Research on Strategy Evolution of Contractor and Resident in Construction Stage of Old Community Renovation Project

Abstract

In order to improve the living environment and meet the daily needs of residents, the Chinese government is vigorously promoting the policy of old community renovation, which is closely related to the life quality and happiness of the residents. However, conflicts often occur between residents and contractors in the construction stage of old community renovation projects as a result of failing to satisfy residents’ demands. This paper uses evolutionary game theory to explore this issue. An evolutionary game model between contractor and resident is established, and then nine different strategy evolution scenarios are derived based on it. Numerical simulation is conducted to analyze the influencing factors of conflict between resident and contractor in the construction stage. It is found that construction cost, reputation, and loss caused by resident’s protest are important factors for the contractor to consider resident’s demand. Protesting cost, probability of winning the protest, and increase in benefit of winning protest exert great impact on the evolution of resident’s strategy decision on whether to protest. The paper can help to predict and affect the strategy evolution of the two parties, which will promote smooth progress of old community renovation.

1. Introduction

With the rapid development of urbanization and the improvement of living standards, old communities can no longer meet the diverse living needs of residents in China. Old communities refer to urban residential communities that have been built for a long time and are still in use with incomplete supporting facilities. There are hidden safety hazards in old communities. There are a large number of old communities in China, involving more than 40 million households [1]. According to data released by the Ministry of Housing and Urban-Rural Development, as of the end of 2019, there were nearly 160,000 old communities across China, involving more than 42 million households [2]. The Chinese government is vigorously carrying out old community renovation through government guidance, social forces participation, and market-oriented operations. At the end of 2017, the Ministry of Housing and Urban-Rural Development selected 15 cities as pilots to carry out old community renovation work. The Politburo Meeting of the CPC Central Committee was held on 17 April 2020, clearly stating that it is necessary to actively expand domestic demand; and that it is necessary to expand effective investment to implement old community renovation. On 20 July 2020, the General Office of the State Council issued the “Guiding Opinions on Comprehensively Promoting the Old Communities Renovation in Urban Areas”. The Fifth Plenary Session of the 19th Central Committee of the Communist Party of China adopted the “Proposals of the Central Committee of the Communist Party of China on Formulating the Fourteenth Five-Year Plan for National Economic and Social Development and the Long-term Goals for 2035”, which proposes to implement urban renewal actions to strengthen the renovation and community construction of old communities in cities and towns. Old community renovation has become an important measure for improving people’s housing conditions and updating urban infrastructure and public services under new urban development. Therefore, old community renovation can promote the sustainable development of communities.

In the construction stage of old community renovation projects, conflicts between residents and contractors often occur. Residents often complain to relevant departments because of old community renovation. Residents usually have different benefit demands on the old community renovation that affects their lives. If their demands are not satisfied, it will cause residents’ dissatisfaction and even conflicts. However, disorderly participation, inappropriate participation, and insufficient participation in old community renovation projects exist widely among residents, which seriously restricts the governance level of old communities. It always caused many complaints and even mass incidents [3]. For example, in the process of sponge renovation in the old city of Wuhan, the masses complained about improper disposal of construction waste [4]. Old community renovation impacts the happiness of the masses. During the promotion of the old community renovation policy, the conflicts between the contractor and the residents have received wide attention. However, previous studies rarely explored the conflict relevant issues between the resident and contractor in old community renovation projects. This study focuses on the strategy evolution of residents and contractors in the construction stage of old community renovation projects, which will help to reduce conflicts between residents and contractors.

The rest of the paper is organized as follows. Section 2 analyzes the existing studies related to old community renovation and application of evolutionary game theory in the construction industry. Section 3 mainly builds an evolutionary game model between contractor and resident in the construction stage of old community renovation project. Section 4 solves the model to obtain different scenarios of strategy evolution. Section 5 conducts numerical simulation to explore the important factors influencing mechanism on the strategy evolution of contractor and resident. Based on the main findings, Section 6 conducts in-depth discussion on the findings and puts forward some suggestions. Section 7 summarizes the paper and then proposes some policy recommendations for the government.

2. Literature Review

2.1. Literature Review on Old Community Renovation

In 1961, Jacobs [5] criticized the old city renovation model of demolition and reconstruction, and proposed that old community renovation should respect the characteristics of each old community and the diversity of residential communities. Jacobs believed renovation should be implemented in a small-scale, incremental manner. Highfield and David [6] believed that the renovation of old residential quarters according to residents’ needs and abilities was an economically feasible way to improve residents’ living conditions. Botta [7] put forward that sustainable residential renovation needed to comprehensively consider various factors such as technology, history, society, natural environment, and residents, and proposed three strategies for residential renewal including sustainable renewal, environment-friendly renewal, and prudent renewal. Weinsziehr et al. [8] found that the main factors hindering energy-saving renovation of existing buildings in aging areas included limited household income, the number of elderly people in the family, and the renovation value of old buildings.

Based on the theory of planned behavior, Li et al. [9] constructed a theoretical model on residents’ willingness to participate in governance and its influencing factors in old community renovation and conducted empirical analysis. Li and An [10] identified risk factors affecting old community renovation and introduced the entropy weight method into the grey relational analysis so as to calculate the priority of risk factors. Wang and Wang [11] analyzed the new problems facing old community renovation and put forward principles and countermeasures for these problems. Zhang et al. [12] proposed establishing a coordination mechanism of five dimensions including status quo assessment system, hierarchical response technology system, policy mechanism system, normative standard system, and capital dispatch system. Ran and Liu [13] established the analytical framework with three dimensions including “policy intervention point”, “policy type”, and “policy intervention process”, and then analyzed the central, ministerial, and local (Beijing) policies related to old residential community renovation under the framework. Xu and Xu [14] held that the introduction of social forces can effectively reduce the pressure on government fiscal expenditures and established a government-led multi-party coordination mechanism that clarified the participation conditions and income methods of social forces.

