Hndaw Publshng Corporaton Mathematcal Problems n Engneerng Volume 16, Artcle ID 3619597, 11 pages http://dxdoorg/11155/16/3619597 Research Artcle Onlne Cooperatve Promoton and Cost Sharng Polcy under Supply Chan Competton Erjang E, 1 Geng Peng, 1, Xn Tan, 1,,3 and Qnghong Chen 4 1 School of Economcs and Management, Unversty of Chnese Academy of Scences, Bejng 119, Chna Key Laboratory of Bg Data Mnng and Knowledge Managements, Chnese Academy of Scences, Bejng 119, Chna 3 Research Center on Fcttous Economy & Data Scence, Chnese Academy of Scences, Bejng 119, Chna 4 Shangha HEADING Informaton Engneerng Co, Ltd, Shangha 111, Chna Correspondence should be addressed to Xn Tan; tanx@ucasaccn Receved 3 December 15; Accepted February 16 Academc Edtor: Mohammed Nouar Copyrght 16 Erjang E et al Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted Ths paper studes onlne cooperatve promoton and cost sharng decsons n competng supply chans We consder a model of one BC e-commerce platform and two supply chans each consstng of a suppler and an onlne retaler The problem s studed usng a multstage game Frstly, the e-commerce platform carres out the cooperatve promoton and sets the magntude of markdown (the value of e-coupon) Secondly, each retaler and hs suppler determne the fracton of promotonal cost sharng when they have dfferent barganng power Lastly, the retalers decde whether to partcpate n the cooperatve promoton campagn We show that the retalers are lkely to partcpate n the promoton f consumers become more prce-senstve However, t does not mply that the retalers can beneft from the prce promoton; the promoton decson game resembles the classcal prsoner s dlemma game The retalers and supplers can beneft from the cooperatve promoton by desgnng an approprate cost sharng contract For a supply chan, the barganng power between suppler and retaler, consumer prce senstvty, and competton ntensty affect the fracton of the promotonal cost sharng We also fnd that equlbrum value of e-coupon set by the e-commerce platform s not optmal for all the partes 1 Introducton The Internet has reduced barrers to nformaton couplng, and buyers have much easer access to the nformaton of products and a great number of potental supplers; prce competton among sellers has become more ntense [1, ] Accordng to 1 Development Report on Chna Retalng Industry, the prce war among BC (Busness to Customer) e-commerce companes was carred out nne tmes n 1 (Source: The webste of the Mnstry of Commerce of the People s Republc of Chna, http://ltfzsmofcomgovcn/ artcle/date/137/137186593shtml) The dffculty does not appear to be wth the transacton volume but wth the problem of transacton proftablty wth low returns to onlne retalers [3] Prce competton may boost demand, buttalsocutstheproductproftabltyforafrm In recent years, cooperatve promoton carred out by cross brands has become more common n the onlne retal ndustry Brynjolfsson et al [4] argue that ncreasng product varety made avalable through electronc markets can be a sgnfcantly larger source of consumer surplus gans For nstance, the daly sales of T-mall (the largest BC e- commerce company n Chna) on the Sngles Day (the largest onlne shoppng day n Chna) grew from $58 bllon n 13 to $93 bllon n 14 In order to gan a bgger share of the retal market, ncreasng e-commerce frms, such as JD and Amazon, and onlne stores choose to partcpate n cooperatve promotonal actvtes For onlne stores n a common platform, provdng customers wth the same dscounts or e-coupon s a popular marketng strategy on the cooperatve promoton campagn In 14, for example, T-mall worked wth some onlne medcal retalers who have hgh market shares to carry out the cooperatve promotonal actvty They provded customers wth 1 CNY e-coupons (about 16 dollars) on the Sngles Day Customers can use ths e-coupon to buy the products of the onlne stores whch
Mathematcal Problems n Engneerng partcpate n the promoton Nevertheless, these onlne retalers compete aganst each other n the common market, and consumers have dfferent prce senstvty n dfferent products Durng the promoton perod, therefore, the sales and profts of onlne retalers would be dfferent Consumer prce senstvty drectly affects a frm s prcng strateges and profts [5] These medcal retalers communcated wth the upstream supplers and requred supplers to share part of promoton costs As a result, a small number of supplers promsed to bear all promoton costs and some others were wllngtosharepartofthecosts,butthereweresomesupplers that refuse to share these costs These onlne retalers faced the problems of whether to partcpate n ths cooperatve promotonal actvty For a frm, whether promoton should be attended depends on whether t generates a postve value (e, ncremental proft) In ths paper, we consder supply chans that compete wth one another, and we seek to nvestgate how promoton decsons depend on consumer prce