game analysis of the multiagent evolution of existing

Research ArticleGame Analysis of the Multiagent Evolution of Existing BuildingGreen Retrofitting from the Perspective of Green Credit

Liwen Chen Mengjia Zhang and Shiwen Zhao

School of Economics and Management Hebei University of Technology Tianjin 300401 China

Correspondence should be addressed to Mengjia Zhang zmj07166163com

Received 20 February 2021 Accepted 2 June 2021 Published 16 June 2021

Academic Editor Junhai Ma

Copyright copy 2021 Liwen Chen et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Existing building green retrofitting can reduce building energy consumption and greenhouse gas emissions which is conducive tothe sustainable development of the construction industry +e financing dilemma of the existing building green retrofittinghinders the large-scale development of green retrofitting in China +is paper establishes the perceived payoff matrix andevolutionary game model of the government Energy Service Companies (ESCOs) banks and owners +rough simulationanalysis the primary factors affecting the choice of game strategy and the stable strategy under different conditions are discussed+e results show that the strategic choices of the government ESCOs banks and owners influence each other in the two gamemodels Government regulations will have an impact on the strategic choices of ESCOs banks and owners +e ownersrsquo strategychoice is closely related to the perceived benefits and costs of retrofitting Based on the results corresponding suggestions areproposed to provide theoretical support for the development of the existing building green retrofitting market

1 Introduction

In recent years environmental and energy issues related tothe construction industry have become the focus ofworldwide attention [1] With the rapid urbanization pro-cess the number of buildings in China has also increased Alarge part of these buildings are high-energy-consumingbuildings leading to large amounts of energy consumptionand carbon emissions As a result Chinarsquos building energyconsumption ranks second in the world and its residentialenergy consumption ranks first [2] +is is not conducive toChinarsquos goal of achieving its carbon peak by 2030 andachieving carbon neutrality by 2060 [3 4] +e existingbuilding green retrofitting is one of the main methods toreduce the energy consumption and carbon emissions ofexisting buildings [5] It is generally accepted that greenretrofitting can generate greater environmental benefits withlower costs and a higher utilization rate and thus achieve thesustainable development of the economy society and en-vironment [6] +e Chinese government regards the existingbuilding green retrofitting as an important energy policy andhas adopted a series of measures to strenuously promote its

development [7] However the implementation of greenretrofitting requires a large amount of funds [8] and fi-nancing difficulties seriously hinder the implementation ofthis policy [9] In particular as one of the most importantstakeholders in the market energy service companies(ESCOs) are facing a financing dilemma that hinders thelarge-scale development of the existing building green ret-rofitting in China

In China bank credit is the most important externalfinancing source for enterprises [10] As an emerging in-dustry the scale of most ESCOs in China is still small andthey do not have strong financing capacities Moreovergreen retrofitting is generally not attractive to investors [11]which makes it difficult for ESCOs to obtain financing [12]+is is the key challenge to realizing the large-scale devel-opment of existing building green retrofitting [13] +eimplementation of green credit policy provides new fi-nancing opportunities for ESCOs However the financialsystem is inherently complex [14] implementing greencredit will result in incremental costs for banks and affecttheir financial performance and the overall proportion ofinvestment and loans to green projects by financial

HindawiDiscrete Dynamics in Nature and SocietyVolume 2021 Article ID 5560671 19 pageshttpsdoiorg10115520215560671

institutions is still low [15] +erefore green credit is stillunable to play an effective role in the development of ESCOs

In addition existing studies on green credit mainly focuson the financing of the green supply chain [16] greentechnology innovation [17] and banksrsquo performance [18]+ere is little research on the impact of green creditimplementation on ESCOs Considering the current re-search status this study explored the ESCO financingproblem in green retrofitting and examined the influencingfactors for the large-scale development of the green retro-fitting market by constructing an interactive evolutionarygame model of the government ESCOs banks and existingbuilding owners

+e remainder of the paper is structured as follows +esecond part reviews the relevant literature and provides themain points of this paper +e third part proposes thecorresponding hypotheses constructs the three-party in-teractive evolutionary game model of the governmentESCOs banks and existing building owners and analyzes it+e fourth part uses MATLAB to conduct the simulationanalysis using the related data +e fifth part provides theconclusion and suggestions

2 Literature Review

Green retrofitting is the retrofitting of existing buildingsincluding architectural design components and operationsto make existing buildings more environmentally friendly[19] Although the implementation of green retrofitting is ofgreat significance to improving environmental problems thelack of funds has been a major obstacle to the imple-mentation of retrofitting In terms of financing barriers thefinancing obstacles faced by green retrofitting include a lackof initial capital investment [20] and difficulty in obtainingloans or third-party financing for the ESCO industry in somecountries [21] In addition Zhang et al [13] found thatunlike other developing countries and emerging economiesmore substantial obstacles do not exist at the system policylevel but at the meso- andmicrolevels of operation in ChinaMany scholars have conducted research on how to solve thefinancing problem of green retrofitting Wang et al [9]proposed a new financing principle model by improving theincome-cost analysis method Brown et al [22] developed ahousing retrofitting financing mechanism with the charac-teristics of capital sources and financial instruments Liuet al [7] found that the use of the EPC mode in buildinggreen retrofitting can solve the problems of insufficientfunds and low efficiency in building retrofitting to a certainextent He et al [8] demonstrated through empirical re-search that the SEU financing mechanism can be an effectivebusiness model that supports building retrofitting Econo-midou et al [23] established a professional financing plat-form as an effective way to enhance the confidence of otherparticipants Guo et al [24] analyzed the effectivenessevaluation content of the operation of the building energy-saving retrofitting financing platform from the two levels ofthe operating mechanism and the behavior of the operatingsubject Existing scholars have conducted in-depth researchon how to solve the financing problem of green retrofitting

However most of these studies focus on financing modelsSince green retrofitting involves multiple stakeholders thecoordination of interests between the participants is the keyto improving financing +erefore analyzing the behavioraldecisions of each participant in different situations is helpfulin obtaining the best behavioral decision to balance theinterests of all participants

+e evolutionary game provides an effective method forstudying behavioral decision making Evolutionary gametheory is based on bounded rationality with groups as theresearch objects It is believed that individual decisionmaking is realized in the dynamic process of imitationlearning and mutation [25] Some scholars have usedevolutionary games to study the related issues of the existingbuilding green retrofitting Liang et al [26] analyzed threeusage scenarios through evolutionary games and clarifiedthe reasons why direct decision makers are unwilling toparticipate in green retrofitting projects Liu et al [27]established a cooperative game model and discussed thedifference between noncooperative scenes and cooperativescenes and the influence of the parameters in the model+rough evolutionary game analysis Yang et al [28]revealed the game strategy changes in government groupsand investment groups to encourage and implement greenretrofitting

Compared with the traditional classical game the evo-lutionary game considers the bounded rationality of thedecision maker but it still objectively constructs the incomematrix and analyzes it based on the classical expected utilitytheory [29]+erefore this paper introduces prospect theoryto improve the credibility of evolutionary games and theeffectiveness of the interpretation of reality Prospect theoryaddresses the lack of rationality and considers the prefer-ences of decision makers It believes that peoplersquos decisionsand choices depend on the difference between results andexpectations rather than the results themselves Because itmeasures the value of prospects under dynamic uncertainconditions it is more in line with peoplersquos decision-makingbehavior in real situations [30]+e combination of prospecttheory and evolutionary games has been used in the researchof actors in the fields of financial supervision [31] con-struction waste recycling [11] and prefabricated buildings[30] Green retrofitting projects are one of the most complexand risky types of projects because there are relatively morestakeholders involved [9] +e behavioral decisions of thesubjects involved in green retrofitting are actually risk de-cisions and the selection of their behavioral strategies isbased on the subjectsrsquo own subjective perceptions of thevalue of the strategy rather than the actual utility obtained+erefore from the perspective of green credit this paperproposes an evolutionary game model of the governmentESCOs banks and existing building owners based onprospect theory

In summary although existing research has devotedmore attention to the issue of retrofitting financing there is alack of research on the behavior and decision making of themajor participants related to green retrofitting financing+erefore this paper combines prospect theory and evo-lutionary game theory to establish a more realistic

2 Discrete Dynamics in Nature and Society

interaction evolutionary game model of the governmentESCOs banks and existing building owners from theperspective of green credit and explores the different situ-ations of each participantrsquos strategic choice +e resultsenrich the research on the participantsrsquo strategic choice inthe field of the existing building green retrofitting

3 Formulation of the Model

+e government ESCOs banks and owners of existingbuildings are all participants and promoters of the marketfor the existing building green retrofitting By regulatingother entities the government encourages ESCOs banksand owners to participate in the existing building greenretrofitting market [32] By implementing green creditbanks provide loans to ESCOs reduce the financing costs ofESCOs and ease financing difficulties ESCOs are the mainimplementer of green retrofitting +e owners of existingbuildings are the demanders of green retrofitting Based onthe above relationship the relationship diagram of thegovernment ESCOs banks and owners is shown inFigure 1

31 Basic Assumptions

Hypothesis 1 +e government ESCOs banks and ownersare the participants in the game model and they are allbounded rational [33 34] Information asymmetry existsamong the four participants and their decisions are influ-enced by their own preferences and the degree of infor-mation mastery +e gains and losses that need to be judgedaccording to the decisions of other players are called theperceived gains and perceived losses respectively Accordingto prospect theory an individualrsquos psychological feeling ofstrategy gain and loss is expressed by the perceived value Vand V is calculated according to the value function V(x) andthe weight function π(p) of prospect theory

] 1113944i

π pi( 1113857U Δxi( 1113857

U(x) xα xge 0

minus λ(minus x)β xlt 0

1113896

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(1)

where Pi is the objective probability of the occurrence ofevent i π(Pi) is the decision weight where π(0) 0 andπ(1) 1 Δxi is the deviation between the actual incomeobtained by participants and the reference point after theoccurrence of event i where Δxi xi minus x0 parameter α isthe risk preference coefficient and β is the risk aversioncoefficient which determines the degree of risk preference ofthe subject α β 1 represents risk neutrality

Hypothesis 2 In the model each participant has twostrategies to choose +e government can choose a ldquoregu-lationrdquo or ldquono regulationrdquo strategy and the policy set isG (G1 G2) which will be chosen for implementation inorder to achieve environmental goals and improve politicalperformance by promoting green retrofitting If the

regulatory costs are too high this will cause the governmentto abandon regulation +e probability that the governmentchooses to regulate is x(0lexle 1) and the probability that itchooses not to regulate is 1 minus x Undertaking retrofitting canenhance the reputation of ESCOs and fulfill the social re-sponsibility of enterprises However if the risk costs andbenefit payback period of retrofitting is too high ESCOs willbe forced to give up green retrofitting ESCOs can choose toldquoundertake retrofittingrdquo or ldquonot undertake retrofitrdquo and thepolicy set is C (C1 C2) +e probability of choosing toundertake green retrofitting is y(0leyle 1) and the proba-bility of not undertaking retrofitting is 1 minus y +e imple-mentation of green credit can make banks better complywith national policies but may adversely affect the perfor-mance of banks +erefore banks can choose to ldquoimple-mentrdquo or ldquonot implementrdquo strategies +e policy set isB (B1 B2) +e probability that banks choose to implementgreen credit is z (0le zle 1) and the probability that they donot implement green credit is 1 minus z Existing building ownerscan benefit from energy conservation by conducting greenretrofitting but they need to pay the corresponding costs+e policy set is O (O1 O2) +e probability of ownersconducting retrofitting is r (0le rle 1) and the probability ofowners not conducting retrofitting is 1 minus r

Hypothesis 3 When the government implements regula-tion the perceived benefit of the government is V1 and theregulatory cost is C1 +e fiscal subsidy that ESCOs canobtain when undertaking green retrofitting is β1C2 and theextra tax that should be paid when not undertaking it is MWhen banks implement green credit the subsidy they re-ceive is β2I and when they do not implement green creditthe penalty they suffer is ωI When owners conduct ret-rofitting the government gives the owners a subsidy of BWhen the government does not implement regulation theperceived benefit is V2 If ESCOs do not undertake retro-fitting green retrofitting projects cannot be promotednormally which will cause a decrease in the governmentrsquoscredibility At this time the perceived loss of the governmentis S1

Hypothesis 4 When ESCOs undertake green retrofittingthe perceived benefit is V3 and the cost is C2 When ESCOsdo not undertake green retrofitting the perceived benefit isV4 and the cost is C3 When ESCOs do not undertake greenretrofitting banks implement green credit and ownersconduct retrofitting or ESCOs undertake green retrofittingbut owners do not conduct retrofitting ESCOs will causeperceived loss S2

Hypothesis 5 When banks implement green credit theirperceived benefit is V5 and their cost is C4 When banks donot implement green credit the perceived benefit is V6 andthe cost is C5 When ESCOs undertake green retrofitting butbanks do not implement green credit the banksrsquo reputationwill be affected At this time the perceived loss is S3

Hypothesis 6 When owners conduct retrofitting theirperceived benefit is V7 and the cost they need to pay is C6

Discrete Dynamics in Nature and Society 3

When the energy-saving income after retrofit fails to meetthe expectation of owners the perceived loss is S4

32 Construction of the Evolutionary GameModel Based onthe above assumptions this paper constructs the payoffmatrix of the two evolutionary game models shown inTables 1 and 2

In the model since the cost and subsidy for each agent tochoose each strategy are predictable it is a definite value+egains and losses that need to be judged according to thedecisions of other players are called perceived gains andperceived losses

