Green Building Design and Sustainable Development Optimization Strategy Based on Evolutionary Game Theory Model

Abstract

This study introduces an evolutionary game model to investigate the strategic interaction among government regulatory agencies, shopping center investors, and tenants in the global energy-saving renovation market. The focus is on three innovative aspects. Firstly, the model reveals that positive tenant behavior can stimulate investors’ participation in energy-saving renovation projects by triggering potential market demand, thereby establishing a dynamic balance between supply and demand. This viewpoint has been previously overlooked in energy renovation research. Secondly, the model demonstrates the dynamic transformation of government regulatory strategies. In the early stages of market development, direct intervention through subsidies and penalties is crucial, and investors’ decisions are constrained by both returns and costs. When returns exceed the cost premium, investors actively participate, and policy incentives lower early cost barriers to promote market expansion. As the market matures, a transition toward policy guidance optimizes sustainable outcomes. Thirdly, extensive numerical simulations have confirmed the existence of multiple stable equilibrium states under different incentive and cost conditions, providing new evidence for the stability and adaptability of the energy-saving renovation market. These findings significantly advance the theoretical understanding of multi-stakeholder interactions in green building transformation and provide practical guidance for developing adaptive and effective policy frameworks.

1. Introduction

With the increasingly serious problems of global climate change and resource scarcity, the construction industry, as an important source of energy consumption and carbon emissions, has become central to sustainable development and achieving “dual carbon” goals [1]. In this context, energy-saving renovation of buildings, especially the green transformation of large-scale commercial buildings, has gradually received great attention from both academia and practical fields [2]. Optimizing energy efficiency and green building technology reduces energy consumption and environmental impact while boosting social and economic benefits [3]. Although policy systems and technologies for building energy conservation continue to improve, the energy-saving renovation market remains fragmented. Its diverse participants, complex interests, and coordination challenges lead to immature market mechanisms and low stakeholder engagement [4]. Therefore, it is urgent to explore effective ways to promote the development of the building energy-saving renovation market through multi-party cooperation under the guidance of the government [5]. In building energy-saving renovations, the government, as a market regulator, plays a key role in guiding and supervising. Shopping center investors represent the capital market and directly benefit from green building renovations. Tenants, who drive market demand, directly experience improvements in energy efficiency and comfort. Studying the interactions among government, investors, and tenants provides a theoretical basis and practical guidance for achieving green building goals [6]. At present, the development of the building energy-saving renovation market still faces many challenges, mainly reflected in three aspects. Firstly, the market structure is not perfect; the interests and demands of participating entities are complex and difficult to coordinate, especially in the early stage of the market, and there is a lack of systematic mechanisms to balance the distribution of benefits and costs among all parties [7]. Secondly, the cost of technology is high and the benefits are uncertain, especially when green technology is not yet fully mature. Investors are cautious about projects due to cost premiums, while tenants may lack the willingness to participate due to short-term high cost transfers [8]. Thirdly, there is a bottleneck in the marginal effect of policy incentives, and relying solely on government regulation and subsidy policies makes it difficult to fully mobilize the autonomy and enthusiasm of market entities. Therefore, it is particularly important to explore more scientific theoretical models and policy tools to systematically analyze the evolutionary paths of multi-party behavior choices and market mechanism dynamics.

In response to the above issues, this study has innovatively designed theories and methods. At the theoretical level, it breaks through the limitations of traditional single subject behavior analysis [9], incorporates the behavior of the government, investors, and tenants into a unified framework, constructs an evolutionary game model, and studies its dynamic game process and stable strategies under different policy conditions [10]. By introducing system dynamics tools, it is possible to simulate nonlinear relationships and dynamic feedback mechanisms in complex systems, reveal key driving factors and constraints in the market evolution process, and provide a theoretical basis for multi-party collaborative participation in energy-saving transformation. Methodologically, this study employs a three party game approach to quantitatively evaluate the impact of policy incentives (such as subsidies and fines), market structure adjustments (such as changes in technology costs and benefits), and tenant behavior expectations across multiple dimensions through numerical simulations and parameter sensitivity analysis. This method not only intuitively presents the path dependence and dynamic balance of market evolution but also provides more accurate data support for policy optimization design.

The main objective of this study is to investigate the dynamic evolution and stability characteristics of multi-party decision making in the energy-saving renovation market, with a particular focus on advancing green building design and sustainable development optimization strategies. Specifically, our research addresses the following key questions. (1) How do government policies shape the decision making of investors and tenants through incentive and constraint mechanisms to foster environmentally friendly green building practices? (2) In scenarios with uncertain cost–benefit outcomes, how can investors and tenants strategically adjust their decisions to maximize utility while supporting sustainable development? (3) What is the dynamic evolution path of market mechanisms under different policy parameter conditions? (4) How can the collaborative mechanism among the government, investors, and tenants be refined to enhance market efficiency and maximize both the social and economic benefits of energy-saving transformation and sustainable development?

