3.1 Role recognition

With reference to the interactive model of participants in the digital transformation of the construction industry by Chen et al. [28], this paper proposes that the digital service ecosystem of the construction industry is a complex network system consisting of a service-oriented value chain at the core of the system and external auxiliary institutions (including universities and scientific research institutions, governments, financial institutions, and industry network platforms). The internal value chain, supported by external auxiliary institutions, meets the needs of customers through a clear division of labor and cooperation, integration, and sharing of data resources and aims to achieve value co-creation through systematic collaborative innovation [29]. The digital service ecosystem of the construction industry is shown in Fig 1.

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Fig 1. Digital service ecosystem in the construction industry.

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Fig 1 shows that the main body of value co-creation in the service-oriented digital transformation of the construction industry consists of construction enterprises, digital solution suppliers, and customers. Construction enterprises are the key node and leading force of the whole value co-creation system. They use digital technology, digital products, and digital management in the whole life cycle of project construction to transform customers’ needs into entities. Enterprises are not only the demanders of digital transformation but also the implementation terminals, driving and leading the digital transformation and coordinated development of the whole system. Overall, the construction industry is relatively decentralized, which also leads to the fragmentation of data storage in all stages of construction. The intelligent construction collaborative management platform based on project construction can effectively break the status of isolated data islands. As the developers of digital technology integration, digital software, and hardware products and services, digital solution suppliers are the key node in the value chain. Customers are the source of value creation for construction enterprises and digital solution suppliers in the service-oriented value chain, and their personalized needs and use of information feedback are the innovative force of the whole value co-creation system.

3.2 Tripartite game analysis and research hypothesis

1. Collaboration between construction enterprises and customers

In the context of digital transformation, customers are not the end of transactions but the nodes that create value for enterprises. With the help of digital technology, construction enterprises enable customers to participate in all aspects of the whole life cycle of construction projects from planning, design, and construction to operation and maintenance and create platforms and opportunities for communication and feedback with customers. Through the feedback data provided by customers, construction enterprises can more clearly and directly guide how to meet their needs, thereby enhancing customer perceived value, achieving the goal of maximizing corporate profits, and expanding the profit space and scope. In addition, customers can combine the products or services provided by construction enterprises with their resources to stimulate their creative needs and create value through interaction with construction enterprises. However, customers participating in the collaborative process must bear a certain amount of energy and opportunity costs. If customers do not participate in collaboration, their own perceived value will be reduced and collaborative benefits will be lost. Meanwhile, construction enterprises will suffer information losses.

Based on the above analysis, the following theoretical hypotheses are proposed:

1. H1: Under the supervision of construction enterprises, customers will ultimately choose to participate in the collaboration.

2. Collaboration between construction enterprises and digital solution suppliers

The collaboration between construction enterprises and digital solution suppliers can improve the ability to collaborate and integrate resources between value co-creators to achieve a rapid response to changes, an accurate connection between supply and demand, a flexible allocation of resources, and more innovation possibilities. The whole value chain uses digital technology to realize efficient connections and optimize research and development design, construction, operation management, marketing, and after-sales service through a data-oriented service model. At the same time, it can also deeply endow the wisdom and value of each element in the operation process of construction enterprises and promote the optimization of the whole service-oriented operation process and operational efficiency. In addition, according to resource-based theory, the integration and full utilization of resources is the main source for enterprises to maintain competitive advantages [30]. In the process of service-oriented digital transformation, service quality is an important factor affecting the core competitiveness of construction enterprises. Therefore, construction enterprises will also outsource their non-core professional digital after-sales service business to digital solution suppliers to provide more professional services. However, after signing the service outsourcing agreement, digital solution suppliers are likely to damage the interests of construction enterprises and customers by reducing the quality of digital software and hardware facilities, leaking information, and lowering the service level to maximize their own interests. To prevent these risks, construction enterprises need to impose certain regulatory measures on digital solution suppliers to improve their service quality. In this process, construction enterprises have to bear the cost of collaborative supervision, and digital solution suppliers have to bear the cost of collaborative innovation. If construction enterprises do not implement collaborative supervision strategies, due to the lack of coordination and communication with digital solution suppliers and customers, as well as the reduction of service quality of digital solution suppliers, construction enterprises and digital solution providers will lose some customers. If digital solution providers do not participate in collaborative innovation, construction enterprises may incur losses due to the lack of digital services support.

