Evolutionary Game Analysis of Resilient Community Construction Driven by Government Regulation and Market

Abstract

As the basic unit of residents’ activities and social management, communities are the disaster bearers of various public security emergencies. To improve the ability and level of community governance, as well as to strengthen the construction of resilient communities, a tripartite evolutionary game model of local government, developers, and home buyers is built, and numerical simulation is carried out using Matlab to analyze the impact mechanism of main parameters on the evolutionary stability strategy. The results show that: (1) The three parties’ different initial intentions will lead to different evolutionary stability strategies of the system, and the system’s final evolution result will reach the ideal state only when the initial willingness of developers and buyers is high. (2) The greater the government’s subsidy coefficient and the greater the regulatory intensity, the more likely it is that developers will choose to build resilient communities. (3) Public awareness of disaster prevention and mitigation is an important determinant of the purchase of resilient community housing strategies. To achieve rapid development of resilient communities, the intensity of regulation must be continuously improved, the public’s awareness of disaster prevention and mitigation must be strengthened, and the government’s regulatory costs must be reduced.

1. Introduction

There were 313 natural disasters in the world in 2020, affecting 123 countries and regions. Global natural disasters resulted in direct economic losses totaling 173.133 billion US dollars [1]. The frequency of global natural disasters in 2021 increased by 13% compared to the average over the previous three decades, and direct economic losses increased by 82% [2]. Natural disasters and public health events pose multiple threats to countries all over the world. To better deal with these threats, relevant government departments and scholars have focused more on incorporating resilience into urban construction and disaster prevention and reduction. “We should build resilient cities, raise the level of urban governance, and reinforce risk prevention and control in the governance of megacities”, concluded the Fifth Plenary Session of the Communist Party of China’s 19th Central Committee. This is the first time that resilience has been officially written into a central document, indicating that the Chinese government recognizes the importance of resilience in the safe and stable operation of urban systems.

The community is the fundamental unit of residents’ activities and urban management, as well as the primary location of disaster and shock occurrence and response. The United Nations proposed “developing community-based disaster reduction strategies” in 2001, and community disaster reduction was included as an important topic at the 2005 World Conference on Disaster Reduction [3]. This set of strategies and measures reflects the critical role of community disaster reduction in international disaster reduction. According to the report of the 19th CPC National Congress, we should strengthen the construction of community governance systems, promote the focus of social governance to move down to the grass-roots level, and play the role of social organizations. The national “14th Five-Year Plan” further puts forward the development goals of “significantly raising the level of social governance, especially grassroots governance, continuously improving the institutional mechanism for preventing and resolving major risks, and significantly enhancing the emergency response capacity for public emergencies”. Improving community disaster emergency management capability is an unavoidable trend in urban disaster prevention and reduction. General Secretary Xi stated during an inspection of the Qingheju community in Wuhan, “The community is the grassroots foundation, and only when the foundation is solid can the national building be stable.” The safety of the community is related to the stable operation of the urban system, and community capacity building for disaster prevention and mitigation is even more related to the city’s overall emergency management capacity. As a result, building resilient communities has become critical to improving cities’ overall risk prevention and emergency response capacity [4,5], and the success of resilient city construction is largely determined by this. Improving the city’s ability to resist and recover from various natural disasters and public security emergencies through the construction of resilient communities is an important part of the current construction of a grass-roots social emergency management system. With governments paying increasing attention to resilient cities and communities, academic research on the construction of resilient communities and risk prevention has increasingly attracted the attention of academia, and China is no exception. Under the overarching requirement of promoting the modernization of the national governance system and governance capacity, how to improve community governance capacity, particularly community disaster resilience, has emerged as an important research topic in the new era.

The following are the main research topics of this paper: First and foremost, this is one of the few articles that investigates the relationship between consumers and resilient communities. Second, this paper constructs an evolutionary game model between government, developers, and consumers from the perspective of early planning and construction of resilient communities, and then analyzes the evolutionary game relationship between resilient community construction and developers and consumers. Finally, this paper examines the impact of government regulation strength and subsidy coefficient, as well as consumer awareness of disaster prevention and mitigation, on developers’ decision-making to build resilient communities using numerical simulation.

2. Literature Review

The community’s shortcomings in responding to natural disasters and public health emergencies, particularly the COVID-19 epidemic, have made people acutely aware of the urgency and necessity of constructing resilient communities [6]. People are paying more attention to the importance of resilient community construction for disaster prevention and reduction as their awareness of disaster prevention and reduction grows. Academics have also conducted extensive and in-depth research on resilient communities, focusing primarily on resilience evaluation [7,8,9,10,11,12] and resilience-influencing factors [13,14,15,16,17,18]. The goal of toughness evaluation research is to either develop a toughness evaluation model or use a relatively mature toughness evaluation model to evaluate the resilience of a city or community and determine whether or not the city or community has resilience. The purpose of resilience impact factor research is to investigate the factors that have an impact on the development of resilient cities or communities. Both the study of resilience evaluation and the study of resilience impact factors aim to improve the resilience level of cities or communities.

