Pricing for Local and Global WiFi Markets

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1 1 Prcng for Local and Global WF Markets Lngje Duan, Member, IEEE, Janwe Huang, Senor Member, IEEE, and Byng Shou arxv: v1 [cs.gt] 16 Jul 014 Abstract Ths paper analyzes two prcng schemes commonly used n WF markets: the flat-rate and the usage-based prcng. The flat-rate prcng encourages the maxmum usage, whle the usage-based prcng can flexbly attract more users especally those wth low valuatons n moble Internet access. Frst, we use theoretcal analyss to compare the two schemes and show that for a sngle provder n a market, as long as the WF capacty s abundant, the flat-rate prcng leads to more revenue. Second, we study how a global provder e.g., Skype collaborates wth ths monopolst n each local market to provde a global WF servce. We formulate the nteractons between the global and local provders as a dynamc game. In Stage I, the global provder bargans wth the local provder n each market to determne the global WF servce prce and revenue sharng agreement. In Stage II, local users and travelers choose local or global WF servces. We analytcally show that the global provder prefers to use the usage-based prcng to avod a severe competton wth the local provder. At the equlbrum, the global provder always shares the majorty of hs revenue wth the local provder to ncentvze the cooperaton. Fnally, we analytcally study how the nteracton changes f the local market has more than one local provder. In ths case, the global provder can ntegrate the coverages of multple local provders and provde a better servce. Compared to the local monopoly case, local market competton enables the global provder to share less revenue wth each of the local provders. However, we numercally show that the global provder s revenue could decrease, as he shares hs revenue wth more provders and can only charge a lower prce. Index Terms WF markets, Flat-rate prcng, Usage-based prcng, Nash barganng, Collaboraton and competton 1 INTRODUCTION The standard based wreless local area network technology, also known as WF, s one of the most successful stores n modern wreless communcatons []. Operatng n the unlcensed.4ghz and 5GHz spectrum band, WF networks do not requre exclusve spectrum lcenses as ther cellular counterparts, and can provde hgh-speed wreless access to moble users wthn tens to hundreds of meters of WF access ponts APs [3]. Furthermore, APs n WF networks are nexpensve and can be easly deployed and mantaned [4]. These explan why the annual revenue n the WF ndustry s growng rapdly n recent years and s expected to worth $93.3 bllon by 018 e.g., [5], [7]. In order to provde close to seamless hgh performance moble communcaton experences, many WF provders e.g., AT&T n US, BT Openzone n UK, Pass n some EU countres, and PCCW n Hong Kong are deployng a large number of WF APs n ther local markets. For example, Pass has set up more than 1. mllon publc WF venues, and hs revenue keeps growng 14 Lngje Duan s wth Engneerng Systems and Desgn Pllar, Sngapore Unversty of Technology and Desgn, Sngapore. Janwe Huang s wth the Network Communcatons and Economcs Lab, Department of Informaton Engneerng, The Chnese Unversty of Hong Kong, Hong Kong. Byng Shou s wth the Department of Management Scences, Cty Unversty of Hong Kong, Hong Kong. Emal: lngje duan@sutd.edu.sg, jwhuang@e.cuhk.edu.hk, and byng.shou@ctyu.edu.hk. Part of the results appeared n IEEE INFOCOM 013 [1]. Ths work s supported by the SUTD-MIT Internatonal Desgn Center Grant Project no.: IDSF100106OH, SUTD Start-up Research Grant Project no.: SRG ESD 01 04, and the General Research Funds Project Number CUHK and CUHK establshed under the Unversty Grant Commttee of the Hong Kong Specal Admnstratve Regon, Chna. Ths work s also partally supported by the Hong Kong General Research Fund Project No. CtyU and grants from Cty Unversty of Hong Kong Project No and percent quarter-over-quarter reachng $0.3 mlllon n the second quarter of 013 [6]. In the Hong Kong market alone, PCCW has ncreasngly rolled out more than twelve thousand publc APs coverng almost all popular places e.g., convenent stores and shoppng malls, coffee shops and hotels, tran statons, and educaton nsttutes. Note that some of these provders e.g., AT&T and PCCW are also cellular operators; however, they provde the WF servces separately from ther cellular data plans to cater to moble devces wthout ntrnsc cellular connectvty e.g., tablets and laptops as well as users who are not ther current cellular subscrbers but are wllng to use ther WF servces. Generally, cellular data servces and WF servces target at dfferent users: one supportng hgh user moblty and the other supportng hgh data throughput. For many local provders, we often observe them chargng local users subscrbers a monthly flat fee e.g., [8] [10], where a user pays a fxed amount per month ndependent of the actual usage. Ths motvates us to ask the frst key queston n ths paper: Why does a local WF provder prefer to charge hs local users a flat fee nstead of a usage-based fee? Notce that a WF AP can serve not only local users, but also travelers who vst a partcular cty/country for a short perod of tme. But payng a monthly flat fee s often not a good choce for a traveler. To cater to the needs of travelers, Skype has poneered n provdng a global WF servce under the band name of Skype WF, through collaboratng wth many local WF provders who own a total of more than 1 mllon WF APs worldwde [11]. Once a user subscrbes to the Skype WF servce, he can use any of the assocated WF AP wth hs Skype account, and pays accordng to usage wth hs Skype Credt.e., only pays for the tme you

