Joint Opaque booking systems for online travel agencies


 Julian Boyd
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1 Jont Opque bookng systems for onlne trvel gences Mlgorzt OGOOWSKA nd Domnque TORRE Mrch 2010 Abstrct Ths pper nlyzes the propertes of the dvnced Opque bookng systems used by the onlne trvel gences n conjuncton wth ther trdtonl trnsprent bookng system. In secton 2 we present n updted lterture revew. Ths revew underlnes the nterest nd the specfctes of Opque goods n the Toursm Industry. It lso chrcterzes propertes of the meyourownprce (YOP) chnnel ntroduced by Prcelne nd offerng probblstc goods to potentl trvelers. In the secton 3 of the pper we present theoretcl model, n whch we wonder wht knd of Opque system cn be mplemented by gven onlne monopoly. We compre the Opque Hotwre system, YOP system wthout ny possblty of rebddng nd the jont mplementton of these two systems. We fnd tht the YOP system nd the jont mplementton cn hve chllengng propertes f consumer s nformton s complete. Then, n secton 4, we nlyze the cse of ncomplete nformton. We develop n pproprte settng to ntegrte the lck of complete nformton of potentl pssengers on ther reltve propensty to py. We nlyze three cses correspondng to dfferent levels of uncertnty nd number of tckets vlble. We fnd tht n some relevnt cses (verge number of tckets, moderte uncertnty), the jont mplementton of 2 dfferent Opque bookng systems s dvntgeous for the Onlne trvel Agences (OTAs)nd rlnes. Ths result csts doubt on the current OTAs strteges. JEL Clssfcton: D49, L93 Keywords: Opque Sellng, meyourownprce, Economcs of Toursm, Onlne Trvel Agences, Probblstc Goods. 1 Introducton In ths pper we nlyze the dvnced Opque bookng systems used by onlne trvel gences n conjuncton wth ther trdtonl trnsprent bookng system. Ths type of prcng system hs been ntroduced snce mny yers by onlne trvel gences n the Unversty of ce SophAntpols  GREDEG (DEMOS)  CRS, 250 rue Albert Ensten, Vlbonne, Frnce. Eml: 1
2 USA. They offer the consumers prce dvntge, s counterprt of opcty nd uncertnty. Conversely, they provde the compnes nd ntermedres good wy to mnge dynmclly the fluctutons of demnd functon when supply s rgd n the short term. These new systems hve lredy nterested few speclsts. On the one hnd some ppers focus on prcng system s nture nd ther propertes, nd on the other hnd  other ones nterested n the rectons of demnd to ths prcng nnovton. Wht re the dvntges of usng such prcng system for supplers (crrers, rlnes nd toursm servces provders), ntermedres (GDS, trvel gences) nd consumers? Wht sort of competton or segmentton do they nvolve on the toursm servces mrkets? Does the nture of toursm products chnge becuse of these new prcng systems reducng the vlble nformton? These ponts hve been rsed for ech vrnt of these new Opque system. We present brefly the results of these works nd the methodology tht they hve dopted. Then, we consder n mportnt ssue stll not elucdted: snce mny vrnts of Opque systems exst, s there n dvntge to use smultneously more thn one dstrbuton chnnel? The lterture revew s presented n secton 2. It underlnes Opque product specfctes nd dvntges for Toursm Industry. It lso chrcterzes propertes of the YOP chnnel ntroduced by Prcelne nd offerng probblstc goods to potentl trvelers. In secton 3, we present theoretcl model, n whch we wonder wht knd of Opque system cn be mplemented by gven onlne monopoly. We compre n Opque postedprce Hotwre system, YOP system wthout ny possblty of rebddng nd the jont mplementton of these two systems. We fnd tht when nformton s mperfect (the trvelers do not know the nture nd the number of tckets vlble) but complete (the Opque system s potentl clents know ther number nd ther respectve propensty to py), t s equvlent to mplement the most effcent system (the YOP system) or both of the systems n prllel. We ntroduce n secton 4 n ssumpton of ncomplete nformton (the trvelers know ther number but not ther reltve propensty to py). In ths cse, we fnd tht, under moderte uncertnty, the jont mplementton of two bookng systems domntes the mplementton of the YOP chnnel only. 2 YOP nd Opque products: lterture revew In the lst yers, the emergence of the Internet hs deeply chnged the ndustry of toursm, the orgnzton of mrkets nd the prcng mechnsms developed by frms. Toursm s by fr the most developed nd nnovtve onlne busness, fostered by the creton of onlne trvel gences (OTAs) of dfferent knds nd sophstcted prcng nd segmentton strteges. Domnnt globl OTAs hve emerged, Exped, Trvelocty, Orbtz, Opodo, whch domnte the dstrbuton of trvel nd toursm servces, but the extensve uses of the Internet hve gven rse to nche plyers. Most of these plyers hve speclzed n specfc segment of the mrket, n terms of destnton or servces, but some others hve been more nventve, expermentng nnovtve prcng models. Hotwre.com (cqured by Exped n 2003) nd Prcelne.com re the two most mportnt compnes hvng successfully developed ths strtegy on the US mrket, to ccount for 6.7% of worldwde onlne hotel bookngs n 2006 for nstnce. They hve developed 2
3 onlne prcng mechnsms such smeyourownprce n whch nsted of postng prce, the seller wts for n offer of the potentl buyer tht he cn then ether ccept or reject, or such s Opque offers, n whch the chrcterstcs of the servces re hdden (hotel or rlnes brnds, trvel schedule). These emprcl developments open mny dfferent questons. Why would hotels nd rlne compnes be wllng to sell ther products through Prcelne/Hotwre nd lose the dvntge (nd pro?t) tht product dfferentton gves them (Shpro nd Sh, 2008)? Why frms would devte from the stndrd prctces of postng tketorlevet offer? Certnly frms should fnd these strteges more proftble. But s ponted out by Pnker et l. (2003), nd underlned n Wlson nd Zhng (2008), though onlne uctons re multbllon dollr nnul ctvty, wth growng vrety of sophstcted trdng mechnsms, scentfc reserch on them s t n erly stge. evertheless, some nterestng dvnces cn be trced n the recent lterture, relted to the nnovtve strteges mplemented by Prcelne or Hotwre. Ths short revew focuses on the two mn types of relted lterture whch hve been developed. The frst one nlyses meyourownprce sellng mechnsm, whle the second focuses on the Opque sellng wth posted prces. 