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Research ArticleResearch on the Dynamics Game Model in a Green Supply ChainGovernment Subsidy Strategies under the Retailerrsquos SellingEffort Level

Xigang Yuan 12 Xiaoqing Zhang 1 and Dalin Zhang3

1Business School Jiangsu Normal University Xuzhou 221116 China2School of Economics and Management Southwest Jiaotong University Chengdu 610031 China3School of Computing Science and Engineering University of New South Wales Sydney 2052 Australia

Correspondence should be addressed to Xiaoqing Zhang xqzhang22163com

Received 1 February 2020 Accepted 27 May 2020 Published 16 June 2020

Academic Editor Dimitri Volchenkov

Copyright copy 2020 Xigang Yuan 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

Based on dynamic game theory and the principal-agent theory this paper examined different government subsidy strategies ingreen supply chain management Assuming that the retailerrsquos level of selling effort involved asymmetric information this studyanalyzed the impact of different government subsidy strategies on the wholesale price the product greenness level retail price thelevel of selling effort the manufacturerrsquos profit and the retailerrsquos profit e results showed that (1) the governmentrsquos subsidystrategy can effectively not only improve the product greenness level but also increase the profits of an enterprise in a green supplychain which helps the retailer to enhance their selling effort (2) regardless of whether the retailerrsquos level of selling effort was highor low as the governmentrsquos subsidy coefficient increased the wholesale price continued to decrease and the product greennesslevel and retailerrsquos selling effort level also increased

1 Introduction

With the rapid development of the economy and societyliving standards are improving and there is a trend of rapidgrowth with respect to energy consumption all of which haveled to intense pressure to control the emissions of harmfulgases and reduce the impact of the greenhouse effect and cubenvironmental harm [1] us the development of the greeneconomy and the control of greenhouse gas emissions havegradually become a hot topic Green development and theenvironmental protection have become indispensable factorsto measure healthy economic and societal developmentGreen supply chain management (GSCM) has also become akey point in academic research [2] GSCM aims to enhance afirmrsquos profit andmaintain ecological efficiency at each stage ofthe product life cycle [3] GSCM can enable firms to realizetheir coordination and development efforts e integrationof a green supply chain encourages enterprises to share in-formation and cooperate with each other e relationshipbetween the supply chain and the environment means that

GSCM represents an inevitable trend in the area of sustainableeconomic development

More and more enterprises have focused on GSCM andhave implemented it in practice As a result enterprises paygreater attention to environmental protection and seek toreduce environmental pollution For example in terms ofsustainable development Lenovo explored the constructionand implementation of GSCM and the company strives todevelop leading environmental products so as to minimizethe impact on environment Huawei has begun to work onGSCM and integrate the green concept into their entireprocurement and production process Apple Inc encouragessuppliers to participate in GSCM implements energytransformation and uses recycled or renewable materials asmuch as possible Wal-Mart announced that in the nearfuture the company will utilize only renewable energysources employ a zero waste strategy and sell products thatsatisfy environmental standards

However as more and more enterprises participate inGSCM activities they must also incur higher costs

HindawiComplexityVolume 2020 Article ID 3083761 15 pageshttpsdoiorg10115520203083761

erefore it is far from enough to rely on enterprises topromote GSCM practice and the government should offersubstantially more subsidies to firms that implement theGSCM model e environmental laws and regulations thathave been introduced by the government have encouragedenterprises to attach greater importance to GSCM activitiesFor example ldquoe directive restricting the use of hazardoussubstances in electrical and electronic equipmentrdquo wasimplemented in the European Union in 2006 while ldquoeenergy-saving products for the benefit of peoplerdquo was carriedout in China in 2009 It provided financial subsidies for tencategories of high-efficiency energy-saving products whichhave an energy efficiency grade one or above and it isadvantageous as it promotes the development of energy-saving products It is evident that the government plays avery important role in GSCM activity On the one hand thegovernment can either reward or penalize the manufacturerwith respect to their carbon emissions from their productionprocesses and this reward-penalty mechanism can be usedto reduce carbon emissions On the other hand in order toimprove the sale of green products the government cansubsidize retailers based on their selling effort us theimpact of different types of government subsidy strategies onthe green supply chain management should be worthy ofconsidering

e mainly purpose of this study is to discuss the impactof different types of government subsidy strategies on thegreen supply chain management us we consider a two-level green supply chain system with one manufacturer andone retailer Assuming that the retailerrsquos level of selling effortinvolves asymmetric information we examined the impactof different government subsidy strategies on their decision-making behavior by using dynamic game theory e ob-jectives of this paper include the following (1) to explorehow the different government subsidy strategies influenceenterprise decision-making behavior and (2) to identifywhich types of government subsidy strategies are more ef-fective for implementing GSCM

emain contributions of this paper are as follows (1) webuild three dynamic game models ie a game model withouta government subsidy strategy (NG model) a game modelwith a government subsidized manufacturer (MG model)and a game model with a government subsidized retailer (RGmodel) in GSCMMoreover the retailerrsquos level of selling effortis represented by asymmetric information (2) We discuss theimpact of different government subsidy strategies on deci-sion-making behavior by using dynamic game theoryMoreover we aimed to explore how different governmentsubsidy strategies influence enterprise decision-making be-havior (3) We identify which types of government subsidystrategies are more effective for implementing GSCM

e remainder of this paper was organized as followsSection 2 reviews the relevant literature the problem de-scription and model assumptions are provided in Section 3Section 4 presents the dynamics game model which wasdeveloped to analyze the impact of different governmentsubsidy strategies on decision-making behavior the simu-lation analysis and management implications are outlined inSection 5 and Section 6 presents the conclusions

2 Literature Review

e government subsidy strategy has been thoroughlystudied in the context of GSCM e literature related togovernment subsidy strategies and the application of dy-namic game theory in SCM and GSCM is reviewed andanalyzed in this section GSCM refers to the process ofconsidering environmental problems at each link in thesupply chain and an emphasis is placed on environmentalprotection while promoting the coordinated development ofthe economy and the environment

21 Government Subsidy Strategy in SCM and GSCM egovernment plays a very important role in SCM and inGSCM e government can implement a reward-penaltymechanism or subsidy strategy in order to reduce the cost ofproducing green products and improve the productgreenness level Runkel [4] analyzed the impact of gov-ernment subsidy policies on GSCM Subsequently Aksenet al [5] and Sheu [6] expanded the scope of research in thisarea by examining the influence of government policy onGSCM Aksen et al [5] studied the different impacts of thegovernmentrsquos supportive policy and legislative policy onGSCM Sheu [6] pointed out that the governmentrsquos greenlegislation and the financial intervention policy couldachieve the enterprisersquos interest coordination mechanism ofGSCM Ma et al [7] studied how the consumption-subsidystrategy impacts dual channel GSCM Benjaafar et al [8]used low-carbon factors to solve operational managementproblems in GSCM Toptal et al [9] discussed the carbonemission reduction investment strategy problem in GSCMChen et al [10] analyzed the retailerrsquos optimal decision withgreen technology investment in GSCM Chen et al [11]developed an evolutionary game theory model of the in-teraction between governments and manufacturers based onstatic carbon taxes and subsidiese results showed that thestatic carbon tax and subsidy mechanism implemented bythe governments could not provide the needed positiveimpact on manufacturers decision-making Kang et al [12]examined supply chain operations when the supply chainparticipants acted individually and cooperatively in a ldquogreenpoverty alleviationrdquo supply chain in which the manufacturerinitiated product ldquogreeningrdquo and provided microfinance toalleviate the poverty of poor raw material suppliers by usingdynamics game model He et al [13] considered a dual-channel closed-loop supply chain (CLSC) where a manu-facturer could distribute new products through an inde-pendent retailer and sell remanufactured products via athird-party firm or platform (3P) in the presence of possiblegovernment subsidy ey found that government couldencourage the manufacturer to adopt desired channelstructures by setting appropriate subsidy levels