2. Literature Review

Since the concept of building greening and sustainable development was proposed globally, building energy efficiency and green transformation have gradually become important areas of academic research. In modern large-scale commercial buildings, how to achieve energy conservation in lighting, fire prevention, and other equipment systems has become a key issue of concern. Related studies have shown that prioritizing the replacement of energy-saving light sources and fixtures is an effective strategy when carrying out low-cost energy-saving renovations [11,12]. In addition, scholars have explored the complex relationships between influencing factors in the green transaction system of construction enterprises through the Analytic Hierarchy Process and the MICMAC method [13]. The successful implementation of green buildings requires policy support, market recognition, and broad public participation [14]. With the intensification of global environmental problems, the gradual increase in green building projects, and the improvement of related policy systems [15], the acceptance of green buildings by market participants and consumers continues to increase [16]. Research has shown that the government plays a crucial role in promoting energy-saving renovations in the construction industry [17]. By formulating green building policies, the government has triggered spillover effects in the field of green buildings, which not only include incentive measures but also involve penalties for investors who have not undergone energy-saving renovations [18]. These regulatory mechanisms have enhanced society’s awareness of the importance of energy conservation, strengthened public environmental awareness and responsibility, and created a positive social atmosphere for achieving carbon neutrality goals globally [19]. However, research has also shown that relying solely on government regulation is not enough to ensure active participation from all parties, especially in the early stages of market development, where the effectiveness of policy implementation is often uncertain [20]. At the same time, multiple empirical studies have shown that cooperation barriers frequently arise in the early stages of energy-saving renovation projects due to information asymmetry and uneven distribution of benefits among stakeholders [21]. Therefore, it is necessary to improve the policy system to promote the development of market mechanisms and ensure the sustainability of the energy-saving and environmental protection renovation market [22]. The market mechanism plays a decisive role in energy-saving renovation, and investors’ behavior is often driven by project profitability [23]. If energy-saving renovation can bring significant economic benefits, investors’ willingness to participate will be significantly increased [24]. However, in the market’s early stages, the immaturity of green technology and high cost premiums typically result in low investor enthusiasm. Through government subsidies and incentive policies, the cost pressure on investors can be partially alleviated, and they can be encouraged to participate in energy-saving renovations [25]. Meanwhile, for tenants in the market demand side, their willingness to accept and support green renovation projects also greatly affects investors’ decisions. Therefore, increasing tenants’ acceptance of energy-saving projects is also a key factor in promoting market development. In summary, building energy efficiency and green transformation have become a global focus of attention. Research suggests prioritizing the use of energy-saving light sources, emphasizing policy support and public participation while improving market mechanisms to incentivize active participation from investors and tenants, and jointly promoting the sustainable development of the energy-saving renovation market. However, there is still limited research on stakeholder games in the existing literature. Therefore, this article introduces a three party game model and combines it with system dynamics simulation methods to dynamically adjust the behavior choices of all parties, providing targeted optimization suggestions for stakeholders in the field of green building.

3. Evolutionary Game Model Analysis

In Section 2, we reviewed the key theories of green building design and sustainable development optimization. Based on this, this section will construct a model based on evolutionary game theory to explore the interaction mechanism and decision making dynamics between the government, investors, and tenants, laying a theoretical foundation for subsequent numerical simulations.

As a policymaker and regulator of energy-saving transformation, the government bears a heavy social responsibility of protecting the environment and achieving sustainability to a large extent. Under market pressure, shopping mall investors could reduce energy costs through energy-saving renovations [26,27]. Tenants can benefit from energy-efficient retrofit projects. The energy efficiency market is primarily driven by tenants’ potential benefits in the later stages and their desire for a high-quality working environment. In addition, as stakeholders aim to maximize profits while balancing various external conditions, their strategies can be dynamically adjusted. This approach can deeply impact the transformation of the energy efficiency market. This study selects the government, shopping mall investors, and tenants as participants.

3.1. Model Assumptions

The derivation of model parameters is based on quantified benefits and costs. The expected benefits of different stakeholders are different, and the model is established to discuss the evolution path under the corresponding interests of each stakeholder. The following are the parameters set in the hypothesis, as shown in

Table 1. Parameter definitions.

Key Players	Parameter	Definitions
Government	GP	The cost of active government regulation, the comprehensive cost required by the government to implement energy transformation and regulation, including labor costs (such as salaries, training, and management expenses for regulatory personnel), material costs (such as office equipment, monitoring facilities, and technical support), and financial expenditures (such as special funds, operation and maintenance expenses, etc.). This parameter is calculated by quantitatively evaluating different resource inputs and using a weighted sum method.
	αGP	Cost of passive government regulation (0 < α < 1). The determination of this parameter is based on historical regulatory data and expert evaluations, reflecting the proportion of resources that the government can save when reducing regulatory investment. For example, the specific value of alpha can be determined by comparing the actual expenditures of the government under active and passive regulation using statistical regression or expert scoring methods and used as a reduction factor in the model.
	SR	Direct financial subsidies provided by the government to encourage investors to implement energy transformation.
	SU	The economic incentives provided by the government to encourage tenants to accept renovation projects.
	W	Environmental and social benefits from energy-saving retrofits.
	P	Investors refuse to implement energy-saving retrofits and government fines.
	D	Losses caused by the government’s failure to meet tenants’ expectations.
Investors	C1	The investor’s base cost, including funds, equipment, technology, and management expenses.
	E1	Traditional income for investors.
	∆C1	Increased costs for investors due to energy-saving retrofit, including technical renovation costs, equipment renewal costs, and related management and maintenance costs. When calculating it specifically, various costs in the renovation project can be decomposed, such as technical renovation fees, equipment procurement and installation fees, and subsequent operation and maintenance fees. Then, actual project data or market research data can be used for quantification and, finally, summarized to form the total incremental cost.
	∆E1	Energy-saving retrofits bring additional income to the investor, including cost savings brought by energy conservation and consumption reduction, premium income generated by enhancing market competitiveness, etc. The specific composition can be divided into direct energy-saving benefits and indirect brand effect benefits. The data sources can include financial statements of enterprises, market research data, and relevant industry literature. After determining the contribution ratio of each form of income through expert evaluation and quantitative models, the total incremental income value can be obtained through weighted summation.
	T	T represents the turnover cost incurred by investors due to tenants choosing to move out after energy transformation, including rental penalties, tenant relocation, and the cost of finding new tenants. By collecting actual case data and market research results, various expenses are segmented and quantified, and, finally, the total cost of the item is synthesized using a weighted method.
Tenants	C2	The basic cost of the tenant, including rent, energy consumption, and daily management expenses.
	E2	The traditional income of the tenant.
	∆C2	Tenants accept the incremental cost of energy-efficient retrofit; this includes adjustment costs incurred due to renovation, adaptation to new systems or technologies, as well as rental changes that may be caused by environmental improvements. By collecting actual operational data and market research data from tenants, refining the composition of various costs, and using quantitative methods for comprehensive evaluation, the total incremental cost of tenants can ultimately be obtained.
	∆E2	Tenants receive additional income from energy-efficient retrofit; the main sources are the improved working environment, reduced energy consumption, resulting in cost savings, and possible rental discounts. By collecting business operation data, preferential information in lease contracts, and market research results, these benefits can be quantified, and the weighted sum method can be used to calculate the overall incremental income of the lessor.