(1) When the government implements regulationsESCOs banks and owners all choose green be-havior and the probability of the successful pro-motion of the retrofit project is p1 1 In this casethe actual income obtained by the governmentESCOs banks and owners is r1 r2 r3 andr4 re-spectively +en

V1 π p1( 1113857v r1( 1113857 + π 1 minus p1( 1113857v(0) π p1( 1113857v r1( 1113857




⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(2)

(2) When the government does not implement regula-tions and ESCOs banks and owners do not choosegreen behavior the probability p2 1 that the ret-rofit project cannot be promoted results in the actual

profits obtained by ESCOs banks and owners beingr5 r6 and r7 and the credibility loss suffered by thegovernment due to its failure to adopt environ-mentally friendly behavior is s1




S1 π p2( 1113857v s1( 1113857 + π 1 minus p2( 1113857v(0) π p2( 1113857v s1( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(3)

(3) In other cases the probability of project imple-mentation failure is p3 therefore the actual losses ofESCOs banks and owners are s2 s3 and s4 re-spectively +us




⎧⎪⎪⎨

⎪⎪⎩

(4)

33 Stability Analysis of Government-ESCOs-BanksEquilibrium

331 Analysis of Governmentrsquos Strategy Selection As Table 1shows the expected perceived values UG1 when the gov-ernment chooses the regulation strategy and UG2 when thegovernment chooses the no regulation strategy arerespectively

Government

Banks ESCOs Owners

Existing building

green retrofitmark

Regulate

Regulate

Funds

Interest Profit

Retrofit services

Implementretrofit

Environmentperformance

Environment performance


Accept retro fitFunds

Regulate

Regulate

Figure 1 Relationship of the government ESCOs banks and owners


UG1 yz V1 minus β1C2 minus β2I minus C1( 1113857 + y(1 minus z) V1 minus C1 minus β1C2 + wI( 1113857 + z(1 minus y) V1 minus C1 minus β2I + M( 1113857

+(1 minus z)(1 minus y) V1 minus C1 + wI + M( 1113857(5)

UG2 yzV2 + y(1 minus z)V2 + z(1 minus y) V2 minus S1( 1113857 +(1 minus z)(1 minus y) V2 minus S1( 1113857 (6)

+e average expected perceived value of government UG

is as follows

UG xUG1 +(1 minus x)UG2

x yz V1 minus β1C2 minus β2I minus C1( 1113857 + y(1 minus z) V1 minus C1 minus β1C2 + wI( 1113857 + z(1 minus y) V1 minus C1 minus β2I + M( 11138571113858

+(1 minus z)(1 minus y) V1 minus C1 + wI + M( 11138571113859

+(1 minus x) yzV2 + y(1 minus z)V2 + z(1 minus y) V2 minus S1( 1113857 +(1 minus z)(1 minus y) V2 minus S1( 11138571113858 1113859

(7)

+e governmentrsquos replication dynamic equation is asfollows

F1(x) dx

dt x UG1 minus UG( 1113857 x(1 minus x) y minus β1C2 minus M minus S1( 1113857 + z minus β2I minus wI( 1113857 + V1 minus C1 minus V2 + S1 + M + wI1113858 1113859 (8)

+e derivative with respect to F1(x) is as follows

F1prime(x) dF(x)

dx (1 minus 2x) y minus β1C2 minus M minus S1( 1113857 + z minus β1I minus wI( 1113857 + V1 minus C1 minus V2 + S1 + M + wI1113858 1113859 (9)

Table 1 Government ESCOs and banks perceived payoff matrix

GovernmentRegulation (x) No regulation (1 minus x)

ESCOs

Undertakingretrofitting (y) Banks

Implementing (z) (V1 minus β1C2 minus β2I minus C1 V3 + β1C2 minus C2V5 minus C4 + β2I)

(V2 V3 minus C2 V5 minus C4)

Not implementing(1 minus z)

(V1 minus β1C2 minus C1 + ωI V3 + β1C2 minus C2V6 minus C5 minus ωI minus S3)

(V2 V3 minus C2 V6 minus C5 minus S3)

Not undertakingretrofitting (1 minus y) Banks

Implementing (z) (V1 minus β2I minus C1 + MV4 minus C3 minus S2 minus M V5 minus C4 + β2I)

(V2 minus S1V4 minus C3 minus S2 V5 minus C4)


(V1 minus C1 + ωI + M V4 minus C3 minus MV6 minus C5 minus ωI) (V2 minus S1 V4 minus C3 V6 minus C5)

Table 2 Government ESCOs and owners perceived payoff matrix


ESCOs

Undertaking retrofitting(y) Owners

Conducting retrofitting(r)

(V1 minus β1C2 minus B minus C1 V3 + β1C2 minus C2V7 + B minus C6)


Not conductingretrofitting (1 minus r) (V1 minus C1 V3 minus C2 minus S2 0) (V2 V3 minus C2 minus S2 0)

Not undertakingretrofitting (1 minus y) Owners


V1 minus C1 + M V4 minus C3 minus M minus S2V7 minus C6 minus S4)

(V2 minus S1 V4 minus C3 minus S2V7 minus C6 minus S4)

Not conductingretrofitting (1 minus r) (V1 minus C1 V4 minus C3 0) (V2 minus S1 V4 minus C3 0)


Let F1(X) 0 +en the stabilization strategy point ofthe government is x1 0 x2 1 and z0 y(minus β1C2 minus M minus

S1) + V1 minus C1 minus V2 + S1 + M + wIβ1I + wI and the discus-sion can be divided into three situations

(1) If z z0 then F1(X) 0 At this point regardless ofthe value of x there is a stable state +is indicatesthat when the probability of banks implementinggreen credit is y(minus β1C2 minus M minus S1)+ V1 minus C1minus

V2 + S1 + M + wIβ1I + wI the government choosesthe ldquoregulationrdquo or ldquono regulation rdquo strategy to obtainequal benefits

(2) If zlt z0 y(minus β1C2 minus M minus S1)+ V1 minus C1 minus V2+

S1 + M + wIβ1I + wI then F1(x) 0 x1 0 andx2 1 are two stable points At this time F1prime(0)lt 0F1prime(1)gt 0 and x1 0 is the evolutionary stablestrategy of the government indicating that when theprobability of banks implementing green credit islower than y(minus β1C2 minus M minus S1) + V1minus C1 minus V2+

S1 + M + wIβ1I + wI the government changesfrom the ldquoregulationrdquo strategy to the ldquono regulation rdquostrategy and the ldquono regulationrdquo strategy to theevolutionary stable strategy

(3) If zgt z0 y(minus β1C2 minus Mminus S1) + V1 minus C1 minus V2+

S1 + M + wIβ1I + wI then F1(x) 0 x1 0 and

x2 1are two stable points At this time F1prime(0)gt 0F1prime(1)lt 0 and x2 1 is the evolutionary stablestrategy of the government indicating that whenbanks implement green credit with a probabilityhigher than y(minus β1C2 minus Mminus S1) + V1 minus C1minus

V2 + S1 + M + wIβ1I + wI the governmentchanges from the ldquono regulationrdquo strategy to theldquoregulationrdquo strategy and the ldquoregulationrdquo strategy tothe evolutionary stable strategy

+e dynamic trend chart of the government is shown inFigure 2 Let us call the three-dimensional spaceQ A(x y z)|0lexle 1 0leyle 1 0le zle 11113864 1113865 and let us callz0 y(minus β1C2 minus M minus S1) + V1 minus C1 minus V2 + S1 + M + wIβ1I + wI a surfaceΩ1 +e space Q is divided by the surfaceΩ1into two parts Ω11 and Ω12 When Ω11 is the initial state ofthe game the governmentrsquos final strategy after evolution isregulation If the initial state is within Ω12 the ultimatepolicy of the government is no regulation

332 ESCOsrsquo Strategy Selection Analysis Table 1 shows thatESCOsrsquo expected perceived value UC1 when choosing theldquoundertaking retrofitrdquo strategy and UC2 when choosing theldquonot undertaking retrofitrdquo strategy are respectively

UC1 xz V3 + β1C2 minus C2( 1113857 + x(1 minus z) V3 minus C2 + β1C2( 1113857 + z(1 minus x) V3 minus C2( 1113857 +(1 minus x)(1 minus z) V3 minus C2( 1113857 (10)

UC2 xz V4 minus C3 minus M minus S2( 1113857 + x(1 minus z) V4 minus C3 minus M( 1113857 + z(1 minus x) V4 minus C3 minus S2( 1113857 +(1 minus x)(1 minus z) V4 minus C3( 1113857 (11)

+e ESCOsrsquo average expected perceived value UC is

UC yUC1 +(1 minus y)UC2

y xz V3 + β1C2 minus C2( 1113857 + x(1 minus z) V3 minus C2 + β1C2( 1113857 + z(1 minus x) V3 minus C2( 1113857 +(1 minus x)(1 minus z) V3 minus C2( 11138571113858 1113859

+(1 minus y) xz V4 minus C3 minus M minus S2( 1113857 + x(1 minus z) V4 minus C3 minus M( 1113857 + z(1 minus x) V4 minus C3 minus S2( 1113857 +(1 minus x)(1 minus z) V4 minus C3( 11138571113858 1113859

(12)

+e ESCOsrsquo replication dynamic equation is as follows

F2(y) dy

dt y UC1 minus UC( 1113857 y(1 minus y) C3 minus V4 + V3 minus C2 + x β1C2 + M( 1113857 + zS21113858 1113859 (13)

+e derivative with respect to F2(y) is

F2prime(y) dF(y)

dy (1 minus 2y) C3 minus V4 + V3 minus C2 + x β1C2 + M( 1113857 + zS21113858 1113859 (14)


Let F2(y) 0 be the stabilization strategy point ofESCOs as y1 0 y2 1 and z0 V4 minus V3+

C2 minus C3 minus x(β1C2 + M)S2 which can be divided into threecases

(1) If z z0 then F2(y) equiv 0 At this point regardless ofthe value of y it is a stable state

(2) If zlt z0 V4 minus V3 + C2 minus C3 minus x(β1C2 + M)S2then F2(y) 0 y1 0 and y2 1 are two stablepoints At this time F2prime(0)lt 0 F2prime(1)gt 0 and y1 0is the evolutionary stable strategy of ESCOs indi-cating that when the probability of the banksimplementing green credit is lower thanV4 minus V3 + C2 minus C3 minus x(β1C2 + M)S2 ESCOs are

transformed from the ldquoundertaking retrofitrdquo strategyto the ldquonot undertaking retrofitrdquo strategy and theldquonot undertaking retrofitrdquo strategy to the evolu-tionary stable strategy

(3) If zgt z0 V4 minus V3 + C2 minus C3 minus x(β1C2 + M)S2then F2(y) 0 y1 0 and y2 1 are two stablepoints At this point F2prime(0)gt 0 F2prime(1)lt 0 and y2 1is the evolutionary stable strategy of ESCOs indi-cating that when banks implemented green creditwith a probability higher than V4 minus V3+

C2 minus C3 minus x(β1C2 + M)S2 ESCOsrsquo strategy changedfrom ldquonot undertaking retrofitrdquo strategy to theldquoundertaking retrofitrdquo strategy and the ldquoundertakingretrofitrdquo strategy to the evolutionary stable strategy

ESCOsrsquo dynamic trend diagram is shown in Figure 3 Letus call the three dimensions Q A(x y z)|0le1113864

xle 1 0leyle 1 0le zle 1 and let us call z0 V4 minus V3 + C2 minus

C3 minus x(β1C2 + M)S2 a surfaceΩ2+e space Q is divided bythe surface Ω2 into two parts Ω21 and Ω22 When Ω21 is theinitial state of the game then ESCOsrsquo final strategy afterevolution is to undertake retrofitting If the initial state is inΩ22 the ESCOsrsquo final strategy is not undertaking retrofitting

333 Analysis of Banksrsquo Strategy Selection As Table 1 showsthe expected future value UB1 of banks when ldquoimplement-ingrdquo green credit and UB2 of banks when ldquonot imple-mentingrdquo green credit are respectively

UB1 xy V5 minus C4 + β2I( 1113857 + x(1 minus y) V5 minus C4 + β2I( 1113857 + y(1 minus x) V5 minus C4( 1113857 +(1 minus x)(1 minus y) V5 minus C4( 1113857 (15)

UB2 xy V6 minus C5 minus wI minus S3( 1113857 + x(1 minus y) V6 minus C5 minus wI( 1113857 + y(1 minus x) V6 minus C5 minus S3( 1113857 +(1 minus x)(1 minus y) V6 minus C5( 1113857 (16)

+e average expected outlook value of banks is UB

UB zUB1 +(1 minus z)UB2

z xy V5 minus C4 + β2I( 1113857 + x(1 minus y) V5 minus C4 + β2I( 1113857 + y(1 minus x) V5 minus C4( 1113857 +(1 minus x)(1 minus y) V5 minus C4( 11138571113858 1113859

+(1 minus z) xy V6 minus C5 minus wI minus S3( 1113857 + x(1 minus y) V6 minus C5 minus wI( 1113857 + y(1 minus x) V6 minus C5 minus S3( 1113857 +(1 minus x)(1 minus y) V6 minus C5( 11138571113858 1113859

(17)

+e replication dynamic equation of banks is as follows

F3(z) dz

dt z UB1 minus UB( 1113857 z(1 minus z) x w + β2( 1113857I + yS3 + V5 minus C4 minus V6 + C51113858 1113859 (18)

+e derivative with respect to F3(z) is

z

x

y

Ω11

Ω12

Figure 2 Dynamic evolution of government decision making


F3prime(z) dF(z)

dz (1 minus 2z) x w + β2( 1113857I + yS3 + V5 minus C4 minus V6 + C51113858 1113859 (19)

