Sponsoring Content: Motivation and Pitfalls for Content Service Providers

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1 Sponsoring Conn: Moivaion and Pifalls for Conn Srvic Providrs Liang Zhang Dan Wang Dparmn of Compuing Th Hong Kong Polychnic Univrsiy Th Hong Kong Polychnic Univrsiy Shnzhn Rsarch Insiu {cslizhang Absrac Wih h populariy of bandwidh-innsiv mobil applicaions and mobil dvics h daa raffic is incrasing fas nowadays. This poss hug burdn o h Inrn srvic providrs (ISPs) o suppor such wirlss daa raffic as hy nd o invs on dvloping advanc nworks.g. 4G or xpnding h capaciy of h currn nworks in a much fasr pac. On way o kp up financing such invsmn is o ransfr h coss o h nd usrs. Thr ar sudis on nw paymn modls.g. im-dpndn pricing. An alrnaiv way is sponsord conn. Mor spcifically h conn srvic providrs (CSPs) can sponsor h nd usrs for h raffic of viwing hir conn. As an xampl Googl wih India ISPs is currnly sponsoring Gmail Googl+ c. for is nd usrs. Nvrhlss much is unknown abou h impac of such sragy on h CSPs of diffrn scals mor spcifically whhr richr CSPs may harvs mor advanag on h compiiv dg. In his papr w firs analyz h inrplay among CSPs a monopolisic ISP and nd usrs. W conclud: ) small CSPs and larg (or rich) CSPs all may hav par incniv o sponsor conn for is nd usrs whn h monopolisic ISP canno discrimina h charging pric of CSPs; and 2) ohrwis non of hm has h incniv o adop his sragy. W hn sudy h ffc of compiion from shor-run (i.. mark shars ar fixd) and long-run (i.. mark shars ar dynamic) prspcivs in h mark wih on small CSP and on larg CSP. W show ha h small CSP (or larg CSP) may bnfi mor from h adopion of sponsord conn for h shor-run (or long-run) compiion. I. INTRODUCTION Wih h populariy of bandwidh-innsiv mobil dvics such as smar phons abl compurs c. h daa raffic is incrasing fas nowadays. This poss hug burdn o h Inrn srvic providrs (ISPs) o suppor such wirlss daa raffic. Th ISPs always supply raffic plans wih low daa caps du o h scarciy of bandwidh. Th pricing daa s rvald by Googl dmonsras ha almos 85% of all plans offr lss han GB of daa a monh and 36% offr lss han GB a monh []. Evn for GB monhly daa plan i would b fully xhausd in lss han svn hours undr currn 3G bandwidh [2]. Ming his dmand-supply gap rquirs larg invsmn by building advancd nworks.g. 4G or xnding h capaciy of h currn nworks wih mor bandwidhs and bas saions. On way o kp up financing such invsmn is o ransfr h coss o h nd usrs. Thr ar xnsivly sudis on nw paymn modls.g. imdpndn pricing [3] [4]. An alrnaiv way is sponsord conn. Mor spcifically h conn srvic providrs (CSPs) can sponsor h nd usrs by dirc paymns o ISPs or sharing advrising rvnu wih hm. Whn nd usrs accss h conn providd by h CSPs hir raffic is parly or fully xmpd from hir mobil daa caps. For xampl Googl has joind wih India s Bhari Airl o offr fr accss o crain Googl-basd srvics such as Gmail Googl+ and firs pag of wb sis via Googl sarch wihou ringing up daa chargs [5]. This pricing sragy cras a posiiv cycl: nd usrs ar glad o accss mor conn wihou cound ino hir mobil daa cap; CSPs can arac mor usrs and viws; ISP can g mor rvnu by his nw rvnu rsourc so as o suppor br prformanc and chnology upda. I also rmovs h infficincy of currn