained by the CPEs	$c_2$	Cost invested by the CPEs
$r_3$	Benefit obtained by the URIs	$c_3$	Cost invested by the URIs
$L$	Perceived loss of technological innovation risk	$p_1$	Proportions of total risk borne by the Users
$p_2$	Proportions of total risk borne by the CPEs	$p_3$	Proportions of total risk borne by the URIs
$f_1$	Discount coefficient of the risk perception loss for one participant choosing the collaborative cooperation strategy	$f_2$	Discount coefficient of the risk perception loss for two participants choosing the collaborative cooperation strategy
$m$	Cost compression coefficient	$g$	Reward from the government
$w$	Reward from the Users	$k$	Penalty from the Users

.

3.2. Evolutionary Game Payment Matrix

According to the above assumptions, the payment matrix of the evolutionary game among the Users, the CPEs, and the URIs is shown in

Table 3. Technological innovation cooperation in MCPs game gain matrix.

		The URIs
		Collaborative Cooperation $\mathit{z}$	$\mathbf{Simple} \mathbf{Cooperation} 1-\mathit{z}$
The Users collaborative cooperation x	The CPEs collaborative cooperation y	$r_1-c_1+g-2w$	$r_1-c_1-p_{1}L{f}_2-w+k$
		$r_2-c_2+w$	$r_2-c_2-p_{2}L{f}_2+w$
		$r_3-c_3+w$	$r_3-m{c}_3-p_{3}L{f}_2-k$
	The CPEs simple cooperation $1-y$	$r_1-c_1-p_{1}L{f}_2-w+k$	$r_1-c_1-p_{1}L{f}_1+2k$
		$r_2-m{c}_2-p_{2}L{f}_2-k$	$r_2-m{c}_2-p_{2}L{f}_1-k$
		$r_3-c_3-p_{3}L{f}_2+w$	$r_3-m{c}_3-p_{3}L{f}_1-k$
The Users simple cooperation $1-x$	The CPEs collaborative cooperation $y$	$r_1-m{c}_1-p_{1}L{f}_2$	$r_1-m{c}_1-p_{1}L{f}_1$
		$r_2-c_2-p_{2}L{f}_2$	$r_2-c_2-p_{2}L{f}_1$
		$r_3-c_3-p_{3}L{f}_2$	$r_3-m{c}_3-p_{3}L{f}_1$
	The CPEs simple cooperation $1-y$	$r_1-m{c}_1-p_{1}L{f}_1$	$r_1-m{c}_1-p_{1}L$
		$r_2-m{c}_2-p_{2}L{f}_1$	$r_2-m{c}_2-p_{2}L$
		$r_3-c_3-p_{3}L{f}_1$	$r_3-m{c}_3-p_{3}L$

.

For example, when all participants choose collaborative cooperation, $r_1-c_1+g-2w$ is the payment function of the Users, and it means the Users’ income from technological innovation of MCPs minus the investment, plus the government’s reward for the completion of the technological innovation of MCPs, minus the rewards for the collaborative cooperation of the CPEs and the URIs.

4. Model Analysis

4.1. Replicated Dynamic Equation

The expected payoffs functions of the Users’ choices of collaborative cooperation and simple cooperation are $U_x$ and $U_{1-x}$, respectively.

$$\begin{array}{cc}\hfill U_x& =yz\left(r_1-c_1+g-2w\right)\hfill \\ & +y\left(1-z\right)\left(r_1-c_1-w+k-L{f}_2{p}_1\right)\hfill \\ & +\left(1-y\right)z\left(r_1-c_1-w-k-L{f}_2{p}_1\right)\hfill \\ & +\left(1-y\right)\left(1-z\right)\left(r_1-c_1+2k-L{f}_1{p}_1\right)\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill U_{1-x}& =yz\left(r_1-c_{1}m-L{f}_2{p}_1\right)\hfill \\ & +y\left(1-z\right)\left(r_1-c_{1}m-L{f}_1{p}_1\right)\hfill \\ & +\left(1-y\right)z\left(r_1-c_{1}m-L{f}_1{p}_1\right)\hfill \\ & +\left(1-y\right)\left(1-z\right)\left(r_1-c_{1}m-L{p}_1\right)\hfill \end{array}$$

(2)

Based on Equations (1) and (2), from the Malthusian dynamic equation, the Users’ replication dynamic equations $F\left(x\right)$ and $F’\left(x\right)$ can be calculated.

