Discrete Dynamics in Nature and Society

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Complex Evolutionary Games in Enterprise Carbon Emission Reduction

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Volume 2021 |Article ID 5560671 | https://doi.org/10.1155/2021/5560671

Liwen Chen, Mengjia Zhang, Shiwen Zhao, "Game Analysis of the Multiagent Evolution of Existing Building Green Retrofitting from the Perspective of Green Credit", Discrete Dynamics in Nature and Society, vol. 2021, Article ID 5560671, 19 pages, 2021. https://doi.org/10.1155/2021/5560671

Game Analysis of the Multiagent Evolution of Existing Building Green Retrofitting from the Perspective of Green Credit

Academic Editor: Junhai Ma
Received20 Feb 2021
Accepted02 Jun 2021
Published16 Jun 2021

Abstract

Existing building green retrofitting can reduce building energy consumption and greenhouse gas emissions, which is conducive to the sustainable development of the construction industry. The financing dilemma of the existing building green retrofitting hinders the large-scale development of green retrofitting in China. This paper establishes the perceived payoff matrix and evolutionary game model of the government, Energy Service Companies (ESCOs), banks, and owners. Through simulation analysis, the primary factors affecting the choice of game strategy and the stable strategy under different conditions are discussed. The results show that the strategic choices of the government, ESCOs, banks, and owners influence each other in the two game models. Government regulations will have an impact on the strategic choices of ESCOs, banks, and owners. The owners’ strategy choice is closely related to the perceived benefits and costs of retrofitting. Based on the results, corresponding suggestions are proposed to provide theoretical support for the development of the existing building green retrofitting market.

1. Introduction

In recent years, environmental and energy issues related to the construction industry have become the focus of worldwide attention [1]. With the rapid urbanization process, the number of buildings in China has also increased. A large part of these buildings are high-energy-consuming buildings, leading to large amounts of energy consumption and carbon emissions. As a result, China’s building energy consumption ranks second in the world, and its residential energy consumption ranks first [2]. This is not conducive to China’s goal of achieving its carbon peak by 2030 and achieving carbon neutrality by 2060 [3, 4]. The existing building green retrofitting is one of the main methods to reduce the energy consumption and carbon emissions of existing buildings [5]. It is generally accepted that green retrofitting can generate greater environmental benefits with lower costs and a higher utilization rate and thus achieve the sustainable development of the economy, society, and environment [6]. The Chinese government regards the existing building green retrofitting as an important energy policy and has adopted a series of measures to strenuously promote its development [7]. However, the implementation of green retrofitting requires a large amount of funds [8], and financing difficulties seriously hinder the implementation of this policy [9]. In particular, as one of the most important stakeholders in the market, energy service companies (ESCOs) are facing a financing dilemma that hinders the large-scale development of the existing building green retrofitting in China.

In China, bank credit is the most important external financing source for enterprises [10]. As an emerging industry, the scale of most ESCOs in China is still small, and they do not have strong financing capacities. Moreover, green retrofitting is generally not attractive to investors [11], which makes it difficult for ESCOs to obtain financing [12]. This is the key challenge to realizing the large-scale development of existing building green retrofitting [13]. The implementation of green credit policy provides new financing opportunities for ESCOs. However, the financial system is inherently complex [14], implementing green credit will result in incremental costs for banks and affect their financial performance, and the overall proportion of investment and loans to green projects by financial institutions is still low [15]. Therefore, green credit is still unable to play an effective role in the development of ESCOs.

In addition, existing studies on green credit mainly focus on the financing of the green supply chain [16], green technology innovation [17], and banks’ performance [18]. There is little research on the impact of green credit implementation on ESCOs. Considering the current research status, this study explored the ESCO financing problem in green retrofitting and examined the influencing factors for the large-scale development of the green retrofitting market by constructing an interactive evolutionary game model of the government, ESCOs, banks, and existing building owners.