senstvty, competton ntensty, and the magntude of the markdown We also examne how the cost sharng polcy n a supply chan s affected by the barganng power, consumer prce senstvty, and competton ntensty We focus on a model of one BC e-commerce platform and two supply chans each consstng of a suppler and an onlne retaler The retalers compete by sellng partally substtutable products n a common e-commerce platform Some emprcal studes show that consumers are more prcesenstve durng perods of hgh demand such as Chrstmas and Thanksgvng [6 8] Ths vew also apples to the onlne purchasers n the onlne shoppng holday Consumers prce senstvty was uncertan durng the cooperatve promoton perod, and ths state s observable by both retalers but not the supplers The e-commerce platform organzes the retalers to carry out the cooperatve promoton campagn Each retaler and hs suppler decde whether to partcpate n the promoton and share the promoton cost, respectvely Although the case of only two supply chans s a smplfcaton of realty, t s suffcent to capture the man ssue of onlne cooperatve promoton We use a multstage game to study the frms equlbrum promoton decsons In the begnnng, the e-commerce platform sets the magntude of markdown (the value of e-coupon) to nduce the retalers to partcpate n the promoton Next, each retaler shares the nformaton of consumers prce senstvty wth hs suppler and requres hs suppler to share the promoton cost Then, each suppler offers an amount of cost sharng to her retaler based on the expected profts and barganng power After learnng the payment offered by hs suppler, each retaler decdes ether to partcpate n the promoton or not based on the expected sales and profts We frst analyze the retalers promoton arrangement wthout the supplers support (e, there s no cost sharng polcy) We show that the retalers may change ther decsons from no partcpaton to partcpaton when consumers become more prce-senstve or competton becomes more ntense We then analyze the effectofcostsharngpolcynasupplychanwefndthat prce senstvty, competton ntense, proft margns, and barganng power affect the fracton of promotonal cost sharng for a supply chan Fnally we analyze how the e- commerce platform obtans the proft as much as possble by settngthemagntudeofmarkdown(thevalueofe-coupon) We show that a supply chan wth hgher proft margns may be better off when consumers become more prce-senstve or competton less ntense We also fnd that the equlbrum valueofe-couponsetbythee-commerceplatformsnot optmal for all the partes The rest of ths paper s organzed as follows Secton provdes a lterature revew Secton 3 descrbes the model Secton 4 nvestgates supply chans cost sharng polcy and promoton equlbrum decsons and studes the optmal value of e-coupon Secton 5 presents some numercal examples Fnally, Secton 6 summarzes our results The proofs of formal results are gven n the Appendx A Lterature Revew Our study s closely related to three areas: consumer prce senstvty and promoton, supply chan coordnaton, and supply chan competton Ths paper s most related to the lterature whch studes the relatonshp between consumer prce senstvty and promotononestreamofresearchevaluatesthechangeof consumers prce senstvty n the promoton actvty [9 11] Mela et al [1] argue that consumers mght become more prce-senstve wth an ncrease n the frequency of dscounts Frequent prce promotons, however, mght depress sales because consumers expect a lower prce n the future There s a nonlnear relatonshp between the frequency of dscounts and consumers prce senstvty [13] Han et al [14] used an approach that ncorporates probablstc thresholds to examne consumers prce senstvty and fnd that ntense prce promoton by competng brands makes consumers more senstve to losses but not nfluence consumers senstvty to gans Another stream of research more relevant to our work nvestgates the mpact of consumers prce senstvty on frms promoton strategy Kopalle et al [15] proposed the dynamc effect of dscounts on the sales They advse that f deals become more effectve n the current perod, that s, f consumers are more prce senstve, promotons should be used more frequently, and as the negatve dynamc effect of dscounts the optmal level of dscountng should go down Kalyanaram and Wner [16] examned the relatonshp between consumer reference prce and promoton and fnd that an ncrease n dscounts may reduce consumers reference prces and perhaps harmng brand equty Kogan and Herbon [17] nvestgated the effect of customer prce senstvty for supply chan s proft under a lmted-tme promoton Then they fnd that the promoton s not always benefcal f customer senstvty ncreases Based on the above lterature, we examne how supply chans promoton decsons and cost sharng polcy depend on consumers prce senstvty Wth the emergence of new promoton forms,suchasgroup-buyngandfreeshppng,somescholars began to study e-consumer buyng behavor on the onlne promoton [18 ] Lttle attenton has been gven to the consumer prce senstvty n the cooperatve promoton