Based on the above analysis, the following theoretical hypotheses are proposed:

1. H2: Whether digital solution suppliers participate in collaborative innovation depends on the strategic choices of construction enterprises.

3. Collaboration between digital solution suppliers and customers

The collaboration between digital solution suppliers and customers is mainly achieved through feedback data provided by construction enterprises or direct feedback data from customers. At this point, the digital platform provides a bridge for digital solution suppliers to interact with customers, which helps digital solution suppliers quickly capture current market needs and personalized customer needs and improve their own and even the entire value chain’s service innovation capabilities. In addition, digital solution suppliers can realize data access in the product after-sales service link with the help of digital platforms. Customers continuously provide feedback data to digital solution suppliers or construction enterprises in direct and indirect ways during the full cycle of services provided by digital solution suppliers, enhancing their ability to create value. If digital solution suppliers do not participate in collaborative innovation, customers will suffer certain losses due to the lack of support from digital services and the decrease in service quality. Similarly, if customers choose not to participate in collaborative innovation, digital solution providers will also lose the motivation for innovation due to a lack of information feedback.

Based on the above analysis, the following theoretical hypotheses are proposed:

1. H3: The customers’ strategic choice is synchronized with the digital solution suppliers.

In addition, the level of digitalization affects the benefits and costs of construction enterprises and digital solution suppliers in the game process. The level of digitalization is reflected by the level of enterprise data collection and analysis, the level of the platform, and the digitalization level of the construction process [31]. First, data are an important information asset for enterprises to understand and develop demand markets and an important medium for enterprises to communicate with customers and enter the ecosystem. Second, in the platform stage, with the help of the data sharing and connection of the construction end, the sales end, and the service end, the digital platform has realized the close connection among the value creation entities, greatly reducing the cost of cooperation and transactions among the entities. Finally, using digital technology to improve the efficiency of operations and construction can provide a new driving force for the digital transformation of construction enterprises and the efficient development of the digital service ecosystem of the construction industry.

Based on the above analysis, the following theoretical hypotheses are proposed:

1. H4: The digital level can promote the collaborative value co-creation of game players.

3.3 Basic assumptions of the model

Based on the above analysis of the synergy mechanism among value co-creators in the service-oriented digital transformation of the construction industry, construction enterprises, digital solution suppliers, and customers, as the main players of value co-creation, are the players in the game. They are all limited rational individuals with the ability to learn and adapt to dynamic environmental changes and adjust and optimize their strategies from their own interests. The strategy set of construction enterprises is {collaborative supervision, no collaborative supervision}, and the probability that construction enterprises choose the strategy of collaborative supervision at time t is x; then, the probability that they choose the strategy of no collaborative supervision is 1−x. The strategy set of digital solution suppliers and customers is {collaborate, not collaborate}. Where the probability of digital solution suppliers and customers choosing the “participate in collaboration” strategy at time t is y and z, respectively, then the probability of choosing the “not participate in collaboration” strategy is 1−y and 1−z, respectively, x,y,z∈[0,1], and both are functions of time t.

The initial revenues of construction enterprises, digital solution suppliers, and customers are I₁, I₂ and I₃, respectively. When all three parties participate in value co-creation, additional synergy benefits will be created, and the synergy benefits will be distributed proportionally among the participants [30]. The distribution coefficient of the collaborative income of construction enterprises is α, that of digital solution suppliers is β, that of customers is γ = 1−α−β, and α,β,γ∈[0,1]. When construction enterprises, digital solution providers, and customers choose to participate in value co-creation, it is assumed that the collaboration cost that the three parties need to bear is C, and the collaboration cost will be distributed proportionally among the participants [32]. The collaborative cost-sharing coefficient of the construction enterprises is λ, the collaborative cost-sharing coefficient of the digital solution suppliers is η, the collaborative cost-sharing coefficient of the customers is σ = 1−λ−η, and λ,η,σ∈[0,1]. The losses caused to construction enterprises and digital solution suppliers due to their failure to choose collaborative supervision are L₁. The losses caused to construction enterprises and customers by digital solution suppliers choosing not to participate in collaborative innovation are L₂. The losses caused to construction enterprises and digital solution suppliers by customers choosing not to participate in collaborative innovation are L₃. The coefficients of the three factors reflecting the level of digitalization affect the benefits and costs of participants. The data collection and analysis coefficient is expressed as μ, the platform coefficient is expressed as ν, and the digitization of the construction process coefficient is expressed as ω, and μ,ν,ω∈[0,1].