.

(1) Establish a game model with the government, shopping center investors, and tenants as the main participants. As the three major participants in the game, they are boundedly rational, and their strategies will dynamically adjust (limitations in information acquisition, prediction ability, decision making process, cognitive biases, interest coordination, risk assessment, etc.) and finally form a specific stabilization strategy.

(2) Each participant has two choices. The probability of active supervision by the government is x, and passive supervision is 1 − x, 0 < x < 1. The odds of the renovation of the shopping center investor are y, and not implementing are 1 − y, 0 < y < 1; the odds of tenants accepting the energy-saving renovation are z, and the odds of not accepting it are 1 − z, 0 < z < 1.

(3) The government regards incentives and punishments as active regulation, while negative regulation is the opposite. If actively supervised, the government alleviates the cost pressure on investors through financial subsidies and other means, and the allowance is recorded as S_R. If the investor fails to carry out the renovation, the government will impose a fine P on them. The government will also give subsidy S_U to tenants to increase their acceptance of energy-efficient retrofits. The cost of active regulation is G_P and passive regulation is αG_P, 0 < α < 1. The environmental and social benefits of energy-saving renovation are “W”.

(4) Energy-saving retrofits will generate additional revenue ∆E₁ and incremental cost ∆C₁ for investors. In general, tenants have the traditional income of E₂ and the base cost of C₂. If the energy-saving retrofit is accepted, they can receive incremental revenue ∆E₂ and pay incremental costs ∆C₂. If the investor does not carry out the renovation and the tenant wants to receive the services related to the energy efficiency retrofit, the tenant decides to relocate, and the cancellation of the lease will increase the turnover cost T for the investor.

(5) In this study, tenant expectation constraints are incorporated into the game model. When tenants have environmental awareness and are likely to use energy-efficient buildings, the government suffers if it adopts passive regulation that is contrary to tenant expectations D.

3.2. Model Building

Taking into account the above assumptions,

Table 2. Tripartite evolutionary game payment and profit matrix.

Strategies of Key Players		Tenants (z)	Tenants (1 − z)
Government (x)	Investors (y)	W − GP − SR − SU	W − GP − SR
		E1 + ∆E1 + SR − C1 − ∆C1	SR − C1 − ∆C1
		E2 + ∆E2 + SU − C2 − ∆C2	E2 − C2
	Investors (1 − y)	P − GP	P − GP
		E1 − C1 − T − P	E1 − C1 − P
		E2 − C2	E2 − C2
Government (1 − x)	Investors (y)	W − αGP − D	W − αGP
		E1 + ∆E1 − C1 − ∆C1	−C1 − ∆C1
		E2 + ∆E2 − C2 − ∆C2	E2 − C2
	Investors (1 − y)	−αGP − D	−αGP
		E1 − C1 − T	E1 − C1
		E2 − C2	E2 − C2

sets out a matrix of benefits involving governments, investors, and tenants.

Proactive regulation effectively reduces the economic burden on investors and tenants implementing green transformation by providing S_R and S_U subsidies. Additionally, direct government intervention quickly transmits market signals, prompting rapid behavioral adjustments in the early stages. Again, proactive regulation also boosts market confidence, indirectly driving environmental and social benefits (W). Based on these factors, we construct the expected return expression for government behavior and derive the corresponding dynamic replication equation.

The expected benefit of active government regulation is E₁₁, and the expected benefit of passive regulation is E₁₂, with an average expected benefit of $\overline{\mathrm{E}1}$, and the expression is as follows:

E₁₁ = yz(W − G_P − S_R − S_U) + y(1 − z)(W − G_P − S_R) + (1 − y)z(P − G_P) + (1 − y)(1 − z)(P − G_P)

E₁₂ = yz(W − αG_P − D) + y(1 − z)(W − αG_P) + (1 − y)z(−αG_P − D) + (1 − y)(1 − z)(−αG_P)

$$\overline{{\mathrm{E}}_1}={\mathrm{E}}_1=\mathrm{x}{\mathrm{E}}_{11}+(1-\mathrm{x}){\mathrm{E}}_{12}$$

The dynamic equation for government replication is as follows:

$$\mathrm{F}={\displaystyle \frac{\mathrm{d}\mathrm{x}}{\mathrm{d}\mathrm{t}}}=\mathrm{x}({\mathrm{E}}_{11}-\overline{{\mathrm{E}}_1})=\mathrm{x}(\mathrm{x}-1)[\mathrm{y}({\mathrm{S}}_{\mathrm{R}}+\mathrm{P})-\mathrm{z}\mathrm{D}+\mathrm{y}\mathrm{z}{\mathrm{S}}_{\mathrm{U}}-\mathrm{P}+(1-\alpha ){\mathrm{G}}_{\mathrm{P}}]$$

The expected return of the investor if they implement the energy-saving renovation project is E₂₁, and the expected return of non-implementation is E₂₂, with an average expected return of $\overline{{\mathrm{E}}_2}$, as follows:

E₂₁ = xz(E₁ + ΔE₁ + S_R − C₁ − ΔC₁) +x(1 − z)(S_R − C₁ − ΔC₁) + (1 − x)z(E₁ + ΔE₁ − C₁ − ΔC₁)+ (1 − x)(1 − z)(−C₁ — ΔC₁)

E₂₂ = xz(E₁ — C₁ — T − P)+ x(1 — z)(E₁ − C₁ − P) + (1 — x)z(E₁ − C₁ − T) + (1 − x)(1 — z)(E₁ — C₁)

$$\overline{\mathrm{E}2}=\mathrm{y}{\mathrm{E}}_{21}+(1-\mathrm{y}){\mathrm{E}}_{22}$$