The community resilience evaluation can understand the community’s shortcomings in disaster prevention and mitigation, take targeted measures to improve the community’s resilience, ensure the safe and stable operation of the city [7], and protect and optimize the value of the urban building environment and its building assets [8]. In academic circles, there is no unified definition of a toughness evaluation model. Suleimany et al. [9] proposed a five-dimensional toughness evaluation model that takes into account the system, society, economy, infrastructure, and population. Bruneau et al. [10] proposed a four-dimensional community resilience assessment framework comprised of technology, organization, society, and economy to assess communities’ seismic resistance and resilience. Furthermore, some researchers believe that the disaster resilience index of communities can be calculated using the social, economic, material, and human factors [11]. Although scholars disagree on the dimension composition of the resilient community evaluation model, they all agree on the importance of the economy in the resilient community evaluation. It is clear that the development and construction of resilient communities cannot be separated from economic support. Other researchers focused on the analysis of resilience assessment tools and identified six performance criteria for resilience community assessment tools: Solve multiple elasticity dimensions, consider cross-scale relationships, capture time dynamics, solve uncertainty, use participatory methods, and develop action plans [12]. The determination of the resilience assessment tool’s performance standard provides a measurement standard for future research on community resilience assessment.

Many factors influence the development of resilient communities, and research into the influencing factors of resilient communities will help to improve community resilience. Some scholars have discussed the macro-level impact factors of resilient communities and believe that ecological, social development [13], regional economy [14], and other factors will have an impact on resilient communities. Because these influencing factors are at the macro level, in practice, the relevant functional departments of the government take certain measures to regulate them in order to promote the development of resilient communities; however, their power is limited. In this context, some scholars discussed the impact of micro-level factors on the development of resilient communities, such as information communication among community members [15], community members’ understanding of resilience, community members’ participation in some activities to improve community resilience [16], and community members’ values [17], and proposed strategies to promote the development of resilient communities from the micro-level of community members. Furthermore, scholars have noted the impact of community management on community resilience, investigating the impact of management innovation, ‘change’ leadership, and policy implementation on community resilience [18]. These micro-level studies have revealed that community members are the main actors influencing the development of resilient communities, and with China’s large population base, influencing the development of resilient communities through the specific actions of community members is an effective way to promote their rapid development.

Evolutionary game theory focuses on the decision-making process and can solve multiple decision-making problems, making it one of the most commonly used research methods for solving problems in many research fields. Evolutionary games emphasize that decisions made by participants with limited rationality in different situations will have different effects on their interests [19]. The participants’ bounded rationality makes it difficult for them to make the best decision during the decision-making process. On the contrary, they keep learning and imitate in the decision-making process [20,21]. Because evolutionary games can clearly see changes in the decision-making behavior of the participants and explain how the participants obtain the best strategy, they have been widely used in the field of multi-agent participation in decision-making in the field of sustainable development, e.g., of prefabricated houses [22,23], carbon emission reduction behavior [24,25], pollution control [26,27], green supply chain [28,29,30], environmental supervision [31,32], etc. The development of resilient communities should center on the decision-making logic of relevant stakeholders, and each stakeholder exhibits obvious signs of limited rationality. Evolutionary games provide ideas for discussing such issues, and scholars have already used them to study sponge community construction [33,34] and green building development [35,36,37,38]. Among them, Guo [33] and Chen et al. [34] investigated their impact on the evolutionary path of sponge community construction by devising a two-sided evolutionary game between the government and developers and provided a series of optimization suggestions. Residents’ involvement in managing public affairs is becoming more and more acknowledged by all spheres of society. The current evolutionary game model for community development does not analyze home buyers. In the development of resilient communities, consumer participation can form a closed loop. The government is in charge of oversight and direction. The primary force behind creating resilient communities is developers. Buyers are willing to purchase resilience community housing under the market mechanism, allowing for the quick development of resilient communities.

To summarize, scholars have studied resilient communities from various perspectives and achieved certain research results, but the following deficiencies remain: First, there are not many studies using evolutionary games to discuss communities in community research. The majority of past studies have constructed a two-party evolutionary game model of the government and developers without including consumers as a primary research body. Second, most existing studies focus on resilience in existing traditional communities, with few focusing on early planning and construction of resilient communities. As a result, this paper takes consumers into account as a party subject and builds a three-party evolutionary game model of local government, developers, and consumers. On the one hand, the dynamic realization process of tripartite strategy equilibrium under different situations is examined from the standpoint of early planning and construction of resilient communities. On the other hand, Matlab is used to run numerical simulations to further investigate the impact of relevant parameters on evolutionary equilibrium. This research provides a scientific foundation for the government to make policy recommendations to encourage the development of resilient communities. This research provides a scientific foundation for the government to make policy recommendations to encourage the development of resilient communities.

3. Evolutionary Game Model of Resilient Community Construction

3.1. Basic Assumptions

Facilitating the development of resilient communities necessitates the collaboration of the government, developers, buyers, and other stakeholders. Based on the literature [33] and the current situation of the development of resilient communities in China, we put forward the following assumptions, which are always valid in the subsequent analysis:

(1)

Local governments, developers, and buyers are the main players in the game, and all three are rational. Local governments can choose between regulatory and non-regulatory strategies, developers can build resilient communities or traditional communities, and consumers can buy resilient or traditional community housing. Furthermore, we assume that the likelihood of local government regulation is $x\left(0\le x\le 1\right)$, the likelihood of non-regulation is $1-x$, the likelihood of developers building resilient communities is $y\left(0\le y\le 1\right)$, the likelihood of developers building traditional communities is $1-y$, the likelihood of consumers buying resilient community housing is $z\left(0\le z\le 1\right)$, and the likelihood of consumers buying traditional community housing is $1-z$.