Let F3(z) 0 +en the stable strategy point of thebanks is z1 0 z2 1andy0 V6 minus C5 minus V5 + C4 minus x(w + β2)IS3 and then it canbe divided into the following three situations

(1) If y y0 V6 minus C5 minus V5 + C4 minus x(w + β2)IS3 thenF3(z) equiv 0 At this point regardless of the value of zit is a stable state +is indicates that when theprobability of ESCOs undertaking retrofitting isV6 minus C5 minus V5 + C4 minus x(w + β2)IS3 banks will ob-tain equal benefits from the ldquoimplementing greencreditrdquo or ldquonot implementing green creditrdquo strategy

(2) If ylty0 V6 minus C5 minus V5 + C4 minus x(w + β2)IS3 thenF3(z) 0 z1 0 and z2 1 are two stable pointsAt this point F3prime(0)lt 0 F3prime(1)gt 0 and z1 0 is theevolutionary stable strategy of the banks indicatingthat when the probability of ESCOs undertakingretrofitting is lower than V6 minus C5 minus V5+C4 minus x(w + β2)IS3 the banks change from theldquoimplementing green creditrdquo strategy to the ldquonotimplementing green creditrdquo strategy and the ldquonotimplementing green creditrdquo strategy to evolutionarystable strategy

(3) If ygty0 V6 minus C5 minus V5 + C4 minus x(w + β2)IS3 thenF3(z) 0 z1 0 and z2 1 are two stable pointsAt this point F3prime(0)gt 0 F3prime(1)lt 0 and z2 1 is theevolutionary stable strategy of the banks indi-cating that when ESCOs undertake retrofittingwith a probability higher than V6 minus C5 minus V5+

C4 minus x(w + β2)IS3 banks change from the ldquonot

implementing green creditrdquo strategy to theldquoimplementing green creditrdquo strategy and theldquoimplementing green creditrdquo strategy to evolu-tionary stable strategy

+e dynamic trend chart of banks is shown in Figure 4Let us call the three dimensions Q A(x y1113864 z)|0lexle 1 0leyle 1 0le zle 1 and let us call y0 V6 minus C5 minus V5 +

C4 minus x(w + β2)IS3 a surface Ω3 +e space Q is divided bythe surfaceΩ3 into two parts called Ω31 andΩ32 WhenΩ31is the initial state of the game the final strategy of the banksafter evolution is to implement green credit If the initialstate is in Ω32 the banksrsquo final strategy is not implementinggreen credit

334 Stability Analysis of Equilibrium Points By solving thesimultaneous replication dynamic equation of the govern-ment ESCOs and banks and lettingF1(x) F2(y) F3(z) 0 the stable point of the three-party game system can be obtained If the evolutionary gameequilibriumX is asymptotically stable thenXmust be a strictNash equilibrium and the strict Nash equilibrium must be apure strategic Nash equilibrium Based on this this paperonly needs to study the stability of eight points includingE1(0 0 0) E2(1 0 0) E3(0 1 0) E4(0 0 1) E5(1 1 0)E6(1 0 1) E7(0 1 1) and E8(1 1 1) in the tripartite gamesystem of the government ESCOs and banks According tothe replication dynamic equation the Jacobian matrix islisted +e Jacobian matrix of the game system is as follows

J

(1 minus 2x) y minus β1C2 minus M minus S1( 1113857 + z minus β2I minus wI( 1113857 + V1 minus C1 minus V2 + S1 + M + wI1113858 1113859 minus x minus x2

1113872 1113873 minus β1C2 minus M minus S1( 1113857 minus x minus x2

1113872 1113873 minus β1I minus wI1113858 1113859

y minus y2

1113872 1113873 β1C2 + M( 1113857 (1 minus 2y) C3 minus V4 + V3 minus C2 + x β1C2 + M( 1113857 + zS21113858 1113859 minus y minus y2

1113872 1113873S2

z minus z2

1113872 1113873 w + β2( 1113857I z minus z2

1113872 1113873S3 (1 minus 2z) x w + β2( 1113857I + yS3 + V5 minus C4 minus V6 + C51113858 1113859

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(20)

According to the above Jacobian matrix the above 8equilibrium points are substituted into the Jacobian matrix to

obtain the eigenvalues of the Jacobian matrix correspondingto each equilibrium point +e results are shown in Table 3

z

x

y

Ω21

Ω22

Figure 3 Dynamic evolution of the ESCOsrsquo decision making


According to the Lyapunov indirect method when theeigenvalues of the equilibrium point are all negative theequilibrium point is an evolutionarily stable strategy oth-erwise it is an unstable point Table 3 shows that the stabilityof the eight points cannot be determined and their stabilityneeds to be judged by combining the specific conditions andthe values of the parameters According to prospect theorythe decision of each subject is determined by its psycho-logical perception of benefits When the governmentchooses to regulate the perceived value gained by thegovernment should be greater than the perceived costsV1 gtC1 Similarly regardless of the strategy the banks andESCOs choose the perceived benefits obtained should be

greater than the costs As a result whenV1 minus C1 + M + wIltV2 minus S1 V3 minus C2 ltV4 minus C3 andV5 minus C4 ltV6 minus C5 E1(0 0 0) is a stable point At this timethe strategy choice is that the government does not regulateESCOs do not undertake retrofitting and the banks do notimplement green credit When V1 minus C1 minus β1C2 + wIgtV2V3 minus C2 + β1C2 gtV4 minus C3 minus M and V5 minus C4 + β2IltV6minus C5 minus wI minus S3 E5(1 1 0) is a stable point that is thegovernment regulates ESCOs undertake retrofitting andbanks do not implement green credit WhenV1 minus C1 minus β1I minus β2C4 gtV2 β1C2 + V3 minus C2 gtV4minus

C3 minus S2 minus M and V5 minus C4 + β2Igt V6 minus C5 minus S3 minus wIE8(1 1 1) is a stable point At this time the governmentimplements regulation ESCOs undertake retrofitting andbanks implement green credit+erefore the initial values ofthe different parameters have different effects on the gamersquosevolutionary process

34 Stability Analysis of the Government-ESCOs-OwnersEquilibrium

341 Analysis of Governmentrsquos Strategy SelectionAccording to Table 2 it is assumed that the expected per-ceived value UG1 when the government chooses the ldquoreg-ulationrdquo strategy and the expected perceived value UG2 whenthe government chooses the ldquono regulationrdquo strategy arerespectively

UG1 yr V1 minus β1C2 minus B minus C1( 1113857 + r(1 minus y) V1 minus C1 + M( 1113857 +(1 minus r)y V1 minus C1( 1113857 +(1 minus r)(1 minus y) V1 minus C1( 1113857

UG2 yrV2 + r(1 minus y) V2 minus S1( 1113857 + y(1 minus r)V2 +(1 minus r)(1 minus y) V2 minus S1( 1113857(21)

+e average expected perceived value of the governmentUG is


x yr V1 minus β1C2 minus B minus C1( 1113857 + r(1 minus y) V1 minus C1 + M( 1113857 +(1 minus r)y V1 minus C1( 1113857 +(1 minus r)(1 minus y) V1 minus C1( 11138571113858 1113859

+(1 minus x) yrV2 + r(1 minus y) V2 minus S1( 1113857 + y(1 minus r)V2 +(1 minus r)(1 minus y) V2 minus S1( 11138571113858 1113859

(22)


F4(X) dx

dt x UG1 minus UG( 1113857 x(1 minus x) yr minus β1C2 minus M minus B( 1113857 + rM minus yS1 + V1 minus C1 minus V2 + S11113858 1113859 (23)

+e derivative with respect to F4(x) is

z

x

y

Ω 2

Ω 1

Figure 4 Dynamic evolution of banksrsquo decisions making


Tabl

e3

Eigenv

aluesof

each

equilib

rium

point

Equilib

rium

points

Result

State

middotmiddotλ 1

middotλ2

middotλ3

E 1(00

0)

V1

minusC1

+S1

minusV

2+

M+ωI

C3

minusV

4+

V3

minusC2

V5

minusC4

+C5

minusV

6Uncertainty

E 2(10

0)

minus(

V1

minusC1

+S1

minusV

2+

M+ωI

)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

V5

minusC4

+C5

minusV

6+

(ω

+β 2

)IUncertainty

E 3(01

0)

V1

minusC1

minusV

2minusβ 1

C2

+ωI

minus(

C3

minusV

4+

V3

minusC2)

V5

minusC4

+C5

minusV

6+

S3

Uncertainty

E 4(00

1)

V1

minusC1

+S1

minusV

2+

Mminusβ 1

IC3

minusV

4+

V3

minusC2

+S2

minus(

V5

minusC4

+C5

minusV

6)Uncertainty

E 5(11

0)

minus(

V1

minusC1

minusV

2minusβ 1

C2

+ωI

)minus

(C3

minusV

4+

V3

minusC2

+β 1

C2

+M

)V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3

Uncertainty

E 6(10

1)

minus(

V1

minusC1

+S1

minusV

2+

Mminusβ 2

I)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I]

Uncertainty

E 7(01

1)

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2

minus(

C3

minusV

4+

V3

minusC2

+S2)

minus(

V5

minusC4

+C5

minusV

6+

S3)

Uncertainty

E 8(11

1)

minus(

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2)

minus(

C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2)

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3]

Uncertainty


F4prime(x) dF(x)

dx (1 minus 2x) yr minus β1C2 minus M minus B( 1113857 + rM minus yS1 + V1 minus C1 minus V2 + S11113858 1113859 (24)

Let F4(X) 0 +en the stable strategy points x1 0x2 1 and y0 V1 minus C1 + rM + S1 minus V2r(β1C2+ M+ B) +

S1 of the government can be divided into three situations fordiscussion

(1) If y y0 V1 minus C1 + rM+ S1 minus V2r(β1C2+

M + B) + S1 then F4(X) equiv 0 At this point re-gardless of the value of x this is a stable state +isshows that when the ESCOsrsquo probability of under-taking retrofitting is V1 minus C1 + rM+

S1 minus V2r(β1C2 + M + B) + S1 the government willobtain equal benefits by choosing the ldquoregulationrdquo orldquono regulationrdquo strategy

(2) If ylty0 V1 minus C1 + rM + S1 minus V2 r(β1C2+

M + B) + S1 then F4(X) 0 x1 0 and x2 1 aretwo stable points At this point F4prime(0)lt 0 F4prime(1)gt 0and x1 0 are the evolutionary stable strategy of thegovernment indicating that when the probability ofESCOs undertaking retrofitting is lower thanV1 minus C1 + rM + S1 minus V2r(β1C2 + M + B) + S1 thegovernment changes from the ldquoregulationrdquo strategyto the ldquono regulationrdquo strategy and the ldquono regula-tionrdquo strategy to the evolutionary stable strategy

(3) If ygty0 V1 minus C1 + rM + S1 minus V2r (β1C2+

M + B) + S1 then F4(X) 0 x1 0 and x2 1 are

two stable points At this point F4prime(0)gt 0 F4prime(1)lt 0and x2 1 are the evolutionary stable strategy of thegovernment indicating that when ESCOs undertakeretrofitting with a probability higher thanV1 minus C1 + rM + S1 minus V2r(β1C2 + M + B) + S1 thegovernment changes from the ldquono regulationrdquostrategy to the ldquoregulationrdquo strategy and the ldquoregu-lationrdquo strategy to the evolutionary stable strategy

+e trend chart of the governmentrsquos evolutionary gameis shown in Figure 5 Let us call the three dimensionsN B(x y r)|0lexle 1 0leyle 1 0le rle 11113864 1113865 and let us cally0 V1 minus C1 + rM + S1 minus V2r(β1C2 + M + B) + S1 surfaceΦ1 +e space N is divided by the surface Φ1 into two partscalledΦ11 andΦ12 WhenΦ11 is the initial state of the gamethe governmentrsquos final strategy after evolution is regulationIf the initial state is Φ12 the governmentrsquos ultimate strategyis not regulation

342 ESCOsrsquo Strategy Selection Analysis According toTable 2 assume that the expected perceived value UC1 whenESCOs choose the ldquoundertaking retrofitrdquo strategy and theexpected perceived value UC2 when ESCOs choose the ldquonotundertaking retrofitrdquo strategy are

UC1 xr V3 minus C2 + β1C2( 1113857 + x(1 minus r) V3 minus C2 minus S2( 1113857 + r(1 minus x) V3 minus C2( 1113857 +(1 minus x))(1 minus r) V3 minus C2 minus S2( 1113857 (25)

UC2 xr V4 minus C3 minus M minus S2( 1113857 + x(1 minus r) V4 minus C3( 1113857 + r(1 minus x) V4 minus C3 minus S2( 1113857 +(1 minus x)(1 minus r) V4 minus C3( 1113857 (26)

ESCOsrsquo average expected perceived value UC is


y xr V3 minus C2 + β1C2( 1113857 + x(1 minus r) V3 minus C2 minus S2( 1113857 + r(1 minus x) V3 minus C2( 1113857 +(1 minus x)(1 minus r) V3 minus C2 minus S2( 11138571113858 1113859

+(1 minus y) xr V4 minus C3 minus M minus S2( 1113857 + r(1 minus x) V4 minus C3 minus S2( 1113857 + x(1 minus r) V4 minus C3( 1113857 +(1 minus x)(1 minus r) V4 minus C3( 11138571113858 1113859

(27)