The dynamic equation for investor replication is as follows:

$$\mathrm{G}={\displaystyle \frac{\mathrm{d}\mathrm{y}}{\mathrm{d}\mathrm{t}}}=\mathrm{y}({\mathrm{E}}_{21} — \overline{{\mathrm{E}}_2})=\mathrm{y}(1-\mathrm{y})[\mathrm{x}(\mathrm{P}+{\mathrm{S}}_{\mathrm{R}})+\mathrm{z}(\mathrm{T}+{\mathrm{E}}_1+\Delta {\mathrm{E}}_1)-\Delta {\mathrm{C}}_1-{\mathrm{E}}_1]$$

The expected benefit of the tenant accepting the energy efficiency renovation project is E₃₁, and the expected benefit of not accepting it is E₃₂, with an average expected benefit of $\overline{\mathrm{E}3}$, and the expression is as follows:

E₃₁ = xy(E₂ + ΔE₂ + S_U — C₂ — ΔC₂) + x(1 − y)(E₂ — C₂) + (1 − x)y(E₂ + ΔE₂ — C₂ — ΔC₂)+ (1 − x)(1 − y)(E₂ — C₂)

E₃₂ = xy(E₂ — C₂) + x(1 − y)(E₂ — C₂) + (1 − x)y(E₂ — C₂) + (1 − x)(1 − y)(E₂ — C₂)

$$\overline{\mathrm{E}3}=\mathrm{z}{\mathrm{E}}_{31}+(1-\mathrm{z}){\mathrm{E}}_{32}$$

The replication dynamic equation for a tenant is as follows:

$$\mathrm{H}={\displaystyle \frac{\mathrm{d}\mathrm{x}}{\mathrm{d}\mathrm{t}}}=\mathrm{x}({\mathrm{E}}_{31}—\overline{{\mathrm{E}}_3})=\mathrm{z}(1-\mathrm{z})(\mathrm{x}{\mathrm{S}}_{\mathrm{U}}+\Delta {\mathrm{E}}_2-\Delta {\mathrm{C}}_2)\mathrm{Y}$$

3.3. Discussion of the Model Evolution Stability Strategy (ESS)

ESS suggests that over time, participants will choose strategies that are beneficial to them. Determine the existing equilibrium point based on the above equation. Because the mixed strategy equilibrium is not evolutionarily stable, this article only discusses the stability of the pure strategy equilibrium point: (0,0,0), (1,0,0), (0,1,0), (0,0,1), (1,1,0), (1,0,1), (0,1,1), (1,1,1).

The following is the calculation process of the Jacobian matrix:

$$J\mathrm{=}\left[\begin{array}{lll}{\displaystyle \frac{\partial \mathrm{F}}{\partial \mathrm{x}}}& {\displaystyle \frac{\partial \mathrm{F}}{\partial \mathrm{y}}}& {\displaystyle \frac{\partial \mathrm{F}}{\partial \mathrm{z}}}\\ {\displaystyle \frac{\partial \mathrm{G}}{\partial \mathrm{x}}}& {\displaystyle \frac{\partial \mathrm{G}}{\partial \mathrm{y}}}& {\displaystyle \frac{\partial \mathrm{G}}{\partial \mathrm{z}}}\\ {\displaystyle \frac{\partial \mathrm{H}}{\partial \mathrm{x}}}& {\displaystyle \frac{\partial \mathrm{H}}{\partial \mathrm{y}}}& {\displaystyle \frac{\partial \mathrm{H}}{\partial \mathrm{z}}}\end{array}\right]\mathrm{=}\left[\begin{array}{lll}{\mathrm{J}}_1& {\mathrm{J}}_2& {\mathrm{J}}_3\\ {\mathrm{J}}_4& {\mathrm{J}}_5& {\mathrm{J}}_6\\ {\mathrm{J}}_7& {\mathrm{J}}_8& {\mathrm{J}}_9\end{array}\right]$$

$$\left[\begin{array}{l}{\mathrm{J}}_1=\left(1 - 2\mathrm{x}\right)\left[- \mathrm{y}\left({\mathrm{S}}_{\mathrm{R}}+\mathrm{P}\right){+\mathrm{zD} - \mathrm{yzS}}_{\mathrm{U}}+\mathrm{P}+\left(\mathsf{\alpha } - 1\right){\mathrm{G}}_{\mathrm{P}}\right]\\ {\mathrm{J}}_2=\mathrm{x}\left(\mathrm{x} - 1\right)\left({\mathrm{S}}_{\mathrm{R}}{+\mathrm{P}+\mathrm{zS}}_{\mathrm{U}}\right)\\ {\mathrm{J}}_3=\mathrm{x}\left(1 - \mathrm{x}\right)\left({\mathrm{D} - \mathrm{yS}}_{\mathrm{U}}\right)\\ {\mathrm{J}}_4=\mathrm{y}\left(1 - \mathrm{y}\right)\left({\mathrm{P}+\mathrm{S}}_{\mathrm{R}}\right)\\ {\mathrm{J}}_5=\left(1 - 2\mathrm{y}\right)[\mathrm{x}\left({\mathrm{P}+\mathrm{S}}_{\mathrm{R}}\right){+\mathrm{z}(\mathrm{T}+\mathrm{E}}_1+\mathrm{\Delta }{\mathrm{E}}_1) -\mathrm{\Delta }{\mathrm{C}}_1{- \mathrm{E}}_1]\\ {\mathrm{J}}_6=\mathrm{y}\left(1 - \mathrm{y}\right){(\mathrm{T}+\mathrm{E}}_1+\mathrm{\Delta }{\mathrm{E}}_1)\\ {\mathrm{J}}_7=\mathrm{z}\left(1 - \mathrm{z}\right){\mathrm{S}}_{\mathrm{U}}\mathrm{y}\\ {\mathrm{J}}_8=\mathrm{z}\left(1 - \mathrm{z}\right){(\mathrm{xS}}_{\mathrm{U}}+\mathrm{\Delta }{\mathrm{E}}_2-\mathrm{\Delta }{\mathrm{C}}_2)\\ {\mathrm{J}}_9=\left(1 - 2\mathrm{z}\right){(\mathrm{xS}}_{\mathrm{U}}+\mathrm{\Delta }{\mathrm{E}}_2-\mathrm{\Delta }{\mathrm{C}}_2)\mathrm{y}\end{array}\right.$$