2.1 meyourownprce sellng mechnsm Wlson nd Zhng (2008) present model of YOP ntermedry, who sells economy cr rentls on specfc dte. The retler cpcty s n excess. He provdes consumers wth functon tht descrbes the chnce of bd to get ccepted. Intermedry clents re lmted to sngle bd. The retler objectve s to force the consumers to bd mxmum tht wll mxmze hs profts, whle consumers ntend to mxmze ther own surpluses. Consequently, the ntermedry wll choose n pproprte functon of bd s probblty of success so s hs clents wll bd mxmum. Snce he provdes ths functon, whch s the sme for ll consumers, ech of them s treted frly, even f the prces they py re dfferent. Usng dfferent method (expermentl economcs), Shpro nd Zllnte (2007) nlyze seller profts mxmzton. They emphsze tht ther mportnce s result of trdeoff between the number of bds ccepted nd ther mounts, whch depends on the threshold prce nd on the presence of opcty. They outlne tht concelng some of good nformton s detrmentl for consumers nd does not chnge nythng for the seller, unless the threshold prce s too low. In such cse hs profts wll decrese. On the opposte, Wng, GlOr nd Chtterjee (2005) show tht moderte opcty level cn be proftble for the retler. Indeed, t helps to segment the demnd nd though to prce dscrmnte the consumers. It wll ttrct some supplementry clents wthout cretng cnnblston effects of the postedprce chnnel. The pper consders monopoly servce provder dstrbutng fxed cpcty through ts own web ste usng postedprce mechnsm nd through YOP ntermedry durng two stge gme. He fces n uncertn nd heterogeneous demnd. He perceves sgnl of the stte of the demnd fter the frst stge of the gme. On one hnd, f the sgnl s perfectly or hghly nformtve, the uncertnty lmost dsppers. Then, the mrket segmentton s only fesble nd proftble wth suffcently low or hgh cpcty. On the other hnd, f the sgnl provdes no nformton bout the demnd nd f cpcty s hgh, the servce provder wll use only the postedprce chnnel; otherwse, he wll use only the YOP chnnel. The optml precson of demnd sgnl s n ntermedte vlue, wht mens 3
4 tht some uncertnty remns. Hnn nd Terwesch (2003) dentfy double source of profts for the YOP retler: ntermedry mrgn, whch s defned s dfference between the prce pd for the product to servce provder nd the threshold prce, nd the nformtonl mrgn, whch corresponds to the dfference between the prce pd by consumer nd the threshold prce. The customers re heterogeneous n ther experence nd though n the level of frctonl nd trnscton costs tht they fford. Ths heterogenety leds to mrket segmentton tht llows the retler to prce dscrmnte hs clents nd mprove ts profts. Fy (2008) lso demonstrtes tht frctonl costs hve n nfluence on mrket segmentton nd on seller profts. Becuse of mrket segmentton, prce competton on the mrket s reduced. The duopoly model developed n the pper 1 emphszes tht mplementton of YOP chnnel wll reduce the competton nd mprove overll profts n comprson to the stuton when both retlers choose postedprce mrket formt. The model stresses tht f one of compettors chooses YOP formt, whle hs rvl selects postedprce mrket, he should restrct ts customers to only one bd. Becuse repeted bddng ncreses consumer s nterest for YOP sellng, t cuses loss of postedprce seller profts, who, n order to ttrct some consumers, decreses hs prce, wht derves the bd s mounts down. In contrst, Spnn, Sker nd Schäfers (2004) show tht llowng consumers to repet ther bds my mprove seller profts, becuse the possblty of rebddng leds to hgher mounts of mxmum bds. Another type of consumer s heterogenety s presented by Fy (2004). Some consumers, clled sophstcted mnge to bypss the restrcton of sngle bd nd the others  do not. Ths cretes new segmentton of demnds. The pper compres three stutons: sngle bd, repet bddng nd prtlrepet bddng. The model demonstrtes tht ntermedry profts re exctly the sme f the restrcton of sngle bd s kept up or f t s not mposed. On the opposte, prtlrepet bddng deterortes retler profts, but ths relton s not monotonc. On one hnd, f the number of sophstcted consumers s very low, frm s profts wll reduce s ther number ncreses. On the other hnd, f ther percentge s very mportnt, profts wll ncrese wth ther number. Therefore, ths pper gves the gudelnes how to well mplement YOP strtegy n order to better segment the demnd nd thus reduce prce competton. Terwesch, Svn nd Hnn (2005) present demnd segmentton bsed on dfferences n hgglng costs occurred by consumers. Retler cn prce dscrmnte hs clents, becuse of ths dfferentl. They provde model of n onlne hgglng process t YOP seller web ste wth no opcty, constnt threshold prce nd possblty of rebddng. Retler cn mnpulte consumer s hgglng cost by complctng hs webste nterfce or by modfyng the tme dely wth whch the customer s notfed tht hs bd ws rejected, n order to dmnsh cnnblston effect of hgglng. Thus, seller profts ncrese when consumers re suffcently heterogeneous nd f there s postve correlton between ther vlutons nd hgglng costs. Fy nd Lrn (2008) dd n orgnl de to the lterture on YOP mechnsm. 1 It s the only exstng pper consderng the cse of competton nd YOP sellng. 4
5 They nlyze the stuton, where the threshold prce vres under repet bddng. Every consumer s bd rejecton provdes hm wth new nformton. If he expects tht the threshold prce s constnt, hs bddng pttern s monotonclly ncresng. However, f he suppose tht the threshold prce wll vry, hs bddng behvor wll depend on the degree of expected vrblty nd on hs ptence. The pper s mn mplcton s tht chngng threshold prce my ttrct nd retn more customers. Spnn, Bnhrdt, Häubl nd Sker (2005) compre the YOP formt wth Select YourPrce (SYP) mechnsm, where consumers re nfluenced by the rnge of possble cnddte bds. Provdng lst of possble bds my be perceved s formt gvng more nformton bout the seller threshold prce nd thus decreses customer s uncertnty bout product s vlue. The medn nd men bds re the lowest n the YOP formt, so t s domnted by the SYP one. As the threshold prce ncreses, seller profts rse monotonclly. They re t ther mxmum, when the threshold prce s equl to vrble cost. However, when the cnddte bds re hgh, the profts depend on the trdeoff between the ncrese n bd s mounts nd the reducton n the number of plced bds. 2.2 Opque Products The second type of lterture nlyses nother type of Opque sellng, where prces re posted. These ppers focus on the fct tht some of the product