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Autho's pesoa copy Avaabe oe at www.scecedect.com Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 www.eseve.com/ocate/eo Bcks-ad-mota vs. ccks-ad-mota : A equbum aayss Feado Beste a, *, Jg-Sheg Sog a, Xaoa Zheg b a The Fuqua Schoo of Busess, Duke Uvesty, Towevew Dve, Box 9020, Duham, NC 27708, Uted States b Guaghua Schoo of Maagemet, Pekg Uvesty, Beg 0087, Cha Receved 30 August 2005; accepted 24 Ap 2006 Avaabe oe 9 Novembe 2006 Abstact The Iteet has povded tadtoa etaes a ew meas wth whch to seve customes. Cosequety, may bcks-ad-mota etaes have tasfomed to ccks-ad-mota by copoatg Iteet saes. Exampes of compaes makg such a tasto cude Best Buy, Wa-Mat, Baes & Nobe, etc. Despte the ceasg pevaece of ths pactce, sevea fudameta questos ema: () Does t pay off to go oe? (2) Whch s the equbum dusty stuctue? (3) What s the mpcato of ths busess mode fo cosumes? We study these ssues a ogopoy settg ad show that ccks-ad-mota ases as the equbum chae stuctue. Howeve, we fd that ths equbum does ot ecessay mpy hghe pofts fo the fms: some cases, athe, t emeges as a stategc ecessty. Cosumes ae geeay bette off wth ccks-ad-mota etaes. If fms ag wth pue e-taes to each the oe maket, we show that a psoe s demma-type equbum may ase. Ó 2006 Eseve B.V. A ghts eseved. Keywods: Suppy cha maagemet; Game theoy; E-commece; MNL mode; Aace. Itoducto The apd deveopmet of fomato techooges has povded ew meas fo etaes to each the ed maket. As substatay moe cosumes have gaed Iteet access ad foud t both coveet ad secue to shop oe, e-commece has become attactve to moe fms. Vaous Iteet-eabed busess modes have emeged. Amog those, a mpotat oe deas wth the tegato of the Iteet chae ad the tadtoa eta chae, the so-caed ccks-ad-mota busess mode. Ideed, etaes agg fom depatmet stoes to specaty stoes, fom ow-ed to hgh-ed, have auched Iteet saes stes besde the pe-exstg eta chaes. Exampes cude Boomgdaes, Best Buy, Baes & Nobe, Les N Thgs, ad WaMat, to ame ust a few of the most we-kow. * Coespodg autho. Te.: + 996607854; fax: + 99660797. E-ma addess: feado@ma.duke.edu (F. Beste). 0377-227/$ - see fot matte Ó 2006 Eseve B.V. A ghts eseved. do:0.06/.eo.2006.04.047

Autho's pesoa copy 672 F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 I the case of tadtoa etaes, the Iteet chae s ofte vewed as a ogca exteso of the stoefot s physca pesece, a compemet to exstg custome eatoshps, busess pocesses, ad dstbuto systems (Zeega, 999). Scott Svema, decto of Iteet etag at the Natoa Reta Fedeato, says: Badg s a temedous advatage ad coss-pomotg t ove the Iteet ad physca stoes w ope up ew seg oppotutes. Messa Bae, a aayst wth the Yakee Goup, agees: Some of the smate oes ae statg to eaze that t s the game to ose. They aeady have the customes, ad ow they ca use the Iteet the stoes as a too to expad the shae of customes (Tedesch, 999). These busess pactces ad obsevatos woud seem to suggest that bcks-ad-mota (heeafte efeed to as B) etaes ae, o shoud ecessay be, tasfomg to ccks-ad-mota (heeafte efeed to as C) etaes. Howeve, f a etaes the maket adopt the C busess mode, the esutg competto may aso decease the vaue of a dua-chae stuctue. Theefoe, the wdespead shft to ccks-ad-mota suppy chas may ot bg a substata beeft to etaes. Rathe, t may favo oy cosumes. Motvated by these coces, ou eseach ams to addess the foowg fudameta questos:. Ae compaes makg the ght decso adoptg the C busess mode? 2. What s the dusty equbum busess mode? 3. Gve that some etaes may ot be capabe of estabshg ad effcety opeatg Iteet saes, how does the dusty equbum chage whe etaes eed to ag wth pue Iteet fms ode to go oe? To addess these questos, we aayze the suppy cha chae stuctue choce a ogopoy settg. Thee ae exstg B etaes, each seg oe poduct. The poducts ae cose substtutes. Whe etaes have the capabty of effcety maagg a C stuctue, the stategc decso coces whch suppy cha mode to adopt: B o C. The equbum of ths chae stuctue game s deved by compag the outcomes of thee sceaos: B vs. B competto, C vs. B competto, ad C vs. C competto. I each sceao, the etaes decso vaabes cosst of the pces at the eta stoes ad the pces at the Iteet stoes (f appcabe). We dffeetate the sge tadtoa eta chae (B stuctue) fom the dua ccks-ad-mota chae (C stuctue) tems of the opeatoa ad tasactoa costs voved maagg each type of suppy cha ad the way cosumes assess the poduct vaue each settg. Specfcay, we mode cosume demad by devg a mutoma ogt (MNL) mode fom cosume utty maxmzato. Cosumes vauato fo poducts depeds o whee the poducts ae puchased (ethe at a eta stoe of a B etae, at a eta stoe of a C etae, o though a C etae s oe chae). We cosde two vaats of the MNL mode that dffe accodg to how cosumes vaue the poduct. I the fst settg, vauato fo the poduct s hgh eough o, ateatvey, cosumes have vey ow pce sestvty fo the poduct, to duce a cosumes to make a puchase. I the secod settg, thee exsts a outsde opto ad some cosumes may choose ot to buy the poduct. Hee, cosume vauato fo the poduct s modeate ad fms must compete wth the outsde ateatve. Cosumes seect a vaat by tadg off the beefts of owg the poduct wth the pce they eed to pay fo t ad the vaue obtaed fom esgg the puchase. Reated to these two settgs ae the woks of Rhee (996) ad Saop (979). Rhee (996) studes fms stategc quaty decsos a duopoy settg. Aayzg a sceao sma to ou fst settg, the autho assumes that poducts cosumpto vaue s age eough fo cosumes to buy oe of two poducts. The pape deves cosed-fom soutos ude ths assumpto. Saop (979) studes Chambea moopostc competto wth outsde goods. The autho fds that the equbum behaves dffeety fom that the teatue obtaed wthout cosdeg outsde goods. I each mode settg, we chaacteze equbum pces, quattes ad pofts whe each fm has a fxed chae stuctue (B o C). Based o that, we deve the equbum chae stuctue. We fd that a fms adopt, equbum, the C busess mode. I othe wods, C vs. C ases as the dusty equbum stuctue. Howeve, ths dusty equbum may ot cease fms poftabty compaed to the base B vs. B settg. Ths actuay tus out to be the case the absece of a outsde opto. I those cases, adopto of the Iteet becomes a stategc ecessty, athe tha a souce of addtoa eveue fo the etae. I cotast, whe thee s a outsde ateatve, busess poftabty at the C vs. C dusty equbum s stcty age tha the B vs. B settg. These esuts have teestg mpcatos. Fst, the udeyg co-

