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Article

Research on Cooperation Strategy Between Owner and Contractor of Prefabricated Building Based on Evolutionary Game Theory

by
Sunmeng Wang
1,*,
Chengjun Wang
1 and
Wenlong Li
2
1
School of Management, Xi’an University of Architecture and Technology, Xi’an 710055, China
2
School of Urban Economics and Management, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
*
Author to whom correspondence should be addressed.
Sustainability 2025, 17(3), 811; https://doi.org/10.3390/su17030811
Submission received: 4 November 2024 / Revised: 6 January 2025 / Accepted: 17 January 2025 / Published: 21 January 2025
Browse Figures
Figure 1
<p>Research framework.</p> "> Figure 2
<p>Phase diagram of evolution system in scenario 1.</p> "> Figure 3
<p>Phase diagram of evolution system in scenario 2.</p> "> Figure 4
<p>Phase diagram of evolution system in scenario 3.</p> "> Figure 5
<p>Phase diagram of evolution system in scenario 4.</p> "> Figure 6
<p>Initial assignment evolution simulation results.</p> "> Figure 7
<p>The evolutionary game trajectory of different <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <mi>E</mi> </mrow> </semantics></math>.</p> "> Figure 8
<p>The evolutionary game trajectory of different <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p> "> Figure 9
<p>The evolutionary game trajectory of different C values.</p> "> Figure 9 Cont.
<p>The evolutionary game trajectory of different C values.</p> "> Figure 10
<p>The evolutionary game trajectory of different <math display="inline"><semantics> <mi>β</mi> </semantics></math>.</p> "> Figure 11
<p>The evolutionary game trajectory of different <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <mi>Q</mi> </mrow> </semantics></math>.</p> "> Figure 12
<p>The evolutionary game trajectory of different <math display="inline"><semantics> <mi>δ</mi> </semantics></math> values.</p> ">
Versions Notes

Abstract

:
As a new construction method, prefabricated buildings have many benefits. The majority of owners and contractors still work together using conventional approaches at the moment. However, the standardization and batch production of prefabricated components are challenging to achieve using these methods. Furthermore, they prevent economies of scale from being realized. A thorough examination of the developmental dynamics of the cooperative relationship between prefabricated building owners and contractors is necessary to support the high-quality expansion of the prefabricated building industry. This paper presents an evolutionary game model that analyses the cooperation relationship between the owner and the contractor of a prefabricated building. Following this, the model is numerically simulated with an emphasis on key variables, such as excess benefits, transaction costs, and the decrease in risk costs. The results indicate that the excess benefit factor positively influences the system’s evolution toward strategic cooperation. Additionally, establishing an appropriate partition coefficient of excess benefit can effectively enhance strategic cooperation between the two parties. The presence of transaction costs in collaboration between owners and contractors hinders the system’s progression toward strategic cooperation. Appropriately allocating transaction expenses can improve the parties’ strategic cooperation. The reduction in risk costs has a favorable impact on the system’s evolution toward strategic cooperation. With the goal to maximize strategic cooperation, there is also an ideal partition coefficient for risk cost reduction. The issue of inadequate risk cost consideration in previous research is successfully resolved with the model proposed in this work. The research findings hold significant value in guiding the formulation of incentive measures, optimizing profit distribution mechanisms, and enhancing the cooperative environment within enterprises.

1. Introduction

Prefabricated buildings, as an emerging mode of production, offer numerous advantages [1]. These include enhanced production efficiency, effective quality control, optimized resource utilization, and reduced construction waste emissions, among others. Following the proposal of “new industrialization and informatization” at the 18th National Congress of the Communist Party of China, various levels of government have actively released numerous documents to facilitate the advancement of prefabricated buildings. Consequently, prefabricated buildings have now entered a phase of full-scale implementation. According to the statistical data released by the Ministry of housing and urban rural development, the newly started prefabricated building area in China was 740 million square meters in 2021, with a year-on-year increase of 18%, accounting for 24.5% of the newly built building area. The rapid development of the prefabricated construction industry can be observed under the requirements of ecological civilization and the construction of new urbanization, with strong support from governments at all levels.
Currently, the construction cost of prefabricated buildings in China is higher compared to that of traditional buildings [2]. This high construction cost serves as a significant obstacle in the advancement of prefabricated building development [3]. The research shows that economies of scale can effectively reduce construction costs [4]. The fundamental concept behind economies of scale is to pursue an optimal project collaboration arrangement that enables the efficient production of prefabricated components on a large scale [5]. At present, the proportion of projects invested by real estate developers far exceeds that invested by the government. In the present scenario, where the advancement of prefabricated buildings is still in its early stages, the majority of projects undertaken by developers continue to adhere to conventional management practices. These practices tend to prioritize the individual responsibilities, risks, and interests of the involved parties, while neglecting the integration of resources and information exchange between organizations. Consequently, partnerships often dissolve upon completing a project. For prefabricated construction projects, one-time or short-term cooperation makes the production mold of prefabricated components usable only once, and the cost is large. It is difficult to realize the standardization and batch production of prefabricated components, which is not conducive to the realization of economies of scale. Hence, in light of the conflict between the conventional cooperative management approach and the widespread production of prefabricated buildings, it is imperative for owners and contractors to enhance the amalgamation of valuable resources and the frequency of information exchange [6]. By establishing a long-term collaborative partnership, the aim of achieving large-scale production and construction can be realized, ultimately leading to the reduction in construction costs.
The real estate industry in China has experienced significant growth since 2000, thanks to the advantageous policy dividend. Due to the rapid development, the management ability of enterprises is difficult to keep up with the development scale [7]. To ensure the quality of the development project and promote the long-term growth of the enterprise, numerous owners and contractors have established strategic cooperative relationships. In the context of strategic cooperation relationships, the owners and contractors trust and rely on each other, begin maintaining multi-project cooperation, reduce unfair behavior and opportunistic behavior, and establish common strategic goals. However, despite their own capabilities or the development goals of the enterprise, many small- and medium-sized enterprises continue to rely on the conventional short-term project collaboration model [8]. They opt for a competitive bidding process and prioritize low prices when selecting contractors. By leveraging the inherent advantage of developers, these enterprises transfer the associated risks to the contractors. Opportunistic behavior continues to be prevalent [9].
China’s prefabricated construction projects encompass cooperation at the enterprise level, alongside traditional collaborative relationships within the contracting departments [10]. Based on the one-time nature of construction projects and considering the influence of internal and external environments, the relationship of cooperation between prefabricated building owners and contractors is not static. Based on the bounded rationality and dynamic changes in the cooperative behaviors of owners and contractors, it is appropriate and meaningful to apply evolutionary game theory to analyze the choice of their cooperative relationships. Existing research has primarily concentrated on collaborative efforts within the supply chain of prefabricated buildings. There is a notable gap in the investigation of the dynamic game relationship between the cooperative behaviors of prefabricated building owners and contractors [11]. In contrast to other game studies, the interaction between prefabricated building owners and contractors is shaped not only by initial strategies and surplus benefits but also by elements such as transaction costs, risk costs, and their respective allocation coefficients. All relevant factors must be thoroughly evaluated during the development of evolutionary models. Furthermore, the impact of various factors on the cooperation strategies employed by owners and contractors requires further investigation.
In the context of the previous analysis, this article aims to address the gaps in research regarding the evolutionary game model of cooperation between owners and contractors in prefabricated buildings. It will also consider the influence of excess returns, transaction costs, and risk costs on strategic choices, which have been overlooked in the existing literature. To achieve this, an evolutionary game model was developed to examine the cooperative relationship between owners and contractors in prefabricated buildings. Furthermore, a simulation analysis was conducted to assess the effects of key parameters, including excess returns, transaction costs, and risk costs, on the selection of cooperative strategies, ultimately revealing the evolutionary path and stable strategies of these cooperative approaches. This study offers theoretical guidance for the collaboration between owners and contractors in prefabricated buildings. It also holds significant importance for facilitating the joint development of these parties and enhancing the benefits associated with prefabricated buildings.
The research framework of the full text is shown in Figure 1.

