Risk Perception Thresholds and Their Impact on the Behavior of Nearby Residents in Waste to Energy Project Conflict: An Evolutionary Game Analysis

Abstract

In China, waste to energy (WTE) projects are currently considered the best choice for dealing with municipal solid waste (MSW), but their siting often leads to conflicts. The perceptions of proximate residents to the changes and uncertainty induced by WTE projects are the main reasons for such conflicts. Determining the indicators used to measure these changes is crucial for an evaluation of surrounding residents’ risk perception. One indicator is residents’ risk perception thresholds. Our paper employs evolutionary game theory to deduce the risk perception threshold of surrounding residents related to a WTE project, which provides a novel contribution to the literature. The results of a case study and simulations show that the level of the risk perception threshold has a crucial effect on the behavior choices of surrounding residents. Two important parameters that affect the value of this risk perception threshold are possible economic compensation and possible resistance costs. A change to the values of these two parameters can change the value of the risk perception threshold of nearby residents. If the change in the risk perceived by surrounding residents is lower than the threshold they can tolerate, they will accept construction of the project. However, if surrounding residents are worried about this risk fluctuating as a result of construction of the plant, they will behave more cautiously and conservatively, and if the possible risk exceeds the threshold that they are willing to tolerate, then they will boycott the plan and protest against the construction of the project. In this case, the surrounding residents will still show restraint. This study tries to provide a theoretical and practical basis for effective resolution by government of the public’s risk concerns and existing or imminent conflicts.

1. Introduction

Recent urbanization developments in China have resulted in the production and disposal of many tons of municipal solid waste (MSW). According to Ministry of Housing and Urban-Rural Development of China data, MSW volumes in China increased from 163.96 million t in 2011 to 235.12 million t in 2020, an average annual growth rate of about 4%. Harmless disposal of MSW increased from 130.90 million t in 2011 to 234.52 million t in 2020, an average annual growth of about 7%. Rapidly developing Chinese cities are facing severe problems related to waste disposal. Harmless disposal of MSW in the Chinese context includes mainly sanitary landfill and incineration, alongside some other methods, with incineration being the optimal means of disposing of MSW. Incineration both reduces the MSW and provides electric power for China’s cities. It is less harmful to the environment than sanitary landfill and is widely considered the most promising and preferred solution to disposing of MSW in China [1]. Official statistics show that China’s incineration capacity increased from 25.99 million t in 2011 to 146.08 million tin 2020, an average annual growth rate of about 21%, while China’s demand for waste to energy (WTE) facilities increased from 109 in 2011 to 463 in 2020, an average annual growth rate of about 17%. As China’s urbanization increases, MSW will also increase, which will require more WTE facilities.

WTE plants cause environmental pollution and are subject to NIMBYism [2]. NIMBYism is demonstrated by residents in the surrounding area who adopt a protectionist attitude and take measures to resist and protest against the construction of an unwelcome facility near their homes [3]. Accidents at WTE facilities have a negative effect on real estate values, generate toxic gases, and cause air and noise pollution and other risks [4,5,6]. WTE plants can have serious adverse effects on the life and health of surrounding residents which results in their siting and construction being opposed by these residents. Conflicts over the construction and operation of WTE projects in China first emerged in 2009 with the Beijing Asuwei anti-WTE incident which occurred in that year, followed among others by the Qingyuan Fenshui anti-WTE incident in 2012, the Zhejiang Yuhang anti-WTE incident in 2014, the Qingyuan Shili anti-WTE incident in 2017, and the Zhongshan Jiufeng anti-WTE incident in 2019. Research by Maria [7] shows that in most cases, unpopular projects are either abandoned or are realized only after modifications demanded by the local community. Resistance from the public and especially from residents living closest to a facility has continuously hindered government efforts to implement reasonable plans that satisfy the needs of the urban environment; this has resulted in keenness from policymakers to identify the specific causes of conflicts and propose methods or measures to resolve these conflicts effectively.

Scholars from a range of disciplines have used a range of different perspectives to study NIMBY conflicts, which include those related to WTE projects. Most of this work focuses on two main aspects: the causes and governance of conflicts, and the evolutionary mechanism of the conflicts. The causes of conflicts and their governance have been the subject of much scholarly research focused on allocation of costs and benefits [8], spatial distance [9], decision-making mode [10], psychological cognitive [11], and risk perception [12,13]. There is a consensus that this last element is a critical influencing factor and decisive for the public’s reaction to a risk event [14,15]. This applies especially to the context of WTE facilities; numerous empirical studies provide evidence of the critical role of risk perception [16,17,18].

Conflict is a type of game, and games involve the interaction of game participants’ behaviors. Research in this area mainly analyzes the behavior interactions among the parties involved in a conflict, and several studies employ evolutionary game theory to study conflict behavior interactions [19,20]. Conflicts over WTE projects in China often involve the local government and surrounding residents, which constitutes a game between these two parties.

Much current work ignores the important role of risk perception, and those studies that do acknowledge the critical role of risk perception do not propose a method for calculating changes in the risk perception of surrounding residents. We suggest that the fluctuation in and uncertainty linked to the risk perception of surrounding residents are the main reasons for WTE project-related conflicts. This makes it important to determine the level of this fluctuation.

To fill the research gap, this study aims to apply evolutionary game theory to determine the value of residents’ risk perception thresholds, and to discuss how surrounding residents’ behaviors evolve, including in relation to their risk perception threshold. The aim is to propose a theoretical and practical basis for effective resolution by government or responsible agencies of the public’s risk concerns and existing or imminent conflicts.

The remainder of the paper is organized as follows: Section 2 reviews the relevant literature; Section 3 describes the model and calculates the risk perception threshold value; Section 4 presents a stability analysis; Section 5 describes the numerical simulations; and Section 6 concludes the paper with a discussion.