Zhang et al. [15] studied the meaning, main points, and practice of ‘+sponge’ old community renovation and conducted a case study on the Sanhe Jiayuan Community renovation project in the east area of Ningbo Airport. Li and Wang [16] analyzed the process of installing elevators for an old residential community in Guangzhou and applied collective action theory to discuss the difficulties in negotiation scale and value preference dilemma. Wang and Li [17] discussed the conflict of installing elevators for old residential buildings projects and applied deliberative role playing-based policy analysis to explore the possible solutions. Combining the characteristics of traditional property management and the problems of property management after old community renovation, Liang et al. [18] analyzed and classified the needs of old community renovation and proposed the management mode suitable for the property enterprise and the relevant property management transformation and upgrading suggestions. Ni [19] introduced the formulation and deviation analysis of the schedule management plan of the renovation project and put forward some measures to guarantee progress management of reconstruction project of old residential area.

2.2. Literature Review on Evolutionary Game Theory in the Construction Industry

Game theory is an effective tool to analyze the strategy interactions and decision making process of different parties of multiple stakeholders [20]. It has been used in various disciplines, including public policy [21], environmental [22,23,24], and transportation [25,26]. Traditional game theory often assumes players to be rational when comparing outcomes of choosing different strategies [27,28]. Evolutionary game developed from the traditional game theory and combined the essence of evolution theory. Evolutionary game theory assumes players to be boundedly rational [29,30,31,32] and allows players to adjust their strategies because of continuous learning ability [33,34,35].

Some scholars have conducted research on strategy evolution of different parties in the construction industry. Sun [36] built an evolutionary model among construction employers, workers, and government to explore the dynamic evolution of their attitudes towards vocational skills trainings. Li et al. [37] developed an evolutionary game model between the private sector and government supervision departments to study the mutual evolutionary track and the impact of public participation on both parties. Feng et al. [38] built an evolutionary game model to analyze the behavior evolution of producers in the supply chain of prefabricated construction. Zheng et al. [39] studied the BIM (Building Information Modeling) benefit sharing and stakeholders’ behaviors based on evolutionary game theory. Shi et al. [40] developed an evolutionary game to analyze the cooperative evolution relationship and its influencing factors among construction suppliers in the overall supply chain system of a construction project. Yin et al. [41] constructed three-party game models including building materials enterprises, government, building developers, and building consumers, and conducted numerical simulation to explore the multi-stage governance mechanism. Chen et al. [42] applied evolutionary game theory to study the strategic interaction between governments and developers in sponge city construction projects, and put forward some advice to encourage the developers. Yang et al. [43] built an evolutionary game model between government groups and investment groups so as to explore the strategy change of implementing green renovations. Xu et al. [44] used evolutionary game theory to analyze the collaboration of designers and contractors in building energy activities and put forward some solutions to improve collaboration between designers and contractors. Shen et al. [45] used evolutionary game theory and behavioral economics theory to explore the behavioral decision-making of stakeholders in construction and demolition waste recycling under environmental regulation. Su [46] developed an evolutionary game model among three stakeholders, including the government agency, waste recycler, and waste producer in the construction waste recycling industry and explored the decision making and stable strategies of the three parties.

In recent years, with the advancement of old community renovation policy in China, some scholars have carried out research on old community renovation. It could be seen from the above studies that the current research related to the management aspects of old community renovation mainly focused on case studies, policy analysis, renovation mode, problems faced, and countermeasures. However, in general, there were relatively few studies on quantitative analysis. Although some papers analyzed the issue from the perspective of residents, they mainly focused on resident’s willingness to participate and resident’s satisfaction. The aspect remains to be further explored in the future research. The purpose of this paper is to explore the strategy adoption and dynamic evolution of resident and contractor on whether to consider resident’s needs during the construction phase of the old community renovation. This paper will also analyze the influencing factors and influencing mechanisms that affect the strategies of both parties. The findings of this paper can help predict the strategy evolution of both parties and reduce conflicts between residents and contractors.

3. Model Establishment

3.1. Model Description

The purpose of old community renovation is to satisfy the living demands of most residents. However, considering the demands of residents may have an important impact on the cost and construction progress of an old community renovation project. The model established in this paper focused on the dynamic game between residents and contractors in the construction stage of old community renovation. In the model, the contractor can choose to consider or not to consider the demands of the resident. The resident can choose whether to protest so as to protect their own interests. When any party chooses different strategies, the benefit of the party will be different. Both parties can change their strategies over time.

3.2. Model Assumption and Establishment

Assumption 1.$I_1^A$ is assumed as the benefit that the resident can get when the resident’s demand is considered by the contractor. $I_2^A$ is assumed as the benefit of resident when the contractor does not consider resident’s demand. Old community renovation involves the adjustment in the benefit of the resident, and therefore the benefit is an important cause of conflict [47].

Assumption 2. $L_1^A$ is assumed as the resident’s loss caused by construction when the contractor considers the resident’s demand, including the expenses that the resident needs to bear, and the loss caused by various inconveniences, etc. $L_2^A$ is assumed as the loss of the resident caused by the contractor not considering resident’s demands. It can be derived from the assumption that $L_1^A<L_2^A$. Residents often need to bear certain expenses in old community renovation projects [10].

Assumption 3. $C_1^A$ is assumed as the protesting cost of the resident when the contractor considers resident’s demand and the resident chooses to protest, such as the opportunity cost caused by the time spent, litigation costs, etc. Even if the contractor considers the resident’s demand in the construction stage, the resident may be still dissatisfied. The resident may take some measures to require better solution. $C_2^A$ is assumed as the resident’s protesting cost when the contractor does not consider resident’s demand and the resident chooses to protest, such as the opportunity cost caused by the time spent, litigation costs, etc.

Assumption 4. $P_1$ is assumed as the probability that the resident will win in the protest if the contractor considers the resident’s demand. $R_1^A$ is assumed as the increase in resident’s benefit after winning the protest when the contractor chooses to consider the resident’s demand in the construction stage. $P_2$ is assumed as the probability that the resident will win in the protest when the contractor adopts the strategy of not considering the resident’s demand. $R_2^A$ denotes increase in the resident’s benefit after winning the protest when the contractor does not consider resident’s demand.

Assumption 5. $I_1^B$ is assumed as the income that the contractor can obtain when considering the resident’s demand. $I_2^B$ is assumed as the income that contractor can obtain from not considering the resident’s demand on construction. $R_1^B$ is the contractor’s benefit when the resident’s demand is considered, including reputation, benefit increase because of good reputation, etc.