The remainder of the paper is structured as follows. The second part reviews the relevant literature and provides the main points of this paper. The third part proposes the corresponding hypotheses, constructs the three-party interactive evolutionary game model of the government, ESCOs, banks, and existing building owners, and analyzes it. The fourth part uses MATLAB to conduct the simulation analysis using the related data. The fifth part provides the conclusion and suggestions.

2. Literature Review

Green retrofitting is the retrofitting of existing buildings, including architectural design, components, and operations, to make existing buildings more environmentally friendly [19]. Although the implementation of green retrofitting is of great significance to improving environmental problems, the lack of funds has been a major obstacle to the implementation of retrofitting. In terms of financing barriers, the financing obstacles faced by green retrofitting include a lack of initial capital investment [20] and difficulty in obtaining loans or third-party financing for the ESCO industry in some countries [21]. In addition, Zhang et al. [13] found that, unlike other developing countries and emerging economies, more substantial obstacles do not exist at the system policy level, but at the meso- and microlevels of operation in China. Many scholars have conducted research on how to solve the financing problem of green retrofitting. Wang et al. [9] proposed a new financing principle model by improving the income-cost analysis method. Brown et al. [22] developed a housing retrofitting financing mechanism with the characteristics of capital sources and financial instruments. Liu et al. [7] found that the use of the EPC mode in building green retrofitting can solve the problems of insufficient funds and low efficiency in building retrofitting to a certain extent. He et al. [8] demonstrated through empirical research that the SEU financing mechanism can be an effective business model that supports building retrofitting. Economidou et al. [23] established a professional financing platform as an effective way to enhance the confidence of other participants. Guo et al. [24] analyzed the effectiveness evaluation content of the operation of the building energy-saving retrofitting financing platform from the two levels of the operating mechanism and the behavior of the operating subject. Existing scholars have conducted in-depth research on how to solve the financing problem of green retrofitting. However, most of these studies focus on financing models. Since green retrofitting involves multiple stakeholders, the coordination of interests between the participants is the key to improving financing. Therefore, analyzing the behavioral decisions of each participant in different situations is helpful in obtaining the best behavioral decision to balance the interests of all participants.

The evolutionary game provides an effective method for studying behavioral decision making. Evolutionary game theory is based on bounded rationality with groups as the research objects. It is believed that individual decision making is realized in the dynamic process of imitation, learning, and mutation [25]. Some scholars have used evolutionary games to study the related issues of the existing building green retrofitting. Liang et al. [26] analyzed three usage scenarios through evolutionary games and clarified the reasons why direct decision makers are unwilling to participate in green retrofitting projects. Liu et al. [27] established a cooperative game model and discussed the difference between noncooperative scenes and cooperative scenes and the influence of the parameters in the model. Through evolutionary game analysis, Yang et al. [28] revealed the game strategy changes in government groups and investment groups to encourage and implement green retrofitting.

Compared with the traditional classical game, the evolutionary game considers the bounded rationality of the decision maker, but it still objectively constructs the income matrix and analyzes it based on the classical expected utility theory [29]. Therefore, this paper introduces prospect theory to improve the credibility of evolutionary games and the effectiveness of the interpretation of reality. Prospect theory addresses the lack of rationality and considers the preferences of decision makers. It believes that people’s decisions and choices depend on the difference between results and expectations rather than the results themselves. Because it measures the value of prospects under dynamic uncertain conditions, it is more in line with people’s decision-making behavior in real situations [30]. The combination of prospect theory and evolutionary games has been used in the research of actors in the fields of financial supervision [31], construction waste recycling [11], and prefabricated buildings [30]. Green retrofitting projects are one of the most complex and risky types of projects, because there are relatively more stakeholders involved [9]. The behavioral decisions of the subjects involved in green retrofitting are actually risk decisions, and the selection of their behavioral strategies is based on the subjects’ own subjective perceptions of the value of the strategy rather than the actual utility obtained. Therefore, from the perspective of green credit, this paper proposes an evolutionary game model of the government, ESCOs, banks, and existing building owners based on prospect theory.