2. Literature Review

2.1. Research on the Causes of Conflict and Its Governance

The causes of conflict and the governance of conflict have been studied in depth. Some of the earliest work in this area assumes that the main reason for conflict is unfairness caused by the unbalanced distribution of regional interests and local costs related to location of the facility and also assumes that such conflicts can be alleviated by the offer of appropriate economic compensation for residents who will experience some economic loss [8,21,22,23]. A factor common to unpopular facility sitings is spatial distance. Furuseth and O’Callaghan [9] studied the location of municipal waste incinerators and showed that the shorter the distance between the plant and people’s homes, the greater their level of opposition. However, in the context of the siting of wind turbines in the Wadden region Wolsink’s [24] survey locations show that attitudes to their location were unrelated to proximity. A Swedish attitude study of green power confirms the lack of correlation between people’s attitudes and distance from the project [25]. Lin et al.’s [6] study of the relationship between waste incinerators and residents’ risk perceptions, attitudes, and avoidance behaviors shows that residents’ risk perceptions and attitudes are unaffected by distance. It seems that what matters for successful facility site selection might be the type of facility rather than the spatial distance from residents [26].

Some studies suggest that conflict is related mainly to top-down unilateral decision-making [10] which tends to exclude the public or allow their involvement at too late a stage [27,28]. Siting assessments that do not involve public consultation are perceived as unfair by the local community, and such top-down unilateral decisions tend to lead to social conflicts and delayed or cancelled projects [29]. It has been argued that public participation would allow the bureaucracy to be more responsive to public concerns and could facilitate conflict resolution [30]. Those that are against involvement of the public argue that the general population lacks the relevant expertise, and their involvement could increase administrative complexity and reduce decision-making efficiency [31]. There is a strand of work which focuses on public trust in government, and a common theme in these studies is that lack of trust in the government results in the commitment of residents to oppose the construction of facilities [13]. However, there is empirical evidence showing that there is no direct relationship between public trust and residents’ attitudes [12,23].

Some quite recent research suggests that conflict stems from cognitive bias [11], and the biased public values of stakeholders in the facility planning process [32]. The key to resolving conflict lies in effective communication of risk and management of cognitive bias. The study by Wu and Li [33] conclude that anxiety is the main reason for conflict and propose that conflict governance should focus on reducing anxiety among residents. There are other emotional factors which can strengthen and promote conflict events and accelerate their development and evolution [34]. Kojola [35] found that decisions about mining developments were controversial due to their resonance with people’s emotional meaning of place. Zhang and Tong [36] analyzed the causes of conflict at both the individual and group levels and found that conflict is neither emotional catharsis nor an inevitable result of simple economic injustice. They show that different types of nimbyism display different characteristics and different mechanisms. Some studies suggest that the rapid development of social media has accelerated diffusion of online rumors and that this is intensifying social conflicts and nimbyism [37].

There is a major stream of research showing that the main reason why people oppose the construction of unpopular facilities is their perception of the risks implied [13,14] (Flynn et al., 1992; Slovic et al., 1991), including concern over declining property values [38]. Johnston et al. [14] and Lindell and Perry [15] believe that risk perception is the main cause of public reaction to a risk event. The general public tends to overestimate the risks when assessing the effect of facilities on their living area [9]. Song et al. [39] show that a major obstacle to nuclear energy as a decarbonization policy is the public’s perception of the risk of nuclear radiation leaks from reactors. Residents oppose the location of nuclear reactors in their community because they overestimate the risk related to these facilities. In the context of WTE facilities, Furuseth and O’Callaghan [9] argue that concerns over health and the environment, and economic loss promote strong opposition to incinerators. Incineration of waste is controversial, but debate tends to focus on the environmental and health risks rather than the economic and waste reduction benefits [40]. Ren et al. [16] studied a WTE plant in Shanghai and found that local residents were most concerned about the risks to their health, and that anxiety about compensation was lower than among residents living at a greater distance from the facility. Hou et al. [17] conducted an empirical study of the acceptance of WTE projects; hierarchical regression analysis showed that institutional trust is a crucial factor affecting social acceptance, but anti-WTE plant sentiment has indirect effects through risk perception. Liu et al. [18] believe that environmental impact assessments play an important role in the siting of WTE facilities and enhance public acceptance of WTE projects by reducing the perceived risks. It would seem that in the context of WTE projects risk perception is a critical factor which affects the attitudes and behaviors of proximate residents and that conflicts related to WTE projects can be reduced through appropriate assessment and consideration of the risk perception of these residents [41].

2.2. Research on the Mechanisms of Evolutionary Conflict

Conflict is a type of game, and games involve interaction between the behaviors of game participants. Research in this area mainly analyzes the behavior interactions among the parties involved in a conflict, in order to study the causes of players’ behaviors and how they evolve. Kang and Du [42] draw on stakeholder theory to conduct theoretical analysis and scenario simulations related to the roles and functions of stakeholders related to polluting NIMBY facilities. Eguchi [43] studied NIMBY conflicts employing a two-person normal form game and showed that residents either experience a prisoner’s dilemma or a war of attrition, which leads to the emergence of a NIMBY conflict. These studies are all based on traditional game theory which assumes that people are completely rational. However, information limitations and other factors mean that in reality, people cannot be completely rational in their decision-making. To try to overcome the shortcomings of traditional game theory, Smith and Price [44] proposed evolutionary game theory. This is founded on the hypothesis of individual bounded rationality, considers the group as the research object, and believes that real life individual decision-making is based on dynamic processes, such as imitation, learning, and mutation among individuals [45]. Evolutionary game theory is particularly suited to studying boundedly rational group behavior. It has been applied by many scholars to enable interactive study of conflict behavior. Liu and Chen [46] studied the co-evolutionary mechanism of nimbyism from the perspective of co-evolution of information dissemination and a benefit game, and conducted simulation analysis under various information parameter scenarios. Xu et al. [19] focused on participants’ emotions and constructed an evolutionary game model between polluting NIMBY enterprises and the proximate population, and analyze the impact on the evolution of the conflict events and the different emotional states of the two parties. Chen et al. [20] exploited evolutionary game theory to construct a stochastic evolutionary construction company game which included the nearby population, to model a risk-aggregate NIMBY conflict and simulate and analyze the strategic behavior chosen by the parties. Yu [47] conducted a numerical simulation analysis on the evolution of the behaviors of the parties involved in an evolutionary game model, which included local government and the local community and demonstrations of emotional catharsis. Tian and Han [48] studied conflict related to a negotiation decision-making model using evolutionary game theory; they analyzed the negotiations related to two WTE projects.