ESCOsrsquo replication dynamic equation is as follows

F5(y) dy

dt y UB1 minus UB( 1113857 y(1 minus y) xr M + β1C2( 1113857 + 2rS2 + V3 minus C2 minus V4 + C3 minus S21113858 1113859 (28)



F5prime(y) dF(y)

dy (1 minus 2y) xr M + β1C2( 1113857 + 2rS2 + V3 minus C2 minus V4 + C3 minus S21113858 1113859 (29)

If F5(y) 0 then the ESCOsrsquo stable strategy point isy1 0y2 1 and x0 V4 + S2 + C2 minus V3 minus C3minus

2rS2r(M + β1C2) +en there are three cases as follows

(1) If x x0 V4 + S2+ C2 minus V3 minus C3 minus 2rS2r(M + β1C2) then F5(y) equiv 0 At this point regard-less of the value of y it is a stable state If XneX0 theny1 0 and y2 1 are two stable points +is showsthat when the probability of the governmentimplementing regulations is V4 + S2 + C2minus

V3 minus C3 minus 2rS2r(M + β1C2) ESCOs choose theldquoundertaking retrofitrdquo or ldquonot undertaking retrofitrdquostrategy to obtain equal benefits

(2) If xltx0 V4 + S2 + C2minus V3 minus C3 minus 2rS2r(M + β1C2) then F5(y) 0 y1 0 and y2 1 aretwo stable points At this time F5prime(0)lt 0 F5prime(1)gt 0and y1 0 are the evolutionary stable strategy ofESCOs indicating that when the probability ofgovernment regulation was lower than V4 + S2+

C2 minus V3 minus C3 minus 2rS2r(M + β1C2) ESCOs changedfrom the ldquoundertaking retrofitrdquo strategy to the ldquonotundertaking retrofitrdquo strategy and the ldquonot under-taking retrofitrdquo strategy to the evolutionary stablestrategy

(3) If xgt x0 V4 + S2 + C2 minus V3minus C3 minus 2rS2r(M+

β1C2) then F5(y) 0 y1 0 and y2 1 are two

stable points At this time F5prime(0)gt 0 F5prime(1)lt 0 andy2 1 are the evolutionary stable strategy of ESCOsindicating that when the government regulates witha probability higher than V4 + S2 + C2minus

V3 minus C3 minus 2rS2r(M + β1C2) ESCOsrsquo strategy istransformed into the undertake retrofitting strategyand the undertake retrofitting strategy becomes theevolutionary stable strategy

ESCOsrsquo dynamic trend diagram is shown in Figure 6 Letus call the three dimensions N B(x y r)|0lex1113864

le 1 0leyle 1 0le rle 1 and let us call x0 V4 + S2 + C2 minus

V3 minus C3 minus 2rS2r(M + β1C2) the surface Φ2 +e space N isdivided by the surfaceΦ2 into two partsΦ21 andΦ22 WhenΦ21 is the initial state of the game then ESCOrsquos final strategyafter evolution is to undertake retrofitting If the initial stateis in Φ22 ESCOsrsquo final strategy is not to undertakeretrofitting

343 Existing Building Ownersrsquo Decision AnalysisAccording to Table 1 it is assumed that the expected per-ceived value UO1 when the existing building owners choosethe ldquoconducting retrofittingrdquo strategy and the expectedperceived value UO2 when the existing building ownerschoose the ldquonot conducting retrofittingrdquo strategy arerespectively

UO1 xy V7 + B minus C6( 1113857 + x(1 minus y) V7 minus C6 minus S4( 1113857 + y(1 minus x) V7 minus C6( 1113857 +(1 minus x)(1 minus y) V7 minus C6 minus S4( 1113857 (30)

UO2 xylowast 0 + x(1 minus y)lowast 0 + y(1 minus x)lowast 0 +(1 minus x)(1 minus y)lowast 0 (31)

+e average expected perceived value of existing buildingowners UO is

r

x

y

Φ12

Φ11



UO rUO1 +(1 minus r)U02

r xy V7 + B minus C6( 1113857 + x(1 minus y) V7 minus C6 minus S4( 1113857 + y(1 minus x) V7 minus C6( 1113857 +(1 minus x)(1 minus y) V7 minus C6 minus S4( 11138571113858 1113859

+(1 minus r)[ xylowast 0 + x(1 minus y)lowast 0 + y(1 minus x)lowast 0 +(1 minus x)(1 minus y)lowast 0]

(32)

+e replication dynamic equation of existing buildingowners is as follows

F6(r) dr

dt r UO1 minus UO( 1113857 r(1 minus r) xyB + yS4 + V7 minus C6 minus S41113858 1113859 (33)

+e derivative with respect to F6(r) is

F6prime(r) dF(r)

dr (1 minus 2r) xyB + yS4 + V7 minus C6 minus S41113858 1113859

(34)

Let F6(r) 0 +en the stable strategy points of existingbuilding owners are r1 0 r2 1 and x0 C6 + S4minus

yS4 minus V7yB which can be divided into three situations

(1) If x x0 C6 + S4 minus yS4 minus V7yB then F6(r) equiv 0At this point regardless of the value of r it is a stablestate

(2) If xltx0 C6 + S4 minus yS4 minus V7yB then F6(r) 0r1 0 and r2 1 are two stable points At this pointF6prime(0)lt 0F6prime(1)gt 0 and r1 0 are the evolutionarystable strategy of the owners indicating that whenthe probability of government regulation is lowerthan C6 + S4 minus yS4 minus V7yB the owners change fromthe ldquoconducting retrofittingrdquo strategy to the ldquonotconducting retrofittingrdquo strategy and the ldquonot con-ducting retrofittingrdquo strategy to the evolutionarystable strategy

(3) If xgtx0 C6 + S4 minus yS4 minus V7yB then F6(r) 0r1 0 and r2 1 are two stable points At this point

F6prime(0)gt 0 F6prime(1)lt 0 and r2 1 are the ownersrsquoevolutionary stable strategy indicating that when theprobability of government regulation is higher thanC6 + S4 minus yS4 minus V7yB the ldquonot conducting retro-fittingrdquo strategy is transformed into the ldquoconductingretrofittingrdquo strategy and the ldquoconducting retrofit-tingrdquo strategy is transformed into the evolutionarystable strategy

+e dynamic trend chart of the owners is shown inFigure 7 Let us call the three dimensionsN B(x y r)|0lexle 1 0leyle 1 0le rle 11113864 1113865 and let us callx0 C6 + S4 minus yS4 minus V7yB surface Φ3 +e space N is di-vided by the surface Φ3 into two parts called Φ31 and Φ32WhenΦ31 is the initial state of the game the final strategy ofthe owners after evolution is conducting retrofitting If theinitial state is in Φ32 the ownersrsquo final strategy is notconducting retrofitting

344 Analysis of the Stable Strategy of a =ree-Party Evo-lutionary Game Let F4(x) F5(y) F6(r) 0 +e stablepoint of the three-party game system is obtained and theJacobian matrix is given +e Jacobian matrix of the three-party game system is as follows

r

x

y

Φ22

Φ21

Figure 6 Dynamic evolution of ESCOsrsquo decisions making


J

(1 minus 2x) yr minus β1C2 minus M minus B( 1113857 + rM minus yS1 + V1 minus C1 minus V2 + S11113858 1113859 x minus x2

1113872 1113873 r minus β1C2 minus M minus B( 1113857 minus S11113858 1113859 x minus x2

1113872 1113873 y minus β1C2 minus M minus B( 1113857 + M1113858 1113859

y minus y2

1113872 1113873r M + β1C2( 1113857 (1 minus 2y) xr M + β1C2( 1113857 + 2rS2 + V3 minus C2 minus V4 + C3 minus S21113858 1113859 y minus y2

1113872 1113873 x M + β1C2( 1113857 + 2S21113858 1113859

r minus r2

1113872 1113873B r minus r2

1113872 1113873S4 (1 minus 2z) xyB + yS4 + V7 minus C6 minus S41113858 1113859

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(35)

Based on the above Jacobian matrix the determinantand trace of each equilibrium point are calculated as shownin Table 4

When the government chooses to regulate the per-ceived value obtained by the government should begreater than the perceived costs V1 gtC1 Similarly theperceived value obtained by the owners when they chooseto conduct green retrofitting should be greater than theretrofitting costs V7 gtC6 +is is consistent with theactual situation +erefore points E3(0 1 0) andE5(1 1 0) are unstable points and the stability of theremaining six points is uncertain which needs to bejudged in combination with specific conditions WhenV1 minus C1 minus β1C2 minus BltV2 and V3 minus C2 gtV4 minus C3 minus S2E7(0 1 1) is the stable point that is the government doesnot regulate ESCOs undertake retrofitting and theowners conduct green retrofitting When V1 minus C1 minus β1C2 minus

BgtV2 and β1C2 + V3 minus C2 gtV4 minus C3 minus S3 minus M E8(1 1 1) isthe stable point At this time the government implementsregulations ESCOs undertake retrofitting and the ownersconduct retrofitting

4 Numerical Simulation and Results

In order to investigate the influence and significance ofvarious factors on the strategy selection of the governmentESCOs banks and existing building owners according tothe known conditions in the hypothesis MATLAB is used tosimulate the dynamic evolutionary process of each partic-ipantrsquos behavior [35ndash38] +e values of the relevant pa-rameters are as follows V1 30 V2 18 V3 25 V4 23V5 30 V6 26 V7 15 C1 4 C2 10 C3 7 C4 12C5 7 C6 5 S1 5 S2 4 S3 5 S4 3 B 2 β1 01β2 01 ω 01 I 50 and M 2 In addition differentinitial values are given to the government ESCOs banksand owners to study the influences of major factor changeson the evolutionary stable strategy

41 Baseline Evolution Path Analysis As Figures 8 and 9show based on the above assignment the initial proportionis constantly changed Finally the government will choose toimplement regulations ESCOs will undertake retrofittingbanks will implement green credit and owners will conductretrofitting

On the basis of the above analysis the influence ofdifferent parameter values on the strategy selection of eachsubject is explored by changing the correspondingparameters

42 Effects of β1 and β2 By changing the values of β1 and β2the influences on the governmentrsquos ESCOsrsquo and banksrsquostrategy choices are explored As Figure 10 shows as thegovernment subsidy coefficient increases the governmentrsquosstrategy will change from implementing regulations to notimplementing regulations ESCOs choose to undertakeretrofitting and banks choose to implement green credit at afaster speed +is indicates that the governmentrsquos regulatorycosts increase with the strengthening of subsidies When thesubsidy exceeds a certain amount the government will notregulate However the more subsidies that ESCOs and banksreceive can promote ESCOs to undertake retrofitting andbanks to implement green credit

43 C2 and S2 Influence on ESCOsrsquo Strategy Selection Bychanging the values of C2 and S2 the influence of S2 and S2on ESCOsrsquo strategy selection was explored As Figures 11and 12 show asC2 increases the ESCOsrsquo strategy will changefrom undertaking retrofitting to not undertaking retrofit-ting ESCOs need to pay corresponding costs to undertakegreen retrofitting and improve their own technology Whenthe costs of ESCOs to undertake retrofitting exceed a certainamount the benefits of ESCOs decrease and ESCOs tend tochoose not to undertake retrofitting while as S2 increasesESCOs choose to undertake retrofitting at a faster speed

r

x

y

Φ 1

Φ 2

Figure 7 Dynamic evolution of ownersrsquo decision making


44 Influence of S3 on Banksrsquo Strategy Selection Explore thechange in banksrsquo strategy selection by changing the value ofS3 As Figure 13 shows as S3 increases banks will be moreinclined to implement green credit +e credibility of a bankis extremely important A good reputation helps the bankgain public trust +erefore failure to implement greencredit will have a serious negative impact on banks and theywill suffer greater losses and the banks will be increasinglymore inclined to implement green credit

45 Influence of C6 and B on Ownersrsquo Choice of StrategyBy changing the values of C6 and B we explore the influenceof different values on owners Figures 14 and 15 show that asC6 increases the strategy of the owners will gradually changefrom conducting retrofitting to not conducting retrofittingwhile as B increases the speed of the owners choosing to

conduct retrofitting will accelerate Whether owners con-duct retrofitting is closely related to the income and costs ofgreen retrofitting and the ownersrsquo perceived benefit and

Table 4 Eigenvalues of each equilibrium point

Equilibrium points Result Statemiddot middot λ1 middotλ2 middotλ3

E1 (0 0 0) V1 minus C1 minus V2 + S1 V3 minus C2 minus V4 + C3 minus S2 V7 minus C6 minus S4 UncertaintyE2 (1 0 0) minus (V1 minus C1 minus V2 + S1) V3 minus C2 minus V4 + C3 minus S2 V7 minus C6 minus S4 UncertaintyE3 (0 1 0) V1 minus C1 minus V2 minus (V3 minus C2 minus V4 + C3 minus S2) V7 minus C6 Instability pointE4 (0 0 1) M + S1 minus V2 + V1 minus C1 V3 minus C2 minus V4 + C3 + S2 minus (V7 minus C6 minus S4) UncertaintyE5 (1 1 0) minus (V1 minus C1 minus V2) minus (V3 minus C2 minus V4 + C3 minus S2) V7 minus C6 + B Instability pointE6 (1 0 1) minus (M + S1 minus V2 + V1 minus C1) V3 minus C2 minus V4 + C3 + S2 + M + β1C2 minus (V7 minus C6 minus S4) UncertaintyE7 (0 1 1) V1 minus V2 minus C1 minus β1C2 minus B minus (V3 minus C2 minus V4 + C3 + S2) minus (V7 minus C6) UncertaintyE8 (1 1 1) minus (V1 minus V2 minus C1 minus β1C2 minus B) minus (V3 minus C2 minus V4 + C3 + S2 + M + β1C2) minus (V7 minus C6 + B) Uncertainty

