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Heliyon 10 (2024) e34775
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Research article
Synergizing stakeholder collaboration for value co-creation in
China’s prefabricated decoration diffusion: A tripartite
evolutionary game perspective
Hongjuan Wu
a
, Yipin Huang
b
, Guiwen Liu
c
,
*
, Lizi Luo
d
, Yuhang Luo
e
a
School of Management Science and Real Estate, Chongqing University, No.174 Shazheng Street, Shapingba District, 400044, Chongqing, China
b
School of Management Science and Real Estate, Chongqing University, No.174 Shazheng Street, Shapingba District, 400044, Chongqing, China
c
School of Management Science and Real Estate, Chongqing University, No.174 Shazheng Street, Shapingba District, 400044, Chongqing, China
d
School of Economics and Management, Wuhan University, 430072, Wuhan, China
e
School of Management Science and Real Estate, Chongqing University, No.174 Shazheng Street, Shapingba District, 400044, Chongqing, China
ARTICLE INFO
Keywords:
Prefabricated decoration
Value co-creation
Tripartite evolutionary game model
Stakeholders’ strategies
ABSTRACT
The emerging prefabricated decoration (PD) sector in China offers a compelling avenue for
revolutionizing the construction industry, aligning with the imperatives of sustainability and
industrialization. However, the outlook for the diffusion of PD in China’s construction industry is
less than promising. The development of PD is closely related to its value creation and the
intricate interplay of stakeholder strategies and their ramications on PD’s value co-creation
necessitates thorough exploration. Based on evolutionary game theory, this study elucidates
the dynamic interactions among local governments, developers, and decoration contractors in
China’s evolving PD landscape. A tripartite evolutionary game model was established, investi-
gating the evolutionary stable equilibriums and the corresponding strategies. Then, an empirical
analysis in Chongqing City validates the game models and primary conclusions. Scrutinizing
subsidy thresholds, local subsidy biases, PD proportion in prefabrication, and binary innovation
allocation, the research unveils nuanced insights pertinent to boosting PD’s value co-creation.
Findings advocate an assembly rate threshold of subsidy (65%–70 %) and a shift towards
incentivizing decoration contractors to catalyze PD adoption. Additionally, excessive PD pro-
portion and immature product investments may hinder industry development, prompting
stakeholders to recalibrate strategies dynamically. These ndings characterize the mechanisms of
stakeholder value co-creation during the PD diffusion, enriching the implications of value co-
creation theory in the emerging industry of the construction sector. They also furnish stake-
holders committed to promoting the diffusion of PD in the domestic and international con-
struction sectors with practical strategic guidance, particularly tailored for cities in the early
stages of PD development.
* Corresponding author.
E-mail addresses: hongjuanwu@cqu.edu.cn (H. Wu), yipin@stu.cqu.edu.cn (Y. Huang), gwliu@cqu.edu.cn (G. Liu), lizi.luo@whu.edu.cn
(L. Luo), yuhangluo@stu.cqu.edu.cn (Y. Luo).
Contents lists available at ScienceDirect
Heliyon
journal homepage: www.cell.com/heliyon
https://doi.org/10.1016/j.heliyon.2024.e34775
Received 29 February 2024; Received in revised form 8 July 2024; Accepted 16 July 2024
Heliyon 10 (2024) e34775
2
1. Introduction
Globally, the construction industry is shifting towards sustainability, energy efciency, and intelligent practices, with a focus on
industrialization as a key strategy for achieving these goals [1]. Prefabrication serves as an effective means for industrializing the
construction industry, initially pioneered by developed countries [2]. With advancements in technology and the growing global de-
mand for sustainable construction, prefabrication has extended beyond structural construction to the decoration phase, giving rise to
an emerging practice known as prefabricated decoration (PD) [3]. PD involves the on-site installation of factory-produced decoration
components and modules [4]. This approach extends prefabricated construction into decoration, exhibiting several advantages over
traditional decoration. PD surpasses traditional decoration, reducing carbon emissions by 48 % [5], construction waste by 50 %, and
construction time by 70 % [6]. The numerous benets of PD have contributed to its extensive adoption in both developing and
developed countries with large-scale construction industries. China, facing the challenges such as the disappearance of demographic
dividends [7], escalating resource costs [8] and an aging population [9], is one of the representatives. Consequently, PD has garnered
signicant attention and investment within the Chinese context, prompting authorities to issue a series of supportive policies, such as
the “Opinions on Accelerating the Development of New Type of Building Industrialization” and the “14th Five-Year Plan for the
Development of the Construction Industry” [10,11]. Nevertheless, PD’s current implementation is mostly limited to prefabricated
bathrooms and kitchens [12], indicating that PD in China is still in an early developmental stage.
The signicant resistance encountered in PD diffusion can manifest in several aspects. From a holistic perspective of industry, the
PD industry involves multiple stakeholders, including decoration contractors, developers, and local governments, among others. In
cases lacking a cooperative purpose, stakeholders may lean towards independent operations rather than collectively striving for value
co-creation [13]. From the perspective of private stakeholders, stakeholders often operate within limited information, exhibiting a
deciency in comprehending industry dynamics and trends among other stakeholders. This information asymmetry poses a hindrance
to effective communication and collaborative efforts [14]. From the perspective of public stakeholders, the industry grapples with
further exploration of unied standards and regulations, and the lack of standardized protocols may impede consensus on design,
production, and transportation, thereby adversely affecting the efciency and quality of the PD project [15]. These real-world chal-
lenges impede PD diffusion, collectively underscoring the absence of concerted efforts among PD stakeholders, namely the lack of
value co-creation. In emerging industries, value co-creation necessitates stakeholders to collaboratively engage without compromising
the interests of others, thereby fostering a more optimal realization of economic, environmental and social values realization [16].
Therefore, it is imperative to establish a conducive environment for value co-creation to facilitate the PD diffusion in China’s con-
struction industry.
Existing studies focus on PD diffusion via technological advancements and economic considerations. Technological approaches in
China adhere to the principle of separating piping and structure while coordinating various systems, including partition and wall
systems, ceiling systems, oor systems, kitchen systems, etc [17]. Exploratory efforts have also been made to incorporate green
building materials in integrated suspended ceilings [18] and to integrate roof wall modules to enhance the quality and efciency of
healthcare spaces [19]. Other researchers have investigated the economic factors, such as production cost and labor productivity, that
impede the value co-creation of PD in China [18]. However, existing studies overlook the crucial management aspect: the lack of
strategic alignment among key stakeholders, leading to a collective inability to achieve concerted efforts in value co-creation, which is
the essence of PD diffusion. In the context of China, local governments, developers, and decoration contractors exert their signicant
inuence on the dissemination and diffusion of PD. Usually, these diverse stakeholders individually pursued varied values based on
their own interests, which is rooted in their confusion to collaborate in generating value aligned with the diffusion of PD. Resolving this
issue necessitates the application of a dynamic multi-stakeholder game approach tailored to the intricacies of the emerging PD
industry.
Evolutionary game theory, with its mature theoretical foundation and effective tools, provides a valuable framework for under-
standing multi-stakeholder game relationships [20,21]. It serves as a key guide for cultivating value co-creation and studying
stakeholder dynamics, especially for emerging industries [22]. Building upon it, this study seeks to offer pragmatic value co-creation
strategies through the lens of evolutionary game theory, investigating stakeholders’ optimal strategies for maximizing the value
creation in PD projects, thereby expediting the diffusion of the PD industry in China. Specically, this study is expected to address the
following questions systematically: 1) What are the evolutionary stable equilibriums and the corresponding strategies for the value
co-creation of PD? 2) How do specic interests embedded in stakeholders’ strategies inuence the evolutionary equilibrium within the
dynamic evolution of the PD industry? 3) How can each stakeholder contribute to boosting PD’s value co-creation by taking appro-
priate strategies through their crucial behaviors? Based on insights from China, this study extends the applicability of evolutionary
game theory in emerging industries and provides more effective strategies for promoting PD in the global construction industry,
especially in regions where PD is in the early stages of development.
