Two kinds of Online Retailers Price Competition on B2C Market

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1 Two kin of Onlin Railr Pri Coiion on BC Mark Hao Fu, Jiyao Ding, Lili Liu Hao Fu, Hrbr A.Sion & Rinhar Sln Bhavioral Diion Rarh Lab, Shool of Eonoi an Managn, Souhw Jiaoong Univriy, ChngDu 600, China ; ; Jiyao Ding, Lili Liu, Hrbr A.Sion & Rinhar Sln Bhavioral Diion Rarh Lab, Shool of Eonoi an Managn, Souhw Jiaoong Univriy, ChngDu 600, China Abra. Uing ga hory a rarh ool, hi ar inviga ly on ri oiion bhavior bwn Muli-Channl Railr MCR an Pur Onlin Railr Doo on -or ark, lii four kin of ark ruur. Furhror, i giv ou rf quilibriu ri a wll a ark al unr ah oniion of ark ruur. On hi bai, wo rla rooiion an wo rla onluion ar oin ou. Fir, i g MCR an Doo riial ri. Sonly, a h nra ra of - buin inraing, wo kin railr rf ri will ra, an hr xi a abl rlaionhi bwn h raio of lining.. Inrouion A h bginning of Inrn arin, baing on h ogniiv of Inrn inforaion hnology hararii, ol hol ha on h -buin ark, hrough inving vn l han on raiional onoi, onur an arh an fa wih or ulir whih ay la oiion aong ulir. A a rul, h onur an g a lowr ri. In r of onoi, oaring wih raiional off-lin ra o, -buin o highr ark ffiiny an lowr ark friion, ru ra an arh o ffivly, an onqunly ra ulir onooly rofi [,]. Th o-all fr-friion ra hyohi whih an b irly hrough oaring ri lvl on -buin ark ara any rarhr oing horial an irial ui on oaring ri oiion bwn onlin railr an off-lin railr []. I an b onlu ha xin rarh on oling h ri oiion bwn raiional railr an onlin railr hav bn vlo uffiinly [4].

2 6 Hao Fu, Jiyao Ding, Lili Liu Howvr i i noiabl ha, rn yar, along wih onlin ark xaning, or an or raiional railr nr ino BC ark. A uli-hannl railr MCR, hy o irly wih ur onlin railr Doo. Bu hr i lil rarh on h ri oiion bwn h wo kin of onlin railr wihin onlin ark inrnal. In xiing rfrn, an ioran analyial ol an irial analyi ar inviga on ri oiion bwn MCR an Doo ba on Horlling ol [5]. A h auhor ai, hir analyi ol i ba on Holling linar iy frawork an i lii by i auion. Rlaxing o of h auion an ak h ol rihr, albi or olx. Morovr, Fribrg [6] gav ou a or gnral ol abou ri oiion bwn MCR an Doo, an i rlvan irial rarh. Bu in hi rarh work, h ff of -buin nra ra qual o nubr of Inrn ur/oal oulaion on ri oiion i no akn ino onir. Thrfor, rgaring wo kin of railr inrnal -buin ark a rarh obj, ba on Fribrg [6,7] an Chng Yun [8]oling hoology abou ri oiion bwn raiional off-lin railr an ur onlin railr, hi ar ak furhr vlon an gnralizaion in orr o g a or lar rogniz on ri oiion bwn MCR an Doo. Aoring o O kf an MEahrn [9] onur iion aking ol, whn onur ar oniou abou h ibalan bwn ial onuing an raial onuing, hy fa wih hannl hooing robl whr o buy afr i wha goo o buy for h uro of offing hi ibalan. Thrfor, w uo ha: in h ra of -onoi, whn onur who an urha onlin hoo hir hoing o whr o buy, hr ar wo layr for h o ak hoi: urha onlin or off-lin; if hoo urha onlin, hn wigh h wo onlin urhaing hannl: MCR an Doo. So rarhing on onur iion aking bwn wo onlin urhaing hannl, hi ar boo xi rul fro working ovr ri oiion bwn raiional railr an onlin railr ino wo kin of railr oiion in onlin ark inrnal.. Hyohi Baing on rviou an, w fir ivi rail ark ino wo ar: raiional off-lin ark an -buin onlin ark. Thn by ing u ga ol, oarnaliz ark har aong off-lin hannl an on-lin hannl rivly. Furhr, o or ga analyi on ri oiion bwn MCR an Doo. In hor, hi ar ivi h rail ark ino h following ruur figur :

