# How Does the Government Policy Combination Prevents Greenwashing in Green Building Projects? An Evolutionary Game Perspective

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## Abstract

**:**

## 1. Introduction

## 2. Related Literature

#### 2.1. Research on Evolutionary Game Application

#### 2.2. Government Policies on Green Buildings

## 3. Model Description and Hypothesis

#### 3.1. Analysis of the Game Relationship between Government and Construction Enterprises

#### 3.2. Model Description and Hypothesis

- (1)
- This paper supposed that the game system contains two subjects: construction enterprises and government regulators, which play the roles of implementer and regulator. Both are finite and rational in the construction process and can continuously learn to achieve increased income. The final equilibrium is finding the optimal decision through continuous game and learning.There are only two strategic options for both sides of the game.
- (2)
- Construction enterprise: Based on the reality of GBs’ construction in China, the strategic choices of enterprises are abstracted into “green construction” and “non-green construction.” The “green construction” strategy means that the enterprise can strictly follow the GBs’ design standards, including using environmentally friendly construction materials, continuous improvement of construction technologies, etc., to ensure that the final GBs meet the design requirements. The “non-green construction” strategy refers to the moral risk behavior that enterprises’ constructions do not meet the design requirements, resulting in a waste of energy and resources [47]. The “non-green construction” behavior will eventually harm the vital interests of the government and the public and cause environmental pollution to reduce social benefits.
- (3)
- Government: As the subject of market regulation and the defender of public interest, government chooses the strategy of “positive supervision” and “passive supervision” in the abstract. With adequate information and analysis, government departments usually make decisions based on their experience and existing conditions. The “active supervision” strategy refers to the active performance of supervisory duties, adopting regular daily supervision and occasional non-daily supervision to focus on the construction process. Accordingly, the government regulator must bear the cost of supervision. Assuming an “active supervision” strategy, the government can decide to punish or reward construction companies as appropriate. However, in the actual supervision work, the government needs to invest a certain amount of human, material, and financial resources in supervising. In addition to being responsible for the supervision of GBs, it also shoulders many other tasks; Out of consideration of cost and benefit and based on the analysis of the construction information of existing construction enterprises, the government decides whether to actively supervise the construction enterprises.
- (4)
- The probability of the behavior strategy of both sides of the game.In the game process between the government and the construction companies, assuming the probability of active supervision is $x$. Thus, passive supervision is $1-x$, the likelihood of construction companies complying with the law is $y$, and non-green construction is $1-y$.
- (5)
- Cost-Benefit parameter assumptions and interpretation.The following parameter settings and instructions are given to construct the game’s payment matrix further. Assuming that the cost that construction enterprises need to pay when choosing green construction is ${S}_{1}$, such as the adoption of new technologies, new materials, and training fees for construction personnel, etc., and the construction enterprise chooses non-green construction, the cost to be paid is ${S}_{2}$, obviously ${S}_{1}>{S}_{2}$; Similarly, when the government regulatory department is actively supervised, the cost of supervision is ${S}_{3}$, and the price paid when passive supervision is ${S}_{4}$, obviously ${S}_{3}>{S}_{4}$; When the government actively supervises, it will carry out corresponding subsidies or penalties according to the green construction quality, and give subsidies $B$ to the construction enterprise; otherwise, a fine $P$ will be imposed, and the fine shall be owned by the government; The good green construction situation of the construction unit will be included in the integrity assessment system, and linked to the award evaluation, accumulating advantages for future undertaking projects, the potential future income is ${R}_{1}$, and the government department will obtain additional income ${R}_{2}$ due to “free riding” behavior. In addition, when the construction enterprise adopts non-green construction behavior, the government’s credibility loss is caused by passive supervision by the government department $L$.