Assumption 6. $C_1^B$ is assumed as the relevant cost of the contractor when the resident’s demand is considered in the construction stage of old community renovation, including construction cost, coordination cost, etc. Considering the resident’s demand often result in the increase in construction cost and coordination [10]. $C_2^B$ is assumed as the relevant cost of the contractor when the resident’s demand is not considered by the contractor in the construction stage of old community renovation.

Assumption 7. $L_1^B$ is assumed as the loss of the contractor when the contractor considers resident’s demand and the resident chooses to protest, such as coordination cost, construction delay, loss caused by violent conflicts, etc.

Assumption 8. $L_2^B$ represents the relevant loss of the contractor caused by bad performance when the resident’s demand is not considered. $L_3^B$ is assumed as the loss of the contractor when the contractor does not consider the resident’s demand and the resident chooses to protest, such as coordination cost, construction delay loss, loss caused by violent conflicts, etc. It can be known from the assumption that $L_3^B<L_1^B$.

Assumption 9. $T_1^B$ is assumed as the loss of the contractor when the resident’s demand is considered in the construction stage of old community renovation project and the resident wins in the protest. It includes the cost increase because of transforming to the other plans, and the loss compensation of the resident, etc. $T_2^B$ is assumed as the contractor’s loss when the resident’s demand is not considered and the resident wins in the protest.

Assumption 10. $x$ is assumed as the probability that the contractor chooses to consider the resident’s demand, and the probability that the contractor chooses not to consider the resident’s demand is $1-x$. Assume $y$ as the probability that the resident chooses not to protest, so the probability that the resident chooses to protest is $1-y$.

In order to help readers to understand the paper, all symbols noted in the study are summarized in

Table 1. List of symbols and meaning.

Symbols	Meaning
$I_1^A$	Benefit that resident can get when resident’s demand is considered by the contractor
$L_1^A$	Resident’s loss caused by construction when the contractor considers resident’s demand, including the expenses that the resident needs to bear, and the loss caused by various inconveniences, etc.
$C_1^A$	Protesting cost of resident when contractor considers resident’s demand and resident chooses to protest
$P_1$	Probability that resident will win in the protest when the contractor adopts the strategy of considering resident’s demand
$R_1^A$	Increase in resident’s benefit after winning protest when the contractor chooses to consider resident’s demand
$I_2^A$	Benefit that the resident can get when the contractor does not consider resident’s demand
$L_2^A$	Resident’s loss when contractor does not consider resident’s demand
$C_2^A$	Resident’s protesting cost when contractor does not consider resident’s demand and the resident chooses to protest
$P_2$	Probability that resident will win in the protest when the contractor adopts the strategy of not considering the resident’s demand
$R_2^A$	Increase in resident’s benefit after winning protest when the contractor does not consider resident’s demand on construction
$I_1^B$	Income that contractor can obtain when considering resident’s demand on construction
$C_1^B$	Contractor’s cost when the resident’s demand is considered in construction, including construction costs, coordination costs, etc.
$R_1^B$	Contractor’s benefit of considering the resident’s demand, including reputation, increase in benefit because of good reputation, etc.
$L_1^B$	Contractor’s loss when contractor considers resident’s demand and the resident chooses to protest
$T_1^B$	Contractor’s loss when resident’s demand is considered and resident wins in the protest
$I_2^B$	Income that contractor can obtain when not considering resident’s demand
$C_2^B$	Contractor’s cost when the resident’s demand is not considered in the renovation, including construction costs, coordination costs, etc.
$L_2^B$	Contractor’s loss caused by bad performance when the resident’s demand isn’t considered
$L_3^B$	Contractor’s loss when contractor does not consider resident’s demand and resident chooses to protest, such as coordination cost, construction delay loss, loss caused by violent conflicts, etc.
$T_2^B$	Contractor’s loss when resident’s demand is not considered and the resident wins in the protest
$x$	Probability that the contractor chooses the strategy of considering the resident’s demand
$y$	Probability that the resident chooses not to protest
$\overline{{\pi }_1^A}$	Resident’s expected income when the resident does not protest
$\overline{{\pi }_2^A}$	Resident’s expected income when the resident chooses to protest
$\overline{{\pi }^A}$	Whole expected income of resident
$\overline{{\pi }_1^B}$	Expected income of contractor considering resident’s demand
$\overline{{\pi }_2^B}$	Contractor’s expected income when the contractor chooses not to consider resident’s demand
$\overline{{\pi }^B}$	Whole expected income of resident

.

Figure 1 shows a tree diagram between the contractor and the resident, drawn based on the evolutionary game model.

The expected income of the contractor considering resident’s demand is assumed as $\overline{{\pi }_1^B}$. Based on the assumptions, it can be calculated that

$$\begin{array}{l}\overline{{\pi }_1^B}=y(I_1^B-C_1^B+R_1^B)+(1-y)(I_1^B-C_1^B+R_1^B-L_1^B-P_{1}T{R}_1^B)=\\ I_1^B-C_1^B+R_1^B+(1-y)(-L_1^B-P_1{T}_1^B)\end{array}$$

(1)

The contractor’s expected income when the contractor chooses not to consider resident’s demand is assumed as $\overline{{\pi }_2^B}$. Similarly, $\overline{{\pi }_2^B}$ is expressed as Equation (2).

$$\begin{array}{l}\overline{{\pi }_2^B}=y(I_2^B-C_2^B-L_2^B)+(1-y)(I_2^B-C_2^B-L_2^B-L_3^B-P_2{T}_2^B)=\\ I_2^B-C_2^B-L_2^B+(1-y)(-L_3^B-P_2{T}_2^B)\end{array}$$

(2)

The expression $\overline{{\pi }^B}$ denotes the whole expected income of contractor. It is expressed as Equation (3).

$$\begin{array}{l}\overline{{\pi }^B}=x\overline{{\pi }_1^B}+(1-x)\overline{{\pi }_2^B}=x[I_1^B-C_1^B+R_1^B+(1-y)(-L_1^B-P_1{T}_1^B)]+\\ (1-x)[I_2^B-C_2^B-L_2^B+(1-y)(-L_3^B-P_2{T}_2^B)]\end{array}$$