2. Literature Review

Currently, the development of prefabricated buildings in China is still in its early stages. The ongoing research in this field primarily focuses on the following areas.

2.1. Research Status of Prefabricated Building

2.1.1. Policy Research on Prefabricated Building

The study conducted by Liu et al. determined that China’s policies regarding prefabricated buildings exhibit certain issues. These issues include conflicts arising from discrepancies between established standards and individual requirements, inadequate supporting systems, and a lack of compatibility among specifications [12]. Xia et al. identified that an optimal salary system implemented by the government plays a crucial role in advancing the prefabricated construction market [13]. In their study, Park et al. employed system dynamics to model the output value of prefabricated buildings. They manipulated the policy situation and effectiveness to simulate various scenarios. Additionally, the researchers examined the cost of prefabricated components and the development willingness of enterprises under different circumstances [14]. Based on the theory of policy tools, Wang et al. analyzed the prefabricated construction policy in less developed areas in China and found that the policy in less developed areas should be mainly mandatory. In addition, stakeholders in less developed regions should also pay attention to consumer demand and development willingness [15]. According to Wang et al., a limited number of studies have been conducted on the evolution of prefabricated building policy. The analysis conducted using text mining and collaborative network methods revealed significant changes in the prefabricated building policy objectives, policy tools, policy objects, and performance indicators across different stages, namely the initial stage, fluctuating stage, stable development stage, and rapid growth stages [16].

2.1.2. Research on Limiting Factors for the Application of Prefabricated Buildings

Guo et al. focused on research on the integration of BIM technology and regional norms, regional characteristics, industry development, and design data direction, and analyzed the positive effects of China’s BIM independent technology in improving efficiency and optimizing the production process [17]. Pan et al. identified a significant issue in the field of [specific field] in China, namely the shortage of professionals. To address this concern, the researchers proposed a set of specific measures aimed at enhancing talent training and improving teaching methods [18]. Gan et al. identified the factors hindering the application of prefabricated building technology based on the fuzzy cognitive map method. The study found that different stakeholders have different views on the technical barriers of prefabricated buildings, and improving knowledge and expertise can better alleviate technical barriers [19]. Liu et al. introduced the concept of manufacturing theory and conducted an analysis of the organization and operation mode within the construction industry. They concluded that the integrated management system is an industrial organization mode that facilitates the advancement of prefabricated construction [20].

2.1.3. Research on Related Costs of Prefabricated Buildings

Samani et al. employed the Net Present Value (NPV) method to conduct a comparative analysis of construction costs between traditional buildings and prefabricated buildings. The analysis was conducted across four stages, namely construction, operation, maintenance, and demolition. The findings indicated that the costs associated with the maintenance and demolition of prefabricated buildings were comparatively elevated [21]. Zewdu et al. used SPSS Statistics 22.0 software to analyze the survey data and found that the main reasons for the high construction cost of prefabricated buildings are the large fluctuation of raw material prices, non-standard design, etc. [22]. Lou et al. considered the construction cost of prefabricated buildings as a dynamic formation process and carried out systematic research encompassing product systems, technical systems, construction processes, and management modes [23]. Luo et al. established a fuzzy cognitive map (FCM) approach to analyze the relationship between influencing factors and the cost of prefabricated buildings, taking into account dynamic interactions [24]. Huang et al. presented the incremental cost allocation coefficient and examined the allocation ratio of the incremental cost input for prefabricated buildings using game theory [25]. Ye et al. suggested that incorporating integrated management into the management of prefabricated buildings could lead to a reduction in construction costs. This approach would also enable the utilization of complementary resources and minimize transaction costs by establishing cooperative relationships [26].
Therefore, current research on prefabricated buildings mainly focuses on policies, limiting factors, and cost aspects. Compared with traditional buildings, prefabricated buildings have significant differences in organizational mode and construction methods, and their advantages require fundamental changes to traditional cooperative relationships. At present, the concept of cooperation between prefabricated building owners and contractors has not been fully understood or promoted by researchers.

2.2. Research Status of Prefabricated Building Cooperative Relationship

2.2.1. Research on Partnership of Prefabricated Buildings

According to Halil et al., the cooperative relationship of prefabricated buildings can be understood as a network of relationships that are structured around various activities. This network should be built upon principles of long-term cooperation, shared vision, mutual trust, and ongoing improvement [27]. Gerhard et al. believed that the cumbersome process hinders the development of prefabricated buildings. In establishing cooperative relationships with multiple participants, even if the system cannot be completely controlled, opportunistic behavior can still be weakened. In his proposal, Gerhard suggests that the utilization of cooperative relationships has the potential to enhance the level of prefabrication and offer effective solutions for the successful implementation of mass customization [28]. Mohammad et al. summarized that the obstacles to the cooperation of prefabricated buildings include the lack of a communication mechanism of high-level enterprises, the lack of common goals, large differences in corporate culture, the lack of participation of design units, imperfect standards and specifications, and the lack of trust [29].

2.2.2. Information Management in Prefabricated Building Cooperation

Nenad et al. examined the integration of material information flow across the entire supply chain. They focused on the establishment of an information bridge during the design, production, and construction stages. The findings demonstrated that integrating these stages and ensuring transparency in material resources can yield significant benefits to stakeholders [30]. Huang et al. studied the impact of information sharing on reducing inventory and increasing revenue. The research findings indicate that as time progresses, the act of sharing information has a noteworthy influence on the decrease in inventory levels and overall costs. Moreover, it is observed that information sharing holds greater value in this context [31]. Xue et al. proposed an information platform based on BIM and the p-iso map algorithm to solve the visualization problem of the whole life of prefabricated buildings. The research study discovered that the utilization of information visualization had a positive impact on enhancing production and construction quality. It also facilitated the effective monitoring of construction progress. Additionally, the final data report generated through information visualization could be incorporated into the completion report [32].