In summary, the causes and governance of NIMBY conflicts has been studied by numerous disciplines from different perspectives, and this strand of work provides rich results. This strand of work shows that risk perception is a critical and highly valued influencing factor which is unanimously recognized. The literature does not provide a method for calculating the risk perception threshold values of surrounding residents. This study tries to fill this gap by applying evolutionary game theory to construct a behavior choice game involving local government and those residents nearest to the WTE project. We try to determine the value of residents’ risk perception thresholds and conduct a case study and numerical simulation to analyze the interaction between and the specific evolution mechanisms used by the two parties in the game. We also discuss the evolution of surrounding residents’ behaviors relative to their risk perception thresholds.

3. Model Construction and Analysis of Risk Perception Threshold

3.1. Research Hypotheses

In a conflict game involving WTE plant site selection and construction, the two parties involved are local government and surrounding residents. Both are subject to bounded rationality. Under the condition of information asymmetry and limited resources, each makes behavior choices based on its own current benefits. As the decision maker, local government has two possible behavior choices related to site selection and plant construction: not relocation, and relocation. The surrounding residents also have two choices: to accept the plant, and to protest against it.

We propose the following basic hypotheses:

Hypothesis 1.

Construction of the WTE plant would result in reductions to, recycling of, and risk-free MSW which would provide social benefits for local government and are denoted$R$ . At the same time, construction of the plant would involve acquisition of a large area of land and sizeable economic compensation which we denote $E$ . Although local residents might be offered appropriate compensation, construction of the WTE plant would have some effects on health, daily life, and the economy which represent the risk loss, denoted $D·i$, where $i$ is the increased risk in the local area caused by the plant construction and $0<i<1$ .

Hypothesis 2.

If nearby residents demonstrate opposition and resistance to the plant, local government can choose to relocate the plant, which will require more acquisition of land and will incur a cost$F$ , which could result in loss of local government credibility, denoted $S$ . Resistance and protect from the proximate residents could result in a cost, denoted $C$ , which includes punishment by local government.

Hypothesis 3.

If local government decides to stand firm and continues construction of the plant on the original site, this could incite fierce resistance from residents. In the face of severe conflict and to avoid greater social risks, local government might try to negotiate with nearby residents. This negotiation could involve certain demands on the part of the residents, such as compensation, which we denote$M.$In the case that the local government agrees to pay the levels of compensation proposed by the surrounding residents, then$\theta$, $0<\theta <1$Again, the local government will suffer loss of credibility, denoted$\left(1+p\right)S$where$0<p$, and the surrounding residents will also incur a higher cost, denoted$\left(1+r\right)C$where$0<r$.

Hypothesis 4.

In the initial state, the proportion of local government not choosing relocation behavior is denoted$x$where$0\le x\le 1$, and the proportion choosing relocation behavior is denoted$1-x$ . The proportion of surrounding residents choosing acceptance behavior is denoted $y$ where $0\le y\le 1$ , and the proportion choosing resistance is denoted $1-y$.

Table 1. Payoff matrix for a game between the local government and surrounding residents.

Players		Surrounding Residents
		Acceptance	Resistance
Local government	Not relocation	$R-E, E-iA$	$R-E-\theta M-\left(1+p\right)S, E-iA-\left(1+r\right)C+\theta M$
	Relocation	$R-F,$0	$R-F-S,-C$

presents the payoff matrix of both of the parties to the game, based on the above assumptions and analysis of both parties’ behavior choices.

3.2. Model Construction

One of the most common models of learning in evolutionary games is the replicator dynamic equation, in which the proportional rate of growth among a group of players adopting a particular strategy is a strictly increasing function of the difference between the pure strategy utility and the group’s average expected utility [44]. The growth rate of the strategy is equal to its relative fitness. As long as the fitness of the individual who adopts the strategy is higher than the average fitness of the group, the strategy will grow over time. We propose an evolutionary strategic behavior game involving local government and nearby residents, using the replicator dynamic equation. In the context of our theoretical analysis, the evolutionary game replicator dynamic equation for the strategic behavior of the participants in a conflict over a WTE plant is written as:

$$\dot{\theta }=d\theta \left(t\right)/dt=\theta \left(t\right)\times \left(u-\overline{u} \right)$$

(1)

where $\theta \left(t\right)$ is the proportion of participants who choose a certain strategy, $\dot{\theta }=d\theta \left(t\right)/dt$ is the rate of growth in the proportion of participants choosing a certain strategy at time $t$, $u$ is the payoff derived from choosing a particular strategy, and $\overline{u}$ is the group’s average or the expected average payoff. The replicator dynamic equation model of local government and surrounding residents is derived from combining the payoff matrix presented in Table 1 with the replicator dynamic Equation (1).