(3)

The replicator dynamic equation is the core of the evolutionary game model [29,48] and represents each party’s changes in the decision adoption [49,50]. The replicator dynamic equation is expressed by the change rate of probability of strategy adoption for each party. The replicator dynamic equation of the contractor can be expressed as Equation (4).

$$\begin{array}{l}F(x,y)=\frac{\mathrm{d}x}{\mathrm{d}t}=x(\overline{{\pi }_1^B}-\overline{{\pi }^B})=x(1-x)[I_1^B-C_1^B+R_1^B+(1-y)(L_3^B+\\ P_2{T}_2^B-L_1^B-P_1{T}_1^B)-I_2^B+C_2^B+L_2^B]\end{array}$$

(4)

The expected income of the resident when the resident does not protest is assumed as $\overline{{\pi }_1^A}$. It is expressed as Equation (5).

$$\overline{{\pi }_1^A}=x(I_1^A-L_1^A)+(1-x)(I_2^A-L_2^A)$$

(5)

The expected income of the resident choosing to protest is assumed as $\overline{{\pi }_2^A}$; $\overline{{\pi }_2^A}$ can be calculated according to Equation (6).

$$\overline{{\pi }_2^A}=x(I_1^A-L_1^A-C_1^A+P_1{R}_1^A)+(1-x)(I_2^A-L_2^A-C_2^A+P_2{R}_2^A)$$

(6)

The whole expected income of the resident is assumed as $\overline{{\pi }^A}$.

$$\begin{array}{l}\overline{{\pi }^A}=y[x(I_1^A-L_1^A)+(1-x)(I_2^A-L_2^A)]+(1-y)[x(I_1^A-L_1^A-\\ C_1^A+P_1{R}_1^A)+(1-x)(I_2^A-L_2^A-C_2^A+P_2{R}_2^A)]\\ =x(I_1^A-L_1^A)+(1-x)(I_2^A-L_2^A)+(1-y)[x(-C_1^A+P_1{R}_1^A)+\\ (1-x)(-C_2^A+P_2{R}_2^A)]\end{array}$$

(7)

The proportion of the resident choosing not to protest depends on the resident’s replicator dynamic equation, which is expressed as Equation (8).

$$G(x,y)=\frac{\mathrm{d}y}{\mathrm{d}t}=y(\overline{{\pi }_1^A}-\overline{{\pi }^A})=y(1-y)[x(C_1^A-P_1{R}_1^A)+(1-x)(C_2^A-P_2{R}_2^A)]$$

(8)

On the basis of Equations (4) and (8), a two-dimensional dynamic system for contractor and resident in the construction stage of old community renovation can be obtained as shown in Equation (9).

$$\{\begin{array}{l}\frac{\mathrm{d}x}{\mathrm{d}t}=x(\overline{{\pi }_1^B}-\overline{{\pi }^B})=x(1-x)[I_1^B-C_1^B+R_1^B+(1-y)(L_3^B+P_2{T}_2^B-\\ L_1^B-P_1{T}_1^B)-I_2^B+C_2^B+L_2^B]\\ \frac{\mathrm{d}y}{\mathrm{d}t}=y(\overline{{\pi }_1^A}-\overline{{\pi }^A})=y(1-y)[x(C_1^A-P_1{R}_1^A)+(1-x)(C_2^A-P_2{R}_2^A)]\end{array}$$

(9)

4. Model Solution

4.1. Local Equivalent Point Analysis

Let $\mathrm{Equation}\left(9\right)=0$, and then we can obtain five local equilibrium points for the two-dimensional dynamic system. The five local equilibrium points are E₁ (0,0), E₂ (0,1), E₃ (1,0), E₄ (1,1), and E₅ ($x^{*}$,$y^{*}$), where

$$x^{*}=\frac{-C_2^A+P_2{R}_2^A}{C_1^A-P_1{R}_1^A-C_2^A+P_2{R}_2^A}$$

(10)

$$y^{*}=1-\frac{I_2^B-C_2^B-L_2^B-I_1^B+C_1^B-R_1^B}{L_3^B+P_2{T}_2^B-L_1^B-P_1{T}_1^B}$$

(11)

It should be noted that when $0\le x^{*}\le 1$ and $0\le y^{*}\le 1$, E₅ ($x^{*}$,$y^{*}$) exists in the system; $x^{*}$ and $y^{*}$ are both probabilities. Therefore, when the above two conditions are not satisfied, E₅ ($x^{*}$,$y^{*}$) does not exist in the system. Not all the five points are equivalent stability strategy points [51,52]. According to the theory put forward by Friedman [53], the evolutionary equilibrium points can be found by analyzing the local stability of each local equivalent point based on the Jacobian matrix. The Jacobian matrix, which is derived from the two-dimensional dynamic system (as shown in Equation (9)), is expressed as Equation (12).

$$J=\left[\begin{array}{l}\frac{\partial F}{\partial x} \frac{\partial F}{\partial y}\\ \frac{\partial G}{\partial x} \frac{\partial G}{\partial y}\end{array}\right]=\left[\begin{array}{l}{a}_{11} a_{12}\\ a_{21} a_{22}\end{array}\right]$$

(12)

where

$$\begin{array}{l}{a}_{11}=(1-2x)[I_1^B-C_1^B+R_1^B+(1-x)(L_3^B+P_2{T}_2^B-L_1^B-P_1{T}_1^B)-\\ I_2^B+C_2^B+L_2^B]\end{array}$$

(13)

$$a_{12}=-x(1-x)(L_3^B+P_2{T}_2^B-L_1^B-P_1{T}_1^B)$$

(14)

$$a_{21}=y(1-y)(C_1^A-P_1{R}_1^A-C_2^A+P_2{R}_2^A)$$

(15)

$$a_{22}=(1-2y)[x(C_1^A-P_1{R}_1^A)+(1-x)(C_2^A-P_2{R}_2^A)]$$

(16)

The Jacobian matrix of each local equilibrium point has different values under different conditions. Whether a local equivalent point is ESS depends on the values of $a_{11}$, $a_{12}$, $a_{21}$, and $a_{22}$. The local equivalent points where both of the following two conditions are satisfied are ESS of the system.

$$\mathrm{tr} J=a_{11}+a_{22}<0$$

(17)

$$\det J=\left|\begin{array}{l}{a}_{11} a_{12}\\ a_{21} a_{22}\end{array}\right|=a_{11}{a}_{22}-a_{12}{a}_{21}>0$$

(18)

4.2. Strategy Stability Analysis

After analyzing the strategy stability of each local equivalent point, it is found that the evolutionary stability strategy is different when the values of parameters change in the system. The evolutionary paths are classified into nine scenarios according to the phase diagrams under different conditions.