In the in-depth discussion of the stability analysis of the model, we conduct a detailed study of the stable equilibrium point of the system based on the principle of Lyapunov discriminant method. Specifically, if all eigenvalues of the Jacobian matrix are negative, based on Lyapunov’s stable theory, this means that the equilibrium point has asymptotic stability, i.e., the solution of the system near that point gradually approaches that equilibrium point over time. Conversely, if there is at least one positive eigenvalue in the Jacobian matrix, the equilibrium point is unstable, and the solution near the equilibrium point of the system will not tend to the equilibrium point but may exhibit distant or divergent behavior. However, when the eigenvalues of the Jacobian matrix do not contain positive values but contain zeros, stability assessment of the system equilibrium point becomes complicated, and such cases are not considered. In this study, we first substitute each possible equilibrium point into the Jacobian matrix and calculate the eigenvalues associated with these equilibrium points. Then, according to the principles of the Lyapunov discriminant method, we analyze these eigenvalues in detail and judge the stability state.

In

Table 3. Jacobian feature values at the equilibrium point.

Balance Point	Eigenvalue	Eigenvalue Symbol
(0,0,0)	0; −∆C1 − E1; P + (α − 1)GP	(0, −, *)
(1,0,0)	0; (1 − α)GP − P; P − E1 + SR − ∆C1	(0, *, *)
(0,1,0)	∆C1 + E1; ∆E2 − ∆C2; (α − 1)GP − SR	(+, *, −)
(0,0,1)	0; T − ∆C1 + ∆E1; D + P + (α − 1)GP	(0, *, *)
(1,1,0)	(1 − α)GP + SR; SU + ∆E2 − ∆C2; E1 − P − SR + ∆C1	(+, *, *)
(1,0,1)	0; (1 − α)GP − P − D; T + P + SR − ∆C1 + ∆E1	(0, *, *)
(0,1,1)	∆C2 − ∆E2; ∆C1 − T − ∆E1; D − SR − SU + (α − 1)GP	(*, *, *)
(1,1,1)	∆C2 − SU − ∆E2; ∆C1 − P − SR − T − ∆E1; (1 − α)GP − D + SR + SU	(*, *, *)

Note: * indicates uncertain symbol.

, the balanced points (0,0,0), (1,0,0), (0,1,0), (0,0,1), (1,1,0), and (1,0,1) are not stable points. The stable conditions of (0,1,1) and (1,1,1) are further discussed.

Condition 1: ∆E₁ < ∆C₁ and ∆E₂ < ∆C₂, investors and tenants benefit less than their incremental costs from energy efficiency retrofits. As the energy transition market is still in its early days and the technology is not mature, the government used incentive measures to push the realization of energy transformation. Only when D − S_R − S_U + (α − 1)G_P > 0, S_U + ∆E₂ − ∆C₂ > 0 and P + S_R + T + ∆E₁ − ∆C₁ > 0 will the government, investors, and tenants take positive measures. The equilibrium point is (1,1,1).

Condition 2: When ∆E₁ > ∆C₁ and ∆E₂ < ∆C₂, the benefits of active investor action outweigh the additional costs brought about by advances in green renovation technologies. The premium paid by tenants for energy-efficient buildings is still higher than the incremental earnings, and active actions will only be taken if the government provides subsidies. When D − S_R − S_U + (α − 1)G_P > 0 and S_U + ∆E₂ − ∆C₂ > 0, the government subsidy makes up the cost burden of tenants’ premiums, and the benefits of active government regulation outweigh those of passive regulation. The equilibrium point is (1,1,1).

Condition 3: When ∆E₁ < ∆C₁ and ∆E₂ > ∆C₂, on the basis of D − S_R − S_U + (α − 1)G_P > 0 and ∆C₁ − P − S_R − T − ∆E₁ < 0, the benefits of active action for the three participants are better than the costs. The optimal balance is (1,1,1). On the basis of D − S_R − S_U + (α − 1)G_P < 0 and T + ∆E₁ − ∆C₁ > 0, the benefits of active government regulation are smaller than those of passive regulation. The constraints of turnover costs on investors make investors inclined to take positive measures. The balanced point is (0,1,1).

Condition 4: When ∆E₁ > ∆C₁ and ∆E₂ > ∆C₂, both the investor and the tenant will receive more benefits than the incremental cost. On the basis of D − S_R − S_U + (α − 1)G_P > 0, the efficiency of active government regulation is higher, and the best equilibrium point is (1,1,1). When D − S_R − S_U + (α − 1)G_P < 0, the costs of government passive regulation are higher, and the balanced point is (0,1,1).

This section details the mechanism of interest interaction among the government, investors, and tenants by constructing an evolutionary game model. Although the model provides theoretical support for the actual energy-saving renovation market, some limitations in model assumptions remain. The next section will validate the model using numerical simulation and compare the results with existing research.

4. Numerical Simulation

To ensure the scientific and reproducible nature of the numerical simulation of the model, this section provides a detailed description of the numerical calculation process. Firstly, we constructed the corresponding difference equation system based on the theoretical model. Secondly, numerical solutions were performed using MATLAB R2023b, and the impact of various variables on system evolution was verified through parameter sensitivity analysis. Finally, we compared the stable equilibrium point predicted by the model with empirical data in the literature to further validate the rationality and applicability of the model.