2.2.3. Research on the Structure Mode of Prefabricated Building Cooperative Organization

Yue et al. proposed the establishment of a strategic alliance within the prefabricated construction supply chain. This alliance would involve design institutions, sales teams, transportation enterprises, and operation service companies, with prefabricated component manufacturers at its core [33]. Mostafa et al. pointed out that to reduce construction costs, stakeholders of prefabricated buildings should establish long-term cooperative relationships, explore group standards together, and pursue mass production [34]. Zou et al. analyzed the current design processes, standards, and methods for prefabricated structures, and introduced a design method based on BIM technology [35]. Li et al. successfully established an information platform that seamlessly integrates various stages of the project lifecycle, including design and development, production, transportation, and construction. The project’s performance has been significantly enhanced through the improved frequency of communication, information sharing, and trust among partners. This improvement can be attributed to the effective sharing of information and the complementary use of resources [36]. Yuan et al. found that the lack of professional management ability of managers is the most critical obstacle to the organizational ability of prefabricated construction projects [37].
Based on the aforementioned analysis, an extensive body of research has been conducted on prefabricated buildings and cooperative relationships. These studies have consistently highlighted the significance of cooperative relationships in engineering projects, thereby offering theoretical backing for the present paper. The current body of research on the evolutionary dynamics of contractual partnerships in prefabricated construction projects is limited. Although the existing research began to pay attention to the analysis of the motivation for the formation of cooperative relationships, this kind of research mostly focused on the supply chain cooperation with contractors and suppliers as the strategic cooperative relationship, and the research objects were mostly traditional engineering projects, while the research on prefabricated buildings mostly stayed in the analysis of policy, technology, and cost. Furthermore, the current body of research has not adequately acknowledged the importance of establishing a cooperative relationship to facilitate the advancement and utilization of prefabricated buildings. Additionally, there remains a dearth of comprehensive analysis regarding the essential components involved in transforming the cooperative relationship between the owner and contractor of prefabricated buildings. These components include practical challenges, power dynamics, and the implementation process.
Given these facts, it is imperative to address the gap in the current body of research about the evolutionary game model that examines the cooperative dynamics between owners and contractors involved in prefabricated building projects. Furthermore, it is crucial to acknowledge the absence of research that takes into account the impact of excessive interest on the decision-making process regarding strategy selection. This paper aims to examine the evolutionary stability strategy of the cooperative relationship between owners and contractors of prefabricated buildings using evolutionary game theory. Additionally, it will analyze the primary factors influencing the evolutionary stability strategy through numerical simulation. The findings of this study hold significant reference value in enhancing the collaboration between owners and contractors in the prefabricated building industry, controlling cooperative behavior, improving the cooperation mode between owners and contractors, and fostering the sustainable and healthy growth of prefabricated buildings. Based on this, the remaining part of the article mainly focuses on the hypothesis of the evolutionary game model, the construction of the evolutionary game model, and game model simulation analysis.

3. Hypothesis of Evolutionary Game Model

3.1. Basic Assumptions of the Model

In the context of the construction process for prefabricated buildings, stakeholders such as owners and contractors have the option to opt for either strategic cooperation or traditional cooperation. In the process of cooperative relationship evolution, it is necessary to determine the key factors that affect the evolution of cooperative relationships [38]. Wang et al. conducted a comprehensive literature review and research to develop an evolutionary game model that examines supply chain cooperation. The study specifically investigated the influence of excess returns and coordination costs on strategic decision making [39]. When Yang et al. studied the evolutionary game of core enterprise cooperation in the prefabricated construction industry chain, they considered the impact of transaction costs and government intervention [40]. Currently, there exists a scarcity of research concerning the evolutionary dimensions of the collaborative relationship between owners and contractors in the context of prefabricated buildings. In their study, Xue et al. examined the effects of resource integration, collaborative performance, and relationship governance on stakeholder collaboration mechanisms using the B-Z response model as a framework [41]. When Shan et al. studied the evolution model of technological cooperation innovation in the Industrial Housing Enterprise Alliance, they carried out an in-depth study on the impact of technological innovation spillover effect and default cost [42]. However, the previous research failed to take into account the potential consequences of risk loss. Currently, the progress of prefabricated building development in China is in its early stages. The primary enterprises exhibit a deficiency in comprehensive comprehension of prefabricated buildings, including their mode, management, technology, and various other aspects. Consequently, there are numerous risks associated with collaboration in this domain. Hence, it is imperative to evaluate the potential consequences of risk expenditure. In addition, the existence of excess benefits and transaction costs is the main purpose of cooperation between enterprises. Owners and contractors have different core resources. Only when excess benefits are generated and transaction costs are reduced through cooperation will the relationship of cooperation be constantly promoted and the efficiency of cooperation be improved.
Based on the relevant research on the traditional and strategic cooperative relationship between owners and contractors [43], this study constructed an evolutionary game model of the cooperative relationship between prefabricated building owners and contractors, and proposed the following assumptions:
Hypothesis 1. 
In the context of selecting strategies for a cooperative relationship in prefabricated building contracting, the owner and the contractor, who are the primary participants in this process, can be considered as bounded, rational decision-makers. They will modify their strategies based on the choices made by other members, considering the presence of incomplete information. Enhancing the level of information sharing and the capability for resource integration among partners can effectively address bounded rationality. In addition, implementing consistent high-level communication channels and developing information-sharing platforms significantly enhances the information accessible to owners and contractors [44].
Hypothesis 2. 
Strategies employed by owners and contractors of prefabricated buildings typically encompass non-cooperation, traditional cooperation, and strategic cooperation. However, this paper focuses solely on two strategies, namely “traditional cooperation” and “strategic cooperation,” when examining the selection of cooperative relationship strategies in the game model [39,40,41].
Hypothesis 3. 
This concerns the proportion of behavioral strategies. If the probability of the owner adopting the “strategic cooperation” strategy at time t is  x , then the probability of adopting a “traditional cooperation” strategy is  1 − x ; similarly, the probability of the contractor adopting the “strategic cooperation” strategy at time t is  y , and the probability of adopting the “traditional cooperation” strategy is  1 − y .
Hypothesis 4. 
The primary entities involved in the collaborative process of a prefabricated building project are the owner and the contractor. When the owner adopts the “traditional cooperation” strategy, the original income is  E 1 ; the original benefit for contractors adopting a “traditional cooperation” strategy is  E 2 .
Hypothesis 5. 
The primary objective of the strategic collaboration between the owner and the contractor is to acquire supplementary advantages. This benefit rarely exists or does not exist in traditional cooperation. Here, this part of additional benefits of 1 + 1 > 2 is called excess benefits, denoted as Δ E . The presence of excess benefits fosters a stronger bond between the parties involved and promotes enduring and stable collaboration.  α  is defined as the distribution coefficient of the owner for excess benefits,  0 ≤ α ≤ 1 . The fair distribution of excess benefits has a direct impact on the readiness and consistency of collaborative efforts. Excess benefits ought to be allocated according to the contribution level of the enterprise, and a suitable incentive mechanism should be evaluated. The allocation mechanism must undergo regular evaluation and improvement to effectively respond to dynamic changes [42].
Hypothesis 6. 
In the case where the owner and the contractor opt for the “strategic cooperation” approach, a transaction cost denoted as C is incurred. Transaction costs encompass search costs, negotiation costs, and the extra manpower and funds allocated [45]. The owner’s share coefficient for this transaction cost is represented by the variable  β , 0 ≤ β ≤ 1 .
Hypothesis 7. 
The potential for experiencing loss due to uncertain events or circumstances is referred to as risk. The nascent prefabricated building industry in China is currently facing several challenges in terms of cognition, management, capital, technology, and methods. When engaging in a collaborative project with a contractor in the field of prefabricated buildings, the owner should be aware of potential risks. These risks include the possibility of receiving inaccurate and inflated cost estimates, the need for extensive rework to ensure quality standards are met, the complexity involved in operating and maintaining the prefabricated structure, and the potential for delays in the construction timeline. For contractors, there may be risks that R&D is not recognized, or production investment is not recognized due to an unclear splitting scheme. It is expected that the risk loss can be reduced through strategic cooperation. Among them,  Q 1  represents the risk cost when the owner adopts a “traditional cooperation” strategy;  Q 2  is the risk cost when contractors adopt a “traditional cooperation” strategy; and  Δ Q  is the reduction value of risk cost when both parties adopt a “strategic cooperation” strategy. The probability of risk occurrence is  γ  ; the partition coefficient of the owner’s risk cost reduction value is  δ .