s ttrbutes or chrcterstcs re conceled from the consumers. In the trdtonl chnnels t ws lredy not lwys benefcl to fully nform consumers bout mrket prces, becuse of the rsk of ncrese of ther prce senstvty nd then  of creton of downwrd prce pressures. In tht cse t s benefcl for servce provders to mplement multchnnel dstrbuton cross the mechnsms wth dfferent levels of mrket trnsprency. Grndos, Gupt nd Kuffmn (2008) present model of suppler, who dstrbutes hs product over two onlne chnnels, dfferentted by the levels of mrket trnsprency, chrcterzed by the sme mrgnl dstrbuton costs. They provde mechnsms for suppler to set optmlly the prces nd to nfluence trnsprency n order to successfully prce dscrmnte hs clents. Frst, they estmte demnd functon of the product, then dentfy the dfferences n the demnd functons cross the two onlne sellng mechnsms nd fnlly, set the optml prces bsed on those dfferences. Emprcl nlyss presented n the pper confrms the model s results nd provdes n ddtonl outcome, whch sttes tht suppler n order to ncrese ts revenues cn ncrese the prce dfferentl cross the sellng mechnsms. Y. Jng (2007) models monopoly who dstrbutes toursm devces (rlne tckets, hotel rooms) on two types of mrkets: fullnformtonl nd Opque, nd wonders re the consequences of the use of the Opque chnnel on frm s profts nd the globl welfre. He defnes lso the condtons of successful mplementton of prce dscrmnton. The frm s profts s well s the overll welfre re greter whle servng only the fullnformtonl mrket. Thngs get more complcted when the frm decdes to serve both of the mrkets. The frm s strtegy wll depend on the degree of homogenety of demnd. If the demnd s too homogeneous or too heterogeneous, the monopoly wll choose to serve only the fullnformtonl mrket, becuse of the rsk of cnnblston 5
6 effect. When the demnd s heterogeneous enough, the two types of mrket wll coexst. The dulmrket strtegy wll mprove frm s profts, by reducng the unsold nventory nd socl welfre, by servng some extremely prce senstve consumers, who would not trvel otherwse. Ths result s confrmed by Sh nd Shpro (2008), who wonder why the servce provders decde to sell ther products through Opque stes nd though lose the dvntges gven by product dfferentton; for the consumers Opque products re ndstngushble nd become perfect substtutes. Frst of ll, sellng through the Opque chnnel helps the servce provders to respond to chnges n demnd wthout the need to chnge current brndng nd prcng polces. In the model the Opque trvel gency ct s colluson devce whch fclttes prce dscrmnton between dfferent types of consumers nd ncreses overll profts, even f the totl mrket demnd s perfectly nelstc. The model s vrton of Hotellng s (1929) nd Slop s (1979) models. The pper s mn result s tht for certn rnge of prmeters vlues dstrbuton through n Opque gency enbles hotels to dscrmnte ther customers. Wthout the Opque gency the hotels would compete for both hgh nd low type consumers on the non Opque chnnel. The presence of lowtype consumers ntensfes the competton nd drves down the equlbrum prce nd profts. When the Opque chnnel s ntroduced new equlbrum rses, derved from the Bertrnd competton model. In the new equlbrum, hotel s competton for the lowtype consumers ncreses, but decreses for the hghtype ones. It stll remns Hotellng competton, but the hotels do no longer compete for the lowtype segment. If there re enough hghtype consumers, the overll profts wll ncrese. The ntensfed competton for the lowtype consumers enbles hotels to decrese the competton for the hgh type ones. Another pper, nlyzng the cse of competton, s the Fy s (2007) one. He models duopoly competton wth multple servce provders who use common ntermedry. The pper ntroduces brnd loylty 2. If there s lttle brnd loylty n the mrket, the ntroducton of Opque sles wll rse prce competton nd lower ndustry profts. If there s suffcent brnd loylty, the Opque sles wll reduce prce competton nd rse the ndustry profts. The degree of prce competton wll depend on the number of unts llocted to the Opque chnnel. Servce provders hve n ncentve to contrct wth the Opque ntermedry, f there s enough brndloylty n the ndustry. One of the model s hypotheses s tht the frms hve no constrnts, so the Opque chnnel wll led to mrket expnson. Opque products cn be seen s probblstc goods, s emphszed by Fy nd Xe (2007). They defne probblstc good s gmble nvolvng probblty of gettng ny one of set of multple dstnct tems. Accordngly, we spek bout probblstc sellng, when seller cretes probblstc good usng exstng dstnct products or servces (clled component goods), whch he offers s ddtonl purchse possblty. Consequently, mplementton of probblstc sellng helps the retler to segment the mrket by cretng new dfferent type of consumer s uncertnty. Thus, the retler mplements prce dscrmnton tht cn consderbly ncrese hs profts f mrgnl costs re suffcently low. When there s n dvntge from ntroducng probblstc good, t s generlly optml to ssgn n equl probblty to ech component products, even f the demnd s symmetrc. On the opposte cnnblston effects my pper. Moreover, 2 Ide developed lso n Fy(2008) concernng the YOP chnnel. 6
7 probblstc sellng s most dvntgeous when the component goods hve moderte dfferences. An mportnt dvntge of probblstc sellng concerns seller own demnd uncertnty. It provdes buffer gnst ts negtve effects nd ts proft dvntges re even greter wth demnd uncertnty. Indeed, ntroducton of probblstc good reduces or even elmntes the dependence of prcng decsons on the dentty of the more populr product. The most optml results were obtned wth suffcently hgh demnd uncertnty nd mdrnge cpcty level. 