2. Literature review
2.1. Emerging of prefabricated decoration in China
Prefabricated decoration (PD) in China refers to the on-site installation of factory-produced decoration components and modules,
encompassing various building systems such as partition and wall, ceiling, oor, kitchen, bathroom, storage, internal door and
window, and equipment and piping systems [17]. In developed countries with advanced construction industrialization practices like
the United States, Japan and Sweden, modular building and prefabricated building have integrated structure and decoration without
H. Wu et al.
Heliyon 10 (2024) e34775
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distinct separation [23,24].
In China, the emergence of PD responds to the evolution of prefabricated building and the upgrading of traditional decoration
practices. Historically, prefabrication has primarily focused on the building structure, with separate contractors handling decoration
[25]. However, this fragmented approach has limited the realization of prefabrication’s full production efciency. With the
advancement of Building Information Modeling (BIM), integrating structure and decoration has become feasible, and facilitating the
application of PD [26]. PD has been emerging as an extending area of prefabricated construction, with its rst technical standard
published in 2021 [17]. Fig. 1 illustrates the emergence of PD along with the development of prefabricated building in China.
Furthermore, the demand for high-quality homes has driven the popularity of PD. Previously, individual homeowners would un-
dertake decoration themselves, leading to time-consuming processes, pollution and resource waste [12]. The integration of PD
technology eliminates labor-intensive tasks such as cutting, grooving, and coating at the construction site [3]. This results in a
reduction in carbon emissions, noise, and waste, making PD more environmentally friendly than traditional cast-in-place concrete
buildings. Given the needs and motivations of both suppliers and consumers, PD has emerged as a promising and necessary industry for
promoting green production practices.
Currently, PD is still in its early stages of development in China, primarily applied in public housing, hotels and buildings with less
personalized decoration requirements [3]. Despite its promising benets, consumer demand, and technological advancements, the
wider adoption of PD faces signicant challenges and decision-making frictions. Stakeholders in the PD industry include developers,
decoration contractors, local governments, prefabricated component manufacturers, logistics companies, and consumers [27]. Local
governments serve as market regulators, ensuring compliance with policies and regulations [28]. They play a crucial role in guiding
the transformation of the decoration market by encouraging PD adoption through policies and regulations, which have proven
effective in stimulating prefabrication development [29]. Developers, as the ultimate decision-makers in PD implementation, engage
private stakeholders for construction activities [30]. Decoration contractors are responsible for designing, procuring prefabricated
products, and assembling components. Their strategies directly impact the quality, productivity, and technological advancements in
PD projects [31]. Thus, the decisions and strategies of local governments, developers, and decoration contractors are pivotal in the
success of PD’s value co-creation. The dynamic interactions among these stakeholders signicantly inuence PD’s wider adoption and
sustainable growth in China. In addressing this issue, it is crucial to identify the values of key stakeholders and quantify the specic
interests therein.
2.2. Values of PD and interests of the key stakeholders
The value co-creation in the PD context signies the collaborative endeavors of stakeholders to collectively generate and distribute
additional benets. This process involves key stakeholders, including local governments, developers, and decoration contractors,
integrating their respective resources, knowledge, and skills to collectively achieve more efcient, comprehensive, and sustainable
benets, thereby driving the diffusion of the PD industry [27]. Nevertheless, existing studies have yet to comprehensively discern the
precise interests stakeholders seek when engaging in value creation, leaving a gap in understanding how these varied interests
motivate stakeholders to adopt specic behaviors. Therefore, as depicted in Fig. 2, motivated by diverse interests, key stakeholders
contribute to the creation of social, economic, and environmental value.
Local governments (LGs): are primarily engaged in actively creating social and environmental values. Social values include the
growth of the local economy driven by PD and increased tax revenue [32]. Environmental values are related to PD’s contribution to
low-carbon and energy-efcient sustainable development, leading to reduced environmental management costs [33]. To obtain these
Fig. 1. The emergence of PD along with the development of prefabricated building in China.
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values, LGs implement regulations and subsidy policies to promote PD [34]. However, despite these policies, some developers and
decoration contractors remain hesitant to embrace PD, thereby hindering LGs’ access to core values. Thus, governments need to
evaluate the effectiveness of incentive policies and consider applying, stopping, or increasing policy support efforts.
Developers: take the economic value as a priority, emphasizing income maximization and cost minimization in PD projects. In
addition to project prots, government subsidies serve as a signicant source of income [35]. PD projects can also bring additional
social values to developers, such as enhanced reputation and increased brand value [33]. However, in the initial stage of PD devel-
opment, developers may need to incur additional costs when working with contractors due to the increased expenses associated with
PD construction [22]. Consequently, developers may be hesitant to adopt PD.
Decoration contractors (DCs): also prioritize the economic value, highlighting the prot generation [36]. Based on their pro-
jections of costs and revenues, DCs have the discretion to choose whether to engage in PD projects [22]. In the initial stage of PD
development, DCs bear additional costs for technology research and development as well as marketing [33]. As a result, contractors
may demand higher contract prices from developers to compensate for these expenses. And in this process, government subsidies can
play a role in encouraging contractors to embrace PD. Furthermore, DCs must carry out technology innovation to keep competitiveness
in the market. Dual innovation theory introduces an enterprise’s technology innovation capability into two distinct categories:
exploitative innovation and exploratory innovation [37]. Exploitative innovation involves leveraging existing technology to enhance
products or processes, while exploratory innovation concentrates on novel technology, introducing new value propositions, in-
novations, and inventions with potential long-term benets [31]. In the PD industry, the six product systems exhibit two different types
of innovation in the PD guideline [27]. The integrated ceiling, prefabricated panel, and kitchen systems are categorized as exploitative
innovations, as they are relatively mature in the market and have fewer pain points. On the other hand, prefabricated partitions,
prefabricated oors, and integrated bathrooms represent exploratory innovations, as they have signicant differences in craftsmanship
from traditional decoration and there is still a tonne of potential for innovation.
As summarized in Table 1, while LGs focus on social and environmental values, developers are dedicated to the creation of eco-
nomic value by prioritizing maximizing prots and avoiding penalties associated with traditional construction practices. DCs, akin to
developers in the pursuit of economic value creation, seek favorable nancial outcomes and consider the costs and revenues of PD
projects. Stakeholders’ divergent interests give rise to disparate attitudes towards PD, consequently impeding collaborative efforts to
realize the creation of PD’s value, namely, hindering the attainment of PD’s value co-creation. Therefore, in navigating the intricate
Fig. 2. Values of PD and interests of the key stakeholders.
Table 1
The values and interests of the three key stakeholders in PD projects.
Stakeholders Values Interests References
Local governments Social value, environmental value Social benets [32,33]
Environment benets [38,39]
Scientic subsidy standards [33,34]
Developers Economic value Contract prots [32,39]
Subsidies [22,39]
Social benets [32,40]
Decoration contractors Economic value Contracting price [32,36]
Subsidies [22,32]
Decoration costs [3,33]
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dynamics of interest relationships to achieve the value co-creation of PD, the utilization of evolutionary game theory becomes
imperative.
2.3. Evolutionary game theory
Evolutionary game theory (EGT) originates from the concept of Evolutionary Stable Strategy, which was rst introduced by Smith
and Price [20,41]. The core concepts of EGT are evolutionary stable strategy and replicator dynamic equation [42]. Unlike traditional
game theory, EGT acknowledges bounded rationality and information asymmetry, recognizing that individuals may not be entirely
rational and possess complete information. This realism makes evolutionary games more suitable for modeling real-world situations
[43].
Evolutionary Game Theory (EGT) has been extensively applied to examine the dynamics of value co-creation among stakeholders
in industries marked by rapid iteration and large-scale development. In the agricultural sector, researchers have examined the game
relationships among governments, farmers [44], manufacturers [45], e-commerce retailers [46], and urban residents to identify
optimal value co-creation strategies that facilitate the transformation and upgrading of the agricultural industry chain. In the
manufacturing sector, scholars have explored the game relationships among local governments, green suppliers [47], manufacturers
[48], and retailers [40] to derive ideal co-creation strategies for the green and low-carbon transformation of the manufacturing in-
dustry chain. Similarly, in the construction eld, researchers have investigated the game relationships among governments, developers
[38], contractors [49], consumers [22] to identify optimum value co-creation strategies that promote the industrialization of con-
struction. These studies demonstrate the wide application of EGT in analyzing stakeholder relationships and understanding key factors
inuencing transformation and upgrading processes. By providing guidance to stakeholders, EGT enables them to make informed
decisions and judgments, thereby promoting value co-creation and development in the industry.