3.2. Model Parameter Setting

According to the basic assumptions of the model, the model parameters are summarized. See Table 1 for details.

4. Construction of Evolutionary Game Model

4.1. Game Revenue Matrix

The game payment matrix between the owner and the contractor of prefabricated buildings was constructed based on the assumptions and parameter settings outlined in Section 3. The matrix is presented in Table 2.

4.2. Establish Replication Dynamic Equation

Based on the game income matrix presented in Table 2, the replication dynamic equations for the “strategic cooperation” strategy implemented by the owner and the contractor are established individually.
(1)
The owner replicates the dynamic equation.
The owner chooses the “strategic cooperation” strategy, and the expected benefits are
E 11 = y [ E 1 + α Δ E − β C − γ ( Q 1 − δ Δ Q ) ] + ( 1 − y ) ( E 1 − β C − γ Q 1 ) = y ( α Δ E + γ δ Δ Q ) + E 1 − β C − γ Q 1
The owner chooses the “traditional cooperation” strategy, and the expected benefits are
E 12 = y ( E 1 − γ Q 1 ) + ( 1 − y ) ( E 1 − γ Q 1 ) = E 1 − γ Q 1
The average expected return of the owner is
E o = x E 11 + ( 1 − x ) E 12
The duplicate dynamic equation of the owner can be expressed based on the hypothetical conditions, and the expression of the duplicate dynamic equation is
F ( x ) = d x d t = x ( E 11 − E o ) = ( x − x 2 ) [ y ( α Δ E + γ δ Δ Q ) − β C ]
(2)
The contractor replicates dynamic equations.
The contractor chooses the “strategic cooperation” strategy, and the expected benefits are
E 21 = x { E 2 + ( 1 − α ) Δ E − ( 1 − β ) C − γ [ Q 2 − ( 1 − δ ) Δ Q ] } + ( 1 − x ) [ E 2 − ( 1 − β ) C − γ Q 2 ]                    = x [ ( 1 − α ) Δ E + γ ( 1 − δ ) Δ Q ] + E 2 − ( 1 − β ) C − γ Q 2
The contractor chooses the “traditional cooperation” strategy, and the expected benefits are
E 22 = x ( E 2 − γ Q 2 ) + ( 1 − x ) ( E 2 − γ Q 2 ) = E 2 − γ Q 2
The average expected return of the contractor is
E c = y E 21 + ( 1 − y ) E 22
Based on the assumptions and the expression of the replication dynamic equation, the contractor’s replication dynamic equation can be expressed as
F ( y ) = d y d t = y ( E 21 − E c ) = ( y − y 2 ) { x [ ( 1 − α ) Δ E + γ ( 1 − δ ) Δ Q ] − ( 1 − β ) C }
By combining Equations (4) and (8) to obtain the duplicate dynamic equations, letting F(x) = F(y) = 0, and solving the duplicate dynamic equations, we can obtain the equilibrium points as O(0, 0), A(0, 1), B(1, 0), C(1, 1), and M(x*, y*), where x * = ( 1 − β ) C ( 1 − α ) Δ E + γ ( 1 − δ ) Δ Q , and y * = β C α Δ E + γ δ Δ Q .

4.3. Evolutionary Stability Analysis of Cooperation Strategy

Based on the earlier results, it is possible to derive the partial derivative of the replication dynamic equation in the context of evolutionary game theory. Based on Equation (4), d F ( x ) d x can be expressed as follows:
d F ( x ) d x = ( 1 − 2 x ) [ y ( α Δ E + γ δ Δ Q ) − β C ]
d F ( x ) d y = ( x − x 2 ) ( α Δ E + γ δ Δ Q )
Based on Equation (8), d F ( y ) d y can be expressed by the following Equation:
d F ( y ) d y = ( 1 − 2 y ) { x [ ( 1 − α ) Δ E + γ ( 1 − δ ) Δ Q ] − ( 1 − β ) C }
d F ( y ) d x = ( y − y 2 ) ( 1 − α ) Δ E + γ ( 1 − δ ) Δ Q