This study uses MATLAB R2023b as the main simulation tool, utilizing its powerful numerical calculation and visualization functions for model solving and parameter sensitivity analysis. The computer configuration used for simulation is an Intel Core i7 processor and 16 GB of memory running on a Windows 10 operating system. In addition, to ensure the reproducibility of the results, a fixed random number seed was set in all simulation experiments to eliminate uncertainty caused by random initialization.

4.1. Model Validation

In the simulation experiment, each iteration represents a quarterly update of market behavior, with a total of 60 iterations run. The convergence criterion is set as follows: if the probability changes of the behavior of the government, investors, and tenants in two consecutive iterations are all less than 0.01, it is considered that the system has reached a stable state. The selection of 60 iterations is based on preliminary experiments indicating that this time scale is sufficient to stabilize all variables in the system. The original values of the parameters meet the relevance of ∆E₁ > ∆C₁, ∆E₂ > ∆C₂, D − S_R -S_U + (α − 1)G_P < 0. The simulation results show that (0,1,1) is a stable point coherent with the result of condition 4. Therefore, the simulation verifies the stable analysis of participants’ strategy, and the model has a certain reliability (see Figure 1).

In the numerical simulation section, we further demonstrated the correspondence between the theoretical model in Section 3 and the actual simulation results. By comparing the role of each key parameter in theoretical derivation with the dynamic changes in simulated images, it can be seen that when the model parameters satisfy a certain stability condition, the simulation results converge exactly to the stable equilibrium point predicted by the theory.

For the key parameters in the model, this study selected representative initial values based on the previous literature, market research data, and theoretical derivation [28,29] (see

Table 4. Initial values of main parameters.

Key Player	Parameters	Initial Values	Key Player	Parameters	Initial Values
Government	GP	26	Investors	∆C1	175
	α	0.7		∆E1	240
	SR	100		T	32
	SU	55	Tenants	∆C2	190
	P	25
	D	17		∆E2	200

for details). For example, the value of G_P (government regulatory cost) is estimated based on the actual expenditure of the government in energy consumption renovation, while ∆E₁ and ∆C₁, respectively, reflect the additional benefits and incremental costs of investors in green renovation projects. Similarly, ∆E₂ and ∆C₂ reflect the additional income and costs incurred by tenants due to energy efficiency improvements. In terms of the initial strategy combination, this article selects (0,1,1) as the benchmark starting point, where the government initially adopts passive supervision (0), while investors and tenants actively implement the transformation (1), which is in line with the current situation in the green transformation market, where investors and tenants are relatively active while the government gradually withdraws from direct supervision.

4.2. Simulation Analysis

To comprehensively explore the influence of various parameters on the system’s evolution path, this study selected the range of changes of key parameters (such as ∆E₁, ∆E₂, G_P, etc.) in single factor sensitivity analysis. E₁ ranges from 130 to 320, and G_P ranges from 0 to 150). We conducted at least 100 repeated simulations for each parameter setting and calculated the mean and the standard deviation of government, investor, and tenant behavior strategies in each simulation. On this basis, a multi-factor joint variation experiment was also conducted to observe the influence of the interaction between parameters on the convergence speed and stable state of the system.

4.2.1. The Impact of the Initial Strategy on the Change of the System

Keeping y = 0.5 and z = 0.5, the government’s initial policy of aggressive regulation x increased from 0.2 to 0.7. The chart shows that the more prominent the initial strategic value, the better the aggressive actions of investors and tenants will evolve. Figure 2a shows that if the odds of active regulation are less, investors are unlikely to initially carry out energy-saving rebuilding. As x raises, y converges faster. Green technology is not mature in the early stage of the green transformation market, and the premium of the cost is relatively high, resulting in investors being reluctant to transform. Government incentives can incentivize investors to keep up with the turn of the market and improve the energy crisis. In Figure 2b, even if the government’s willingness to act is low, it does not have much impact on tenants’ behavior, but increasing the willingness of the government to participate to a certain extent will accelerate tenants’ acceptance of energy-efficient buildings.

Keeping x = 0.5 and z = 0.5 constant, the initial strategy y for investors to choose to enforce energy-saving rebuilding increased from 0.2 to 0.7. As seen in Figure 3, the convergence speed of government and tenant action has a positive correlation with y, but there is no significant difference. Figure 3a shows that governments are more likely to be passive in regulation, as investors are more likely to make modifications. This suggests that investors may play an important part in market changes. When the market matures, the government may decide to withdraw. Figure 3b shows that investors and tenants are, to a certain extent, a community of interests and that the investor’s active participation in energy-saving renovation projects can have a positive impact on tenants’ willingness when the renovation can bring benefits to both parties.

Keeping x = 0.5 and y = 0.5, the initial policy z for tenants to choose to undergo energy efficiency rebuilding is increased from 0.2 to 0.7. In Figure 4a, when tenants have a high probability of taking positive action, the government will not provide such measures, thus tending to passive regulation. When the odds of tenants taking action is low, the government will initially take measures to subsidize tenants to increase their willingness to act, but, over time, the market matures and tenants can reap positive benefits from the renovation project, and the government tends to be passive in regulation. Figure 4b shows that y converges faster with the increase in z, and the convergence curve varies greatly, indicating that demand-side tenants have a strong influence on investor behavior. When z is small, the initial willingness of investors is also very small, but because the energy-saving renovation will bring positive benefits in the later stage, with the advancement of time, the willingness of investors that declines from the beginning will gradually rise, and they will tend to accept energy-saving renovation projects.