3 The dversfcton of Opque Chnnels wth complete nformton In ths pper we tend to nswer one mn queston: s t sutble nd effcent for gven onlne gency to use smultneously more thn one lterntve Opque chnnels? The nswer s complex nd depends on mny crcumstnces, nd mnly on the compettve envronment. If we consder compettve gme, n whch every compettor chooses one sngle chnnel, the equlbrum could be n symmetrc equlbrum where ech ntermedry speclzes nd dstrbutes on specfc chnnel. If Agences A, B nd C compete t the lterntve chnnels: posted  prce Opque Chnnel, Lst Mnute chnnel nd YOP chnnel, ech one should speclze n dfferent type of sellng. If there s only one Agency n stuton of monopoly nd tht the pont s to fnd the best llocton of potentl trvelers on lterntve chnnels, the best soluton would be, theoretclly, the frst degree prce dscrmnton. As n mny other cses, ths strtegy s probbly not fully mplementble due to ts complexty. The YOP Opque soluton (the Prcelne system ) seems however to be the closest one. Supposng tht the populton of trvelers s rsk neutrl, fully nformed bout the chrcterstcs of remnng tckets on lterntve chnnels (compny, hour of deprture... ) nd knows lso perfectly the dstrbuton of the propenstes to py of the others potentl trvelers, ech consumer wll be ble to bd (or not) prce correspondng to hs reservton prce, gven the uncertnty on the number of sets nd on ther ttrbutes. However, ths result vldty depends on the level of ncompleteness of potentl trveler nformtons. Suppose for nstnce tht potentl trvelers wth hgh propensty to py re lso less nformed on tcket s dstrbuton nd on the propensty to py of other gents: they wll probbly overestmte the utlty they cn derve from the YOP chnnel nd bd lower prce thn they would, f the nformton ws complete. In ths cse, mplementton of Lst mnute chnnel would be better strtegy. However, ths soluton hs n nconvenent: t does not resst to tme deprecton. If trvelers wnt to book hotel rooms, to rent cr..., more generlly f the rlne tcket s n element mong others of pckged product provdng them n overll utlty, the Lst mnute soluton wll shrply decrese ther utlty. In ths pper we consder Lst mnute sellng s complementry chnnel to the Opque one. It s qute complcted to decde f two or more forms of Opque chnnels cn coexst. Consder for nstnce the YOP Prcelne chnnel nd the Opque Hotwre one. Both of these chnnels re Opque,.e. do not provde precsely the trvelers wth the certnty 7
8 on the qulty of the trvel. Once more, f ll pssengers hd complete nformton on the flght s frequency nd the other tcket s ttrbutes nd f they knew precsely the dstrbuton of the other s consumer s propenstes to py, ll of them would be ble to choose to use the YOP system only, nd leve the Opque chnnel, whch could be redundnt. In the followng subsecton we wll try to confrm ths ntuton. 3.1 The model We suppose tht everydy there re 2 flghts from cty 1 to cty 2: the frst leves cty 1 t 7:00 m nd the other t 6:00 pm. These flghts bookng level on the trdtonl chnnel s ordnrly estmted wth smll error only few dys before the dte of deprture. Ths short slot mkes the Lst Mnute soluton npproprte for mptent low prce trvelers. Indeed, t ctully concerns dstnct ptent subpopulton of trvelers, whch we re not gong to consder n ths pper. Subsequently the gency decdes to mplement n dpted Opque chnnel nd to offer to the mptent low rte trvelers n dpted bookng system. The gency knows the dstrbuton of the sttes of the world, whch re defned by tble 1. Sttes of the world umber nd type of Probblty vlble sets 1 m t 7:00 m 1/4 2 m t 6:00 pm 1/4 3 2m t 7:00 m 1/8 4 m t 7:00 m 1/4 m t 6:00 pm 5 2m t 6:00 pm 1/8 Tble 1: Avlble sets for the flghts from cty 1 to cty 2 on gven dte The gency cn mplement ether: () n Opque Hotwre style postedprce system; () YOP Prcelne style system; () both of the systems. The sequence of the ctons s s follows:  At stge 1, the onlne trvel gency (OTA) chooses between (), () nd (). If () or () hs been selected, the gency fxes the prce of the Opque chnnel. If () or () hve been chosen, the trvel gency lunches sngle bd process for the tckets.  At stge 2, f the OTA hs ntlly chosen (), the potentl trvelers decde to buy or not tcket on the Opque chnnel. If the OTA hs chosen (), they choose to post or not sngle bd. If the OTA hs chosen (), they chose to buy tcket on the Opque 8
9 chnnel, or to post bd on the YOP chnnel or to reserve.  At stge 3, the OTA knows the number nd the nture of the vlble sets on ech flght. If () or () hve been chosen t stge 1, the OTA dstrbutes the tckets to the buyers on the Opque chnnel. If () or () hve been chosen, the gency decdes the threshold prce for the YOP chnnel nd sells the tckets to those whose bds exceed ths prce. Ech successful bder pys the posted rte. The relevnt equlbrum concept s Stckelberg equlbrum, where the trvel gency s leder. The gme s solved by bckwrd nducton. At stge 3, the trvel gency chooses the best cton (.e. fxes the lower lmt prce of the YOP chnnel f the devces () nd () hve been selected), gven the cton prevously tken by the trvelers t stge 2. At stge 2 the potentl trvelers choose ther own best ctons, gven the trvel gency s decsons t tme 1 (the mplemented system nd the Opque chnnel prce f the () or () schemes hve been mplemented), ther expecttons of the trvel gency s decsons t stge 3 nd the level of nformton on the chnce tht ther bds get ccepted, f the nformton on the chrcterstcs of the ucton process, when the devces () or () re mplemented, s mperfect. At stge 1, the trvel gency chooses the pproprte devce nd the rtes of the Opque chnnel f the devces () or () re mplemented. We suppose tht nformton s mperfect but complete (trvelers know the sttes of the world nd ther respectve probblty). 3.2 The optml choces of the gency Let s consder successvely the three knds of solutons for the trvel gency. () If the Opque chnnel s mplemented lone, the gency fxes t stge 1 the prce p O such tht p O mxmzes the jont proft of the rlne nd the trvel gency π(p O ) = mp O. The quntty of vlble sets for the Opque chnnel s m, becuse t s the hgher level of sets vlble t stge 3 n ll sttes of the world. The level of p O s then such tht the gency extrcts the whole surplus of the lst trveler choosng the Opque chnnel. Whtever the rte of the Opque chnnel fxed t stge 1 would be, the potentl trvelers whose net utlty s greter or equl to zero t ths rte wll choose to buy tcket on ths chnnel. The best soluton for the trvel gency s then to chrge rte tht exhusts the lst potentl Opque chnnel trveler s surplus. These trvelers wll be locted on ther respectve segment on ponts 1 such tht ( 1 )/ = m/2n,.e. t 1 = (2n m)/2n. The resultng vlue of p O whch vnshes the net utlty of the gents locted on 1 s then such tht 1 (u+ū/2) p O = 0 snce the sttes of the world nd the dstrbuton of gents on the segments [0, ] s common knowledge. Then we obtn p O = (2n m)(u+ū/2)/2n nd π O = mp O = (2nm m 2 )(u + ū/2)/2n (1) () If the YOP chnnel s the only to be mplemented, t stge 3 nd n ech stte of the world, the trvel gency wll choose the hgher threshold vlue such tht ll the 9