arrangmn undr which h CSPs driv profi from showing advrismns whil nd usrs pay h cos of viwing hm. Nvrhlss his nw pricing modl in cllular nworks has bn linkd o n nuraliy dba rcnly bcaus som conn wouldn b cound agains monhly daa caps s by CSPs [6]. Th n nuraliy advocaors including rprsnaivs from public inrss group concrn ha such plan will favor rich and larg CSPs ovr small ons [7]. In fac n nuraliy ruls hav bn havily discussd from h poins of compur scinc conomics and law. Y h cor issu of n nuraliy for his nw pricing modl is whhr h CSPs will comp unfairly undr his policy insad of h radiional issus such as whhr h ISPs can ransmi packs wih prioriy or h las-mil ISPs can charg CSPs for h conn ransmiing o hir consumrs. Th CSPs also chang hir apiud o nwork nuraliy from showing srong proponn o bing inrsd in his nw pricing modl [8]. For xampl ESPN rid o alk wih US s mobil carrirs abou h oll-fr daa plans [9]. I rmains an inrsing qusion: which kind of CSPs will prfr his nw pricing sragy. Th concrn announcd by h nuraliy advocaors is also dsrvd daild discussion. In his papr w focus on h impac of sponsord conn sragy on h CSPs of diffrn scals. W firs provid an analysis on h complicad inrplay among CSPs h monopolisic ISP and nd usrs. Thn w considr h ffc of compiion for h adopion of sponsord conn policy from shor-run (i.. mark shars ar fixd) and long-run (i.. mark shars ar dynamic) prspcivs in h mark wih on small CSP and on larg CSP. Our sudy shows h following conclusions: Conn srvic providr is also known as Inrn conn providr (ICP).

2 Whn h monopolisic ISP canno discrimina h charging pric of CSPs small CSPs and larg CSPs all may hav par incniv o sponsor conn. Ohrwis non of hm adops sponsord conn plans. For h shor-run compiion h small CSP is mor likly o bnfi from sponsord conn plans bu no for h larg on. For h long-run compiion h mark shar of h larg CSP bcoms largr and h small CSP bcoms smallr. II. RELATED WORK Thr ar xnsiv sudis on nwork nuraliy problm dspi of a shor hisory. Ma al. [] focusd on paid prioriizaion of conn analyzd from h viw of consumrs. Thy inroducd h noaion of public opion ISP showd o b a br choic han nwork nural mannr for boh monopolisic ISP and oligopolisic scnario. Hand al. [] sudid h sragy of pricing conn-providrs for hir connciviy o nd-usrs. Thy showd ha in addiion o gains in oal and nd-usr surplus conn-providrs will xprinc a n surplus from paricipaion in ra allocaion undr low cos of connciviy. Choi al. [2] sudid h ffc of nural rgulaions on invsmn incnivs for ISPs and CSPs. Thy found ha capaciy xpansion dcrass h sal pric of h prmium srvic. Nvrhlss non of hm considrd h sponsord conn sragy. In fac hr ar currnly fw acadmic works dircly rlad o his nw pricing sragy. From h conomic poin of viw Andrws al. [3] sudid h conracual rlaionship bwn h srvic providrs and conn providrs. Thy modld h inracion bwn h srvic providrs and h conn providrs as a Sacklbrg gam wih random dmand. Thir work concludd ha a coordinaing conrac can maximiz oal sysm profi and h addiional profi. From h chnical poin of viw Raj al. [2] dvlopd a nw compuing absracion calld SIMl basd on h ida of spli billing. Th SIMl can provid rusworhy proofs of a dvic s mobil raffic ha can b rdmd a conn providr involvd in