$$\begin{array}{cc}\hfill F\left(x\right)=\frac{dx}{dt}& =x\left(1-x\right)\left(U_x-U_{1-x}\right)=x\left(1-x\right)(-c_1+2k+L{p}_1+c_{1}m-ky-kz-wy-L{f}_1{p}_1-L{p}_{1}y-L{p}_{1}z\hfill \\ & +gyz+L{p}_{1}yz+2L{f}_1{p}_{1}y-L{f}_1{p}_{1}y+2L{f}_1{p}_{1}z-L{f}_2{p}_{1}z-3L{f}_1{p}_{1}yz+3L{f}_2{p}_{1}yz\hfill \end{array}$$

(3)

$$F^{\prime }\left(x\right)=\left(1-2x\right)\left\{2k-\left(k+w\right)\left(y+z\right)+gyz+L{p}_1\left[\left(1-f1\right)+\left(y+z\right)\left(2f_1-f_2-1\right)+yz\left(1-3f_1+3f_2\right)\right]-c_1\left(1-m\right)\right\}$$

(4)

The expected payoffs functions of the CPEs’ choices of collaborative cooperation and simple cooperation are $P_y$ and $P_{1-y}$, respectively.

$$\begin{array}{cc}\hfill P_y& =xz\left(r_2-c_2+w\right)\hfill \\ & +x\left(1-z\right)\left(r_2-c_2+w-L{f}_2{p}_2\right)\hfill \\ & +\left(1-x\right)z\left(r_2-c_2-L{f}_2{p}_2\right)\hfill \\ & +\left(1-x\right)\left(1-z\right)\left(r_2-c_2-L{f}_1{p}_2\right)\hfill \end{array}$$

(5)

$$\begin{array}{cc}{P}_{1-y}& =xz\left(r_2-c_{2}m-k-L{f}_2{p}_2\right)\hfill \\ & +x\left(1-z\right)\left(r_2-c_{2}m-k-L{f}_1{p}_2\right)\hfill \\ & +\left(1-x\right)z\left(r_2-c_{2}m-L{f}_1{p}_2\right)\hfill \\ & +\left(1-x\right)\left(1-z\right)\left(r_2-c_{2}m-L{p}_2\right)\hfill \end{array}$$

(6)

Based on Equations (5) and (6), from the Malthusian dynamic equation, the CPEs’ replication dynamic equations $F\left(y\right)$ and $F’\left(y\right)$ can be calculated:

$$\begin{array}{c}F\left(y\right)=\frac{dy}{dt}=y\left(1-y\right)\left(P_y-P_{1-y}\right)=y\left(1-y\right)(L{p}_2-c_2+c_{2}m+kx+wx-L{f}_1{p}_2-L{p}_{2}x-L{p}_{2}z\\ +L{p}_{2}xz+2L{f}_1{p}_{2}x-L{f}_2{p}_{2}x+2L{f}_1{p}_{2}z-L{f}_2{p}_{2}z-3L{f}_1{p}_{2}xz+3L{f}_2{p}_{2}xz\end{array}$$

(7)

$$\begin{array}{c} F^{\prime }\left(y\right)=\left(1-2y\right)\left\{x\left(k+w\right)+L{p}_2\left[\left(x+z\right)\left(2f_1-f_2-1\right)+xz\left(1-3f_1+f_2\right)\right]-c_2\left(1-m\right)\right\}\end{array}$$

(8)

The expected payoffs functions of the URIs’ choices of collaborative cooperation and simple cooperation are $S_z$ and $S_{1-Z}$, respectively.

$$\begin{array}{cc}\hfill S_z& =xy\left(r_3-c_3+w\right)\hfill \\ & +x\left(1-y\right)\left(r_3-c_3+w-L{f}_2{p}_3\right)\hfill \\ & +\left(1-x\right)y\left(r_3-c_3-L{f}_2{p}_3\right)\hfill \\ & +\left(1-x\right)\left(1-y\right)\left(r_3-c_3-L{f}_1{p}_3\right)\hfill \end{array}$$

(9)

$$\begin{array}{cc}\hfill S_{1-z}& =xy\left(r_3-c_{3}m-k-L{f}_2{p}_3\right)\hfill \\ & +x\left(1-y\right)\left(r_3-c_{3}m-k-L{f}_1{p}_3\right)\hfill \\ & +\left(1-x\right)y\left(r_3-c_{3}m-L{f}_1{p}_3\right)\hfill \\ & +\left(1-x\right)\left(1-y\right)\left(r_3-c_{3}m-L{p}_3\right)\hfill \end{array}$$