The expected payoff for a local government which chooses not to relocate ${\Psi }_1$, and the expected payoffs from choosing relocation behavior ${\Psi }_2$, and the average expected payoff from choosing some other behavior $\overline{\psi }$, can be written as:

$${\Psi }_1=R·y+\left[R-E-\theta M-\left(1+p\right)S\right]·\left(1-y\right)$$

$${\Psi }_2=\left[R-F\right]·y+\left(R-F-S\right)·\left(1-y\right)$$

$$\overline{\psi }={\Psi }_1·x+{\Psi }_2·\left(1-x\right)$$

Then, based on Equation (1), the replicator dynamic equation for local government choosing not to relocate is:

$$\dot{x}=dx/dt=x·\left(1-x\right)·\left[(F-E-\theta M-pS)+y\left(\theta M+pS\right)\right]$$

(2)

and the replicator dynamic equation for the surrounding residents’ choice to adopt acceptance behavior is:

$$\dot{y}=dy/dt=y·\left(1-y\right)·\left[C-x\left(\theta M-rC\right)\right]$$

(3)

Equations (2) and (3) form an evolutionary game model which describes the interaction between the behaviors of local government and surrounding residents in a conflict over a WTE plant:

$$\{\begin{array}{c}\dot{x}=dx/dt=x·\left(1-x\right)·\left[(F-E-\theta M-pS)+y\left(\theta M+pS\right)\right] \\ \dot{y}=dy/dt=y·\left(1-y\right)·\left[C-x\left(\theta M-rC\right)\right] \end{array}$$

(4)

3.3. Risk Perception Threshold

Analysis of the risk perception threshold requires some examination and discussion of the relationship between some of the important variables.

3.3.1. Relationships among the Variables

(1)

Between $M$ and $i$. Parameter $M$ encompasses the various demands of local residents, including compensation. These demands are related to residents’ opposition to the WTE plant. Local government may choose to negotiate with the residents likely to be affected in order to allow the plant to go ahead. If residents’ perceived risk is higher, their demands and levels of compensation will also be higher. The relationship between $M$ and $i$ will be positive and takes the following functional form:

$$M=E·h·i$$

(5)

In Equation (5), $h$ is a constant and satisfies $0<h<1$.

(2)

The value $\theta$. The value of $\theta$ refers to the probability of residents benefiting from negotiations with the local government. It is affected by the attitude of surrounding residents and their past experience of negotiation and conflict with the local authority. If the surrounding residents do not adopt a tough stance, the probability of successful negotiation will be higher. Observation of negotiations over previous NIMBY projects are likely to induce a more robust response and demand for higher levels of compensation which the local government might find impossible to meet. The probability of successful negotiation will be relatively low, and we assume $0<\theta <0.5$.

3.3.2. Calculation of Risk Perception Threshold

To calculate the risk perception threshold, we substitute Equation (5) into Equation (3) to obtain:

$$\dot{y}=dy/dt=y·\left(1-y\right)·\left[C-x\left(\theta hi·E-rC\right)\right]$$

(6)

To calculate the level of the risk perception threshold which would affect the behavior choice of surrounding residents, we consider the two cases of Equation (6):

(1)

If $\dot{y}>0$.

Let $x=0$, then $\dot{ y}=dy/dt=y·\left(1-y\right)·C$, and $\dot{y}>0$ must be satisfied. If local government chooses relocation behavior, the best behavior choice for the surrounding residents is to accept this decision.

Let $x=1$, then $\dot{ y}=dy/dt=y·\left(1-y\right)·\left[C-\theta hi·E+rC\right]$. In order to satisfy $\dot{y}>0$, the condition $C-\theta hi·E+rC>0$ must also be satisfied and is derived from further sorting: Equation (7).

If $\dot{ y}>0$, then regardless of the local government’s behavior choice, the behavior choice of surrounding residents will always be acceptance. The risk perception threshold for the surrounding residents to adopt acceptance behavior is:

$$i<\left(1+r\right)C/\theta hE$$

(7)

(2)

If $\dot{y}<0$.

Let $x=0$, then $\dot{ y}=dy/dt=y·\left(1-y\right)·C$, and the condition $\dot{y}<0$ cannot be satisfied; if the local government chooses relocation behavior, surrounding residents will be unable to resist this decision.

Let $x=1$, then $\dot{ y}=dy/dt=y·\left(1-y\right)·\left[C-\theta hi·E+rC\right]$, and in order to satisfy $\dot{y}<0$, the condition $C-\theta hi·E+rC<0$ must be satisfied, and can be derived by further sorting Equation (8).

If $\dot{y}<0$ then no matter which behavior local government chooses, the surrounding residents’ behavior choice will always be resistance. The risk perception threshold for surrounding residents to resist is:

$$i>\left(1+r\right)C/\theta hE$$

(8)

From Equations (7) and (8), we can obtain that the risk perception threshold which affects the behavior choices of surrounding residents is:

$$i=\left(1+r\right)C/\theta hE$$

(9)

4. Stability Analysis of the Parties’ Behavior Choices

The previous analysis shows that Equation (4) is an evolutionary game model which describes the behavior interactions of both the parties in a conflict over a WTE plant. Friedman [49] showed that the stability of the equilibrium point in Equation (4) can be obtained from stability analysis of the Jacobian matrix. The general form of the Jacobian matrix is:

$$J=\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right)=\left(\begin{array}{cc}\frac{\partial \dot{x}}{\partial x}& \frac{\partial \dot{x}}{\partial y}\\ \frac{\partial \dot{y}}{\partial x}& \frac{\partial \dot{y}}{\partial y}\end{array}\right)$$

(10)

when, if Equation (4) satisfies the determinant $D=\mathit{det}\left(J\right)=a_{11}{a}_{22}-a_{12}{a}_{21}>0$ and the trace $T=tr\left(J\right)=a_{11}+a_{22}<0$, the equilibrium point in Equation (4) will become an evolutionary stable strategy (ESS) point.

From Equation (10), we can derive the specific values of the Jacobian matrix elements $a_{11}, a_{12}, a_{21}, a_{22}$ at each equilibrium point in Equation (4). To facilitate the analysis, let $U=F-E$, $V=\theta M+pS$, $W=\theta M-rC$, and substitute them in Equation (4).

Table 2. The specific value of the Jacobian matrix element at the equilibrium point.

Equilibrium Point	${\mathit{a}}_{11}$	${\mathit{a}}_{12}$	${\mathit{a}}_{21}$	${\mathit{a}}_{22}$
(0,0)	$U-V$	0	0	$C$
(0,1)	$U$	0	0	$-C$
(1,0)	$-\left(U-V\right)$	0	0	$C-W$
(1,1)	$-U$	0	0	$-\left(C-W\right)$

presents the values of each element.