4.3.1. Local Stability Analysis of Game Evolution

As per Friedman’s theory, the construction of a Jacobian matrix involves replicating the dynamic equation [46]. The stable point (ESS) is determined by the condition that the determinant is greater than 0 and the trace is less than 0. The evolutionary stable strategy refers to a strategy that can maintain stability in the spread and competition of a group, so that no other strategy can replace it in a short period of time. This concept is widely applied in research in economics and social sciences to analyze stable strategies in various competitive and cooperative contexts. According to Equations (9)–(12), the Jacobian matrix is
J = ( 1 − 2 x ) [ y ( α Δ E + γ δ Δ Q ) − β C ] ( x − x 2 ) ( α Δ E + γ δ Δ Q ) ( y − y 2 ) [ ( 1 − α ) Δ E + γ ( 1 − δ ) Δ Q ]     ( 1 − 2 y ) { x [ ( 1 − α ) Δ E + γ ( 1 − δ ) Δ Q ] − ( 1 − β ) C }
(1)
When x = 0 and y = 0, the Jacobian matrix at the equilibrium point O(0, 0) is
− β C 0 0 − ( 1 − β ) C
det . J = β ( 1 − β ) C 2
t r . J = − C
Because C > 0 , β ∈ [ 0 , 1 ] , det . J > 0 , and t r . J < 0 , the system is stable at the equilibrium point O(0, 0).
(2)
When x = 0 and y = 1, the Jacobian matrix at equilibrium point A(0, 1) is
α Δ E + γ δ Δ Q − β C 0 0 ( 1 − β ) C
det . J = ( α Δ E + γ δ Δ Q − β C ) ( 1 − β ) C
t r . J = α Δ E + γ δ Δ Q + C − 2 β C
Because 1 − β C > 0 , when α Δ E + γ δ Δ Q − β C > 0 , i.e., α Δ E + γ δ Δ Q > β C , det . J > 0 , and t r . J > 0 , it indicates that the system is unstable at equilibrium point A(0, 1).
(3)
When x = 1 and y = 0, the Jacobian matrix at equilibrium point B(1, 0) is
β C 0 0 ( 1 − α ) Δ E + γ ( 1 − δ ) Δ Q − ( 1 − β ) C  
det . J = [ ( 1 − α ) Δ E + γ ( 1 − δ ) Δ Q − ( 1 − β ) C ] β C
t r . J = ( 1 − α ) Δ E + γ ( 1 − δ ) Δ Q + 2 β C − C
When 1 − α Δ E + γ 1 − δ Δ Q − 1 − β C > 0 , i.e., 1 − α Δ E + γ 1 − δ Δ Q > 1 − β C , det . J > 0 , and t r . J > 0 , it indicates that the system is unstable at equilibrium point B(1, 0).
(4)
When x = 1 and y = 1, the Jacobian matrix at equilibrium point C(1, 1) is
− ( α Δ E + γ δ Δ Q − β C ) 0 0 − [ ( 1 − α ) Δ E + γ ( 1 − δ ) Δ Q − ( 1 − β ) C ]  
det . J = α Δ E + γ δ Δ Q − β C Δ E + γ Δ Q − C − α Δ E + γ δ Δ Q − β C
t r . J = C − Δ E − γ Δ Q
When α Δ E + γ δ Δ Q − β C < 0 Δ E + γ Δ Q − C < α Δ E + γ δ Δ Q − β C , det . J > 0 , and t r . J > 0 , it indicates that the system is unstable at equilibrium point C(1, 1). When α Δ E + γ δ Δ Q − β C > 0 Δ E + γ Δ Q − C > α Δ E + γ δ Δ Q − β C , det . J > 0 , and t r . J < 0 , it indicates that the system is stable at equilibrium point C(1, 1).
(5)
When x = ( 1 − β ) C ( 1 − α ) Δ E + γ ( 1 − δ ) Δ Q and y = β C α Δ E + γ δ Δ Q , the Jacobian matrix of the evolutionary game at equilibrium point M(x*, y*) can be obtained. Based on the provided solution, it can be concluded that the matrix has a trace of 0 and a determinant less than 0, and the determinable point M(x*, y*) is identified as the saddle point of the game.

4.3.2. Discussion on Stability Parameters of Game Evolution

Given the presence of multiple instances of stability at point C(1, 1), it becomes imperative to categorize and analyze the various forms of stability.
(1) When α Δ E + γ δ Δ Q − β C > 0 Δ E + γ Δ Q − C > α Δ E + γ δ Δ Q − β C , at point C, det . J > 0 and t r . J < 0 . This suggests that the system is stable when it reaches equilibrium point C. Based on the findings from the local stability analysis conducted on the five equilibrium points discussed in Section 4.3.1, it has been determined that the local equilibrium points exhibit a stable state. Please refer to Table 3 for further information.
Based on the findings presented in Table 3, it can be observed that out of the five equilibrium points, only O(0, 0) and C(1, 1) exhibit stability. This implies that the selection strategy available to both the owner and the contractor is limited to either strategic cooperation or traditional cooperation. Furthermore, it should be noted that points A(0, 1) and B(1, 0) exhibit unstable behavior, while point M(x*, y*) can be classified as a saddle point. The phase diagram depicting the evolution system of the prefabricated building owner and contractor has been obtained, as illustrated in Figure 2.
① When x < x ∗ = 1 − β C 1 − α Δ E + γ 1 − δ Δ Q and y < y ∗ = β C α Δ E + γ δ Δ Q , the game area between the prefabricated building owner and the contractor is region I, converging to point (0, 0), indicating that the probability of the prefabricated building owner choosing the strategic cooperation tends to zero. Currently, y α Δ E + γ δ Δ Q − β C < 0 , and then as lim x → 0 + f ( x ) < 0 , the owner chooses the traditional cooperation strategy and is in a stable state. Similarly, the probability that the contractor chooses strategic cooperation tends to be zero, x 1 − α Δ E + γ 1 − δ Δ Q − 1 − β C < 0 ; then, as lim y → 0 + f ( y ) < 0 , the contractor chooses the traditional cooperation strategy, which is in a stable state.
② When x < x ∗ = 1 − β C 1 − α Δ E + γ 1 − δ Δ Q and y > y ∗ = β C α Δ E + γ δ Δ Q , the region selected by the contracting game is region IV. The likelihood of the owner opting for strategic cooperation is lower, while the likelihood of the contractor choosing strategic cooperation is higher. As a result, the game outcome may converge toward either O(0, 0) or C(1, 1). Based on the provided information, it is evident that the contractor anticipates engaging in strategic collaboration with the owner in order to secure additional projects. However, it remains uncertain whether the owner will opt for strategic cooperation or traditional cooperation. Many factors such as previous cooperation experience with the contractor, the contractor’s ability, and whether the advantageous resources are complementary have an impact on the final choice of the owner. Upon receiving the owner’s approval, the game’s outcome will converge to C(1, 1). If approval is not granted, the outcome will tend toward zero.
③ When x > x ∗ = 1 − β C 1 − α Δ E + γ 1 − δ Δ Q and y < y ∗ = β C α Δ E + γ δ Δ Q , the region chosen by the contracting game is region II. Since the probability of the owner choosing strategic cooperation is greater and the contractor choosing strategic cooperation is less, the game result may converge to O(0, 0) or C(1, 1). In contrast to the contractor, the owner anticipates engaging in strategic collaboration. In this scenario, the contractor possesses significant advantage in terms of their own capabilities, which effectively compensates for any shortcomings on the part of the owner. Additionally, the contractor’s abundant resources further contribute to their superiority. Furthermore, the owner unit holds the contractor in high regard due to their past successful collaborations. As a result, the owner unit eagerly anticipates establishing a strategic partnership with the contractor. However, the contractor’s strategy is still uncertain. It is possible to carry out strategic cooperation or traditional cooperation, and the final choice of strategy is based on the contractor’s final consideration of the owner.
④ When x > x ∗ = 1 − β C 1 − α Δ E + γ 1 − δ Δ Q and y > y ∗ = β C α Δ E + γ δ Δ Q , the region selected by the contracting game is region III. Given that the probability of the owner choosing strategic cooperation is higher than that of the contractor, and the probability of the contractor choosing strategic cooperation is also higher, the game outcome will converge to C(1, 1). In this scenario, both the owner and the contractor acknowledge the presence of a “two-way rush” situation, where the contractor’s strengths and advantageous resources can effectively complement those of the owner. The past experience of successful cooperation has been highly recognized by the owner. The reputation and strength of the owner have also won the trust of the contractor. Both parties are eager to carry out strategic cooperation and finally converge to C(1, 1).
(2) When α Δ E + γ δ Δ Q − β C < 0 Δ E + γ Δ Q − C > α Δ E + γ δ Δ Q − β C , the determinant, positive and negative trace, and stability of each equilibrium point are shown in Table 4.
It can be seen from Table 4 that among the five equilibrium points, point O(0, 0) is locally stable, which is ESS point B(1, 0) is unstable; and point A(0, 1), point C(1, 1), and point M(x*, y*) are saddle points. The specific evolution phase diagram is shown in Figure 3.
(3) When α Δ E + γ δ Δ Q − β C > 0 Δ E + γ Δ Q − C < α Δ E + γ δ Δ Q − β C , the determinant, positive and negative trace, and stability of each equilibrium point are shown in Table 5.
Table 5 illustrates the characteristics of the five equilibrium points. Point O(0, 0) is identified as both locally stable and an evolutionarily stable strategy (ESS). Conversely, point A(0, 1) is deemed unstable. Points B(1, 0), C(1, 1), and M(x*, y*) are classified as saddle points. For a visual representation, refer to Figure 4, which displays the specific evolution phase diagram.
(4) When α Δ E + γ δ Δ Q − β C < 0 Δ E + γ Δ Q − C < α Δ E + γ δ Δ Q − β C , at point C, det . J > 0 and t r . J > 0 . This indicates that the system at equilibrium point C(1, 1) is unstable, and the stable state of the local equilibrium point is obtained. See Table 6 for details.
It is found that O(0, 0) is a stable point, point C(1, 1) is an unstable point, and A(0, 1), B(1, 0), and M(x*, y*) are saddle points; the phase diagram of the evolution system is shown in Figure 5.
The game strategy options for prefabricated building owners and contractors are strategic cooperation or traditional cooperation. The critical point of evolution is denoted as point M(x*, y*). The selection of collaboration methods varies between owners and contractors, influenced by factors such as their respective capabilities, resources, reputation, and environmental constraints.