Autho's pesoa copy F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 673 sume mode has a o-tva mpact o the outcome of the game: wthout a outsde opto the maket, fms do ot deve addtoa pofts by addg oe saes, whe they do settgs whee thee s a outsde ateatve. I settgs wth a outsde opto, the addto of oe saes may aow fms to captue a poto of the maket that woud have opted fo the outsde opto had the Iteet chaes ot bee avaabe. I cotast, whe a customes make a puchase, the addto of oe saes mpes chages the equbum pces that esut the same fms aggegate (eta ad oe) maket shaes as the eta maket shaes the settg wth tadtoa stoes oy. We aso show that the adopto of a Iteet chae ceases poductvty by educg tasacto costs. Moeove, ths stuato beefts ae passed aog to cosumes. Cosume supus ceases fo two easos: Fst, a poto of educed tasacto costs ae passed o to cosumes the fom of owe pces, ad secod, the C stuctue typcay ceases customes vauato fo the poduct, thus ceatg addtoa supus. These fdgs ae cosstet wth empca obsevatos by Htt ad Byofsso (996). These authos use fm-eve data o IT (fomato techoogy) spedg by 370 age fms ad exame thee measues of IT vaue: poductvty, busess poftabty ad cosume supus. They suggest that IT has mpoved poductvty ad ceated vaue fo cosumes. They do ot fd evdece that these beefts have esuted hghe busess poftabty. Tadtoa bcks-ad-mota fms may ot ecessay have the capabtes to effcety opeate a C busess stuctue. I those cases, etaes may eed to ag wth exstg Iteet compaes. Fo exampe, Toys- R-Us ad Amazo fomed a aace the yea 2000 to se toys oe. I ths cotext, we vestgate the equbum dusty stuctue that ases whe oe o moe B etaes fom a aace wth a pue Iteet coutepat to estabsh a dua-chae maket stategy. I patcua, we study two duopoy settgs. I the fst settg, ethe etae s capabe of effcety opeatg ts ow Iteet chae. Istead, they each may cosde fomg a aace wth a Iteet etae. I the secod settg, oe etae ca successfuy opeate a C suppy cha, whe the othe etae ca se oe oy by agg wth a pue e-tae. I these settgs, we fd that a psoe s demma-type equbum may ase. The focus of ths pape s o exstg tadtoa etaes ad the decso o whethe o ot to se ove the Iteet. That s, we cosde ety decsos tems of the etaes choce of expadg the opeatos by addg oe saes. We cosde both the cases whe the etae maages both ts eta stoes ad ts ow Iteet ste (e.g., Wa-Mat), ad cases whe the tadtoa etae ags wth a pue Iteet etae to se oe (e.g., Toys-R-Us ad Amazo). I addto, we povde a bef dscusso o how ou esuts exted to settgs wth pue Iteet fms the maket (see Footote 7). Fay, we befy vestgate the mpact of Iteet peetato o dusty equbum. We fd that at the dusty s equbum, as the addtoa maket eached by use of the Iteet ceases, fms pofts cease but the pofts fom the oga maket decease. We aso fd that Iteet pces ae owe, may due to the expaded cosume each of the Iteet. To the best of ou kowedge, ou wok s amog the fst to study the dusty equbum stuctue espose to the Iteet as a ew seg chae fo tadtoa etaes, ad to aaytcay vestgate the vaue of the Iteet as a seg chae fo both etaes ad cosumes. The eated teatue ca be gouped to thee steams. The fst studes competto amog sge-chae etaes. Lppma ad McCade (997) aayze competg ewsvedos ad exame equbum vetoy eves. Beste ad Fedegue (2003) cosde a mut-peod mode ad study the vetoy ad pcg ssues that ase whe a suppe ses though mutpe competg etaes. Fo othe woks o etae competto, see Mahaa ad va Ryz (200) ad Beste ad Fedegue (2005), ad the efeeces cted thee. Athough ou study aso cosdes hozota competto, the afoe metoed studes focus o a fxed umbe of ateatves, whe ou mode the umbe of vaats esuts fom the etae s chae choce decsos. The secod eated steam of eseach addesses pce competto o the Iteet. Fo exampe, Bakos (997) expoes the effect of buye seach costs o competto makets wth dffeetated poduct offegs. The adopto of a eectoc maketpace s ot the decso of a dvdua see ad o dua-chae Accodg to a speca epot sposoed by Tvesty The Nato s Reta Powe Payes 2005, by Schuz (2005), thee s oy oe pue Iteet etae amog the 00 agest etaes the US Amazo.com.

Autho's pesoa copy 674 F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 stuctue ases. Baasubamaa (998) modes hozota competto betwee a dect makete ad covetoa etaes. Ths wok aso exames the oe of fomato mut-chae makets ad fds that hgh maket coveage may depess pofts. Ths pape does ot cosde competto amog dua-chae payes. La ad Savay (996) aayze competto betwee two etaes that each se oe ad offe. They detfy codtos ude whch the Iteet mght educe pce competto. They compae two settgs: two tadtoa etaes vs. two dua-chae etaes. The etaes chae choce, howeve, s ot expcty modeed. Othe woks eated to the Iteet cude Zettemeye (2000), who studes competto acoss chaes a cotext whch cosumes ae uceta about the pefeeces, Dewa et a. (2003) that expoes the effect of poduct customzato o pce competto a duopoy settg, Baaksha et a. (2004) that aayzes how the abty of cosumes to swtch betwee eta ad oe chaes affects pces, ad Wu et a. (2004) that exames a see s cetve to povde fomato sevces oe the pesece of fee dg compettos. Athough these studes cosde pce competto o the Iteet, oe of them expoes the equbum dusty stuctue that ases whe fms choose betwee sge- ad dua-chae stateges. Fay, the thd steam of eseach expoes the mpacts of the Iteet o suppy cha pefomace ad aayzes the choce of chae stuctue fom a maufactue s pespectve. See Be et a. (2002), Catta et a. (2003), Catta et a. (fothcomg), Chag et a. (2003), Kuma ad Rua (2004), Beste et a. (2004), Dueh ad Poteus (2005), Tsay ad Agawa (2004b) ad the suveys by Catta et a. (2004) ad Tsay ad Agawa (2004a). These papes focus may o chae cofct ad coodato the pesece of a maufactue s dect chae. The est of the pape s ogazed as foows. Secto 2 toduces the mode. Secto 3 aayzes the dusty equbum stuctue wthout a outsde ateatve, whe Secto 4 we expoe settgs wth a outsde opto. We dscuss extesos Secto 5, whe Secto 6 cocudes the pape. 2. The mode We cosde a -fm ogopoy settg to study the suppy cha chae stuctue game. Tadtoa etae, that ses a poduct to the ed maket though a eta stoe, may choose to ope a Iteet chae ad move fom a B to a C suppy cha. I the B settg, etae chooses a ut eta pce p, ad the C settg, etae decdes o two pces: the pce at the tadtoa chae, p, ad the oe at the Iteet chae, p e. (Ou esuts ema vad f p e s costaed to equa p.) We use I ¼f; 2;...; g to deote the set of etaes. 2.. Cosume utty mode The meas by whch the poduct s dstbuted has a mpact o cosume s choce. A cosume deves dffeet uttes whe obtag the poduct fom a etae s physca stoe (ateatves ) tha fom a etae s Iteet ste (ateatves e). Let the set of ateatves be deoted by A. We fst assume that thee s o outsde opto. Secto 4 cosdes the settg wth a outsde ateatve. Ude the assumpto of o outsde opto, the set of ateatves s A B ¼f;...; g whe a fms opeate as bcks-ad-mota, whe t s A C ¼f; e; 2; e2;...; ; eg whe a opeate as ccks-ad-mota. Whe k fms, say fms,...,k, opeate as ccks-ad-mota, whe the emag fms opeate ude the tadtoa stuctue, the set of ateatves s A CB ðkþ ¼f; e;...; k; ek; k þ ;...; g. (I the settg wth a outsde opto, A ¼ A [f0g.) A cosume assocates a utty U a fo ateatve a 2 A. To mode U a, we use the addtve adom utty mode, whch s composed of two pats, a detemstc epesetatve compoet v a p a ad a adom compoet a that accouts fo the cosumes dosycatc tastes about the optos. Theefoe, U a ¼ v a p a þ a ; a 2 A; whee v a s the cosumpto vaue. The pobabty that vaat a s chose s gve by q a ¼ PðU a ¼ max b2a U b Þ; a 2 A; whch depeds o the adom compoets a. We assume that a ae..d. adom vaabes wth a Gumbe (o doube expoeta) dstbuto wth mea zeo ad vaace 2 p 2, whee > 0 s a scae paamete epesetg the degee of heteogeety amog 6 cosumes.2 The, the pobabty of choosg chae s gve by the mutoma ogt (MNL) demad mode 2 Ths paamete epesets the stadad devato of the taste dstbuto. See Adeso et a. (992).