## 4. Model Building and Analysis

#### 4.1. Static Reward and Static Punishment

#### 4.1.1. Evolutionary Stabilization Analysis of Static Reward and Punishment Model

#### Evolutionary Stabilization Analysis of Government Strategies

- (1)
- When $P+{S}_{4}-{S}_{3}<0$, $y>\frac{P+{S}_{4}-{S}_{3}}{P+B}$ is constant, and the evolutionarily stable strategy (ESS) is $x=0$.
- (2)
- When $P+{S}_{4}-{S}_{3}>0$, there are two cases:
- (a)
- When $P+{S}_{4}-{S}_{3}>P+B$, $y<\frac{P+{S}_{4}-{S}_{3}}{P+B}$, and the ESS is $x=1$.
- (b)
- When $P+{S}_{4}-{S}_{3}>P+B$, $0<\frac{P+{S}_{4}-{S}_{3}}{P+B}<1$, The government’s stabilization strategy depends on the size of $y$. When $y>\frac{P-{S}_{3}+{S}_{4}}{P+B}$, there is ${\left.\frac{dF(x)}{dx}\right|}_{x=0}<0$, and $x=0$ is the ESS. When $y<\frac{P-{S}_{3}+{S}_{4}}{P+B}$, there is ${\left.\frac{dF(x)}{dx}\right|}_{x=0}<0$, and $x=1$ is the ESS.

#### Evolutionary Stabilization Analysis of Construction Enterprise Strategies

- (1)
- When ${S}_{1}-{S}_{2}-{R}_{1}<0$, $x>\frac{{S}_{1}-{S}_{2}-{R}_{1}}{P+B}$ is constant, and the evolutionary stabilization strategy is $y=1$.
- (2)
- When ${S}_{1}-{S}_{2}-{R}_{1}>0$, there are two cases:
- (a)
- When ${S}_{1}-{S}_{2}-{R}_{1}>P+B$, $x<\frac{{S}_{1}-{S}_{2}-{R}_{1}}{P+B}$, and the evolutionary stabilization strategy is $y=0$.
- (b)
- When ${S}_{1}-{S}_{2}-{R}_{1}<P+B$, $0<\frac{{S}_{1}-{S}_{2}-{R}_{1}}{P+B}<1$, The government’s stabilization strategy depends on the size of $x$. When $x>\frac{{S}_{1}-{S}_{2}-{R}_{1}}{P+B}$, and $y=1$ is the evolutionary stabilization strategy. When $x<\frac{{S}_{1}-{S}_{2}-{R}_{1}}{P+B}$, and $y=0$ is the evolutionary stabilization strategy.

#### Evolutionary Stabilization Analysis of Hybrid Strategies between Government and Construction Enterprises

**Proposition**

**1.**

**Proposition**

**2.**

#### 4.2. Dynamic Reward and Static Punishment

**Proposition**

**3.**

- 1.
- The system with four fixed equilibrium points always, namely$(0,0),(0,1),(1,0),(1,1).$
- 2.
- $\mathit{When}0\frac{{S}_{1}-{S}_{2}-{R}_{1}}{B(y)+P}1$$\mathit{and}0\frac{P-{S}_{3}+{S}_{4}}{B(y)+P}1$, there is an equilibrium point (${{x}_{2}}^{*},{{y}_{2}}^{*}$),$\mathit{where}{{x}_{2}}^{*}=\frac{{S}_{1}-{S}_{2}-{R}_{1}}{B(y)+P}$, ${{y}_{2}}^{*}=\frac{P-{S}_{3}+{S}_{4}}{B(y)+P}=\frac{-P+\sqrt{4qP+{P}^{2}-4q{S}_{3}+4q{S}_{4}}}{2q}$.

**Proposition**

**4.**

**Proof.**

**Proposition**

**5.**

- (1)
- $\frac{\partial {{x}_{2}}^{*}}{\partial {R}_{1}}<0,\frac{\partial {{x}_{2}}^{*}}{\partial P}>0,\frac{\partial {{x}_{2}}^{*}}{\partial q}<0,\frac{\partial {{x}_{2}}^{*}}{\partial {S}_{1}}>0,\frac{\partial {{x}_{2}}^{*}}{\partial {S}_{2}}<0,\frac{\partial {{x}_{2}}^{*}}{\partial {S}_{3}}<0,\frac{\partial {{x}_{2}}^{*}}{\partial {S}_{4}}>0$
- (2)
- $\frac{\partial {{y}_{2}}^{*}}{\partial P}>0$,$\frac{\partial {{y}_{2}}^{*}}{\partial q}<0$,$\frac{\partial {{y}_{2}}^{*}}{\partial {S}_{3}}<0$,$\frac{\partial {{y}_{2}}^{*}}{\partial {S}_{4}}>0$.