(10)

Based on Equations (9) and (10), from the Malthusian dynamic equation, the URIs’ replication dynamic equations $F\left(z\right)$ and $F’\left(z\right)$ can be calculated:

$$\begin{array}{c}F\left(z\right)=\frac{dz}{dt}=z\left(1-z\right)\left(S_z-S_{1-z}\right)=z\left(1-z\right)(L{p}_3-c_3+c_{3}m+kx+wx-L{f}_1{p}_3-L{p}_{3}x-L{p}_{3}y\\ +L{p}_{3}xy+2L{f}_1{p}_{3}x-L{f}_2{p}_{3}x+2L{f}_1{p}_{3}y-L{f}_2{p}_{3}y-3L{f}_1{p}_{3}xy+3L{f}_2{p}_{3}xy\end{array}$$

(11)

$$\begin{array}{c} F^{\prime }\left(z\right)=\left(1-2z\right)\left\{x\left(k+w\right)+L{p}_3\left[\left(x+y\right)\left(2f_1-f_2-1\right)+xz\left(1-3f_1+f_2\right)\right]-c_3\left(1-m\right)\right\}\end{array}$$

(12)

4.2. Asymptotic Stability

4.2.1. Asymptotic Stability Analysis for the Users

Based on Equation (3), if $2k-\left(k+w\right)\left(y+z\right)+gyz+L{p}_1\left[\left(1-f_1\right)+\left(y+z\right)\left(2f_1-f_2-1\right)+yz\left(1-3f_1+3f_2\right)\right]-c_1\left(1-m\right)=0$, there is $F\left(x\right)\equiv 0$. At this time, the Users’ strategic selection will not change over time; that is, the Users’ strategy is stable.

Based on Equation (4), If $k\left(2-y-z\right)+gyz+L{p}_1\left[\left(1-f_1\right)+\left(y+z\right)\left(2f_1-f_2-1\right)+yz\left(1-3f_1+3f_2\right)\right]>c_1\left(1-m\right)+w\left(y+z\right)$, there is $F^{\prime }\left(0\right)>0, F^{\text{'}}\left(1\right)<0$ and then $x=1$ is the only equilibrium point. It shows that if the cost saving when the Users adopt a simple cooperation strategy and rewards for collaborative cooperation of the participants is less than the government support, penalties for simple cooperation of the participants, and the total risk perceived loss of technological innovation borne by the Users, then the collaborative cooperation is the evolutionary stable strategy for the Users. From the above equation, it can be seen that the strategy choice of the Users is influenced by the strategy choices of the CPEs and the URIs.

Based on Equation (4), if $k\left(2-y-z\right)+gyz+L{p}_1\left[\left(1-f_1\right)+\left(y+z\right)\left(2f_1-f_2-1\right)+yz\left(1-3f_1+3f_2\right)\right]<c_1\left(1-m\right)+w\left(y+z\right)$, there is $F^{\prime }\left(0\right)<0, F^{\text{'}}\left(1\right)>0$ and then $x=0$ is the only equilibrium point. It shows that if the cost saving when the Users adopt a simple cooperation strategy and rewards for collaborative cooperation of the participants exceed the government support, penalties for simple cooperation of the participants, and the total risk perceived loss of technological innovation borne by the Users, then the collaborative cooperation is the evolutionary stable strategy for the Users. From the above equation, it can be seen that the strategy choice of the Users is influenced by the strategy choices of the CPEs and the URIs.

4.2.2. Asymptotic Stability Analysis for the CPEs

Based on Equation (7), if $x\left(k+w\right)+L{p}_2\left[\left(1-f_1\right)+\left(x+z\right)\left(2f_1-f_2-1\right)+xz\left(1-3f_1+3f_2\right)\right]-c_2\left(1-m\right)=0$, there is $F\left(y\right)\equiv 0$. At this time, the CPEs’ strategic selection will not change over time; that is, the CPEs’ strategy is stable.

Based on Equation (8), if $x\left(k+w\right)+L{p}_2\left[\left(1-f_1\right)+\left(x+z\right)\left(2f_1-f_2-1\right)+xz\left(1-3f_1+3f_2\right)\right]>c_2\left(1-m\right)$, there is $F^{\prime }\left(0\right)>0, F^{\text{'}}\left(1\right)<0$, and then $x=1$ is the only equilibrium point. It shows that if the cost saving when the CPEs adopt a simple cooperation strategy is less than the sum of users’ incentives, users’ penalties, and the total perceived risk loss of technological innovation borne by the CPEs, then the collaborative cooperation is the evolutionary stable strategy for the CPEs. From the above equation, it can be seen that the strategy choice of the CPEs is influenced by the strategy choices of the Users and the URIs.