In summary, although existing research has devoted more attention to the issue of retrofitting financing, there is a lack of research on the behavior and decision making of the major participants related to green retrofitting financing. Therefore, this paper combines prospect theory and evolutionary game theory to establish a more realistic interaction evolutionary game model of the government, ESCOs, banks, and existing building owners from the perspective of green credit and explores the different situations of each participant’s strategic choice. The results enrich the research on the participants’ strategic choice in the field of the existing building green retrofitting.

3. Formulation of the Model

The government, ESCOs, banks, and owners of existing buildings are all participants and promoters of the market for the existing building green retrofitting. By regulating other entities, the government encourages ESCOs, banks, and owners to participate in the existing building green retrofitting market [32]. By implementing green credit, banks provide loans to ESCOs, reduce the financing costs of ESCOs, and ease financing difficulties. ESCOs are the main implementer of green retrofitting. The owners of existing buildings are the demanders of green retrofitting. Based on the above relationship, the relationship diagram of the government, ESCOs, banks, and owners is shown in Figure 1.

3.1. Basic Assumptions

Hypothesis 1. The government, ESCOs, banks, and owners are the participants in the game model; and they are all bounded rational [33, 34]. Information asymmetry exists among the four participants, and their decisions are influenced by their own preferences and the degree of information mastery. The gains and losses that need to be judged according to the decisions of other players are called the perceived gains and perceived losses, respectively. According to prospect theory, an individual’s psychological feeling of strategy gain and loss is expressed by the perceived value V, and V is calculated according to the value function V(x) and the weight function π(p) of prospect theory:where is the objective probability of the occurrence of event ; is the decision weight, where and ; is the deviation between the actual income obtained by participants and the reference point after the occurrence of event , where ; parameter is the risk preference coefficient; and is the risk aversion coefficient, which determines the degree of risk preference of the subject. represents risk neutrality.

Hypothesis 2. In the model, each participant has two strategies to choose. The government can choose a “regulation” or “no regulation” strategy; and the policy set is G = (G1, G2), which will be chosen for implementation in order to achieve environmental goals and improve political performance by promoting green retrofitting. If the regulatory costs are too high, this will cause the government to abandon regulation. The probability that the government chooses to regulate is x, and the probability that it chooses not to regulate is 1 − x. Undertaking retrofitting can enhance the reputation of ESCOs and fulfill the social responsibility of enterprises. However, if the risk, costs, and benefit payback period of retrofitting is too high, ESCOs will be forced to give up green retrofitting. ESCOs can choose to “undertake retrofitting” or “not undertake retrofit,” and the policy set is C = (C1, C2). The probability of choosing to undertake green retrofitting is y, and the probability of not undertaking retrofitting is 1 − y. The implementation of green credit can make banks better comply with national policies but may adversely affect the performance of banks. Therefore, banks can choose to “implement” or “not implement” strategies. The policy set is B = (B1, B2). The probability that banks choose to implement green credit is z, and the probability that they do not implement green credit is 1 − z. Existing building owners can benefit from energy conservation by conducting green retrofitting, but they need to pay the corresponding costs. The policy set is O = (O1, O2). The probability of owners conducting retrofitting is , and the probability of owners not conducting retrofitting is .

Hypothesis 3. When the government implements regulation, the perceived benefit of the government is and the regulatory cost is . The fiscal subsidy that ESCOs can obtain when undertaking green retrofitting is , and the extra tax that should be paid when not undertaking it is . When banks implement green credit, the subsidy they receive is ; and when they do not implement green credit, the penalty they suffer is . When owners conduct retrofitting, the government gives the owners a subsidy of . When the government does not implement regulation, the perceived benefit is . If ESCOs do not undertake retrofitting, green retrofitting projects cannot be promoted normally, which will cause a decrease in the government’s credibility. At this time, the perceived loss of the government is .