In the emerging context of China’s PD industry, the relationships between key stakeholders remain unclear, and stakeholders lack a
comprehensive understanding of the impact of their strategies on value co-creation. In such a scenario, the application of EGT becomes
highly relevant as it allows for the depiction of dynamic market cooperation mechanisms and the clarication of complex game re-
lationships among stakeholders from the perspective of PD’s values. ETG possesses the capacity to elucidate the interests of all
stakeholders, establish effective policies and support mechanisms, foster value co-creation, and drive sustainable growth in China’s PD
industries.
3. Methods
3.1. Model assumptions
PD industry characterizes a high degree of integration and collaboration of multiple stakeholders. Among them, local governments,
developers and decoration contractors are the key stakeholders in the development process of the PD industry. Hence, based on EGT,
this study constructs a tripartite evolutionary game model of LGs, developers and DCs to analyse the gaming process of them to co-
Table 2
Description of major Parameters.
Stakeholders Strategies Parameters Descriptions
Local Governments Incentive GB1 Social benets when developers and DCs choose to execute PD projects.
GB2 Environmental benets when developers and DCs choose to execute PD projects.
GC1 Subsidies when the developer meets the subsidy requirements for prefabricated building.
GC2 Subsidies when the DC chooses to supply prefabricated technologies.
GC3 Incremental costs (excluding economic subsidies) brought by the LG’s implementation of incentive
policies.
α
Assembly rate threshold of subsidy (
α
∈(0,1)).
Developers Prefabricated DB1 Economic benets of executing PD project.
DB2 Subsidies’ benets by the LG, DB2=GC1.
DC1 Incremental costs when making full use of prefabricated structure in achieving projects’ assembly rate (β
=0.65–0.6 =0.05).
DC2 Incremental costs when making full use of PD in achieving projects’ assembly rate (β =0.4).
β Contribution of PD for projects’ prefabrication [50]
Traditional DB3 Economic benets of executing traditional decoration projects.
DC3 Costs when both the structure and decoration are traditionally constructed.
Decoration
contractors
Prefabricated CB1 Incremental benets when the DC supplies PD technologies.
CB2 Subsidies’ benets by the LG, CB2=GC2.
CB3 Incremental benets when the PD technologies supplied purely rely on exploratory innovation.
CB4 Incremental benets when the PD technologies supplied purely rely on exploitative innovation.
CC1 Incremental costs when the DC supplies PD technologies compared with the traditional counterpart.
CC2 Incremental costs when the PD technologies supplied purely rely on exploratory innovation.
CC3 Incremental costs when the PD technologies supplied purely rely on exploitative innovation.
γ Proportion of exploratory technologies in PD implementation (γ ∈(0,1)).
Traditional CB5 Benets when the DC supplies traditional decoration technologies.
CC4 Costs when the DC supplies traditional decoration technologies.
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create values to promote the PD industry in the context of China’s construction industry, and the three basic assumptions are as
follows.
•Assumption 1. Asymmetric Information. Given the intricate nature of the PD industry chain, characterized by its extensive
network of stakeholders, each stakeholder possesses varying degrees of industry information, leading to information asymmetry
among them. Consequently, the inter-stakeholder strategies are subject to dynamic changes inuenced by their respective infor-
mation asymmetry proles.
•Assumption 2. Bounded rationality. Compared to developers and DCs, LGs have relatively comprehensive information and clear
strategic objectives and are therefore relatively more rational. The developers and DCs, on the other hand, need to learn and adjust
their strategies constantly before they can nd their optimal ones.
•Assumption 3. Strategic space. (1) The LGs inuence the process of promoting PD through policy instruments, with two strategies
of (non-incentive, incentive) policies. The probability that LGs choose to implement incentive policies is x (0≤x ≤1), and the
probability that LGs choose not to implement incentive policies is 1 −x. If LGs opt for implementing incentive policies, they
formulate relevant policies and regulations and subsidize developers and DCs. (2) The strategy set available to developers is to
execute (traditional, prefabricated) decoration projects. The probability that developers choose to execute PD projects is y (0≤y ≤
1), and the probability that developers choose to execute traditional decoration projects is 1−y. Developers execute PD projects by
signing a contract with DCs. The application of PD objectives and construction plans is specied in the project contract. To obtain
the LG subsidies, the developer must execute PD projects and allocate the proportion of prefabrication in the structure and the
decoration to ensure that the assembly rate of the whole project meets the minimum requirements settled by the LG. In this game, it
is assumed that all developers who choose to execute PD projects meet the requirements and receive subsidies. Furthermore, the
social benets that developers can receive during the initial stages of PD are modest, hence they are not taken into account in this
study. (3) The strategy set available to the DCs is to supply (traditional, prefabricated) decoration technologies. The probability that
DCs choose to supply PD technologies is z (0≤z ≤1), and the probability that DCs choose to supply traditional technologies is 1−z.
If DCs opt for PD technologies, they are engaged in PD technology innovation when adopting specic technologies in PD projects.
Based on the above assumptions, parameters for describing the strategies of the three key stakeholders are dened, as shown in
Table 2.
3.2. Model establishment and equilibrium solution
In this game model, there is a contractual relationship between the developer and the DC. If the developer and DC have conicting
attitudes towards PD, the contract cannot be achieved, leading to the inability to develop the PD project. Thus, only the situations
when both developers and contractors are willing to develop PD projects were considered in this study. According to the above-
Fig. 3. The strategy combinations of the tripartite game model.
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mentioned analysis and assumptions, the expected payoffs for the LGs, developers and DCs under different combinations of their
strategies are presented in Fig. 3. Based on the above payoff matrix, the expected payoffs of each stakeholder under different strategies
and the replicated dynamic equation can be calculated. Here uses Gi, Di and Ci to denote the payoffs when i is chosen respectively,
where i =1, 2 denotes the different strategy choices of each stakeholder, e.g. G1 denotes the payoffs when the LG chooses the strategy
of “incentive".
(1) Local governments:
The expected payoffs function for LGs choosing the “incentive” strategy is:
G1=yz(GB1+GB2−GC1−GC2−GC3) + (1−y)(1−z)(− GC3)(1)
The expected payoffs function for LGs choosing the “non-incentive” strategy is:
G2=yz(GB1+GB2)(2)
The average expected payoffs for the LGs is:
G=xG1+ (1−x)G2(3)
From equation (1)(2)(3), the replicated dynamic equation for LGs’ choice of the “incentive” strategy is:
F(x) = dx
dt =x(G1−G) = x(1−x)(G1−G2)
=x(1−x)[ − yz(GC1+GC2+2GC3) + yGC3+zGC3−GC3](4)
Based on the stable theorem of the differential equation (4), when F(x) = 0 and F(x)ʹ<0, the LGs’ strategy is stable. Let dx
dt =0,
x∗
1=0, and x∗
2=1. Therefore,
y∗=(1−z)GC3
−z(GC1+GC2+2GC3) + GC3
(5)
Based on equation (5), when y=y∗, F(x) ≡ 0. It indicates that whether or not LGs implement incentive policies, they will gain the
same benets. When y＞y∗, the probability of ‘incentive’ exceeds y∗. To ensure F(x) ≥ 0, x∗
2=1 must be satised and a stable strategy
of ‘incentive’ is obtained. In this circumstance, the local government’s strategy shifts from ‘non-incentive’ to ‘incentive’. When y＜y∗,
the probability of ‘incentive’ is less than y∗. As a result, x∗
1=0 is required and a stable strategy of ‘non-incentive’ is achieved. LGs’
strategy shifts from ‘incentive’ to ‘non-incentive’. Based on the calculation above, the evolution trend for the LGs’ strategy regarding
the promotion of the PD is illustrated in Fig. 4.
(2) Developers:
Fig. 4. Evolution trend of the LGs’ strategies.