Some scholars concentrated on the coordination prob-lem under different government strategies Huang et al [14]discussed the governmentrsquos subsidy strategy and highlightedhow customersrsquo bargaining power can influence customerrsquowelfare Zakeri et al [15] analyzed the effect of carbonemission policies on operational management in the case of

2 Complexity

GSCM Li et al [16] studied the relationship between themanufacturer and retailer within the context of governmentcarbon regulations and the results showed that the in-vestment cost contract can reduce carbon emissions inGSCM Li et al [17] analyzed the impact of governmentsubsidy strategies on welfare by employing Nash gametheory Li and Hu [18] developed the Stackelberg gamemodel which considered the government reward-penaltymechanism and analyzed the optimal solution under dif-ferent situations Zhang et al [19] established four gamemodels under fairness preferences in GSCM and comparedthe impact of parameters on the decision-making processGharaei et al [20] proposed a green supply chain gamemodel under a reward-penalty mechanism and green in-vestment policy

e above literature discussed the impact of differentgovernment strategies on GSCM However fewer scholarsdiscuss this problem within the context of asymmetric in-formation In contrast to previous studies this paper ex-amined the effect of government subsidy strategies on thedecision-making process in GSCM under the situation ofasymmetric information

22 Application of Dynamic Game -eory in SCM andGSCM Dynamic game theory proposes that the actions ofthe players are in sequence and that the latter can observethe choice of the former and make corresponding choicesDynamic game theory has become a very important methodthat can be employed in theoretical and applied researchMany scholars discuss human economic decision-makingbehavior and solve operational management problems [21]

Although an extensive amount of research has studiedmany problems in different fields few papers have examinedthe impact of government subsidy strategies on GSCM byusing dynamic game theory Wang et al [22] developed aGSCM model with a dual collection channel without thegovernmentrsquos reward-penalty mechanism and compared itwith the governmentrsquos reward-penalty mechanism Su et al[23] considered the impact of the environmental protectioninput on the whole green supply chain and analyzed theeffect of centralized decision-making and decentralizeddecision-making on the returns and pricing strategies ofeach participant by using dynamic game theory Sun et al[24] studied green investment strategies under a governmentsubsidy policy in a two-echelon green supply chain byemploying dynamic game theory He et al [25] consideredan online-to-offline (O2O) tourism supply chain (TSC)consisting of an offline tourism service provider (TSP) andan online travel agency (OTA) who has a corporate socialresponsibility (CSR)ey built three game-theoretic modelsto explore the optimal online selling model and pricingdecisions for the TSC and its members e result showedthat the TSC should pay more attention to CSR and improveconsumersrsquo channel acceptance for the reselling channel tocreate more total utility Chen et al [26] introduced theconcept of equity as the incentive mechanism to coordinatethe GSCM and established a new network equilibriummodel using dynamic game theory Zhang et al [27] built

three closed-loop supply chain dynamic game models usingdynamics game theory and principal-agent theory More-over they discussed the impact of governmentrsquos reward-penalty mechanism on the decision variables He et al [28]investigated a service supply chain (SC) consisting of aservice provider (SP) who was in charge of carbon emissionreduction and service and a service integrator (SI) who wasresponsible for low-carbon advertising considering cor-porate social responsibility (CSR) ey found that con-sumersrsquo low-carbon preference and chain membersrsquomarginal profits and CSR behaviors significantly influencethe optimal solutions

Based on the above analysis large numbers of studieshave considered governmental strategies in their research onGSCM However the aforementioned studies simply as-sumed that the information between all enterprises issymmetric On the contrary this paper considered a two-level green supply chain system with one manufacturer andone retailer and the retailerrsquos level of selling effort is rep-resented by asymmetric information We build three dy-namic game models ie a game model without agovernment subsidy strategy (NG model) a game modelwith a government subsidized manufacturer (MG model)and a game model with a government subsidized retailer(RG model) in GSCM We discuss the impact of differentgovernment subsidy strategies on decision-making behaviorby using dynamic game theory Moreover we aimed toexplore how different government subsidy strategies influ-ence enterprise decision-making behavior e resultsshowed that governmentrsquos subsidy strategy effectively im-proves not only the product greenness level but also theprofits of an enterprise in GSCM which helps the retailer toimprove their own selling effort level

3 Problem Description andModel Assumptions

31 ProblemDescription In this section we consider a two-level green supply chain system with one manufacturer andone retailer (as shown in Figure 1) e manufacturer (asleader) sells green products to the retailer at the wholesaleprice w and the retailer (as follower) sells green products tothe consumer at pricep Assume that the level of selling effortrepresents asymmetric information Furthermore the re-tailerrsquos selling cost not only corresponds to their own level ofselling effort but also relates to the greenness level and it canbe expressed as cr e2g To simplify the analysis the sellingcost is divided into two types H-type and L-type While themanufacturer does not know the real information about theretailerrsquos selling cost it knows the probability distribution asp(eH) v andp(eL) 1 minus v In order to identify the re-tailerrsquos true information about the selling cost the manu-facturer can design a screening contract thus permitting theretailer to make a rational choice by using the informationscreening method e government can formulate differentsubsidy strategies for the manufacturer and the retailererefore the government can incentivize the manufacturerto produce green products while also encouraging the re-tailer to improve their selling effort

Complexity 3

e following symbols are used in the paper

cm the manufacturerrsquos production costwi the manufacturerrsquos wholesale price which is thedecision variable i isin H L where wH expresses thehigh wholesale price and wL expresses the lowwholesale priced consumerrsquos demand for green products from retailera potential demand in consumer market where agt 0b the sensitivity of market demand to price where bgt 0pi the retailerrsquos selling price which is the decisionvariable i isin H L where pH expresses the high sellingprice and pL expresses the low selling priceλ consumer preference for green productsgi product greenness level which is the decision variablei isin H L where gH expresses a high greenness level andgL expresses a low greenness level (Ghosh and Shah[29 30] Yang and Xiao [31] and Zhu and Dou [32])cri the retailerrsquos selling cost i isin H L where crH

expressesa high selling cost and crL expresses a low selling costei the retailerrsquos selling effort i isin H L where eH ex-presses a high selling effort and eL expresses a selling effortθ the coefficient of the unit product subsidy received bythe manufacturerμ the coefficient of selling cost subsidy received by theretailerz manufacturerrsquos research and develop impact factor