Based on Equation (8), if $x\left(k+w\right)+L{p}_2\left[\left(1-f_1\right)+\left(x+z\right)\left(2f_1-f_2-1\right)+xz\left(1-3f_1+3f_2\right)\right]<c_2\left(1-m\right)$, there is $F^{\prime }\left(0\right)<0, F^{\prime }\left(1\right)>0$, and then $x=0$ is the only equilibrium point. It shows that if the cost saving when the CPEs adopt a simple cooperation strategy exceeds the sum of users’ incentives, users’ penalties, and the total perceived risk loss of technological innovation borne by the CPEs, then the simple cooperation is the evolutionary stable strategy for the CPEs. From the above equation, it can be seen that the strategy choice of the CPEs is influenced by the strategy choices of the Users and the URIs.

4.2.3. Asymptotic Stability Analysis for the URIs

Based on Equation (11), if $x\left(k+w\right)+L{p}_3\left[\left(1-f_1\right)+\left(x+y\right)\left(2f_1-f_2-1\right)+xy\left(1-3f_1+3f_2\right)\right]-c_3\left(1-m\right)=0$ there is $F\left(z\right)=0$. At this time, the URIs’ strategic selection will not change over time; that is, the URIs’ strategy is stable.

Based on Equation (12), if $x\left(k+w\right)+L{p}_3\left[\left(1-f_1\right)+\left(x+y\right)\left(2f_1-f_2-1\right)+xy\left(1-3f_1+3f_2\right)\right]>c_3\left(1-m\right)$, there is $F^{\prime }\left(0\right)>0, F^{\text{'}}\left(1\right)<0$, and then $x=1$ is the only equilibrium point. It shows that if the cost saving when the URIs adopt a simple cooperation strategy is less than the sum of users’ incentives, users’ penalties, and the total perceived risk loss of technological innovation borne by the URIs, then collaborative cooperation is the evolutionary stable strategy for the URIs. From the above equation, it can be seen that the strategy choice of the URIs is influenced by the strategy choices of the CPEs and the URIs.

Based on Equation (12), if $x\left(k+w\right)+L{p}_3\left[\left(1-f_1\right)+\left(x+y\right)\left(2f_1-f_2-1\right)+xy\left(1-3f_1+3f_2\right)\right]<c_3\left(1-m\right)$, there is $F^{\prime }\left(0\right)<0, F^{\text{'}}\left(1\right)>0$, and then $x=0$ is the only equilibrium point. It shows that if the cost saving when the URIs adopt a simple cooperation strategy exceeds the sum of users’ incentives, users’ penalties, and the total perceived risk loss of technological innovation borne by the URIs, then simple cooperation is the evolutionary stable strategy for the URIs. From the above equation, it can be seen that the strategy choice of the URIs is influenced by the strategy choices of the CPEs and the URIs.

4.3. Equilibrium Point

In Section 4.1, the replicated dynamic equations of the Users, the CPEs, and the URIs are established respectively, and their behaviors will keep changing with time. According to the differential equation theorem, the system will tend to a steady state when the condition replicated dynamic equations are all equal to 0, and Equation (13) can be used to solve the equilibrium point of this tripartite game model.

$$\left\{\begin{array}{cc}\hfill F\left(x\right)& =x\left(1-x\right)(-c_1+2k+L{p}_1+c_{1}m-ky-kz-wy-L{f}_1{p}_1-L{p}_{1}y-L{p}_{1}z+gyz\hfill \\ & +L{p}_{1}yz+2L{f}_1{p}_{1}y-L{f}_1{p}_{1}y+2L{f}_1{p}_{1}z-L{f}_2{p}_{1}z-3L{f}_1{p}_{1}yz+3L{f}_2{p}_{1}yz\hfill \\ \hfill F\left(y\right)& =y\left(1-y\right)(L{p}_2-c_2+c_{2}m+kx+wx-L{f}_1{p}_2-L{p}_{2}x-L{p}_{2}z+L{p}_{2}xz\hfill \\ & \hspace{1em} +2L{f}_1{p}_{2}x-L{f}_2{p}_{2}x+2L{f}_1{p}_{2}z-L{f}_2{p}_{2}z-3L{f}_1{p}_{2}xz+3L{f}_2{p}_{2}xz\hfill \\ \hfill F\left(z\right)& =z\left(1-z\right)(L{p}_3-c_3+c_{3}m+kx+wx-L{f}_1{p}_3-L{p}_{3}x-L{p}_{3}y+L{p}_{3}xy\hfill \\ & \hspace{1em} +2L{f}_1{p}_{3}x-L{f}_2{p}_{3}x+2L{f}_1{p}_{3}y-L{f}_2{p}_{3}y-3L{f}_1{p}_{3}xy+3L{f}_2{p}_{3}xy\hfill \end{array}\right.$$