3.4 Construction of the evolutionary model

Based on the above assumptions, the evolutionary game income matrix of construction enterprises, digital solution suppliers, and customers can be constructed as shown in Table 1.

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Table 1. The payoff matrix of the tripartite game.

https://doi.org/10.1371/journal.pone.0285697.t001

4.1 Model equilibrium analysis

According to the income matrix of the evolutionary game, the expected income E₁(x) or E₁(1−x) of construction enterprises when they choose the “cooperative supervision” or “no cooperative supervision” strategy are, respectively: (1) (2)

The average expected income of construction enterprises is: (3)

According to Formulas (1), (2), and (3), we can further obtain the replicator dynamics equation of the strategy selection of construction enterprises as follows: (4)

Similarly, the expected income E₂(y) or E₂(1−y) of digital solution suppliers when they choose “participating in collaboration” or “not participating in collaboration” strategy are, respectively: (5) (6)

The average expected income of digital solution suppliers is: (7)

According to Formulas (5), (6), and (7), we can further obtain the replicator dynamics equation of the strategy selection of digital solution suppliers as follows: (8)

Similarly, the expected income E₃(z) or E₃(1−z) of customers when they choose “participating in collaboration” or “not participating in collaboration” strategy are, respectively: (9) (10)

The average expected income of customers is: (11)

According to Formulas (9), (10), and (11), we can further obtain the replicator dynamics equation of the strategy selection of customers as follows: (12)

The three replicator dynamic equations F(x), F(y), and F(z) can be combined to obtain a 3D dynamic system of the dynamic evolution for construction enterprises, digital solution suppliers, and customers. Let F(x) = 0, F(y) = 0, and F(z) = 0, the eight local equilibrium points of the dynamic system are (0,0,0), (1,0,0), (0,1,0), (0,1,0), (0,0,1), (1,1,0), (1,0,1), (0,1,1), (1,1,1), and (1,1,1), respectively, which form the equilibrium solution domain N of the three-way evolutionary game. That is, , and there is also a mixed-strategy solution (x*,y*,z*) in the region. Only the pure strategy Nash equilibrium point is asymptotically stable in the three-way evolutionary game, so it is only necessary to discuss the stability of the eight pure strategy equilibrium points.

4.2 Stability analysis of the equilibrium point

The above equilibrium point is not completely an evolutionary stability strategy for replicating a dynamic system. It is necessary to further discuss the stability of the system equilibrium point by using the Jacobian matrix local stability analysis method proposed by Friedman [33]. The Jacobian matrix can be constructed according to the partial derivative of the three-dimensional dynamic system with respect to x,y,z. (13) where

The eigenvalues of the Jacobian matrix corresponding to the eight equilibrium points are calculated, as shown in Table 2.

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Table 2. Each equilibrium point corresponds to the eigenvalue of the Jacobian matrix.

https://doi.org/10.1371/journal.pone.0285697.t002

According to Lyapunov’s method, the stability of the equilibrium point of the system can be judged by the sign of the eigenvalue of the Jacobian matrix. Only when all the eigenvalues of the Jacobian matrix are negative is the equilibrium point the evolutionary stability point ESS of the system [33]. In this paper, the life cycle of the digital transformation of construction enterprises is divided into three stages according to industry cycle theory: early stage, middle stage, and mature stage. The collection and analysis of data and the research and development of digital technology are the basis for the digital transformation of enterprises. Enterprises need to invest in digital technology, which is the main task in the early stage of digital transformation. With the accumulation of data, the value of a large amount of data needs to be developed. By building a digital platform to fully activate data and starting to establish contacts with other companies in data sharing to develop value networks, services across company boundaries will be provided to create value for customers, and digital transformation will enter the middle stage [34]. The continuous expansion of customer groups will lead to a diversity of customer needs, which will be met by various digital solutions. Digital services will enter the stage of mass customization, and digital transformation will enter the mature stage [35]. Combined with the analysis of the above stages and the Jacobian matrix eigenvalue expression corresponding to each equilibrium point in Table 2, the stability analysis of each equilibrium point is carried out under the following three conditions, and the specific analysis results are shown in Table 3.