Hypothesis 4. When ESCOs undertake green retrofitting, the perceived benefit is and the cost is . When ESCOs do not undertake green retrofitting, the perceived benefit is and the cost is . When ESCOs do not undertake green retrofitting, banks implement green credit, and owners conduct retrofitting, or ESCOs undertake green retrofitting, but owners do not conduct retrofitting, ESCOs will cause perceived loss .

Hypothesis 5. When banks implement green credit, their perceived benefit is and their cost is . When banks do not implement green credit, the perceived benefit is and the cost is . When ESCOs undertake green retrofitting, but banks do not implement green credit, the banks’ reputation will be affected. At this time, the perceived loss is .

Hypothesis 6. When owners conduct retrofitting, their perceived benefit is , and the cost they need to pay is . When the energy-saving income after retrofit fails to meet the expectation of owners, the perceived loss is .

3.2. Construction of the Evolutionary Game Model

Based on the above assumptions, this paper constructs the payoff matrix of the two evolutionary game models shown in Tables 1 and 2.


Government
Regulation (x)No regulation (1 − x)

ESCOsUndertaking retrofitting (y)BanksImplementing (z)(, , )(, , )
Not implementing (1 − z)(, , )
Not undertaking retrofitting (1 − y)BanksImplementing (z)(, )(, )
Not implementing (1 − z)(, , )(, )


Government
Regulation (x)No regulation (1 − x)

ESCOsUndertaking retrofitting (y)OwnersConducting retrofitting (r)(, , )(, , )
Not conducting retrofitting (1 − r)(, , )(, , )
Not undertaking retrofitting (1 − y)OwnersConducting retrofitting (r), , )(, , )
Not conducting retrofitting (1 − r)(, , )(, , )

In the model, since the cost and subsidy for each agent to choose each strategy are predictable, it is a definite value. The gains and losses that need to be judged according to the decisions of other players are called perceived gains and perceived losses:(1)When the government implements regulations, ESCOs, banks, and owners all choose green behavior; and the probability of the successful promotion of the retrofit project is . In this case, the actual income obtained by the government, ESCOs, banks, and owners is , and, respectively. Then,(2)When the government does not implement regulations and ESCOs, banks and owners do not choose green behavior, the probability that the retrofit project cannot be promoted results in the actual profits obtained by ESCOs, banks, and owners being , and , and the credibility loss suffered by the government due to its failure to adopt environmentally friendly behavior is :(3)In other cases, the probability of project implementation failure is ; therefore, the actual losses of ESCOs, banks, and owners are , and , respectively. Thus,

3.3. Stability Analysis of Government-ESCOs-Banks Equilibrium
3.3.1. Analysis of Government’s Strategy Selection

As Table 1 shows, the expected perceived values when the government chooses the regulation strategy and when the government chooses the no regulation strategy are, respectively,

The average expected perceived value of government is as follows:

The government’s replication dynamic equation is as follows:

The derivative with respect to is as follows:

Let . Then, the stabilization strategy point of the government is , , and and the discussion can be divided into three situations:(1)If , then . At this point, regardless of the value of x, there is a stable state. This indicates that when the probability of banks implementing green credit is , the government chooses the “regulation” or “no regulation ” strategy to obtain equal benefits.(2)If , then , and are two stable points. At this time, , , and is the evolutionary stable strategy of the government, indicating that when the probability of banks implementing green credit is lower than , the government changes from the “regulation” strategy to the “no regulation ” strategy, and the “no regulation” strategy to the evolutionary stable strategy.(3)If , then , , and are two stable points. At this time, , , and is the evolutionary stable strategy of the government, indicating that when banks implement green credit with a probability higher than , the government changes from the “no regulation” strategy to the “regulation” strategy and the “regulation” strategy to the evolutionary stable strategy.