Scenario 1. When the three conditions $C_2^A-P_2{R}_2^A<0$, $I_1^B-C_1^B+R_1^B+L_3^B+P_2{T}_2^B-$$L_1^B-P_1{T}_1^B-I_2^B+C_2^B+L_2^B<0$, and $C_1^A-P_1{R}_1^A<0$ are satisfied, ESS of the system is (0,0), namely (not consider, protest). The contractor’s strategy will evolve toward the strategy of not considering the resident’s demand, and the strategy of the resident will evolve towards the strategy of protesting.

Table 2. Stability analysis of each local equilibrium point under Scenario 1.

LEP	$\mathbf{tr}\mathit{J}$	$\mathbf{det}\mathit{J}$	Stability
(0,0)	-	+	ESS
(0,1)	Uncertain	-	Saddle point
(1,0)	Uncertain	-	Saddle point
(1,1)	+	+	Instable point
(x*,y*)	Meaningless

shows the stability analysis of each local equilibrium point under Scenario 1. According to Hofbauer and Sigmund [54], the replication dynamic phase diagram can describe the dynamic evolutionary path of the two-party game [55]. Figure 2 depicts the phase diagram of Scenario 1.

Scenario 2. When the values of parameters can meet the three conditions $C_2^A-P_2{R}_2^A<0$, $I_1^B-C_1^B+R_1^B+L_3^B+P_2{T}_2^B-$$L_1^B-P_1{T}_1^B-I_2^B+C_2^B+L_2^B<0$, and $C_1^A-P_1{R}_1^A<0$, the ESS is (0,0), namely (not consider, protest). Stability analysis of each local equilibrium point under Scenario 2 is shown in

Table 3. Stability analysis of each local equilibrium point under Scenario 2.

LEP	$\mathbf{tr}\mathit{J}$	$\mathbf{det}\mathit{J}$	Stability
(0,0)	-	+	ESS
(0,1)	Uncertain	-	Saddle point
(1,0)	+	+	Instable point
(1,1)	Uncertain	-	Saddle point
(x*,y*)	Meaningless

. Figure 3 depicts the phase diagram of Scenario 2.

Scenario 3. When the values of parameters can meet the three conditions $C_2^A-P_2{R}_2^A<0$,

$I_1^B-C_1^B+R_1^B+L_3^B+P_2{T}_2^B-L_1^B-P_1{T}_1^B-I_2^B+C_2^B+L_2^B>0$, $I_1^B-C_1^B+R_1^B-$$I_2^B+C_2^B+L_2^B<0$, and $C_1^A-P_1{R}_1^A<0$, ESS of the system is (1,0), namely (consider, protest). The strategy of the contractor will evolve toward the strategy of considering the resident’s demand. The resident’s strategy adoption will evolve towards the strategy of protesting. The resident is still dissatisfied with the construction status. Stability analysis of each local equilibrium point under Scenario 3 is shown in

Table 4. Stability analysis of each local equilibrium point under Scenario 3.

LEP	$\mathbf{tr}\mathit{J}$	$\mathbf{det}\mathit{J}$	Stability
(0,0)	Uncertain	-	Saddle point
(0,1)	Uncertain	-	Saddle point
(1,0)	0	-	ESS
(1,1)	+	+	Instable point
(x*,y*)	0	+	Central point

. Figure 4 depicts the phase diagram of Scenario 3.

Scenario 4. When all of the four conditions $C_2^A-P_2{R}_2^A<0$, $I_1^B-C_1^B+R_1^B+L_3^B+$$P_2{T}_2^B-L_1^B-P_1{T}_1^B-I_2^B+C_2^B+L_2^B>0$, $I_1^B-C_1^B+R_1^B-I_2^B+C_2^B+L_2^B<0$, and $C_1^A-P_1{R}_1^A>0$ are satisfied, there is no ESS in the system. Neither the contractor’s strategy nor the resident’s strategy will evolve toward any fixed strategy in old community renovation.

Table 5. Stability analysis of each local equilibrium point under Scenario 4.

LEP	$\mathbf{tr}\mathit{J}$	$\mathbf{det}\mathit{J}$	Stability
(0,0)	Uncertain	-	Saddle point
(0,1)	Uncertain	-	Saddle point
(1,0)	Uncertain	-	Saddle point
(1,1)	Uncertain	-	Saddle point
(x*,y*)	0	+	Central point

shows the stability analysis of each local equilibrium point under Scenario 4. Figure 5 depicts the phase diagram of Scenario 4.

Scenario 5. When the values of parameters meet the three conditions $C_2^A-P_2{R}_2^A<0$, $I_1^B-C_1^B+R_1^B-I_2^B+C_2^B+L_2^B>0$, and $C_1^A-P_1{R}_1^A<0$, the ESS of the system is (1,0), namely (consider, protest). It means that the probability that the contractor chooses to consider the resident’s demand will increase and the probability of the resident protesting will grow as well. Stability analysis of each local equilibrium point under Scenario 5 is shown in

Table 6. Stability analysis of each local equilibrium point under Scenario 5.

LEP	$\mathbf{tr}\mathit{J}$	$\mathbf{det}\mathit{J}$	Stability
(0,0)	Uncertain	-	Saddle point
(0,1)	+	+	Instable point
(1,0)	0	+	ESS
(1,1)	Uncertain	-	Saddle point
(x*,y*)	Meaningless

. Figure 6 depicts the phase diagram of Scenario 5.