Mathematcal Problems n Engneerng 3 actvty One contrbuton, consderng the effect of consumer prce senstvty n competng supply chans, s made by our paper Contracts of cost sharng or revenue-sharng n supply chans have been studed extensvely A substantal amount of work n ths lterature consders supply chans coordnaton under dfferent stuaton [1, ] Cachon and Larvere [3] compared revenue-sharng to a number of other supply chan contracts, such as buy-back contracts and prce dscount contracts, and then analyzed the strengths and lmtatons of the revenue-sharng contract n supply chan coordnaton Yao et al [4] studed a revenue-sharng contract for a supply chan consstng of one manufacturer and two competng retalers They show that the provson of revenue-sharng n the contract can obtan better performance than a prceonly contract Tsao and Sheen [5] argue that the sales learnng curve of retalers should be taken nto account Dana and Sper [6] examned the effectveness of the revenuesharng contract n vertcally separated ndustres when there s ntrabrand competton among the downstream frms and fnd that revenue-sharng s a valuable nstrument L et al [7] consdered a supply chan consstng of one retaler and two competng supplers under an envronment of supply dsrupton and devse a coordnaton mechansm (Nash barganng game) to maxmze the profts of both supplers We make a contrbuton to ths lterature by consderng supply chans coordnaton wth cost sharng polcy n a compettve envronment Currently, t s no longer a frm versus a frm but rather a supply chan versus a supply chan n the competton for many marketplaces [8] Increasng attenton has been pad to the ssues of supply chan competton The exstng work on supply chan competton can be dvded nto two categores The frst s that how channel structure depends on competton ntensty and the type of competton [9, 3] McGure and Staeln [31] consdered a model of vertcal dstrbuton structures wth two manufactures and two exclusve retalers They nvestgated the effect of product substtutablty and fnd that manufacturers wll be more lkely to use a decentralzed dstrbuton system for the more hghly compettve goods Coughlan [3] analyzed the ssue of choosng marketng channel n a duopoly market, and the results are appled to the nternatonal semconductor ndustry Ha et al [33] nvestgated how supply chan s nformaton sharng decsons depend upon producton dseconomes of scale, nformaton accuracy, competton ntensty, and the type of competton The second s that how the contract desgn s affected by the uncertanty of demand or supply [34 36] A et al [37] nvestgated a full-returns polcy of competng supply chan wth demand uncertanty Demrag et al [38] analyzed the performance of customer rebate and retaler ncentve promotons under supply chan competton Ha and Tong [39] analyzed the nformaton sharng strateges of two competng supply chans n the cases of contract menus and lnear prce contracts In addton, Cheng [4] proposed the concept of vrtual busness He suggests that a producton chan and a supply chan should be combned by usng the cloud computng, Internet of Thngs, bg data, and other advanced nformaton technologes In ths way, Suppler 1 Retaler 1 E-commerce platform Consumers Suppler Retaler Fgure 1: The relatonshp between supply chans the stuaton of overall optmzaton can be realzed n the ndustry chan ncludng producton chan and supply chan They also explctly menton supply chan coordnaton n the compettve envronment but do not dscuss the problem of supply chan coordnaton n a cooperatve promoton campagn 3 Model Consder two supply chans, each consstng of one suppler sellng a partally substtutable product to one onlne retaler The retalers compete n a common e-commerce market The supplers, the retalers, and the supply chans are ndexed by =1, Fgure 1 llustrates the relatonshp between supply chans n ths paper ThetmngofthegamesasfollowsInthefrststage,the e-commerce platform organzes the cooperatve promoton campagn and sets the magntude of markdown (such as unfed e-coupon for all retalers) In the second stage, each retaler and hs suppler determne the fracton of promotonal cost sharng In the last stage, the retalers decde whether to partcpate n the cooperatve promoton campagn We solve the game backward for ts subgameperfect Nash equlbrum n the Secton 4 31 Basc Model The demand functon for retaler s gven by q =a +b (P p ) d (P j p j ) ( = 1, ; j = 3 ) Normally, retaler sells the goods wth customers at the lst prce P,andhscompettor(retalerj) sellsthe partally substtutable product at the lst prce P j Intheprce promoton perod, decson varables p and p j correspond, respectvely, to the promoton prce for retaler and j Parameters b and d ndcate consumers prce senstvty and competton ntensty for retaler,respectvely,b >d Thus (1)