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Similarly, the expected payoffs function for developers choosing the “prefabricated” strategy is:
D1=xz(DB1+DB2−
α
−β
60% DC1−β
40%DC2−DC3)
+(1−x)z(DB1−
α
−β
60% DC1−β
40%DC2−DC3)(6)
The expected payoffs function for developers choosing the “traditional” strategy is:
D2=x(1−z)(DB3−DC3) + (1−x)(1−z)(DB3−DC3)(7)
The average expected payoffs for developers is:
D=yD1+ (1−y)D2(8)
From equation (6)(7)(8), replicated dynamic equation for the developers’ choice of " prefabricated " strategy is:
F(y) = dy
dt =y(D1−D) = y(1−y)(D1−D2)
=y(1−y)[xzDB2+z(DB1+DB3−2DC3−
α
−β
60% DC1−β
40%DC2)−DB3+DC3](9)
Based on the stable theorem of the differential equation (9), when F(y) = 0 and F(y)ʹ<0, the LG’s strategy is stable. Let dy
dt =0,
y∗
1=0, and y∗
2=1.Therefore,
z∗=DB3−DC3
xDB2+DB1+DB3−2DC3−
α
−β
60% DC1−β
40%DC2
(10)
Based on equation (10), when z=z∗, F(y) ≡ 0. It indicates that whether or not developers execute PD projects, they will gain the
same benets. When z＞z∗, the probability of ‘prefabricated’ exceeds z∗. To ensure F(y) ≥ 0, y∗
2=1 must be satised and a stable
strategy of ‘prefabricated’ is obtained. In this circumstance, the developers’ strategy shifts from ‘traditional’ to ‘prefabricated’. When
z＜z∗, the probability of ‘prefabricated’ is less than z∗. As a result, y∗
1=0 is required and a stable strategy of ‘traditional’ is achieved.
Developers’ strategy shifts from ‘prefabricated’ to ‘traditional’. The trend of the evolution of developers is shown in Fig. 5.
(3) Decoration contractors:
Fig. 5. Evolution trend of the developers’ strategies.
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9
Similarly, the expected payoffs function for DCs when they choose the “prefabricated” strategy is:
C1=xy[CB5+CB2−CC4+γ(CB3−CC2) + (1−γ)(CB4−CC3)]
+(1−x)y[CB5−CC4+ +γ(CB3−CC2) + (1−γ)(CB4−CC3)] (11)
The expected payoffs function for DCs choosing the “traditional” strategy is:
C2=x(1−y)(CB5−CC4+ (1−x)(1−y)(CB5−CC4)) (12)
The average expected payoffs for the DCs is:
C=yC1+ (1−y)C2(13)
From equation (11)(12)(13), the replicated dynamic equation for the DCs’ choice of the “prefabricated” strategy is:
F(z) = dz
dt =z(C1−C) = z(1−z)(C1−C2)
=z(1−z)[xyCB2+y(2CB5−2CC4+γ(CB3−CC2) + (1−γ)(CB4−CC3)) − CB5+CC4](14)
Based on the stable theorem of the differential equation (14), when F(z) = 0 and F(z)ʹ<0, the LG’s strategy is stable. Let dz
dt =0,
z∗
1=0, and z∗
2=1.Therefore,
y∗∗ =CB5−CC4
xCB2+2CB5−2CC4+γ(CB3−CC2) + (1−γ)(CB4−CC3)(15)
Based on equation (15), when y=y∗∗, F(z) ≡ 0. It indicates that whether or not DCs supply PD technologies, they will gain the same
benets. When y＞y∗∗, the probability of ‘prefabricated’ exceeds y∗∗. To ensure F(y) ≥ 0, z∗
2=1 must be satised and a stable strategy
of ‘prefabricated’ is obtained. In this circumstance, the DCs’ strategy shifts from ‘traditional’ to ‘prefabricated’. When y＜y∗∗ , the
probability of ‘prefabricated’ is less than y∗∗ . As a result, z∗
1=0 is required and a stable strategy of ‘traditional’ is achieved. DCs’
strategy shifts from ‘prefabricated’ to ‘traditional’. The trend of the evolution of DCs is shown in Fig. 6.
Based on (4)(9)(14), the replication dynamic equations for the LGs, developers and DCs are:
⎧
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎩
F(x) = x(1−x)[ − yz(GC1+GC2+2GC3) + yGC3+zGC3−GC3]
F(y) = y(1−y)[xzDB2+z(DB1+DB3−2DC3−
α
−β
60% DC1−β
40%DC2)−DB3+DC3]
F(z) = z(1−z)[xyCB2+y(2CB5−2CC4+γ(CB3−CC2) + (1−γ)(CB4−CC3)) − CB5+CC4]
(16)
The equilibrium points and stability of the strategies of the tripartite evolutionary game are analysed. When the rate of change of
Fig. 6. Evolution trend of the DCs’ strategies.
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the strategy choice of the tripartite evolutionary game system is 0, there are dx
dt =0, dy
dt =0, and dz
dt =0 , and according to equation (16),
four pure strategy equilibrium points of the evolutionary game model can be identied: E1 (0, 0, 0), E2 (1, 0, 0), E3 (1, 1, 1) and E4 (0, 1,
1).
3.3. Stability analysis of the equilibrium point in the tripartite game
To assess the stability of the equilibrium point in the tripartite game of PD, we employ Lyapunov’s stability theory [51], which
establishes that an equilibrium can only be an deemed asymptotically stable. Under this condition, the equilibrium qualies as an
Evolutionary Stable Strategy (ESS). As the equilibrium point, denoted as e*, represents a mixed-strategy Nash equilibrium, this study
focuses on analyzing the asymptotic stability of eight pure-strategy equilibria. Verication of their stability can be accomplished by
scrutinizing the eigenvalues of the system’s Jacobi matrix [41]. According to Lyapunov’s stability discriminant, the following criterion
on the Jacobi matrix can be used to determine whether the Nash equilibrium point is an ESS [52].
1. When all eigenvalues λ＜0 are present, the equilibrium point is classied as an ESS, indicating stability.
2. When all eigenvalues λ＞0 are present, the equilibrium point is deemed unstable.
3. When both positive and negative eigenvalues are present, the equilibrium point is a saddle point and remains unstable.
Based on Equation (16), the Jacobi matrix for this tripartite evolutionary game model is described as follows:
J=⎡
⎣
J11 J12 J13
J21 J22 J23
J31 J32 J33
⎤
⎦
where
J11 = (1−2x)[ − yz(GC1+GC2+2GC3) + yGC3+zGC3−GC3]
J12 =x(1−x)[ − z(GC1+GC2+2GC3) + GC3]
J13 =x(1−x)[ − y(GC1+GC2+2GC3) + GC3]
J21 =y(1−y)(zDB2)
J22 = (1−2y)[xzDB2+z(DB1+DB3−2DC3−
α
−β
60% DC1−β
40%DC2)−DB3+DC3]
J23 =y(1−y)(xDB2+DB1+DB3−2DC3−
α
−β
60% DC1−β
40%DC2)
J31 =z(1−z)(yCB2)
J32 =z(1−z)(xCB2+2CB5−2CC4+γ(CB3−CC2) + (1−γ)(CB4−CC3))
J33 = (1−2z)[xyCB2+y(2CB5−2CC4+γ(CB3−CC2) + (1−γ)(CB4−CC3)) − CB5+CC4]
Based on assumption 5, the developer executing traditional decoration projects has greater economic benets than costs and the
DC supply traditional technologies has greater economic benets than costs, which indicates that DC3−DB3<0 and CC4−CB5<0.
There are two Scenarios corresponding to different ESS.
Scenario 1. The benets of the developer in executing PD projects are less than the costs of that. The benets of the DC in supplying
Table 3
The analysis table for adjudging the stability of equilibrium points.