Scenario 6. When the values of parameters can meet the three conditions $C_2^A-P_2{R}_2^A<0$, $I_1^B-C_1^B+R_1^B-I_2^B+C_2^B+L_2^B>0$, and $C_1^A-P_1{R}_1^A>0$, the ESS is (1,1), namely (consider, not protest). The strategy of the contractor will evolve toward considering the resident’s demand. The strategy of the resident will evolve towards the strategy of not protesting. Stability analysis of each local equilibrium point under Scenario 6 is shown in

Table 7. Stability analysis of each local equilibrium point under Scenario 6.

LEP	$\mathbf{tr}\mathit{J}$	$\mathbf{det}\mathit{J}$	Stability
(0,0)	Uncertain	-	Saddle point
(0,1)	+	+	Instable point
(1,0)	Uncertain	-	Saddle point
(1,1)	-	+	ESS
(x*,y*)	Meaningless

. Figure 7 depicts the phase diagram of Scenario 6.

Scenario 7. When the three conditions $C_2^A-P_2{R}_2^A>0$, $I_1^B-C_1^B+R_1^B+L_3^B+P_2{T}_2^B-$$L_1^B-P_1{T}_1^B-I_2^B+C_2^B+L_2^B<0$, and $C_1^A-P_1{R}_1^A>0$ are all satisfied, the ESS of the system is (0,1), namely (not consider, not protest). The contractor’s strategy will evolve toward the strategy of not considering the resident’s demand. The resident’s strategy will evolve towards the strategy of not protesting.

Table 8. Stability analysis of each local equilibrium point under Scenario 7.

LEP	$\mathbf{tr}\mathit{J}$	$\mathbf{det}\mathit{J}$	Stability
(0,0)	Uncertain	-	Saddle point
(0,1)	-	+	ESS
(1,0)	+	+	Instable point
(1,1)	Uncertain	-	Saddle point
(x*,y*)	Meaningless

shows the stability analysis of each local equilibrium point under Scenario 7. Figure 8 depicts the phase diagram of Scenario 7.

Scenario 8. When the values of parameters can satisfy the four conditions $C_2^A-P_2{R}_2^A>0$, $I_1^B-C_1^B+R_1^B+L_3^B+P_2{R}_2^A-L_1^B-P_1{R}_1^A-I_2^B+C_2^B+L_2^B>0$, $I_1^B-C_1^B+R_1^B-$$I_2^B+C_2^B+L_2^B<0$, and $C_1^A-P_1{R}_1^A>0$, the ESS of the system is (0,1), namely (not consider, not protest). The strategy of the contractor will evolve toward the strategy of not considering the resident’s demand. The probability of the resident will evolve towards the strategy of not protesting. The stability analysis of each local equilibrium point under Scenario 8 is presented in

Table 9. Stability analysis of each local equilibrium point under Scenario 8.

LEP	$\mathbf{tr}\mathit{J}$	$\mathbf{det}\mathit{J}$	Stability
(0,0)	+	+	Instable point
(0,1)	-	+	ESS
(1,0)	Uncertain	-	Saddle point
(1,1)	Uncertain	-	Saddle point
(x*,y*)	Meaningless

. Figure 9 depicts the phase diagram of Scenario 8.

Scenario 9. When the values of parameters can meet the three conditions $C_2^A-P_2{R}_2^A>0$, $I_1^B-C_1^B+R_1^B-I_2^B+C_2^B+L_2^B>0$, and $C_1^A-P_1{R}_1^A>0$, the ESS of the system is (1,1), namely (consider, not protest). The probability that the contractor considers the resident’s demand will grow in the construction stage of the old community renovation project. The strategy of not protesting will be adopted more by residents. Stability analysis of each local equilibrium point under Scenario 9 is shown in

Table 10. Stability analysis of each local equilibrium point under Scenario 9.

LEP	$\mathbf{tr}\mathit{J}$	$\mathbf{det}\mathit{J}$	Stability
(0,0)	+	+	Instable point
(0,1)	Uncertain	-	Saddle point
(1,0)	Uncertain	-	Saddle point
(1,1)	-	+	ESS
(x*,y*)	Meaningless

. Figure 10 depicts the phase diagram of Scenario 9.

5. Numerical Simulation of Important Influencing Factors

In order to further study how the important factors influence the strategy evolution of contractor and resident, a numerical example is conducted using MATLAB 2014a.

5.1. Influence of $C_1^B$ on strategy evolution of the contractor

Set $C_1^A$ = 0.5 thousand yuan, $P_1$ = 0.2, $R_1^A$ = 5 thousand yuan, $C_2^A$ = 4 thousand yuan, $P_2$ = 0.6, $R_2^A$ = 12 thousand yuan, $I_1^B$ = 80 thousand yuan, $R_1^B$ = 1 thousand yuan, $L_3^B$ = 2 thousand yuan, $L_1^B$ = 0.5 thousand yuan, $I_2^B$ = 78 thousand yuan, $C_2^B$ = 50 thousand yuan, $L_2^B$ = 0.2 thousand yuan, $T_1^B$ = 6 thousand yuan, $T_2^B$ = 18 thousand yuan, and the initial point (0.5, 0.5); $C_1^B$ denotes the construction cost of considering the resident’s demand. The influence of $C_1^B$ on the strategy evolution of the contractor in the old community construction is shown in Figure 11. When $C_1^B$ is set as 55 thousand yuan or 60 thousand yuan, the contractor’s strategy evolves towards the strategy of considering the resident’s demand. When $C_1^B$ is set as 65, the contractor’s strategy evolves toward not considering the resident’s demand. The reason is because the increase in the construction cost of considering the resident’s demand makes the net income of the contractor become lower. When considering the resident’s demand, the contractor must spend more time in collecting the demands of many residents and then communicate with residents whose demands may be different from or opposed to each other. The construction cost of considering the resident’s demand is much higher than that of not considering resident’s demand. Figure 11 proves that the high cost of considering the resident’s demand reduces the willing of the contractor to consider the resident’s demand in old community renovation.