spli billing. Ohr sudis.g. imdpndn pricing (TDP) ar orhogonal o sponsord conn sragy. For xampl Ha al. [3] prsnd h archicur implmnaion and a usr rial of h sysm for TDP calld TUBE. W also hav a horical sudy [4] [5] abou h incnivs of TDP and comparison bwn usag-basd and fla-ra schms in TDP. In his papr w focus on h impac of sponsord conn sragy on h CSPs of diffrn scals. W dmonsra which kind of CSPs prfr h sponsord conn sragy and whhr his nw pricing sragy will rsul in unfair compiion bwn rich and larg CSPs and small CSPs. III. BASIC SYSTEM MODEL In his scion w considr h basic sysm modl in h mark wih CSPs a monopolisic ISP and nd usrs. Th monopolisic ISP provids h conncion srvics o CSPs and nd usrs. Th usrs viw h conn providd by CSPs. W dno x as h raffic volum of a CSP viwd by nd usrs. L f(x) b h uiliy obaind from viwing h conn of h CSP whr facor rprsns h uiliy lvl of nd usrs. W assum ha f( ) is a non-dcrasing and concav funcion wih dcrasing marginal saisfacion. This rflcs h dcrasing marginal prfrnc of nd usrs. Th ISP chargs nd usrs for pr uni raffic. 2 This pric can b parly sponsord by h CSP. W dno h sponsord prcnag as α. Thus nd usrs can dcid hir opimal raffic volum by maximizing hir own payoff as follows: (EU-P): max x u(x) = f(x) ( α)x s.. x. () Givn h pric chargd by h ISP and h sponsord prcnag i.. { α} h opimal raffic usag for nd usrs is: x = f (( α) / ) (2) whr f ( ) is h invrs funcion of firs ordr drivaiv of f( ). A common xampl of funcion f( ) is f(x) = β x β < β <. In his cas h opimal raffic consumpion is x σ (α ) = ( ( α) ) /β. Th pric lasiciy can b xprssd as ϵ = x (α ) x (αp = ) β which characrizs how much h ra provisioning changs as h pric changs. Small pric lasiciy mans ha i is hardr o chang h raffic consumpion by charging pric. Similarly w considr h payoff of CSPs. W us g(x) o rprsn h rvnu of h CSP whr rflcs h rvnu lvl of h CSP. Diffrn yps of CSPs may hav much diffrn rvnu lvls [6]. Evn for h sam yp of CSPs h rvnu lvls may b much diffrn. For insanc h larg CSPs usually hav highr rvnu lvl han ha of small ons [7]. Th rvnu can b gnrad by advrismn.g. YouTub or by valu-addd srvics.g. Tncn and ohr -commrc.g. Amazon. W assum ha g( ) is a non-dcrasing and concav funcion. I mans ha h marginal rvnu dcrass wih h incras of raffic. Th monopolisic ISP chargs CSPs p c for pr uni raffic. Th payoff funcion for his CSP is: v(x) = g(x) αx xp c. (3) Givn h sponsord prcnag α h pric pr uni chargd o CSPs p c and nd usrs h CSP also has is own opimal raffic volum: x c = g ((α + p c )/ ). (4) Wih h funcion g(x) = β c x β c < β c < h opimal raffic volum for h CSP is x σ c(α p c ) = ( c α +p c ) /β c. Th pric lasiciy of h CSP is ϵ c = x c (αp c) p c p c x c (αp c) = β c. No ha h ffciv raffic volum is dcidd by boh nd usrs and h CSP i.. x = min{x c x }. If x c < x hn h ffciv raffic volum is limid by h CSP. For xampl som wb sis limi h numbr of simulanous onlin usrs du o h gap bwn limid capaciy of srvrs and hug dmand. If x c x hn h ffciv raffic volum is jus 2 In pracic mos of currn plans providd by ISPs ar in form of fixd prics for som daa caps insad of usag-basd prics. Y his form of pricing sragy can b viwd as usag-basd pricing sragy sinc boh schms ncourag usrs viwing mor imporan conn [4].