(2)

To encourage the construction and development of resilient communities in China, developers who choose to build those will be rewarded by local governments $R$, while developers who choose to build traditional communities will be punished by local governments $R$, where $R$ is the regulatory intensity of local governments. The local government will provide $\beta \left(0<\beta <1\right)$ intensity subsidies to developers who choose to build resilient communities. The publicity of resilient communities is reflected in enhancing the public’s awareness of disaster reduction and prevention, among which the public’s awareness of disaster prevention and reduction is $\omega \left(\omega >0\right)$. When local governments regulate, they can obtain certain policy benefits $u$ directly indirectly or indirectly from the central government, and the cost of regulation is $c_1$, whereas when local governments do not regulate, they must bear the economic and reputational losses caused by disasters or sudden accidents in the construction of traditional communities by developers $c_2$, and the probability of disasters and accidents is $\alpha$.

(3)

Resilient communities can effectively improve community resilience and resilience to various disasters [39]. Developers who choose to build resilient communities can gain a certain brand benefit b while incurring an additional cost $c_3$. To facilitate analysis, the cost of traditional community construction has been set to 0. When developers choose to build resilient communities, they may receive $Rq$ awards from local governments, while traditional communities may face $Rq$ penalties. Housing market demand is $q$, and prices per unit in resilient and traditional communities are $p_1$ and $p_2$. Pricing does not take into account other factors influencing housing prices, such as location and plot ratio, in order to focus on the core research theme.

(4)

According to the market-driven and consumer preference theory, awareness of disaster prevention and mitigation positively influences home buyers’ preference for resilient communities, which then drives home buyers to purchase resilient communities. As a result, the basic value obtained by purchasing housing is assumed to be $u_1$, and the preferred income obtained by purchasing resilient community housing is assumed to be $\phi$. When the government implements a regulatory strategy, consumers can reap $u_2$ indirect benefits. According to the current state of resilient community development, the emphasis on promoting the rapid development of resilient communities is that developers are willing to build them, and buyers prefer to purchase resilient community housing. We will assume that $u_1>p_2$ and $p_1>u_1$ in this case.

3.2. Model Construction

The benefits of the three players in the game differ depending on the strategy used. Clarify the specific income and expenditure of each game subject under various strategies, add and subtract the income and expenditure of each party under various strategies, and then determine the income function of the three parties under various strategy combinations in accordance with the presumptions in the previous section, as shown in

Table 1. Tripartite benefit matrix of game under local government regulation strategy.

Developers Build Resilient Communities(y)
	Local Government	Developers	Home Buyers
Home buyers purchase resilient community housing(z)	$-Rq+u-c_1$	$Rq+q{p}_1+bq-\left(1-\beta \right)c_3$	$\left(\phi \omega -p_1+u_1\right)q+u_2$
Home buyers purchase traditional community housing(1-z)	$u-c_1$	$bq$	$u_2$
Developers build traditional communities(1-y)
	Local government	Developers	Home buyers
Home buyers purchase resilient community housing(z)	$u-c_1$	0	$u_2$
Home buyers purchase traditional community housing(1-z)	$Rq+u-c_1-\alpha c_2$	$p_{2}q-Rq$	$u_2+u_{1}q-p_{2}q$

and

Table 2. Tripartite benefit matrix of game under local government’s unregulated strategy.

Developers Build Resilient Communities(y)
	Local Government	Developers	Home Buyers
Home buyers purchase resilient community housing(z)	0	$q{p}_1+bq-c_3$	$\left(\phi \omega -p_1+u_1\right)q$
Home buyers purchase traditional community housing(1-z)	0	$bq$	0
Developers build traditional communities(1-y)
	Local government	Developers	Home buyers
Home buyers purchase resilient community housing(z)	0	0	0
Home buyers purchase traditional community housing(1-z)	$-\alpha c_2$	$p_{2}q$	$u_{1}q-p_{2}q$

. It is necessary to limit the relationship between some variables in order to conform to the actual situation. Developers choose to build resilient communities on purpose, and buyers prefer to buy resilient community housing. The government’s regulatory strategy is effective on this basis. Therefore, $-Rq+u-c_1>0$ is established. When buyers choose to buy resilient community housing and local governments choose an irregular strategy, developers choose to build resilient community after weighing their gains, and thus should meet the $qb+p_{1}q-c_3>0$.

The game subject in the evolutionary game system is bounded rational and cannot make the optimal decision in the initial decision. It will evolve in the system until it reaches the optimal decision [40,41]. The system’s evolution process can be described by replicating the dynamic equation [42].

Assume $G_x$ and $G_{1-x}$ represent the expected returns of local governments with and without regulation, and $\overline{G}$ represents the average expected return of local governments, which is obtained from Table 1 and Table 2:

$$\left\{\begin{array}{l}{G}_x=Rq+u-c_1-yRq-\alpha c_2+y\alpha c_2+z\alpha c_2-yz\alpha c_2-zRq\\ G_{1-x}=-\alpha c_2+y\alpha c_2+z\alpha c_2-yz\alpha c_2\\ \overline{G}=x{G}_x+\left(1-x\right)G_{1-x}\end{array}\right.$$

(1)

The replication dynamic equation for local government is:

$$F\left(x\right)=x\left(G_x-\overline{G}\right)=x\left(1-x\right)\left(G_x-G_{1-x}\right)=x\left(1-x\right)[Rq+u-yRq-c_1-zRq]$$

(2)

Assuming K_y and K_1−y are the expected incomes of developers for building resilient and traditional communities, and $\overline{K}$ is the average expected income of developers, then:

$$\left\{\begin{array}{l}{K}_y=xz\beta c_3-z{c}_3+qb+\mathrm{x}zRq+zq{p}_1\\ K_{1-y}=xRq-p_{2}q+xzRq+z{p}_{2}q\\ \overline{K}=y{K}_y+\left(1-y\right)K_{1-y}\end{array}\right.$$