4.2.2. The Effect of Parameters of Benefits and Costs on Evolution

Figure 5 illustrates the influence of added income on investors. All other parameters remain constant, and the range of the ∆E₁ is between 130 and 320. As shown in Figure 5, extra income is a key milestone in the development of the energy-saving renovation market. When extra income exceeds incremental costs, investors tend to accept the implementation of green and energy-saving renovation projects. As profit margins increase, the rate at which investor behavior strategies converge accelerates over time. In the state of less profit, the value of y is initially fluctuating, and it does not show an upward trend, but it first falls and then rises. Due to the immature market, investors are more conservative at first, but with the maturity of the market, they eventually tend to accept the implementation of energy-saving renovation projects. When the additional income is lower than the incremental cost, under the condition of government policy constraints, the y image shows a cyclical trend over time, but the greatest willingness to accept is always lower than 0.7, which may be because the government’s reward and punishment policy has a certain impact on the investor’s decision making, which makes the investor’s willingness fluctuate periodically. But, due to the negative income brought by the long-term development of energy-saving transformation, even under the supervision of government policies, the acceptance of the investor’s energy-saving renovation project is always not high.

Figure 6 shows the impact of incremental revenue on tenants. All other parameters remain the same, and ∆E₂ ranges between 120 and 280. When the incremental benefit is greater than the incremental cost, tenants eventually tend to develop an energy-saving rebuilding project, and the greater the incremental benefits, the faster the tenants converge. When the cost of energy-efficient architecture to a premium exceeds the additional revenue, tenants often hold a conservative attitude. However, incremental returns may not be able to compensate for cost premiums, but tenants may still have some acceptance, albeit low, over time. This phenomenon may indicate that the government’s subsidy policy has a positive impact on tenant acceptance, even if the cost premium is higher than the revenue increment. With the government’s encouragement, there is still a certain degree of willingness to maintain energy-efficient renovation projects. Furthermore, it may indicate that with the progress of social development, tenants will pay more and more attention to comfort and the improvement of work quality.

Figure 7 illustrates the effect of regulatory costs on governments. The parameters remain unchanged, and the G_P is between 0 and 150. As the cost of policy increases, government behavior converges faster and faster. According to the initial data, both tenants and investors can obtain positive returns, and green energy-saving renovation projects tend to be implemented. This indicates that the greater the regulatory cost, the greater the government’s supervision, which accelerates the convergence speed of the game and then promotes the formation of the green market. The image also seems to show that the cost of regulation does not seem to be the crucial factor in government actions and that when the green market matures, the government eventually opts out of market regulation. In addition, the government may be willing to pay a fee to promote the implementation of green energy-saving renovation projects, focusing more on the environmental and social benefits of energy-saving retrofits.

Figure 8 illustrates the influence of costs on investors. All other parameters remain unchanged, and T ranges from 0 to 130. Figure 8 shows that investor behavior converges faster as turnover costs increase. Therefore, investors are more sensitive to the losses caused by tenant relocation. This is in agreement with the consequence shown in Figure 4b (tenants have a greater impact on the speed of convergence for investors).

4.2.3. The Effect of Reward and Punishment Parameters

The following table illustrates the impact of changes on the profitability of energy efficiency renovation projects under government subsidies. When ΔE₁ = 240, energy-saving renovation can bring additional profits to investors, but when ΔE₁ = 100, investors will face losses. Figure 9 shows that subsidies do not have a critical impact on investor actions. If the incremental benefit of the investor is greater than the cost premium, the investor will tend to implement the project, regardless of the amount of government subsidy. However, when the incremental income of the investor is less than the cost premium, the government’s reward and punishment policy will have a cyclical impact on the investor’s decision making, as the higher the subsidy, the greater the extent of acceptance can increase the acceptance of the investor, but the acceptance will eventually have an upper limit, which does not reach the level of 100% acceptance. But, if the subsidy is less, investors will eventually tend not to accept the implementation of energy-saving renovation projects.

Figure 10 explains the impact of government subsidies on tenants at different profit and loss levels. When ΔE₂ = 100, ΔE₂ < ΔC₂; when ΔE₂ = 200, ΔE₂ > ΔC₂. At that time, the incremental revenue is less than the cost premium, and even if the government provides subsidies as an incentive, tenants will take a wait-and-see attitude and maintain low acceptance of energy-efficient renovation projects. If the incremental benefits exceed the cost premium, the increased subsidy will incentivize tenants to embrace green and energy-efficient retrofit projects more quickly.

Figure 11 describes the role of government penalties when investors face different profitability of energy-saving renovation projects. When profitable, investors take positive action. In this situation, the difference in the amount of penalty will have a certain impact on the enthusiasm of investors for transformation. In the case of investors who will lose money, the penalties will not have the desired effect. Despite the increase in fines, the investor will ultimately decide not to carry out the renovation.

Figure 12 shows the effect of subsidies or penalties on the government in a profit and loss situation. Under the game mechanism, each subject will dynamically adjust due to the interaction of various factors. In the early days, the government’s measures towards the market tend to adopt active regulation. If the industry matures, investors and tenants make enough additional profits, and the government’s passive regulation will not significantly affect their decision making. The government, as an external stakeholder in the market, complements the actions of internal stakeholders.

4.2.4. The Effect of Tenant Expectations on System Evolution

Figure 13 illustrates the effect of tenant expectation constraints on the government. Tenant expectations reflect the tenant’s level of environmental awareness. The amount of loss caused by violating tenants’ expectations has a certain impact on the speed of government convergence. When the government has not implemented the incentive measures that participants expect, such as subsidies to tenants, there may be some losses by violating tenants’ expectations. Initially, the government is likely to respond to tenant expectations and regulate in a more proactive manner. With the expansion of the green energy-saving renovation market, the benefits of passive regulation have gradually exceeded those of active regulation. It may be in the interest of governments to exit and let mature markets dominate. This is consistent with the results of condition 4.

In summary, through numerical simulations, we observed that the evolution trajectories of the government, investors, and tenants exhibit distinct dynamic characteristics under different initial strategies and parameter conditions. In particular, the impact of various variables on system stability has revealed to us the inherent mechanism of multi-party games in the market. Next, in the discussion section, we will further analyze the similarities and differences between these simulation results and the existing literature and explore their implications for practical policymaking.