(13)

The replicated dynamic equation can be obtained by calculating a total of 14 solutions. Eight of them are pure strategy equilibrium points $E_1\left(0,0,0\right), E_2\left(1,0,0\right),E_3\left(0,1,0\right), E_4\left(0,0,1\right), E_5\left(1,1,0\right),E_6\left(1,0,1\right),E_7\left(0,1,1\right),E_8\left(1,1,1\right),$ and there exist six equilibrium points where a single subject uses a pure strategy.

4.4. Evolutionary Stable Strategy

In the asymmetric evolutionary game model, only pure strategies have asymptotic evolutionary stability, so only the stability of the eight pure strategy equilibrium points from $E_1~E_8$ are judged [58]. The eigenvalues of $E_1~E_8$ are calculated by establishing the Jacobi matrix, as in Equation (14).

$$J=\left[\begin{array}{ccc}\frac{\partial F\left(x\right)}{\partial x}& \frac{\partial F\left(x\right)}{\partial y}& \frac{\partial F\left(x\right)}{\partial z}\\ \frac{\partial F\left(y\right)}{\partial x}& \frac{\partial F\left(y\right)}{\partial y}& \frac{\partial F\left(y\right)}{\partial z}\\ \frac{\partial F\left(z\right)}{\partial x}& \frac{\partial F\left(z\right)}{\partial y}& \frac{\partial F\left(z\right)}{\partial z}\end{array}\right]$$

(14)

Only when the eigenvalues ${\lambda }_1$, ${\lambda }_2$, and ${\lambda }_3$ are all less than 0 the equilibrium point is an evolutionary stable strategy. As can be seen by observing the eigenvalues of each equilibrium within

Table 4. Eigenvalues of the Jacobian matrix.

Eigenvalue Point	$\mathbf{Eigenvalue} {\mathit{\lambda }}_1$	$\mathbf{Eigenvalue} {\mathit{\lambda }}_2$	$\mathbf{Eigenvalue} {\mathit{\lambda }}_3$
$E_1\left(0,0,0\right)$	$2k+L{p}_1\left(1-f_1\right)-\left(1-m\right)c_1$	$L{p}_2\left(1-f_1\right)-\left(1-m\right)c_2$	$L{p}_3\left(1-f_1\right)-\left(1-m\right)c_3$
$E_2\left(1,0,0\right)$	$-2k-L{p}_1\left(1-f_1\right)+\left(1-m\right)c_1$	$k+w+L{p}_2\left(f_1-f_2\right)-\left(1-m\right)c_2$	$k+w+L{p}_3\left(f_1-f_2\right)-\left(1-m\right)c_3$
$E_3\left(0,1,0\right)$	$k-w+L{p}_1\left(f_1-f_2\right)-\left(1-m\right)c_1$	$-L{p}_2\left(1-f_1\right)+\left(1-m\right)c_2$	$L{p}_3\left(f_1-f_2\right)-\left(1-m\right)c_3$
$E_4\left(0,0,1\right)$	$k-w+L{p}_1\left(f_1-f_2\right)-\left(1-m\right)c_1$	$L{p}_2\left(f_1-f_2\right)-\left(1-m\right)c_2$	$-L{p}_3\left(1-f_1\right)+\left(1-m\right)c_3$
$E_5\left(1,1,0\right)$	$-k+w-L{p}_1\left(f_1-f_2\right)+\left(1-m\right)c_1$	$-k-w-L{p}_2\left(f_1-f_2\right)+\left(1-m\right)c_2$	$k+w+L{p}_3{f}_2-\left(1-m\right)c_3$
$E_6\left(1,0,1\right)$	$-k+w-L{p}_1\left(f_1-f_2\right)+\left(1-m\right)c_1$	$k+w+L{p}_2{f}_2-\left(1-m\right)c_2$	$-k-w-L{p}_3\left(f_1-f_2\right)+\left(1-m\right)c_3$
$E_7\left(0,1,1\right)$	$-2w+g+L{p}_1{f}_2-\left(1-m\right)c_1$	$-L{p}_2\left(f_1-f_2\right)+\left(1-m\right)c_2$	$-L{p}_3\left(f_1-f_2\right)+\left(1-m\right)c_3$
$E_8\left(1,1,1\right)$	$2w-g-L{p}_1{f}_2+\left(1-m\right)c_1$	$-k-w-L{p}_2{f}_2+\left(1-m\right)c_2$	$-k-w-L{p}_3{f}_2+\left(1-m\right)c_3$