Equilibrium
points
Eigenvalue Sign Stability
λ1 λ2 λ3
E1 (0, 0, 0) −GC3 DC3−DB3 CC4−CB5 −−− ESS
E2 (1, 0, 0) GC3 DC3−DB3 CC4−CB5 + − − Unstable
E3 (1, 1, 1) GC1+GC2+GC3 DC3−DB2−DB1+5
α
3DC1−5β
3DC1+
5β
2DC2
CC4−CB2−CB5−γ(CB3−CC2) − (1−
γ)(CB4−CC3)
+++ Unstable
E4 (0, 1, 1) −GC1−GC2−
GC3
DC3−DB1+5
α
3DC1−5β
3DC1+5β
2DC2 CC4−CB5−γ(CB3−CC2) − (1−γ)(CB4−CC3) − + + Unstable
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PD technologies are less than the costs of that. The inequality (17) and inequality (18) are established.
DC3−DB1+5
α
3DC1−5β
3DC1+5β
2DC2>0(17)
CC4−CB5−γ(CB3−CC2) − (1−γ)(CB4−CC3)>0 (18)
The local stability of each equilibrium point is summarized in Table 3. “+” means the values of λi are more than 0, and "-" means the
values are less than 0. If the value of λi＜0(i=1,2,3)
,
an ESS exists. Otherwise, there is not an ESS. Therefore, the evolutionary stability
point is E1 (0, 0, 0) and a nal equilibrium state of (non-incentive, traditional, traditional) would be obtained.
Scenario 2. The benets of the developer in executing PD projects are greater than the costs of that. The benets of the DC in
supplying PD technologies are greater than the costs of that. The inequality (19) and (20) are established.
DC3−DB1+5
α
3DC1−5β
3DC1+5β
2DC2<0(19)
CC4−CB5−γ(CB3−CC2) − (1−γ)(CB4−CC3)<0 (20)
The local stability of each equilibrium point is summarized in Table 4. The evolutionary stability point is E1 (0, 0, 0) and E4 (0, 1, 1).
According to the different initial points, two nal equilibrium state would be obtained, which are (non-incentive, prefabricated,
prefabricated) and (non-incentive, traditional, traditional).
4. Empirical study and simulation results
To provide a comprehensive validation of the tripartite evolutionary game model and ascertain the correlation between stake-
holders’ strategies and system stability, a numerical analysis is conducted within the specic context of Chongqing. This verication
involves assigning numerical values to the model and simulating the game process using MATLAB2016b, thus capturing the evolu-
tionary trajectory from the initial state to the nal equilibrium in its entirety. Through this numerical simulation, the effectiveness and
reliability of the proposed model are thoroughly examined, shedding light on the intricate dynamics among three key stakeholders and
their impact on system stability.
4.1. Empirical study in Chongqing
4.1.1. Study area
This study selected Chongqing as the focal area for exploring the rational promotion strategies of stakeholders in the PD industry
with the consideration of three aspects: a supportive development foundation, a promising market with considerable potential, and a
strong motivation from the local government to promote PD. Firstly, as a demonstration city for prefabricated buildings [10],
Chongqing’s experience in terms of PD, extending and completing the prefabrication industrial chain, can apply to other cities as well.
Secondly, with the introduction of many PD policies and standards by Chongqing’s government, the market has paid more attention to
PD, which has great development potential in Chongqing [53]. Lastly, as of 2020, the proportion of new prefabricated building
construction in Chongqing accounted for only 15 % of new buildings [54], which is comparatively lower than in other demonstration
cities for prefabricated buildings. This indicates a strong motivation from the government to promote PD and bridge the gap between
the current state and the desired level of adoption. Based on these considerations, the study utilizes Chongqing as a case for a detailed
PD industry analysis, aiming to uncover reasons for stagnation and propose solutions, fostering industry progress locally and globally.
Table 4
The analysis table for adjudging the stability of equilibrium points.
Equilibrium
points
Eigenvalue Sign Stability
λ1 λ2 λ3
E1 (0, 0, 0) −GC3 DC3−DB3 CC4−CB5 −−− ESS
E2 (1, 0, 0) GC3 DC3−DB3 CC4−CB5 + − − Unstable
E3 (1, 1, 1) GC1+GC2+GC3 DC3−DB2−DB1+5
α
3DC1−5β
3DC1+
5β
2DC2
CC4−CB2−CB5−γ(CB3−CC2) − (1−
γ)(CB4−CC3)
+ − − Unstable
E4 (0, 1, 1) −GC1−GC2−
GC3
DC3−DB1+5
α
3DC1−5β
3DC1+5β
2DC2 CC4−CB5−γ(CB3−CC2) − (1−γ)(CB4−CC3) − − − ESS
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4.1.2. Data collection
Data for the cost and benets parameters of the PD tripartite game model were unavailable from the ofcial statistics in its initial
stage of promotion in China, either not able to be procured on the project level owing to the commercial sensitivity. In this circum-
stance, a mixed method of data acquisition is adopted in this study, including literature analysis, policy analysis, and expert interview
to collect the practical data that reects the current application of PD in Chongqing. By means of literature analysis, this study gathered
a wide range of scholarly articles about the eld of PD in China, by which the evolutionary trajectory, technical attributes, and
prevailing market dynamics in the realm of PD were comprehensively understood. In the pursuit of policy analysis, we delved into an
assortment of policy documents, regulations, and governmental reports that bear relevance to the domain of PD, spanning both na-
tional and provincial echelons. Within the connes of these cogent materials, we scrutinized the multifaceted facets of supporting
policies, exacting market entry prerequisites, and stringent quality standards. Expert interviews were conducted with 12 experts and
scholars from various sectors to obtain quantitative evaluations of payoff information related to PD. At the beginning of the interview,
the interviewer explained the purpose and the expected duration of the interview, and asked for the interviewee’s consent to
participate. After obtaining the interviewees’ consent, they also acknowledged and agreed that all interview content would be used
solely for academic research and publication. The specic list of expert interviews is described in Table 5, and the payoff data is
summarized in Table 6.
Local Government: The benets indicators for LGs are GB1and GB2.This study represents GB1 with the time saved by imple-
menting PD projects. Based on experience from the Chongqing Sheltered Housing Centre, a 50m2 public rental housing unit takes only
6 days to renovate using PD, compared to 30 days for traditional interiors, i.e., a saving of 24 days in construction time. According to
the Chinese real estate rental and sales service platform “ANJUKE” (https://cc.anjuke.com/) and “LIANJIA"(https://cq.lianjia.com/),
the average price of a two-room apartment in Chongqing in 2023 is 1541 CNY/m2, thus GB1 is 1541*24/30/50 =24.66 CNY/m2. GB2
is represented with the excremental cost of the carbon emission governance cost. The carbon emissions per unit m
2
for PD and the
carbon emissions per unit m
2
for traditional decoration are 35.8 kg and 134.7 kg respectively [6]. The unit carbon emission control cost
is 0.97 CNY/kg [55], so GB2 is (134.7–35.8)*0.97 =95.93 CNY/m2.
The cost indicators for LGs are GC1,GC2and GC3. The LG will provide a subsidy of 200 CNY/m2 to demonstration projects with an
assembly rate greater than 65 % [56], so GC1 is 200 CNY/m2. The LG will reduce the corporate income tax at a rate of 15 % for the DC
that satises the relevant requirements (the corporate income tax should have been levied at 25 % [56]) To simplify the calculation,
this study takes YASHA, a representative PD enterprise, as an example. Based on expert research of the enterprise’s southwest branch
and analysis of its nancial statements for 2021, it is known that the enterprise’s corporate income tax in 2021 is approximately 130
million CNY, and the business revenue of the PD segment accounts for approximately 60 % of its total revenue and the total area for the
implementation of the segment’s projects is about 5 million m2, so GC2 is 130,000,000*0.6/5,000,000*(25%–15 %) =1.56 CNY/m2.
GC3 are derived from the specic experiences of experts in the expert interview method.
Developers: The benets indicators for developers are DB1,DB2and DB3. DB2 refers to the benets from government subsidies of
executing PD projects ( DB2=GC1). The cost indicators for the developers are DC1,DC2and DC3. According to the add cost analysis
for prefabricated structure construction, DC1 is 483.3 CNY/m2 and DC2 is 900 CNY/m2 [57]. DB1,DB2,DB3 and DC3 are all derived
from the specic experiences of experts in the expert interview method.