4 Mathematcal Problems n Engneerng Table 1: The payoff matrx of two retalers Retaler 1 No partcpaton (X 1 =N) Partcpaton (X 1 =Y) No partcpaton (X =N) Retaler Partcpaton(X =Y) (π N,N, π N,N r ) (π N,Y, πy,n r ) (π Y,N, πn,y r ) (πy,y, πy,y r ) a s the demand under antcpated lst prcng f retaler and her compettor do not carry out prce promoton actvty, P =p, P j =p j Our demand functon s smlar to Kogan and Herbon [17], but they dd not consder the nfluence from the compettor, d (P j p j ) Through a smple transform, the demand functon can be rewrtten as q =g b p +d p j () The demand potental for retaler s g,whereg =a + b P d P j Ths s a classcal Bertrand retal competton Snce consumers have dfferent senstvty n dfferent products, t means b =b j In order to descrbe how the sales of retalers affected by the dfference of prce senstvty, we assume that d =k b j (3) Ths equaton ndcates that the sales of retaler would be nfluenced by the prce senstvty of hs compettor (e, larger or smaller b j ) Parameter k can be defned as the nfluence coeffcent, <k <b /b j 3 E-Commerce Platform s Problem For an e-commerce platform, extractng a percentage of the commsson from the onlne retalers revenues s the man source of ncome Thus the proft functon for the e-commerce platform s gven by π e =φ =1 [a +b (P p ) k b j (P j p j )] p c e (4) Parameter φ represents the percentage of commsson on the revenues of retalers The operatng cost s constant c e for the e-commerce platform Now the e-commerce platform sets the magntude of markdown (the value of e-coupon) to nduce the retalers to partcpate n the cooperatve promoton Consumers can use the e-coupon to buy the products of retalers wthout beng lmted by the purchase amount Let V be the value of e-coupon to consumers, V If retaler chooses to partcpate n the promoton, we have P p =V Hence, the proft functon of the e-commerce platformcanbeexpressedas π e =φ =1 (a +b V k b j V) (P V) c e (5) Gven any retal prce P set by retaler and fxed parameter φ, the e-commerce platform maxmzes ts expected proft by settng the value of e-coupon V Note that, the demand states of the retalers are also observable by e-commerce platform 33 Retalers Problem The retalers maxmze expected profts by decdng whether to partcpate n promoton and demandng the supplers to bear part of the promoton cost Retaler makes a promoton arrangement n the last stage, whch we denote by X = Y (partcpaton) or N (not partcpaton) The promoton arrangement X n retaler s unknown to hs compettor (retaler j) Durng the promoton perod, the proft functon of retaler s π X,X j r (6) =(a +b V k b j V) [(1 φ) (P V) w +S ] The fracton of promotonal cost sharng offered by suppler s denoted by S,andthewholesaleprceforretaler s w Thesuperscrptsofπ X,X j r ndcate the dependency of retaler s decson on the promoton arrangements n both supply chans, where the frst superscrpt refers to the arrangement n retaler and the second superscrpt represents the arrangement of the rval retaler For example, denotes the profts of retaler 1 when he chooses to partcpate n the promoton and retaler does not partcpate n the promoton Based on the strategy combnatons of the retalers, we obtan the payoff matrx of retalers as shown n Table 1 π Y,N 34 Supplers Problem The supplers also want to maxmze expected profts by selectng proper fracton of promotonal cost sharng The proft functon for suppler s gven by π X,X j s =(a +b V k b j V) (w c s S ) (7) The unt purchase costs ncurred by suppler are denoted by c s We do not consder the retalers nventory here The proft functon for supply chan s π X,X j =π X,X j r +π X,X j s =(a +b V k b j V) [(1 φ) (P V) c s ] 4 Model Analyss and Soluton In ths secton, we frst analyze the stuaton that each retaler bears the promotonal cost wthout hs supplers support and makes promoton decsons based on consumers prce senstvty, competton ntensty, and compettor s reacton Secondly,theeffectofcostsharngpolcyonthepromoton would be nvestgated Fnally, we analyze how the e- commerce platform obtans the profts as much as possble by settngthevalueofe-couponmeanwhle,theoptmalvalue of e-coupon for all the partes wll also be explored (8)
Mathematcal Problems n Engneerng 5 41 Promoton Decsons wthout Supplers Support In order to study how consumer prce senstvty and competton ntensty affect the promoton decsons of retalers, we assume each suppler does not share any promoton cost (also called decentralzed decson) The retalers profts are calculated based on the expected prce senstvty and competton ntensty Here we assume that a retaler wll choose to partcpate n the promoton f he s ndfferent between partcpaton and not partcpaton Accordng to (6), retaler wll choose to partcpate n the promoton f π Y,X j r π N,X j r Hence,thelowerboundofconsumerprce senstvty for retaler s gven by b L D (N, Y) b =k 1 1 b 1 (N, N) L D 11 (N, N) or (Y, Y) (Y, Y) L D 1 b L D 1 = (1 φ) (a k b j V) (1 φ) (P V) w or (9) (N, N) (N, N) (Y, N) b =k b 1 b L D = (1 φ) a (1 φ) (P V) w L D 1 b 1 The symbols L D 1 and LD denote the lower bound of consumer prce senstvty when rval retaler j chooses to partcpate n the promoton and when not partcpatng, respectvely It s easy to see that L D 1 <LD ( = 1, ) Lemma 1 Suppose each suppler ( = 1, ) does not share promoton cost, S = (a)ifb L D, Y s the domnant strategy for retaler (b)ifb [L D 1,LD ), Y s the optmal strategy for retaler when hs compettor chooses Y; andn s the optmal strategy when hs compettor chooses N (c)if b <L D 1, N s the domnant strategy for retaler The retalers promoton decsons would be affected by the ntensty of market competton The promoton decsons of retaler may change from N (not partcpaton) to Y (partcpaton) when competton becomes more ntense (larger k ) The equlbrum promoton decsons (X 1,X ) are drven by consumers prce senstvty and can be characterzed as follows Theorem Suppose both supplers do not share promoton cost, S 1 =S =(a)ifb 1 L D 1 and b L D, (Y, Y) s the unque equlbrum (b) If b 1 [L D 11,LD 1 ) and b [L D 1,LD ), (Y, Y) and (N, N) are the (only) two equlbra, but (N, N) s Pareto optmalty (c) If b 1 <L D 11 and b <L D 1, (N, N) s the unque equlbrum; (d) f b 1 <L D 11 and b L D, (N, Y) s the unque equlbrum (e) If b 1 [L D 11,LD 1 ) and b <L D 1, (N, N) stheunqueequlbrum(f)ifb 1 [L D 11,LD 1 ) and b L D, (Y, Y) s the unque equlbrum The results n Theorem are llustrated n Fgure The ntensty of competton n the market drectly affects the equlbrum promoton decson The dashed lnes, L D 11 and, shft to the lower left corner as competton becomes L D 1 more ntense (larger k ) At the same tme, the sold lnes, b = k b 1 and b =k 1 1 b 1,shftupwardanddownward,respectvely The equlbrum may change from (Y, N) to (Y, Y) as the curve L D 1 or LD 11 shfts downward It s worth mentonng that when Fgure : Equlbrum promoton decsons for two retalers L D b < L D +k b j, the domnant strategy for retaler ( = 1, ) s to partcpate n the promoton; (Y, Y) s the unque equlbrum, but both retalers would be better off at (N, N) Under certan parametrc condtons, the promoton game resembles the classcal prsoner s dlemma game Corollary 3 Suppose both supplers do not share promoton costs, S 1 =S =Ifb 1 L D 1 +k 1b and b L D +k b 1, (Y, Y) stheunqueequlbrum,andπ Y,Y >π N,N, π Y,Y r >π N,N r,and the prsoner s dlemma was dssolved The mplcaton of Corollary 3 s that the degree of product s heterogenety should be ncreased for a supply chan In ths way, the supply chan can beneft from the prce promoton f consumers are more prce-senstve for hs product (larger b ) or the nfluence of compettors can be reduced (smaller k ) 4 The Effect of Cost Sharng Polcy on the Promoton In ths subsecton, we examne the effect of cost sharng polcy on the promoton for a supply chan (also called centralzed decson) Whether the promoton cost wll be shared depends on whether promoton generates a postve value (e, ncremental proft) for a supply chan Accordng to (7), there s a negatve correlaton between the supplers profts and the amount of cost sharng Here we assume a suppler wll agree to share promoton cost f she s ndfferent between sharng and not sharng Suppler wll choose to share the promoton cost f and only f π Y,X j s π N,X j s Thus, the upper bound of the fracton of the promotonal cost sharng for suppler s gven by S max = (w c s )b V a +b V k b j V (1)
6 Mathematcal Problems n Engneerng And the lower bound of the fracton of the promoton cost sharng for suppler s gven by S mn = (1 φ) [a b (P V) k b j V]V+b w V (11) a +b V k b j V Theorem 4 When retaler j chooses to partcpate n the promoton, the upper bound of the fracton of the promotonal cost sharng for suppler s S max ; the lower bound of the fracton of the promotonal cost sharng for suppler s S mn From the results of Theorem 4, a hgher proft margn means the stronger capablty of cost sharng for a suppler (larger S max ) Because of S max / b > and S max / k >, the largest fracton suppler can offer ncreases wth the prce senstvty and compettve ntensty Furthermore, the fracton suppler should offer decreases wth the prce senstvty and compettve ntensty because of S mn / b < and S mn / k < Lemma 5 When the fracton of the promotonal cost sharng S ( = 1, ) s wthn the approprate range (S mn,s max ), retaler s promoton decsons may change from N to Y as the fracton of the promotonal cost sharng S ncreases Accordng to (8), supply chan wll choose to partcpate n the promoton f π Y,X j π N,X j Therefore, the lower bound of consumerprce senstvtyfor supply chan s formulated as follows: L I 1 = L I = (1 φ) (a d V) (1 φ) (P V) c s or (1 φ) a (1 φ) (P V) c s (1) The symbols L I 1 and LI denote the lower bound of consumer prce senstvty when supply chan j chooses to partcpate n the promoton and when not partcpatng, respectvely It s easy to see that L I 1 < L I < L D and L I 1 <LD 1 <LD Lower ntensty of