32 Model Assumption To formulate the problem severalassumptions were made

(1) e manufacturer and the retailer are participants inthe Stackelberg game whereby the manufacturer is

the leader and the retailer is the follower and theycan achieve optimal equilibrium by using dynamicgame theory

(2) Both the manufacturer and the retailer are riskneutral and they pursue the maximization of theirown interests

(3) e retailerrsquos level of selling effort is expressed as eii isin H L eL lt eH which indicates that the retailerrsquoshigh level of selling effort is higher than the retailerrsquoslow level of selling effort

(4) To improve the greenness level the government subsidizesthe manufacturer According to Yang and Xiao [31] Li etal [33] Yan et al [34] and Zhang et al [35] θg expressesthe unit product subsidy received by the manufacturer

(5) e government subsidizes the retailer on the basisof the selling cost and μe2g expresses the totalamount of subsidies received by the retailer

(6) e manufacturerrsquos production capacity is infiniteand it can meet the market demand

4 Dynamics Game Model in GSCM

In the paper the retailerrsquos level of selling effort whichrepresents asymmetric information can form a principle-agent relationship between the manufacturer and the re-tailer Information discrimination theory can be used toidentify the type of the retailerrsquos true selling cost In additionthe contract design which is expressed as (eH wL)1113864

(eL wH) (eH wL)1113864 1113865 indicates that the high level of theretailerrsquos selling effort prompts the manufacturer to offer alow wholesale price to the retailer (eL wH)1113864 1113865 indicates thatthe low level of the retailerrsquos selling effort prompts themanufacturer to offer a high wholesale price to the retailere government subsidy strategy was introduced into thegame model e government can implement a subsidy

w d w d w d

p d p d p d

ManufacturerwH wL gH gL

RetailereH eL pH pL

Consumer

ManufacturerwH wL gH gL

RetailereH eL pH pL

Consumer

Governmentθ

ManufacturerwH wL gH gL

RetailereH eL pH pL

Consumer

Governmentμ

(a) NG model (b) MG model (c) RG model

Figure 1 e theoretical model of the green supply chain considering governmentrsquos subsidy strategy under asymmetric information

4 Complexity

strategy for the manufacturer or retailer We also carried outa comparative analysis with the nongovernment subsidystrategy

41GSCMGameModelwithoutGovernment Subsidy Strategy(NG Model) is game model does not consider the gov-ernment subsidy strategy and the manufacturer and theretailer pursue the maximization of their own interests Asthe entrusting party the manufacturer identifies the type ofthe retailerrsquos true selling cost and the contract design as(eH wL) (eL wH)1113864 1113865 e game model is constructed asfollows

When the retailerrsquos selling cost is high its profit functioncan be expressed as

maxpHeH

πNGRH

pH minus ωL( 1113857 a minus bpH + λgH + eH( 1113857 minus e2HgH

(1)

When the retailerrsquos selling cost is low its profit functioncan be expressed as

maxpLeL

πNGRL

pL minus ωH( 1113857 a minus bpL + λgL + eL( 1113857 minus e2LgL (2)

e manufacturerrsquos profit function can be expressed as

maxgHgLωHωL

πNGM v ωL a minus bpH + λgH + eH( 1113857 minus zg

2H1113966 1113967

+(1 minus v) ωH a minus bpL + λgL + eL( 1113857 minus zg2L1113966 1113967

(3)

e constraints can be expressed as

pH minus ωL( 1113857 a minus bpH + λgH + eH( 1113857 minus e2HgH ge π0 (4)

pL minus ωH( 1113857 a minus bpL + λgL + eL( 1113857 minus e2LgL ge π0 (5)

pH minus ωL( 1113857 a minus bpH + λgH + eH( 1113857 minus e2HgH ge pL minus ωH( 1113857 a minus bpL + λgL + eL( 1113857 minus e

2LgL (6)

pL minus ωH( 1113857 a minus bpL + λgL + eL( 1113857 minus e2LgL ge pH minus ωL( 1113857 a minus bpH + λgH + eH( 1113857 minus e

2HgH (7)

where π0 is the retailerrsquos retained profit and constraints (4)and (5) are the participation constraints which indicate thatthe retailer can accept the manufacturerrsquos commission whenthe retailerrsquos profit is greater than the retained profitConstraints (6) and (7) are incentive constraints and indicatethat the retailer can maximize profit by choosing a contractthat corresponds to their own type of selling cost

Proposition 1

(a) -e manufacturerrsquos optimal wholesale price and theoptimal product greenness level are expressed asfollows

ωNGlowast

H aλ + b(2v + 1) 2v2 + a( 1113857

a2 + 8bz

ωNGlowast

L aλ + a(v minus 1)2 b + v2( 1113857

a2 + 8bz

gNGlowast

H 4azλ +(1 minus v) a + 4bv2( 1113857

a2 + 8bz

gNGlowast

L 4az(1 minus v) 4zv + bv2( 1113857

a2 + 8bz

(8)

(b) -e retailerrsquos optimal level of selling effort and theoptimal selling price are expressed as follows

eNGlowast

H 3λ + 2bv(v + 1)

a2 + 8bz

eNGlowast

L λ + bv(v + 1)

a2 + 8bz

pNGlowast

L 12b

a +4λaz(1 minus v) 4zv + bv2( 1113857

a2 + 8bz1113888

+abλ + ab(v minus 1)2 b + v2( 1113857

a2 + 8bz1113889

pNGlowast

H 12b

a +4λaz +(1 minus v) a + 4bv2( 1113857

a2 + 8bz1113888

+abλ + b2(2v + 1) 2v2 + a( 1113857

a2 + 8bz1113889

(9)

Proof First we can obtain the first and second derivatives ofpNG

H eNGH pNG

L eNGL from functions (1) and (2)

Complexity 5

zπNGRH

zpNGH

minus2bpNGH + a + λg

NGH + e

NGH + bw

NGL

z2πNGRH

z pNGH( 1113857

2 minus2blt 0

zπNGRH

zeNGH

pNGH minus ωNG

L1113872 1113873 minus 2eNGH g

NGH

z2πNGRH

z eNGH( 1113857

2 minus2gNGH lt 0

zπNGRL

zpNGL

minus2bpNGL + a + λg

NGL + e

NGL + bw

NGH

z2πNGRL

z pNGL( 1113857

2 minus2blt 0

zπNGRL

zeNGL

pNGL minus ωNG

H1113872 1113873 minus 2eNGL g

NGL

z2πNGRL

z eNGL( 1113857

2 minus2gNGL lt 0

(10)

Assuming that the first derivative of thepNG

H eNGH pNG

L eNGL is equal to zero we can derive the

following

pNGH

a + cg minus bwL

4bg minus 1

eNGH

a minus bwH + λg

4bg minus 1

pNGL

2ag minus wL + 2λg2 + 2bgwL

4bg minus 1

eNGL

2ag minus wH + 2λg2 + 2bwHg

4bg minus 1

(11)