5. Game Model Simulation Analysis

This study conducted a simulation analysis using MATLAB 2014a software [47,48]. The analysis involved assigning varying values to each factor individually, allowing for a more intuitive examination of the impact of factor changes on strategic choices and the evolution paths of both partners. Additionally, this study investigated the key factors influencing the system’s convergence to point (1, 1) and proposed corresponding countermeasures and suggestions [49].
The parameters of a prefabricated project in XA city were established according to Cen’s research on economic policy related to prefabricated construction [50], Feng’s cost data about prefabricated construction [51], and Luo’s prefabricated policy game research [52]. Furthermore, the relevant provisions of contract law served as a reference for simulation purposes. The relevant parameters were determined by setting the following values: Δ E = 250 , α = 0.6 , C = 80 , β = 0.4 , Δ Q = 50 , γ = 0.15 , and δ = 0.5 . The initial probability x was 0.5 and y was 0.2, 0.4, 0.6, and 0.8, respectively. According to the initial assignment of the above parameters, the evolutionary game model was simulated. The dynamic evolution process of the strategy selection of the owner and the contractor is shown in Figure 6. Over the course of time, the evolutionary stability strategy employed in the game was characterized by strategic cooperation. This analysis examined the evolutionary trajectory of the owner and the contractor’s behavior by manipulating the initial parameter values. Additionally, it investigated the impact of each parameter on the game players’ behavior choices and the stability of the evolutionary strategy.
(1)
Strategic cooperation and excess benefits Δ E
During the initial parameter assignment operation, the game ultimately achieves an evolutionary stable state characterized by strategic cooperation between the owner and contractor [53]. Over time, the rate of evolution toward strategic cooperation further intensifies for both parties involved. The remaining parameters remain unaltered, while the surplus return achieved by both the owner and the contractor is maintained within the range of 0 to 500 when implementing the “strategic cooperation” approach. The progression of the game group strategy can be observed in Figure 7.
According to the running image, it can be seen that when Δ E = 0 , the two game groups of the owner and the contractor both evolved to the “traditional cooperation” strategy and finally reached a stable state. With the increase in the excess return obtained by adopting the strategy of “strategic cooperation”, some owners have the trend of choosing “strategic cooperation”. Nevertheless, as time progresses, the stakeholders from both parties continue to opt for “traditional cooperation” and ultimately achieve an evolutionary stable state. As the probability of the contractor selecting “strategic cooperation” initially increases, the game progresses toward a state of {strategic cooperation, strategic cooperation}. When the initial probability of the contractor selecting “strategic cooperation” is smaller, the game will tend toward {traditional cooperation, traditional cooperation}. Thus, the game between the two parties has yet to reach an evolutionary stable state. With further increase (that is, Δ E ≥ 300 ), the game evolves to {strategic cooperation, strategic cooperation} and reaches a stable state. Consequently, a positive correlation exists between excess benefits and the willingness of prefabricated building owners and contractors to engage in strategic cooperation; specifically, as excess benefits increase, so does the willingness of both parties to opt for strategic collaboration. There exists a threshold of excess interest that can alter the final evolutionary outcome of the strategic choices made by both parties, shifting from traditional cooperation to strategic cooperation.
(2)
Excess benefit distribution coefficient
According to Figure 8, the initial probability x of the owner selecting the “strategic cooperation” strategy was set at 0.5. Additionally, the initial probability y of the contractor selecting the “strategic cooperation” strategy varied at values of 0.2, 0.4, 0.6, and 0.8. All other parameters remained constant. The owner’s partition coefficient of excess returns is maintained within the range of [0, 1] when both parties employ the “strategic cooperation” strategy. The objective is to observe the trend of strategy evolution in the two-game groups. When α = 0 , the contractor tends to choose “strategic cooperation” at the beginning of the game, but as the game progresses, after observing the owner’s strategic choice, both parties ultimately choose “traditional cooperation” and reach an evolutionary stable state. As α continues to increase ( α ∈ [ 0.25 , 0.5 ] ), both parties choose a “strategic cooperation” strategy and reach an evolutionary stable state. During this process, the larger the α , the faster the behavior evolution speed of both parties. As α continues to increase ( α > 0.5 ), the greater the value of y, and the game develops in the direction of {strategic cooperation, strategic cooperation}; if the value of y is smaller, the game develops in the direction of {traditional cooperation, traditional cooperation}. The lack of an evolutionary stable state in the interaction between the two parties can be linked to the influence of the initial probability, referred to as y. At this stage, it is evident that the value of y greatly influences the cooperation strategy. As α continues to increase, i.e., α = 1 , owners initially tend to choose “strategic cooperation”. However, over time, owners are influenced by contractor behavior choices and ultimately choose “traditional cooperation”, and the game reaches a stable state in {traditional cooperation, traditional cooperation}. The strategic choice of prefabricated building owners and contractors is contingent upon the specific situation, thus making the impact of the excess return partition coefficient a determining factor. The evolution of the relationship between owners and contractors toward an ideal strategic partnership can be facilitated by a fair allocation of the excess return partition coefficient.
(3)
Transaction cost of strategic cooperation C
Compared with the initial parameter assignment, other parameters are kept unchanged, the transaction cost C paid by the owner and the contractor for strategic cooperation is kept within the [0, 300] range, and the evolution trend of the game group strategy is observed, as shown in Figure 9. Based on the analysis of the current image, it is evident that when the owner and contractor engage in the game, both parties eventually adopt the strategy of “strategic cooperation” and achieve a state of stability. The transaction cost, denoted as C, necessary for the implementation of strategic cooperation, which has been observed to steadily increase. Despite this increase, the evolutionarily stable strategy remains unaltered. However, it is worth noting that the rate of evolution for “strategic cooperation” in both directions noticeably decelerates. According to this premise, as the value of C increases (i.e., C = 100, 120, 150), the probability of the contractor opting for “strategic cooperation” at the outset directly influences the game’s progress toward {strategic cooperation, strategic cooperation}. Conversely, a lower initial probability of the contractor choosing “strategic cooperation” leads the game to evolve toward {traditional cooperation, traditional cooperation}. It is important to note that the game between the two parties has yet to reach a state of evolutionary stability. With the further increase in C (i.e., C ≥ 200), the evolution of the game to {traditional cooperation, traditional cooperation} reaches a stable state, and the higher the transaction cost for both parties to choose strategic cooperation, the faster the evolution of the “traditional cooperation” strategy. Hence, there is a negative correlation between transaction costs and the selection of cooperation strategies; specifically, as transaction costs decrease, the propensity for owners of prefabricated buildings and contractors to engage in strategic cooperation increases. Strategic cooperation between owners and contractors is likely to occur only when transaction costs are managed efficiently within a narrow range.
(4)
Transaction cost-sharing coefficient
As depicted in Figure 10, it is recommended to maintain all other parameters at their current values while systematically adjusting the coefficient of transaction costs shared by owners within the range of [0, 1], and the evolution trend of the game between the two sides is observed. When β = 0 , the contractors tend to choose “traditional cooperation” at the initial stage of the game, but with the development of the game, after observing the owner’s strategic choice, both parties eventually choose “strategic cooperation” and reach an evolutionary stable state. As it continues to increase ( β = 0.25 ), the evolutionary stability strategies of both sides remain unchanged, and the evolutionary speed of the game players’ choice of “strategic cooperation” strategy increases. When the transaction cost-sharing coefficient of the owner group increases, (i.e., β = 0.6 , 0.8 , 1.0 ), and the initial probability of the contractor choosing “strategic cooperation” is low, the owner’s behavior is influenced by the contractor’s choice. As a result of the mutual acquisition and imitation of individual behaviors within groups, a distinct phase in evolutionary development emerges, where the owner shows a tendency to choose “traditional cooperation”. The lower the value of y, the more pronounced this characteristic becomes. However, over time, the game groups on both ends ultimately persist in selecting the “strategic cooperation” strategy, thereby attaining an evolutionary stable state. In general, the owner’s sharing coefficient of transaction costs has little impact on the final evolutionary result of the game.
(5)
Risk cost reduction
Δ Q represents the reduced value of risk cost when both parties adopt the “strategic cooperation” strategy [54]. When both the owner and the contractor opt for the “strategic cooperation” approach, the risk cost associated with the construction process of prefabricated buildings will be mitigated. It is important to note that the initial values of other parameters will remain unaltered, while the reduction in risk cost will vary continuously within the [0, 200] range. The impact of this parameter on the evolutionary game process of both parties will be discussed, as shown in Figure 11. When Δ Q = 0 , the final behavior choice of the group is greatly affected by the learning and imitation among individuals. In scenarios where the initial probability of both the owner and contractor selecting the “strategic cooperation” strategy is low, the game ultimately progresses toward the state of {traditional cooperation, traditional cooperation}. When the initial probability of both the owner and contractor selecting the “strategic cooperation” strategy is high, the game ultimately converges to a state where both parties continue to choose the “strategic cooperation” strategy. In this scenario, the game does not reach a stable state in terms of evolution. With the continuous increase of Δ Q , both the owner and the contractor evolve to the “strategic cooperation” strategy to reach a stable state of the game, and the evolutionary game speed of both sides accelerates with the increase. Hence, the value of the risk cost reduction for owners and contractors of prefabricated buildings is positively associated with their willingness to engage in strategic cooperation. In other words, as the risk cost reduction value increases, so does the inclination of both parties to opt for a strategic cooperation relationship.
(6)
Distribution coefficient of risk cost reduction value δ
δ represents the distribution coefficient of the owner for the risk reduction value, as shown in Figure 12. Other parameters are kept unchanged, the distribution coefficient of the owner for the risk cost reduction value in the range [0, 1] is kept constantly changing, and the evolution trend of the game between the two sides is observed. According to the evolutionary trajectory of both parties, it can be seen that in the case where the distribution coefficient values are 0, 0.25, 0.75, and 1, both the owner and the contractor transition toward adopting the strategy of “strategic cooperation” and ultimately reach an evolutionary stable state. However, the rate of evolution in the behavior of both parties shows an initial rise, which is subsequently followed by a decline, although this change is only marginally discernible in response to the increasing value of δ .