3 nd usrs dmand. Th CSP dcids h opimal sponsord prcnag wih his ffciv volum by solving h following problm: (CSP-P): max v(α) = g(x (α)) αx (α) x (α)p c α s.. α. (5) Sinc v(α) is coninuous and boundd ovr inrval [ ] h opimal soluion of abov opimizaion xiss. In gnral i is hard o quanify h propris of his opimal soluion. In ordr o show som inrsing insighs w considr h spcial cas whr β = β c = β. Whn α σcp σpc (+) h ffciv raffic volum is dcidd by raffic{ usag of nd usag } i.. x = x. Similarly whn α max σc p c ( + ) h ffciv raffic volum is dcidd by bs raffic volum of h CSP i.. x = x c. In paricular whn p c w hav x = x c. Th following horm shows h opimal sponsord prcnag of h CSP o nd usrs. Thorm : Givn h prics {p c } chargd by h ISP o CSPs and nd usrs h opimal sponsord prcnag α (p c ) for h CSP is: { if β + pc α (p c ) = / β p c/ / + β if > β + pc. Du o h limi of spac all proofs in his papr ar omid and availabl in h chnical rpor [8]. Thorm sas ha h CSP supplis no sponsord conn o is nd usrs i.. α = whn h condiion β + p c is saisfid. Ohrwis h CSP has srong incniv o supply sponsord conn plan for is conn. In paricular whn h CSP undraks almos all h raffic cos of is nd usrs gnrad by viwing is conn. In ohr words h conn providd by h CSP wih high rvnu lvl and consumd by nd usrs wih rlaivly low uiliy lvl ar mor likly o b oll-fr undr h CSP s sponsord conn plan. Th highr pric chargd o nd usrs and lowr pric chargd o h CSP rsuls in h highr sponsord prcnag. For xampl Googl has srong incniv o supply sponsord conn plan o nd usrs du o wo rasons: () h rvnu lvls ar much high for is srvics such as Gmail and sarching srvic; and (2) h ransi coss for Googl ar clos o zro du o is homgrown infrasrucur [9] i.. p c is small. Wih h opimal sponsord prcnag of conn h ffciv raffic volum can b drmind: ( ) /β p c if σc p c x (p c ) = ( ) /β if p c < σc β + p c ( ) /β σc+( β)σ p c + if σc > β + p c. Th ffciv raffic volum ar dividd ino r rgions corrsponding o r yps of CSPs shown in Fig.. Th hr yps of CSPs ar as follows: Non-incniv CSPs: h CSPs ha hav lowr xpcd raffic usag han nd usrs. I mans ha nd usrs ar inrsd in h conn providd by nonincniv CSPs bu h CSPs can hardly suppor such (6) (7) hug amoun of raffic du o low rvnu lvl and high cos. Obviously h CSPs hav no incniv o offr sponsord conn plan; Ponial CSPs: h CSPs ha hav highr willingnss o supply conn han h dmand bu do no provid sponsord conn plan o nd usrs. Th ponial CSPs hav highr cos of sponsoring h conn han h bnfi from his sragy; Incniv CSPs: h CSPs ha hav srong incniv o sponsor nd usrs viwing is conn. Th rvnu lvl of h incniv CSPs is rlaivly high whil h uiliy lvl of hir nd usrs is rlaivly low. Th propr sponsord conn plan can ncourag raffic usag of nd usrs and incras h profi of his yp of CSPs. Non-incniv CSPs Ponial CSPs Incniv CSPs Fig. : Thr yps of CSPs Th monopolisic ISP obains is rvnu from charging CSPs and nd usrs. If h ISP can discrimina h prics of CSPs i can dcid opimal prics {p c } chargd o h CSP and nd usrs rspcivly so as o maximiz is profi. This profi is impacd by wo facors: ) h srvic fs chargd o h CSP and nd usrs modld as p c x and x rspcivly; and 2) h variabl cos 3 modld as cx whr c is h marginal cos. Thus h ISP drmins h opimal prics {p c } by solving h following problm: (ISP-P): max {p c} π = ( + p c c)x (p c ) s.. p c. (8) Thorm 2: Wih h bs rspons of h CSP and nd usrs h opimal prics {p c p } chargd by h monopolisic ISP o h CSP and nd usrs ar: p c = c ( + )( β) p = c ( + )( β). (9) Thorm 2 shows h bs pric sragy for h monopolisic ISP. No ha p c p = σ c /. According o horm w hav α =. I mans ha wih h monopolisic powr for h ISP o discrimina h prics of CSPs h bs sragy of h CSP is no o adop h plan of sponsord conn. Th inuiion is ha h monopolisic ISP liminas h gap bwn h opimal raffic volum for CSPs and raffic dmand for nd usrs by pricing hm in an opimal way rsuling in no incniv for CSPs sponsoring conn. Y in pracic h monopolisic ISP canno discrimina h prics of CSPs du o h nwork nuraliy ruls. In fac h pric chargd o CSPs is usually low. Th currn CDNs charg h raffic disribuion for abou $. o $.2 pr GB [2] much lowr han h pric chargd o nd usrs by ISPs. YouTub vn has buil is own homgrown infrasrucur so as o rduc ransi 3 Th oal cos consiss of variabl cos and fixd cos. W only considr h variabls cos sinc h fixd cos is jus a consan and dos no affc h conclusions.