(3)

The developer’s replication dynamic equation is:

$$F\left(y\right)=y\left(K_y-\overline{K}\right)=y\left(1-y\right)\left(K_y-K_{1-y}\right)=y\left(1-y\right)[xz\beta c_3-z{c}_3+qb+xRq-p_{2}q+zq{p}_1+zq{p}_2]$$

(4)

Assuming that $X_z$ and $X_{1-z}$ are the expected returns for consumers who purchase resilient community housing and traditional community housing, and $\overline{X}$ is the average expected return for consumers, then:

$$\left\{\begin{array}{l}{X}_z=y\phi \omega q+y{u}_{1}q-y{p}_{1}q+x{u}_2\\ X_{1-z}=x{u}_2-p_{2}q+u_{1}q+yq{p}_2-y{u}_{1}q\\ \overline{X}=z{X}_z+\left(1-z\right)X_{1-\mathrm{z}}\end{array}\right.$$

(5)

The dynamic equation for replication for home buyers is:

$$F\left(z\right)=z\left(X_z-\overline{X}\right)=z\left(1-z\right)\left(X_z-X_{1-z}\right)=z\left(1-z\right)[y\phi \omega q+2y{u}_{1}q-y{p}_{1}q-y{p}_{2}q-u_{1}q+q{p}_2]$$

(6)

4. Stability and Evolution Path Analysis

Letting F(x) = 0, F(y) = 0, F(z) = 0, eight equilibrium points result: E1(0, 0, 0), E2(0, 0, 1), E3 (0, 1, 0), E4 (0, 1, 1), E5 (1, 0, 0), E6 (1, 0, 1), E7 (1, 1, 0) and E8 (1, 1, 1). Except for equilibrium points E1 to E8, the stable solution of the system in a multi-agent evolutionary game is a strict Nash equilibrium solution [43]. As a result, this paper only analyzes these eight equilibrium points. This evolutionary system’s Jacobian matrix is as follows:

$$J=\left[\begin{array}{ccc}\frac{\partial F\left(x\right)}{\partial x}& \frac{\partial F\left(x\right)}{\partial y}& \frac{\partial F\left(x\right)}{\partial z}\\ \frac{\partial F\left(y\right)}{\partial x}& \frac{\partial F\left(y\right)}{\partial y}& \frac{\partial F\left(y\right)}{\partial z}\\ \frac{\partial F\left(z\right)}{\partial x}& \frac{\partial F\left(z\right)}{\partial y}& \frac{\partial F\left(z\right)}{\partial z}\end{array}\right]$$

(7)

where

$\frac{\partial F\left(x\right)}{\partial x}=\left(1-2x\right)[\mathrm{Rq}+\mathrm{u}-\mathrm{yRq}-\mathrm{zRq}]$;

$\frac{\partial F\left(x\right)}{\partial y}=-x\left(1-x\right)Rq$;

$\frac{\partial F\left(x\right)}{\partial z}=-x\left(1-x\right)Rq$;

$\frac{\partial F\left(y\right)}{\partial x}=y\left(1-y\right)[z\beta c_3+Rq]$;

$\frac{\partial F\left(y\right)}{\partial y}=\left(1-2y\right)[xz\beta c_3-z{c}_3+zq{p}_1+xTq-p_{2}q+z{p}_{2}q+qb]$;

$\frac{\partial F\left(y\right)}{\partial z}=y\left(1-y\right)[x\beta c_3-q{p}_1-p_{2}q]$;

$\frac{\partial F\left(z\right)}{\partial x}=0$;

$\frac{\partial F\left(z\right)}{\partial y}=z\left(1-z\right)[\phi \omega q+2u_{1}q-p_{1}q+p_{2}q]$;

$\frac{\partial F\left(z\right)}{\partial z}=\left(1-2z\right)[y\phi \omega q+2y{u}_{1}q-y{p}_{1}q-y{p}_{2}q-u_{1}q+p_{2}q]$;

When all of the eigenvalues of the Jacobian matrix are negative, the equilibrium point is the system’s evolutionary stability point (ESS) [44,45,46], according to Lyapunov’s stability theory. The Jacobian matrix is used to calculate the eigenvalues of the system’s equilibrium points, as shown in

Table 3. Eigenvalues of Jacobian matrix and determinant.

Equilibrium Point	Eigenvalue λ1	Eigenvalue λ2	Eigenvalue λ3
$E_1$ (0, 0, 0)	$Rq+u-c_1$	$\left(b-p_2\right)q$	$\left(p_2-u_1\right)q$
$E_2$ (1, 0, 0)	$-\left(Rq+u-c_1\right)$	$\left(R+b-p_2\right)q$	$\left(p_2-u_1\right)q$
$E_3$ (0, 1, 0)	$u-c_1$	$-\left(b-p_2\right)q$	$\left(\phi \omega -p_1+u_1\right)q$
$E_4$ (0, 0, 1)	$u-c_1$	$qb+p_{1}q-c_3$	$-\left(p_2-u_1\right)q$
$E_5$ (1, 0, 1)	$-\left(u-c_1\right)$	$\beta c_3-c_3+q{p}_1+Tq+qb$	$-\left(p_2-u_1\right)q$
$E_6$ (1, 1, 0)	$-\left(u-c_1\right)$	$-\left(R+b-p_2\right)q$	$\left(\phi \omega -p_1+u_1\right)q$
$E_7$ (0, 1, 1)	$-Rq+u-c_1$	$-\left(qb+p_{1}q-c_3\right)$	$-\left(\phi \omega -p_1+u_1\right)q$
$E_8$ (1, 1, 1)	$-\left(-Rq+u-c_1\right)$	$-\left(\beta c_3-c_3+q{p}_1+Tq+qb\right)$	$-\left(\phi \omega -p_1+u_1\right)q$