Autho's pesoa copy q ¼ exp v p P2I exp v p : ðþ (Whe thee s a outsde ateatve, the expesso () s modfed by addg the tem exp(v 0 /) tothe deomato, whee v 0 s the vauato fo the outsde ateatve.) We omaze cosume popuato to equa oe. The MNL mode possesses the foowg popetes:. The ow ad coss-pata devatves of the choce pobabtes wth espect to the pces ae: oq ¼ q op ð q Þ < 0, oq ¼ q op q > 0. That s, ceasg the pce fo a vaat educes ts ow demad but ceases demads fo othe vaats. Theefoe, the MNL mode captues the substtuto effect amog the ateatves. 2. If v p = v p, a ateatves ae equay pobabe,.e., q ¼ ; 2 I. I The MNL choce mode aows us to study demad as a fucto of cosumes vauatos fo the vaous chae ateatves. Ths mode aso captues cosumes uobsevabe adom pefeeces fo dffeet ateatves. I addto, the MNL mode captues the dea of bouded atoaty, because a cosume does ot ecessay choose the ateatve that yeds the hghest utty, but stead has a (postve) pobabty of choosg each of the possbe ateatves. Fay, the MNL mode eds tsef to mode chages the umbe of ateatves ( ths case, chaes) avaabe. 2.2. Iteet featues F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 675 We dstgush the Iteet chae fom the eta chae by compag two featues the opeatg cost ad cosume vauato. Fo poducts dstbuted though the physca stoe, etae cus a ut cost c, ad fo poducts sod at the Iteet ste, the ut cost s c e. We assume that c e < c, efectg dffeeces stockg costs, empoyee abo costs, facty mateace costs, etc. I fact, empca evdece shows that IT ad the Iteet educes tasacto costs ad the cost of goods sod (Gacao ad Kapa, 200; Zhu, 2004). To mode the mpact of the Iteet chae o cosume vauato, we toduce a paamete b ad assume that a custome s vauato fo etae 0 s poduct chages fom v to bv whe a fm ses though both tadtoa ad Iteet chaes. I Sectos 3 ad 4, we assume that b P, whe Secto 5. we povde a dscusso o settgs whee b <. The assumpto b P s easoabe may settgs because oce a etae chages ts chae stuctue, a cosume s peceved vaue fo ths etae may mpove. Ideed, cosumes vauato may cease as the etae povdes them wth a ateatve chae whch to buy ts poduct. Specfcay, cosumes peceved vaue fo etae 0 s poduct may be postvey fueced sevea ways: () Cosumes eoy the coveece of buyg the poduct ethe oe o the stoe; (2) cosumes ca obta fomato fom oe chae but make the puchase the othe chae; (3) cosumes ae ofte aowed to etu oe poducts to a oca stoe; (4) taoed emas may ase a cosume s dese to puchase the poduct. Theefoe, cosumes vaue fo the bad of etae may cease. I fact, may cosumes epot that a dua-chae stuctue ceases the wgess to puchase. A 28-yea-od Mahatta Web-advetsg poduce fgues that she s spedg 0 5% moe at Gap eve sce Gap auched ts webste ad seds he taoed emas twce a moth (Lee, 999). Gaps s chef executve, Jeae Jackso, says, ths s about beg ccks ad mota ettg customes access the Gap bads. She beeves that by aggessvey maketg both the stoes ad the webste ad aowg each to eveage the stegths of the othe, both chaes w pospe (Lee, 999). I ths exampe, b P makes sese. I some othe settgs, howeve, t may be easoabe to expect that b <. That s, fo ceta poducts, cosumes vauato may be owe whe fms se though both chaes tha whe they oy opeate though tadtoa eta stoes. A the esuts the pape cotue to hod these cases, povded that b s ot too sma. We povde a detaed dscusso o the mpact of othe paamete ages Secto 5.. Note that fo etae wth a B stuctue, cosume vauato emas at v. I Secto 5.2., we expoe a settg whee the adopto of a Iteet chae ceases the ovea maket sze.

Autho's pesoa copy 676 F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 Fay, whe cosume vauato fo a poduct obtaed at the tadtoa stoe of a C etae s bv, ts vauato fo a poduct obtaed at ths etae s Iteet ste s bhv. The paamete h (whch ca take ay postve vaue) measues the dffeece vauato betwee the physca ad Iteet chaes. Lag ad Huag (998) show that, ovea, cosumes pefe makg the puchases at tadtoa eta stoes athe tha though the Iteet. A suvey by Kace et a. (2002) shows that, fo poduct categoes such as books, shoes, toothpaste ad DVD payes, h vaes fom 0.769 to 0.904. Thoughout the pape, we assume symmety of a etaes the maket. That s, c = c, c e = c e ad v = v, fo a etaes. Ths assumpto esues that ou esuts ae dve by puey compettve easos ad ot by asymmetes amog etaes. 3. Choce of chae stuctue: Wthout a outsde opto Thoughout ths secto, we assume that a cosumes make a puchase. The absece of a outsde ateatve aows us to obta cosed-fom expessos fo equbum pces, quattes ad pofts vaous competto sceaos. Late, we dscuss addtoa mpcatos of ths assumpto. To study whethe a etae has cetve to ope a Iteet chae aog wth ts exstg tadtoa chae, we cosde thee sceaos: (I) A etaes opeate a B busess mode (ths s the base settg, efeed to as B vs. B competto); (II) Some etaes adopt the C busess mode ad the est mata the B busess mode (C vs. B competto); (III) A etaes adopt the C busess mode (C vs. C competto). Fg. shows these sceaos wth k 2 {,2,...,}. We st otato fo the equbum outcomes ude dffeet sceaos beow. Subscpts ae dopped whe the esuts ae detca fo a etaes. p B p CB p CB e p C p C e P B P CB P C equbum pce fo etae ude B vs. B competto; equbum pce at the tadtoa chae fo etae ude C vs. B competto; equbum pce at the Iteet chae fo a C etae ude C vs. B competto; equbum pce at the tadtoa chae fo etae ude C vs. C competto; equbum pce at the Iteet chae fo etae ude C vs. C competto (sma otato s used fo quattes o maket shaes q); equbum poft fo etae ude B vs. B competto; equbum poft fo etae ude C vs. B competto; equbum poft fo etae ude C vs. C competto. 3.. Sceao I: B vs. B I Sceao I, the set of ateatves fo cosumes s A B ¼f; 2;...; g. Demad etae 0 s tadtoa stoe s gve by () wth the set A ¼ A B. A etaes smutaeousy set the pces p. Each etae 0 s obec- Fg.. Thee foms of suppy cha competto.

Autho's pesoa copy tve s to maxmze ts poft P =(p c)q. The foowg esut estabshes the exstece of a uque Nash equbum (the poof foows fom Adeso et a., 992, p. 222). Poposto. Wthout a outsde opto, Sceao I, the pce-settg game has a uque Nash equbum wth p B ¼ þ c, qb ¼, ad PB ¼. We aso compute the cosume supus (deoted by s) as a bass fo compaso wth othe sceaos. I ths case, s B ¼ E½UŠ ¼v p B ¼ v þ c : It foows fom the poposto that as the umbe of fms ceases, the equbum pce, quatty ad poft fo each fm deceases. O the othe had, cosume supus ceases. 3.2. Sceao II: C vs. B I Sceao II, we assume that k ( 6 k 6 ) etaes (say, etaes,2,...,k) adopt a C busess mode. The emag k etaes (etaes k +,k +2,...,) mata the B busess mode. The set of ateatves fo cosumes s A CB ðkþ ¼A B [fe; e2;...; ekg. The choce pobabtes ae as (), wth v = bv ad v e = bhv fo =,2,...,k, adv = v fo = k +,k +2,...,. Fo a C etae, sce oq /op < 0 ad oq e / op > 0, a decease p ceases q but deceases q e. Hece, a sese, etae 0 s two chaes ae aso competg, but the etae has coto ove the two pces. Fo each C etae, the pobem s to choose p ad p e to maxmze ts poft P =(p c)q +(p e c e )q e, =,2,...,k, ad fo each B etae, the obectve s to choose p to maxmze P =(p c)q, = k +,k +2,...,. It w be hepfu to defe the foowg quatty a ¼ exp c c e bð hþv Fo a C etae, q e ¼ a exp ðp cþðp e c e Þ q : The equbum s the chaactezed the esut beow. : ð2þ Poposto 2. Wthout a outsde opto, ude Sceao II, the pcg game has a uque Nash equbum. Moeove, at equbum, ay C-etae s poft mags both chaes ae the same,.e., p CB c ¼ p CB e c e. I addto, each C-etae chooses the same pce p CB (ad p CB e ) ad each B-etae chooses the same pce p CB. Next, we compae the equbum soutos Sceaos I ad II. Fom (), the defto of a (2), ad Poposto 2, we have that q CB q CB ¼ kð þ aþþð kþ exp ¼ kð þ aþ exp ðbþv pcb pcb. exp. ; ¼ ; 2;...; k; exp pcb pcb ðbþv ; ¼ k þ ; k þ 2;...; ; þð kþ sce p CB ¼¼p CB k ad p CB kþ ¼¼pCB. Ths eads to the foowg esut. Poposto 3. Compag the equba Sceaos I ad II, we have: () p CB < p B < p CB, () q CB > ad qcb ðþaþ <, () P CB < P B ¼ < PCB, F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 677 fo =,2,...,k ad = k +,k + 2,...,.