3 Two kin of Onlin Railr Pri Coiion on BC Mark 7 Figur. Channl Diviion for Rail Mark Aoring o onur hoi onlin/offlin an iffrn arar rlaionhi, variou ark ruur ar buil. Conur who hoo urhaing onlin will ak on layr hoi MCR or Doo. Conrly, whn, Uiliy onur gain whn hy urha onlin;, Uiliy onur gain whn hy urha off-lin, hr ar- gr of -buin i aualiz; riial valua valu of onur who hoo -buin onur who hoo urha onlinwhn, hr ar - onur who hoo urha onlin. For il, unr h wo oniion, hi ar analyi furhr on ri oiion bwn MCR an Doo. For h onur who urly urha onlin onlin onur, hr ar wo kin of onlin railr MCR an Doo on -buin ark, hrfor hy hav o hoo urhaing hannl fro MCR an Doo. Suo uiliy funion ha onlin onur hoo MCR or Doo U, onur valuaion on ooiy0, uiliy ha onur gain whn urha a ooiy. Manwhil hyoh i uniforiy iribu on [0, ]. P, ooiy ri whn onur urha on MCR, P ooiy ri whn onur urha on Doo., ooiy ooruniy o offiin whn onur urha on MCR 0< <;, ooiy ooruniy o offiin whn onur urha on Doo 0< <; Thrfor, onur riial valu valuaion on MCR an Doo ar rivly ; Nx, w analyi iffrn ark ruur for by ri oiion bwn MCR an Doo ba on h valu of an.

4 8 Hao Fu, Jiyao Ding, Lili Liu Diviion of ark ruur. Whn h nubr of onlin onur i -,.. Whn = Hr, h onur who riial valuaion valu i or on h righ of h axi an hoo boh MCR an Doo whih an - onur an hoo ihr way. For h onur, whn hy hoo MCR, i i nary ha - -P - P ha - P -P Thrfor, whn - >0, h onur who valu valuaion i bwn P -P / -,will hoo MCR, an h onur who valu valuaion i bwn,p -P / - will hoo Doo. Whn - <0, h onur who valu valuaion i bwn,p -P / - will hoo MCR, an h onur who valu valuaion i bwn P - P / -,will hoo Doo. Conrly, bau, P /- P /-, hn P -P - - P Whn - >0, P -P / -, hr riial valuaion of h onur who hoo MCR finally i = P -P / -. Pri oiion in MCR an Doo for h ark ruur a follow, Figur.. Mark Sruur On For fro Pri Coiion Bwn MCR an Doo whn - <0, P -P / -, hr onur who hoo MCR finally i y whih an MCR ark har i zro. W fou on analyi of oiion bwn MCR an Doo in onlin ark an hi oniion i xlu fro our rarh ara, o w on ak i ino onir. Mark Sruur On: Unr h oniion ha h nubr of onlin onur i -, whn an only whn - >0, hr xi a ark ruur ha MCR an Doo oxi. Thn, hr ar - onur hoo urhaing on MCR, an hr

5 Two kin of Onlin Railr Pri Coiion on BC Mark 9 ar - onur hoo urhaing on Doo... Whn < = Hr, h onur who riial valuaion valu i or on h righ of h axi an hoo boh MCR an Doo whih an - onur an hoo ihr way. For h onur, whn hy hoo MCR, i i nary ha - -P - P So ha - P -P Thrfor, whn - >0, h onur who valu valuaion i bwn P -P / -,will hoo MCR, an h onur who valu valuaion i bwn,p -P / - will hoo Doo. Whn - <0, h onur who valu valuaion i bwn,p - P / - will hoo MCR, an h onur who valu valuaion i bwn P -P / -, will hoo Doo. < P / - <P / - - P < - P P - P < P - P + P - P - P -P < - P So ha: whn - >0, ha P -P / - < = Bau a hi i, h nubr of onur who hoo Doo i,p - P / -, i ha bn rov bfor ha > o i i no akn ino onir. Pri oiion in MCR an Doo for h ark ruur a follow Figur.. Mark Sruur Two For fro Pri Coiion Bwn MCR an Doo Mark Sruur Two: Unr h oniion ha h nubr of onlin onur i -, <, whn an only whn - <0, hr xi a ark ruur ha MCR an Doo oxi. Thn, hr ar - onur hoo who urhaing on MCR, an hr ar - onur who hooing urha on Doo.