5.2. Influence of $R_1^B$ on strategy evolution of the contractor

Set $C_1^A$ = 0.5 thousand yuan, $P_1$ = 0.2, $R_1^A$ = 5 thousand yuan, $C_2^A$ = 4 thousand yuan, $P_2$ = 0.6, $R_2^A$ = 12 thousand yuan, $I_1^B$ = 78 thousand yuan, $C_1^B$ = 60 thousand yuan, $L_3^B$ = 2 thousand yuan, $L_1^B$ = 0.5 thousand yuan, $I_2^B$ = 78 thousand yuan, $C_2^B$ = 48 thousand yuan, $L_2^B$ = 0.2 thousand yuan, $T_1^B$ = 6 thousand yuan, $T_2^B$ = 18 thousand yuan, and the initial point (0.5, 0.5). Figure 12 depicts the strategy evolution of the contractor when $R_1^B$ is set as 0, 1.5, and 3 thousand yuan. Strategy adoption of the contractor evolves towards the strategy of not considering resident’s demand when the value of $R_1^B$ is set as 0 and 1.5 thousand yuan. The strategy evolution of the contractor changes to the strategy of considering the resident’s demand when $R_1^B$ grows to 3 thousand yuan. If the reputation effect is considered in the decision on the construction plan, the contractor may change the strategy adoption in the old community renovation construction. Reputation has become an important factor for enterprises. Considering the resident’s demand will earn good reputation for the contractor, which may also help the contractor to take more similar projects in the future. When the reputation and relevant benefit become larger, the possibility of contractor considering resident’s demand will be higher.

5.3. Influence of $L_3^B$ on strategy evolution of the contractor

Set $C_1^A$ = 0.5 thousand yuan, $P_1$ = 0.2, $R_1^A$ = 5 thousand yuan, $C_2^A$ = 4 thousand yuan, $P_2$ = 0.6, $R_2^A$ = 12 thousand yuan, $I_1^B$ = 78 thousand yuan, $C_1^B$ = 62 thousand yuan, $R_1^B$ = 4 thousand yuan, $L_1^B$ = 0.5 thousand yuan, $I_2^B$ = 78 thousand yuan, $C_2^B$ = 48 thousand yuan, $L_2^B$ = 0.2 thousand yuan, $T_1^B$ = 6 thousand yuan, $T_2^B$ = 16 thousand yuan, and the initial point (0.5, 0.5). Figure 13 depicts the strategy evolution of the contractor when $L_3^B$ increases from 1 thousand yuan to 5 thousand yuan. The strategy evolution of the contractor changes from not considering the resident’s demand to the strategy of considering the resident’s demand. When residents find the construction of old community renovation does harm to their benefits, they may take actions to protest the construction. Disputes and violent fights often occur in the construction period, which will affect the construction progress. The development of social media makes it accessible for residents to browse and publish posts online. A lot of residents may express their dissatisfaction online, which exerts a negative impact on the contactor’s reputation and may thus reduce future income of the contractor. When the contractor’s loss caused by resident’s protest becomes larger, the contractor will be more inclined to consider the resident’s demand.

5.4. Influence of $C_2^A$ on strategy evolution of the resident

Set $C_1^A$ = 0.5 thousand yuan, $P_1$ = 0.2, $R_1^A$ = 5 thousand yuan, $P_2$ = 0.3, $R_2^A$ = 15 thousand yuan, $I_1^B$ = 80 thousand yuan, $C_1^B$ = 68 thousand yuan, $R_1^B$ = 1 thousand yuan, $L_3^B$ = 2 thousand yuan, $L_1^B$ = 0.5 thousand yuan, $I_2^B$ = 78 thousand yuan, $C_2^B$ = 43 thousand yuan, $L_2^B$ = 0.2 thousand yuan, $T_1^B$ = 6 thousand yuan, $T_2^B$ = 16 thousand yuan, and the initial point (0.5, 0.5). Figure 14 depicts the strategy evolution of the resident when the value of $C_2^A$ is set as 4, 5, 6 thousand yuan. It can be easily seen that the increase of $C_2^A$ makes the strategy evolution result of the resident change from “protest” to “not protest”. The increase of $C_2^A$ means that the resident needs to pay a higher cost to protest the construction that does not consider the resident’s demand. When it is difficult for residents to protest, the protesting cost will be larger. For example, the relevant law and regulations are not sufficient or the residents do not know how to protest. It proves that the high cost (including the relevant time and money) reduces the resident’s willing to protest.

5.5. Influence of $R_2^A$ on strategy evolution of the resident

Assume $C_1^A$ = 0.5 thousand yuan, $P_1$ = 0.2, $R_1^A$ = 5 thousand yuan, $C_2^A$ = 4 thousand yuan, $P_2$ = 0.3, $I_1^B$ = 80 thousand yuan, $C_1^B$ = 68 thousand yuan, $R_1^B$ = 1 thousand yuan, $L_3^B$ = 2 thousand yuan, $L_1^B$ = 0.5 thousand yuan, $I_2^B$ = 78 thousand yuan, $C_2^B$ = 43 thousand yuan, $L_2^B$ = 0.2 thousand yuan, $T_1^B$ = 6 thousand yuan, $T_2^B$ = 16 thousand yuan, and the initial point (0.5, 0.5). As shown in Figure 15, when $R_2^A$ grows from 12 thousand yuan to 20 thousand yuan, the strategy evolution of the resident changes from not protesting to protesting. The reason is that an increase of $R_2^A$ represents the construction of old community renovation that does not consider the resident’s demand will seriously damage the resident’s benefit, so they are strongly opposed to the renovation plan. Therefore, they will make more effort to protest the construction. When the residents believe they can obtain much more benefit from winning the protest, they will be determined to prevent the contractor from neglecting their demands.

5.6. Influence of $P_2$ on strategy evolution of the resident

Set $C_1^A$ = 0.5 thousand yuan, $P_1$ = 0.2, $R_1^A$ = 5 thousand yuan, $C_2^A$ = 4 thousand yuan, $R_2^A$ = 12 thousand yuan, $I_1^B$ = 80 thousand yuan, $C_1^B$ = 68 thousand yuan, $R_1^B$ = 1 thousand yuan, $L_3^B$ = 2 thousand yuan, $L_1^B$ = 0.5 thousand yuan, $I_2^B$ = 78 thousand yuan, $C_2^B$ = 43 thousand yuan, $L_2^B$ = 0.2 thousand yuan, $T_1^B$ = 6 thousand yuan, $T_2^B$ = 16 thousand yuan, and the initial point (0.5, 0.5). Figure 16 depicts the change in the strategy evolution of the resident when the value of $P_2$ is set as 0.3, 0.5, and 0.7. It can be seen in Figure 16 that the resident’s strategy evolution result changes from the strategy of not protesting to the strategy of protesting. The increase in $P_2$ means that the possibility of the resident winning the protest becomes higher. When residents think the possibility of winning the protest is larger, they will be more willing to take actions to hinder the construction that does not consider the residents’ demands. Otherwise, when the residents think the possibility that they win the protest is very small, they will be inclined not to protest. It proves that the possibility of winning the protest is also an important factor influencing the strategy evolution of residents.