According to the Jacobian matrix stability analysis method, the stability under the two scenarios $i<\left(1+r\right)C/\theta hE$ and $i>\left(1+r\right)C/\theta hE$ can be analyzed, and lead to some important propositions.

Scenario 1.

If$i<\left(1+r\right)C/\theta hE$.

Proposition 1.

In this scenario, if①, this satisfies the parameter$U>V$; if②, this satisfies the parameter$0<U<V$and there is a unique ESS point in Equation (4) which is a pure strategy equilibrium point (1,1).

Proof. 

Under condition ① or ②, the evolution phase diagrams of Equation (4) are as depicted in Figure 1 and Figure 2, where the direction of the arrows indicates that the pure strategy equilibrium point (1,1) is the ESS point. The results of the Jacobian matrix stability analysis presented in

Table 3. Jacobian matrix stability analysis under condition ① or ②.

Equilibrium Point	${\mathit{a}}_{11}$	${\mathit{a}}_{12}$	${\mathit{a}}_{21}$	${\mathit{a}}_{22}$	$\mathit{det}\left(\mathit{J}\right)$	$\mathit{t}\mathit{r}\left(\mathit{J}\right)$	Stability Results
(0,0)	+/−	0	0	+	+/−	+/uncertain	unstable point/saddle point
(0,1)	+	0	0	−	−	uncertain	saddle point
(1,0)	−/+	0	0	+	−/+	uncertain/+	saddle point/unstable point
(1,1)	−	0	0	−	+	−	ESS point

show that only the pure strategy equilibrium point (1,1) satisfies the determinant $D=\mathit{det}\left(J\right)>0$ and the trace $T=tr\left(J\right)<0.$ This is the ESS point in Equation (4) and proves Proposition 1. □

Proposition 2.

In this scenario, if③, the parameter$U<0$is satisfied, there is a unique ESS point in Equation (4), which is the pure strategy equilibrium point (0,1).

Proof. 

Under condition ③, the evolution phase diagram of Equation (4) is as depicted in Figure 3 where the direction of the arrows indicates that the pure strategy equilibrium point (0,1) is the ESS point. The results of the Jacobian matrix stability analysis which are presented in

Table 4. Jacobian matrix stability analysis under condition ③.

Equilibrium Point	${\mathit{a}}_{11}$	${\mathit{a}}_{12}$	${\mathit{a}}_{21}$	${\mathit{a}}_{22}$	$\mathit{det}\left(\mathit{J}\right)$	$\mathit{t}\mathit{r}\left(\mathit{J}\right)$	Stability Results
(0,0)	+	0	0	+	+	+	unstable point
(0,1)	−	0	0	−	+	−	ESS point
(1,0)	−	0	0	+	−	uncertain	saddle point
(1,1)	+	0	0	−	−	uncertain	saddle point

show that only the pure strategy equilibrium point (0,1) satisfies the determinant $D=\mathit{det}\left(J\right)>0$ and the trace $T=tr\left(J\right)<0.$ This is the ESS point in Equation (4) and proves Proposition 2. □

Scenario 2.

If$i>\left(1+r\right)C/\theta hE$.

Proposition 3.

In this scenario, if④, then parameter$U>V$ is satisfied, and there is a unique ESS point in Equation (4) which is the pure strategy equilibrium point (1,0).

Proof. 

Under condition ④, the evolution phase diagram of Equation (4) is depicted in Figure 4, where the direction of the arrows indicates that the pure strategy equilibrium point (1,0) is the ESS point. The results of the Jacobian matrix stability analysis are presented in

Table 5. Jacobian matrix stability analysis under condition ④.

Equilibrium Point	${\mathit{a}}_{11}$	${\mathit{a}}_{12}$	${\mathit{a}}_{21}$	${\mathit{a}}_{22}$	$\mathit{det}\left(\mathit{J}\right)$	$\mathit{t}\mathit{r}\left(\mathit{J}\right)$	Stability Results
(0,0)	+	0	0	+	+	+	unstable point
(0,1)	+	0	0	−	−	uncertain	saddle point
(1,0)	−	0	0	−	+	−	ESS point
(1,1)	−	0	0	+	−	uncertain	saddle point

and show that only the pure strategy equilibrium point (1,0) satisfies the determinant $D=\mathit{det}\left(J\right)>0$ and the trace $T=tr\left(J\right)<0.$ This is the ESS point in Equation (4) and proves Proposition 3. □

Proposition 4.

In this scenario, if⑤, then parameter$U<0$is satisfied and there is a unique ESS point in Equation (4) which is the pure strategy equilibrium point (0,1).

Proof. 

Under condition ⑤, the evolution phase diagram of Equation (4) is depicted in Figure 5, where the direction of the arrows indicates that the pure strategy equilibrium point (0,1) is the ESS point. The results of the Jacobian matrix stability analysis are presented in

Table 6. Jacobian matrix stability analysis under condition ⑤.

Equilibrium Point	${\mathit{a}}_{11}$	${\mathit{a}}_{12}$	${\mathit{a}}_{21}$	${\mathit{a}}_{22}$	$\mathit{det}\left(\mathit{J}\right)$	$\mathit{t}\mathit{r}\left(\mathit{J}\right)$	Stability Results
(0,0)	+	0	0	+	+	+	unstable point
(0,1)	−	0	0	−	+	−	ESS point
(1,0)	−	0	0	+	−	uncertain	saddle point
(1,1)	+	0	0	−	−	uncertain	saddle point

and show that only the pure strategy equilibrium point (0,1) satisfies the determinant $D=\mathit{det}\left(J\right)>0$ and the trace $T=tr\left(J\right)<0.$ This is the ESS point in Equation (4) and proves Proposition 4. □

Proposition 5.