0102030405060708091010203040506070809

1

GovernmentESCOs

Bank

s

01 02 03 04 05 06 07 08 09 1

Figure 8 Government-ESCOs-banks

010203040506070809

1

GovernmentESCOs

Ow

ners

01 002030405060708091

01 02 03 04 05 06 07 08 09 1

Figure 9 Government-ESCOs-owners

0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

Government β1 = 01 β2 = 01ESCO β1 = 01 β2 = 01Bank β1 = 01 β2 = 01Government β1 = 02 β2 = 02ESCO β1 = 02 β2 = 02

Bank β1 = 02 β2 = 02Government β1 = 03 β2 = 03ESCO β1 = 03 β2 = 03Bank β1 = 03 β2 = 03

Figure 10 +e evolutionary trajectory of the governmentrsquosESCOsrsquo and banksrsquo behaviors under different β1 and β2

0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

C2 = 12C2 = 14C2 = 16

C2 = 18C2 = 20

Figure 11 ESCOsrsquo behavior evolution trajectory under differentC2


willingness to retrofit will decrease as the cost increases +esubsidy given by the government will reduce the cost ofretrofitting and increase their willingness to conductretrofitting

5 Conclusions and Recommendations

+is paper introduces prospect theory takes green credit asthe perspective and analyzes the evolutionary processes ofthe four types of participantsrsquo strategic choices by con-structing a three-party interactive evolutionary game modelof the government ESCOs banks and existing buildingowners Moreover MATLAB is used for the simulationanalysis +e results show the following

(1) In the two game models the strategy choices of thegovernment ESCOs banks and owners are influ-enced by each other and the initial probability of

each participant participating in the green retrofitwill have an impact on the enthusiasm of otherparticipants participating in green retrofitting

(2) +e strategic choice of the government is related tothe perceived benefits regulatory costs and subsidyof the implemented regulation +e governmentrsquoswillingness to implement regulation is directlyproportional to the governmentrsquos perceived benefitsOn the contrary when the total cost of governmentregulation exceeds the benefit the government willnot choose regulation

(3) For banks loan interest is a major source of income+e implementation of green credit means that

0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

S2 = 1S2 = 3S2 = 5

S2 = 7S2 = 9

Figure 12 Evolutionary trajectory of ESCOsrsquo behavior underdifferent S2

0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

S3 = 5S3 = 9S3 = 13

Figure 13 Evolutionary trajectory of banksrsquo behavior underdifferentS3

0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

C6 = 5C6 = 7C6 = 9

C6 = 11C6 = 13

Figure 14 Evolutionary trajectory of ownersrsquo behavior underdifferent C6

0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

B = 2B = 6B = 10

Figure 15 Evolutionary trajectory of ownersrsquo behavior underdifferent B


banksrsquo lending objects are limited which will have acertain impact on banksrsquo profits As governmentregulation increases subsidies and penalties willencourage banks to implement green credit

(4) ESCOsrsquo strategy choice is mainly influenced by thecosts and benefits of retrofitting and the intensity ofgovernment regulation Government subsidies cancompensate for the incremental costs of ESCOs toundertake retrofitting In prospect theory agentsalways overestimate low probability losses so thepunitive measures implemented will increase theperceived losses of ESCOs and enhance the will-ingness of ESCOs to undertake retrofitting ESCOsare actively undertaking retrofitting and can push thegovernment to regulate and banks to implementgreen credit

(5) Owners will evaluate the additional costs and ben-efits of improving their energy efficiency [34] andmake strategic choices based on the costs andbenefits +e government should subsidize theowners who conduct retrofitting so as to motivatethe owners to conduct retrofitting improve thedemand for green retrofitting drive the supply sidefrom the demand side and promote the develop-ment of the green retrofitting market

Based on the above research conclusions the followingsuggestions are proposed

(1) +e government should build a good policy envi-ronment and formulate corresponding policies lawsand regulations Increasing publicity effortschanging the thinking modes of market participantsand improving the environmental protectionawareness of all participants play extremely im-portant roles in building energy conservation +egovernment should implement tax support policiesto improve the financial environment and promotethe rapid development of green credit Corre-sponding financial subsidies should be given tocommercial banks implementing the green creditpolicy and discount interest loans should be given togreen development projects [17] which will urgebanks ESCOs and owners to actively participate inthe existing building green retrofitting Furthermorethe earlier all stakeholders participate in the designprocess the more successful they will be [39] +egovernment can establish a multiagent informationlinkage mechanism to achieve information trans-parency increase information disclosure and im-plement ESCO ratings so as to alleviate theinformation asymmetry among various subjectsEffective information helps reduce ownersrsquo riskperception thus stimulating their initiative for co-operation [40]

(2) As important financial institutions banks play animportant role in green retrofitting+erefore banksshould improve their sense of responsibility respondto the call of the government actively implement

green credit establish a responsibility system orfunctional department focusing on environmentalrisk inspection and identification formulate corre-sponding assessment and incentive mechanisms[40] and establish a sound corporate environmentalprotection rating system We can increase loans toenvironmental enterprises and actively solve theirfinancing problems

(3) ESCOs should actively fulfill their social responsi-bility take the initiative to undertake green retro-fitting improve technological innovation ability andregularly conduct technological exchanges or es-tablish enterprise alliances with technologically ad-vanced enterprises In addition enterprises canimprove their service efficiency by developing newtechnologies reduce project management costs witha high-quality service level and improve energyefficiency Furthermore ESCOs should improvetheir own financial management system and enhancetheir own strength which is more conducive toobtaining financing

(4) Whether owners conduct retrofitting is the key to thelarge-scale development of the existing building greenretrofitting market Owners should change their utilitymaximization concept pay active attention to envi-ronmental issues timely grasp the policies and relevantknowledge of green retrofitting and further improvetheir initiative to participate and cooperate By en-hancing the ownersrsquo awareness of energy conservationand changing the unique concept of interests theownersrsquo recognition of the existing building greenretrofitting can be improved+is will make it easier totransform potential demand into explicit demandproviding space for market development

Data Availability

In order to investigate the influence and significance ofvarious factors on the strategy selection of the governmentESCOs banks and existing building owners according tothe known conditions in the hypothesis MATLAB is used toconduct numerical simulation of the game system to sim-ulate the dynamic evolution process of each participantsrsquobehavior

Conflicts of Interest

+e authors declare that they have no conflicts of interest

References

[1] K H Kim S S Jeon A Irakoze and K Y Son ldquoA study of thegreen building benefits in apartment buildings according toreal estate prices case of non-capital areas in South KoreardquoSustainability vol 12 no 6 Article ID 2206 2020

[2] T Huo H Ren and W Cai ldquoEstimating urban residentialbuilding-related energy consumption and energy intensity inChina based on improved building stock turnover modelrdquoScience of the Total Environment vol 650 pp 427ndash437 2019


[3] J H Ma Y M Hou Z X Wang and W H Yang ldquoPricingstrategy and coordination of automobile manufacturers basedon government intervention and carbon emission reductionrdquoEnergy Policy vol 148 Article ID 111919 2021

[4] J H Ma Y M Hou W H Yang and Y Tian ldquoA time-basedpricing game in a compet-itive vehicle market regarding theintervention of carbon emission reductionrdquo Energy Policyvol 142 Article ID 111440 2020

[5] U Ali M H Shamsi M C Hoare K Purcell E Manginaand J OrsquoDonnell ldquoA data-driven approach to optimize urbanscale energy retrofit decisions for residential buildingsrdquoApplied Energy vol 267 Article ID 114861 2020

[6] Z Ma P Cooper D Daly and L Ledo ldquoExisting buildingretrofits methodology and state-of-the-artrdquo Energy andBuildings vol 55 pp 889ndash902 2012

[7] G Liu X H Li Y T Tan and G M Zhang ldquoBuilding greenretrofit in China policies barriers and recommendationsrdquoEnergy Policy vol 139 Article ID 111356 2020

[8] Y He N Liao J Bi and L Guo ldquoInvestment decision-makingoptimization of energy efficiency retrofit measures in multiplebuildings under financing budgetary restraintrdquo Journal ofCleaner Production vol 215 pp 1078ndash1094 2019

[9] X Wang M Lu W Mao J Ouyang B Zhou and Y YangldquoImproving benefit-cost analysis to overcome financing dif-ficulties in promoting energy-efficient renovation of existingresidential buildings in Chinardquo Applied Energy vol 141pp 119ndash130 2015

[10] L He R Liu Z Zhong D Wang and Y Xia ldquoCan greenfinancial development promote renewable energy investmentefficiency A consideration of bank creditrdquo Renewable Energyvol 143 pp 974ndash984 2019

[11] Y Liu T Liu S Ye and Y Liu ldquoCost-benefit analysis forenergy efficiency retrofit of existing buildings a case study inChinardquo Journal of Cleaner Production vol 177 pp 493ndash5062018

[12] G Liu S Zheng P Xu and T Zhuang ldquoAn ANP-SWOTapproach for ESCOs industry strategies in Chinese buildingsectorsrdquo Renewable and Sustainable Energy Reviews vol 93pp 90ndash99 2018

[13] M S Zhang Y Lian H Zhao and C Xia-Bauer ldquoUnlockinggreen financing for building energy retrofit a survey in thewestern Chinardquo Energy Strategy Reviews vol 30 Article ID100520 2020

[14] Q Gao and J HMa ldquoChaos andHopf bifurcation of a financesystemrdquo Nonlinear Dynamics vol 58 no 1-2 pp 209ndash2162009

[15] N N Liu C Z Liu Y F Xia Y Ren and J Z LiangldquoExamining the coordination between green finance andgreen economy aiming for sustainable development a casestudy of Chinardquo Sustainability vol 12 no 9 Article ID 37172020

[16] S An B Li D Song and X Chen ldquoGreen credit financingversus trade credit financing in a supply chain with carbonemission limitsrdquo European Journal of Operational Researchvol 292 no 1 pp 125ndash142 2021

[17] Q Guo M Zhou N Liu and Y Wang ldquoSpatial effects ofenvironmental regulation and green credits on green tech-nology innovation under low-carbon economy backgroundconditionsrdquo International Journal of Environmental Researchand Public Health vol 16 no 17 Article ID 3027 2019

[18] W Yin Z Y Zhu K U Berna and Y P Zhu ldquo+e deter-minants of green credit and its impact on the performance ofChinese banksrdquo Journal of Cleaner Production vol 286Article ID 124991 2021

[19] X Zhao Y T Tan L Y Shen G M Zhang and J H WangldquoCase-based reasoning approach for supporting buildinggreen retrofit decisionsrdquo Building and Environment vol 160Article ID 106210 2019

[20] E Bertone O Sahin R A Stewart et al ldquoRole of financialmechanisms for accelerating the rate of water and energyefficiency retrofits in Australian public buildings hybridbayesian network and system dynamics modelling approachrdquoApplied Energy vol 210 pp 409ndash419 2018

[21] P Bertoldi and B Boza-Kiss ldquoAnalysis of barriers and driversfor the development of the ESCO markets in EuropendashS-cienceDirectrdquo Energy Policy vol 107 pp 345ndash355 2017

[22] D Brown S Sorrell and P Kivimaa ldquoWorth the risk Anevaluation of alternative finance mechanisms for residentialretrofitrdquo Energy Policy vol 128 pp 418ndash430 2019

[23] M Economidou P Zangheri A Muller and L KranzlldquoFinancing the renovation of the cypriot building stock anassessment of the energy saving potential of different policyscenarios based on the InvertEE-Lab modelrdquo Energiesvol 11 no 11 Article ID 3071 2018

[24] H Guo W Qiao and Y Zheng ldquoEffectiveness evaluation offinancing platform operation of buildings energy savingtransformation using ANP-fuzzy in China an empiricalstudyrdquo Sustainability vol 12 no 7 Article ID 2826 2020

[25] X Liu Z ZhangW Qi and DWang ldquoAn evolutionary gamestudy of the behavioral management of bid evaluations inreserve auctionsrdquo IEEE Access vol 8 pp 95390ndash95402 2020

[26] X Liang Y Peng and G Q Shen ldquoA game theory basedanalysis of decision making for green retrofit under differentoccupancy typesrdquo Journal of Cleaner Production vol 137pp 1300ndash1312 2016

[27] H M Liu X Y Zhang and M Y Hu ldquoGame-theory-basedanalysis of energy perform-ance contracting for building retro-fitsrdquo Journal of Cleaner Production vol 231 pp 1089ndash1099 2019

[28] X Yang J Zhang G Q Shen and Y Yan ldquoIncentives forgreen retrofits an evolutionary game analysis on Public-Private-Partnership reconstruction of buildingsrdquo Journal ofCleaner Production vol 232 pp 1076ndash1092 2019

[29] H Shen Y Peng and C X Guo ldquoAnalysis of the evolutiongame of construction an-d demolition waste recycling be-havior based on prospect theory under environmental reg-ulationrdquo International Journal of Environmental Research andPublic Health vol 15 no 7 Article ID 1518 2018

[30] Y Liu D Cai C X Guo and H Z Huang ldquoEvolutionarygame of government subsidy strategy for prefabricatedbuildings based on prospect theoryrdquo Mathematical Problemsin Engineering vol 2020 Article ID 8863563 2020

[31] X R Yu G L Dong and C Y Liu ldquo+e tripartite regulationgame of carbon financial products based on the prospecttheoryrdquo Frontiers in Environmental Science vol 8 Article ID610732 2020