4 coss [9]. Hnc w considr h cas of ignoring h pric chargd o h CSP i.. p c =. Th opimal conn sharing prcnag is dmonsrad in h following corollary. Corollary : Whn p c = h opimal pric chargd by h ISP o nd usrs is p = c β. Th opimal conn sharing prcnag α is: { if α σ ( ) = β / β () /+ β if σc > β. Corollary dmonsras ha h opimal pric chargd o nd c usrs is β much highr han ha whn h monopolisic ISP can discrimina h prics of CSPs. Whn h conn σ is sponsord parly by CSPs i.. c > β h f paying o h ISP by nd usrs is sill highr. No ha h summaion of prics for CSPs and nd usrs in Thorm 2 is qual o h opimal pric in corollary. I mans ha whn h monopolisic ISP can discrimina h pric of CSPs i can ransfr par of h cos from nd usrs o h CSP. Y whn h ISP canno discrimina h pric of CSPs h sponsord conn sragy can b sill a good choic for h ISP o ransfr is cos o h CSP. Corollary also shows ha h sponsord prcnag is indpndn of h pric o nd usrs. This prcnag only dpnds on h rvnu lvl of h CSP and is usrs uiliy lvl. Summary. Whn h monopolisic ISP canno discrimina h prics of CSPs h CSPs can b dividd ino hr yps i.. non-incniv CSPs ponial CSPs and incniv CSPs according o hir incnivs of adoping sponsord conn sragy. This sragy provids an fficin way o ransfr h cos of h ISP from nd usrs o CSPs. Ohrwis h monopolisic ISP liminas h gap bwn h opimal raffic volum for CSPs and raffic dmand for nd usrs by pricing hm in an opimal way rsuling in no incniv for CSPs sponsoring conn. IV. COMPETITION ANALYSIS In his scion w sudy h ffc of compiion o h adopion of sponsord conn for CSPs. W considr h mark wih on small CSP and on larg CSP. Th larg CSP rfrs o h CSP ha has high rvnu lvl whil h small CSP has low rvnu lvl. In addiion h iniial numbr of nd usrs of h larg CSP is also much highr han ha of h small on. W divid h compiion of wo CSPs ino wo cass: shor-run compiion and long-run compiion. In shor-run compiion h numbrs of nd usrs for boh CSPs ar fixd whil in h long-run compiion h numbrs of nd usrs ar changd wih h im. A. Shor-run compiion For shor-run compiion h numbr of nd usrs for h wo CSPs ar assumd o b unchangd du o h consisn usag habis during a shor im. W dno n i i = 2 as h usr numbr of CSP i. Th numbr of nd usrs for boh CSPs can also b rad as h mark shar if w normaliz oal numbr of nd usrs o. Wihou loss of gnraliy w l CSP b h small on and CSP 2 b h larg on i.. n n 2. W assum ha h monopolisic ISP canno charg diffrn CSPs h diffrn prics. W dno h rvnu lvl of CSP i as i. No ha h rvnu lvl of h larg on is highr i.. σ σ 2. Th uiliy lvl for h nd usrs of CSP i is dnod as i. Eihr h small CSP or larg CSP may hav highr uiliy lvl for is nd usrs. For insanc h posiiv nwork xrnaliy own by larg CSP or h br srvics providd by small CSPs can mak h nd usrs hav high uiliy lvl. Th prcnag of sponsord conn for CSP i is dnod as α i. Givn h pric chargd by h monopolisic ISP h opimal racions for h CSPs and nd usrs ar h sam wih scion III. W dnod h ffciv raffic volum for CSP i as x i (p c ). Hr w only nd considr h opimal pric {p c } dcidd by maximizing h uiliy funcion of h ISP: (ISP-P): p