, we cannot accurately determine the sign of the eigenvalues of each equilibrium, and numerous factors affect the participants’ strategies, which will lead to constant changes in the participants’ behavioral choices [59].

From the perspective of the whole technological innovation process of MCPs, the equilibrium point $E_8\left(1,1,1\right)$ is a more appropriate choice. The main reasons are as follows: Firstly, the risk perception loss will not only damage the interests of the participant, but also the loss of the whole project. The direct benefit of the technological innovation of MCPs is the Users and the Users collaborate to innovate, make a reasonable allocation of resources and coordinate the management of participants to promote the technological innovation of MCPs smoothly. Secondly, the CPEs can improve their reputation and win the trust of the Users through collaborative cooperation in the technological innovation of MCPs, which will lay the foundation for its development and ensure sustainable gains in the future. Thirdly, the benefits of the collaborative cooperation strategy chosen by the URIs will be more than economic income. Based on the technological innovation of MCPs, a large number of talents can be cultivated, academic publications can be published, and discipline rankings can be improved.

5. Simulation Analysis

Based on the eigenvalues of equilibrium points in Section 4, this section applies matlab2020a to simulate and analyze the evolutionary stable strategy with related parameters, which is helpful to understand the evolutionary path more intuitively as well as to recognize the sensitivity to each parameter more clearly.

5.1. Parameter Setting

Under different conditions, each equilibrium point may become the evolutionary stable strategy. According to the above analysis, it can be concluded that the collaborative cooperation strategy chosen by all participants can better meet the needs of MCPs through technological innovation. Therefore, the values of each variable are assigned, as shown in

Table 5. Parameter assignment.

${\mathit{c}}_1$	${\mathit{c}}_2$	${\mathit{c}}_3$	$\mathit{m}$	$\mathit{L}$	${\mathit{p}}_1$	${\mathit{p}}_2$	${\mathit{p}}_3$	${\mathit{f}}_1$	${\mathit{f}}_2$	$\mathit{g}$	$\mathit{w}$	$\mathit{k}$
12	5	5	0.7	15	0.5	0.2	0.3	0.7	0.5	1	0.3	0.3

. Since the benefits of technological innovation of MCPs are difficult to be accurately quantified in a short period of time, and the eigenvalues of this model do not contain $r_1,r_2,r_3$, therefore parameters $r_1,r_2,r_3$ are not assigned.

5.2. Numerical Simulation

Using matlab2020a to simulate the government support, reward and penalty, perceived loss of technological innovation risk, risk-taking ratio, technological innovation investment, and cost compression coefficient, we set four different initial probabilities of collaborative cooperation of 0.2, 0.4, 0.6, and 0.8, and set a reasonable time of evolutionary game according to the convergence rate of strategy choice under the change of different parameters.

5.2.1. Government Support, $g=1,3,5$

The evolution of the equilibrium strategy after the change in government support for technological innovation in MCPs is shown in Figure 2. From Figure 2, it can be seen that as the government’s support for technological innovation in MCPs becomes greater, the faster the rate at which the Users tend to collaborate, and as the government’s support increases, the CPEs and the URIs will also tend to collaborate. From Figure 2c, it can be seen that when the government support reaches 5, the participant with an initial collaborative cooperation probability of 0.6 will eventually also tend to collaborative cooperation.

The government’s support for the technological innovation of MCPs can motivate each participant to tend to cooperate collaboratively. Even though the participant was not strongly willing to cooperate collaboratively in the technological innovation of MCPs initially, the government’s encouragement can stimulate the motivation of participants to cooperate collaboratively.