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Table 3. Each equilibrium point corresponds to the eigenvalue symbol judgment.

https://doi.org/10.1371/journal.pone.0285697.t003

Case 1: Construction enterprises are in the early stage of digital transformation, and the level of digitalization is low. They need to invest considerable manpower, material resources, time, and capital to learn and absorb digital technology and knowledge. Therefore, the cost of implementing the whole value chain collaborative supervision for construction enterprises is high, and the digital profits and benefits are not significant. When , it is found that the equilibrium point of evolutionary stability can only be (0,0,0). In the early stage of digital transformation, for construction enterprises, digital solution suppliers, and customers, when at least one party chooses collaborative supervision or to collaboration, the coordination costs paid by the entities involved in value co-creation are greater than the benefits obtained. To achieve their own goal of maximizing benefits, the three parties will give up the cooperation strategy with the growth of the number of evolution periods, and the value co-creation strategy of the three parties will finally evolve into no collaborative supervision, no collaboration, or no collaboration, respectively.

Case 2: When the digital transformation of construction enterprises has been ongoing for a period of time, the enterprises have initially mastered a certain amount of digital resources and technologies. The digital level is in the middle, the cost of collaborative supervision is reduced, and the digital level coefficient is increased. In this case, although λC>L₁, , , two equilibrium points (0,0,0) and (1,1,1) can be identified to achieve steady equilibrium. It shows that with the growth of evolution periods, game players will eventually choose to participate in value co-creation or not to achieve the goal of maximizing benefits, and the system will eventually evolve into a state of complete non-collaboration or complete collaboration. Compared with Case 1, it is found that the improvement of the digital level encourages game players to choose the strategy of participating in value co-creation.

Case 3: The digital transformation of construction enterprises has entered a mature stage. Enterprises already have rich digital technologies and resources, and the construction of digital platforms is relatively mature. The digital level is higher, the cost of collaborative supervision is lower, and the coefficient of the digital level is higher. At the same time, the importance of customers in the entire value chain has also increased dramatically. In this case, ; thus, it can be concluded that the equilibrium point of the system evolutionary stability strategy is only (1,1,1). In the mature stage of digital transformation, the benefits gained by all three parties participating in value creation are greater than the collaborative costs paid. With the continuous growth of the evolution period, the strategy of game players participating in value co-creation in the process of maximizing profits will eventually evolve into a fully collaborative state, i.e., collaborative supervision, collaboration, and collaboration, respectively. On the other hand, it also shows that when the digitalization level of enterprises is very high, the choice of collaborative innovation is more conducive to maximizing the interests of enterprises and high-quality development.

5.1 Evolutionary path of tripartite participants at different stages

To verify the validity of evolutionary stability analysis and more intuitively describe the dynamic evolution of the collaborative strategy of value co-creators in the early stage, the middle stage, and the mature stage during the service-oriented digital transformation of the construction industry, this paper conducts a numerical simulation of the optimal evolutionary stability strategies in the above three stages. At the same time, according to the suggestions of relevant experts and with reference to the analog values of relevant parameters set by Gao [36], Peng [37], and Mei [38] et al., the parameters in the early, middle and mature stages of digital transformation were assigned.

In the early stage of digital transformation, the initial values of each parameter are I₂ = 20, I₃ = 10, α = β = 1/3, ΔI = 30, L₁ = 4, L₂ = 6, C = 60, λ = η = 1/3, and μ = ν = ω = 0.1. The above parameters meet the conditions of Case 1 and evolve 50 times from different initial strategy combinations. The evolution results are shown in Fig 2. The results show that the system eventually evolves into a stable strategy combination, i.e., no collaborative supervision, no collaboration, and no collaboration, respectively, under different combinations of the initial strategy probability values of the game players, which is consistent with the conclusion of Case 1. It shows that even though there is a certain proportion of construction enterprises, digital solution suppliers and customers that initially choose to participate in value co-creation, the low level of digitalization makes the cooperation costs between construction enterprises and digital solution suppliers higher, the channels for customers to collaborate are fewer, and the three parties do not participate in value co-creation to obtain greater benefits. Driven by interests, the three parties eventually tend to choose not to collaborate.