Autho's pesoa copy 678 F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 The addto of a Iteet chae aows a etae to chage a hghe stoe pce ad obta a age tota maket shae, eadg to a hghe poft. Theefoe, the k C-etaes beeft by movg fom B to C,.e., by estabshg oe saes. O the othe had, each emag B etae obseves a decease maket shae ad poft whe some of ts compettos adopt the C busess mode. We ow vestgate how the equbum pofts of a fms chage as oe addtoa etae moves fom a B stuctue to a C stuctue, eadg to a maket wth {,...,k,k + } C-etaes ad {k +2,...,} B-etaes. (Note that ths aayss makes sese whe P 3.) To factate the compasos, we deote a C-etae s poft by P CB ðþ ad a B-etae s poft by P CB ðþ, whe thee ae C-etaes the maket. Fst, we show how etae k + s poft chages whe t shfts ts stategy fom bcks-ad-mota to ccks-ad-mota. Fom Poposto 3, ote that fo ay, P CB ðþ > ; ¼ ;...; ; ad PCB ðþ < ; ¼ þ ;...; : Ths mpes that P CB kþðk þ Þ > PCB kþðkþ. Note that the eft-had sde of the equaty s etae k + s poft whe thee ae k + C-etaes (cudg etae k + ), whe the ght-had sde s etae k + s poft whe thee ae oy k C-etaes (ad etae k + opeates ude a B stuctue). Hece, the (k + )st etae beefts by adoptg a ccks-ad-mota stuctue. We ext expoe how P CB ðþ ad P CB ðþ chage whe ceases fom k to k +, fo < k +ad > k +. Poposto 4. Fo C-etaes =,...,k, P CB ðkþ. P CB ðk þ Þ < P CB ðkþ. Fo B-etaes = k + 2,...,, P CB ðk þ Þ < Poposto 4 shows that whe the umbe of C-etaes ceases fom k to k +, the od set of C- ad B- etaes suffe, sce they a expeece tesfed competto. Oy etae k + beefts fom the move. 3.3. Sceao III: C vs. C I Sceao III, a etaes adopt a C busess mode. The set of ateatves s the A C ¼f; e; 2; e2;...; ; eg. Cosumes vauato fo a poduct obtaed fom a etae s physca stoe s bv, ad the vauato fo a poduct obtaed fom a etae s webste s bhv. The choce pobabtes q ae gve by () wth A ¼ A C. The etaes smutaeousy set the pces. I patcua, each etae chooses p ad p e to maxmze ts poft, P =(p c)q +(p e c e )q e. Poposto 5. Wthout a outsde opto, ude Sceao III, the pcg game has a uque Nash equbum wth p C c ¼ p C e c e fo a. I patcua, p C ¼ þ c, pc e ¼ þ c e, ad P C ¼ fo =,...,. Iteestgy, Sceao III, a etaes set stoe pces as Sceao I ( whch a of them se oy though physca eta stoes) ad make exacty the same pofts. Ths occus because p c = p e c e mpes that each etae s oe maket shae ad poft s popotoa to ts eta stoe s maket shae ad poft, espectvey, wth the popotoaty costat beg a. Whe oy a subset of the etaes adopt the C busess mode, a poto of the cosumes that pevousy puchased at a eta stoe ow buy oe, so the emag B etaes ose maket shae to the C etaes. Whe a fms adopt a dua-chae stategy, equbum, they keep the same eta pce ad seect a owe oe pce so that the aggegate (eta ad oe) maket shae s the same as the maket shae woud be as pue tadtoa etaes. That s, because a cosumes make a puchase, fms set the equbum pces to mata the same aggegate maket shae as ude the B vs. B sceao. Gve the equbum pces Poposto 5, cosume supus ude the C vs. C sceao s s C ¼ E½UŠ ¼q C ðbv pc ÞþaqC ðhbv pc þ c c e Þ¼ bvð þ ahþþaðc c eþ þ a Compag the cosume supus ude Sceaos I ad III, we have that s C s B ¼ ðbð þ ahþð þ aþþv aðc e cþ : þ a þ c :

Autho's pesoa copy The, cosume supus s hghe Sceao III whe b > þ a þ ah aðc c eþ ð þ ahþv : That s, f the ceased vauato fo puchases at a ccks-ad-mota etae s suffcety hgh (.e., b suffcety hgh), cosumes ae, o aveage, bette off a maket wth cck-ad-mota etaes. Note that whe h =,.e., whe vauato fo puchases at the tadtoa eta stoe ad the webste ae the same, cosume supus Sceao III s hghe tha Sceao I fo a b P. Ths s due to the owe cost to seve the Iteet cosumes, whch s passed o to a cosumes the fom of owe pces. 3.4. Equbum stuctue Compag the outcomes of Sceaos I, II, ad III, we deve the foowg esut. Theoem. I a ogopoy settg, C vs. C s the equbum stuctue. I fact, adoptg the C busess mode s a domat stategy fo ay etae. We cocude that the esutg equbum cossts of a ccks-ad-mota etaes. Moeove, f a customes puchase fom oe of the avaabe chae ateatves, estabshg a Iteet chae becomes a stategc ecessty athe tha a addtoa souce of eveue. That s, equbum evey fm auches a Iteet chae, but oe of them s bette off. Howeve, the vaue ceated by the Iteet geeay beefts cosumes. 4. Choce of chae stuctue: Wth a outsde opto Suppose ow that customes have a outsde opto (abeed 0), whch epesets the defaut choce of ot puchasg the poduct fom ay of the fms. The cosumpto vaue fo ths outsde ateatve s gve by v 0. The set of possbe ateatves s ow A O ¼ A O [f0g, O = B, CB, C. The choce pobabtes ae exp vp q O ¼ P2A exp vp O þ exp v 0 : We ext aga aayze thee sceaos coespodg to thee dffeet maket compostos. 4.. The equbum stuctue 4... Sceao I: B vs. B I Sceao I, the set of ateatves s A B ¼f0; ; 2;...; g. Each etae chooses p to maxmze ts poft, P =(p c)q, whee q s gve by (3) wth A O ¼ A B. The outcome of ths game s chaactezed beow (the poof foows fom Adeso et a., 992). Poposto 6. Wth a outsde opto, ude Sceao I, the pcg game has a uque Nash equbum. At equbum, p B ¼¼pB ¼ pb, ad p B c F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 679 ¼ q B ; ð4þ whee q B s a etae s maket shae, gve by q B ¼ P B ¼ qb. q B exp exp ð vpb vp B þexp ð3þ Þ. The equbum poft fo each etae s ð Þ I the settg wth a outsde opto, t s ot possbe to deve cosed-fom expesso fo the equbum pces, quattes ad pofts. Nevetheess, the expessos obtaed Poposto 6 aow us to cocude that q B < q B, p B < p B ad P B < P B. I othe wods, the exstece of a outsde opto dves dow the fms pces, maket shaes, ad pofts. v 0