In this scenario, if ⑥, then parameter$0<U<V$is satisfied and Equation (4) does not contain an ESS point.

Proof. 

Under condition ⑥, the evolution phase diagram of Equation (4) is depicted in Figure 6 where the direction of the arrows indicates the absence of an ESS point. The results of the Jacobian matrix stability analysis are presented in

Table 7. Jacobian matrix stability analysis under condition ⑥.

Equilibrium Point	${\mathit{a}}_{11}$	${\mathit{a}}_{12}$	${\mathit{a}}_{21}$	${\mathit{a}}_{22}$	$\mathit{det}\left(\mathit{J}\right)$	$\mathit{t}\mathit{r}\left(\mathit{J}\right)$	Stability Results
(0,0)	−	0	0	+	−	uncertain	saddle point
(0,1)	+	0	0	−	−	uncertain	saddle point
(1,0)	+	0	0	−	−	uncertain	saddle point
(1,1)	−	0	0	+	−	uncertain	saddle point

and show that there is no pure strategy equilibrium point which satisfies the determinant $D=\mathit{det}\left(J\right)>0$ and the trace $T=tr\left(J\right)<0.$ There is no ESS point in Equation (4) which proves Proposition 5. □

5. Numerical Simulation Analysis

To further verify and analyze the behavior interaction process and the specific evolution mechanisms of local government and surrounding residents in a conflict over a WTE plant, we conduct numerical simulation analysis of the evolutionary interaction between the parties’ behaviors. We also introduce an additional parameter $k$ and make $k=C/E$; the value of $E$ generally tends to be larger than the value of $C$, so we also assume that $0<k<1$. We set the relevant parameter values at the beginning of simulation, and the results are based on computer simulations. According to Equation (4), there is a total of 10 parameter values which were set based on theoretical analysis. We set the relevant parameter values as follows: $r=0.5$, $\theta =0.3$, $h=0.6$, $k=0.01$, $p=0.5$, $F=12$, $S=2$. We used Matlab software (2016a version) to perform the simulations, whose results are depicted in Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11. By substituting the relevant parameter values into Equation (9) we obtain the value of the surrounding residents’ risk perception threshold:$i=\left(1+r\right)C/\theta hE\approx 8.3\%$. If the fluctuation in risk perception is greater than the threshold, the surrounding residents will adopt resistance behavior, and otherwise they will adopt acceptance behavior. A more intuitive explanation for the specific evolution mechanism governing the interaction between local governments and the surrounding residents’ behaviors in a conflict context is obtained by studying the underlying theory using the case of the Guangzhou Panyu WTE plant incident.

5.1. Description of the Case and Collection of Data

The Guangzhou Panyu WTE plant conflict occurred in 2009 when the Guangzhou Municipal Government announced a WTE plant project and issued a notification of the intention to construct the WTE plant in Panyu district. The plant would be designed to have a daily processing capacity of 2000 t of MSW and was scheduled to be completed and become operational in 2010. News of the plan spread rapidly among those living near to the site, and as a result of internet searches residents learned that WTE plants produced dioxins and other harmful gases which could cause serious harm to people’s health. The announcement of the plan to construct a WTE plant began to affect house prices in the proximate communities. On hearing about the WTE project, some owners immediately put their properties up for sale and received prices of between USD 9241 and USD 10,781 lower than previous valuations. News of the decline in house prices in the area began to be reported by the national CCTV station.

Before the proposed plant construction was announced, the average price of real estate in neighborhoods surrounding the proposed WTE plant site was around USD 1078/${\mathrm{m}}^2$. The average dwelling in the area was between 80 ${\mathrm{m}}^2$ and 90 ${\mathrm{m}}^2$. Based on the data available and preliminary calculation, the presence of a WTE plant would reduce housing prices by about 10%, while messages left by netizens suggested that this reduction could be as much as 30%. Real estate agents experienced a drop in transactions of almost 20%.

We use the impact of construction of the WTE plant on surrounding housing prices as an indicator of surrounding residents’ risk perception. We assume that construction of the WTE plant would increase this risk threshold by about 10%—higher than the 8.3% threshold calculated previously for surrounding residents. Based on our theoretical findings, since the fluctuation in the risk perception of surrounding residents exceeds the threshold, they will adopt resistance behavior. In order to identify the specific evolution mechanism, we conduct simulation analysis to consider the development specific to this case to test the theory. Before beginning the simulation, we set the following three sets of parameter values: (1) $U=2, ($2) $U=1$, (3) $U=-2$. The starkest difference among these three value sets is the difference in the value of parameter $U$. If $U=2$, the parameter $U>V$ is satisfied, if $U=1$, the parameter $0<U<V$ is satisfied, and if $U=-2$, the parameter $U<0$ is satisfied. In order to demonstrate the specific evolution mechanism involved, we assume that the local government’s initial behavior choice is not relocation, which gives a behavior proportion for local government of $x$ which is close to 1, and a behavior proportion of $y=0.5$ for surrounding residents choosing acceptance. We assume that the fluctuation in surrounding residents’ risk perceptions is 10%.

5.2. Model Validation

We can identify three stages in the Guangzhou Panyu WTE plant conflict: conflict, stalemate, and relocation. In what follows we analyze the specific evolution processes related to these three stages.