10 potentl trvelers whose bds re greter or equl tht the threshold wll exhust the mrket. As the OTA determnes ths vlue fter observng the stte of the world, there re two possbltes. If only m tckets re vlble, the prce p H wll be hgh: t wll correspond to the reservton prce of the lst of the m hgh propensty to py gents tht ntegrte n ther expected utlty the possblty to py less f 2m sets re vlble. If the number of vlble tcket s 2m, the prce p H wll be lower s t corresponds to the propensty to py of the lst of the 2m trvelers who ntegrte n ther expected utlty the uncertnty. At stge 2, the bdders wll be ble to ntegrte the optml choces of the gency n ther own decson nd, mong other, to consder ther bds gettng ccepted. From usul deductons reltve to the optml bdders behvor, we deduce tht, gven the resultng expected vlue of ther choces, the bdders wll not bd lower prce thn ther reservton prce. If they re ble to understnd correctly the YOP system, they wll clculte the prce tht they wll ctully py s the reservton prce of the lst successful bd n ech stte of the world. In fct, there exst two possble bddng prces: bddng prces greter or equl thn p H tht gurntee the trvel nd bddng prces greter or equl to p L but smller thn p H tht mke the trvel uncertn. Whtever the level of ther bds, f they re greter thn p H or between p L nd p H, the pssengers wll only py p L or p H : ther net expected utlty s then defned by (u + ū/2) p H f they decde to bd t prce p L nd [ ] (u + ū/2) p L /2 f they decde to bd t rte p L. From elementry clculus, we deduce the threshold vlues 2 nd 2 seprtng respectvely on ech segment [0, ] the potentl trvelers choosng to reserve nd the potentl trvelers choosng to bd p L, nd the potentl trvelers choosng to bd p L nd p H. These vlues re 2 = (n m)/n nd 2 = (2n m)/2n. Then we deduce the equlbrum prces p L = (n m)(u + ū/2)/n nd p H = (2n m)(u + ū/2)/2n, the jont proft of the rlne nd of the trvel gency p = mph + mp L /2 or π O/ = mp O + mp /2 = (3nm 2m 2 )(u + ū/2)/2n (2) () If the two chnnels re jontly mplemented, the OTA lloctes the frst set of m sets to the Opque chnnel, where t trgets the hgh propensty to py customers. The second set of m sets s llocted to the YOP chnnel  to the trvelers wth lower propensty to py. At stge 1, the gency chooses the prce for the Opque chnnel nd offers to the trvelers the possblty to bd n the OYP chnnel. As n cse (), the prce of the Opque chnnel s p O = (2n m)(u + ū/2)/2n. The YOP chnnel trgets the next m pssengers nd s ctvted t prce p = (n m)(u + ū/2)/n. The jont proft of the rlne nd the trvel gency s then π O/ = mp O + mp /2 or: π = (2mp H + mp L )/2 = (3nm 2m 2 )(u + ū/2)/2n (3) Subsequently we deduce the followng proposton: Proposton 1. If potentl low rte trvelers re completely nformed on the rndom number nd dstrbuton of vlble sets nd on the propensty to py of every gent, t s equvlent for the rlne nd the gency to mplement YOP chnnel lone nd to relze the jont mplementton of n Opque nd YOP chnnel. Proof : Expressons (1), (2) nd (3) represent the mounts of the jont profts of the rlne nd the trvel gency t Stckelberg equlbrums ssocted respectvely to the 10
11 mplementton of n Opque chnnel, YOP chnnel nd jontly n Opque chnnel nd YOP chnnel. The comprson of (1), (2) nd (3) proves tht, whtever the vlues of the prmeters u, ū,, n, nd m re, π O/ = π > π O In ccordnce wth ntuton, the Opque Hotwre style chnnel s not n optml soluton for potentl trvelers f t s mplemented lone: the trvelers wth hgh propensty to py re ndfferent between ths sellng mechnsm nd ts jont mplementton wth the YOP chnnel, whle the trvelers wth low propensty to py prefer the two other sellng technologes. Another observton s tht, f trvelers re rsk neutrl (s we hve supposed them to be), t s equvlent for hgh propensty trvelers to py p O for the Opque chnnel or to use the YOP chnnel whch theoretclly provdes them wth rndom prce. ote however tht when we ntroduce even lttle rsk verson, the gents wth hgh propensty to py wll prefer to py p O : ths observton cn provde the bckground for the jont mplementton of n Opque nd YOP chnnels whch then could be more effcent thn the YOP chnnel consdered lone. 4 Jont Opque Chnnels wth ncomplete nformton A frst type of ncompleteness s lnked wth the bd knowledge from trvelers of the stochstc dstrbuton of the demnd of tckets from the trdtonl chnnels. The sesonl, dly nd hourly evoluton of trdtonl demnd follows complex lws whch re not esly understood by trvelers. The sttstcl dstrbuton of demnd vrtons durng the perod could nvolve nformton ncompleteness for trvelers or nformtonl symmetres between the OTA nd the trvelers on the one hnd, nd on the other hnd  between the trvelers. It s however dvntgeous for the rlnes to dpt prtly ther supply to these vrtons. Consequently, t s dvntgeous for rlnes nd OTA to dffuse pproprte sttstcs on sets dstrbuton for ech destnton nd for every subperod of tme. Then we suppose tht ths cuse of bd nformton s not the mjor motve of uncertnty nd concentrte on second type of ncompleteness. Indeed, bdders lck relevnt nformton on the other consumers propenstes to py. The number of the potentl trvelers from whch the smple of bdders for gven destnton s extrcted mkes for ech bdder very dffcult to perceve ts reltve propensty to py or the level of ts own propensty to py compred wth the propenstes to py of the other bdders. Ths lck of nformton hs drmtcl consequences: wth nformton completeness, our exmple provdes only two bddng prces when the YOP s mplemented or when the Opque system nd the YOP re jontly mplemented: s we verfed nlytclly, whtever the propensty to py of the trveler s, t wll never be nterestng for hm to bd t prce dfferent from p L or p H. Once trvelers cnnot clculte p L or p H or clculte the sme level from these threshold prces, t could be rtonl for ech of them to offer dfferent prces when the sellng system s the YOP mechnsm or nother bookng system. 11
