Prce Settng n Two-sded Markets for Internet Connectvty Thorsten Hau 1 and Walter Brenner 1 1 Insttute of Informaton Management, Unversty of St. Gallen Müller-Fredberg-Strasse 8, CH-9000 St. Gallen, Swtzerland Phone +41 (0)71 4 3803 Fax +41 (0)71 4 396 thorsten.hau@unsg.ch Abstract. Due to a lack of ncentves, Internet peerngs are a notorous bandwdth bottleneck. Through the use of drect nterconnecton and content delvery networks, content provders are able to provde better servces to ther customers. These technologes have a profound mpact on the busness models of nternet servce provders. Instead of competng for consumers and keepng uplnk connecton costs low, ISPs face a two-sded market n whch they compete for EUs and generate revenues on the CP sde of the market. Ths work presents a formal model for the provders prcng decson towards content provders and dscusses consequences for the Internet. Keywords: Qualty of Servce, Network Economcs, Peerng, Internet
Introducton The Internet s made up of many ndependent sub-networks so called autonomous systems (AS). Generally speakng these ASs correspond to dfferent carrers or Internet servce provders (ISPs): frms that own and operate the nfrastructure (cables and routers) that make up the Internet. These ISPs have customers who are ether content provders (CP) wth mostly outgong traffc or end-users (EU) wth mostly ncomng traffc. To form the Internet, each ISP offers all of ts customers connectvty to all of the other ISPs customers. In order to uphold ths unversal connectvty, the ISPs have to exchange user traffc, an actvty that s governed by contractual agreements between the ISPs and physcally enabled by nfrastructure that nterconnects ther networks. Thus, even though the Internet conssts of many ndependent subnetworks, each user can reach every webste on the web. However, t s also well known, that ISPs are not very cooperatve n ther peerng behavor [7]. The decson to nterconnect usually s more expensve for one party than for the other and therefore peerngs tend to have smaller capacty than what would be optmal. The rules regulatng the exchange of traffc between ISPs have been subject to extensve treatment n the lterature. Issues lke hot potato routng [0, ] and determnaton of access charges have been extensvely studed and are qute well understood [8, 9, 16]. However, the avalable lterature studes an dealzed Internet n whch there are EUs, CPs and ISPs that have relatons as depcted n fg. 1. The Internet s modeled as a strctly herarchcal system n whch traffc flows from a CP to ts ISP, s exchanged wth the requestng user s ISP and s then sent to the EU. Fg. 1. A key characterstc of ths setup s that traffc s exchanged through a peerng pont. Dependng on the contract between two ISPs ths traffc exchange may happen n exchange for a payment or for free. Due to lackng ncentves to extend peerng capacty suffcently, these peerngs represent major traffc bottlenecks [1, 7, 14]. In contrast to the avalable work [16, 17, 1], ths paper focuses on two mportant varatons of ths dealzed model of Internet nfrastructure as shown n fgures and 3. The exstng lterature has gnored the possblty that content provders and termnatng nternet servce provders nterconnect drectly.
Prce Settng n Two-sded Markets for Internet Connectvty 3 There are two modes of drect nterconnecton that we wll consder. Frstly, a content provder can drectly buy transt from the termnatng ISPs, thus effectvely payng them for preferental access to end-users. Ths practce shown n fg. s called mult-homng (MH) and contrbutes to exponental growth of routng tables [5]. Secondly, content delvery networks (CDNs) shown n fg. 3 are a popular way to enhance the flow of nformaton on the Internet. A CDN uses local caches to keep dstrbuted mages of content close to EUs wthout the need to traverse several ISPs networks [4]. Both technologes provde vable means to mprove the speed and relablty of data transport from a CP s webste to EUs. They allow bypassng peerngs and ganng more drect access to the EUs, thus ncreasng the probablty of tmely delvery of data to the end-user. The motvaton to use CDN or MH s to provde better qualty of servce (QoS) wth the followng chan of causalty: Traversng peerngs degrades user experence by creatng delays QoS access to EUs through CDN and MH creates better user experence more vstors to a webste hgher revenues from sellng ad space on the webste. Fg.. Fg. 