Taking equation (11) into the manufacturerrsquos profit wecan determine that

maxgωHωL

πNGM v ωL a minus b

a + cg minus bwL

4bg minus 1+ λg +

a minus bwH + λg

4bg minus 11113888 1113889 minus zg

21113896 1113897

+(1 minus v) ωH a minus b2ag minus wL + 2λg2 + 2bgwL

4bg minus 1+ λg +

2ag minus wH + 2λg2 + 2bwHg

4bg minus 11113888 1113889 minus zg

21113896 1113897

(12)

From equation (12) we can obtain the first and secondderivatives of ωNG

H and gNGH and the Hessian matrix H1 can

be expressed as follows

H1

b(v minus 1)minusλ(v minus 1)

2

minusλ(v minus 1)

22z(v minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(13)

If λ2 minus 2bzlt 0 the Hessian matrix H1 is negative suchthat πNG

M is the concave function while equation (12) has themaximum so we can obtain the optimal value ωNGlowast

H andgNGlowast

H On the contrary from equation (12) we can obtainthe first and the second derivatives of ωNG

L and gNGL and the

Hessian matrix H2 can be expressed as follows

H2

b(v minus 1)minusλ(v minus 1)

2

minusλ(v minus 1)

22z(v minus 1)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(14)

If λ2 minus 2bzlt 0 the Hessian matrix H2 is negative suchthat πNG

M is the concave function while equation (12) has themaximum so we can obtain the optimal value ωNGlowast

L andgNGlowast

L us we can determine Proposition 1

Theorem 1 Assume that the retailerrsquos level of selling effort isrepresented by asymmetric information Without the gov-ernment subsidy strategy and with an increasing greenpreference among consumers the wholesale price manufac-turerrsquos product greenness level retailerrsquos selling effort leveland retailerrsquos selling price continue to increase

According to Proposition 1 and eorem 1 we obtainthe following managerial insight Without the governmentsubsidy strategy the level of selling effort is the retailerrsquosprivate information in order to obtain more profit themanufacturer should invest more in the production of greenproducts and strive to improve the greenness level of theproduct e manufacturer should communicate with theretailer so as to motivate them to sell more green productsand make more profits

6 Complexity

42GSCMGameModelwithGovernment Subsidization of theManufacturer (MG Model) In order to encourage themanufacturer to produce more green products the gov-ernment should subsidize the manufacturers According toDai et al (2017) and Yang and Xiao [31] θg expresses theunit product subsidy received by the manufacturer egame model can be constructed as follows

When the retailerrsquos selling cost is high its profit functioncan be expressed as

maxpHeH

πNGRH

pH minus ωL( 1113857 a minus bpH + λgH + eH( 1113857 minus e2HgH

(15)

When the retailerrsquos selling cost is low its profit functioncan be expressed as

maxpLeL

πNGRL

pL minus ωH( 1113857 a minus bpL + λgL + eL( 1113857 minus e2LgL (16)

e manufacturerrsquos profit function can be expressed as

maxgHgLωLωH

πMGM v ωL + θgH( 1113857 a minus bpH + λgH + eH( 1113857 minus zg

2H1113966 1113967

+(1 minus v) ωH + θgL( 1113857 a minus bpL + λgL + eL( 1113857 minus zg2L1113966 1113967

(17)

e constraints can be expressed as follows

pH minus ωL( 1113857 a minus bpH + λgH + eH( 1113857 minus e2HgH ge π0 (18)

pL minus ωH( 1113857 a minus bpL + λgL + eL( 1113857 minus e2LgL ge π0 (19)

pH minus ωL( 1113857 a minus bpH + λgH + eH( 1113857 minus e2HgH ge pL minus ωH( 1113857 a minus bpL + λgL + eL( 1113857 minus e

2LgL (20)

pL minus ωH( 1113857 a minus bpL + λgL + eL( 1113857 minus e2LgL ge pH minus ωL( 1113857 a minus bpH + λgH + eH( 1113857 minus e

2HgH (21)

where π0 is the retailerrsquos retained profit constraints (18) and(19) are the participation constraints which indicate that theretailer can accept the manufacturerrsquos commission when theretailerrsquos profit is greater than the retained profit Con-straints (20) and (21) are incentive constraints which in-dicate that the retailer can maximize profit by choosing acontract that corresponds to their own type of selling cost

Proposition 2

(a) -e manufacturerrsquos optimal wholesale price and theoptimal product greenness level are expressed asfollows

ωMGlowastH

aλ minus bθ + b(2v + 1) 2v2 + a( 1113857

a2 + 8bz

ωMGlowastL

aλ minus bθ + a(v minus 1)2 b + v2( 1113857

a2 + 8bz

gMGlowastH

4zbθλ + 4az +(1 minus v) a + 4bv2( 1113857

a2 + 8bz

gMGlowastL

4zbλθ + 4az 4zv + bv2( 1113857

a2 + 8bz

(22)

(b) -e retailerrsquos optimal selling effort level and the op-timal selling price can be expressed as follows

eMGlowastH

3λ + 2bv(v + 1) + 4vθ2

a2 + 8bz

eMGlowastL

λ + bv(v + 1) + 2vθa2 + 8bz

pMGlowastL

12b

a +4zbλ2θ + 4azλ 4zv + bv2( 1113857

a2 + 8bz1113888

+abλ + 4b2θ + ab(v minus 1)2 b + v2( 1113857

a2 + 8bz1113889

pMGlowastH

12b

a +4zbθλ2 + 4azλ + λ(1 minus v) a + 4bv2( 1113857

a2 + 8bz1113888

+abλ + 4b2θ + b2(2v + 1) 2v2 + a( 1113857

a2 + 8bz1113889

(23)

-e proof process is similar to that of Proposition 1

Theorem 2 Assume that the retailerrsquos level of selling effort isrepresented by asymmetric information Considering that thegovernment subsidizes the manufacturer and given in-creasing green preferences among consumers there is anincrease in the wholesale price the manufacturerrsquos productgreenness level the retailerrsquos level of selling effort and re-tailerrsquos selling price

Complexity 7

Theorem 3 Assume that the retailerrsquos level of selling effort isrepresented by asymmetric information Considering that thegovernment subsidizes the manufacturer and given a higherunit product subsidy coefficient there is an increase in themanufacturerrsquos product greenness level the retailerrsquos sellingeffort level and the retailerrsquos selling price However themanufacturerrsquos wholesale price decreases

According to Proposition 2 and eorems 2 and 3 weobtain the following managerial insight When the gov-ernment subsidizes the manufacturer the manufacturerobtains the subsidy so that the manufacturer can reduce thewholesale price of green products In this way the purchasecost of the retailer can be reduced so that the retailer can bemore effectively encouraged to sell more green products Asa result the manufacturer can obtain much more profit

43GSCMGameModelwithGovernment Subsidization of theRetailer (MG Model) e government encourages the re-tailer to sell more green products Based on the retailerrsquosselling cost the government subsidizes the retailer e total

amount of subsidies received by the retailer can be expressedas μe2g e game model can be constructed as follows

When the retailerrsquos selling cost is high its profit functioncan be expressed as

maxpHeH

πNGRH

pH minus ωL( 1113857 a minus bpH + λgH + eH( 1113857 +(μ minus 1)e2HgH

(24)