Decoration Contractors: The benets indicators for decorators are CB1,CB2,CB3,CB4and CB5. CB1 refers to the incremental
benets when the DC supplying PD technologies(CB1=CB5+γCB3+ (1−γ)CB4). CB2 refers to the benets from government
subsidies of supplying PD projects(CB2=GC2). The cost indicators for decorators are CC1,CC2,CC3and CC4. CC1 refers to the in-
cremental costs when the DC supplying PD technologies (CC1=CC4+γCC2+ (1−γ)CC3). CB1,CB3,CB4,CB5,CC1,CC2,CC3and CC4
all are derived from the specic experiences of experts in the expert interview method.
Table 5
List of expert interviews.
No. Stakeholder Position Department unit
1 LG Clerk Marketing Housing and Urban-Rural Construction Commission
2 LG Clerk Marketing Housing and Urban-Rural Construction Commission
3 LG Clerk Marketing Housing and Urban-Rural Construction Commission
4 D Regional Sales Manager Sales China Vanke Co., Ltd.
5 D Regional Sales Manager Sales China Vanke Co., Ltd.
6 D Regional Marketing Director Marketing Longfor Properties Co. Ltd.
7 DC Regional Marketing Director Marketing Zhejiang Yasha Decoration Co., Ltd.
8 DC Regional Marketing Adviser Marketing Zhejiang Yasha Decoration Co., Ltd.
9 DC General Manager South West Region Zhejiang Yasha Decoration Co., Ltd.
10 Designer Deputy President Architectural Design Institute
11 Researchers Associate Professor Chongqing university
12 Researchers Research Assistant Institute of Urban-Rural Construction and Development
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Table 6
The initial values of all parameters (unit =CNY/m2).
Parameters Values
(Mean.)
Description Sources
GB1 24.66 Time saved by implementing PD:1541*24/30/50 =24.66 Interviewees (No.1, No.3), literature [27]
GB2 95.93 Environmental governance excremental costs:(134.7–35.8) *0.97 =95.93 Literature [6,55]
GC1 200 Subsidy for developers. Policy [58]
GC2 1.56 Subsidy for DCs: 130,000,000*0.6/500,000,000*(25%–15 %) =1.56 Interviewees (No.4, No.5), policy [58]
GC3 20 Government-incurred promotion costs. Interviewees (No.2)
α
0.65 Assembly rate threshold of subsidy. Policy [58]
DB1 11,000 Sales price of commercial housing. Interviewees (No.6, No.10)
DB2 200 DB2=GC1 Policy [58]
DC1 483.30 Incremental costs when all structures are constructed using prefabricated
construction
Literature [57]
DC2 900 Incremental costs when all decoration is constructed using prefabricated
construction
Interviewees (No.7, No.8, No.9)
β 0.20 Contribution of PD for projects’ prefabrication. Interviewees (No.4, No.5, No.6)
DB3 11000 Sales price of commercial housing. Interviewees (No.4, No.5, No.6)
DC3 3390 Cost of traditional construction of commercial housing. Interviewees (No.4, No.6, No.11)
CB1 =CB5+γCB3+ (1−γ)CB4
CB2 1.56 CB2 =GC2 Interviewees (No.4, No.6, No.12), policy
[58]
CB3 390 Incremental benets of PD’s exploratory innovation. Interviewees (No.7, No.8, No.9)
CB4 240 Incremental benets of PD’s exploitative innovation. Interviewees (No.7, No.8, No.9)
CC1 =CC4+γCC2+ (1−γ)CC3
CC2 360 Incremental costs of PD’s exploratory innovation. Interviewees (No.7, No.8, No.9)
CC3 190 Incremental costs of PD’s exploitative innovation. Interviewees (No.7, No.8, No.9)
γ 0.50 Proportion of exploratory technologies in PD implementation. Interviewees (No.7, No.8, No.9)
CB5 2400 Contract price for traditional decoration. Interviewees (No.7, No.8, No.9)
CC4 1500 Costs for traditional decoration. Interviewees (No.7, No.8, No.9)
Fig. 7. Evolution results of different initial values of (x, y, z).
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4.2. Dynamic evolution results
The practical data of Chongqing (as presented in Table 6) were assigned to the parameters of strategies in meet the inequality (19)
and (20) of Scenario 2 to validate the tripartite game model and conrm the stability of equilibrium points. The simulation process
involved setting a step size of 0.1 and generating 100 sets of initial participation proportion values (x, y, z) to observe the trajectory of
evolution from various starting points to equilibrium. Through these simulations, it was veried that the equilibrium points E1 (0, 0, 0)
and E4 (0, 1, 1) are both asymptotically stable equilibrium points in the dynamic system, as illustrated by the convergence of the
different colored lines in Fig. 7. The resulting ESS for local governments, developers, and decoration contractors were identied as
(non-incentive, prefabricated, prefabricated) and (non-incentive, traditional, traditional), respectively. This dynamic evolution
simulation diagram strongly supports the theoretical analysis conducted earlier, conrming the effectiveness of the previous ndings.
Specically, in Scenario 2, regardless of the initial proportion of developers and DCs both choosing the strategy of ‘prefabricated’, the
strategy of LGs ultimately stabilizes at ‘non-incentive’ (x =0). This observation implies that the benets associated with not imple-
menting incentive policies outweigh those of implementing incentive policies, thereby establishing ‘non-incentive’ as the stable
strategy for LGs.
The stable strategies observed in the simulation results reect the dynamic decision-making process inuenced by the trade-off
between benets and costs in PD projects. Developers and DCs adapt their strategies based on market conditions and perceived ad-
vantages of prefabricated construction, while LGs’ incentive policies gradually phase out, indicating a transition to a market-driven
environment. This withdrawal can be attributed to industry maturation, increased competition, and the emergence of self-
sustaining mechanisms. This trend aligns with the experience of other industries, where incentive policies gradually phase out as
Fig. 8. The effect of the assembly rate threshold of subsidy (
α
) on (a) the evolution trajectories of three stakeholders, (b) local governments, (c)
developers, and (d) decoration contractors.
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the industry matures [48]. As the PD industry matures, reliance on LGs’ incentive policies diminishes, emphasizing the need for a
gradual shift towards a self-sustaining market where project benets and advantages drive adoption and innovation.
4.3. Sensitivity analysis for the critical strategies
To gain valuable insights into the dynamics of stakeholders’ strategies and provide deeper managerial signicance for diffusion of
PD, a sensitivity analysis was conducted based on empirical analysis. The threshold of the assembly rate for subsidy, the LGs’ subsidy
inclination, the proportion of PD in prefabricated projects, and the proportion of exploratory technologies were analysed. These four
indicators are the curtail strategies of key stakeholders that have a certain degree of subjective variability and can be adjusted
independently by stakeholders. In-depth research on these core strategies can identify the fundamental barriers to the development of
the PD industry, providing a foundation for developing targeted development plans and policies.
4.3.1. Assembly rate threshold of subsidy (
α
)
As shown in Fig. 8(a), higher values of assembly rate threshold of subsidy tend to direct both developers and DCs towards adopting
the ‘traditional’ strategy. The results, as depicted in Fig. 8(c) and (d), demonstrate that when
α
is relatively low (<65 %), both de-
velopers and DCs tend to adopt the ‘prefabricated’ strategy in their evolutionary paths. However, as the value of ɑ exceeds 65 %, their
strategies toward the ‘traditional’ and developers are evolving faster than DCs. Additionally, Fig. 8(b) reveals that the stable strategy of
LGs consistently reaches ‘non-incentive’, while when
α
exceeds 70 %, the speed of evolution slows down signicantly.
Fig. 9. The effect of the local governments’ subsidy allocation bias on (a) the evolution trajectories of three stakeholders, (b) local governments, (c)
developers, and (d) decoration contractors.
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4.3.2. Local governments’ subsidy allocation bias
Taking into account the practical bias in LGs’ subsidy allocation, the PD tripartite evolutionary game model was explored under
three inclination situations between GC1 and GC2 most subsidies favor developers (GC1 =200, GC2 =50), fair subsidies (GC1 =125,
GC2 =125), and most subsidies favor DCs (GC1 =50, GC2 =200). It is observed from Fig. 9(a) that when the predominant subsidies are
allocated to DCs (GC1 <GC2), the evolutionary paths of developers and DCs tend to shift towards the ‘prefabricated’ strategy (x, y =1).