:

The model parameters are not known. Except for $b-p_2$, $\phi \omega -p_1+u_1$, and $b-p_2+R$, we can judge the positive and negative of the equations from the hypothesis section. As a result, all that remains is to examine the positive and negative conditions of the three equations $b-p_2$, $\phi \omega -p_1+u_1$, and $b-p_2+R$. The findings of the analysis are as follows.

(1)

When $R+b-p_2<0$ is less than the price of traditional community housing, the sum of the brand benefits brought by the developer’s decision to build a resilient community and the intensity of government regulation.

Table 4. Analysis of local stability of equilibrium point.

Equilibrium Point	Case 1				Case 2				Case 3
	λ1	λ2	λ3	Stability	λ1	λ2	λ3	Stability	λ1	λ2	λ3	Stability
${\mathrm{E}}_1$ (0, 0, 0)	+	±	−	Unstable point	+	±	−	Unstable point	+	±	−	Unstable point
${\mathrm{E}}_2$ (1, 0, 0)	−	−	−	ESS	−	+	−	Unstable point	−	±	−	Unstable point
${\mathrm{E}}_3$ (0, 1, 0)	+	−	±	Unstable point	+	±	−	Unstable point	+	±	+	Unstable point
${\mathrm{E}}_4$ (0, 0, 1)	+	+	+	Saddle point	+	+	+	Saddle point	+	+	+	Saddle point
${\mathrm{E}}_5$ (1, 0, 1)	−	+	+	Unstable point	−	+	+	Unstable point	−	+	+	Unstable point
${\mathrm{E}}_6$ (1, 1, 0)	−	+	±	Unstable point	−	−	−	ESS	−	±	+	Unstable point
${\mathrm{E}}_7$ (0, 1, 1)	+	−	±	Unstable point	+	−	+	Unstable point	+	−	−	Unstable point
${\mathrm{E}}_8$ (1, 1, 1)	−	−	±	Unstable point	−	−	+	Unstable point	−	−	−	ESS

shows that the three eigenvalues of the equilibrium point E2 = (1, 0, 0) are all less than zero, indicating that when the condition $R+b-p_2<0$ is met, E2 = (1, 0, 0) is the stable point of system evolution.

(2)

When $R+b-p_2>0$ and $\phi \omega -p_1+u_1<0$. That is, the sum of brand revenue and government regulatory intensity is greater than the housing price of resilient communities, whereas the housing price of traditional communities is greater than the sum of basic housing value and resilience preference income. Table 4 shows that the three eigenvalues of the equilibrium point E6 = (1, 1, 0) are negative at this time. As a result, when $R+b-p_2>0$ and $\phi \omega -p_1+u_1<0$ are satisfied, the stable point of system evolution is E6 = (1, 1, 0).

(3)

When $\phi \omega -p_1+u_1>0$ is met, the cost of traditional community housing is less than the sum of the housing’s basic value and the preferred return. Table 4 shows that the three characteristic values of the equilibrium point E8 = (1, 1, 1) are all less than zero, indicating that when $\phi \omega -p_1+u_1>0$ is reached, E8 = (1, 1, 1) is the stable point of system evolution. This evolutionary stability point is an ideal state that governments strive for.

5. Simulation Analysis and Results

In this paper, Matlab is used to perform numerical simulation analysis of the constructed evolutionary game model and to demonstrate the impact of parameter changes such as government subsidies on game subject strategy selection. According to the current situation of the development of resilient communities in China, referring to [33,34], and at the same time meeting the conditions of $-Rq+u-c_1>0$ and $qb+p_{1}q-c_3>0$, set the parameters to: $R=0.2$, $\beta =0.3$, $\omega =1$, $u=3$, $c_1=1$, $c_3=7$, $q=5$, $p_1=1.5$, $p_2=0.8$, $\phi =0.6$, $b=0.6$ and $u_1=1$. The initial willingness of the three parties in the game is set to (0.5, 0.5, 0.5).

5.1. Equilibrium Point Stability Test

In the case of $R+b-p_2<0$, set the parameter values: $R=0.2$, $\beta =0.3$, $\omega =1$, $u=3$, $c_1=1$, $c_3=7$, $q=5$, $p_1=1.5$, $p_2=0.8$, $\phi =0.6$, $b=0.1$ and $u_1=1$. The game subject’s initial intention is 0.5. As shown in Figure 1, the final evolution and stability results are (1, 0, 0), indicating that local governments select regulation strategies, developers select traditional communities, and buyers select traditional community housing. This demonstrates that when the price of traditional community housing is higher, the brand income is low, and the government’s regulatory intensity is low, developers prefer to build traditional communities.