When the retailerrsquos selling cost is low its profit functioncan be expressed as

maxpLeL

πNGRL

pL minus ωH( 1113857 a minus bpL + λgL + eL( 1113857 +(μ minus 1)e2LgL

(25)

e manufacturerrsquos profit function can be expressed as

maxgHgLωLωH

πMGM v ωL a minus bpH + λgH + eH( 1113857 minus zg

2H1113966 1113967

+(1 minus v) ωH a minus bpL + λgL + eL( 1113857 minus zg2L1113966 1113967

(26)

e constraints can be expressed as follows

pH minus ωL( 1113857 a minus bpH + λgH + eH( 1113857 +(μ minus 1)e2HgH ge π0 (27)

pL minus ωH( 1113857 a minus bpL + λgL + eL( 1113857 +(μ minus 1)e2LgL ge π0 (28)

pH minus ωL( 1113857 a minus bpH + λgH + eH( 1113857 +(μ minus 1)e2HgH ge pL minus ωH( 1113857 a minus bpL + λgL + eL( 1113857 +(μ minus 1)e

2LgL (29)

pL minus ωH( 1113857 a minus bpL + λgL + eL( 1113857 +(μ minus 1)e2LgL ge pH minus ωL( 1113857 a minus bpH + λgH + eH( 1113857 +(μ minus 1)e

2HgH (30)

where π0 is the retailerrsquos retained profit constraints (27) and(28) are the participation constraints which indicate that theretailer can accept the manufacturerrsquos commission when theretailerrsquos profit is greater than the retained profit Con-straints (29) and (30) are incentive constraints which in-dicate that the retailer can maximize profit by choosing acontract that corresponds to their own type of selling cost

Proposition 3

(a) -e manufacturerrsquos optimal wholesale price and theoptimal product greenness level can be expressed asfollows

ωRGlowast

H aλ minus 4bμ + b(2v + 1) 2v2 + a( 1113857

a2 + 8bz

ωRGlowast

L aλ minus 4bμ + a(v minus 1)2 b + v2( 1113857

a2 + 8bz

gRGlowast

H 2λμ + 4az +(1 minus v) a + 4bv2( 1113857

a2 + 8bz

gRGlowast

L 2λμ + 4az 4zv + bv2( 1113857

a2 + 8bz

(31)

(b) -e retailerrsquos optimal level of selling effort and theoptimal selling price are expressed as follows

eRGlowast

H 3λ + 2bv(v + 1) + 2vμ

a2 + 8bz

eRGlowast

L λ + bv(v + 1) + vμ

a2 + 8bz

pRGlowast

L 12b

a +2λ2μ + 4azλ 4zv + bv2( 1113857

a2 + 8bz1113888

+abλ + b2λμ + ab(v minus 1)2 b + v2( 1113857

a2 + 8bz1113889

pRGlowast

H 12b

a +2λ2μ + 4azλ + λ(1 minus v) a + 4bv2( 1113857

a2 + 8bz1113888

+abλ + b2λμ + b2(2v + 1) 2v2 + a( 1113857

a2 + 8bz1113889

(32)

-e proof process is similar that of Proposition 1

8 Complexity

Theorem 4 Assume that the retailerrsquos selling effort is rep-resented by asymmetric information Considering that thegovernment subsidizes the retailer and given increasing greenpreferences among consumers there is an increase in thewholesale price the manufacturerrsquos product greenness levelthe retailerrsquos selling effort level and the retailerrsquos selling price

Theorem 5 Assume that the retailerrsquos level of selling effort isrepresented by asymmetric information Considering that thegovernment subsidizes the retailer and given the increasingcoefficient of the selling cost subsidy there is an increase in themanufacturerrsquos product greenness level the retailerrsquos sellingeffort level and the retailerrsquos selling price However themanufacturerrsquos wholesale price decreases

According to Proposition 3 and eorems 4 and 5 weobtain the following managerial insight When the greenpreferences among consumers is higher on the one handthe manufacturer should improve the investment and in-crease the greenness level of the product so that it can meetthe consumerrsquos demand On the other hand the retailer getsthe governmentrsquos subsidy and it can improve the sellingeffort level and enlarge the selling quantity of green prod-ucts As a result the manufacturer and the retailer can obtainmuch more profit

5 Result Analysis andManagement Implications

51 Comparative Basis Based on eorems 3 and 5 thegovernment subsidy not only improves the degree ofgreenness but also increases the retailerrsquos level of sellingeffort and the retailerrsquos selling price Based on the samegovernment subsidy expenditure we can compare andanalyze the different effects of the two types of subsidystrategies e total government subsidy expenditure underthe two types of subsidy strategies can be expressed asfollows

EMGlowast(θ)

θ a + 3bλ + b2 +(2v + 1) v2 + 2( 1113857( 1113857

(a + 8bz)3

ERGlowast

(μ) μ(3λ + 2bv(v + 1) + 2v) 4az +(1 minus v) a + 4bv2( 1113857( 1113857

a2 + 8bz( )3

(33)

In order to get the same amount of government subsidyexpenditure it makes the comparison more meaningfuleparameters θ and μ should satisfy a quantitative relationshipAssuming that EMGlowast

(θ) ERGlowast

(μ) we can obtain the valueμ(θ)RG lowast which can be expressed as follows

μ(θ)RGlowast

θ a + 3bλ + b2 +(2v + 1) v2 + 2( 1113857( 1113857

(3λ + 2bv(v + 1) + 2v) 4az +(1 minus v) a + 4bv2( )( )

(34)

52 Comparative Analysis e reasons as to why the gov-ernment would subsidize the enterprise in GSCM can be

explained as follows on the one hand the government canimprove the greenness of the products produced by themanufacturer on the other hand it can encourage the re-tailer to sell more green products Based on the aboveanalysis the optimal solutions of GSCM in each of the threesituations can be compared and analyzed and it is beneficialto examine the different effects of government subsidystrategies We can derive the following corollaries

Corollary 1 Under the same amount of government subsidyexpenditure when the retailerrsquos level of selling effort is highthere is a negative relationship between the coefficient of theunit product subsidy received by manufacturer and thewholesale price -ere is a positive relationship between thecoefficient of the unit product subsidy received by the man-ufacturer and the product greenness level the retailerrsquos level ofselling effort and the retailerrsquos selling price When the re-tailerrsquos selling effort is low we arrive at the same conclusionIn addition when the retailerrsquos level of selling effort is highthere is a negative relationship between the coefficient of theselling cost subsidy received by the retailer and the wholesaleprice -ere is a positive relationship between the coefficient ofthe selling cost subsidy received by the retailer and the productgreenness level the retailerrsquos level of selling effort and theretailerrsquos selling price When the retailerrsquos selling effort is lowwe arrive at the same conclusion