6. Discussion

It was found in Section 5 that the strategies of both parties evolve towards different results under different conditions. The conflict between the contractor and resident depends on the strategy adoption of both parties. Construction cost, reputation, and loss caused by the resident’s protest are important factors for the contractor to consider the resident’s demand. Protesting cost, probability of winning the protest, and an increase in the benefit of winning the protest exert great impact on the resident’s strategy evolution. Construction cost [10], resident’s benefit [47], and resident’s cost [10] have been proven to be important in old community renovation. However, the previous studies did not explore the strategy evolution of the contractor and the resident in old community renovation projects. Here are some suggestions for contractors and residents.

The contractor should fully communicate with the residents living in the community before construction in order to understand most residents’ demands in advance. Important issues should be publicized online or in the community for a period before construction. In this way, the residents can understand the community renovation in advance, which can reduce unnecessary conflicts in the construction stage. In the event of conflicts between the contractors and the residents, contractors should try their best to avoid violent conflicts and do good job of coordination. The contractors can cooperate with community management staff to explain to the residents in detail. If the contractors choose not to consider residents’ demands to save cost and time, it may lead to residents’ protest during the construction period.

Residents should be concerned about the posts and announcements in the community. In old community renovation projects, residents should actively put forward their demands to the relevant departments and contractors as soon as possible. When a resident’s demand cannot be satisfied, he should learn to take the legal measures to protect his own interests rather than solve it by force. Learning the laws and regulations related to old community renovation can help residents know whether their demands are reasonable and whether they will be protected by law. When there are conflicting demands among different residents, the residents also need to consider from the perspective of most residents’ interests and understand the relevant laws and regulations. Through the efforts of both parties, the occurrence of conflicts can be effectively reduced.

In urban renewal projects in other countries, there were some conflicts caused by residents’ protests, which made these projects face much controversy. Some scholars [5,6,7] in other countries also believed that residents’ demands are very important in urban renewal projects. The results of this study also have certain significance for other countries. (1) The proportion of residents protesting is higher when the residents’ interests are seriously damaged in renovation projects. Therefore, important needs for residents should be given high priority. (2) When the renovation plan affects the interests of many residents, large-scale protests may occur because of residents’ serious dissatisfaction. (3) In some countries with relatively unsound legal systems, or areas where residents do not know much about the laws and regulations, residents are more likely to take violent actions in order to protect their own interests. The above findings can help other countries reduce the occurrence of residents’ protests in urban renewal projects.

7. Conclusions

Old community renovation is an important action that the Chinese government has been vigorously promoting in recent years, with the purpose of making the functions of old communities meet the living needs of residents. In the old community renovation projects, the resident is a critical participant, and the resident’s demands are important factors that the contractor needs to consider in the construction stage. However, disputes and even violent conflicts often occur between contractors and residents in old community renovation projects [3], which have a negative impact on the progress of old community renovation. This paper explored the dynamic strategy evolutions of resident and contractor in the construction stage of old community renovation. The findings of the paper will help predict the strategy evolutions of contractor and resident and reduce conflicts between the two parties. An evolutionary game model between the contractor and the resident was developed to explore the strategy evolution of the both parties. Evolutionary stability strategy of the model was obtained and discussed. Finally, a numerical simulation was carried out to study the influencing mechanism of important factors. The main findings in the papers include: (1) Under different conditions, the evolutionary stability strategies of the contractor and the resident are different to a large extent. (2) As for the contractor, construction cost, reputation, and loss caused by resident’s protest are important factors for the strategy evolution of the contractor when making decisions on considering the resident’s demand. (3) Protesting cost, probability of winning the protest, and increase in benefit of winning the protest are important factors influencing the strategy evolution of the resident when making decision on whether to protest. The government can use the model established in the paper to predict the strategy evolution of the contractor and the resident in old community renovation and take some measures to change the values of key influencing factors with the purpose of reducing conflicts between the contractors and the residents. Based on these findings, the following policy recommendations are put forward for the government.

• The relevant laws and regulations related to old community renovation should be further improved, including attracting social capital investment by using PPP (Public -Private-Partnership) mode, addressing different residents’ demands, developing dispute resolution mechanisms, etc. Community management staff should fully play a coordinating role between residents and contractors.
• The governments should encourage and organize residents to learn about laws and regulations related to old community renovation. On one hand, it can help residents to take legal measures to protect their own interests when their rights are violated. On the other hand, it helps residents know whether their demands are reasonable and predict the probability of winning when filing a lawsuit, which can avoid unnecessary conflicts.
• There should be an effort to strengthen the management of a contractor with a bad reputation. These efforts could include establishing relevant reputation management mechanisms to impose penalties on the contractor or placing the contractors on a blacklist when quality problems or other serious problems caused by the contractors are discovered. It will have a certain impact on its future earnings of contractors.
• The government can further enhance public participation in the process of formulating the renovation plan, so that residents can understand the difficulties faced by the government in the renovation process. It can help the government to obtain residents’ understanding in advance and thus reduce possible conflicts.

The main contributions of this paper lie in the following aspects. (1) The paper develops an evolutionary game model on conflicts between contractor and resident in the construction stage of old community renovation projects, which helps to understand strategy evolution on whether the contractors will consider residents’ demands and whether the residents will protest. It also helps to predict the strategy evolution of both parties. (2) It conducts in-depth exploration on the influencing factors and the influencing mechanisms that affect the strategy evolution of contractors and residents. The findings can be applied to predict and affect the strategy evolution trend of contractors and residents. (3) Based on the main findings, the paper put forwards suggestions for residents, contractors, and the government. It can further help to reduce the conflicts between the two parties, thereby promoting smooth progress of old community renovation.