- (i)
- Active supervision’s probability is positively correlated with the cost of green construction ${S}_{1}$. When the cost of GBs is higher, construction enterprises will likely have a fluke mentality and believe the government will not detect non-compliance. Based on which government authorities will generally strengthen supervision. Active supervision’s probability is inversely correlated with the cost of non-green construction. When non-green construction ${S}_{2}$ cost is higher, governmental thinks that construction enterprises will choose green construction and loosen supervision.
- (ii)
- As the cost of active supervision increases, the cost of human and financial resources will also rise accordingly. This phenomenon will put pressure on the government departments, so the probability of active supervision will decrease, and the probability of GBs will also reduce. On the contrary, with the increase in the cost of passive regulation by governmental departments, the government is more willing to take the initiative to effectively regulate and improve the green construction enthusiasm of construction enterprises.
- (iii)
- The higher the fine $P$ is, the greater the expense construction enterprises pay for non-green construction and the higher the subjective consciousness of conducting green construction behaviors. The higher the governmental supervision will raise the fine to prevent construction enterprises from unethical risk behaviors.
- (iv)
- The higher the reward $q$ means more of the financial burden, the lower the probability of active supervision. Nevertheless, construction enterprises think the government may loosen regulations after giving higher subsidies. Enterprises may adopt non-green construction, leading to a lower probability of their green construction.
- (v)
- In addition, regulatory motivation is negatively correlated with the potential future benefits of green construction. The government believes that the higher the foreseeable benefits of construction enterprises, the more they will choose green construction, leading to decreased regulatory motivation.

#### 4.3. Static Reward and Dynamic Punishment

**Proposition**

**6.**

- 1.
- The system with four fixed equilibrium points always, namely$(0,0),(0,1),(1,0),(1,1).$
- 2.
- $\mathit{When}0\frac{{S}_{1}-{S}_{2}-{R}_{1}}{B+P(y)}1$$\mathit{and}0\frac{P(y)-{S}_{3}+{S}_{4}}{B+P(y)}1$, there is another equilibrium point (${{x}_{3}}^{*},{{y}_{3}}^{*}$), where${{x}_{3}}^{*}=\frac{{S}_{1}-{S}_{2}-{R}_{1}}{B+P(y)}$,${y}_{3}{}^{*}=\frac{P(y)-{S}_{3}+{S}_{4}}{B+P(y)}$.

**Proposition 7.**

**Proposition**

**8.**

- (1)
- $\frac{\partial {x}_{3}{}^{*}}{\partial {S}_{1}}>0,\frac{\partial {x}_{3}{}^{*}}{\partial {S}_{2}}<0,\frac{\partial {x}_{3}{}^{*}}{\partial {S}_{3}}<0,\frac{\partial {x}_{3}{}^{*}}{\partial {S}_{4}}>0,\frac{\partial {x}_{3}{}^{*}}{\partial {R}_{1}}<0,\frac{\partial {x}_{3}{}^{*}}{\partial r}>0,\frac{\partial {x}_{3}{}^{*}}{\partial B}<0$.
- (2)
- $\frac{\partial {y}_{3}{}^{*}}{\partial {S}_{3}}<0,\frac{\partial {y}_{3}{}^{*}}{\partial {S}_{4}}>0,\frac{\partial {y}_{3}{}^{*}}{\partial r}>0,\frac{\partial {y}_{3}{}^{*}}{\partial B}<0$.