Autho's pesoa copy 680 F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 4..2. Sceao II: C vs. B Suppose ow that k ( 6 k 6 ) etaes (say, etaes,2,...,k) estabsh a Iteet chae besde the tadtoa eta chaes. The othe k etaes (etaes k +,k +2,...,) mata the B busess mode. The set of ateatves fo cosumes s A CB ¼f0; ; e; 2; e2;...; k; ek; k þ ; k þ 2;...; g, ad the choce pobabtes ae as (3) wth A O ¼ A CB, v = bv ad v e = bhv, fo =,2,...,k, adv = v, fo = k +,k +2,...,. Foowg sma agumets as fo the case of o outsde ateatve, we cocude the foowg: Poposto 7. Wth a outsde opto, ude Sceao II, the pcg game has a uque Nash equbum, p CB. Moeove, at equbum, a C-etae s poft mags both chaes ae the same,.e., p CB c ¼ p CB e c e.i addto, each C-etae chooses the same eta pce p CB ad the same Iteet pce p CB e, ad each B-etae chooses the same pce p CB. Reca the defto of a (2). A C-etae s poft aga educes to P =(p c)( + a)q, =,2,...,k. Moeove, the equbum pces ad quattes aga satsfy Eqs. (6) ad (7). We ow compae the equbum pces, quattes ad pofts ude C vs. B, wth ad wthout a outsde opto. Because the pas ðp CB ; q CB Þ ad ðp CB ; q CB Þ satsfy (6) fo 6 6 k ad (7) fo k +6 6, t foows that P p CB P p CB f ad oy f q CB P q CB fo ay =,...,. The, p CB P p CB fo a =,..., mpy that k ¼ qcb þ P ¼kþ qcb P, whch caot happe the pesece of a outsde opto. Suppose ow that p CB P p CB fo 6 6 k (eca that a C etaes choose the same eta pce, both wth ad wthout a outsde opto). Ths aga mpes that q CB P q CB fo ay 6 6 k. Compag the expessos fo q CB ad q CB, t foows that p CB P p CB fo k + 6 6 eeds to hod as we, aga eadg to a cotadcto. Theefoe, we cocude that q CB < q CB, p CB < p CB fo a =,...,, whch tu mpes that P CB < P CB fo a =,...,. Thus, the competto ceated by a outsde opto educes the equbum pces, maket shaes, ad pofts, fo a B ad C etaes. The foowg esut estabshes a compaso betwee Sceaos I ad II. Poposto 8. Compag the equba Sceaos I ad II, we have: () p CB () P CB < p B < p CB. < P B < P CB. As fo the case of o outsde ateatve, we ow dscuss the chage equbum pofts fo a fms as oe addtoa etae adopts the C busess mode. Whe thee ae C-etaes the maket, we deote by P CB ðþ ad P CB ðþ the equbum pofts fo a C-etae ad fo a B-etae, espectvey. Fom Poposto 8, we have that P CB ðk þ Þ > P B ; ¼ ; 2;...; k þ ; P CB ðk þ Þ < P B ; ¼ k þ 2; k þ 3;...; ; whch mpes that P CB kþ ðk þ Þ > PCB kþ have that fo each C-etae, P CB ðkþ. I addto, foowg sma agumets as Poposto 4, we ðk þ Þ < P CB ðkþ, ad fo each B-etae, P CB ðk þ Þ < P CB ðkþ. 4..3. Sceao III: C vs. C I Sceao III, a etaes se both though a tadtoa stoe ad a Iteet webste. The set of ateatves s gve by A C ¼f0; ; e;...; ; eg. Cosumes vauatos ae v = bv ad v e = bhv fo the tadtoa ad Iteet stoes, espectvey. A etaes smutaeousy choose p ad p e to maxmze the pofts P =(p c)q +(p e c e )q e. Poposto 9. Wth a outsde opto, ude Sceao III, the pcg game has a uque Nash equbum. I patcua, p C c ¼ p C e c e ad p C ¼¼pC ¼ pc, whch s chaactezed by p C c ¼ q C ; ð5þ

Autho's pesoa copy whee q C ¼ ðþaþ exp bvpc ðþaþ exp bvpc þexp v 0 s a etae s maket shae. Each etae s poft s ð Þ P C ¼ qc q : C Foowg sma agumets as fo Sceao II, we aga cocude that, whe a fms adopt a C busess mode, the exstece of a outsde opto educes a etaes equbum pces, maket shaes, ad pofts. Next, we compae the equbum pces ad pofts betwee Sceaos I ad III. Poposto 0 () p C > p B, () q C > q B, ad () P C > P B. F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 68 I cotast to the settg wthout a outsde opto, Poposto 0 suggests that the pesece of a outsde ateatve, the equbum poft acheved by ay fm ude C vs. C s stcty age tha that ude B vs. B. Ideed, the addto of the oe chaes ceates competto to the exstg tadtoa chaes ad to the outsde ateatve. Moe pecsey, the oe chaes stea some maket shae away fom the tadtoa chaes ad fom the outsde ateatve. I equbum, fms set pces a way that the mgato of customes fom tadtoa stoes to oe stes does ot educe each fm s aggegate custome base. Howeve, ths settg, the ewy toduced Iteet chaes offe pces that appea to a poto of the customes that pevousy opted fo the outsde ateatve. As a esut, a fms maket shaes ad pofts cease. Ideed, ote that pat () of Poposto 0 mpes that the facto of customes that seect the outsde ateatve s age ude B vs. B tha ude C vs. C. Iteestgy, t s easy to vefy that P C > P B st hods whe c e = c ad/o b =. I othe wods, eve f the addto of a Iteet chae does ot owe the aveage poducto cost of a fm, ad eve f t does ot cease cosumes vauato, a fms ae, at equbum, stcty bette off by opeatg both -stoe ad oe saes. 4.2. Equbum stuctue Gve the equbum outcomes ude Sceaos I, II ad III, we ca estabsh the foowg esut. Theoem 2. The equbum suppy cha stuctue cossts of a fms choosg a ccks-ad-mota busess mode. I addto, the C busess mode s a domat stategy fo ay etae. A mpotat dstcto betwee the esuts ths secto ad the pevous oe eates to the equbum pofts of a fms ude the equbum suppy cha stuctue C vs. C. Wthout a outsde ateatve, estabshg Iteet saes becomes a stategc ecessty. I settgs wth a outsde ateatve, howeve, the poft of each fm ude the equbum ccks-ad-mota outcome s stcty hghe tha ts poft ude the B vs. B settg. I cotast to the settg studed Secto 3, the exstece of a facto of customes that opt fo the outsde ateatve aows a fms to captue a poto of ths maket by estabshg Iteet saes. We cocude ths secto by expog the extet to whch busess poftabty ceases the C vs. C equbum sceao. To that ed, we defe the dffeece betwee the poft ude C vs. C ad ude B vs. B by DP ¼ P C P B, ad deve the foowg compaatve statcs. Poposto. The dffeece busess poftabty DP ceases as () b ceases, () h ceases, o () c e deceases. The above esut shows that the cease busess poftabty at the equbum C vs. C stuctue s postvey affected by ceases b ad h, ad s egatvey affected by ceases c e. A cease b mpes that the addto of Iteet opeatos ceases cosumes vauato by a age magtude. I patcua, moe of the poteta customes who woud have chose to fogo a puchase ude the B vs. B sceao w actuay make a puchase a maket composed of ccks-ad-mota etaes. A hghe vaue of h meas that the

Autho's pesoa copy 682 F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 dffeece vauato betwee makg a puchase at a stoe ad oe deceases, aga ceasg the facto of customes that ae wg to buy the poduct fom oe of the avaabe chaes. Fay, owe Iteet opeatoa costs tasate to owe maket pces whch aga duce moe customes to buy the poduct. 5. Extesos 5.. Othe paamete ages We beg wth a bef dscusso o the mpact of the assumpto that b P o the esuts Sectos 3 ad 4. Ths assumpto aows us to deve the equates show Popostos 2,4 ad 3, whch mpy that C vs. C s the esutg dusty equbum stuctue. Cose specto of the poofs of these esuts eveas that they cotue to appy as og as the foowg codto hods: z def ðb Þv ¼ð þ aþ exp > ; whee a s gve by (2) (ote that b P mpes z > ). Ths codto hods f b ad/o h ae ot too sma, ad/o f c e s suffcety owe tha c. A of these mpy a dua-chae stuctue that opeates eatvey effectvey ad effcety. Foowg the poofs of Popostos 2,4 ad 3, t ca be vefed that f z <, the a equates these esuts ae evesed, mpyg that B vs. B s the dusty equbum stuctue. That s, z ca be thought of as a measue of the effcecy of a dua-chae stuctue. Fo exampe, a ow vaue of b, epesetg a substatay deceased cosume vauato the face of a dua stuctue (pehaps dve by the cofuso ceated by ucetaty about shppg o etu poces heet to ccks-ad-mota etaes), woud ead to a B vs. B equbum. Fay, f the paametes ead to z =, the pofts ae the same ude ay stuctue (B vs. B, C vs. B, o C vs. C) ad mutpe (detca) equba exst. I what foows, we expoe addtoa vaatos of the oga mode. 5.2. Aace to se oe I pevous sectos, we studed the choce of chae stuctue assumg that a fms had the capabty to estabsh ad opeate the ow Iteet saes chaes. Howeve, ot a have the abty to successfuy mpemet e-commece opeatos. Fo exampe, Toys-R-Us auched ts Iteet chae Toysus.com 998 ad soo foud t a copoate ad pubc eatos headache [...] thgs fe apat ust as qucky as they came togethe (Ese et a., 2003). Due to ts ta faue, Toys-R-Us fomed a aace wth Amazo.com 2000: Ths dea soved the pobem that may bck-ad-mota compaes wee havg at the tme. Toys-R- Us [...] had ot fgued out how to go fom ecevg a oe ode to gettg poducts to the doostep [...] the dea shows that Amazo o oge beeved t coud sge-hadedy be a goba oe shoppg cete... (Ese et a., 2003). I ths secto, we expoe the choce of chae stuctue settgs whee some o a of the fms eed to costtute a aace wth a exstg e-tae to estabsh a oe pesece. I such cotext, we aga vestgate the dusty equbum stuctue. We mode a aace foowg the Toys-R-Us/Amazo exampe. I that case, Amazo eceves fom Toys-R-Us egua fxed cash paymets (whch we do ot copoate, as they do ot affect the pce decsos) ad a pecetage paymet fo toys sod. 3 We deote by that pecetage, wth 0 < <. I addto, we assume that the etae makes the pce decso fo ts stoe whe the Iteet fm decdes o the oe pce. Athough eaty the etae may fuece the pce of ts goods o the Iteet, ths assumpto epesets a easoabe appoxmato of how such aaces usuay opeate. Ideed, the case of Toys-R-Us/ Amazo, a cosume affas webste 4 epots o how pces fo toys may dffe at the stoes ad o the web, ad how the stoes do ot have coto o pces chaged ove the Iteet, Fo exampe, based o a custome s expeece at Toys-R-Us, [a stoe maage expaed that] Toys-R-Us o the web ad the stoe wee 3 http://ews.bbc.co.uk//h/busess/876090.stm. 4 http://www.cosumeaffas.com/toys/toys us.htm.