competton (smaller k ) and hgher proft margns can create a compettve advantage for a supply chan Lemma 6 When the fracton of the promotonal cost sharng s negotated at S ( = 1, ),then the ncremental proft for suppler s that Δπ s = =(S max S )q ; π Y,X j s π N,X j s thencrementalproftforretaler s that Δπ r =π Y,X j r π N,X j r =(S S mn )q ; the ncremental proft for supply chan s that Δπ = Δπ s +Δπ r =(S max S mn )q Cost sharng can be acheved f t benefts the supply chan Let α(α )denote each suppler s Nash barganng power, and let β(β ) denote each retaler s Nash barganng power, α+β = 1 Accordng to Nash s model [41], we obtan the approprate fracton of the promotonal cost sharng whch s S =αs mn +βs max Theorem 7 The approprate fracton of promotonal cost sharng for suppler ( = 1, ) s S =αs mn +βs max The barganng power between suppler and retaler affects the choce of the fracton of promotonal cost sharng S Suppler shares the smallest fracton of the promotonal cost S mn, when she has the complete barganng power (α = 1, β = ) On the contrary, suppler bears the largest fracton of the promotonal cost S max, when her retaler has the complete barganng power (α =,β=1) Theorem 8 When each suppler and her retaler take the cooperatve strategy, (a) f b 1 L I 1 and b L I, (Y, Y) s the unque equlbrum; (b) f b 1 [L I 11,LI 1 ) and b [L I 1,LI ), (Y, Y) and (N, N) are the (only) two equlbra, but (N, N) s Pareto optmalty; (c) f b 1 <L I 11 and b <L I 1, (N, N) s the unque equlbrum; (d) f b 1 <L I 11 and b L I, (N, Y) s the unque equlbrum; (e) f b 1 [L I 11,LI 1 ) and b <L I 1, (N, N) s the unque equlbrum (f) If b 1 [L I 11,LI 1 ) and b L I, (Y, Y) s the unque equlbrum Promoton equlbrum decsons may be changed f the supplers bear the approprate promoton cost Under the condton of wthout consderng competton, supply chan may be better off when suppler shares the promotonal cost and retaler chooses to partcpate n the promoton However, after knowng the acton of supply chan, supply chan j mayalsochoosetopartcpatenthepromotonfor the threat posed by the compettor As a result, competton between supply chans becomes more ntense 43 The Optmal Value of E-Coupon Now we consder theequlbrumvalueofe-couponsetbythee-commerce platform The e-commerce platform sets the value of e- coupon to nduce the retalers to partcpate n the promoton Based on Lemma 1 and Theorem 8, we have the upper bound of the value of e-coupon: 1 = (1 φ) (b P a ) b w, (1 φ) (b k b j ) V D V D = (1 φ) (b P a ) b w (1 φ) b, V I 1 = (1 φ) (b P a ) b c s, (1 φ) (b k b j ) V I = (1 φ) (b P a ) b c s (1 φ) b (13) The symbols V D 1 and VD denote the maxmum value of e-coupon that retaler can accept when the rval retaler chooses to partcpate n the promoton and when not partcpatng, respectvely Smlarly, V I 1 and VI ndcate the
Mathematcal Problems n Engneerng 7 maxmum value of e-coupon that supply chan can accept when the rval supply chan chooses to partcpate n the promoton and when not partcpatng, respectvely It s easy to see that V D <VD 1 <VI 1 and VD <VI <VI 1 Accordng to (5), when π e / V=, the optmal value of e-coupon for the e-commerce platform s gven by V e = =1 (b k b j )P a =1 (b (14) k b j ) Theorem 9 The equlbrum value of e-coupon s gven by V Table : Profts dstrbuton of supply chan 1 under dfferent cost sharng polces S 1 π s1 π Δπ s1 Δπ Δπ s1 /Δπ 1 Equlbrum 1 7 (N, Y) 117 556 7 1356 1 (Y, Y) 178 1878 1398 678 678 5 (Y, Y) 1538 1 76 1356 (Y, Y) Notes: V=, b 1 = 1,andd 1 = 15 V e, { = V I 1, { { V I, f V e mn {max {V I,VI j },mn {VI 1,VI j1 }} ; f VI 1 <VI j, Ve V I 1 ; f VI j <VI <VI j1, Ve V I (15) Actually,thevalueofe-couponsetbythee-commerce platform V snotoptmalforallthepartesthetotalprofts of two supply chans and the e-commerce platform are gven by π=π e +π X 1,X 1 +π X,X 1 = =1 (a +b V k b j V) (P c s V) (16) Gven consumers prce senstvty and compettve ntensty, all the partes maxmze the proft through settng the optmal value of e-coupon, π/ V= Therefore, we get the optmal value of e-coupon: The largest fracton suppler 1 can offer (S 1 max ) 1 5 d 1 = d 1 = 4 6 8 1 Consumer prce senstvty (b 1 ) d 1 = 4 d 1 = 6 V opt = =1 (b k b j )(P c s ) a =1 (b (17) k b j ) Theorem 1 The optmal value of e-coupon for all the partes s V opt ; the total profts wth the optmal value are hgher than the total profts wth the equlbrum value, π(v opt )>π(v ) The value of e-coupon V opt was superor to the value set by the e-commerce platform V Under ths condton, bothsupplychanswouldbebetteroffandthee-commerce platform would be worse off The results of Theorem 1 wll be explaned n Secton 5 n detal 5 Numercal Examples In ths secton, we present numercal examples whch are amedatllustratngsomesgnfcantfeaturesofthemodels establshed n prevous sectons In all examples, we set a 1 = a = 1, P 1 = 1, w 1 =85, c s1 =65, P =95, w =8, c s =65,andφ = 3 Gven the rval retaler s promoton decsons, a supply chan takng