The dynamic trend chart of the government is shown in Figure 2. Let us call the three-dimensional space , and let us call a surface . The space is divided by the surface into two parts, and . When is the initial state of the game, the government’s final strategy after evolution is regulation. If the initial state is within , the ultimate policy of the government is no regulation.

3.3.2. ESCOs’ Strategy Selection Analysis

Table 1 shows that ESCOs’ expected perceived value when choosing the “undertaking retrofit” strategy and when choosing the “not undertaking retrofit” strategy are, respectively,

The ESCOs’ average expected perceived value is

The ESCOs’ replication dynamic equation is as follows:

The derivative with respect to is

Let be the stabilization strategy point of ESCOs as , , and which can be divided into three cases:(1)If , then . At this point, regardless of the value of y, it is a stable state.(2)If , then , , and are two stable points. At this time, , , and is the evolutionary stable strategy of ESCOs, indicating that when the probability of the banks implementing green credit is lower than , ESCOs are transformed from the “undertaking retrofit” strategy to the “not undertaking retrofit” strategy and the “not undertaking retrofit” strategy to the evolutionary stable strategy.(3)If , then , , and are two stable points. At this point, , , and is the evolutionary stable strategy of ESCOs, indicating that when banks implemented green credit with a probability higher than , ESCOs’ strategy changed from “not undertaking retrofit” strategy to the “undertaking retrofit” strategy and the “undertaking retrofit” strategy to the evolutionary stable strategy.

ESCOs’ dynamic trend diagram is shown in Figure 3. Let us call the three dimensions , and let us call a surface . The space is divided by the surface into two parts, and . When is the initial state of the game, then ESCOs’ final strategy after evolution is to undertake retrofitting. If the initial state is in , the ESCOs’ final strategy is not undertaking retrofitting.

3.3.3. Analysis of Banks’ Strategy Selection

As Table 1 shows, the expected future value of banks when “implementing” green credit and of banks when “not implementing” green credit are, respectively,

The average expected outlook value of banks is :

The replication dynamic equation of banks is as follows:

The derivative with respect to is

Let . Then, the stable strategy point of the banks is , , and; and then it can be divided into the following three situations:(1)If , then . At this point, regardless of the value of z, it is a stable state. This indicates that when the probability of ESCOs undertaking retrofitting is , banks will obtain equal benefits from the “implementing green credit” or “not implementing green credit” strategy.(2)If , then , , and are two stable points. At this point, , , and is the evolutionary stable strategy of the banks, indicating that when the probability of ESCOs undertaking retrofitting is lower than , the banks change from the “implementing green credit” strategy to the “not implementing green credit” strategy and the “not implementing green credit” strategy to evolutionary stable strategy.(3)If , then , , and are two stable points. At this point, , , and is the evolutionary stable strategy of the banks, indicating that when ESCOs undertake retrofitting with a probability higher than , banks change from the “not implementing green credit” strategy to the “implementing green credit” strategy and the “implementing green credit” strategy to evolutionary stable strategy.

The dynamic trend chart of banks is shown in Figure 4. Let us call the three dimensions , and let us call a surface . The space is divided by the surface into two parts, called and . When is the initial state of the game, the final strategy of the banks after evolution is to implement green credit. If the initial state is in , the banks’ final strategy is not implementing green credit.

3.3.4. Stability Analysis of Equilibrium Points

By solving the simultaneous replication dynamic equation of the government, ESCOs, and banks, and letting , the stable point of the three-party game system can be obtained. If the evolutionary game equilibrium X is asymptotically stable, then X must be a strict Nash equilibrium, and the strict Nash equilibrium must be a pure strategic Nash equilibrium. Based on this, this paper only needs to study the stability of eight points including , , , , , , , and in the tripartite game system of the government, ESCOs, and banks. According to the replication dynamic equation, the Jacobian matrix is listed. The Jacobian matrix of the game system is as follows:

According to the above Jacobian matrix, the above 8 equilibrium points are substituted into the Jacobian matrix to obtain the eigenvalues of the Jacobian matrix corresponding to each equilibrium point. The results are shown in Table 3.