#### 4.4. Dynamic Reward and Dynamic Punishment

**Proposition**

**9.**

- 1.
- The system always has four fixed equilibrium points, namely$(0,0),(0,1),(1,0),(1,1).$
- 2.
- When$0\frac{{S}_{1}-{S}_{2}-{R}_{1}}{B(y)+P(y)}1$,$0\frac{P(y)-{S}_{3}+{S}_{4}}{B(y)+P(y)}1$, there is another equilibrium point (${{x}_{4}}^{*},{{y}_{4}}^{*}$), where${x}_{4}{}^{*}=\frac{{S}_{1}-{S}_{2}-{R}_{1}}{B(y)+P(y)},{y}_{4}{}^{*}=\frac{P(y)-{S}_{3}+{S}_{4}}{B(y)+P(y)}$.

**Proposition**

**10.**

**Proposition**

**11.**

- (1)
- $\frac{\partial {x}_{4}{}^{*}}{\partial {S}_{1}}>0,\frac{\partial {x}_{4}{}^{*}}{\partial {S}_{2}}<0,\frac{\partial {x}_{4}{}^{*}}{\partial {S}_{3}}<0,\frac{\partial {x}_{4}{}^{*}}{\partial {S}_{4}}>0,\frac{\partial {x}_{4}{}^{*}}{\partial {R}_{1}}<0,\frac{\partial {x}_{4}{}^{*}}{\partial r}>0,\frac{\partial {x}_{4}{}^{*}}{\partial q}<0.$
- (2)
- $\frac{\partial {y}_{4}{}^{*}}{\partial {S}_{3}}<0,\frac{\partial {y}_{4}{}^{*}}{\partial {S}_{4}}>0,\frac{\partial {y}_{4}{}^{*}}{\partial r}>0,\frac{\partial {y}_{4}{}^{*}}{\partial q}<0$.

## 5. Results

#### 5.1. Simulation Analysis

#### 5.2. Discussion

## 6. Conclusions

- (1)
- Under the static reward and punishment policy, the behavioral of the government and construction enterprises evolves in a cyclical cycle and does not exist ESS. The reward and punishment are set as fixed constants in the game process according to the construction quality and green construction management level. The evolution game is in a cyclical change process, which cannot achieve a stable equilibrium state under the static incentive mechanism.
- (2)
- With the dynamic policy combinations, the strategy choice of the two subjects will eventually stabilize at the system equilibrium point, independent of the initial strategy choices of both sides. If the government can adjust the reward and punishment in real-time according to the construction quality, impose more severe punishment on the non-green construction behaviors of construction enterprises and give higher subsidies to the GB construction. Regardless of the initial strategy choice, when the dynamic incentive mechanism is adopted, the evolutionary trajectories of game systems are spirally approaching the stable equilibrium point, which is infinitely close to the evolutionary stability point.
- (3)
- As the main body of GBs implementation, the choice of behavior strategy of construction enterprises is mainly affected by the government’s strategies. Adopting a dynamic reward policy has a more obvious restraining effect on construction enterprises. When considering the bounded rationality of government and companies, the numerical simulation shows that the adoption of dynamic reward and static punishment, as well as dynamic reward and dynamic punishment policy combinations, can better promote the development of GBs.
- (4)
- Under the dynamic incentive mechanisms, the probability of active supervision is inversely proportional to the reward ceiling value. The government tends to adopt a passive regulatory attitude with the reward ceiling value increase. At the same time, the probability of active supervision is proportional to the upper limit of punishment. The government is willing to choose an active supervision strategy as its value increases.
- (5)
- Under the dynamic incentive mechanisms, the probability of green construction by construction enterprises is inversely proportional to the upper limit of subsidies and positively proportional to the fine. Unlike traditional intuition, this shows that enterprises, as a bounded rational decision-making subject, have a certain risk aversion and are more sensitive to losses than subsidies. Accordingly, when the government implements GB supervision, it is necessary to increase the punishment of “greenwashing,” thereby increasing the probability of enterprises constructing according to regulations. This conclusion provides a theoretical reference for formulating policies and the green construction of construction enterprises.