Stage 1: Conflict

News of the planned construction of the Guangzhou Panyu WTE plant spread rapidly among nearby residents who all began to consult the internet to obtain more information on the consequences. The amount of negative information they found increased unease among surrounding residents who began to express this through various forms of protest. These protests tended to be relatively rational, and many took the form of inquiries to and petitioning of relevant government departments; at this stage, there were no large-scale demonstrations. These early protests and petitions were ignored by local government, which instead held a press conference where it declared its determination to forge ahead with the project. The lack of response to what local residents considered were reasonable demands of local government, combined with the local government’s seemingly tough stance added fire to the attitudes of surrounding residents. They organized more extreme protests, and as a collective body confronted the relevant government departments and officials. The numbers of protesters eventually ran to thousands. Some wore masks, some wore homemade cultural shirts, and some carried boards bearing anti-WTE slogans. They also chanted slogans, sang the Chinese national anthem, and gathered en masse at the gates to the local city hall. As the numbers of petitioners grew, the numbers of police trying to control them also increased. The police were not armed and aimed only at trying to disperse the crowd. At this stage, the outcome was resistance and not relocation. Figure 7 depicts the results of the numerical simulation analysis of the group (1) parameter, which show the harsh attitude adopted by local government and the not relocation behavior choice. The final behavior outcome of surrounding residents was resistance but the evolution towards this behavior was slower; surrounding residents were initially relatively restrained and passive. The outcomes of this stage for both parties (1,0) were not relocation and resistance which is consistent with Proposition 3 and with what happened at the time.

Figure 7. Evolution of the parties’ behaviors for $i=10\%$, $U=2$.

Figure 7. Evolution of the parties’ behaviors for $i=10\%$, $U=2$.

Stage 2: Stalemate

The strength and growth of the protests from surrounding residents were noted by various news media, and this led to the involvement of higher-level government and demands for local government to communicate more fully with and pay attention to the demands of nearby residents. The protests and demands were such that local government was unable to deal with the situation, and it agreed to suspend construction of the project. Local government then focused on preventing the demonstrations from getting out of control and embarked on a series of discussions and negotiations with local residents. Two years later, there was no resolution to the situation and no agreement about where the WTE plant should be sited, and the case entered the stalemate stage. Figure 8 presents the results of the numerical simulation analysis of the group (2) parameter, which show that the system was in constant oscillation. Neither of the parties was able to achieve a stable ESS point—the surrounding residents continued to display resistance and local government continued to keep changing its proposals. This result is consistent with Proposition 5 and also with what happened in reality.

Figure 8. Evolution of the parties’ behaviors for $i=10\%$, $U=1$.

Figure 8. Evolution of the parties’ behaviors for $i=10\%$, $U=1$.

Stage 3: Relocation

In 2011, local government held a press conference to discuss “comprehensive waste treatment in Panyu”, and experts from the Guangzhou Urban Planning and Design Institute presented a revised plan for dealing with Panyu’s waste. The local government proposed five alternative sites for the construction of a WTE plant, with final site selection to be determined based on extensive discussion and public consultation, Environmental Impact Assessment reports, and expert demonstrations. In July 2012, following consultations that extended for nearly three years, it was agreed and announced that the WTE plant would be relocated to the equipment base in Darang Town, Panyu district, and the residents most affected agreed to this choice. The final outcome was relocation and acceptance. Figure 9 presents the results of the numerical simulation analysis of the group (3) parameter and shows that the final result is (0,1), which is consistent with Proposition 4 and what actually happened in this case.

Figure 9. Evolution of the parties’ behaviors for $i=10\%$, $U=-2$.

Figure 9. Evolution of the parties’ behaviors for $i=10\%$, $U=-2$.

The evolution process depicted in Figure 9 shows that local government’s original insistence and dictatorial behavior was resisted by surrounding residents who felt they would be put at risk. This is represented by the strategic proportion line for surrounding residents. These residents initially converged towards resistance which led to local government choosing compromise, which converged in relocation behavior.

A limitation of our theoretical analysis is that the proportion of surrounding residents who converged to resistance is quite small. In the real-life case, after the media became involved, the proportion of residents that were opposed to the plant was over 93% but the simulation results show that the proportion of the surrounding population that converged towards resistance behavior was less than 60%, well below the actual proportion. This difference is due to our estimate of the risk perception threshold (8.3%) which was perhaps overly pessimistic. It is possible that the actual risk perception threshold of local residents was over 10%. Although the survey results show that 93% of the local residents objected to the plant it is possible that not all of this 93% took part in the protests. If only 50% of them participated in the demonstrations, this would produce a value that is close to the results of our theoretical analysis.

5.3. Theoretical Model Verification and Analysis for $i<\left(1+r\right)C/\theta hE$

Our case analysis supports the evolution mechanism and the results for the behavior interaction between the two players if $i>\left(1+r\right)C/\theta hE$. We next analyze the specific evolution mechanism and results of the behavior interaction if $i<\left(1+r\right)C/\theta hE$, and assuming $i=5\%$. We consider the following situations:

(1)

We set the relevant parameter to $U=1$, and to demonstrate the specific evolution mechanism, we assume that the initial behavior choice of the surrounding residents is resistance and set the behavior proportion $y$ to a value very close to 0, and that the proportion of local government choosing not to relocate is $x=0.5$. Figure 10 presents the simulation results which show that at the beginning of the game, the resistance behavior of the surrounding residents fosters the tendency for local government behavior to converge towards relocation. The high cost of relocation and the small perceived risk of the surrounding residents fosters convergence towards acceptance by local residents. Local government persistence causes a gradual convergence towards acceptance, and a final result of (1,1). This is consistent with Proposition 1. When the risk caused by construction of the plant was lower than the surrounding residents’ risk perception threshold and despite lack of local government response to all of the residents’ requirements and demands for compensation, negotiation and better communication by local government, the proposal was eventually accepted. The time taken to reach this position was long and the final outcome required a high level of persistence from the local government.

Figure 10. Evolution of the parties’ behaviors for $i=5\%$, $U=1$.

Figure 10. Evolution of the parties’ behaviors for $i=5\%$, $U=1$.

(2)

We set the relevant parameter to $U=-2;$ we assume that the initial behavior choice of surrounding residents is resistance and set the behavior proportion $y$ to a value very close to 0. The initial behavior choice of the local government is not relocation, therefore we set the behavior proportion $x$ to a value very close to 1. Figure 11 presents the simulation results which show that although the respective behaviors of the parties at the beginning of the game are not relocation and resistance, over time their choices change, and the final evolution result is (0,1). This is consistent with Proposition 2 and suggests that initiative and decision-making power are stronger for local government than for the surrounding residents. Although the fluctuation in the risk caused by the plant is lower than the surrounding residents’ risk perception thresholds, residents are still worried about the plant and will continue to demonstrate cautious and conservative behavior.