5.2.2. Reward and Penalty, $w=0.3,0.5,0.7;k=0.3,0.5,0.7$

The evolution of the equilibrium strategy after the change of the reward and penalty from the Users to the CPEs and the URIs is shown in Figure 3. From Figure 3, it can be seen that as the reward and penalty of the Users are greater, the rate of the CPEs and the URIs converge to the strategy of collaborative cooperation is greater. There is a threshold value of the reward and penalty of the Users, when the reward for the CPEs and the URIs is too large, the Users will tend to simple cooperation. From Figure 3c, it can be seen that when the Users choose the simple cooperation strategy, the CPEs and the URIs will choose the simple cooperation strategy because of the lack of reasonable supervision.

The Users need to coordinate and manage the technological innovation of MCPs, but the rewards and punishments for the CPEs and the URIs should not exceed the limits that the Users can bear, and only under the collaborative cooperation of the Users can the order of technological innovation of MCPs be maintained and the collaborative cooperation of other participants be ensured.

5.2.3. Perceived Loss of Technological Innovation Risk, $L=10,15,20$

The evolution of the equilibrium strategy after the change of technology innovation risk perceived loss in MCPs is shown in Figure 4. From Figure 4a,b, it can be seen that there is a threshold value of risk perceived loss, and if the risk perceived loss is less than this value, the participants will converge to simple cooperation. From Figure 4b,c it can be seen that the larger the risk perception loss is, the greater the rate at which the participants converge to cooperate collaboratively.

The risk of technological innovation of MCPs will hinder the research and application of new technologies, and the risk needs to be perceived in advance to prevent the risk in time. The perceived risk of technological innovation of MCPs can be predicted through past case studies, expert interviews, questionnaires, etc., and only when the participants understand that their simple cooperation will bring risks to the technological innovation of MCPs, can participants be driven to choose a collaborative cooperation strategy.

5.2.4. Risk-Taking Ratio, $p_1=0.5,0.6,0.7;p_2=0.2,0.1,0.1;p_3=0.3,0.3,0.2$

The evolution of the equilibrium strategy after the change in the technological innovation risk-taking ratio of the participants in MCPs is shown in Figure 5. From Figure 5a,b, it can be seen that the proportion of risk borne by the Users increases and the proportion of risk borne by the CPEs decreases, and the Users will tend to simple cooperation, but from Figure 5b,c, it can be seen that when the proportion of risk borne by the Users continues to increase, the Users will tend to collaborative cooperation. From Figure 5, it can be seen that with the decrease in the proportion of risks borne by the CPEs and the URIs, they will tend to simple cooperation.

In the technological innovation of MCPs, there is often no detailed risk-sharing ratio, and there is a lack of quantitative analysis of the risk-sharing ratio in the relevant theoretical studies. In a word, when the proportion of risks increases, the participant will tend to cooperate collaboratively, but only by finding the appropriate value of the risk proportion of each participant, can all participants choose to cooperate collaboratively, and finally achieve the goal of technological innovation of MCPs.

5.2.5. Technological Innovation Investment, $c_1=12,15,12;c_2=5,5,8;c_3=5,5,8$

The evolution of the equilibrium strategy after the change of investment of the technological innovation participants of MCPs is shown in Figure 6. From Figure 6a,b, it can be seen that the greater the cost of the Users to invest in technological innovation of MCPs, the more it will tend to simple cooperation. From Figure 6b,c, it can be seen that the greater the cost of the CPEs and the URIs to invest in technological innovation in MCPs, the more they will tend to simple cooperation.

The investment of the participants in the technological innovation of MCPs should be borne by themselves. If the investment is too high, the participants will choose simple cooperation to reduce the cost. Therefore, before participating in the technological innovation of MCPs, participants need to reasonably estimate their investment in the technological innovation of MCPs.

5.2.6. Cost Compression Coefficient,$m=0.5,m=0.7,m=0.9$

The evolution of the equilibrium strategies of the participants after the change in the technology innovation cost compression coefficient is shown in Figure 7. The larger the cost compression coefficient the higher the degree of cooperation. As can be seen in Figure 7, the greater the cost compression coefficient, the smaller the cost that can be compressed by simple cooperation of participants, and each participant will gradually tend to cooperate collaboratively.

The cost compression coefficient can be understood as “the degree of cooperation”. The higher the degree of cooperation, the higher the cost will be. If the cost saved is greater than the risk loss, the participant will probably choose a simple cooperation strategy. Therefore, a reasonable management system and incentive policy are needed to improve the degree of cooperation.