5. Conclusions

It is important to explore how stakeholders make decisions in renovating existing buildings for energy efficiency, accelerate the formation of the energy efficiency renovation market, and enhance sustainable development. In the study, a game model of the government, shopping center investors, and tenants is constructed, and we test its stability point. Combined with relevant policies and the literature, the energy efficiency transformation was carried out. Through simulation, the effects of initial strategies and different parameters on stakeholders were analyzed separately. Finally, a suggestion is put forward to inspire all stakeholders actively involved in energy efficiency transformation.

Based on the numerical simulation results in Section 4, our study reveals that the dynamic evolution of strategies among the government, investors, and tenants exhibits distinct characteristics that differ in important ways from earlier findings. In our simulations, active government incentives combined with moderate regulatory costs led to a more rapid and pronounced adoption of positive behaviors by both investors and tenants. This contrasts with Oyewo’s [30] assertion, where policy incentives were found to be effective but did not explicitly capture the rapid dynamic adjustment observed here. Moreover, under certain parameter settings, our results show that investor behavior can exhibit periodic fluctuations—a phenomenon that, while similar to Singh and Kumar’s [31] description of early market instability, appears to be more sensitive to parameter variations in our model. Furthermore, our findings indicate that when tenants display a higher level of environmental awareness and acceptance, the evolution of government and investor strategies accelerates significantly. Although Higuchi and Maehara [32] reported that technological maturity and market demand positively affect green transformation, our model further quantifies this effect and shows a stronger, more rapid response in strategy adjustments. Overall, our research suggests that during the early stages of green building renovation, direct incentives and subsidy policies from the government can partially offset market failures. However, as the market matures, the model indicates that government intervention should gradually shift from direct supervision to a more guiding and supportive role—a nuance that adds depth to the existing literature. By integrating the strategies and behaviors of the main stakeholders through an innovative evolutionary game model, our study not only corroborates some of the earlier research findings but also highlights key differences that can inform policy adjustments. The detailed conditional simulation analysis of strategic sensitivity provides a more comprehensive theoretical basis and empirical reference, thereby offering new insights for practical operations and enhancing the understanding of green transformation in the context of shopping centers.

The results show the following. (1) The convergence of the system stability strategy is closely related to the initial strategy choice of each stakeholder, and the change of the initial state of tenants has the greatest impact. (2) Investors’ profit and loss situation dominates their decision making, and, at the same time, investors’ positive actions are affected by tenants’ turnover and relocation costs, while tenants are less sensitive to changes in costs and benefits, which is not the decisive factor for government actions. (3) Government incentives play an active part, but the role depends on the profit–loss scenario, not the extent of regulation, and government regulation is only a supplement to internal stakeholders in an efficient market. (4) The government is affected by tenant expectations; however, it is the government’s position that ultimately determines the size of market development. In terms of theoretical contributions, this article integrates the strategies and behaviors of key stakeholders in the energy efficiency transformation market through an innovative game model, which provides a reference for related fields. The special contractual relationship considers the relationship between the construction investor and the tenant, expanding the study of the shopping center as a building type. With regard to the actual contribution, the strategic sensitivity of each actor in terms of energy is analyzed through the use of conditional simulations, which offers a useful reference for guiding the practical activities of various stakeholders.

Of course, this study also has some limitations. Firstly, the parameter settings are based on certain assumptions, but the actual situation is much more complex than the model; future work can be further optimized by combining more measured data. Secondly, the impact of reward measures is limited, and dynamic regulatory measures have not yet been discussed. Thirdly, the research scope is limited to the relationships between three stakeholders. To further broaden the horizon, researchers might consider defining investors and tenants and introducing professional service agencies and long-term lessees in order to more comprehensively reflect the overall market situation.

6. Recommendations and Countermeasures

6.1. Recommendations

Promoting energy-efficient renovation requires coordinated actions among government regulatory agencies, shopping center investors, and tenants. The evolutionary game model indicates that the strategic behaviors of these three parties are interdependent; changes in one participant’s strategy significantly affect the others. In this context, fostering mutual understanding and effective communication among the stakeholders is essential. This study underscores the following high-level recommendations:

(1) Enhance Collaboration. Develop policies that encourage active participation from all parties, taking into account the complex leasing relationships between tenants and investors. This collaborative approach can accelerate the transformation of the energy efficiency retrofit market.

(2) Improve the Market Mechanism. A more robust market mechanism is necessary to ensure that incentive measures and regulatory policies effectively drive energy-saving renovations. The findings suggest that while direct incentives (such as subsidies and penalties) are crucial in the early stages, there is a need for a gradual shift toward a guiding role as the market matures.

(3) Increase Profitability and Reduce Cost Premiums. The analysis reveals that investor decisions are highly sensitive to profit and loss scenarios. Therefore, strategies to lower the incremental cost burden and improve profitability can significantly influence the adoption of energy-efficient measures, leading to more sustainable outcomes.

6.2. Countermeasures

To address the identified challenges and implement the above recommendations, the following specific countermeasures are proposed:

(1) Improve the Market Mechanism. Develop standardized evaluation systems that provide reliable feedback on retrofit projects, thereby increasing stakeholder confidence. Compile comprehensive databases that offer real-world project data and market insights. These resources can serve as references for stakeholders to assess potential investments. Promote the involvement of non-profit organizations and professional agencies through targeted incentive measures and skills training, ensuring the development of qualified professionals capable of managing large-scale renovations.

(2) Decrease Incremental Costs and Increase Profitability. Implement measures like income tax exemptions, carbon tax relief, lowering loan thresholds, and simplifying application procedures to improve the economic feasibility of energy-saving renovations. Facilitate collaborations between government, investors, and research institutions to drive innovation in energy-saving technologies, ultimately reducing cost premiums. Use media platforms and establish a one-stop website to disseminate reliable information on retrofit technologies and policy updates. Additionally, pilot projects and success stories should be highlighted to improve information usability and reduce transaction costs related to acquiring expert knowledge. Given that the cost of tenant relocation influences investor strategies, setting up effective communication mechanisms between investors and tenants can help mitigate relocation costs and enhance overall market stability.