6. Discussion and Conclusions

6.1. Discussion

It can be seen that current research on the evolution of cooperative relationships in prefabricated buildings is limited, with most studies remaining at the level of policy, technology, and cost. The existing research on the elements of cooperative evolution mainly analyzes the aspects of profit distribution, spillover effects, coordination costs, government intervention, reward and punishment mechanisms, etc., ignoring the influence of factors such as excess benefits, transaction costs, and risk losses. Based on the above analysis and the development status of prefabricated buildings, the following suggestions are put forward:
(1)
Effective profit distribution mechanisms should be established between enterprises. Reasonable incentive measures and subsidy systems may expand the additional advantages of enterprise cooperation and enhance the tendency of enterprises to engage in strategic cooperation. In addition, a reasonable profit distribution mechanism can effectively alleviate opportunistic behavior exhibited by enterprises, thereby creating a favorable environment for mutually beneficial cooperation between enterprises. When facing various policy systems or industrial frameworks, significant differences arise in the investments and risks encountered by enterprises. Therefore, the surplus benefits ought to be distributed following the enterprise’s contribution. The distribution mechanism for excess profits must be assessed and refined regularly to align with ongoing changes.
(2)
Enterprises should strengthen communication and cooperation. Through effective communication and cooperation, not only can resource waste and transaction costs be reduced during the cooperation process but also understanding between enterprises can be enhanced, thereby improving cooperation efficiency.
(3)
Based on the inherent characteristics of the prefabricated construction industry, enterprises should develop appropriate contract frameworks. This measure aims to alleviate the moral hazard dilemma, curb opportunistic behavior by all relevant parties, and create a favorable external environment for promoting strategic cooperation between the two sides.