Equilibrium pointsResultState

E1 (0, 0, 0)Uncertainty
E2 (1, 0, 0)Uncertainty
E3 (0, 1, 0)Uncertainty
E4 (0, 0, 1)Uncertainty
E5 (1, 1, 0)Uncertainty
E6 (1, 0, 1)Uncertainty
E7 (0, 1, 1)Uncertainty
E8 (1, 1, 1)Uncertainty

According to the Lyapunov indirect method, when the eigenvalues of the equilibrium point are all negative, the equilibrium point is an evolutionarily stable strategy; otherwise, it is an unstable point. Table 3 shows that the stability of the eight points cannot be determined, and their stability needs to be judged by combining the specific conditions and the values of the parameters. According to prospect theory, the decision of each subject is determined by its psychological perception of benefits. When the government chooses to regulate, the perceived value gained by the government should be greater than the perceived costs, . Similarly, regardless of the strategy the banks and ESCOs choose, the perceived benefits obtained should be greater than the costs. As a result, when , , and , is a stable point. At this time, the strategy choice is that the government does not regulate, ESCOs do not undertake retrofitting, and the banks do not implement green credit. When , , and , is a stable point, that is, the government regulates, ESCOs undertake retrofitting, and banks do not implement green credit. When , , and , is a stable point. At this time, the government implements regulation, ESCOs undertake retrofitting, and banks implement green credit. Therefore, the initial values of the different parameters have different effects on the game’s evolutionary process.

3.4. Stability Analysis of the Government-ESCOs-Owners Equilibrium
3.4.1. Analysis of Government’s Strategy Selection

According to Table 2, it is assumed that the expected perceived value when the government chooses the “regulation” strategy and the expected perceived value when the government chooses the “no regulation” strategy are, respectively,

The average expected perceived value of the government is

The government’s replication dynamic equation is as follows:

The derivative with respect to is

Let . Then, the stable strategy points , , and of the government can be divided into three situations for discussion:(1)If , then . At this point, regardless of the value of x, this is a stable state. This shows that when the ESCOs’ probability of undertaking retrofitting is , the government will obtain equal benefits by choosing the “regulation” or “no regulation” strategy.(2)If , then , , and are two stable points. At this point, , , and are the evolutionary stable strategy of the government, indicating that when the probability of ESCOs undertaking retrofitting is lower than , the government changes from the “regulation” strategy to the “no regulation” strategy and the “no regulation” strategy to the evolutionary stable strategy.(3)If , then , , and are two stable points. At this point, , , and are the evolutionary stable strategy of the government, indicating that when ESCOs undertake retrofitting with a probability higher than , the government changes from the “no regulation” strategy to the “regulation” strategy and the “regulation” strategy to the evolutionary stable strategy.

The trend chart of the government’s evolutionary game is shown in Figure 5. Let us call the three dimensions , and let us call surface . The space N is divided by the surface into two parts, called and . When is the initial state of the game, the government’s final strategy after evolution is regulation. If the initial state is , the government’s ultimate strategy is not regulation.

3.4.2. ESCOs’ Strategy Selection Analysis

According to Table 2, assume that the expected perceived value when ESCOs choose the “undertaking retrofit” strategy and the expected perceived value when ESCOs choose the “not undertaking retrofit” strategy are

ESCOs’ average expected perceived value is

ESCOs’ replication dynamic equation is as follows:

The derivative with respect to is

If , then the ESCOs’ stable strategy point is ,, and . Then, there are three cases as follows:(1)If , then . At this point, regardless of the value of y, it is a stable state. If , then and are two stable points. This shows that when the probability of the government implementing regulations is , ESCOs choose the “undertaking retrofit” or “not undertaking retrofit” strategy to obtain equal benefits.(2)If , then , , and </