c = or max π = ( + p c c)(n x (p c ) + n 2 x 2(p c )) { p c } s.. p c () Thorm 3: Th opimal prics {p c } chargd by h monopolisic ISP ar on of h following cass: c ( + )( β) cσ p = ( + )( β) (2) p c = c2 (2 + 2 )( β) p = c2 (2 + 2 )( β). (3) Thorm 3 shows ha h opimal pric is only dcidd by on CSP. In boh cass h summaions of prics for CSPs and nd c usrs ar h sam i.. β. For h firs cas h opimal pric only dpnds on h rvnu lvl of h CSP and h uiliy of is nd usrs. This happns whn h numbrs of nd usrs uiliy lvls and rvnu lvls for CSP and 2 saisfy h following condiion: n + n 2 [max{ 2 2 +( β)2 + }] /β [n ( σc 2 ) /β + n 2 ]( σc 2 +σ 2 + ). (4) Ohrwis h opimal pric dpnds on h CSP 2 i.. p c p = 2 2. Usually h numbr of h larg CSP is much highr han h small on. Thus w hav h following proposiion. Proposiion : Whn n n 2 h prcnags of sponsord conn for wo CSPs ar as follows: { σ if c α β = / β 2 /2 / if β+ > β + 2 (5) 2 and α 2 =. Proposiion dmonsras ha h larg CSP dosn bnfi from h sponsord conn sragy. Th small CSP bnfis from his sragy if and only if h rvnu lvl and h uiliy lvl of is nd usrs saisfy β. Th inuiion is ha h ISP can obain mor profi by charging pric closr o h opimal pric for h larg CSP. This pric liminas h incniv of sponsoring conn for larg CSP bu lavs nough spac o h small on. Whn considring h spcial cas i.. p c = w hav h following corollary. Corollary 2: Whn p c = h opimal pric chargd by h ISP o nd usrs is p = c β. Th opimal sponsord prcnag for CSP i can b shown as: { σ if ci αi i β (p c ) = i /i β i /i if i (6) + β i > β.

5 Similar o h corollary whn h ISP can only charg nd usrs h opimal pric is indpndn of h rvnu lvl of CSPs and h uiliy lvl of nd usrs. In addiion h opimal prcnag of sponsord conn for ach CSP is also indpndn of h numbr of hir nd usrs. In ohr words ach CSP jus dcid how much o sponsor is nd usrs according o is own rvnu lvl and h uiliy lvl of is nd usrs. B. Long-run compiion Th mark shars for ach CSP ar usually changd if w considr long-run mark wih compiion. Thy ar graly affcd by h payoff of nd usrs. Th CSP wih highr payoff of is nd usrs is mor likly o hav much highr mark shar. Th mos commonly usd conomic modl for mark shars is Holling Modl. Th Holling Modl assums ha h nd usrs ar uniformly locad along a uni inrval wih wo CSPs locad a wo ndpoins. Each usr has ransporaion cos by uni of disanc squard dnod as whn dciding is CSP. If h nd usr is a a disanc n i o on of h CSPs is ransporaion cos is n 2 i. Th ransporaion cos pr uni can b much diffrn for diffrn kinds of srvics. For xampl h usrs of Facbook surfr high ransporaion cos pr uni o ohr social nwork srvics such as Googl+ whil h usrs of YouTub can asily visi ohr vido sharing sis if h rquird vidos providd. Wih h Holling Modl givn h payoff of nd usrs for CSP i.g. u i h mark shar for CSP i is: n i = 2 + u i u i (7) 2 whr u i dnos h uiliy of nd usrs no blonging o CSP i. Each CSP comps for h mark shar by improving h payoff lvl of is nd usrs.g. incrasing h sponsord prcnag. Manwhil i also has o balanc h mark shar and h profi obaind from on nd usr. Th oal