3. Ths paper uses the economc theory of two-sded markets to understand the prcng decson an ISP has to make wth respect to the charges leved on the CP sde of the market n settngs such as those n fgs. and 3. Nether the Internet as a whole, nor ndvdual nternet servce provders (ISPs) can straghtforwardly be consdered platforms that optmze ther revenue from two sdes of a market. Wth the standard Internet busness model, each termnatng ISP lacks the power to charge content provders that are sgned up wth another ISP. There are techncal as well as contractual barrers to charge some remote content provder for sngle data packets t sends to an ISP s network. The access charge (the nterconnecton fee) exchanged between two ISPs s only an mperfect tool to explot an access monopoly on the Internet due to the fact that t s often recprocal or zero for external reasons [, 1, 16]. Ths s a key dfference between the Internet and telephone servces (PSTN), where for each call, sender and recever can be dentfed and blled per unt of tme and a per unt settlement between provders s possble [4, 6, 9]. Wth CNDs or MH, the property of PSTN that the partcpatng partes can be dentfed (and are bllable customer) s recreated. The CDN s a thrd party medatng between CP and ISP but the ISP can charge the CDN for delvery of traffc whch wll pass ths cost on to ts CPs. Ths stuaton s
4 dfferent from the case of access charges between dfferent provders (as analyzed by [16]) because n a CDN relatonshp there s no recprocty or two way access whch s an mportant condton for that model to be applcable. For the rest of ths artcle we smplfy the role that CDNs play on the Internet by treatng them as pure medators between atomc CPs and ISPs. The paper s structured as follows: Frstly we revew the relevant lterature on twosded markets and related topcs n telecommuncatons prcng. Then we explan the abstracted stuaton we wsh to understand and motvate our use of a two-sded market model. Thrdly, we present a formalzed model for an ISP facng a two-sded market, dervng results from the market setup. Lastly we summarze our fndngs and dscuss mplcatons and future research topcs. Lterature Revew Armstrong s dscusson of competton n two-sded markets [3] provdes much of the foundaton for ths work. Two-sded markets are markets where a platform optmzes proft across two dstnct sets of customers nstead of just one. In the credt card ndustry, the card ssung company would be the platform and the merchants acceptng the card consttute one group of customers whle the buyers usng the card to pay form the other. Armstrong analyses three dstnct settngs wth dfferent customer behavors and levels of platform competton. The stuaton relevant for ths work s termed compettve bottleneck : One group of customers can use any number of platform provders smultaneously, whle the other group chooses only one of the competng platforms. In our problem, ths stuaton corresponds to EUs beng subscrbed to only one sngle ISP whle CPs can deal wth any number of ISPs at the same tme. Rochet et al. [19] provde a comprehensve overvew of the current lterature on two-sded markets. They defne two-sded markets as markets n whch not only the total prce but also the prce structure nfluences the number of transactons on the market. For the case at hand, the ISP provdes the platform on whch transactons between EUs and CPs can take place. They also provde defntons for membershp and usage externaltes. In the frst case one party profts from the sheer presence of the other, whle a usage externalty s a network effect that arses n an transacton between members of the two sdes. They also dscuss the effects of fxed and varable prces on the platform. Snce varable prces reduce the externalty exerted by one group of customers on the other, partcpaton ncentves are reduced. Laffont et al. [16] are not drectly concerned wth two-sded markets. Ths work analyzes the access charge pad from one ISP to another for passng traffc on to that ISP s network. In ther model the ISP optmzes the prces t charges to CPs and EUs subject to the access charges t pays (for sendng traffc to an EU on another ISP s network) and receves (for termnatng traffc wth ts own EUs). In ther model the access charge turns out to be a pure tool for reallocatng termnaton costs between EUs and CPs. In the common case of zero access charges all termnaton costs are born by the EU whch corresponds to a subsdy to CPs.