6. Discussion

The technological innovation of MCPs involves multiple stakeholders, as in the stakeholder theory [8,60]. The convergence state of cooperation is not unchangeable, and in this study, it is shown that the collaborative cooperation of all participants can better achieve the technological innovation goals of MCPs [61]. However, collaborative cooperation in the technological innovation of MCPs is disturbed by many factors, both internal and external, and each factor has different effects on the different participants. Moreover, it is necessary to consider the technological innovation of MCPs as a system, and the strategic choice of participants will affect each other and will have an impact on the system [62].

Under risk orientation, this paper proposes a perspective. We explore the key factors of participants’ behaviors in the technological innovation of MCPs from the perspective of risk as orientation [63]. When the perceived loss of technological innovation risk increases, the participants will tend to cooperate collaboratively, and the conclusion is consistent with Wang et al. [55]. The proportion of risk-taking needs to find a suitable value to ensure that all participants cooperate collaboratively [64]. In addition, the final behavior of the participant in the technological innovation of MCPs will be influenced by the initial behavior. As the MCPs ultimately serve society, the government should take appropriate incentives to motivate each subject to research and develop in technological innovation of MCPs, for example, the government can set up relevant awards and provide convenience by tax exemptions [65,66]. The Users also need to effectively supervise the participants in the technological innovation of MCPs and improve the degree of collaborative cooperation to ensure the orderly promotion of the technological innovation of MCPs [67]. The CPEs and the URIs need to complete the research and development task on time and with high quality and fully integrate theory and practice [68]. To complete the technological innovation of MCPs, all participants need to cooperate collaboratively.

7. Conclusions and Applications

This paper is under the guidance of game thinking, and the influencing factors are parameterized. Unlike most studies, this paper focuses on exploring the factors influencing behavior from a risk perspective. A tripartite evolutionary game model of the technological innovation system of MCPs is constructed, and the evolutionary paths of the behaviors of the Users, the CPEs, and the URIs are analyzed. Parameterized factors have been analyzed to regulate the evolutionary path of the tripartite cooperative behavior of stakeholders is clarified. Through the above analysis, it can be concluded that: First, the progressive stability conditions of different participants in the technological innovation of MCPs are different, and the strategy of one participant will be affected by the strategies of other participants. Second, the tripartite strategy will eventually converge into an optimal balance of collaborative cooperation in the technological innovation of MCPs. Third, the final strategic stability is influenced by multiple variables. The sensitivity of the participants to different parameters is different, and they are more sensitive to the perceived loss of technological innovation risk, risk-taking ratio, technological innovation investment, and cost compression coefficient. Finally, some effective recommendations are proposed as follows.

• The Users can perceive the technology innovation risk loss of MCPs in advance, quantify the technology innovation risks caused by the simple cooperative behavior, and reasonably share the technological innovation risks of MCPs. The simple cooperation of the participants will cause the risk of the whole technological innovation of MCPs, and driven by common interests, the participants will also form a mutual monitoring mechanism. Moreover, if the technological innovation risk loss of each participant can be perceived in advance, it can improve the probability of participants choosing collaborative cooperation at the initial time.
• The Users can regulate the behavior of participants by establishing collaborative cooperation evaluation indexes. In MCPs, the Users can give reasonable rewards to cooperative participants and punish simple cooperative participants to improve the degree of cooperation, and an effective cooperation mechanism is established so that all participants can actively communicate with each other, realize rapid information transmission and share, avoid the phenomenon of information silos, and establish a collaborative network of technological innovation in MCPs.
• In the MCPs, a lot of technical difficulties will emerge. The government needs to encourage participants to carry out technological innovation, reward participants who cooperate collaboratively in technological innovation, and ensure that the technological innovation results of MCPs can be transformed and applied to the actual project. The technological innovation of MCPs is the embodiment of the national level of scientific and technological development, and in China, it is a carrier to achieve the 14th Five-Year Plan and the long-range objectives through the year 2035. Promoting the development of the construction industry requires the joint efforts of all participants.

The evolutionary game study of cooperative behavior in technological innovation of MCPs has important theoretical and practical value for promoting collaborative cooperation. However, there are some limitations in this research. First, the parameters f1 and f2 (discount coefficient of risk perception loss) involved in the hypothesis only consider the number of participants, and future research should be undertaken to explore the different contributions of different participants. Second, there is a lack of research on the risk list of technological innovation of MCPs, and considerably more work will need to be done to organize the risk of technological innovation due to the behavior of the participants. Third, in this paper, only generalized technological innovation of MCPs is considered. However, any technological innovation of MCP has its peculiarities, and the application of real cases will be more convincing.