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Fig 2. Evolutionary paths in the early stage of digital transformation.

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In the middle stage of digital transformation, the initial values of each parameter are I₂ = 20, I₃ = 10, α = β = 1/3, ΔI = 40, L₁ = 7, L₂ = 6, C = 30, λ = η = 1/3, and μ = ν = ω = 0.4. The above parameters meet the conditions of Case 2 and evolve 50 times from different initial strategy combinations. The evolution results are shown in Fig 3. The results show that there are two stable strategies under different combinations of the initial strategy probability values of the game players, i.e., all three parties collaborate or do not collaborate, which is consistent with the conclusion of case 2. It shows that the construction capacity and service efficiency of enterprises have improved with the development of digitalization, thus, increasing the total revenue of the three parties. At the same time, the application of digital technology provides a variety of collaboration channels, which promotes effective communication and knowledge sharing among various entities, reduces their collaboration costs, and greatly increases the possibility of choosing to participate in collaborative innovation.

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Fig 3. Evolutionary paths in the middle stage of digital transformation.

https://doi.org/10.1371/journal.pone.0285697.g003

In the mature stage of digital transformation, the initial values of each parameter are I₂ = 20, I₃ = 10, α = β = 1/3, ΔI = 50, L₁ = 7, L₂ = 7, C = 20, λ = η = 1/3, and μ = ν = ω = 0.85. The above parameters meet the conditions of Case 3 and evolve 50 times from different initial strategy combinations. The evolution results are shown in Fig 4. The results show that the system eventually evolves into a stable strategy,i.e., collaborative supervision, collaboration, and collaboration, respectively, under different combinations of the initial strategy probability values of the game players, which is consistent with the conclusion of Case 3. It shows that even though there is a certain proportion of construction enterprises, digital solution suppliers, and customers who choose not to collaborate at first, high-level enterprise digitalization can bring high benefits and low costs to all entities. Compared with the medium term, the loss of the three parties not cooperating will increase. Driven by interests, the three parties eventually tend to choose to participate in cooperation.

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Fig 4. Evolutionary paths in the mature stage of digital transformation.

https://doi.org/10.1371/journal.pone.0285697.g004

According to the constructed Jacobi matrix, it can be seen that the equilibrium point is affected by different parameters of different subjects, which makes the three parties form different equilibrium states in different stages of Digital transformation. However, according to the above simulation analysis, from the perspective of the whole Digital transformation cycle, the strategy combination (0, 0, 0) in the early stage will develop into the strategy combination (0, 0, 0) or (1, 1, 1) in the middle stage, and finally will reach the equilibrium state of (1, 1, 1) in the mature stage. It indicates that with the improvement of the digitalization level, the value co-creation entities have finally reached the ideal state of (construction enterprises cooperating in supervision, digital solution suppliers participating in cooperation, customers participating in cooperation), and H1 and H4 are accepted. At the same time, the strategy of digital solution suppliers changes with the strategy of construction enterprises, and the strategic choice of customers is also synchronized with digital solution suppliers, H2 and H3 are accepted. Goldfar and Tucker [39] believe that digital technology has achieved permanent and real-time data sharing, fully reduced the degree of information asymmetry in enterprises, and thus reduced the cost of collaborative innovation between enterprises and customers. At the same time, digital transformation helps enterprises shorten the cycle of product production and innovation, further amplifying the driving effect of interests [40]. Obviously, the higher the level of digitalization, the greater the difference between collaborative benefits and costs, and the system will inevitably evolve into an ideal state of complete collaboration eventually.

5.2 Simulation of key parameters

There are two distinct stability strategies in the middle stage of digital transformation, and the entire system will eventually develop into a fully collaborative state in the mature stage. Therefore, it is necessary to further study the impact of the main parameters in the middle stage on the evolution of game players’ behavior to promote the service-oriented digital transformation of the construction industry to achieve the ideal state of full collaboration among value co-creators faster.