Prce Settng n Two-sded Markets for Internet Connectvty 5 Problem Descrpton Ths work uses the theory on two-sded markets to explore two specal cases of nterconnecton that are dfferent from the symmetrc and recprocal case studed by [16]. The standard model of Internet traffc exchange as shown n fg. 1 follows the pattern CP ISPo a ISPt EU (t=termnatng, o=orgnatng, a=access charge) as shown n fg. 4. CP and EU pay ther respectve ISP and the ISPs exchange traffc for a fee a. Ths scheme gnores the source of the CP s fundng and emphaszes the analyss of the nter-isp settlement a, whch has an nfluence on the prces pad to the ISPs. By contrast, ths work focuses on the setup EU ISPt CP Adv. as shown n fg. 5. EUs derve utlty from hgh qualty of servce (QoS) access to CPs webstes whle the CPs generate profts from sellng ad space to thrd partes. There s no monetary flow between CPs and EUs. Both, however, may exchange money wth the ISP, whch acts as a proft maxmzng platform. Ths stuaton corresponds to the majorty of today s Internet busness models. CPs create webstes that appeal to many EUs, thus generatng page vews that translate nto value of ad-space on that ste. (Fgs. 1, and 3 focus on physcal nterconnecton whle fgs. 4 and 5 depct the busness vew on connecton relatonshps.) Fg. 4. Fg. 5. Ths CP busness model has receved wde attenton n the two-sded markets lterature as t corresponds to the busness model of newspapers [3, 18, 19]. Ths work, however, does not consder the busness model of the CP but that of the ISP. CPs pay a transacton ndependent prce for drect connecton to EUs through buyng bandwdth from the termnatng ISP. EUs on the other hand pay a flat rate fee to the ISP to be connected to the Internet and no transacton based fee for vewng content. There s no payment between EU and CP. The case wth payments between the CPs and the EUs has been analyzed n [11]. In the sense of the two-sded market lterature we have the followng setup: Platform = ISP, sngle homng sde = EU, mult-homng sde = CP. The platform charges both sdes a lump sum fee for facltatng transactons. Ths s more reasonable than a lnear fee snce for EUs, flat rates are the common prcng model and CPs commonly buy a certan bandwdth or a fxed traffc volume. Furthermore the prce for Internet servces delvered by an ISP mght depend on the data volume but rarely on the value of a transacton. Therefore we assume that there s no lnear payment that reduces the sze of the externaltes exerted on the other sde of the market, respectvely.
6 ISPs as Platforms n Two-sded Markets The analyss n ths secton s related to the compettve bottleneck case of [3]. Compettve bottlenecks arse, when one frm has a monopoly over access to certan customers. Suppose there are two ISPs n a regon denoted ISP, ε {1; }. There are also two groups of agents. Group one agents are called end-users (EUs) whle group two members are called content provders (CPs) or webstes. There s a fracton n j of agents of Group j partcpatng on platform. In other words, ISP has n 1 subscrbed EUs and n drectly nterconnectng customers from the CP sde. The setup s such that two ISPs are present n a market and serve two dstnct groups of EUs wth Internet connectvty. EUs are sngle-homng wth ther ISP. Ths means that they are only subscrbed wth one ISP at a gven tme. CPs on the other hand mult-home. They may be connected to zero, one or two ISPs n order to reach potental customers (EUs). To analyze ths stuaton we start by modelng the target functon of two ISPs that compete n a market for EUs. The ISPs maxmze ther respectve profts. Symbolcally, π = np+ np C( n, n), {1;} (1) 1 1 1 whch s a functon of the number of EUs tmes the prce they have to pay, plus the number of CPs tmes the prce they have to pay mnus the cost for connectng the two types of customers. The fracton n1 [0,1] of EUs that are customers of ISP s gven as a functon of the utltes offered by the two ISPs: j j 1 u1 u 1 n1 = φ ( u1, u1 ) = +, j. () t The functon φ s thus ncreasng n the frst argument and decreasng n the second. j Note that n 1 + n 1 = 1 holds snce EUs do not mult-home. To further specfy the dfferent behavors of EUs, let the fracton of EUs that are sgned up wth ether ISP be descrbed n a Hotellng [13, 3] way. Ths mples that the two ISPs share the market equally f they are undfferentated from the consumers pont of vew. If, however, one ISP offers superor utlty, t can capture more than half of the market. The utlty EUs get from subscrbng to ISP s gven by u = U ( n ) p = α n -p. (3) 1 1 1 1 It equals the gross utlty they get from beng connected wth superor QoS to n drectly nterconnected CPs mnus the prce they have to pay for that connecton. The