When $R+b-p_2>0$ is satisfied, and $\phi \omega -p_1+u_1<0$, set the parameters: $R=0.2$, $\beta =0.3$, $\omega =1$, $u=3$, $c_1=1$, $c_3=7$, $q=5$, $p_1=1.5$, $p_2=0.8$, $\phi =0.4$, $b=0.8$ and $u_1=1$. The three parties’ initial willingness is 0.5. As illustrated in Figure 2, the stable outcome of system evolution is (1, 1, 0), indicating that local governments choose to regulate, developers choose to build resilient communities, and buyers choose to purchase traditional community housing. This demonstrates that when the housing price of traditional communities is low, the brand income is high, the regulatory intensity of local governments is high, and the housing price of resilient communities is greater than the sum of the preferred benefits of resilient communities and the basic value of housing, developers prefer to build resilient communities, and home buyers prefer to buy traditional community housing.

When $\phi \omega -p_1+u_1>0$ is satisfied, set the parameters: $R=0.2$, $\beta =0.3$, $\omega =1$, $u=3$, $c_1=1$, $c_3=7$, $q=5$, $p_1=1.5$, $p_2=0.8$, $\phi =0.6$, $b=0.6$ and $u_1=1$. The three parties’ initial willingness is 0.5. The three parties’ initial willingness is 0.5. As demonstrated in Figure 3, the stable outcomes of system evolution are (1, 1, 1), indicating that local governments choose to regulate, developers choose to build resilient communities, and buyers choose to purchase resilient community housing. This demonstrates that when the sum of buyers’ disaster prevention and mitigation awareness and basic housing value is greater than the price of resilient community housing, buyers prefer to buy resilient community housing.

The system has three evolutionary stability strategies, as determined by simulation analysis. In comparison to traditional communities, resilient communities are innovative products. According to the life cycle theory [47], innovative products will spread over time among different members of the social system. The three stabilization strategies correspond to the various stages of development of resilient communities.

(1)

Stability strategy 1 (1, 0, 0). That is, local governments choose to regulate, developers choose to build traditional communities, and buyers choose to purchase traditional community housing, corresponding to the initial stage of resilient community development. At this time, local governments are the main body, and the willingness of developers to build resilient communities and buyers to buy resilient community housing is not obvious. The relevant legal system and documents are not perfect in the early stages of resilient community development, the government’s regulatory intensity is not high, and the construction of traditional communities brings greater benefits to developers. Buyers are more likely to purchase traditional community housing because they have a low awareness of risk prevention and do not recognize the benefits of resilient communities over traditional communities.

(2)

Stability strategy 2 (1, 1, 0). That is, local governments choose to regulate, developers choose to build resilient communities, and buyers choose to buy traditional community housing, corresponding to the transitional stage of resilient community development. At this time, the government and developers are the main body, and the willingness of buyers to buy resilient community housing is not obvious. During the transitional stage of resilient community development, relevant laws and documents are gradually improved, and local governments’ regulatory intensity is gradually increased. Moreover, because developers understand that building resilient communities can result in greater brand benefits, they tend to build resilient communities. Because the government does not recognize the importance of increasing consumer awareness of disaster prevention and mitigation for the development of resilient communities, traditional housing provides greater benefits to consumers, making them less willing to purchase resilient housing.

(3)

Stability strategy 3 (1, 1, 1). That is, local governments prefer regulatory strategies, developers select to build resilient communities, and buyers choose to purchase resilient community housing, corresponding to the mature stage of resilient community development. The main body at this point is made up of developers and home buyers. In the mature stage of resilient community development, relevant laws and documents are basically perfect, and the government’s regulatory intensity has increased. In resilient community development, local governments realize the importance of increasing consumer participation for it. Starting with increasing consumer awareness of disaster prevention and mitigation and capacity training, we will innovate original publicity and education methods using modern science and technology such as the Internet, implement a more comprehensive and systematic training and education system to increase consumer awareness of disaster prevention and mitigation, as well as to guide consumers in their participation in the development of resilient communities.

5.2. Impact of Initial Willingness to Share

When $\phi \omega -p_1+u_1>0$ is satisfied, set the parameters: $R=0.2$, $\beta =0.3$, $\omega =1$, $u=3$, $c_1=1$, $c_3=7$, $q=5$, $p_1=1.5$, $p_2=0.8$, $\phi =0.6$, $b=0.6$ and $u_1=1$. The influence of initial willingness and main parameters on the evolution path of game subjects is examined on this basis.

Other parameters remain constant, and the game subject’s initial willingness is adjusted to examine its impact on the three-party strategy selection. As shown in Figure 4, when the initial willingness of the three parties to the game is increased from 0.5 to 0.8, the system’s ultimate evolution consequence remains unchanged, but the time to achieve the evolutionary stability strategy is reduced. When the initial willingness of the three parties is adjusted from 0.5 to 0.1, the system evolution stability strategy is (1, 0, 0). That is, local governments choose regulatory strategies, developers choose to build traditional communities, and buyers choose to buy traditional community housing. This demonstrates that the final stable state of the resilient community evolution system has nothing to do with increasing the initial will of the game players, but increasing the initial will shortens the time for the system to reach the stable state. However, a decrease in the initial willingness of the game subject will affect the system’s evolution and stability strategy, and a decrease in the initial intention of the three parties of the game has the greatest impact on the evolution path of developers and home buyers and has the least impact on the evolution path of local governments. Even if the initial willingness of the three parties to the game is reduced, local governments will continue to choose to regulate the construction of resilient communities, even if the willingness of developers and buyers to participate is unclear. The goal of regulation for local governments is to allow developers and buyers to actively participate in the development of resilient communities and improve the overall resilience of cities, which can reduce economic losses and casualties caused by natural disasters or unexpected accidents. At the same time, because resilient communities have higher environmental requirements than traditional communities, developers who build them can provide environmental benefits to local governments.