Autho's pesoa copy F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 683 two dffeet ettes ad cotues sayg that a custome sevce maage [at the stoe] expaed [...] that they do ot pce match teet saes. I addto, ot a Toys-R-Us stoes chage the same pce. Fo exampe, stoes Mahatta chage fom $2 to $0 moe pe tem. 5 Howeve, Amazo chages a sge pce egadess of whee the toy s shpped to (wth the US). It s woth otg that Zhag ad Zhag (2003) mode stategc aaces betwee fms a sma way. As they descbe, ad cosstet wth ou mode, a stategc aace dffes fom a mege that the aace pates ema sepaate busess ettes ad eta the decso-makg autoomy. I the ocay autoomous settg, each fm a aace ows a shae of the stock of ts pate ad thus makes ts pce/quatty decsos to maxmze ts ow poft, pus a facto of ts pate s poft (ths s efeed to as a equty aace). The esuts ad dscusso ths secto aso appy settgs whee the tadtoa etae ad the Iteet fm fom a equty aace. We vestgate the equbum dusty stuctue the cotext of a duopoy. I ths settg, a tadtoa etae a aace wth a Iteet etae, seects a pce p to maxmze ts poft P I ¼ðp cþq þ ðp e c e Þq e ; whe ts pate seects the oe pce p e to maxmze P I ¼ð Þðp e c e Þq e : Cosume vauato fo the sge/dua-chae ad fo stoe/oe puchases peseve the same fomat as pevous sectos. I othe wods, a bcks-ad-mota/iteet aace (whch we deote by BI), cosumes vauato fo a poduct obtaed fom the B etae s bv ad fo a poduct puchased oe s bhv. Fo smpcty, we assume that thee s o outsde opto. 5.2.. Sceao I: B vs. B Ths settg s detca to Sceao I Secto 3. wth =2. 5.2.2. Sceao II: BI vs. B I ths settg, oy oe etae, say etae, estabshes a aace wth a Iteet fm. The thee payes obectves ae to maxmze the foowg pofts: P I ¼ðp cþq þ ðp e c e Þq e ; P I ¼ ð Þðp e c e Þq e ; P 2 ¼ðp 2 cþq 2 ; wth espect to p, p e, ad p 2, espectvey, whee q s gve by () wth v = bv, v e = bhv ad v 2 = v. Evauatg the secod devatves of these poft fuctos at ay oot of the fst devatves, eads to q /, ( )q e / ad q 2 /, espectvey. The poft fuctos P ae theefoe stcty quas-cocave, =I,I,2 (see Adeso et a., 992). We cocude that thee s a Nash equbum the pcg game. 5.2.3. Sceao III: BI vs. BI Whe both B etaes fom a aace wth a Iteet pate, the fou fms seect pces to maxmze the foowg poft fuctos: P I ¼ðp cþq þ ðp e c e Þq e ; P I ¼ð Þðp e c e Þq e ; P 2I ¼ðp 2 cþq 2 þ 2 ðp e2 c e Þq e2 ; P I2 ¼ð 2 Þðp e2 c e Þq e2 : A sma agumet as Sceao II estabshes the exstece of a Nash equbum the pcg game. We coducted a set of umeca expemets to expoe the outcome of the dusty stuctue game ths settg. As dscussed Secto 2, we assume that the fms ae symmetc ad = 2. Fg. 2 shows two possbe dusty stuctue equba. I ths exampe, v = 20, b =.,h = 0.9, =2,c =,c e = 0.7, ad = 0.3 Case ad = 0.6 Case 2. Whe s sma, the beefts fom seg oe do ot offset the osses esutg fom the competto ceated by the Iteet chae. I ths case, each fm s cetve to fom a aace s weake ad, equbum, both fms mata the B mode. Fo suffcety age, both etaes dvduay have a cetve to 5 http://www.cosumeaffas.com/toys/toys us.htm.

Autho's pesoa copy 684 F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 Fg. 2. Aaces betwee etaes ad teet fms. Fg. 3. Ccks-ad-mota vs. aace. se oe, esutg a dusty equbum whee both fms fom a aace wth a Iteet pate. Howeve, at the equbum, both etaes ae wose off compaed wth a B vs. B settg. That s, a psoe s demma-type outcome ases. Sma obsevatos ca be made the pesece of a outsde opto. Fo exampe, cosde the foowg paametes: v = 20, v 0 = 0, b =., h = 0.9, =2,c =,adc e = 0.7. Whe = 0.2 pofts ae (.86,.86) fo the sceao B vs. B, (0.75,.8) fo B vs. BI, ad (.08,.08) fo BI vs. BI. Theefoe, B vs.b s the equbum. Howeve, whe = 0.6, pofts ae (.86,.86) fo the sceao B vs. B, (0.8, 2.8) fo B vs. BI, ad (.30,.30) fo BI vs. BI. I ths case, BI vs. BI s the equbum stuctue ad pofts fo both fms ae owe tha ude B vs. B. A sma aayss foows settgs whee oe of the fms s capabe of estabshg ad opeatg ts ow Iteet outet, whe the othe fm eeds to fom a aace wth a Iteet pate ode to each oe customes. We ext expoe the possbe equbum dusty stuctue outcomes ths settg. We assume that etae ca seect betwee a pue bcks-ad-mota (B) stuctue ad a ccks-ad-mota (C) stuctue, whe etae 2 s status quo s B ad ca oy effcety access the Iteet maket by agg wth a pue e- tae (BI stuctue). I ths exampe, v = 20, b =., h = 0.9, =2,c =,c e = 0.7, ad = 0.3 case ad = 0.6 case 2. I case, etae 2 s cetve to fom a aace s weak ths fm oy gets a 30% shae of the poft, whe t has to face competto fom ts ow Iteet pate. Whe that s the case, the esutg equbum stuctue s C vs. B. I case 2, whe the gas fom the aace ae hghe fo the etae, both fms opeate a oe chae equbum etae by estabshg ts ow Iteet opeatos ad etae 2 by fomg a aace wth a Iteet pate. Aga, ths case, a psoe s demma-type outcome may ase (see Fg. 3). 5.3. The teet eaches addtoa maket I cotast to physca eta stoes, the Iteet pesets a dffused ad ubqutous etwok of pots of access. Customes ca shop aywhee ad at ay tme. Estabshg oe saes aows etaes to each a age maket tha they woud be abe to by opeatg oy physca stoes. I ths secto, we befy study the effects of the exteded custome each that Iteet saes povde fo a etae. We copoate ths featue of the Iteet by assumg, as befoe, that a B vs. B settg tota popuato s of sze ad that ay fm opeatg a Iteet chae ceases ts tota maket sze by c (ths paamete epesets a popuato of customes that do ot have access to o fd t coveet to puchase fom a physca stoe). I ths settg, we aow fo the exstece of a outsde ateatve to puchases fom ay of the etaes, as Secto 4. To soate the effect of a ceased maket each, we focus o the case whee b = h =.