12 4.1 The generl settng Lets consder the segment where re locted ll potentl trvelers preferrng the 7:00 m (resp. the 6:00 pm) flght to the other one nd ssume tht pssengers do not know precsely ther poston on ths segment. Ths uncertnty mples tht ther estmtons of the other pssengers dstrbuton on the segment nd especlly the dstnce [, ] between ther own locton nd the locton of the gent wth the hghest propensty to py re mprecse. Then, we suppose tht the gent locted on estmtes s ã : ã = q( ) + (1 q), q [0, 1] (4) When q = 0, there s full uncertnty on the poston of nd the trveler loctes hmself on the mddle of the segment [0, ]. When q = 1, the nformton on hs poston s perfect. When q s comprsed strctly between 0 nd 1, the uncertnty on the gent s locton s more or less moderte. We suppose tht the trvel gency knows ths mprecson of the gents on ther reltve propensty to py. ow, lets consder the three vlble possbltes of mplementton of lterntve sellng mechnsms. () If the Opque chnnel s mplemented lone wth prce p O, the trvelers hve ll the nformton on prces whle tkng ther decson t tme 2. Ther behvor s then unchnged. They wll buy tcket f 1 (u + ū/2) p O 0 nd do nothng f 1 (u + ū/2) p O < 0. The result s the sme s n cse of complete nformton,.e., p O = (2n m)(u + ū/2)/2n nd π O = mp O = (2nm m 2 )(u + ū/2)/2n (5) () If the YOP chnnel s mplemented lone, t tme 2 the bdders estmte the probblty of success of ther bd. Gven (4), they stll compre (u + ū/2) p H (ther estmted net utlty f they choose to bd t prce ] p H nd expect beng ble to trvel n ll sttes of the world) nd [ (u + ū/2) p L /2 (ther estmted net utlty f they choose to bd prce hgher then p L, but lower then p H ) nd 0 (ther utlty f they decde to reserve). In ths cse, they re compelled to use ther ndvdul estmtons of 2 nd 2 to evlute p L nd p H. Gven (4), they clculte 2p = (q 2 q + 2 )(n m)/n, 2p = (q 2 q + 2 )(2n m)/2n nd then deduce p L = (q 2 q+2 )(n m)(u+ū/2)/n nd p H = (q 2 q+2 )(u+ū/2)(2n m)/2n s threshold prces (dependng on ther locton when the totl number of sets s respectvely m nd 2m). The hgher s the propensty to py of the trveler locted n, the greter hs expected prces for the YOP chnnel t low nd hgh rtes re. The potentls trvelers locted t on one of the segments [0, ] consder themselves s mrgnl gents between the pssengers choosng reservton nd the gents bddng t low rte f = 2p = (q 2 q+2 )(n m)/n,.e. = q(n m)/[2nq 2mq n+2m]. Agents locted on the sme segment t = 2p = (q 2 q + 2 )(2n m)/2n,.e. = q(2n m)/(4nq 2mq 2n + 2m) consder smlrly themselves s the lmt gents between the low rte bdders nd hgh prce ones. ote tht these thresholds depend on q,.e. on the level of pssengers uncertnty on ther reltve poston on [0, ]. Then t stge 2, potentl pssengers bds depend frst on ther poston on [0, ] nd on the level of uncertnty. At stge 3, three cses re possble ccordng to prmeters vlues nd 12
13 the level of uncertnty: cse 1: 2 cse 2: 2 cse 3: 2p < 2p < 2 < 2 < 2 < 2p < 2 < 2p < 2p < 2p These cses present dfferent propertes nd though need to be nlyzed seprtely. 4.2 Averge number of tckets, reltvely strong uncertnty Lets begn by consderng the 2nd cse, whch s llustrted by Fgure 1. In order to defne t, t s suffcent to compre 2 nd 2p. Despte the number of prmeters nd the dffculty to determne exhustvely the rnges of vrton of n, m nd q correspondng to ths cse, t ppers tht verge number of tckets (m slghtly smller thn n/2) nd qute hgh level of uncertnty (q vlues smller thn 1/2) cn generte such rnkng between 2 nd 2p. P L P H 0 /2 2* 2** 2 p* 2 p** Fgure 1: Cse 2, 2m vlble tckets. From drect observton of fgure (1), we deduce Proposton 2: Proposton 2. In cse of ncomplete nformton, when the threshold reservton utltes re 2 < 2 < 2p < 2p, the jont mplementton of the two systems wll never strongly domnte the sngle mplementton of one of the systems. Proof : Suppose tht the YOP chnnel s domnted by the jont mplementton of the YOP nd the Opque systems. In ths cse, snce the gents locted between 2 nd 2p do not bd when the YOP system s mplemented lone or jontly, only the gents locted between 2 nd re nterested n ths jont mplementton nd wll ll choose the Opque chnnel: consequently, the Opque system mplemented lone s equvlent to the jont mplementton of the two systems. Wth the opposte ssumpton, the YOP system lone domntes the jont mplementton of the two systems, f we consder OTA s profts. In cse 2, the level of nformton ncompleteness s such tht the Opque systems re ll neffcent to cler the mrket. In ths cse, the OTA nd the rlnes should 13
14 develop non Opque lst mnute systems wth trdtonl dynmc prcng, dpted to the lst mnute demnd. Another possblty for the rlnes nd the OTA s to develop nformton systems n order to ncrese q nd though mke the Opque chnnel more effcent. 4.3 Averge number of tckets, moderte uncertnty In cse 1 we suppose tht the number of tckets vlble s smller thn hlf of the number of potentl trvelers (we must remn tht potentl trveler s someone nterested n trvelng t postve rte: t s relstc to suppose tht there re lwys potentl trvelers, especlly durng holdy perods, tht demnd the tckets f the rte decreses suffcently). By moderte uncertnty we men tht 2 s less thn 2p. P L P H 0 /2 2* 2 p* 2** 2 p** Fgure 2: Cse 1, 2m vlble tckets. In ths cse, when the YOP system s ppled, s llustrted n fgure (2), the threshold between the bd of those who expect to trvel n ll sttes of the world nd those who expect to trvel only when there s lrge number of vlble tckets s hgher thn n the cse of perfect nformton. The number of the trvelers ble to trvel n ll condtons s consequently underevluted by themselves. Therefore, the trvelers locted between nd py hgher (nd dfferent) rtes thn n the cse of complete nformton to trvel n ll sttes of the world, whle the trvelers locted between 2 nd 2p py smller (nd lso dfferent) rtes to trvel wth the sme level of certnty. At the sme tme, the trvelers locted between 2p nd 2 py reltve hgh (nd dfferent) rte to trvel only when there re 2m vlble tckets, whle those locted between 2 nd 2p do not bd. When the number of vlble tckets s 2m, the consequence s gn n extrproft for the OTA nd the rlnes on the subset of trvelers locted between 2p nd 2 nd remnder of unsold tckets correspondng to the potentl trvelers between 2 nd 2p 2p 2. When the Opque chnnel s mplemented lone, only the trvelers locted between nd choose to trvel t the unform posted rte 2 When Opque nd YOP systems re mplemented jontly, the trvelers locted between 2 nd stll choose the Opque system whle the trvelers locted between 2p nd 2 stll choose to bd reltvely hgh (nd dfferent) prces to trvel only when there 14.