profi of CSP i is: v i (x i ) = n i i g(x i ) (α i + p c )n i x i. (8) Givn h prcnag of sponsord conn α CSP i has is own opimal raffic volum. Considring h firs-ordr drivaiv of h profi of CSP i w hav: v i(x i) = σ i f (xi ) ( α i ) 2 [i g(x i ) (α i + p c )x i ] +n i (i g (x i ) α i p c ) =. (9) Puing h opimal raffic usag for nd usrs i.. x i = ( σi ( α i ) ) /β ino h abov on-ordr drivaiv of h profi for CSP i i follows: v i (x i ) xi =x x = n i [ i ( α i ) α i p c ]. (2) i i i Whn α i i /i /p c +i /i w hav vi(xi) xi =x. ( ) i σci /β For anohr raffic usag x i = α i +p c x i w hav vi(xi) σci ) /β <. Th opimal raffic usag xi=( α i p+pc [ ( ) for CSP i is wihin h inrval x σci /β i α i +p c ]. Th opimal raffic usag for CSP i dnod as x c i is largr Prcnag of sponsord conn (a) Small CSP wih highr usr uiliy lvl ( = 2 =.5) Prcnag of sponsord conn (b) Larg CSP wih highr usr uiliy lvl ( =.5 2 = ) Fig. 2: An xampl of h prcnag of sponsord conn in h long run ( = 2 = 2 β =.5 =.5 p c = ) han x i i.. h opimal ffciv raffic usag is x i = ( σi ) /β. ( α i) Whn αi i /i /p c +i /i w hav x i = ( ) σci /β α i+p c x i. No ha Vi(xi) σ ) c /β xi =( i > α i p+pc and Vi(xi) xi =x. Th opimal raffic usag for CSP i [ ( ) σci /β i is wihin h inrval α i +p c x i ]. Th ffciv raffic usag is x i = x c i. Thus w can divid h original opimizaion problm ino wo on wih ffciv raffic usag dcidd by nd usrs and h ohr dcidd by h CSP i islf. Givn h sponsord prcnag α i whr α i is h prcnag of sponsord conn for CSPs xcp i w can g h opimal racion by analyzing hs wo opimizaion problms. Dno α o b h Nash quilibrium [2] of sponsord prcnag. W hav h following obsrvaion abou h rlaionship bwn his sponsord prcnag and h ransporaion cos pr uni. Obsrvaion : Givn h pric {p c } chargd o nd usr and CSPs if < n i < h sponsord conn αi () for CSP i is a non-incrasing funcion of. Obsrvaion dmonsras ha as h ransporaion cos pr uni bcoms smallr h prcnag of sponsord conn incrass (no sricly) du o compiion. Whn h ransporaion cos pr uni is small h nd usrs ar mor likly o choos h CSPs wih highr usr payoff lvl. Th CSPs can us sponsord conn sragy o pursu highr mark shar by improving h payoff of nd usrs. This rsuls in high prcnag of sponsord conn. An xampl for h obsrvaion shown in Fig. 2 dmonsras h prcnag of sponsord conn undr wo cass: larg CSP has highr usr uiliy lvl shown in Fig. 2(a) and lowr usr uiliy lvl shown in Fig. 2(b). Undr h firs cas h small CSP has lowr usr uiliy lvl and rvnu lvl. As h dcras of ransporaion cos pr uni h small CSP has o sponsor much highr prcnag of conn so as o rmdy h hug disadvanags. Undr h scond cas h larg CSP has o sponsor h conn so as o ak nough mark shars whil h small on sponsors no conn du o is highr usr uiliy lvl. As h dcras of ransporaion cos pr uni boh h small and larg CSPs hav o sponsor much highr prcnag of conn so as o comp for mor mark shars. Evn hough h CSPs ar likly o adop high prcnag of sponsord conn wih small ransporaion cos pr uni h mark shars may no b improvd. Anohr obsrvaion is akn abou h rlaionship bwn h mark shar and ransporaion cos pr uni.