Autho's pesoa copy q q e q ec F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 685 Beow, we toduce the eevat otato: popoto of cosumes (out of tota popuato of sze ) that puchase fom etae 0 s physca stoe; popoto of cosumes (out of tota popuato of sze ) that puchase fom etae 0 s webste; popoto of cosumes (out of the exteded maket of sze c) that puchase fom e- tae 0 s Iteet chae. Specfcay, q ad q e ae gve by (3) wth A B ¼f; 2g, A CB ¼f; e; 2g (assumg etae s the C- etae) ad A C ¼f; e; 2; e2g. O the othe had, q ec s gve by (3) wth A B ¼ /, A CB ¼feg ad A C ¼fe; e2g. A bcks-ad-mota etae s poft s as Secto 4, whe a C etae s poft fucto s P ¼ðp cþq þðp e c e Þq e þ cðp e c e Þq ec : Exstece of a Nash equbum foows fom sma agumets as those Secto 5.2. We coducted a extesve umeca study based o a settg wth two fms. Specfcay, we cosde the foowg paametes: v = 5, v 0 = 0, c =,c e = 0.7, = 2, ad b = h =. I oe set of expemets, we vaed c e fom 0.5 to. I a secod set, we vaed v 0 fom 5 to 5. I a fa set, we vaed fom 2 to 0. I a cases, c aged fom 0 to. To ustate the fdgs, the foowg tabe exhbts the esuts fo v = 5, v 0 = 0, c = c e =, = 2, ad some vaues of c. c 0 0.2 0.4 0.6 0.8 B vs. B.2.2.2.2.2.2 C vs. B (.7,.0) (2.,.0) (2.5,.0) (2.9,.0) (3.3,.0) (3.7,.0) C vs. C.4.7.9 2.2 2.4 2.6 P C oga maket.450.438.43.426.423.420 p C 4.45 4.44 4.43 4.43 4.42 4.42 p C e 4.45 4.39 4.35 4.32 4.3 4.29 Based o the umeca study, we make the foowg obsevatos:. C vs. C s the dusty equbum. 2. Both oe ad stoe pces decease wth c. Oe pces decease due to the ceased tota poteta maket, ad stoe pces foow ths decease, abet at a owe ate, sce the two makets (tadtoa ad oe) compete fo cosume demad. 3. As the addtoa Iteet maket each ceases, both fms pofts cease at the C vs. C equbum stuctue. Howeve, each fm s poft fom the oga maket (of sze ) deceases. That s, as the ew maket becomes age, fms ae wg to ose some poft the od maket to cease the tota poft. 6. Cocudg emaks I the pe-iteet ea, sge chae was a that compaes eeded to deve poducts o sevces to the customes. Today, espodg to chages the maketpace, compaes have copoated the Iteet as a meas to attact customes that fd t coveet to shop fom the homes o othe paces. I fve yeas tme, says Ite s chama Ady Gove, a compaes w be Iteet compaes, o they wo t be compaes at a. 6 Despte ths optmstc poecto fo e-commece s futue, t s had to pedct ts mpact o the esutg dusty maket stuctue. Ths pape buds a mode to expoe ths ssue. We cosde two sepaate demad modes, oe whch cosumes vauato fo the poduct s hgh eough (o the pce sestvty fo the poduct s ow eough) so that a make a puchase, ad aothe 6 Ecoomst Suvey: Busess ad the Iteet, the Net Impeatve, The Ecoomst, Jue 26, 999.

Autho's pesoa copy 686 F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 oe whch some customes may choose a outsde ateatve. Fo both demad modes, we deve equbum pces, quattes ad pofts whe each fm has a fxed chae stuctue (B o C). The two modes ead to the same dusty equbum outcome, but wth oe mpotat dstcto: a settg wthout a outsde opto, the Iteet does ot bg addtoa vaue to fms. We suggest that, such settgs, the adopto of e-commece opeatos by tadtoa etaes ases fom stategc ecessty. Eve f fms do ot beeft fom the adopto of oe saes, cosumes do. The fdgs ths settg ae sma to those obseved the bakg dusty wth the toducto of ATMs (see Humphey, 994). Ideed, ATMs have heped educe tasacto costs by eay 5% ove the past yeas. At the same tme, tasacto voumes moe tha doubed ad the beefts a wet to cosumes. Athough ATMs do ot add sgfcat vaue to baks, they have become a stategc ecessty the bakg secto. I cotast, settgs wth a outsde opto, we show that a fms stcty beeft, equbum, by estabshg oe opeatos. We fay expoe staces whee some (o a) fms caot effcety opeate the ow Iteet chae, but stead may ag wth pue e-taes to each the oe maket. I such settgs, we show that a psoe demma-type equbum may ase. 7 The Iteet s st ts eay stages of deveopmet ad the expeeces compaes have had thus fa wth t ae mted. Theefoe, addto to may of the essos eaed fom pactce, the sghts povded by ou theoetca mode cotbute to the attempt to ga a ceae pctue of ths evouto. Ackowedgemets Ths wok was peseted at the 2005 Suppy Cha Magemet Wokshop at the Uvesty of Foda, Gaesve ad INFORMS Sa Facsco, 2005. It was aso peseted at the eseach cooqua at the Smea Coege of Busess of Pe State Uvesty, the O Schoo of Busess of Washgto Uvesty at St Lous, ad the Fuqua Schoo of Busess at Duke Uvesty. We thak the sema patcpats fo hepfu feedback ad costuctve suggestos. The eseach was suppoted pat by Awad No. 7032800 fom the Natoa Natua Scece Foudato of Cha. Fay, we thak the Seo Edto ad two aoymous evewes fo the suggestos that have heped us to mpove the pape. Appedx. Poofs Poof of Poposto 2. Dffeetatg P wth espect to p ad p e, espectvey, we obta op op ¼ q ðp cþ q ð q Þþðp e c e Þ q q e ; op op e ¼ q e ðp e c e Þ q eð q e Þþðp cþ q q e : Settg the above devatves equa to zeo ad sovg the esutg equatos smutaeousy, we vefy that p c = p e c e, educg etae 0 s stategc vaabes to p, =,2,...,k. Sce p c = p e c e, we have that q e = aq ad oq op ¼ q ð ð þ aþq Þ. Rewte etae 0 s poft fucto as P =(p c)( + a)q. The, the poof of exstece ad uqueess of the Nash equbum s sma as Poposto. Theefoe, the equbum pces ca be deved by sovg 7 We have aso vestgated settgs whee, addto to the exstg tadtoa etaes, some pue Iteet fms opeate the maket. I these settgs, we have bee abe to show that the ccks-ad-mota busess stuctue cotues to be the dusty equbum, ad that the tadtoa etaes stcty cease the maket shaes ad pofts by addg oe opeatos. As the settg wth a outsde opto, the dua-chae fms absob pat of the cosumes that pevousy puchased at the pue Iteet fms. That s, pue Iteet payes may stad to ose as tadtoa bcks-ad-mota fms addto Iteet saes to the eta opeatos. (Pease cotact the authos fo detas o the aayss.)

Autho's pesoa copy p c ¼ ð þ aþq ; ¼ ; 2;...; k; ð6þ p e ¼ p þ c e c; ¼ ; 2;...; k; p c ¼ ; q ¼ k þ ; k þ 2;...; : ð7þ We vefy that p CB s ae equa fo =,2,...,k. Fo ay two C etaes ad 0, we have fom (6) p c ð þ aþq0 ¼ : ð8þ p 0 c ð þ aþq Suppose that p > p 0. The, the eft-had sde of (8) s geate tha, whe ts ght-had sde s ess tha sce q < q 0, a cotadcto. Smay, we ca vefy that p CB s ae equa fo = k +,k +2,...,. h Poof of Poposto 3. Because fom Poposto 2, p CB ¼¼p CB k ad p CB kþ ¼¼pCB ad cosequety q CB ¼¼q CB k ad q CB kþ ¼¼qCB, we show the esuts fo = ad =. Subtactg (7) fom (6), we have 2 3 p p ¼ 4 k þð kþ exp p p 2 4. kð þ aþ exp 5 ð þ aþ exp ðbþv ðbþv exp p p 3 5 þð kþ : ð9þ Let x ¼ p p, z ¼ð þ aþ expððbþvþ >, f (x) =x, ad f 2 ðx; kþ ¼ : k þð kþ exp ðþ=z x kz= exp ðþþð x kþ Note that sce f (x) s a ceasg fucto, f 2 (x,k) s deceasg wth f 2 (0, k) > 0 (sce z > ), ad f 2 (z,k)=0,f (x) ad f 2 (x,k) oy coss oce at a pot 0 < x CB <z. The pcb pcb ¼ x CB ad z/exp(x CB )>, whch mpes that ðb Þv ð þ aþ exp exp pcb p CB > : ð0þ Thus, q CB ¼. > kð þ aþþð kþ exp pcb pcb exp ð þ aþ ; q CB ¼ kð þ aþ exp.exp pcb ðbþv Futhemoe, p CB ¼ þ c > ð þ aþq CB p CB ¼ þ c < q CB þ c; P CB ¼ðp CB cþð þ aþq CB ¼ P CB ¼ðp CB F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 687 cþq CB ¼ q CB pcb þ c; ð þ aþq CB q CB < : ðbþv < þð kþ : ð þ aþq CB > ;