Prce Settng n Two-sded Markets for Internet Connectvty 7 functon U s ncreasng n n snce more content n better qualty s always better than less. The parameter α1 can be nterpreted as the utlty an EU derves from beng able to reach one hgh QoS CP. The EUs perceve the ISP wth more CPs connected wth QoS as provdng a better connecton to the Internet. The fracton n [0,1] of CPs that s connected to ISP s gven by p n =φ ( n1, p) = 1-F( γ ) wth γ =. (4) n 1 It s a functon of the number of EUs that can be reached through ISP and the prce charged. The number γ of CPs the ISP can persuade to drectly nterconnect depends on the parameter = p n1. Ths parameter s calculated as the fracton of the fxed prce for connectvty over number of reachable EUs. Thus t can be nterpreted as the perceved prce per EU. The dstrbuton F( γ ) then yelds the fracton of CPs that are not wllng to pay that prce and 1-F yelds the fracton of CPs that are wllng to pay that prce because ther expected revenue per EU covers the expense. The CPs do not deal exclusvely wth a sngle ISP but may be connected to zero, one or two ISPs, dependng on ther partcpaton constrant beng fulflled. Therefore j n general n + n 1. Whle equaton (4) only depends on factors under control of ISP, equaton () also depends on factors controlled by the other ISP. Ths reflects the fact that there s competton for EUs, but none for CPs. Costs for nterconnecton are defned as C ( n, n ) = cn. (5) 1 Ths mplctly ncludes the assumpton that the cost of the access network s not part of the consderatons for nterconnectng wth CPs. Ths assumpton s justfed by the fact that access networks largely represent sunk costs. Now, n order to solve the ISPs optmzaton problem max Π, assume that the platforms have reached an equlbrum and offer utlty u ˆ 1 to ther n ˆ 1 EUs, respectvely. That s, we keep these values fxed whle varyng the others. Ths corresponds to today s stuaton n many markets for DSL or cable. There s some churn, but by and large networks operate n saturated markets wth stable customer numbers. Snce (4) defnes n as a functon of p, we can elmnate p and only have n left as a dependent varable. Thus, gven an equlbrum u1 n 1 ( ˆ, ˆ ), we can solve for the optmal number of CPs n. Rewrtng equaton (3) as p1 = U ( n) u1 we can nsert ths expresson nto (1) to get
8 Π = nˆ ( U ( n ) u ) + p (1 F( p nˆ )) C( nˆ, n ) 1 1 1 1 ( ) = nˆ ( α n uˆ ) + p c n. 1 1 1 n (6) Ths expresson shows that gven an arbtrary equlbrum we can explctly wrte the proft of the platform as a functon of the prce charged to ts group two customers (.e. CPs). The platform can thus easly calculate the optmal prce and the resultng number of CPs, gven ts current compettve stuaton on the EU sde of the market. To gve a concrete example, we defne the dstrbuton F and explctly calculate the proft maxmzng prce p. Let the dstrbuton functon F be gven by the probablty densty functon f ( γ ) = 1τ, γ [ 0; τ ] of the unform dstrbuton. γ represents the expected revenue from ad-clcks per EU and τ represents the maxmum prce a CP s wllng to pay for access to such an EU. The correspondng cumulated dstrbuton functon s F= γ τ = p (7) n1 τ. Any other dstrbuton functon would work as well. However, the normal dstrbuton for example s not easly manpulated and thus would only allow a numercal soluton to the problem at hand. Now we nsert (4) and (7) nto (6) Π = nˆ ( α n uˆ ) + ( p c) n 1 1 1 = nˆ ( α n uˆ ) + (1 n ) τnˆ c n 1 1 1 1 (8) and fnd the maxmzer of the resultng expresson: Π n = nˆα + (1 n ) τnˆ c= 0 1 1 1 c nˆ α 1 n = (1 ). τ nˆ 1 1 1! (9) Ths s the optmal number of CPs the ISP should allow on ts platform (snce the nd order condton for a maxmum holds). Together wth (4) and (7) ths yelds the optmal prce to CPs 1 p ˆ ˆ = ( c+ n1τ n1α1 ). (10)
Prce Settng n Two-sded Markets for Internet Connectvty 9 Therefore, CPs pay a prce that s calculated on the bass of the cost they cause, ncreased by a factor relatng to ther per-eu-valuaton and decreased by the externalty they exert on the EUs. The factor 1 should not be over-nterpreted snce t s an artfact of the defnton of the dstrbuton functon n (7). We thus have calculated the optmal number of CPs and the optmal prce that an ISP should charge atomstc and ex-ante dentcal CPs for qualty nterconnecton. Conclusons and Further Research To sum up, we have frstly explaned two phenomena of the Internet that fundamentally change the way CPs and EUs are nterconnected. CDNs and MH foster more drect lnks between these two user groups wth only one medatng ISP nstead of many. Employng the theory of two-sded markets we then went on to show how drect nterconnecton puts the ISP nto a poston to charge CPs drectly. In the man secton we showed how the optmal prce p can be calculated for any gven equlbrum on the EU sde of the market. Whle today t s uncommon to explctly charge content provders for delverng traffc to ther customers, there are clearly developments n the marketplace that can be understood n the above context. Google s effort to provde free W-Lan to customers n the US s only one example. Google wants to control the platform