6 40 Hao Fu, Jiyao Ding, Lili Liu. Whn h nubr of onlin onur i -,.. Whn = Hr, honur who riial valuaion valu i or on h righ of h axi an hoo boh MCR an Doo whih an - onur an hoo boh urhaing way. For h onur, whn hy hoo MCR, i i nary ha - -P - P, ha - P -P Thrfor, whn - >0, h onur who valu valuaion i bwn P - P / -, will hoo MCR, an h onur who valu valuaion i bwn,p -P / - will hoo Doo. Whn - <0, h onur who valu valuaion i bwn, P -P / - will hoo MCR, an h onur who valu valuaion i bwn P - P / -, will hoo Doo. Conrly, bau, P /- P /-, hn P -P - - P Whn - >0, P -P / -, hr riial valuaion of h onur who hoo MCR finally i =P -P / -. Pri oiion in MCR an Doo for h ark ruur a follow Onlin Conur MCR Conur =P -P / - 0 Figur. 4. Mark Sruur Thr For fro Pri Coiion Bwn MCR an Doo Whn - <0, for, hn P /- P /-. So P -P P - P = P - P + P - P = P - P + - P Bau - <0, P -P / - P /-, ha =, hrfor valu valuaion,p -P / - of onur who hoo MCR i y on an i will b no akn ino onir. Mark Sruur Thr: Unr h oniion ha h nubr of onlin onur i -,, whn an only whn - >0, hr xi a ark ruur ha MCR an Doo oxi. Thn, hr ar - onur who hoo urhaing on MCR, an hr ar - onur who hoo urhaing on Doo... Whn < = :

7 Two kin of Onlin Railr Pri Coiion on BC Mark 4 Hr, h onur who riial valuaion valu i or on h righ an hoo boh MCR an Doo whih an - onur an hoo boh urhaing way. For h onur, whn hy hoo MCR, i i nary ha - -P - P, Sill ha - P -P Whn - >0, h onur who valu valuaion i bwn P -P / -, will hoo MCR, an h onur who valu valuaion i bwn, P - P / - will hoo Doo. Whn - <0, h onur who valu valuaion i bwn, P -P / - will hoo MCR, an h onur who valu valuaion i bwn P - P / -, will hoo Doo. < P / - <P / - - P < - P P - P < P - P + P - P - P -P < - P a whn - >0, ha P -P / - < ; b whn - <0, ha P -P / - >. Whn - >0, valuaion lur, P -P / - of onur who hoo Doo i y. Pri oiion in MCR an Doo for h ark ruur a follow Onlin Conur Doo Conur - = P -P / - 0 Figur. 5. Mark Sruur Four For fro Pri Coiion Bwn MCR an Doo Mark Sruur Four: Unr h oniion ha h nubr of onlin onur i -, <, whn an only whn - <0, hr xi a ark ruur ha MCR an Doo oxi. Thn, hr ar - onur who hoo urha on Doo, an hr ar - onur who hoo urha on MCR.

8 4 Hao Fu, Jiyao Ding, Lili Liu 4 Ga analyi unr four ark ruur Uing bakwar inuion, w u wo kin of railr oiu ri an quilibriu oluion a follow: Th an of onur who hoo urhaing hannl of MCR an Doo ar rivly: D D Profi funion ar: =P -C D ; =P -C D Prf ri ar rivly: Thrfor, quilibriu oluion ar a follow: ] [ 9 ] [ ] [ / / D D 9 ] [ Siilarly, rf ri an quilibriu oluion of ruur wo ar:

9 Two kin of Onlin Railr Pri Coiion on BC Mark 4 / / An, rf ri an quilibriu oluion of ruur hr ar: / / La, rf ri an quilibriu oluion of ruur four ar: / / 5 Diuion Baing on four kin of MCR an Doo oxi ark ruur an ah quilibriu oluion onfir by wo- ga analyi, w an u ohr uful rul inluing nary oniion of Nah quilibriu. A for h or of hi ar ri oiion bwn onlin al hannl MCR an Doo on -buin ark inrnal, w an ak onluion hrough oaring wo kin of railr rf ri in ah ark ruur. Rul ar how in Tabl. In orr o ilify h oniion P <P how abov, w inrou arar whih an for -buin ark al. Obviouly, i bwn [0, ], an hr xi rlaionhi aong four kin of ark ruur:

10 44 Hao Fu, Jiyao Ding, Lili Liu ark ark ruur ruur an an 4 Thn w an unify h oniion P <P of four kin of ark ruur C -C < -/v - Co o following rooiion: Prooiion : In h oiion of -buin ark ha wo kin of onlin railr oxi, four faor oghr i h ri of wo kin onlin railr: railr o C an C,, ohr o arar an ha onur riv whn hy urha fro wo kin of railr, -buin ark al an - buin nra ra. Whn wo kin of railr o iffrn i lowr han a riial valu -/v -, rior railr ri i lowr han h lar. Whn h iffrn bwn o ha offiin onur riv whn hy urha fro wo kin of railr i highr han a riial valu C -C /-, rior railr ri i lowr ha h lar. Prov: Fro C -C <-/v - an rlaionhi bwn an of four ark