Proof We can derive the first derivatives of wMGlowastH

wMGlowastL gMGlowast

H gMG lowastL eMGlowast

H eMGlowastL pMGlowast

H andpMGlowastL from

Proposition 2 and we can obtain the followingzωMGlowast

H

zθ minus

b

a2 + 8bzlt 0

zωMGlowastL

zθ minus

b

a2 + 8bzlt 0

zgMGlowastH

zθ

4zbλa2 + 8bz

gt 0

zgMGlowastL

zθ

4zbλa2 + 8bz

gt 0

zeMGlowastH

zθ

8vθa2 + 8bz

gt 0

zeMGlowastL

zθ

2v

a2 + 8bzgt 0

zpMGlowastL

zθ2zλ2 + 2b

a2 + 8bzgt 0

zpMGlowastH

zθ2zλ2 + 2b

a2 + 8bzgt 0

(35)

We can derive the first derivatives of wRGlowast

H wRG lowast

L

gRG lowast

H gRG lowast

L eRGlowast

H eRG lowast

L pRGlowast

H andpRG lowast

L from Proposition 3and we can determine the following

Complexity 9

zωRGlowast

H

zμ minus

4b

a2 + 8bzlt 0

zωRGlowast

L

zμ minus

4b

a2 + 8bzlt 0

zgRGlowast

H

zμ

2λa2 + 8bz

gt 0

zgRGlowast

L

zθ

2λa2 + 8bz

gt 0

zeRGlowast

H

zμ

2v

a2 + 8bzgt 0

zeRGlowast

L

zμ

v

a2 + 8bzgt 0

zpRGlowast

L

zμ

12b

2λ2 + b2λa2 + 8bz

1113888 1113889gt 0

zpRGlowast

H

zθ

12b

2λ2 + b2λa2 + 8bz

1113888 1113889gt 0

(36)

us we can obtain Corollary 1

Corollary 2 Under the same amount of government subsidyexpenditure and when the retailerrsquos level of selling effort ishigh under different situations the manufacturerrsquos optimalwholesale price has the following inequalityωNGlowast

H gtωRG lowast

H gtωMGlowast

H When the retailerrsquos level of selling effortis low under different situations the manufacturerrsquos optimalwholesale price has the following inequalityωNGlowast

L gtωRG lowast

L gtωMGlowast

L

Corollary 2 shows that the governmentrsquos subsidy strategycan lower the manufacturerrsquos wholesale price On the onehand without the government subsidy strategy the man-ufacturer must improve the wholesale price in order toobtain higher profits Under the government subsidystrategy the manufacturer can receive certain economiccompensation from the government so that the manufac-turer can lower the wholesale price However when thegovernment subsidizes the manufacturer the wholesaleprice is lower than that which would be observed in the caseof government subsidization of the retailer

Corollary 3 Under the same amount of government subsidyexpenditure when the retailerrsquos level of selling effort is highunder different situations the manufacturerrsquos optimal level ofgreenness has the following inequality gNGlowast

H ltgRGlowast

H ltgMG lowast

H When the retailerrsquos level of selling effort is low under differentsituations the manufacturerrsquos optimal greenness level has thefollowing inequality gNG lowast

L ltgRG lowast

L ltgMG lowast

L

Corollary 3 shows that the governmentrsquos subsidy strategycan improve the manufacturerrsquos greenness level On the onehand without the government subsidy strategy the man-ufacturer can reduce the cost to earnmoremoney which can

result in a lower greenness level Under the governmentsubsidy strategy the manufacturer can receive certaineconomic compensation from the government so that themanufacturer can improve the greenness level On the otherhand when the government subsidizes the manufacturerthe product greenness level is higher than that which wouldbe observed when the government subsidizes the retailerFrom the perspective of the level of product greenness thegovernmentrsquos subsidization of the manufacturer is moreeffective than subsidization of the retailer

Corollary 4 Under the same amount of government subsidyexpenditure when the retailerrsquos level of selling effort is highthe retailerrsquos optimal selling effort has the following inequalityeNGlowast

H lt eMG lowast

H lt eRGlowast

H When the retailerrsquos level of selling effort islow the retailerrsquos optimal selling effort has the followinginequality eNG lowast

L lt eMGlowast

L lt eRG lowast

L

Corollary 4 shows that the governmentrsquos subsidy strategycan improve the retailerrsquos selling effort In order to increasethe quantity of sales the retailer needs to improve their levelof selling effort which can lead to higher selling costs for theretailer Under the government subsidy strategy the retaileris able to improve their selling effort However under thesame amount of government subsidy expenditure the re-tailer can benefit from the government subsidy strategyus it can strongly motivate the retailer to sell moreproducts From the perspective of the level of selling effortgovernment subsidization of the retailer is more effectivethan subsidization of the manufacturer

53 Numerical Analysis e impact of the governmentsubsidy strategy on the manufacturerrsquos and retailerrsquos profitcan be analyzed using numerical analysis Assuminga 200 b 10 ρ 04 z 2 and v 4e correspondingvalue of subsidy parameters is shown in Table 1

Under two different types of government subsidy strategythe impact of different subsidy parameters on the wholesaleprice greenness level selling price level of selling effort andmanufacturerrsquos and retailerrsquos profit is shown in Figures 2‒7

As shown in Figure 2 whether the retailerrsquos level ofselling effort is either high or low the manufacturerrsquoswholesale price shows a downward trend in theMG and RGmodels Moreover when the retailerrsquos level of selling effort ishigh the manufacturerrsquos wholesale price is higher than whenthe retailerrsquos level of selling effort is low e manufacturercan receive some economic compensation us themanufacturerrsquos wholesale price can decrease under thegovernment subsidy strategy Furthermore the manufac-turerrsquos wholesale price is at the highest level in the RGmodelwhile it is at its lowest level in theMG model is indicatesthat government subsidization of the manufacturer is moreeffective than subsidization of the retailer

As shown in Figure 3 regardless of whether the retailerrsquoslevel of selling effort is high or low as the governmentsubsidy coefficient increases the greenness level increases inthe MG and RG models Moreover when the retailerrsquos levelof selling effort is high the greenness level is higher than

10 Complexity

when the retailerrsquos level of selling effort is low e man-ufacturer can benefit from two types of government subsidystrategy e manufacturer is in a position to increase itsinvestment in the research and development of greenproducts and it can improve the product greenness levelHowever the greenness level in theMGmodel is higher than

that in the RGmodel From the perspective of improving thegreenness level this indicates that the governmentrsquos subsi-dization of the manufacturer is more effective than subsi-dization of the retailer

As shown in Figure 4 regardless of whether the retailerrsquoslevel of selling effort is high or low as the government

Table 1 e corresponding value of subsidy parameters under the same government subsidy expenditure

θ 01 02 03 04 05 06 07 08 09 1μ(θ)RGlowast 015 027 031 044 0521 0684 0781 088 0914 121

0 01 02 03 04 05 06 07 08 09 110

15

20

25

30

35

40

45

50

Coefficient of unit product subsidy from government θ

Man

ufac

ture

rrsquos w

hole

pric

e und

er M

G an

d RM

mod

el W

W (θ)LMGlowast

W (μ(θ))LRGlowast W (μ(θ))H

RGlowast

W (θ)HMGlowast

Figure 2 e impact of different government subsidy coefficients on the manufacturerrsquos wholesale price under two models