[32] B Bao J Ma and M Goh ldquoShort- and long-term repeatedgame behaviours of two parallel supply chains based ongovernment subsidy in the vehicle marketrdquo InternationalJournal of Production Research vol 58 no 24 pp 7507ndash75302020

[33] W Lou and J Ma ldquoComplexity of sales effort and carbonemission reduction effort in a two-parallel household appli-ance supply chain modelrdquo Applied Mathematical Modellingvol 64 pp 398ndash425 2018

[34] J Ma and H Ren ldquoInfluence of government regulation on thestability of dualchannel recycling model based on customerexpectationrdquo Nonlinear Dynamics vol 94 no 3pp 1775ndash1790 2018


[35] J Ma and L Xie ldquo+e comparison and complex analysis ondual-channel supply chain under different channel powerstructures and uncertain demandrdquo Nonlinear Dynamicsvol 83 no 3 pp 1379ndash1393 2016

[36] L Xie J Ma and M Goh ldquoSupply chain coordination in thepresence of uncertain yield and demandrdquo InternationalJournal of Production Research pp 1ndash17 2020

[37] T Xu and J Ma ldquoFeed-in tariff or tax-rebate regulationDynamic decision mod-el for the solar photovoltaic supplychainrdquo Applied Mathematical Modelling vol 89 pp 1106ndash1123 2021

[38] M Achtnicht and R Madlener ldquoFactors influencing Germanhouse ownersrsquo preferences on energy retrofitsrdquo Energy Policyvol 68 pp 254ndash263 2014

[39] X Liang G Shen and L Guo ldquoImproving management ofgreen retrofits from a stakeholder perspective a case study inChinardquo International Journal of Environmental Research andPublic Health vol 12 no 11 pp 13823ndash13842 2015

[40] L Jia Q K Qian F Meijer and H Visscher ldquoStakeholdersrsquorisk perception a perspective for proactive risk managementin residential building energy retrofits in Chinardquo Sustain-ability vol 12 no 7 Article ID 2832 2020


institutions is still low [15] +erefore green credit is stillunable to play an effective role in the development of ESCOs

In addition existing studies on green credit mainly focuson the financing of the green supply chain [16] greentechnology innovation [17] and banksrsquo performance [18]+ere is little research on the impact of green creditimplementation on ESCOs Considering the current re-search status this study explored the ESCO financingproblem in green retrofitting and examined the influencingfactors for the large-scale development of the green retro-fitting market by constructing an interactive evolutionarygame model of the government ESCOs banks and existingbuilding owners

+e remainder of the paper is structured as follows +esecond part reviews the relevant literature and provides themain points of this paper +e third part proposes thecorresponding hypotheses constructs the three-party in-teractive evolutionary game model of the governmentESCOs banks and existing building owners and analyzes it+e fourth part uses MATLAB to conduct the simulationanalysis using the related data +e fifth part provides theconclusion and suggestions

2 Literature Review

Green retrofitting is the retrofitting of existing buildingsincluding architectural design components and operationsto make existing buildings more environmentally friendly[19] Although the implementation of green retrofitting is ofgreat significance to improving environmental problems thelack of funds has been a major obstacle to the imple-mentation of retrofitting In terms of financing barriers thefinancing obstacles faced by green retrofitting include a lackof initial capital investment [20] and difficulty in obtainingloans or third-party financing for the ESCO industry in somecountries [21] In addition Zhang et al [13] found thatunlike other developing countries and emerging economiesmore substantial obstacles do not exist at the system policylevel but at the meso- andmicrolevels of operation in ChinaMany scholars have conducted research on how to solve thefinancing problem of green retrofitting Wang et al [9]proposed a new financing principle model by improving theincome-cost analysis method Brown et al [22] developed ahousing retrofitting financing mechanism with the charac-teristics of capital sources and financial instruments Liuet al [7] found that the use of the EPC mode in buildinggreen retrofitting can solve the problems of insufficientfunds and low efficiency in building retrofitting to a certainextent He et al [8] demonstrated through empirical re-search that the SEU financing mechanism can be an effectivebusiness model that supports building retrofitting Econo-midou et al [23] established a professional financing plat-form as an effective way to enhance the confidence of otherparticipants Guo et al [24] analyzed the effectivenessevaluation content of the operation of the building energy-saving retrofitting financing platform from the two levels ofthe operating mechanism and the behavior of the operatingsubject Existing scholars have conducted in-depth researchon how to solve the financing problem of green retrofitting

However most of these studies focus on financing modelsSince green retrofitting involves multiple stakeholders thecoordination of interests between the participants is the keyto improving financing +erefore analyzing the behavioraldecisions of each participant in different situations is helpfulin obtaining the best behavioral decision to balance theinterests of all participants

+e evolutionary game provides an effective method forstudying behavioral decision making Evolutionary gametheory is based on bounded rationality with groups as theresearch objects It is believed that individual decisionmaking is realized in the dynamic process of imitationlearning and mutation [25] Some scholars have usedevolutionary games to study the related issues of the existingbuilding green retrofitting Liang et al [26] analyzed threeusage scenarios through evolutionary games and clarifiedthe reasons why direct decision makers are unwilling toparticipate in green retrofitting projects Liu et al [27]established a cooperative game model and discussed thedifference between noncooperative scenes and cooperativescenes and the influence of the parameters in the model+rough evolutionary game analysis Yang et al [28]revealed the game strategy changes in government groupsand investment groups to encourage and implement greenretrofitting

Compared with the traditional classical game the evo-lutionary game considers the bounded rationality of thedecision maker but it still objectively constructs the incomematrix and analyzes it based on the classical expected utilitytheory [29]+erefore this paper introduces prospect theoryto improve the credibility of evolutionary games and theeffectiveness of the interpretation of reality Prospect theoryaddresses the lack of rationality and considers the prefer-ences of decision makers It believes that peoplersquos decisionsand choices depend on the difference between results andexpectations rather than the results themselves Because itmeasures the value of prospects under dynamic uncertainconditions it is more in line with peoplersquos decision-makingbehavior in real situations [30]+e combination of prospecttheory and evolutionary games has been used in the researchof actors in the fields of financial supervision [31] con-struction waste recycling [11] and prefabricated buildings[30] Green retrofitting projects are one of the most complexand risky types of projects because there are relatively morestakeholders involved [9] +e behavioral decisions of thesubjects involved in green retrofitting are actually risk de-cisions and the selection of their behavioral strategies isbased on the subjectsrsquo own subjective perceptions of thevalue of the strategy rather than the actual utility obtained+erefore from the perspective of green credit this paperproposes an evolutionary game model of the governmentESCOs banks and existing building owners based onprospect theory

In summary although existing research has devotedmore attention to the issue of retrofitting financing there is alack of research on the behavior and decision making of themajor participants related to green retrofitting financing+erefore this paper combines prospect theory and evo-lutionary game theory to establish a more realistic







] 1113944i

π pi( 1113857U Δxi( 1113857

U(x) xα xge 0


1113896

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(1)

















⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(2)







⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(3)





⎧⎪⎪⎨

⎪⎪⎩

(4)



Government

Banks ESCOs Owners

Existing building

green retrofitmark

Regulate

Regulate

Funds

Interest Profit

Retrofit services

Implementretrofit





Regulate

Regulate







is as follows





(7)


F1(x) dx



F1prime(x) dF(x)




ESCOs














ESCOs































(12)


F2(y) dy



F2prime(y) dF(y)




















(17)


F3(z) dz



z

x

y

Ω11

Ω12



F3prime(z) dF(z)











J



1113872 1113873 minus β1I minus wI1113858 1113859

y minus y2


1113872 1113873S2

z minus z2

1113872 1113873 w + β2( 1113857I z minus z2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(20)



z

x

y

Ω21

Ω22














(22)


F4(X) dx



z

x

y

Ω 2

Ω 1



Tabl

e3

Eigenv

aluesof

each

equilib

rium

point

Equilib

rium

points

Result

State

middotmiddotλ 1

middotλ2

middotλ3

E 1(00

0)

V1

minusC1

+S1

minusV

2+

M+ωI

C3

minusV

4+

V3

minusC2

V5

minusC4

+C5

minusV

6Uncertainty

E 2(10

0)

minus(

V1

minusC1

+S1

minusV

2+

M+ωI

)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

V5

minusC4

+C5

minusV

6+

(ω

+β 2

)IUncertainty

E 3(01

0)

V1

minusC1

minusV

2minusβ 1

C2

+ωI

minus(

C3

minusV

4+

V3

minusC2)

V5

minusC4

+C5

minusV

6+

S3

Uncertainty

E 4(00

1)

V1

minusC1

+S1

minusV

2+

Mminusβ 1

IC3

minusV

4+

V3

minusC2

+S2

minus(

V5

minusC4

+C5

minusV

6)Uncertainty

E 5(11

0)

minus(

V1

minusC1

minusV

2minusβ 1

C2

+ωI

)minus

(C3

minusV

4+

V3

minusC2

+β 1

C2

+M

)V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3

Uncertainty

E 6(10

1)

minus(

V1

minusC1

+S1

minusV

2+

Mminusβ 2

I)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I]

Uncertainty

E 7(01

1)

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2

minus(

C3

minusV

4+

V3

minusC2

+S2)

minus(

V5

minusC4

+C5

minusV

6+

S3)

Uncertainty

E 8(11

1)

minus(

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2)

minus(

C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2)

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3]

Uncertainty


F4prime(x) dF(x)




















(27)


F5(y) dy




F5prime(y) dF(y)



















r

x

y

Φ12

Φ11






(32)


F6(r) dr



F6prime(r) dF(r)


(34)









r

x

y

Φ22

Φ21



J




y minus y2


1113872 1113873 x M + β1C2( 1113857 + 2S21113858 1113859

r minus r2

1113872 1113873B r minus r2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(35)










r

x

y

Φ 1

Φ 2









0102030405060708091010203040506070809

1

GovernmentESCOs

Bank

s

01 02 03 04 05 06 07 08 09 1


010203040506070809

1

GovernmentESCOs

Ow

ners

01 002030405060708091

01 02 03 04 05 06 07 08 09 1


0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p




0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

C2 = 12C2 = 14C2 = 16

C2 = 18C2 = 20










0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

S2 = 1S2 = 3S2 = 5

S2 = 7S2 = 9


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

S3 = 5S3 = 9S3 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

C6 = 5C6 = 7C6 = 9

C6 = 11C6 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

B = 2B = 6B = 10












Data Availability




References

















































] 1113944i

π pi( 1113857U Δxi( 1113857

U(x) xα xge 0


1113896

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(1)

















⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(2)







⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(3)





⎧⎪⎪⎨

⎪⎪⎩

(4)



Government

Banks ESCOs Owners

Existing building

green retrofitmark

Regulate

Regulate

Funds

Interest Profit

Retrofit services

Implementretrofit





Regulate

Regulate







is as follows





(7)


F1(x) dx



F1prime(x) dF(x)




ESCOs














ESCOs































(12)


F2(y) dy



F2prime(y) dF(y)




















(17)


F3(z) dz



z

x

y

Ω11

Ω12



F3prime(z) dF(z)











J



1113872 1113873 minus β1I minus wI1113858 1113859

y minus y2


1113872 1113873S2

z minus z2

1113872 1113873 w + β2( 1113857I z minus z2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(20)



z

x

y

Ω21

Ω22














(22)


F4(X) dx



z

x

y

Ω 2

Ω 1



Tabl

e3

Eigenv

aluesof

each

equilib

rium

point

Equilib

rium

points

Result

State

middotmiddotλ 1

middotλ2

middotλ3

E 1(00

0)

V1

minusC1

+S1

minusV

2+

M+ωI

C3

minusV

4+

V3

minusC2

V5

minusC4

+C5

minusV

6Uncertainty

E 2(10

0)

minus(

V1

minusC1

+S1

minusV

2+

M+ωI

)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

V5

minusC4

+C5

minusV

6+

(ω

+β 2

)IUncertainty

E 3(01

0)

V1

minusC1

minusV

2minusβ 1

C2

+ωI

minus(

C3

minusV

4+

V3

minusC2)

V5

minusC4

+C5

minusV

6+

S3

Uncertainty

E 4(00

1)

V1

minusC1

+S1

minusV

2+

Mminusβ 1

IC3

minusV

4+

V3

minusC2

+S2

minus(

V5

minusC4

+C5

minusV

6)Uncertainty

E 5(11

0)

minus(

V1

minusC1

minusV

2minusβ 1

C2

+ωI

)minus

(C3

minusV

4+

V3

minusC2

+β 1

C2

+M

)V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3

Uncertainty

E 6(10

1)

minus(

V1

minusC1

+S1

minusV

2+

Mminusβ 2

I)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I]

Uncertainty

E 7(01

1)

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2

minus(

C3

minusV

4+

V3

minusC2

+S2)

minus(

V5

minusC4

+C5

minusV

6+

S3)

Uncertainty

E 8(11

1)

minus(

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2)

minus(

C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2)

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3]

Uncertainty


F4prime(x) dF(x)




















(27)


F5(y) dy




F5prime(y) dF(y)



















r

x

y

Φ12

Φ11






(32)


F6(r) dr



F6prime(r) dF(r)