Figure 5 displays that, while the other two parties’ initial intentions remain unchanged, reducing either party’s initial intentions have no effect on the system’s final evolutionary stability strategy. When the initial intentions of developers and buyers are low, regardless of how high the government’s initial intentions are, the evolutionary stability strategy of the system is (1, 0, 0), which means that the local government chooses the regulation strategy, developers choose to build traditional communities, and buyers choose to buy traditional community housing. When the initial willingness of developers and buyers is reduced from 0.5 to 0.1, even if the initial willingness of local governments is increased to 0.8, the resilient community evolution system’s evolutionary stability strategy does not reach the ideal state. This exemplifies that in the development of resilient communities, the high participation of developers and home buyers can make the evolutionary system’s stable strategy ideal.

5.3. Influence of Main Parameters on the Evolution Path of Local Governments

Figure 6 depicts the impact of policy benefits and regulatory costs on local governments’ evolving stability strategies, and when other parameters remain constant, increasing policy returns from 3 to 5 gradually accelerates the pace of local governments’ evolution to stabilization strategies. When the regulatory cost is increased from 1 to 3, local governments transition from regulated to unregulated strategies. This implies that, if all other parameters remain constant, an increase in policy benefits will encourage the government to pursue regulatory strategies, whereas an increase in regulatory costs will dampen local governments’ desire to regulate. Furthermore, the impact of regulatory costs on the evolution path of local governments is greater, whereas the impact of policy benefits is minor.

Figure 7 illustrates the impact of changes in housing demand on local governments’ evolutionary stabilization strategies. Other parameters remain unchanged, When the housing demand is adjusted from 5 to 9, the local government will eventually prefer the regulation strategy, but the time to reach the evolutionary stability strategy will be longer. When housing demand is increased from 9 to 13, local governments shift from regulated to unregulated strategies. This expresses that the system’s evolution stability strategy is related to housing demand, and as it rises, so will the cost of local government regulation, so local governments will prefer unregulated strategies.

5.4. The Influence of Main Parameters on the Evolution Path of Developers

Figure 8 depicts the effect of regulatory intensity and subsidy coefficient on the evolutionary stabilization strategies of developers. If all other parameters remain constant, increasing the intensity of regulation and the subsidy factor will not change the developer’s ultimate evolutionary stabilization strategy but will shorten the time it takes for the developer to reach an evolutionary stabilization strategy. The more intense the regulation and subsidy coefficients, the faster developers can arrive at evolutionary stabilization strategies. This demonstrates that the intensity of government regulation and the subsidy coefficient are positively correlated with the choice of resilient community construction by developers. That is, as regulatory intensity and subsidy coefficient increase, developers converge faster to 1. Furthermore, the impact of regulation intensity on the evolution path of developers is greater, whereas the impact of subsidy coefficients on the evolution path of developers is less significant.

The impact of developers’ construction costs and brand revenue on their evolutionary stabilization strategies is depicted in Figure 9. When the construction cost is increased from 7 to 12, while all other parameters remain constant, the developer’s final evolutionary stabilization strategy remains the same, but the time required to reach the evolutionary stabilization strategy increases progressively. The final evolutionary outcome for the developer remains unchanged when the brand gain is adjusted from 0.6 to 1; however, the greater the brand gain, the shorter the time for the developer to reach an evolutionary stable strategy. This exemplifies that an increase in brand revenue will encourage developers to choose the strategy of building resilient communities, whereas an increase in construction costs will dampen their enthusiasm for building resilient communities, and the impact of construction costs on developers’ evolution paths is greater than the impact of brand revenue.

5.5. The Influence of Main Parameters on the Evolution Path of Home Buyers

Figure 10 depicts the impact of resilient and traditional community housing prices on buyers’ strategic choices. When all other parameters remain constant, and the housing price of traditional communities is adjusted from 0.8 to 1, the buyers’ evolutionary stability strategy remains constant. When the price of resilient community housing is raised from 1.5 to 1.7, buyers switch from purchasing resilient community housing to purchasing traditional community housing. This reveals that an increase in the price of housing in traditional communities encourages buyers to choose resilient community housing, whereas an increase in the price of housing in resilient communities discourages buyers from purchasing it. Furthermore, the price of housing in resilient communities has a significant impact on the strategic choice of buyers, whereas the price of housing in traditional communities has less of an impact.

Figure 11 depicts the effect of resilient community preference income and home buyers’ awareness of disaster prevention and mitigation on home buyers’ strategy evolution and stability. Keeping other parameters constant, the eventual evolutionary stability strategy of home buyers remains unchanged as the resilience preference income and awareness of disaster prevention and reduction increase, but the time to achieve it decreases. This suggests that home buyers are motivated to purchase resilient community housing due to the preference benefits of resilient communities and increased awareness of disaster prevention and mitigation among home buyers. Furthermore, when compared to consumers’ awareness of disaster prevention and mitigation, consumers’ strategic choices are influenced more by their preference income for purchasing resilient communities.

6. Discussion

The evolutionary stability outcome of the system is influenced by the initial willingness of the game players. When developers and consumers alike favor traditional communities, resilient communities do not grow fast enough, even when governments adopt regulatory strategies. This is due to the fact that the development of resilient communities necessitates the collaboration of stakeholders, and the government’s unilateral regulatory power is limited. Only when both developers and consumers favor resilient housing can the development of resilient communities form a closed loop. As a result, we can improve the initial willingness of developers and consumers to promote the resilient community evolution system to an ideal state in order to promote the development of resilient communities.