cooperatve strategy may outperform those choosng noncooperaton From Table, the profts of suppler 1 and retaler 1 ncrease when the fracton of promotonal cost sharng S 1 s wthn (S mn 1,S max 1 ) Fgure 3: The largest fracton of the promotonal cost sharng for suppler 1 The results show that the supplers and retalers can beneft from the promoton f the fracton promotonal cost sharng s wthn the approprate range Cost sharng range of supply chans s drven by consumer prce senstvty and compettve ntensty Fgure 3 dsplays the relaton between the upper bound of the fracton of the promotonal cost sharng and consumer prce senstvty under dfferent ntensty of competton For a gven value of e-coupon, the largest fracton of promotonal cost sharng offered by suppler 1 S max 1 ncreases as consumer prce senstvty ncreases (larger b 1 ), even though the products are completely heterogeneous (d 1 =) For any gven consumers prce senstvty, the upper bound of the fracton of the promotonal cost sharng wll shft upward f competton becomes more ntense (larger d 1 ) Fgure 4 shows that the relaton between the lower bound of the fracton of the promotonal cost sharng for suppler 1 and consumer prce senstvty under dfferent ntensty of competton We can also see that the smallest fracton of the promotonal cost sharng decreases wth the consumer
8 Mathematcal Problems n Engneerng 1 15 The smallest fracton suppler 1 should offer (S 1 mn ) 8 6 4 Nash barganng soluton (S 1 ) 1 5 4 6 8 1 Consumer prce senstvty (b 1 ) 4 5 6 7 8 9 1 Consumer prce senstvty (b 1 ) d 1 = d 1 = d 1 = 4 d 1 = 6 Fgure 4: The smallest fracton of the promotonal cost sharng for suppler 1 α= α = 3 α = 5 α = 7 α=1 Fgure 5: Nash barganng soluton for supply chan 1 5 k 1 =k =, b 1 =b =1 prce senstvty and competton ntensty From Fgures 3 and4,tseasytoseethattheappropraterange(s mn,s max ) becomes wder wth the ncreasng consumer prce senstvty and compettve ntensty Ths mples that each suppler and her retaler have a wder range for negotaton The barganng power affects the choce of the fracton of promotonal cost sharng S For gven competton ntensty andthemagntudeofmarkdown,thepromotoncostsoffered by the supplers depend on consumer prce senstvty and ther barganng power Fgure 5 llustrates the cost sharng polcy of supply chan 1 when suppler 1 and retaler 1 have dfferent barganng power The e-commerce platform wll capture the profts as much as possble by settng the equlbrum value of e-coupon Compared wth both supply chans that do not to partcpate n the promoton, supply chan wth lower margnal profts may be worse off when supply chan 1 chooses to partcpate n the promoton From Fgure 6, we can fnd that the e-commerce platform may be better off when t sets the equlbrum value of e-coupon V In contrary, both supply chans would be better off f the e-commerce platform sets the optmal value of e-coupon V opt The equlbrum value of e-coupon s not optmal for all the partes Fgure 7 dsplays the dfference of the equlbrum value and optmal value The optmal value of e-coupon s always better than the equlbrum value The expected profts of both supply chans and the e-commerce platform decrease wth the competton ntensty The mplcaton of Fgure 7 s that the e-commerce platform should encourage onlne stores to sell heterogenety products and elmnate competton Expected proft (π) 4 3 1 π 1 π V opt V 1 3 4 The value of e-coupon (V) Fgure 6: Expected proft changes wth the value of e-coupon 6 Concluson In ths paper, we have consdered how onlne cooperatve promoton and cost sharng decsons n supply chans depend on consumer prce senstvty, competton ntensty, and the magntude of markdowns Our results show that (1) the retalers are lkely to partcpate n the promoton f π e
Mathematcal Problems n Engneerng 9 Expected proft (π) 11 9 7 5 3 V =1745/(97 97k) π(v opt ) π(v ) k=k 1 =k, b 1 =b =1 V opt = 165 5/(1 k) V =3 5 5 7 Competton ntensty (k) Fgure 7: Expected proft changes wth competton ntensty consumersbecomemoreprce-senstvehowever,tdoesnot mply that retalers can beneft from the prce promoton; the promoton decson game resembles the classcal prsoner s dlemma game () The retalers and supplers can beneft from the cooperatve promoton by desgnng approprate cost sharng polcy Cost sharng contract can coordnate the supply chans and mprove the supply chan performance (3) The approprate range of cost sharng becomes wder as consumers prce senstvty and competton ntensty ncrease The barganng power between supplers and retalers drectly affects the fracton of the promotonal cost sharng (4) The e-commerce platform wll capture the most surplus yelded by cooperatve promoton through settng the value of e-coupon The equlbrum value of e-coupon set by e- commerce platform s not optmal for all the partes We provde some manageral nsghts on the coordnaton of supply chan n the cooperatve promotonal actvty For a frm, ncreasng the degree of product heterogenety s