(34)









r

x

y

Φ22

Φ21



J




y minus y2


1113872 1113873 x M + β1C2( 1113857 + 2S21113858 1113859

r minus r2

1113872 1113873B r minus r2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(35)










r

x

y

Φ 1

Φ 2









0102030405060708091010203040506070809

1

GovernmentESCOs

Bank

s

01 02 03 04 05 06 07 08 09 1


010203040506070809

1

GovernmentESCOs

Ow

ners

01 002030405060708091

01 02 03 04 05 06 07 08 09 1


0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p




0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

C2 = 12C2 = 14C2 = 16

C2 = 18C2 = 20










0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

S2 = 1S2 = 3S2 = 5

S2 = 7S2 = 9


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

S3 = 5S3 = 9S3 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

C6 = 5C6 = 7C6 = 9

C6 = 11C6 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

B = 2B = 6B = 10












Data Availability




References




















































⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(2)







⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(3)





⎧⎪⎪⎨

⎪⎪⎩

(4)



Government

Banks ESCOs Owners

Existing building

green retrofitmark

Regulate

Regulate

Funds

Interest Profit

Retrofit services

Implementretrofit





Regulate

Regulate







is as follows





(7)


F1(x) dx



F1prime(x) dF(x)




ESCOs














ESCOs































(12)


F2(y) dy



F2prime(y) dF(y)




















(17)


F3(z) dz



z

x

y

Ω11

Ω12



F3prime(z) dF(z)











J



1113872 1113873 minus β1I minus wI1113858 1113859

y minus y2


1113872 1113873S2

z minus z2

1113872 1113873 w + β2( 1113857I z minus z2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(20)



z

x

y

Ω21

Ω22














(22)


F4(X) dx



z

x

y

Ω 2

Ω 1



Tabl

e3

Eigenv

aluesof

each

equilib

rium

point

Equilib

rium

points

Result

State

middotmiddotλ 1

middotλ2

middotλ3

E 1(00

0)

V1

minusC1

+S1

minusV

2+

M+ωI

C3

minusV

4+

V3

minusC2

V5

minusC4

+C5

minusV

6Uncertainty

E 2(10

0)

minus(

V1

minusC1

+S1

minusV

2+

M+ωI

)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

V5

minusC4

+C5

minusV

6+

(ω

+β 2

)IUncertainty

E 3(01

0)

V1

minusC1

minusV

2minusβ 1

C2

+ωI

minus(

C3

minusV

4+

V3

minusC2)

V5

minusC4

+C5

minusV

6+

S3

Uncertainty

E 4(00

1)

V1

minusC1

+S1

minusV

2+

Mminusβ 1

IC3

minusV

4+

V3

minusC2

+S2

minus(

V5

minusC4

+C5

minusV

6)Uncertainty

E 5(11

0)

minus(

V1

minusC1

minusV

2minusβ 1

C2

+ωI

)minus

(C3

minusV

4+

V3

minusC2

+β 1

C2

+M

)V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3

Uncertainty

E 6(10

1)

minus(

V1

minusC1

+S1

minusV

2+

Mminusβ 2

I)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I]

Uncertainty

E 7(01

1)

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2

minus(

C3

minusV

4+

V3

minusC2

+S2)

minus(

V5

minusC4

+C5

minusV

6+

S3)

Uncertainty

E 8(11

1)

minus(

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2)

minus(

C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2)

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3]

Uncertainty


F4prime(x) dF(x)




















(27)


F5(y) dy




F5prime(y) dF(y)



















r

x

y

Φ12

Φ11






(32)


F6(r) dr



F6prime(r) dF(r)


(34)









r

x

y

Φ22

Φ21



J




y minus y2


1113872 1113873 x M + β1C2( 1113857 + 2S21113858 1113859

r minus r2

1113872 1113873B r minus r2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(35)










r

x

y

Φ 1

Φ 2









0102030405060708091010203040506070809

1

GovernmentESCOs

Bank

s

01 02 03 04 05 06 07 08 09 1


010203040506070809

1

GovernmentESCOs

Ow

ners

01 002030405060708091

01 02 03 04 05 06 07 08 09 1


0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p




0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

C2 = 12C2 = 14C2 = 16

C2 = 18C2 = 20










0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

S2 = 1S2 = 3S2 = 5

S2 = 7S2 = 9


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

S3 = 5S3 = 9S3 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

C6 = 5C6 = 7C6 = 9

C6 = 11C6 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

B = 2B = 6B = 10












Data Availability




References
















































is as follows





(7)


F1(x) dx



F1prime(x) dF(x)




ESCOs














ESCOs































(12)


F2(y) dy



F2prime(y) dF(y)




















(17)


F3(z) dz



z

x

y

Ω11

Ω12



F3prime(z) dF(z)











J



1113872 1113873 minus β1I minus wI1113858 1113859

y minus y2


1113872 1113873S2

z minus z2

1113872 1113873 w + β2( 1113857I z minus z2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(20)



z

x

y

Ω21

Ω22














(22)


F4(X) dx



z

x

y

Ω 2

Ω 1



Tabl

e3

Eigenv

aluesof

each

equilib

rium

point

Equilib

rium

points

Result

State

middotmiddotλ 1

middotλ2

middotλ3

E 1(00

0)

V1

minusC1

+S1

minusV

2+

M+ωI

C3

minusV

4+

V3

minusC2

V5

minusC4

+C5

minusV

6Uncertainty

E 2(10

0)

minus(

V1

minusC1

+S1

minusV

2+

M+ωI

)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

V5

minusC4

+C5

minusV

6+

(ω

+β 2

)IUncertainty

E 3(01

0)

V1

minusC1

minusV

2minusβ 1

C2

+ωI

minus(

C3

minusV

4+

V3

minusC2)

V5

minusC4

+C5

minusV

6+

S3

Uncertainty

E 4(00

1)

V1

minusC1

+S1

minusV

2+

Mminusβ 1

IC3

minusV

4+

V3

minusC2

+S2

minus(

V5

minusC4

+C5

minusV

6)Uncertainty

E 5(11

0)

minus(

V1

minusC1

minusV

2minusβ 1

C2

+ωI

)minus

(C3

minusV

4+

V3

minusC2

+β 1

C2

+M

)V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3

Uncertainty

E 6(10

1)

minus(

V1

minusC1

+S1

minusV

2+

Mminusβ 2

I)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I]

Uncertainty

E 7(01

1)

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2

minus(

C3

minusV

4+

V3

minusC2

+S2)

minus(

V5

minusC4

+C5

minusV

6+

S3)

Uncertainty

E 8(11

1)

minus(

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2)

minus(

C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2)

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3]

Uncertainty


F4prime(x) dF(x)




















(27)


F5(y) dy




F5prime(y) dF(y)



















r

x

y

Φ12

Φ11






(32)


F6(r) dr



F6prime(r) dF(r)


(34)









r

x

y

Φ22

Φ21



J




y minus y2


1113872 1113873 x M + β1C2( 1113857 + 2S21113858 1113859

r minus r2

1113872 1113873B r minus r2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(35)










r

x

y

Φ 1

Φ 2









0102030405060708091010203040506070809

1

GovernmentESCOs

Bank

s

01 02 03 04 05 06 07 08 09 1


010203040506070809

1

GovernmentESCOs

Ow

ners

01 002030405060708091

01 02 03 04 05 06 07 08 09 1


0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p




0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

C2 = 12C2 = 14C2 = 16

C2 = 18C2 = 20










0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

S2 = 1S2 = 3S2 = 5

S2 = 7S2 = 9


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

S3 = 5S3 = 9S3 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

C6 = 5C6 = 7C6 = 9

C6 = 11C6 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

B = 2B = 6B = 10












Data Availability




References































































(12)


F2(y) dy



F2prime(y) dF(y)




















(17)


F3(z) dz



z

x

y

Ω11

Ω12



F3prime(z) dF(z)











J



1113872 1113873 minus β1I minus wI1113858 1113859

y minus y2


1113872 1113873S2

z minus z2

1113872 1113873 w + β2( 1113857I z minus z2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(20)



z

x

y

Ω21

Ω22














(22)


F4(X) dx



z

x

y

Ω 2

Ω 1



Tabl

e3

Eigenv

aluesof

each

equilib

rium

point

Equilib

rium

points

Result

State

middotmiddotλ 1

middotλ2

middotλ3

E 1(00

0)

V1

minusC1

+S1

minusV

2+

M+ωI

C3

minusV

4+

V3

minusC2

V5

minusC4

+C5

minusV

6Uncertainty

E 2(10

0)

minus(

V1

minusC1

+S1

minusV

2+

M+ωI

)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

V5

minusC4

+C5

minusV

6+

(ω

+β 2

)IUncertainty

E 3(01

0)

V1

minusC1

minusV

2minusβ 1

C2

+ωI

minus(

C3

minusV

4+

V3

minusC2)

V5

minusC4

+C5

minusV

6+

S3

Uncertainty

E 4(00

1)

V1

minusC1

+S1

minusV

2+

Mminusβ 1

IC3

minusV

4+

V3

minusC2

+S2

minus(

V5

minusC4

+C5

minusV

6)Uncertainty

E 5(11

0)

minus(

V1

minusC1

minusV

2minusβ 1

C2

+ωI

)minus

(C3

minusV

4+

V3

minusC2

+β 1

C2

+M

)V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3

Uncertainty

E 6(10

1)

minus(

V1

minusC1

+S1

minusV

2+

Mminusβ 2

I)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I]

Uncertainty

E 7(01

1)

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2

minus(

C3

minusV

4+

V3

minusC2

+S2)

minus(

V5

minusC4

+C5

minusV

6+

S3)

Uncertainty

E 8(11

1)

minus(

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2)

minus(

C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2)

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3]

Uncertainty


F4prime(x) dF(x)




















(27)


F5(y) dy




F5prime(y) dF(y)



















r

x

y

Φ12

Φ11






(32)


F6(r) dr



F6prime(r) dF(r)


(34)









r

x

y

Φ22

Φ21



J




y minus y2


1113872 1113873 x M + β1C2( 1113857 + 2S21113858 1113859

r minus r2

1113872 1113873B r minus r2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(35)










r

x

y

Φ 1

Φ 2









0102030405060708091010203040506070809

1

GovernmentESCOs

Bank

s

01 02 03 04 05 06 07 08 09 1


010203040506070809

1

GovernmentESCOs

Ow

ners

01 002030405060708091

01 02 03 04 05 06 07 08 09 1


0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p




0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

C2 = 12C2 = 14C2 = 16

C2 = 18C2 = 20










0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

S2 = 1S2 = 3S2 = 5

S2 = 7S2 = 9


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

S3 = 5S3 = 9S3 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

C6 = 5C6 = 7C6 = 9

C6 = 11C6 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

B = 2B = 6B = 10












Data Availability




References





























































(17)


F3(z) dz



z

x

y

Ω11

Ω12



F3prime(z) dF(z)











J



1113872 1113873 minus β1I minus wI1113858 1113859

y minus y2


1113872 1113873S2

z minus z2

1113872 1113873 w + β2( 1113857I z minus z2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(20)



z

x

y

Ω21

Ω22














(22)


F4(X) dx



z

x

y

Ω 2

Ω 1



Tabl

e3

Eigenv

aluesof

each

equilib

rium

point

Equilib

rium

points

Result

State

middotmiddotλ 1

middotλ2

middotλ3

E 1(00

0)

V1

minusC1

+S1

minusV

2+

M+ωI

C3

minusV

4+

V3

minusC2

V5

minusC4

+C5

minusV

6Uncertainty

E 2(10

0)

minus(

V1

minusC1

+S1

minusV

2+

M+ωI

)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

V5

minusC4

+C5

minusV

6+

(ω

+β 2

)IUncertainty

E 3(01

0)

V1

minusC1

minusV

2minusβ 1

C2

+ωI

minus(

C3

minusV

4+

V3

minusC2)

V5

minusC4

+C5

minusV

6+

S3

Uncertainty

E 4(00

1)

V1

minusC1

+S1

minusV

2+

Mminusβ 1

IC3

minusV

4+

V3

minusC2

+S2

minus(

V5

minusC4

+C5

minusV

6)Uncertainty

E 5(11

0)

minus(

V1

minusC1

minusV

2minusβ 1

C2

+ωI

)minus

(C3

minusV

4+

V3

minusC2

+β 1

C2

+M

)V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3

Uncertainty

E 6(10

1)

minus(

V1

minusC1

+S1

minusV

2+

Mminusβ 2

I)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I]

Uncertainty

E 7(01

1)

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2

minus(

C3

minusV

4+

V3

minusC2

+S2)

minus(

V5

minusC4

+C5

minusV

6+

S3)

Uncertainty

E 8(11

1)

minus(

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2)

minus(

C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2)

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3]

Uncertainty


F4prime(x) dF(x)




















(27)


F5(y) dy




F5prime(y) dF(y)



















r

x

y

Φ12

Φ11






(32)


F6(r) dr



F6prime(r) dF(r)


(34)









r

x

y

Φ22

Φ21



J




y minus y2


1113872 1113873 x M + β1C2( 1113857 + 2S21113858 1113859

r minus r2

1113872 1113873B r minus r2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(35)










r

x

y

Φ 1

Φ 2









0102030405060708091010203040506070809

1

GovernmentESCOs

Bank

s

01 02 03 04 05 06 07 08 09 1


010203040506070809

1

GovernmentESCOs

Ow

ners

01 002030405060708091

01 02 03 04 05 06 07 08 09 1


0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p




0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

C2 = 12C2 = 14C2 = 16

C2 = 18C2 = 20










0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

S2 = 1S2 = 3S2 = 5

S2 = 7S2 = 9


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

S3 = 5S3 = 9S3 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

C6 = 5C6 = 7C6 = 9

C6 = 11C6 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

B = 2B = 6B = 10












Data Availability




References












































F3prime(z) dF(z)