The benefits of policy and the costs of regulation have a large influence on the evolutionary stability outcomes of local governments. If the cost of regulation is too high, it means that the local government must spend more money, materials, and human resources when implementing the regulation strategy. Over time, the government has become more inclined to pursue a non-regulation strategy. On the contrary, when the local government adopts the regulation strategy, the higher the policy income from the central government, the higher the willingness of the government to adopt the regulation strategy. To improve the likelihood of local governments adopting regulation strategies, we can reduce regulation costs and the material, financial, and human resources that local governments must consume when adopting regulation strategies. In light of the relatively mature development of modern information technology, such as the Internet of Things, big data, and cloud computing, the central government can encourage local governments to fully utilize modern science and technology in the management of resilient communities, thereby reducing regulatory costs and financial expenditures.

Developers’ system evolution results are primarily influenced by regulation intensity, subsidy coefficient, brand income, and construction cost, with construction cost having the greatest impact on their stability strategy. Because resilient communities have significant advantages in resisting natural disasters and recovering from disasters when compared to traditional communities, the construction cost of resilient communities is much higher. When the construction cost of resilient communities is high, developers are less likely to choose to build resilient communities. On the contrary, as regulation intensity, subsidy coefficient, and brand income rise, developers will be encouraged to pursue the strategy of building resilient communities. We can encourage developers to choose to build resilient communities by increasing the intensity of regulation, improving brand revenue, and lowering construction costs. Local governments should gradually improve the relevant legal documents of resilient communities while also strengthening their own regulatory capacity in this area. Developers can publicize their brands through various channels, informing everyone about the advantages of resilient communities in disaster prevention and mitigation over traditional communities, in order to increase enterprise brand awareness. Furthermore, the government can reduce the cost of building resilient communities through loans and subsidies, as well as guide developers in transitioning from traditional to resilient communities. The government can gradually reduce subsidies for developers to build resilient communities as the development of resilient communities progresses from the primary to the mature stage.

The evolution strategy of home buyers is primarily influenced by house price, preference income, and awareness of disaster prevention and mitigation, with resilient housing prices having the greatest impact. The current development of resilient communities in China is still in its early stages, and housing prices provide consumers with the most intuitive sense of economic benefits. When compared to traditional housing, the higher cost of resilient housing may be difficult for consumers to accept. As a result, during the early stages of the development of resilient communities, the government may consider providing some subsidies to developers who build resilient communities, lowering the price of resilient housing to some extent. Secondly, we can adjust the market price of traditional community housing by increasing the deed tax that buyers must pay when purchasing new houses, forcing buyers to purchase resilient community housing. In addition, consumer awareness and comprehension of disaster prevention and mitigation will influence their strategic choices in the evolving system of resilient communities. Consumers may prefer resilient housing if they fully recognize the importance of disaster prevention and mitigation. Relevant government departments can use their own influence to demonstrate the advantages of resilient housing in the ability to withstand disasters and emergencies, as well as the ability to recover from disasters, when compared to traditional housing, and to increase home buyers’ recognition of disaster prevention and mitigation in resilient communities.

7. Conclusions

Consumers and developers should be guided to actively participate in building resilient communities so that communities can respond adequately to natural disasters and other public health emergencies. We use evolutionary games to investigate resilient community construction. We draw some conclusions of reference value for the development of resilient communities by analyzing the impact of changes in relevant parameters on the strategic choices of government, developers, and consumers.

(1)

Different initial intentions of local governments, developers, and buyers will have different outcomes. High initial intention has no effect on the system’s final evolution result, but it does affect the speed with which game players reach the evolutionary stability strategy. When developers and buyers’ initial willingness is low, regardless of whether the government regulates or not, they will choose to build and purchase traditional housing. Creating disaster reduction demonstration communities, raising public awareness of disaster prevention and mitigation, and then guiding resilience preferences and forming market drivers is an effective way to increase developers’ and home buyers’ willingness to invest.

(2)

The greater the policy benefits, the easier it is for local governments to select regulatory strategies. Increased regulatory costs will influence local governments’ regulatory strategies, and when regulatory costs exceed a certain threshold, local governments are more likely to pursue unregulated strategies. Regulatory costs have a greater impact on the evolution path of local governments than policy benefits.

(3)

Local governments should regulate and subsidize the development of resilient communities. The greater the intensity of regulation and the greater the subsidy coefficient, the more eager developers are to build resilient communities. Furthermore, when compared to subsidies, the impact of regulation intensity on the evolution path of developers is greater. An increase in brand revenue may encourage developers to build resilient communities, whereas an increase in construction costs may deter developers from doing so. Construction costs have a greater impact on developers than regulatory intensity and subsidy coefficient.

(4)

The ultimate evolutionary stabilization strategy of home buyers remains the same as traditional community housing prices, resilience preference gains, and awareness of disaster preparedness and mitigation increase, but the time to reach the evolutionary stabilization strategy becomes shorter. The rise in housing prices in resilient communities will have an effect on the system’s evolutionary stabilization strategy. When resilient community housing prices exceed a certain threshold, buyers switch from purchasing resilient housing strategies to purchasing traditional housing strategies.

This paper analyzes the impact of changing relevant parameters on the strategy selection of game players using numerical simulation and draws some preliminary conclusions that provide a scientific basis for relevant policy formulation. However, there are still some shortcomings in this paper. For example, in the development of the resilient community game model, the influence factors of the game players are not fully considered. Furthermore, this paper only considers the effect of static rewards and punishment on resilient community construction. We can consider introducing dynamic rewards and punishment for analysis in the future.