the best way to avod ntense market competton and gan more profts From a supply chan perspectve, the upstream and downstream frms are much more lkely to acheve a wn-wn result n the ferce market competton f they work wth each other In addton, e-commerce platform and retalers may be better off when they make the approprate cost sharng contract n a cooperatve promoton campagn Fnally, we dscuss other future research opportuntes It would be nterestng to study the coordnaton of supply chan consstng of multsuppler and one retaler under supply chan competton when the demand nformaton s mperfect It would be also nterestng to predct the change of consumers prce senstvty durng the onlne promoton perod Appendx Proof of Lemma 1 Retaler ( = 1,) wll choose to partcpate n the promoton f and only f π Y,X j r π N,X j r ;thus we have π Y,Y r π N,Y r =(a +b V k b j V) [(1 φ) (P V) w ] (a k b j V) [(1 φ) P w ] =[(1 φ)(p V) w ]b V (a k b j V) [(1 φ) V] b L D 1 = (a k b j V) [(1 φ) V] [(1 φ) (P V) w ]V ; π Y,N r π N,N r =(a +b V) [(1 φ) (P V) w +S ] a [(1 φ) P w ] =[(1 φ)(p V) w +S ]b V a [(1 φ) V S ] b L D = a [(1 φ)v S ] [(1 φ) (P V) w +S ]V, when b [L D 1,LD ) πy,y r π N,Y r and π Y,N r π N,N r (A1) ProofofTheorem Accordng to the analyss of Lemma 1, the equlbrums are obtaned as follows When b 1 L D 1 and b L D,wehaveπY,Y π N,Y and π Y,Y r π N,Y r ; the equlbrum s (Y, Y) Whenb 1 [L D 11,LD 1 ) and b [L D 1,LD ),wehave π Y,Y >π N,Y, πy,y r >π N,Y r, πy,n <π N,N,andπ Y,N r <π N,N r ; (Y, Y) and (N, N) are the two equlbra We can get other equlbrums at the same procedure Proof of Theorem 4 The upper bound of the fracton of the promotonal cost sharng (the largest fracton suppler can offer) must satsfy π Y,X j s =π N,X j s Thus,wehave S max = (w c s )b V a +b V k b j V (A) Also, the lower bound of the fracton of promotonal cost sharng (the smallest fracton suppler should offer) must satsfy π Y,X j r S mn =π N,X j r Thus,wehave = (1 φ) [a b (P V) k b j V] V + b w V (A3) a +b V k b j V
1 Mathematcal Problems n Engneerng Proof of Theorem 7 To maxmze ths value, (Δπ s ) α (Δπ r ) β, we buld the Lagrange functon: Proof of Theorem 1 Let V e =V opt + A (A > );thuswehave π(v opt )>π(v e ): F=(Δπ s ) α (Δπ r ) β +λ 1 Δπ s +λ Δπ r +λ 3 S α Δπ s = β Δπ r Δπ s =(S max S )q, Δπ r =(S S mn )q (A4) π(v opt ) π(v e )= (P c s V opt ) =1 =1 (a +b V opt k b j V opt ) [a +b (V opt +A) k b j (V opt +A)] (P c s V opt A) (A6) αs mn α(s S mn )=β(s max S ) S =αs mn +βs max We have the fracton of promotonal cost sharng S = +βs max Proof of Theorem 8 Supply chan ( = 1, ) wll choose to partcpate n the promoton f and only f π Y,X j π N,X j ;thus we have π Y,Y π N,Y =(a +b V k b j V) [(1 φ) (P V) c s ] (a k b j V) [(1 φ) P c s ] =[(1 φ)(p V) c s ]b V (a k b j V)(1 φ)v b L I 1 = (1 φ) (a k b j V) (1 φ) (P V) c s ; π Y,N π N,N =(a +b V) [(1 φ) (P V) c s ] a [(1 φ) P c s ] =[(1 φ)(p V) c s ]b V a (1 φ)v b L I 1 = (1 φ) a (1 φ) (P V) c s, when b [L D 1,LD ) πy,y π N,Y and π Y,N π N,N (A5) ProofofTheorem9When V I j VI V V I j1 VI 1, both supply chans wll not to partcpate n the promoton because (N, N) s Pareto optmalty However, when V V I V I j1, the domnant strategy for supply chan s Y and the optmal strategy for supply chan j s Y Hence,the unque equlbrum s (Y, Y) Furthermore,fV e V I and V I j <VI <VI j1, e-commerce platform wll choose VI as the equlbrum value of e-coupon to nduce both supply chans to partcpate n the promoton = + =1 =1 [a +b (V opt +A) k b j (V opt +A)] (k b j b )(P c s V opt )> π(v opt )>π(v e ) Conflct of Interests The authors declare that there s no conflct of nterests regardng the publcaton of ths paper Acknowledgments ThsresearchssupportedbytheMajorProgramofthe Natonal Natural Scence Foundaton of Chna (Project no 713933), Natonal Natural Scence Foundaton of Chna (Projects nos 71114, 7117199, and 71115), and Shandong Independent Innovaton and Achevement Transformaton Specal Fund of Chna (Project no 14ZZCX33) References [1] Y Bakos, The emergng landscape for retal E-commerce, Economc Perspectves,vol15,no1,pp69 8,1 [] M Porter, Strategy and the nternet, Harvard Busness Revew, vol79,no3,pp6 78,1 [3] M Wlson-Jeanselme and J Reynolds, Growth wthout proft: explanng the nternet transacton proftablty paradox, Journal of Retalng and Consumer Servces,vol1,no3,pp165 177, 5 [4] E Brynjolfsson, Y J Hu, and M D Smth, Consumer surplus n the dgtal economy: estmatng the value of ncreased product varety at onlne booksellers, Management Scence,vol 49,no11,pp158 1596,3 [5]JChu,PKChntagunta,andJCebollada, Acomparson of wthn-household prce senstvty across onlne and offlne channels, Marketng Scence,vol7,no,pp83 99,8 [6] M Bls, Prcng n a customer market, The Quarterly Journal of Economcs,vol14,no4,pp699 718,1989 [7] JAChevaler,AKKashyap,andPERoss, Whydon tprces rse durng perods of peak demand? Evdence from scanner
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