However, when GC1>GC2 instead, the developers’ and the DCs’ evolutionary paths all change toward the ‘traditional’ strategy. Fig. 9
(b) indicates that the stable strategy of LGs consistently leans towards ‘non-incentive’, yet this evolution speed slows down signi-
cantly when subsidies are focused on developers. Fig. 9(c) and (d) demonstrate that the stable strategies of developers and DCs tend
towards ‘traditional’ when LGs grant most subsidies to developers. Conversely, the stable strategy of developers and DCs reaches
‘prefabricated’ when subsidies are allocated fairly or mainly favor DCs, with developers exhibiting a slightly faster evolutionary speed
than DCs.
4.3.3. Contribution of PD for projects’ prefabrication (β)
As depicted in Fig. 10(a), high values of β steer both developers and DCs towards the ‘traditional’ strategy (x, y =0). Fig. 10(b)
indicates that the stable strategy of LGs consistently approaches ‘non-incentive’, with a slower decline when β is above 20 %. Moreover,
Fig. 10(c) and (d) demonstrate that the stable strategies of developers and DCs reach ‘prefabricated’ for β values at 15 % and 20 %.
However, as β increases to 25 %, the stable strategy of developers ultimately decreases to ‘traditional’.
Fig. 10. The effect of the contribution of PD for projects’ prefabrication (β) on (a) the evolution trajectories of three stakeholders, (b) local gov-
ernments, (c) developers, and (d) decoration contractors.
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4.3.4. Proportion of exploratory technologies in PD (γ)
To illuminate the imperative of technological innovation in the context of PD and offer actionable insights to contractors, this study
delved into the impact of the proportion of exploratory technologies (γ) within PD projects through comprehensive sensitivity sim-
ulations. Fig. 11(a) shows that high values of γ drive all stakeholders towards adopting the ‘traditional’ strategy (x, y, z =0). The
outcomes, as depicted in Fig. 11(b), underscore a consistent trend in the stable strategy of LGs converging towards ‘non-incentive’.
Notably, this decline slows down when γ is higher than 50 %. Turning attention to Fig. 11(c) and (d), it becomes evident that for γ
values 30 % and 50 %, the stable strategy of both developers and DCs align towards the ‘prefabricated’ approach. In contrast, with the
escalation of γ to 70 %, the stable strategy them regresses to ‘traditional’, with the period for the contractors to abandon PD longer than
the developers.
5. Discussion
5.1. Local governments’ optimal strategies for value co-creation
This study underscores the signicance of subsidies in achieving PD’s value co-creation and challenge the notion that higher
subsidy thresholds always lead to better outcomes. While it is understandable that LGs link subsidies to the assembly rate to attract
developers to adopt PD, this study argues against an excessively high threshold (>70 %) for subsidy allocation. Such an excessive
threshold of the assembly rate can deter the developers and DCs from adopting PD. On the one hand, the heightened use of pre-
fabricated components escalates project costs, thereby reducing the attractiveness of PD projects [32]. On the other hand, excessive
Fig. 11. The effect of the proportion of exploratory technologies in PD (γ) on (a) the evolution trajectories of three stakeholders, (b) local gov-
ernments, (c) developers, and (d) decoration contractors.
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government intervention and a high baseline for subsidies may limit the autonomy of the market, as developers may exclusively pursue
PD methods eligible for subsidies, disregarding other potentially more suitable construction approaches. This rigidity can impede
market vitality [35]. In contrast, a low threshold of prefabricated rate (
α
<60 %) falls short of achieving the PD development goals.
Hence, determining an optimal assembly rate threshold that unlocks the benets of prefabrication while motivating private stake-
holders to embrace PD is of paramount importance. This study recommends a reasonable range for the subsidy threshold that is slightly
higher than Chongqing’s actual threshold (65 % <
α
<70 %) [56]. This range represents a delicate equilibrium where developers and
contractors are incentivized to undertake PD projects while still aligning with the government’s PD diffusion goals.
Prioritizing subsidies towards decoration contractors rather than developers, the local government’s subsidy allocation bias proves
more advantageous for advancing value co-creation of PD. Currently, local subsidy policies tend to prioritize developers based on their
experience of prefabricated construction development, and this trend extends beyond Chongqing [34]. However, while subsidies do
encourage developers to adopt PD [22], this study reveals that establishing a stable relationship among key stakeholders takes time.
Unfortunately, a signicant portion of the subsidies compensates for developers’ prot loss, not beneting the industry’s technical
growth. Conversely, focusing subsidies on DCs encourage advanced knowledge and technology exploration for PD, fostering
commitment and expansion, as seen in emerging industries [59]. However, the current subsidy policies in Chongqing exhibit a clear
preference for subsidizing developers to promote PD development (GC1 =200 and GC2 =1.56 approximately). Given the study’s
ndings, shifting focus to DCs is recommended for maximizing industry potential and achieving value co-creation.
5.2. Developers’ optimal strategies for value co-creation
This study unveiled a latent resistance to boosting PD’s value co-creation among private stakeholders, as indicated by simulation
results showing a negative correlation between the proportion of PD in prefabricated projects and the willingness of developers and
contractors to embrace PD. This is rooted in Chinese prefabricated building policies focusing on both structure and decoration [56].
With mature structural prefabricated technologies compared to decoration [60], developers prefer structure due to ease. Nonetheless,
this study proposes a gradual integration of PD into prefabricated building projects, offering two pertinent considerations. Firstly, PD
could augment developers’ competitiveness by allowing them to achieve higher assembly rates to qualify for incentives (
α
>65 %),
particularly when the maximum structure portion (60 %) is conned by current prefabricated building evaluation standards. Secondly,
PD’s utilization of manufactured materials facilitates expedited project completion with ecologically sustainable practices, making it a
pivotal avenue for green and low-carbon transformation [3]. For practicality, a recommended PD portion (<20 %) in prefabricated
projects is suggested, which holds signicant value for promoting PD in cities during the early stage of its development.
5.3. Decoration contractors’ optimal strategies for value co-creation
During the incubation period of PD new technologies, while both developers and DCs exhibit a proclivity for established techniques
that have already gained maturity in the market, the application of emerging technologies cannot be ignored. The sensitivity analysis
results underscore the fact that an excessive proportion of exploratory technologies substantially dampens the enthusiasm of both
developers and DCs for PD engagement. This aligns with project management literature in China and globally [61,62], where de-
velopers prioritize proven products, and contractors stick to mature systems for stable prots. However, contractors have exhibited
more patience in embracing emerging technologies, highlighting exploratory innovation’s role in maintaining a competitive edge and
capitalizing on emerging market prospects [63]. Consequently, while prioritizing innovations in established products such as ceiling,
wall, and kitchen systems, DCs, especially those with weaker product competitiveness, should learn from similar enterprises in other
industries and place due importance to fostering innovation in less mature aspects of PD [31]. This perspective is also echoed by
designers and researchers in Chongqing, as reected in Interviews 10 and 11 in Table 5. Hence, DCs should strike a balance between
binary innovations and controlled exploratory technology (≤50 % of the total scope) for sustained values creation.
5.4. Practical implementations for stakeholders in boosting value co-creation of PD
In the process of diffusing PD in China’s construction sector, addressing the balance of interests among key stakeholders and
boosting value co-creation emerges as a prioritized challenge. Drawing from the insights of this study, the following strategic im-
plications are proposed to facilitate the diffusion of PD in China.
Local government. This study offers two recommendations for LGs’ PD policies: Firstly, adjusting the inclination objectives of
incentive policies from developers to DCs. This approach entails allocating a portion of incentive resources to DCs to recognize their
contributions. This shift enhances the contractors’ enthusiasm, technological innovation, and market position. To ensure proper
allocation, LGs can establish thresholds based on technical strength, qualications, and project experience, sieving out capable en-
terprises for incentives. Secondly, appropriately regulating the subsidy threshold for prefabricated construction, thus fostering room
for the development of PD. To align with industry growth, LGs should adopt a staged approach for these thresholds. Initially, a modest
reduction encourages broader participation, technology accumulation, and market entry. As the industry matures, gradually raising
the threshold encourages continuous enhancement of technical capabilities and project quality. Engaging industry stakeholders in
setting these thresholds fosters consensus and policy viability. Moreover, establishing a robust monitoring system is essential [64],
allowing for data-driven evaluation and timely adjustments to maintain policy relevance.