Autho's pesoa copy 688 F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 Poof of Poposto 4. Cosde the fucto f 2 (x,k) defed the poof of Poposto 3. It ca be easy vefed that f 2 (x,k) >f 2 (x,k + ) fo a 0 6 x <z ad f 2 ( z,k)=f 2 (z,k + ) = 0. Ths mpes that x CB (k)>x CB (k + ) (as the poof of Poposto 3, x CB () s the uque oot of f 2 (x,) x). Cosde ow q ðx; Þ ¼z= expðxþþðþ, as the poof of Poposto 3, fo 0 < x <z ad = k +2,...,. The, t s easy to vefy that q (x, +)<q (x,). Sce q (x,) s ceasg x, we the have that q CB ðk þ Þ ¼ ðk þ Þz= expðx CB ðk þ ÞÞþð k Þ < kz= expðx CB ðkþþ þ ð kþ ¼ qcb ðkþ: Theefoe, fo = k +2,...,, P ðk þ Þ ¼ q CB ðk þ Þ qcb ðk þ Þ < P ðkþ: Fo =,...,k, we have that f 2 ðx CB ðkþ; kþ ¼ ð þ aþq CB ðkþ q CB ðkþ ¼ xcb ðkþ fo ay k +26 6. The, ð þ aþq CB ðk þ Þ ¼ xcb ðk þ Þþ q CB ðk þ Þ < xcb ðkþþ q CB ðkþ ¼ ð þ aþq CB ðkþ ; whch mpes that P ðk þ Þ ¼ ð þ ð þ aþq CB aþqcb ðk þ Þ < P ðkþ: ðk þ Þ Poof of Poposto 5. Fx ay etae. The poof fo p C c ¼ p C e c e s as Poposto 2. Gve the eatoshp betwee p ad p e, etae 0 s two decso vaabes educe to oe, amey p. Substtutg p e ¼ p C c þ c e, etae 0 s obectve s to maxmze P =(p c)( + a)q, whee a s defed (2). Sma to the poof of Poposto, thee s a uque Nash equbum gve by p C ¼ þ c ad p C e ¼ þ c e. I addto, P C ¼. h Poof of Theoem. The stuctue wth a B-etaes s ot a equbum, sce ay oe fm has a cetve to devate to the C stuctue as P CB ðþ > ¼ PB. Smay, a maket wth k C-etaes ad k B- etaes, ay B-etae has a cetve to devate to the C stuctue. Fay, a settg wth oy C-etaes, o etae has cetve to devate to the B stuctue. h Poof of Poposto 8. Rewtg the choce pobabtes as exp bvp q ¼ kð þ aþ exp bvp þð kþ exp vp þ exp v 0 ; exp vp q ¼ kð þ aþ exp bvp þð kþ exp vp ad subtactg (7) fom (6), we ca aga vefy (see the poof of Poposto 3) that 0 < pcb p CB < ð þ aþ exp ðb Þv þ exp v 0 ; : ðþ Suppose that p CB > p B. The, fom the secod equaty (), we have that 0 ¼@. q CB kð þ aþ exp ðbþv exp p CBp CB þð kþþexp v 0 exp 0 < @ A ¼ þ exp v 0 exp vp B q B vp CB A

Autho's pesoa copy F. Beste et a. / Euopea Joua of Opeatoa Reseach 87 (2008) 67 690 689 > p B.F- eadg to a cotadcto, fom (7) ad (4). Theefoe, p CB ay, t foows fom (6) ad (7) that P CB > P B ad P CB Poof of Poposto 0. Defe g ðpþ ¼ pc, 0 g 2 ðpþ ¼@ þ exp v 0 =ð þ aþ exp bv p A < p B hods. Smay, we ca pove p CB > P B. h ad g 3 ðpþ ¼ þ exp v 0 v = exp p! : Note that p C s the uque tesecto of g ad g 2, whe p B s the uque tesecto pot of g ad g 3.Its easy to vefy that g 2 (p)>g 3 (p) fo a p, mpyg that p C > p B. Pats () ad () the foow fom (5). h Poof of Poposto. Fst ote that q C D ¼ q qb ¼ C q B q ¼ p C q B : C q B We fst exame how g 2 (p) chages fo a gve p whe b ceases. Sce o ð þ aþ exp bv p ¼ hv ob a exp bv p þ v exp bv p > 0; g 2 (p) ceases b. Theefoe, whe b ceases, DP ceases. Smay, as h ceases, a (as defed by (2)) ceases ad so does g 2 (p). Theefoe, DP aso ceases. Fay, as c e deceases, a ceases ad so does DP. h Refeeces Adeso, S., de Pama, A., Thsse, J., 992. Dscete Choce Theoy of Poduct Dffeetato. The MIT Pess, Cambdge, Massachusetts. Bakos, Y., 997. Reducg buye seach costs: Impcatos fo eectoc maketpaces. Maagemet Scece 43 (2), 676 692. Baaksha, A., Sudaesa, S., Zhag, B., 2004. Reta-Oe Competto Ude Vaue Ucetaty. Wokg Pape. Uvesty of Texas at Aust. Baasubamaa, S., 998. Ma vesus ma: A stategc aayss of competto betwee dect maketes ad covetoa etaes. Maketg Scece 7 (3), 8 95. Be, D., Wag, Y., Padmaabha, V., 2002. A Expaato fo Pata Fowad Itegato: Why Maufactues Become Maketes. Wokg Pape. Uvesty of Pesyvaa. Beste, F., Sog, J.-S., Zheg, X., 2004. Fee Rdg a Mut-Chae Suppy Cha. Wokg Pape. Duke Uvesty. Beste, F., Fedegue, A., 2003. Pcg ad epeshmet stateges a dstbuto system wth competg etaes. Opeatos Reseach 5 (3), 409 426. Beste, F., Fedegue, A., 2005. Decetazed suppy chas wth competg etaes ude demad ucetaty. Maagemet Scece 5 (), 8 29. Catta, K., Gad, W., Swamatha, J., 2003. Addg a Dect Chae? How Autoomy of the Dect Chae Affects Pces ad Pofts. Wokg Pape. Uvesty of Noth Caoa at Chape H. Catta, K., Gad, W., Swamatha, J., 2004. Coodatg tadtoa ad teet suppy chas. Suppy cha aayss the e- busess ea. I: Smch-Lev, D., Wu, D., She, M. (Eds.). Kuwe Academc Pubshes. Catta, K., Gad, W., Heese, H.S., Swamatha, J., fothcomg. Bog fogs: Pcg stateges fo a maufactue addg a dect chae that competes wth the tadtoa chae. Poducto ad Opeatos Maagemet. Chag, W., Chhaed, D., Hess, J., 2003. Dect maketg, dect pofts: A stategc aayss of dua-chae suppy-cha desg. Maagemet Scece 29 (), 20. Dewa, R., Jg, B., Sedma, A., 2003. Poduct customzato ad pce competto o the teet. Maagemet Scece 49 (8), 055 070. Dueh, C., Poteus, E., 2005. Oe vesus Offe Pce Competto: Maket Outcomes ad the Effect of Iteet Shoppg Peetato. Wokg Pape. Uvesty of Mayad. Ese, A., Kupema, J., Deehy, R., Doy, J., 2003. Toys-R-Us(A) the oe toy busess & Toys-R-Us (B) foms a oe aace. The Joua of Behavoa ad Apped Maagemet 4 (), 59 70. Gacao, L., Kapa, S., 200. The effects of busess-to busess e-commece o tasacto costs. The Joua of Idusta Ecoomcs XLIX (4), 463 485.