Figure 11. Evolution of the parties’ behaviors for $i=5\%$, $U=-2$.

Figure 11. Evolution of the parties’ behaviors for $i=5\%$, $U=-2$.

6. Conclusions, Implications and Limitations

6.1. Conclusions and Discussion

The causes of NIMBY conflicts, including those related to WTE projects, have been studied by numerous scholars from different perspectives. Previous studies either ignore the critical role of risk perception [6,8,10,11,12,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37] or emphasize its role, but do not propose methods or indices for calculating and measuring changes in the risk perception of surrounding residents [13,14,16,17,18,39,40,41]. We suggest that the risk perception threshold is a good indicator for determining changes in the risk perception of surrounding residents. This study provides a first application of evolutionary game theory to derive the risk perception threshold of surrounding residents in relation to a WTE project. We tested our theory by studying a real case and conducting simulation analysis. We found that the risk perception threshold has a crucial effect on the behavior choices of surrounding residents. If the fluctuation in the risk perceived by local residents from the construction of the plant is lower than the level of risk that residents can tolerate, then surrounding residents will choose to accept construction of the plant. If the risk fluctuation caused by the plant exceeds the level of risk that surrounding residents can tolerate, they will resist construction of the plant.

Two important parameters that affect the risk perception threshold of surrounding residents are possible economic compensation and possible resistance costs. The risk perception threshold is correlated negatively to economic compensation and positively to the resistance cost. The negative relationship between the risk perception threshold and economic compensation shows that increasing the economic compensation paid to the surrounding residents will reduce the value of their risk perception threshold, while reducing the economic compensation will increase the value of their risk perception threshold. A possible explanation for this is that excessive compensation may induce the public to link the project with serious risk and health and other consequences which will increase their risk threshold. Previous studies provide empirical proofs of a negative correlation between risk perception and benefit perception [50,51,52], which are consistent with our research results. Appropriate financial compensation can alleviate conflict to some extent [8,21,22,23]; excessive economic compensation may not necessarily be effective for resolving surrounding residents’ risk concerns and conflicts, especially in relation to facilities that the public considers dangerous or of dubious legality [21]. In some cases, residents are more interested in reassurances about safety and security rather than compensation [53]. Unusually high compensation offers can anger residents who see them either as attempts to bribe them to make them withdraw their objections [54] or as indicating that the project in question is extremely risky.

The positive relationship between risk perception thresholds and surrounding public resistance costs shows that increasing the resistance costs of surrounding residents will increase the level of their risk perception thresholds, and that correspondingly reducing the resistance costs will reduce the level of their risk perception thresholds. It is possible that the negative impact on residents’ daily lives of a high level of the resistance costs may be similar to the effect on their lives of the proposed project which results in a higher tolerance of risk fluctuations. A level of compensation that is perceived as too low will cause the public to lose trust in the local government and will increase the risk tolerance threshold of surrounding residents to fluctuations in the risk. A low cost of resistance may make the public trust less in local governments, making surrounding residents unable to tolerate a high-risk changes. Conflicts over the construction and operation of WTE projects in China are frequent. In line with a policy of maintaining social harmony and stability, local governments often make unprincipled compromises in relation to public resistance. This might reduce the level of conflict over the short term but will increase the public’s distrust of local government [55], which acts in turn to increases the public’s perception of risk [56] and ultimate acceptance of the project. This is the NIMBY dilemma related to “project-protest-discontinuation” [48].

If the fluctuation in the risk perceived by local residents from the construction of the plant is lower than the level of risk that residents can tolerate, then the surrounding residents will choose to accept the construction of the plant. However, despite this lower than the risk perception threshold of the risk fluctuation, the speed of convergence of surrounding residents towards acceptance behavior is relatively slow. This might be because there is continuing concern over the plant which results in more cautious and conservative behavior. If the risk fluctuation caused by the plant exceeds the level of risk that surrounding residents can tolerate, they will resist construction of the plant. In this case, although the risk fluctuation caused by the plant exceeds the risk perception threshold, the speed of convergence of surrounding residents towards resistance behavior will be relatively slow. This may be because the surrounding residents are more willing to express their objections through relatively rational means, such as communication, and then show restraint.

6.2. Implications

Recent urbanization developments in China have resulted in the production and disposal of many tons of MSW which will require more WTE facilities. WTE facilities cause environmental pollution and have serious adverse effects on the life and health of surrounding residents, which results in their siting and construction being opposed by these residents. It is clear that effective resolution by government or responsible agencies of the publics’ risk concerns and existing or imminent conflict is a determining factor in the success and sustainable development of WTE projects in China. These are issues which must be addressed by all levels of government.

Based on our analysis and findings we suggest that to resolve conflicts related to WTE projects, the following measures should be considered. First, better communication of information on the risks to local residents and respect for guarantee of the public’s right to be involved in discussion and decision making.

Promises of high levels of financial compensation risk being perceived as bribery and can fuel rather than reduce conflict. Surrounding residents may be more concerned about safety and health rather than compensation, which means that offers of compensation from the local government must be appropriate and considered.

Local governments should not resort to unprincipled means to try to quell conflicts. Ultimately, such actions will increase both the public’s distrust of local government and their risk perception level related to the project. Compromise may be effective in the short term but is not conducive to resolving conflict over the long run. Local government should penalize unreasonable boycotts and protests in accordance with what is legal, which will work to increase the costs of resistance.

6.3. Limitations

This paper provides a theoretical investigation of the risk perception threshold of residents over the construction of a WTE plant. We showed that the value of their risk perception threshold is affected by economic compensation and the cost of public resistance, and that residents’ resistance costs are correlated positively with their risk perception threshold. Our findings should be confirmed by more empirical research which considers other influencing factors, including residents’ risk thresholds.