- (1)
- The policy combination should be adjusted from static to dynamic. When formulating a dynamic policy combination, the government should adjust the intensity of rewards and punishments according to the construction quality to improve the applicability and effectiveness of the policies. At the same time, relevant departments should set up red lines for GBs construction supervision, accelerate the formulation of relevant laws and regulations, continuously improve supervision mechanisms, strengthen law enforcement, and adopt diversified punishment models.
- (2)
- Construction enterprises should strictly regulate their construction behaviors. High construction costs are the main reason construction enterprises choose illegal construction. Construction enterprises should realize that the potential benefits, such as government reward and reputation accumulation, outweigh the benefits of non-green construction. Companies should regularly conduct self-inspection and self-correction activities and build a sound self-restraint system. In addition, construction companies should also retrain and update the knowledge reserve of on-site construction personnel to master the new construction processes and procedures of GBs and achieve them as a long-term goal.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Appendix A.1. The Proof of Proposition 7

**Proof.**

#### Appendix A.2. The Proof of Proposition 10

**Proof.**

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**Figure 2.**Evolution phase diagram of game system. (F2.I: When the initial state falls in region I, the stabilization strategy of the evolutionary game is (positive supervision, non-green construction); F2. II: When the initial state falls in region II, the stabilization strategy of the evolutionary game is (passive supervision, non-green construction); F2. III: When the initial state falls in region III, the stabilization strategy of the evolutionary game is (passive supervision, green construction); F2. IV When the initial state falls in region IV, the stabilization strategy of the evolutionary game is (positive supervision, green construction)).

**Figure 3.**(

**a**) Evolutionary path diagram under static reward and punishment (When the time $t$ is from 0 to 100, the evolution trajectory of the evolutionary game). (

**b**) Evolutionary path diagram under dynamic reward and punishment. (

**c**) Evolutionary path diagram under dynamic reward and static punishment. (

**d**) Evolutionary path diagram under static reward and dynamic punishment. (

**e**) Evolutionary path diagram under three policies.

Parameters | Meaning |
---|---|

${S}_{1}$ | Green construction needs to pay the cost |

${S}_{2}$ | Non-green construction needs to pay the cost |

${S}_{3}$ | Costs when government regulators actively supervise |

${S}_{4}$ | Costs when government regulators passively supervise |

$B$ | Subsidies given to green construction companies when actively supervision |

$P$ | Fines for green construction companies when actively supervision |

${R}_{1}$ | Potential future benefits of green construction for construction companies |

${R}_{2}$ | Government will gain additional revenue from “free-riding” behavior |

$L$ | The loss of government credibility and the cost of public opinion caused when construction companies adopt non-green construction practices |

$x$ | Probability of active supervision |

$y$ | Probability of green construction |

**Table 2.**The game payment matrix of government and construction enterprises under static reward and static punishment.

Construction Enterprises | |||
---|---|---|---|

Green Construction $\mathit{y}$ | $\mathbf{Non}-\mathbf{Green}\mathbf{Construction}$ $1-\mathit{y}$ | ||

Government | Active supervision $x$ | ${R}_{2}-B-{S}_{3},$ ${R}_{1}+B-{S}_{1}$ | $P-{S}_{3}-L,$ $-P-{S}_{2}$ |

Passive supervision $1-x$ | ${R}_{2}-{S}_{4},$ ${R}_{1}-{S}_{1}$ | $-{S}_{4}-L,$ $-{S}_{2}$ |

Equilibrium Point | $\mathit{d}\mathit{e}\mathit{t}\mathit{J}$ | $\mathit{t}\mathit{r}(\mathit{J})$ |
---|---|---|

$(0,0)$ | $\left(P-{S}_{3}+{S}_{4}\right)*\left(-{S}_{1}+{S}_{2}+{R}_{1}\right)$ | $\left(P-{S}_{3}+{S}_{4}\right)+\left(-{S}_{1}+{S}_{2}+{R}_{1}\right)$ |

$(0,1)$ | $\left(B+{S}_{3}-{S}_{4}\right)*\left(-{S}_{1}+{S}_{2}+{R}_{1}\right)$ | $\left(-B-{S}_{3}+{S}_{4}\right)-\left(-{S}_{1}+{S}_{2}+{R}_{1}\right)$ |