11 Two kin of Onlin Railr Pri Coiion on BC Mark 45 Tabl Coiion Rlaionhi Bwn MCR an Doo on E-Buin Mark Mark Sruur Rlaionhi of Parar Coniion ha Doo ri i lowr ha MCR ri Onlin Mark Sal, > Onlin Mark Sal, < < Onlin Mark Sal C - C < C - C < -, > C -C <+ - 4 Onlin Mark Sal -, < < C -C <+ - ruur, w an fin ha: Unr all four ark ruur, hr i: whn Doo o C <C +-/v -, Doo ri i lowr han MCR. Unr all four ark ruur, hr i: whn ohr arar x ri ha onur riv whn hy urha on Doo > + C -C / -, Doo ri i lowr han MCR. Unr ark ruur an, whn -buin ark al <- C - C / -, Doo ri i lowr han MCR. Unr ark ruur an 4, whn -buin ark al > -C-C / -, Doo ri i lowr han MCR. 4 Unr ark ruur an, whn -buin nra ra >/- C - C / -, Doo ri i lowr han MCR ; Unr ark ruur an 4, whn -buin nra ra </- C -C / -, Doo ri i lowr han MCR ; Finih. Prooiion : A -buin nra ra inraing, wo kin railr rf ri ra an hr i a abl rlaionhi of raio of lin ; in ark ruur an, h iffrn inra; an in ark ruur an 4, h iffrn ra. Prov:

12 46 Hao Fu, Jiyao Ding, Lili Liu Mark Sruur : Thn 0 0; 0; Mark Sruur : Thn 0 0; 0; Mark Sruur : iilar wih ark ruur. Mark Sruur 4: iilar wih ark ruur 4. Finih. 6 Conluion Thi ar i ba on ol Fribr [6,7]; ChngYun al.[8] ha fou on ri oiion robl bwn raiional off-lin ark railr an ur onlin railr, an vlo i furhr ino oniring h ri oiion bhavior of boh Muli-Channl Railr MCR an Pur Onlin Railr Doo on - buin ark. Furhror, w alula rf quilibriu ri of wo kin of -buin railr unr four y of ark ruur, inrou arar ha inia h al of -buin ark, an iu hararii of h hang abou riing ragy an rf ri ha blong o h wo kin of railr. Thi rarh no only onua ri oiion bhavior of oublhannl railr on -buin ark aaially, bu alo rovi horial founaion for furhr irial rarh on -buin ark riing. Aily,

13 Two kin of Onlin Railr Pri Coiion on BC Mark 47 w o no inlu ohr faor uh a ri oiion bhavior of MCR offlin ar an raiional offlin railr. I i worhy uying furhr on hi ar. Rfrn. J.Y. Bako, Ruing Buyr Sarh Co: Iliaion for Elroni Markla, Managn Sin, 997,4:6-60. J.Y. Bako, Th Erging Rol of Elroni Markla on h Inrn, Couniaion of h ACM, 998,48:5-4. S. Balaubraanian, Mail vru Mall: A Sragi Analyi of Coiion bwn Dir Markr an Convnional Railr, Marking Sin, 998,7: M.D. Sih, J. Baily, & E. Brynjolfon, Unraning Digial Mark: Rviw an An, In: E. Brynjolfo & B. KahinE. Unraning h Digial Eonoy. MIT r X. Pan, V. Shankar, & B. Rahfor, Pri Coiion Bwn Pur Play v. Brik-an- Clik -Tailr: Analyial Mol an Eirial Analyi. Avan in Ali Miroonoi, 00,: R. Fribrg, M. Ganlan, & M. Sanrö, E-or an Pri-hory an vin, Working Par, Sokhol Shool of Eonoi, R. Fribrg, M. Ganlan, & M. Sanrö, Priing Sragi in E-or: Brik v. Clik, Working Par, Sokhol Shool of Eonoi, Y. Chn, H,C, Wang, H.Z. Shn, Suy on h Pri Coiion bwn E-or Railr an Convnional Railr, Thory an Prai of Syaial Enginringin Chin006P R.M. O kf, & T. MEahrn, Wb-ba Cuor Diion Suor Sy, Couniaion of h ACM, 998,4:7-78