6.2. Conclusions

Based on existing research, this study constructed an evolutionary game model of the cooperative relationship between prefabricated building owners and contractors and studied its impact on cooperation strategies from the aspects of excess benefits, transaction costs, risk losses, etc. This research study reveals the following:
(1)
The presence of the excess interest factor positively influences the system’s progression toward strategic cooperation. Specifically, as the excess interest increases, the likelihood of the system reaching a stable state of strategic cooperation also increases. Furthermore, the establishment of a well-defined excess benefit distribution coefficient can effectively enhance the strategic collaboration between the contractor and the employer. In other words, a judicious benefit distribution mechanism can guarantee a mutually beneficial outcome for both the owner and the contractor.
(2)
The presence of transaction costs in the cooperation between the contracting parties hinders the system’s progression toward strategic cooperation. Specifically, higher transaction costs associated with strategic cooperation led to a faster evolution toward the “traditional cooperation” strategy. Furthermore, the establishment of an appropriate transaction cost-sharing coefficient can effectively enhance the strategic collaboration between the contracting parties.
(3)
The decrease in risk cost has a beneficial impact on the system’s progression toward strategic cooperation. Specifically, as the risk cost decreases, the likelihood of the system moving toward a stable state of strategic cooperation increases. Furthermore, it is important to consider the allocation coefficient for optimizing the reduction in risk costs.
This study focuses on the analysis of evolutionary and simulation data to examine the impact of parameter changes on the behavioral evolution of both parties involved in the game. The findings of this study can serve as a theoretical foundation for enterprises in making informed decisions regarding the selection of a suitable cooperation scheme. The game model presented in this paper is specifically centered on the selection of parameters relevant to owners and contractors, excluding any parameters associated with other stakeholders. Hence, the forthcoming study’s focus will center on examining the game behavior demonstrated by government departments and other stakeholders. In addition, testing the proposed model in real-world scenarios is essential to confirm its practical applicability.

Author Contributions

Conceptualization, S.W.; Methodology, S.W. and C.W.; Investigation, S.W. and W.L.; Writing—original draft, S.W. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 71872141), the MOHURD Foundation (2018-R2-032), and the Natural Science Foundation in the Shaanxi Provincial Department of Education (18JK0481).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available upon request from the corresponding author. The data are not publicly available due to privacy.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Research framework.
Figure 1. Research framework.
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Figure 2. Phase diagram of evolution system in scenario 1.
Figure 2. Phase diagram of evolution system in scenario 1.
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Figure 3. Phase diagram of evolution system in scenario 2.
Figure 3. Phase diagram of evolution system in scenario 2.
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Figure 4. Phase diagram of evolution system in scenario 3.
Figure 4. Phase diagram of evolution system in scenario 3.
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Figure 5. Phase diagram of evolution system in scenario 4.
Figure 5. Phase diagram of evolution system in scenario 4.
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Figure 6. Initial assignment evolution simulation results.
Figure 6. Initial assignment evolution simulation results.
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Figure 7. The evolutionary game trajectory of different Δ E .
Figure 7. The evolutionary game trajectory of different Δ E .
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Figure 8. The evolutionary game trajectory of different α .
Figure 8. The evolutionary game trajectory of different α .
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Figure 9. The evolutionary game trajectory of different C values.
Figure 9. The evolutionary game trajectory of different C values.
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Figure 10. The evolutionary game trajectory of different β .
Figure 10. The evolutionary game trajectory of different β .
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Figure 11. The evolutionary game trajectory of different Δ Q .
Figure 11. The evolutionary game trajectory of different Δ Q .
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Figure 12. The evolutionary game trajectory of different δ values.
Figure 12. The evolutionary game trajectory of different δ values.
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Table 1. Model parameter setting and meaning.
Table 1. Model parameter setting and meaning.
Serial NumberSymbolMeaning
1 E 1 Normal income of the owner when adopting the “traditional cooperation” strategy
2 E 2 Normal benefits of contractors adopting “traditional cooperation” strategy
3 Δ E Excess benefits obtained by the owner and the contractor when they adopt the “strategic cooperation” strategy
4 α The distribution coefficient of the owner for the excess return when the two sides adopt the strategic cooperation strategy
5 C Transaction costs to be paid when the owner and the contractor adopt strategic cooperation
6 β Owner’s share coefficient of transaction costs
7 Q 1 Risk cost when the owner adopts the “traditional cooperation” strategy
8 Q 2 Risk cost of contractors adopting “traditional cooperation” strategy
9 Δ Q Reduced value of risk cost when both parties adopt a “strategic cooperation” strategy
10 γ Probability of risk occurrence
11 δ Distribution coefficient of the owner for the reduced value of risk cost
Table 2. Game payment matrix between owner and contractor.
Table 2. Game payment matrix between owner and contractor.
Game PlayersThe Contractor
Strategic   Cooperation   ( y ) Traditional   Cooperation   ( 1 − y )
The ownerStrategic cooperation ( x ) E 1 + α Δ E − β C − γ Q 1 − δ Δ Q E 1 − β C − γ Q 1
E 2 + 1 − α Δ E − 1 − β C − γ Q 2 − 1 − δ Δ Q E 2 − γ Q 2
Traditional cooperation ( 1 − x ) E 1 − γ Q 1 E 1 − γ Q 1
E 2 − 1 − β C − γ Q 2 E 2 − γ Q 2
Table 3. Stability analysis of equilibrium point in scenario 1.
Table 3. Stability analysis of equilibrium point in scenario 1.
Equilibrium Point det . J t r . J Stability
(0, 0)>0<0Stable
(0, 1)>0>0Unstable
(1, 0)>0>0Unstable
(1, 1)>0<0Stable
(x*, y*)<00Saddle point
Table 4. Stability analysis of equilibrium point in scenario 2.
Table 4. Stability analysis of equilibrium point in scenario 2.
Equilibrium Point det . J t r . J Stability
(0, 0)>0<0Stable
(0, 1)<0UncertainSaddle point
(1, 0)>0>0Unstable
(1, 1)<0UncertainSaddle point
(x*, y*)<00Saddle point
Table 5. Stability analysis of equilibrium point in scenario 3.
Table 5. Stability analysis of equilibrium point in scenario 3.
Equilibrium Point det . J t r . J Stability
(0, 0)>0<0Stable
(0, 1)>0>0Unstable
(1, 0)<0UncertainSaddle point
(1, 1)<0UncertainSaddle point
(x*, y*)<00Saddle point
Table 6. Stability analysis of equilibrium point in scenario 4.
Table 6. Stability analysis of equilibrium point in scenario 4.
Equilibrium Point det . J t r . J Stability
(0, 0)>0<0Stable
(0, 1)<0UncertainSaddle point
(1, 0)<0UncertainSaddle point
(1, 1)>0>0Unstable
(x*, y*)<00Saddle point
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Wang, S.; Wang, C.; Li, W. Research on Cooperation Strategy Between Owner and Contractor of Prefabricated Building Based on Evolutionary Game Theory. Sustainability 2025, 17, 811. https://doi.org/10.3390/su17030811

AMA Style

Wang S, Wang C, Li W. Research on Cooperation Strategy Between Owner and Contractor of Prefabricated Building Based on Evolutionary Game Theory. Sustainability. 2025; 17(3):811. https://doi.org/10.3390/su17030811

Chicago/Turabian Style

Wang, Sunmeng, Chengjun Wang, and Wenlong Li. 2025. "Research on Cooperation Strategy Between Owner and Contractor of Prefabricated Building Based on Evolutionary Game Theory" Sustainability 17, no. 3: 811. https://doi.org/10.3390/su17030811

APA Style

Wang, S., Wang, C., & Li, W. (2025). Research on Cooperation Strategy Between Owner and Contractor of Prefabricated Building Based on Evolutionary Game Theory. Sustainability, 17(3), 811. https://doi.org/10.3390/su17030811

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