1. (1) Influence of initial willingness to collaborate on the system

On the basis of the values taken in the middle stage of digital transformation, other variables are assumed to remain unchanged, and the initial values of x,y, and z are taken as variables. We set x = y = z = 0.2, x = y = z = 0.3, and x = y = z = 0.4, and the impact of the initial willingness to cooperate of game players on their decision-making behavior is shown in Fig 5. It can be seen from the figure that the initial willingness to cooperate has an impact on the evolution of the behavior strategies of the game players in the middle stage of digital transformation. With the increase in the initial willingness to cooperate, the system gradually evolves from the stable equilibrium point (0,0,0) of complete non-collaboration to the stable equilibrium point (1,1,1) of complete collaboration, and the critical value of the initial collaborative willingness leading to this change is between 0.2 and 0.3. After exceeding the critical value, for the whole system, the higher the initial willingness of the three parties to cooperate, the faster the system will eventually evolve into a stable state of complete cooperation. For a single agent, digital solution suppliers always reach a stable state at a fast speed and choose to collaborate.

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Fig 5. Effect of initial willingness to cooperate on the evolutionary path.

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1. (2) Influence of the digital level coefficient on the system

On the basis of the values taken in the middle stage of digital transformation, the impact of the initial willingness to cooperate of the game players on the system evolution results is eliminated, so the probability of the initial collaboration strategy of construction enterprises, digital solution suppliers, and customers is 0.2. We assume that other variables remain unchanged and set μ = 0.3, μ = 0.4, and μ = 0.7. The simulation results are shown in Fig 6. With the increase in data collection and analysis coefficients, the evolution results of the system have not changed significantly. When the initial collaborative willingness of the game players is low, the changes in data collection and analysis coefficient will not change the final strategy of the game players in the middle stage of the digital transformation.

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Fig 6. Effect of data collection and analysis coefficient on the evolutionary path.

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We assume that other variables remain unchanged and set ν = 0.3, ν = 0.4, and ν = 0.7. The simulation results are shown in Fig 7. With the increase in the platform coefficient, the probability of digital solution suppliers collaborating increases, while the probability of construction enterprises’ collaborative supervision decreases. Although the evolutionary process of the system has changed, the evolutionary stability strategy of the game players is still no collaborative supervision, no participation in collaboration, and no participation in collaboration, respectively. In other words, when the initial collaborative willingness of game players is low, the change in the platform coefficient will not affect the evolutionary stability strategy combination of the system.

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Fig 7. Effect of the platform coefficient on the evolutionary path.

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We assume that other variables remain unchanged and set ω = 0.3, ω = 0.4, and ω = 0.7. The simulation results are shown in Fig 8. With the increase in digital coefficients in the construction process, the evolutionarily stable equilibrium point of the system gradually tends to (1,1,1) from (0,0,0). It shows that the value co-creation behavior of game players will gradually evolve from a completely uncooperative stable equilibrium point (0,0,0) to a completely cooperative stable equilibrium point (1,1,1) with the increase in the digital coefficient in the construction process even if the initial willingness to cooperate of game players is lower than the critical value. The reason is that the digitalization of the construction process optimizes the business chain and supply chain of construction enterprises and digital solution suppliers in an all-around way, and the digitalization business runs through all the activities of the whole life cycle of product design, production, construction, service, and so on. It makes the business activities of both parties more transparent and easier to communicate and reduces the supervision costs of construction enterprises and the collaboration costs of both enterprises. At the same time, the digitalization of the construction process also provides a channel for customers to participate in activities of the entire the whole life cycle, reducing their participation costs and increasing their value perception. The profits obtained by the three parties participating in the collaboration are far higher than the cost they have to pay. The motivation of pursuing profit maximization urges them to choose to participate in the collaboration.

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Fig 8. Effect of digitization coefficient of the construction process on the evolutionary path.

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Furthermore, by comparing the results of Figs 6–8, it is found that the digitalization level of the construction process is the key factor in promoting the development from the middle stage of the digitalization transformation to the mature stage and is an important catalyst and breakthrough for promoting the service-oriented digitalization transformation of the construction industry. This conclusion is consistent with the views of other scholars. The collection and analysis of data only provide a framework for the composition of related technologies, and the digital platform provides new channels for the cooperation of value co-creators. However, the embodiment of their value still depends on production activities. Compared with the level of data collection and analysis and platformization, the digitalization of the construction process has a more direct effect on the collaborative intention of value co-creators [41]. The application of digital technology in the construction process is the focus of construction enterprises. The leaders of government and enterprises should speed up the improvement of the digital infrastructure of construction enterprises, promote the integration and application of advanced digital construction technology in the construction process, and optimize the interaction and construction capacity of various departments.