6 Mark shars.8 Small CSP wihou sponsord conn Larg CSP wihou sponsord conn (a) Small CSP wih highr usr uiliy lvl ( = 2 =.5) Mark shars.8 Small CSP wihou sponsord conn Larg CSP wihou sponsord conn (b) Larg CSP wih highr usr uiliy lvl ( =.5 2 = ) Fig. 3: An xampl of mark shars in h long run ( = 2 = 2 β =.5 =.5 p c = ) Obsrvaion 2: Givn prics {p c } chargd o CSPs and nd usrs sponsord conn sragy in h long run maks h mark shar of larg CSP largr and small CSP smallr. Obvrvaion 2 vrifis h concrns of nuraliy advocaor ha larg CSP can always bnfi mor wih h sponsord conn sragy. Whn h uiliy lvl of h larg CSP is high is mark shar can b xndd largr compard wih h small on wih sponsord conn sragy. Whn h uiliy lvl is low i can us sponsord conn sragy o avoid h mark shar loss or vn obain mor mark shar han small on. An xampl shown in Fig. 3 is givn o dmonsra hs wo kinds of scnarios wih h sam paramrs wih Fig. 2. Fig. 3(a) shows ha as h ransporaion cos pr uni bcoms smallr h small CSP wih highr usr uiliy lvl gs mor mark shar. If h ransporaion cos pr uni is small nough i can vn ak h whol mark. Y wih h sponsord conn sragy h larg CSP can improv h mark shar by providing highr sponsord conn o is nd usrs. This sragy rmdis h disadvanag of is low usr uiliy lvl. Fig. 3(b) dmonsras h cas ha h larg CSP has highr uiliy lvl. Wih h sponsord conn sragy h mark shar gap bwn h larg CSP and h small on bcoms largr. Summary. In h shor run h small CSP may bnfi mor from sponsord conn. In h long run h prcnags of sponsord conn for boh CSPs ar improvd du o compiion. Th largr h ransporaion cos pr uni h highr prcnag h CSPs sponsor hir conn. In addiion h larg CSP can obain mor mark shars by adoping sponsord conn vrifying h concrns of nwork nuraliy advocaors. V. CONCLUSION In his papr w sudy h impac of sponsord conn sragy on h CSPs of diffrn scals. W firs analyz h inrplay bwn CSPs h monopolisic ISP and nd usrs and conclud ha non of CSPs hav h incniv o sponsor hir conn if h monopolisic ISP can discrimina h pric of ach CSP. W hn sudy h ffc of compiion by considring on small and on larg CSP. W analyz h opimal sragis for boh CSPs in h shor-run compiion and long-run compiion. W conclud ha h small CSP may bnfi from h sponsord conn sragy bu no for larg CSP in shor-run compiion. W also obsrv ha in longrun compiion as h ransporaion cos pr uni dcrass h opimal prcnag of sponsord conn incrass. In addiion h mark shar of larg CSP bcoms largr wih h sponsord conn sragy. On dircion of xnding h currn work is o considr h nwork wih mulipl ISPs. Mor daild sudis abou h long-run compiion ar sill ncssary. W xpc o work on hs issus as fuur work. ACKNOWLEDGMENT Dan Wang s work is suppord in par by Naional Naural Scinc Foundaion of China (No ) RGC/GRF PolyU 5264/3E HK PolyU -ZVC2 G-UB72. 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