15 re 2m vlble tckets. The Opque chnnel s then stll domnted by the jont mplementton of the two systems. The relevnt comprson s then between the YOP lone nd the Opque nd YOP systems ppled jontly nd prtculrly, from the OTA s pont of vew, the profts generted by the trvelers locted between 2 nd wth the YOP nd wth the jont mplementton. If the YOP chnnel s mplemented lone, the OTA profts re expressed by (6) wth π = 1/2 π (m) + 1/2 π (2m) (6) m D π H /2 (m) = 2 +2 [ 2p PH k=1 (m m D H )/2 PL k=1 + (k 1)( 2p )/[(m D H /2) 1]] + [ 2 + (k 1)( 2p 2 )/[((m m D H )/2) 1]] nd π (2m) = 2 +2 m D H /2 PH k=1 m D L /2 PL k=1 [ 2p [ 2p + (k 1)( 2p )/(m D H /2) 1] + (k 1)(( 2p 2p ))/(m D L /2) 1] where m D ( 2p ) H = 2n nd m D 2p L = 2n( ), gven the level of uncertnty correspondng to cse (1), re the number of tckets obtned by trvelers ble to bd hgh prces n order to cqure one tcket respectvely n ll sttes of the world nd the number of tckets obtned by trvelers ble to bd hgh prces n order to cqure one tcket f 2m tckets re vlble. If the OTA decdes to mplement jontly both of the chnnels, ts profts re gven by equton (7) 2p π O/ = (2nm m 2 )(u + ū/2)/2n [ P 2p (m D L /2+mD H /2 m/2) + k=1 + (k 1)( 2 2p )/((m D L /2 + (7) md H /2 m/2) 1)] Let s begn by n llustrton of the smllest cse where n = 4 nd m = 2. Then, when there re only 2 tckets vlble, only 1 potentl pssenger from ech subset (or segment) cn trvel wheres 2 from ech subset cn trvel when 4 tckets re vlble. Gven tht q < 1, the pssengers ble to fly when the number of vlble sets s m = 2 overevlute the reservton prce 2 necessry to fly n such condtons nd choose to bd low rte, whle the pssengers ble to fly only when the vlble tckets re 2m = 4 overestmte the reservton prce 2 necessry to fly t low rte nd choose not to bd. The consequence s tht there s only two bdders for the YOP system, both bddng lower thn 2. The recept profts of the OTA re hgher f the Opque system s mplemented jontly, snce n ths cse the two bdders of the YOP system 15
16 choose the Opque system nd py ech one 2. Due to the mnml dmenson of n nd m (the smllest possble), ths exmple s however lmt cse where the jont mplementton nd the mplementton of the Opque system lone provde the sme proft to the OTA. We provde n Appendx 1 nother numercl exmple wth slghtly lrger vlues for m nd n where the jont mplementton strongly domntes the sngle mplementton of the two systems tken sngulrly. We then deduce the followng proposton: Proposton 3. When n, m nd q re such tht 2 < 2p < 2 < 2p, the jont mplementton of the Opque nd the YOP s lwys the best soluton for the OTA. Proof : see Appendx 2. Ths result ndctes tht wth n verge number of potentl pssengers nd level of uncertnty rther moderte, s s dvntgeous for the OTA to propose jontly two (or more... ) Opque bookng systems. 4.4 Lrge number of tckets The cse 3 s represented n fgure (3). It corresponds to lrge number of vlble tckets (qute ll of potentl trvelers cn trvel when 2m tckets re vlble). Ths s not n unrelstc cse. We observe n some perods very low prces on the lst mnute or even the trdtonl chnnel tht ndcte tht few number of potentl pssengers fce lrge supply of sets. The only doubt on the relevnce of ths cse concerns the level of unpredctblty of vlble tckets number. In low seson, low costs compnes tend to offer low prces on the trdtonl chnnel wthout ncresng ndefntely the proporton of Opque supply: ths s probbly the best nswer to rther predctble shortge of demnd. P L P H 0 /2 2 p* 2* 2** 2 p** Fgure 3: Cse 3, 2m vlble tckets. When the cse 3 s relevnt, t cn be consdered s very close to cse 1. As n cse 1, when the OTA consders the opton of offerng the two systems jontly, t evlutes the trdeoff between the hgh rte pssengers (locted between 2p ), tendng to py more when the YOP chnnel s mplemented lone nd the number of those (locted between 2 nd 2p ) who tend to bd t low rte. As n cse 1, the potentl pssengers locted 16
17 between 2p nd < 2 hve the sme choces when the YOP system s mplemented lone or jontly wth the Opque Hotwre system. The only dfference wth cse 1 s tht there exst n these two cses n excess demnd: ndeed one prt of low rte bdders choose to bd prce lower thn 2 nd more or less lrge prt of them cnnot trvel, even when 2m vlble tckets remn. Proposton 4. When n, m nd q re such tht 2p < 2 < 2 < 2p, the jont mplementton of the Opque nd the YOP s lwys the best soluton for the OTA. Proof : see Appendx 3. 5 Comments nd conclusons After the lterture revew nlyzng the propertes of the Opque bookng systems used by the onlne trvel gences, ths pper consders the possblty of jont mplementton of two dfferent Opque systems by the sme trvel gency. We cll the Opque system, the one developed by Hotwre.com nd the meyourownprce system, the one mplemented by Prcelne.com. We buld 3 stge gme model descrbng the optml choces of trvel gency fcng populton of potentl trvelers wth dfferentted reservton prces. We frst develop the gme wth mperfect but complete nformton of potentl pssengers (they do not know how mny sets wll be vlble but know the reservton prces of the other pssengers). In ths cse (whch s stll the only consdered by the lterture) the jont mplementton of the YOP nd Opque system hs no dvntges over the sngle mplementton of the YOP system. We then extend the model to the cse of ncomplete nformton (ech potentl pssenger gnore the reservton utlty of the others). We decompose ths cse n 3 subcses nd prove tht n 2 of them, jont mplementton domntes the other strteges. An extenson of our nlyss wll consder the welfre ssues ssocted to the ncomplete nformton cse. Another extenson could be to develop the cse of duopoly s n exmple of competton. Indeed, n the etoursm mrkets, gret number of OTAs compete nd coexst, mplementng dfferent dstrbuton strteges. More precsely, two OTAs compete n the Opque segment, dsplyng dfferent sellng pproches. We could t lst evlute the possblty of threshold prce vrblty ccordng to the number of tckets vlble nd consumer s rrvls on the mrket. In fct, t s dffcult to pretend tht Prcelne fxes the threshold prce only once t the begnnng of the sellng perod nd mntns t unchnged untl the dte of deprture, despte the evoluton of number of potentl trvelers nd mount of tckets vlble. Ths s forml lmt of our model (nd more generlly the current lmt of models nlyzng Opque chnnels). 17