0 01 02 03 04 05 06 07 08 09 15

10

15

20

25

30

35

40

45

Coefficient of unit product subsidy from government θ

Man

ufac

ture

rrsquos d

egre

e of g

reen

ness

un

der M

G an

d RM

mod

els g

g (θ)LMGlowast

g (μ(θ))LRGlowast g (μ(θ))H

RGlowast

g (θ)HMGlowast

Figure 3 e impact of different government subsidy coefficients on the manufacturerrsquos greenness level under two models

Complexity 11

0 01 02 03 04 05 06 07 08 09 110

20

30

40

50

60

70

Coefficient of unit product subsidy from government θ

Reta

ilerrsquos

selli

ng p

rice u

nder

MG

and

RG m

odel

s

P (θ)LMGlowast

P (θ)HMGlowast P (μ(θ))H

RGlowast

P (μ(θ))LRGlowast

Figure 4 e impact of different government subsidy coefficients on retailerrsquos selling price under two models

0 01 02 03 04 05 06 07 08 09 140

60

80

100

120

140

160

180

Different government subsidy coefficient

The r

etai

ler d

egre

e of s

ellin

g eff

ort

unde

r MG

and

RG m

odel

s

e (θ)LLMGlowast

e (θ)HMGlowast e (μ(θ))H

RGlowast

e (μ(θ))LRGlowast

Figure 5 e impact of different government subsidy coefficients on retailerrsquos level of selling effort under two models

0 01 02 03 04 05 06 07 08 09 1100

200

300

400

500

600

700

800

Different government subsidy coefficient

Man

ufac

ture

rrsquos an

d th

e ret

aile

rrsquos p

rofit

unde

r MG

and

RG m

odel

s

prod (θ)MML

Glowast

prod (μ(θ))MRG

Llowast

prod (θ)MRL

Glowast

prod (μ(θ))RRG

Llowast

Figure 6 e impact of different government subsidy coefficients on the enterprisersquos profit when the selling effort level is low

12 Complexity

subsidy coefficient increases the retailerrsquos selling price showsa downward trend in the MG and RG models e retailerrsquosselling price is at the lowest level under the RGmodel and atthe highest level under theMGmodel In addition when theretailerrsquos level of selling effort is high the retailerrsquos sellingprice is higher than when the retailerrsquos level of selling effort islow From the perspective of improving the retailerrsquos sellingprice this indicates that the governmentrsquos subsidization ofthe retailer is more effective than subsidization of themanufacturer

As shown in Figure 5 as the government subsidy co-efficient increases the retailerrsquos level of selling effort in-creases under two types of government subsidy strategy eretailerrsquos level of selling effort under the RG model is higherthan that under the MG model It is more obvious that thegovernment subsidizes the retailer so that it can improve theretailerrsquos level of selling effort

As shown in Figures 6 and 7 when the retailerrsquos level ofselling effort is low and as the government subsidy co-efficient increases both the manufacturer and retailerrsquosprofit increases For the manufacturer its profit in the RGmodel is higher than that in the MG model On thecontrary for the retailer when it satisfies the conditionθ isin [0 08] the retailerrsquos profit in the MG model is higherthan that in the RG model When it satisfies the conditionθ isin [08 1] the retailerrsquos profit in the RG model is higherthan that in the MG model Moreover when the retailerrsquoslevel of selling effort is high the manufacturerrsquos profit inthe MG model is higher than that in the RG model theretailerrsquos profit in the MG model is higher than that in theRG model

6 Conclusions and Future Research

is study examined a two level green supply chain systemwith one manufacturer and one retailer in which the marketdemand was mainly affected by the product greenness levelthe level of selling effort and the selling price First it was

assumed that the retailerrsquos level of selling effort was rep-resented by asymmetric information and that the manu-facturer designed incentive contracts to induce the retailer todisclose private information by using the principal-agenttheory Second the game models both without a govern-ment subsidy strategy and with two types of governmentsubsidy strategies were constructed e optimal solution ofthe wholesale price the greenness level the selling price thelevel of selling effort and the manufacturer and the retailerrsquosprofit was obtained Finally we arrived at the followingconclusions (1) the government subsidy strategy improvesnot only the greenness level but also the manufacturer andretailerrsquos profit (2) regardless of whether the retailerrsquos levelof selling effort is high or low as the government subsidycoefficient increases the wholesale price greenness leveland the level of selling effort increases (3) when the retailerrsquoslevel of selling effort is low and as the government subsidycoefficient increases the manufacturer and retailerrsquos profitincrease For the manufacturer its profit in the RG model ishigher than that in the MG model Moreover when theretailerrsquos level of selling effort is high the manufacturerrsquosprofit in theMG model is higher than that in the RGmodelthe retailerrsquos profit in theMGmodel is higher than that in theRG model

In the paper we only considered the green supply chaingame dominated by the manufacturer We did not considerthe green supply chain game dominated by the retailer isstudy explored the impact of government subsidy strategieson the green supply chain is paper did not consider theimpact of a government carbon tax strategy or a reward-penalty mechanism on the green supply chain We aim toevaluate these issues in future research

Data Availability

e data used to support the findings of this study are notincluded within the article and are available from the cor-responding author

0 01 02 03 04 05 06 07 08 09 1400

600

800

1000

1200

1400

1600

Different government subsidy coefficient

Man

ufac

ture

rrsquos an

d th

e ret

aile

rrsquos p

rofit

unde

r MG

and RG

mod

els

prod (θ)MMLGlowast

prod (μ(θ))MRGLlowast

prod (θ)MRLGlowast

prod (μ(θ))RRGLlowast

Figure 7 e impact of different government subsidy coefficients on the enterprisersquos profit when the level of selling effort is high

Complexity 13

Conflicts of Interest

e authors declare that there are no conflicts of interest

Authorsrsquo Contributions

Y X and Z X conceptualized the study Y X wrote theoriginal study Z D reviewed and edited the article Y Xprovided funding acquisition

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China (nos 7150116 71502037 and71103149) the Natural Science Foundation of University inJiangsu Province (no 19KJB120006) the outstandingDoctor Scientific Research Fund Project at Jiangsu NormalUniversity (no 18XWRS008) and a project funded by thepriority academic program development of Jiangsu HigherEducation Instituations (PADP) e authors thank Inter-national Science Editing (httpwwwinternational scienceeditingcom) for editing this manuscript

References

[1] B Chekima S A W Syed Khalid Wafa O A IgauS Chekima and S L Sondoh ldquoExamining green consum-erism motivational drivers does premium price and demo-graphics matter to green purchasingrdquo Journal of CleanerProduction vol 112 pp 3436ndash3450 2016

[2] S Zhao Q Zhu and L Cui ldquoA decision-making model forremanufacturers considering both consumersrsquo environmen-tal preference and the government subsidy policyrdquo ResourcesConservation and Recycling vol 128 pp 176ndash186 2018

[3] S Barari G Agarwal W J Zhang B Mahanty andM K Tiwari ldquoA decision framework for the analysis of greensupply chain contracts an evolutionary game approachrdquoExpert System with Application vol 39 no 3 pp 2965ndash29762012

[4] M Runkel ldquoProduct durability and extended producer re-sponsibility in solid waste managementrdquo Environmental andResource Economics vol 24 no 2 pp 161ndash182 2003