J



1113872 1113873 minus β1I minus wI1113858 1113859

y minus y2


1113872 1113873S2

z minus z2

1113872 1113873 w + β2( 1113857I z minus z2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(20)



z

x

y

Ω21

Ω22














(22)


F4(X) dx



z

x

y

Ω 2

Ω 1



Tabl

e3

Eigenv

aluesof

each

equilib

rium

point

Equilib

rium

points

Result

State

middotmiddotλ 1

middotλ2

middotλ3

E 1(00

0)

V1

minusC1

+S1

minusV

2+

M+ωI

C3

minusV

4+

V3

minusC2

V5

minusC4

+C5

minusV

6Uncertainty

E 2(10

0)

minus(

V1

minusC1

+S1

minusV

2+

M+ωI

)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

V5

minusC4

+C5

minusV

6+

(ω

+β 2

)IUncertainty

E 3(01

0)

V1

minusC1

minusV

2minusβ 1

C2

+ωI

minus(

C3

minusV

4+

V3

minusC2)

V5

minusC4

+C5

minusV

6+

S3

Uncertainty

E 4(00

1)

V1

minusC1

+S1

minusV

2+

Mminusβ 1

IC3

minusV

4+

V3

minusC2

+S2

minus(

V5

minusC4

+C5

minusV

6)Uncertainty

E 5(11

0)

minus(

V1

minusC1

minusV

2minusβ 1

C2

+ωI

)minus

(C3

minusV

4+

V3

minusC2

+β 1

C2

+M

)V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3

Uncertainty

E 6(10

1)

minus(

V1

minusC1

+S1

minusV

2+

Mminusβ 2

I)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I]

Uncertainty

E 7(01

1)

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2

minus(

C3

minusV

4+

V3

minusC2

+S2)

minus(

V5

minusC4

+C5

minusV

6+

S3)

Uncertainty

E 8(11

1)

minus(

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2)

minus(

C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2)

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3]

Uncertainty


F4prime(x) dF(x)




















(27)


F5(y) dy




F5prime(y) dF(y)



















r

x

y

Φ12

Φ11






(32)


F6(r) dr



F6prime(r) dF(r)


(34)









r

x

y

Φ22

Φ21



J




y minus y2


1113872 1113873 x M + β1C2( 1113857 + 2S21113858 1113859

r minus r2

1113872 1113873B r minus r2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(35)










r

x

y

Φ 1

Φ 2









0102030405060708091010203040506070809

1

GovernmentESCOs

Bank

s

01 02 03 04 05 06 07 08 09 1


010203040506070809

1

GovernmentESCOs

Ow

ners

01 002030405060708091

01 02 03 04 05 06 07 08 09 1


0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p




0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

C2 = 12C2 = 14C2 = 16

C2 = 18C2 = 20










0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

S2 = 1S2 = 3S2 = 5

S2 = 7S2 = 9


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

S3 = 5S3 = 9S3 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

C6 = 5C6 = 7C6 = 9

C6 = 11C6 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

B = 2B = 6B = 10












Data Availability




References























































(22)


F4(X) dx



z

x

y

Ω 2

Ω 1



Tabl

e3

Eigenv

aluesof

each

equilib

rium

point

Equilib

rium

points

Result

State

middotmiddotλ 1

middotλ2

middotλ3

E 1(00

0)

V1

minusC1

+S1

minusV

2+

M+ωI

C3

minusV

4+

V3

minusC2

V5

minusC4

+C5

minusV

6Uncertainty

E 2(10

0)

minus(

V1

minusC1

+S1

minusV

2+

M+ωI

)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

V5

minusC4

+C5

minusV

6+

(ω

+β 2

)IUncertainty

E 3(01

0)

V1

minusC1

minusV

2minusβ 1

C2

+ωI

minus(

C3

minusV

4+

V3

minusC2)

V5

minusC4

+C5

minusV

6+

S3

Uncertainty

E 4(00

1)

V1

minusC1

+S1

minusV

2+

Mminusβ 1

IC3

minusV

4+

V3

minusC2

+S2

minus(

V5

minusC4

+C5

minusV

6)Uncertainty

E 5(11

0)

minus(

V1

minusC1

minusV

2minusβ 1

C2

+ωI

)minus

(C3

minusV

4+

V3

minusC2

+β 1

C2

+M

)V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3

Uncertainty

E 6(10

1)

minus(

V1

minusC1

+S1

minusV

2+

Mminusβ 2

I)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I]

Uncertainty

E 7(01

1)

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2

minus(

C3

minusV

4+

V3

minusC2

+S2)

minus(

V5

minusC4

+C5

minusV

6+

S3)

Uncertainty

E 8(11

1)

minus(

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2)

minus(

C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2)

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3]

Uncertainty


F4prime(x) dF(x)




















(27)


F5(y) dy




F5prime(y) dF(y)



















r

x

y

Φ12

Φ11






(32)


F6(r) dr



F6prime(r) dF(r)


(34)









r

x

y

Φ22

Φ21



J




y minus y2


1113872 1113873 x M + β1C2( 1113857 + 2S21113858 1113859

r minus r2

1113872 1113873B r minus r2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(35)










r

x

y

Φ 1

Φ 2









0102030405060708091010203040506070809

1

GovernmentESCOs

Bank

s

01 02 03 04 05 06 07 08 09 1


010203040506070809

1

GovernmentESCOs

Ow

ners

01 002030405060708091

01 02 03 04 05 06 07 08 09 1


0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p




0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

C2 = 12C2 = 14C2 = 16

C2 = 18C2 = 20










0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

S2 = 1S2 = 3S2 = 5

S2 = 7S2 = 9


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

S3 = 5S3 = 9S3 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

C6 = 5C6 = 7C6 = 9

C6 = 11C6 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

B = 2B = 6B = 10












Data Availability




References












































Tabl

e3

Eigenv

aluesof

each

equilib

rium

point

Equilib

rium

points

Result

State

middotmiddotλ 1

middotλ2

middotλ3

E 1(00

0)

V1

minusC1

+S1

minusV

2+

M+ωI

C3

minusV

4+

V3

minusC2

V5

minusC4

+C5

minusV

6Uncertainty

E 2(10

0)

minus(

V1

minusC1

+S1

minusV

2+

M+ωI

)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

V5

minusC4

+C5

minusV

6+

(ω

+β 2

)IUncertainty

E 3(01

0)

V1

minusC1

minusV

2minusβ 1

C2

+ωI

minus(

C3

minusV

4+

V3

minusC2)

V5

minusC4

+C5

minusV

6+

S3

Uncertainty

E 4(00

1)

V1

minusC1

+S1

minusV

2+

Mminusβ 1

IC3

minusV

4+

V3

minusC2

+S2

minus(

V5

minusC4

+C5

minusV

6)Uncertainty

E 5(11

0)

minus(

V1

minusC1

minusV

2minusβ 1

C2

+ωI

)minus

(C3

minusV

4+

V3

minusC2

+β 1

C2

+M

)V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3

Uncertainty

E 6(10

1)

minus(

V1

minusC1

+S1

minusV

2+

Mminusβ 2

I)C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I]

Uncertainty

E 7(01

1)

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2

minus(

C3

minusV

4+

V3

minusC2

+S2)

minus(

V5

minusC4

+C5

minusV

6+

S3)

Uncertainty

E 8(11

1)

minus(

V1

minusC1

minusV

2minusβ 2

Iminusβ 1

C2)

minus(

C3

minusV

4+

V3

minusC2

+β 1

C2

+M

+S2)

minus[V

5minus

C4

+C5

minusV

6+

(ω

+β 2

)I+

S3]

Uncertainty


F4prime(x) dF(x)




















(27)


F5(y) dy




F5prime(y) dF(y)



















r

x

y

Φ12

Φ11






(32)


F6(r) dr



F6prime(r) dF(r)


(34)









r

x

y

Φ22

Φ21



J




y minus y2


1113872 1113873 x M + β1C2( 1113857 + 2S21113858 1113859

r minus r2

1113872 1113873B r minus r2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(35)










r

x

y

Φ 1

Φ 2









0102030405060708091010203040506070809

1

GovernmentESCOs

Bank

s

01 02 03 04 05 06 07 08 09 1


010203040506070809

1

GovernmentESCOs

Ow

ners

01 002030405060708091

01 02 03 04 05 06 07 08 09 1


0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p




0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

C2 = 12C2 = 14C2 = 16

C2 = 18C2 = 20










0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

S2 = 1S2 = 3S2 = 5

S2 = 7S2 = 9


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

S3 = 5S3 = 9S3 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

C6 = 5C6 = 7C6 = 9

C6 = 11C6 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

B = 2B = 6B = 10












Data Availability




References












































F4prime(x) dF(x)




















(27)


F5(y) dy




F5prime(y) dF(y)



















r

x

y

Φ12

Φ11






(32)


F6(r) dr



F6prime(r) dF(r)


(34)









r

x

y

Φ22

Φ21



J




y minus y2


1113872 1113873 x M + β1C2( 1113857 + 2S21113858 1113859

r minus r2

1113872 1113873B r minus r2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(35)










r

x

y

Φ 1

Φ 2









0102030405060708091010203040506070809

1

GovernmentESCOs

Bank

s

01 02 03 04 05 06 07 08 09 1


010203040506070809

1

GovernmentESCOs

Ow

ners

01 002030405060708091

01 02 03 04 05 06 07 08 09 1


0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p




0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

C2 = 12C2 = 14C2 = 16

C2 = 18C2 = 20










0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

S2 = 1S2 = 3S2 = 5

S2 = 7S2 = 9


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

S3 = 5S3 = 9S3 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

C6 = 5C6 = 7C6 = 9

C6 = 11C6 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

B = 2B = 6B = 10












Data Availability




References












































F5prime(y) dF(y)



















r

x

y

Φ12

Φ11






(32)


F6(r) dr



F6prime(r) dF(r)


(34)









r

x

y

Φ22

Φ21



J




y minus y2


1113872 1113873 x M + β1C2( 1113857 + 2S21113858 1113859

r minus r2

1113872 1113873B r minus r2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(35)










r

x

y

Φ 1

Φ 2









0102030405060708091010203040506070809

1

GovernmentESCOs

Bank

s

01 02 03 04 05 06 07 08 09 1


010203040506070809

1

GovernmentESCOs

Ow

ners

01 002030405060708091

01 02 03 04 05 06 07 08 09 1


0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p




0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

C2 = 12C2 = 14C2 = 16

C2 = 18C2 = 20










0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

S2 = 1S2 = 3S2 = 5

S2 = 7S2 = 9


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

S3 = 5S3 = 9S3 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

C6 = 5C6 = 7C6 = 9

C6 = 11C6 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

B = 2B = 6B = 10












Data Availability




References















































(32)


F6(r) dr



F6prime(r) dF(r)


(34)









r

x

y

Φ22

Φ21



J




y minus y2


1113872 1113873 x M + β1C2( 1113857 + 2S21113858 1113859

r minus r2

1113872 1113873B r minus r2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(35)










r

x

y

Φ 1

Φ 2









0102030405060708091010203040506070809

1

GovernmentESCOs

Bank

s

01 02 03 04 05 06 07 08 09 1


010203040506070809

1

GovernmentESCOs

Ow

ners

01 002030405060708091

01 02 03 04 05 06 07 08 09 1


0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p




0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

C2 = 12C2 = 14C2 = 16

C2 = 18C2 = 20










0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

S2 = 1S2 = 3S2 = 5

S2 = 7S2 = 9


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

S3 = 5S3 = 9S3 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

C6 = 5C6 = 7C6 = 9

C6 = 11C6 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

B = 2B = 6B = 10












Data Availability




References












































J




y minus y2


1113872 1113873 x M + β1C2( 1113857 + 2S21113858 1113859

r minus r2

1113872 1113873B r minus r2


⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(35)










r

x

y

Φ 1

Φ 2









0102030405060708091010203040506070809

1

GovernmentESCOs

Bank

s

01 02 03 04 05 06 07 08 09 1


010203040506070809

1

GovernmentESCOs

Ow

ners

01 002030405060708091

01 02 03 04 05 06 07 08 09 1


0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p




0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

C2 = 12C2 = 14C2 = 16

C2 = 18C2 = 20










0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

S2 = 1S2 = 3S2 = 5

S2 = 7S2 = 9


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

S3 = 5S3 = 9S3 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

C6 = 5C6 = 7C6 = 9

C6 = 11C6 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

B = 2B = 6B = 10












Data Availability




References


















































0102030405060708091010203040506070809

1

GovernmentESCOs

Bank

s

01 02 03 04 05 06 07 08 09 1


010203040506070809

1

GovernmentESCOs

Ow

ners

01 002030405060708091

01 02 03 04 05 06 07 08 09 1


0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p




0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

C2 = 12C2 = 14C2 = 16

C2 = 18C2 = 20










0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

S2 = 1S2 = 3S2 = 5

S2 = 7S2 = 9


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

S3 = 5S3 = 9S3 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

C6 = 5C6 = 7C6 = 9

C6 = 11C6 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

B = 2B = 6B = 10












Data Availability




References



















































0 02 04 06 08 1 12 14 16 18 20

02

04

06

08

1

12

t

p

S2 = 1S2 = 3S2 = 5

S2 = 7S2 = 9


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

S3 = 5S3 = 9S3 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

C6 = 5C6 = 7C6 = 9

C6 = 11C6 = 13


0 02 04 06 08 1 12 14 16 18 2t

0

02

04

06

08

1

12

p

B = 2B = 6B = 10












Data Availability




References





















































Data Availability




References












































game analysis of the multiagent evolution of existing

Documents