Developers. Within the context of safeguarding their own prots, Chinese developers should be conservative but progressively
integrate PD into construction projects by augmenting its share in prefabrication for each project. This endeavor necessitates two
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pivotal strategies. Firstly, fostering close communication with DCs during the design stages is recommended to ensure that only the
most reliable PD components are designed as part of the decoration, which will help to achieve a higher assembly rate. Secondly,
developers are advised to establish stable collaborations with architects in the realm of PD technology development, thereby facili-
tating the seamless expansion of PD applications across future projects. In sum, the incremental integration of mature PD technologies,
coupled with the exploration of innovative PD technologies, ensures developers’ engagement in the promising PD sector. This
approach paves the way for an extended prefabricated supply chain that yields signicant dividends, including monetary gains, time
efciencies, energy conservation, and enhanced market competitiveness for developers [65].
Decoration contractors. In the current phase, DCs are advised to prioritize matured PD products and well-established technology
offerings, with a supplementary allocation of resources towards exploratory technology innovation. To anchor mature technologies
and exploit innovative advancements as the primary tenets of PD implementation, it becomes imperative for DCs to distinctly dene
their unique PD attributes. This can be achieved through the cultivation of stable collaborations with component suppliers and the
continual enhancement of a comprehensive dataset comprising popular PD components that align with market demands [12].
Moreover, DCs are encouraged to undertake judicious exploratory innovation endeavors, capitalizing on their industry acumen and
forming synergistic partnerships with research institutions, technology providers and labor. This collaborative approach fosters
knowledge exchange and provides access to cutting-edge technologies. By fostering a culture of innovation within their organizations
and building strategic partnerships, DCs can position themselves at the forefront of technological advancements, thus ensuring sus-
tainable growth over the long term.
6. Conclusions
Prefabricated decoration (PD) has emerged as a pivotal avenue for ushering in industrialization within China’s construction sector,
offering substantial integration, energy efciency, and sustainability benets across the entire construction industry. The diffusion of
PD necessitates value co-creation among diverse stakeholders, yet prior studies have largely overlooked the intricate dynamics of
stakeholder relationships and the evolving cooperative mechanisms within this nascent sector from the value perspective. This study
takes a pioneering step by developing a tripartite evolutionary game model encompassing the key stakeholders - local governments,
developers, and decoration contractors. Through a rigorous analysis of the evolutionary process and the intricate strategic interplays
among these stakeholders, this study unveils the complex collaborative mechanisms driving PD’s value co-creation, thus providing
invaluable guidance to forward-thinking stakeholders navigating this evolutionary trajectory. This endeavor yields noteworthy
conclusions.
•In scenarios where PD benets outweigh costs, two evolutionary stable strategies emerge: E1 (0, 0, 0) (non-incentive, traditional,
traditional) and E4 (0, 1, 1) (non-incentive, prefabricated, prefabricated). Irrespective of developers’ and DCs’ stable strategies,
LGs’ incentive policies will eventually phase out from the market. Interestingly, if both adopt ‘traditional’ strategies, LGs shift to
‘non-incentive’ more slowly, extending incentives to encourage private stakeholders to embrace PD. Conversely, with ‘pre-
fabricated’ strategies, signifying industry maturity, governments reduce intervention, phasing out incentives gradually.
•For PD-related incentive policies, maintaining an optimal subsidy threshold and prioritizing subsidy allocation to DCs over de-
velopers are advocated. Firstly, a reasonable subsidy baseline is crucial to strike a harmony between industry diffusion imperatives
and developers’ participation, preventing an excessively high subsidy threshold from dampening developer interest and con-
straining market autonomy. For early-stage emerging PD markets, such as Chongqing, a recommended threshold assembly rate
range of 65%–70 % is proposed. Secondly, directing incentives primarily toward DCs signicantly stimulates PD adoption. Hence, a
recalibration of Chongqing’s current incentive approach is advised, shifting focus from developers to DCs for more effective PD
promotion.
•Amplifying the share of PD in prefabricated projects signicantly dampens developers’ and contractors’ willingness to embrace PD
during its initial development phase. However, it’s imperative to acknowledge that a certain proportion of PD in prefabrication
(<20 % in the case of Chongqing) offers distinct advantages, including shortened project timelines and the opportunity to attain a
higher assembly rate for securing incentives. Consequently, this study underscores the recommendation that Chinese developers
contemplate incorporating a dened proportion of PD within their construction endeavours, rather than dismissing it outright
during the nascent stages of PD implementation.
•Binary technology innovation is advocated in the Chinese PD market, with an accentuated emphasis on exploitative innovation
based on mature products. This entails pursuing technology innovation pertaining to preassembled ceiling, wall, and kitchen
systems, expected to yield stable returns and notable success. Nonetheless, the signicance of exploratory innovation within less
mature technological domains should not be underestimated by DCs. A judicious equilibrium between innovation in mature and
nascent areas stands as pivotal for advancing and disseminating the PD sector holistically.
•It’s worth noting that, when pivotal game player strategies shift, developers consistently outpace DCs in evolutionary speed. This
phenomenon can be attributed to developers’ role as sponsors within Chinese PD projects, granting them access to more infor-
mation and the agility to make swift decisions in response to dynamic circumstances, preserving their prot-generation
capabilities.
This study offers signicant contributions to academia and industry by uncovering the complex value co-creation mechanism
among stakeholders in the PD industry. Through a tripartite evolutionary game model, it reveals dynamic interactions among LGs,
developers, and DCs, and simulates the evolution process of PD’s value co-creation under diverse interests, providing profound insights
H. Wu et al.
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into the value co-creation of PD. Furthermore, ndings from Chongqing provides a valuable template for cities globally that are in the
emerging stages of PD diffusion. Although the goal of this study was achieved, some limitations it persists. Choosing Chongqing city as
a case study inevitably entails regional limitations. Being a specic region, China possesses unique economic, cultural, and political
environments, potentially limiting the generalizability of research ndings to some extent. Further investigation should be conducted
in conjunction with local situations, when extending research outcomes to other regions. Besides, the analysis focuses on governments,
developers, and contractors, omitting other key stakeholders such as architects, prefabricated component manufacturers, and logistics.
Furthermore, simplied incentive policies might not fully capture diverse government schemes. Future research could explore
nuanced models considering varied subsidy structures, thereby providing a more detailed understanding of the PD industry’s effects.
Ethics statement
This study was reviewed and approved by the Academic Committee of School of Management Science and Real Estate, Chongqing
University with the approval number: MSRECQU-ETH-09, dated March 3, 2023. All participants were informed that consent to
participate in the study and publish their data would be assumed on completion and submission of the study survey.
Data availability statement
The data associated with this study has not been deposited into a publicly available repository. Some or all data, models, or code
that support the ndings of this study are available from the corresponding author upon reasonable request.
Funding
This work was supported by the National Natural Science Foundation of China (Grant No.72301044), National Natural Science
Foundation of China (Grant No.72271035), Chongqing Social Sciences Planning Project–Youth Fund (2022NDQN43), and National
Natural Science Foundation of China (Grant No.72101190).
CRediT authorship contribution statement
Hongjuan Wu: Writing – review & editing, Supervision, Investigation, Funding acquisition. Yipin Huang: Writing – original draft,
Visualization, Validation, Methodology, Formal analysis. Guiwen Liu: Writing – review & editing, Writing – original draft, Funding
acquisition. Lizi Luo: Writing – review & editing, Funding acquisition. Yuhang Luo: Writing – original draft, Investigation, Data
curation.
Declaration of competing interest
The authors declare that they have no known competing nancial interests or personal relationships that could have appeared to
inuence the work reported in this paper.
Appendix A. Supplementary data
Supplementary data to this article can be found online at https://doi.org/10.1016/j.heliyon.2024.e34775.
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