[5] D Aksen N Aras and A G Karaarslan ldquoDesign and analysisof government subsidized collection systems for incentive-dependent returnsrdquo International Journal of ProductionEconomics vol 119 no 2 pp 308ndash327 2009

[6] J-B Sheu ldquoBargaining framework for competitive greensupply chains under governmental financial interventionrdquoTransportation Research Part E Logistics and TransportationReview vol 47 no 5 pp 573ndash592 2011

[7] W-m Ma Z Zhao and H Ke ldquoDual-channel closed-loopsupply chain with government consumption-subsidyrdquo Eu-ropean Journal of Operational Research vol 226 no 2pp 221ndash227 2013

[8] S Benjaafar Y Li and M Daskin ldquoCarbon footprint and themanagement of supply chains insights from simple modelsrdquoIEEE Transactions on Automation Science and Engineeringvol 10 no 1 pp 99ndash116 2013

[9] A Toptal H Ozlu and D Konur ldquoJoint decisions on in-ventory replenishment and emission reduction investmentunder different emission regulationsrdquo International Journal ofProduction Research vol 52 no 1 pp 243ndash269 2014

[10] X Chen X Wang V Kumar and N Kumar ldquoLow carbonwarehouse management under cap-and-trade policyrdquo Journalof Cleaner Production vol 139 pp 894ndash904 2016

[11] W T Chen Z H Hu and C Yu ldquoA model of green supplychain with reward and punishment mechanism under dif-ferent government target decisionsrdquo Control and DecisionMaking vol 32 no 1 pp 5ndash14 2018

[12] K Kang Y Zhao Y Ma and Z Li ldquoGreen supply chainpoverty alleviation through microfinance game model andcooperative analysisrdquo Journal of Cleaner Production vol 226no 5 pp 1022ndash1041 2019

[13] P He Y He and H Xu ldquoChannel structure and pricing in adual-channel closed-loop supply chain with governmentsubsidyrdquo International Journal of Production Economicsvol 213 no 3 pp 108ndash123 2019

[14] J Huang M Leng L Liang and J Liu ldquoPromoting electricautomobiles supply chain analysis under a governmentrsquossubsidy incentive schemerdquo IIE Transactions vol 45 no 8pp 826ndash844 2013

[15] A Zakeri F Dehghanian B Fahimnia and J Sarkis ldquoCarbonpricing versus emissions trading a supply chain planningperspectiverdquo International Journal of Production Economicsvol 164 pp 197ndash205 2015

[16] Y D Li X P Xie and G Ying ldquoResearch on cooperativeemission reduction decision-making mechanism of supplychain enterprises under two sharing contractsrdquo Journal ofChinese Management Science vol 24 no 3 pp 61ndash70 2016

[17] B Li M Zhu and Y Jiang ldquoPricing policies of a competitivedual-channel green supply chainrdquo Journal of Cleaner Pro-duction vol 112 pp 2029ndash2042 2016

[18] W Li and Z-H Hu ldquoUsing evolutionary game theory tostudy governments and manufacturersrsquo behavioral strategiesunder various carbon taxes and subsidiesrdquo Journal of CleanerProduction vol 201 no 5 pp 123ndash141 2018

[19] H Zhang J M Huang and Y Y Cui ldquoConsidering the gamemodel and contract coordination of green supply chain withfair preference under government subsidiesrdquo IndustrialTechnology Economy vol 291 no 1 pp 111ndash122 2018

[20] A Gharaei M Karimi and S A Hoseini Shekarabi ldquoAnintegrated multi-product multi-buyer supply chain underpenalty green and quality control polices and a vendormanaged inventory with consignment stock agreement theouter approximation with equality relaxation and augmentedpenalty algorithmrdquo Applied Mathematical Modelling vol 69pp 223ndash254 2019

[21] Y Tian K Govindan and Q Zhu ldquoA system dynamics modelbased on evolutionary game theory for green supply chainmanagement diffusion among Chinese manufacturersrdquoJournal of Cleaner Production vol 80 pp 96ndash105 2014

[22] W B Wang S Y Zhou M Zhang H Sun and L Y He ldquoAclosed-loop supply chain with competitive dual collectionchannel under asymmetric information and reward-penaltymechanismrdquo Sustainability vol 10 p 2031 2018

[23] J F Su C Li Q J Zeng J Q Yang and J Zhang ldquoA greenclosed-loop supply chain coordination mechanism based onthird-party recyclingrdquo Sustainability vol 11 pp 1ndash14 2019

[24] H Sun Y Wan L Zhang and Z Zhou ldquoEvolutionary gameof the green investment in a two-echelon supply chain under agovernment subsidy mechanismrdquo Journal of Cleaner Pro-duction vol 235 pp 1315ndash1326 2019

[25] P He Y He H Xu and L Zhou ldquoOnline selling mode choiceand pricing in an O2O tourism supply chain consideringcorporate social responsibilityrdquo Electronic Commerce Re-search and Applications vol 38 p 100894 2019

14 Complexity

[26] D Chen J Ignatius D Sun M Goh and S Zhan ldquoPricingand equity in cross-regional green supply chainsrdquo EuropeanJournal of Operational Research vol 280 no 3 pp 970ndash9872020

[27] X Q Zhang X G Yuan and D L Zhang ldquoResearch onclosed-loop supply chain with competing retailers undergovernment reward-penalty mechanism and asymmetricinformationrdquo Discrete Dynamics in Nature and Societyvol 2020 Article ID 7587453 20 pages 2020

[28] P He Y He C Shi H Xu and L Zhou ldquoCost-sharingcontract design in a low-carbon service supply chainrdquoComputers amp Industrial Engineering vol 139 p 106160 2020

[29] D Ghosh and J Shah ldquoA comparative analysis of greeningpolicies across supply chain structuresrdquo International Journalof Production Economics vol 135 no 2 pp 568ndash583 2012

[30] D Ghosh and J Shah ldquoSupply chain analysis under greensensitive consumer demand and cost sharing contractrdquo In-ternational Journal of Production Economics vol 164pp 319ndash329 2015

[31] D Yang and T Xiao ldquoPricing and green level decisions of agreen supply chain with governmental interventions underfuzzy uncertaintiesrdquo Journal of Cleaner Production vol 149pp 1174ndash1187 2017

[32] Q Zhu and Y Dou ldquoA game model for GSC managementbased on government subsidiesrdquo Journal of ManagementScience China vol 14 no 6 pp 86ndash95 2011

[33] Q X Li M N Shi and Y M Huang ldquoA dynamic price gamemodel in a low-carbon closed-loop supply chain consideringreturn rates and fairness concern behaviorsrdquo InternationalJournal of Environmental Research and Public Health vol 16no 11 pp 9ndash26 2019

[34] Y Yan R Zhao and H Chen ldquoPrisonerrsquos dilemma oncompeting retailersrsquo investment in green supply chain man-agementrdquo Journal of Cleaner Production vol 184 pp 65ndash812018

[35] P Zhang Y Xiong Z Xiong and W Yan ldquoDesigningcontracts for a closed-loop supply chain under informationasymmetryrdquo Operations Research Letters vol 42 no 2pp 150ndash155 2014

Complexity 15