over whch ts content s delvered so that the profts t makes on the advertsement sde cannot be extracted by ISPs. To nterpret the results obtaned, lets frst compare the predcted prce to today s bll and keep regme. In today s peerng agreements between ISPs, the fee for carryng traffc s very often zero. As [16] pont out, ths corresponds to a subsdy to CPs, snce EUs carry most of the transmsson cost. In our two-sded market framework on the other sde, the CPs have to bear the cost they cause. They may be furthermore charged by the ISP, dependng on ther wllngness to pay. Ths chargng s balanced by a bonus for the externalty they exert on the ISP s EUs. Snce the dfference between beng subsdzed and payng bottleneck prces can be qute large, there wll probably be a transtonal perod before ISPs can leverage ther whole power n chargng CPs. However, the presence of charges to content provders n tself does not represent a market falure. As long as ISPs are competng n the market for EUs, the profts they make on the CPs are used to compete n the EU market [3]. A waterbed effect mght occur, but would merely be a sgn of mperfect competton n the EU market [10]. Secondly, the last term n (10) llustrates a very nterestng result. Imagne that the ISP could perfectly dscrmnate between two dfferent groups of CPs. The group that exerts a hgher externalty on the customers through ts presence would pay a lower prce than the group wth the lower externalty effect. Thus, CPs that are very mportant to EUs wll pay a low prce to the bottleneck ISP, whle those CPs, the presence of whch s less valued by EUs, wll pay a hgh prce for access to EUs. Thus, a power balance could develop, n whch CPs are charged by the network f they have low market power; or charge the network, f ther content s hghly desred by EUs.
10 Lastly, look agan at the externalty exerted by CPs. Here mght le an nterestng opton for future ISP busness models. The ISP could try to capture some of the externalty. Ths could happen for example through transacton dependent charges. Asde from contractual problems ths would fulfll many ISPs long standng vson to capture some of the profts of the content busness. Ths development can already be wtnessed n the moble sector where Vodafone provdes hgh qualty ad-fnanced content to ts customers. An mportant aspect of ths work that requres further research s the effect of the two-sded markets phenomena on the qualty of standard peerngs. As t stands today, peerngs do not generate revenue for ISPs but only costs. Wth CDN and MH generatng revenues there s obvously a strong ncentve for ISPs to move as many CPs as possble to a payng nterconnecton model. The ultmate consequence of ths would be that, n order to foster a self selecton process, standard peerng qualty would be consderably degraded to make sure that all customers wth a wllngness to pay are n the payng group. Whle such prce dscrmnaton s welfare enhancng, t s crucally mportant the market for EUs s compettve snce otherwse, ISPs are n a poston to approprate rents. Ths paper demonstrates the use of two-sded market theory to analyze the decson problems faced by Internet servce provders n more complex setups then the standard peerng scenaro examned n earler works. A frst analyss demonstrates that new busness models such as content delvery networks and mult-homng can fundamentally change the rules for nterconnecton prcng. Ths work thus extends the work on Internet nterconnecton [16] and the work on voce nterconnecton such as [15] or [] (as well as the references cted theren). As ths s only a frst step towards a thorough understandng of the new rules of nterconnecton prcng brought about by new nterconnecton regmes, there remans consderable work to be done: Frstly, the presented analyss cuts short some more n depth equlbrum analyss by assumng a market equlbrum as gven. Furthermore, a more thorough analyss of the effects of the ISPs actons on the secondary markets for advertsements would be nterestng. How do two vertcally dependent two-sded markets nteract? In a smlar lne of thought, the aspect that CDNs are ntermedares between ISPs and CPs has been used as a startng pont of the analyss but s then gnored n the further analyss. Ths can be justfed by assumng that CDNs only pass on costs but ther role certanly deserves more attenton, especally snce CDNs are potent players n the Internet market. A further topc to be analyzed s the role of peer to peer traffc. The paper has shown an aspect of the qualty of servce debate that has been underresearched. The market for Internet nterconnecton has a consderable nfluence on the delverable qualty of Internet servces. Understandng these markets (the contrbuton of ths work) and engneerng them to functon better (future research) propose challengng research topcs that mght shape the next generaton of networks.
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