18 References Bottzz, L., D Rn, M. nd Hellmnn, T. (2004), The Chngng Fce of the Europen Venture Cptl Industry: Fcts nd Anlyss, The Journl of Prvte Equty, 7(2) Sprng, Chowdry, B. nd nd, V. (1996), Stblzton, syndcton nd prcng of IPOS. Journl of Fnncl nd Quntttve Anlyss, 31, Gompers, P. nd Lerner, J. (2004), The Venture Cptl Cycle, 2nd edton, The MIT Press: Cmbrdge, MA.MIT Press. Fy, S. (2007), Sellng n Opque Product through n Intermedry: The Cse of Dsgusng One s Product, Workng Pper, Unversty of Flord, Gnesvlle, FL, USA, Aprl Fy, S. (2008), Reverse Prcng: The Role of Customer Expecttons, Workng Pper, Unversty of Flord, Gnesvlle, FL, USA, June. Fy, S. (2008), Compettve Resons for the meyourownprce Chnnel, Workng Pper, Unversty of Flord, Gnesvlle, FL, USA, September. Fy, S. nd Lrn, J. (2008), Implctons of Expected Vrblty n the Seller s Prce n me YourOwnPrce Auctons, Workng Pper, 2008, Unversty of Flord, Gnesvlle, FL, USA. Fy, S. nd Xe, J. (2007), Probblstc Goods: A Cretve Wy of Sellng Products nd Servces, Workng Pper forthcomng Mrketng Scence, Unversty of Flord, Gnesvlle, FL, USA, August. Grndos,., Gupt, A. nd Kuffmn, R.J. (2008), Desgnng onlne sellng mechnsms: Trnsprency levels nd Prces, Decson Support Systems, Vol. 45, pp Jng, Y. (2007), Prce dscrmnton wth Opque products, Journl of Revenue nd Prcng Mngement, Vol. 6, 2, pp Shpro, D., Sh, X. (2008), Mrket Segmentton: The Role of Opque Trvel Agences, Workng Pper, Belk College of Busness, Unversty of orth Croln, Chrlotte, C, USA, Unversty of Toronto, Toronto, O, Cnd, Februry. Shpro, D. nd Zllnte, A. (2007), mng Your Own Prce Mechnsms: Revenue Gn or Drn?, Workng Pper, Unversty of orth Croln, Chrlotte, C, USA, October. Spnn, M., Bernhrdt, M., Häubl, G. nd Sker, B. (2005), It s All n How You Ask: Effects of Prce Elctton Formt on Bddng Behvor n ReversePrcng Mrkets, Workng Pper, Unversty of Pssu, Pssu, School of Busness nd Economcs, Johnn Wolfgng GoetheUnversty, Frnkfurt m Mn, Germny, School of Busness, Unversty of Albert, Edmonton, AB, Cnd, August. Spnn, M., Sker, B. nd Schäfers, B. (2004), Mesurng Indvdul Frctonl Costs nd WllngnesstoPy v meyourownprce Mechnsms, Journl of Interctve Mrketng, Vol. 18, 4, Autumn, pp Spnn M. nd Tells G., (2006), J. Does the Internet Promote Better Consumer Decsons? The Cse of meyourownprce Auctons, Journl of Mrketng, Vol. 70, Jnury, pp Terwesch, C., Svn, S. nd Hnn, IH. (2005), Onlne Hgglng t meyourownprce Retler: Theory nd Applcton, Mngement Scence, Vol. 51, Vol. 3, Mrch 2005, pp Wng, T., GlOr, E. nd Chtterjee, R. (2005), Why meyourownprce Chnnel Mkes Sense for Servce Provders (or: Who eeds Prcelne, Anywy?), Workng Pper, Kent Stte Unversty, Kent, OH, Unversty of Pttsburgh, Pttsburgh, PA, USA, September. Wlson, J. G. nd Zhng, G. (2008), Optml desgn of nmeyourownprce chnnel, Journl of Revenue nd Prcng Mngement, Vol. 7, 3, pp Appendx Appendx 1: llustrton of smll sze of Proposton 3 We present n exmple of smll sze n whch the jont mplementton of the Opque nd YOP systems strongly domntes the sngle mplementton of the YOP or the Opque system. We choose the cse where n = 9 nd m = 4. In ths cse, ech subset of n gents s locted on the segment [0, ]. In cse of complete nformton, trvelers 8 nd 9 re ble to fly n ll sttes of the world nd trvelers 6 nd 7 only when there re 8 vlble tckets (remnd tht there re 2n trvelers locted on 18
19 two segments). We normlze = 1 nd determne the threshold vlues 2 = 11/18 nd 2 = 15/18 correspondng respectvely to the reservton prces of trvelers 6 nd 8. We choose q = 35/36 whch corresponds to very moderte level of uncertnty (wth q = 1, the potentl trvelers hve complete nformton on the reservton prce of the YOP bdders). Snce n ths cse 2p s between 2 nd, when the YOP system s mplemented lone, only the trveler 9 chooses to bd t hgh prce (wht mkes hs flght certn), whle trvelers 7 nd 8 choose to bd t low prce (wth the probblty p = 1/2 to trvel) nd gent 6 do not bd. When there re m = 4 vlble tckets, only gents 8 nd 9 trvel nd t very (n ths cse) dfferent rtes. Gven the vlues on the prmeters, we obtn 2p = 2p 9 wht cn be deduced from the generl formul 2p = (q 2 q+2 )(2n m 1)/2n whch substtutes when m nd n re smll to the pproxmton 2p = (q 2 q +2 )(2n m)/2n. One obtns 2p 9 = whle 2p 8 = Ther sum s the OTA profts obtned by dstrbutng to hgh rte populton when the YOP system s mplemented lone. When the Opque system s jontly mplemented, gents 8 nd 9 choose ths Opque system nd py ech one the reservton prce 2 8 = of gent 8. The resultng profts re then.e for the OTA. Then we compre these profts wth those obtned f the YOP system s mplemented lone Snce gent 7 stll bd the sme mount 2p 6 wth or wthout the Opque system s mplementton nd gent 6 stll do not bd, the jont mplementton of the two systems then provdes hgher profts to the OTA Appendx 2: Proof of Proposton 3 Gven tht potentl trvelers locted between 2 nd 2 choose the sme cton when the YOP s mplemented lone or jontly wth the Opque system, we consder only the optml ctons of the potentl trvelers locted between 2 nd. Accordng to the reltve vlues of n, m nd q, every gent j belongng to ths subset chooses to bd t prce PHj or P Lj ccordng to hs own poston relted to 2p. If the gent s locted between 2 nd 2p, he chooses to bd low prce PLj. If he s locted between 2p nd, he bds hgh prce PHj. When the two systems re jontly mplemented, ll the potentl trvelers locted between 2 nd py P O. Equtons (6) nd (7) cn be respectvely expressed s (8) nd (9) wth: Profts Jont mplementton 4000 YOP umber of tckets m Fgure 4: Comprson between YOP nd jont mplementton n cse 1 π = 1/(8n 2 (n + m( 1 + q) 2nq) 2 )(n 3 (m( 2 + q) 2n( 1 + q))q +2(m n) 2 ( 1 + q)(m + n( 2 + q) mq)(n + m( 1 + q) 2nq)) +n 3 q((m 2n)(m( 2 + q) 2n( 1 + q)) +(2m(m n)nq(n + m( 1 + q) 2nq))/(n + 2m( 1 + q) 2nq) 2 ))(2u + ū) (8) 19
20 nd π O/ = 1/4(m(2 m/n) ((m n)(mn(5 4q) + 2m 2 ( 1 + q) + 2n 2 ( 1 + q))q) /(n + 2m( 1 + q) 2nq) 2 )(2u + ū) The condtons on prmeters, u, ū, 1/2 < q < 1 nd the condton m n/2 re suffcent to mke n ll cses π smller thn π O/ (see Fgure 4) Appendx 3: Proof of Proposton 4 In the cse 3, f the YOP chnnel s mplemented lone, the OTA profts re expressed by (10): π = 1/2π(m) + 1/2π(2m) (10) (9) Profts 5000 Jont mplementton YOP umber of tckets m Fgure 5: Comprson between YOP nd jont mplementton n cse 3 wth π m D H /2 (m) = 2 +2 PH k=1 (m m D H )/2 PL k=1 [ ] 2p + (k 1)( 2p )/(m D H /2 1) [ ] 2 + (k 1)( 2p 2 )/((m m D H )/2 1) nd π m D H /2 (2m) = 2 +2 k=1 m m D H /2 k=1 P H (2p P L (2 + (k 1)( 2p )/(m D H /2 1)) + (k 1)( 2p 2 )/(m m D H /2 1)) When the two systems re jontly mplemented, the OTA profts re gven by (11): m/2 π O/ = (2nm m 2 )(u + ū/2)/2n + k=1 P [ ] ) (m/2 1) (k 1)(2 Equtons (10) nd (11) cn be respectvely expressed s (12) nd (13) wth: (11) 20
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