$(1,0)$ | $\left({\mathrm{P}+\mathrm{S}}_{3}{-\mathrm{S}}_{4}\right)*\left(P+B-{S}_{1}+{S}_{2}+{R}_{1}\right)$ | $\left(P+B-{S}_{1}+{S}_{2}+{R}_{1}\right)-\left(P-{S}_{3}+{S}_{4}\right)$ |

$(1,1)$ | $\left(-B-{S}_{3}+{S}_{4}\right)*\left(B+P-{S}_{1}+{S}_{2}+{R}_{1}\right)$ | $\left({\mathrm{B}+\mathrm{S}}_{3}-{S}_{4}\right)-\left(B+P-{S}_{1}+{S}_{2}+{R}_{1}\right)$ |

$({x}_{1}{}^{*},{y}_{1}{}^{*})$ | 0 |

Equilibrium Point | $\mathit{d}\mathit{e}\mathit{t}\mathit{J}$ | $\mathit{t}\mathit{r}\mathit{J}$ | Stability |
---|---|---|---|

$(0,0)$ | − | +/− | Saddle point |

$(0,1)$ | − | +/− | |

$(1,0)$ | − | +/− | |

$(1,1)$ | − | +/− |

Construction Enterprises | |||
---|---|---|---|

Green Construction $\mathit{y}$ | $\mathbf{Non}-\mathbf{Green}\mathbf{Construction}$ $1-\mathit{y}$ | ||

Government | Active supervision $x$ | ${R}_{2}-yq-{S}_{3},$${R}_{1}+yq-{S}_{1}$ | $P-{S}_{3}-L,$$-P-{S}_{2}$ |

Passive supervision $1-x$ | ${R}_{2}-{S}_{4},$${R}_{1}-{S}_{1}$ | $-{S}_{4}-L,$$-{S}_{2}$ |

**Table 6.**Stability analysis of equilibrium points under dynamic reward and static punishment mechanism.

Equilibrium Point | $\mathit{d}\mathit{e}\mathit{t}\mathit{J}$ | $\mathit{t}\mathit{r}\mathit{J}$ | Stability |
---|---|---|---|

$(0,0)$ | − | +/− | Saddle point |

$(0,1)$ | − | +/− | |

$(1,0)$ | − | +/− | |

$(1,1)$ | − | +/− | |

$({{x}_{2}}^{*},{{y}_{2}}^{*})$ | + | 0 | ESS |

Parameters | Value | Parameters | Value |
---|---|---|---|

${S}_{1}$ | 1.5 | ${R}_{2}$ | 0.85 |

${S}_{2}$ | 1 | $q$ | 0.85 |

${S}_{3}$ | 0.2 | $r$ | 0.8 |

${S}_{4}$ | 0.1 | $L$ | 0.6 |

$B$ | 0.5 | $x$ | 0.2 |

$P$ | 0.8 | $y$ | 0.5 |

${R}_{1}$ | 0.4 |

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## Share and Cite

**MDPI and ACS Style**

Chen, Y.; Li, Z.; Xu, J.; Liu, Y.; Meng, Q.
How Does the Government Policy Combination Prevents Greenwashing in Green Building Projects? An Evolutionary Game Perspective. *Buildings* **2023**, *13*, 917.
https://doi.org/10.3390/buildings13040917

**AMA Style**

Chen Y, Li Z, Xu J, Liu Y, Meng Q.
How Does the Government Policy Combination Prevents Greenwashing in Green Building Projects? An Evolutionary Game Perspective. *Buildings*. 2023; 13(4):917.
https://doi.org/10.3390/buildings13040917

**Chicago/Turabian Style**

Chen, Yuqing, Zhen Li, Jiaying Xu, Yingying Liu, and Qingfeng Meng.
2023. "How Does the Government Policy Combination Prevents Greenwashing in Green Building Projects? An Evolutionary Game Perspective" *Buildings* 13, no. 4: 917.
https://doi.org/10.3390/buildings13040917