2 are onlne, as Skype puts t. Such flexble Skype WF servce provdes great convenence for travelers, but also ntroduces competton wth local WF provders among local users. In order to promote such cooperaton, Skype needs to share part of the revenue wth the local WF provders who provde the physcal WF APs. Thus, the local WF provders wll have ncentves to collaborate wth Skype and share ther nfrastructure only f they can also gan from ths new servce. Ths motvates us to ask the second key queston n ths paper: Why does a global provder choose usage-based prcng for hs global WF servce, and how should he share the benefts wth the local WF provders? To answer the frst key queston, we focus on a local market wth a monopolstc local WF provder and a group of local users. We model ther nteractons as a two-stage Stackelberg game: the local provder leader determnes prcng scheme flat-fee or usage-based n Stage I, and local users followers decde whether they wll subscrbe to the servce and how much to use n Stage II. We show that the flat-fee prcng can offer a hgher revenue than the usage-based prcng for such a monopolstc local provder. To answer the second key queston, we study how the global provder may provde a global WF servce by cooperatng wth local provders, gven the local provders optmal flat-fee based prcng. We formulate the problem as a twostage dynamc game. In Stage I, the global provder negotates wth each local provder about the global WF prce and the revenue sharng porton based on Nash barganng. In Stage II, local users choose between the global and local provders servces, and travelers choose ther usage levels n the global WF servce. Our key results and contrbutons are as follows: Flat-fee prcng domnates the local WF markets: In Sectons, 3 and 4, we study the prce choces of a monopolstc local provder. We analytcally show that the flat-rate prcng s effectve n attractng the hgh-valuaton users, whle the usage-based prcng s attractve to the low-valuaton ones. When the WF capacty s abundant, the local provder wll choose the flat-fee prcng as t brngs more revenue. Wn-wn stuaton when the global provder chooses the usage-based prcng: In Secton 5, we analytcally show that the global WF provder prefers the usage-based prcng, n order to avod severe competton wth local provders. Such prcng scheme also attracts those not served by local provders e.g., local users wth low-valuatons and travelers from other markets, and hence ncreases the total revenue n the market. When the revenue s shared properly, the global provder and each local provder acheve a wn-wn stuaton. Nash barganng on the global WF prce and revenue sharng: In Secton 6, we decompose the nteractons among dfferent local markets and study each of them separately. We analytcally show that the global provder always needs to share the majorty of hs revenue wth local provders, to compensate the provders revenue loss due to compettons and ncentvze them to share the nfrastructure. If the local user populaton decreases or the traveler populaton from other markets ncreases, the global provder has a larger barganng power and gves away less revenue. Impact of local market competton: In Secton 7, we extend the analyss n the monopolstc local market to a compettve market. We analytcally show that the local provder competton reduces the market prce and attracts more users. The competton provdes more ncentves for local provders to collaborate wth the global provder, and enables the global provder to share less revenue wth each provder. However, we numercally show that the global provder s revenue could decrease, as he can only charge a lower prce and wll share revenue wth more provders. 1.1 Related Work The recent lterature on WF prcng can be dvded nto three categores. The frst category focuses on how a local provder optmzes the prce or multple provders compete on ther prces to maxmze ndvdual revenues e.g., [14], [15], [3]. These results often gnored the WF s lmted coverage and the users movements across dfferent WF markets. Moreover, they often assumed ether flat-rate prcng or usage-based prcng, wthout an analytcal comparson between the two schemes. 1 The second category focused on the perspectve of an ndvdual WF AP owner, who charges vstors for usng hs AP s resources e.g., [17] [19]. The key desgn challenge here s the asymmetrc nformaton,.e., vstors know more about ther own utlty functons than the AP owner. The thrd category studed wreless socal communty networks, where WF owners form a communty to share ther APs wth each other, so that one AP owner can use other APs to access the Internet durng travel e.g., [4], [0]. In ths lne of lterature, the man desgn objectve s to encourage as many AP owners to jon the communty as possble. The revenue maxmzaton becomes a secondary concern. In ths paper, we study the optmal prcng schemes n both local and global WF markets. We consder several key and practcal features of WF networks e.g., WF s lmted coverage and users movement across dfferent WF markets, and compare the pros and cons of the flat-rate and the usage-based prcng. Furthermore, we are the frst to study how a global WF servce provder such as Skype may cooperate wth local provders, negotate prcng and revenue sharng schemes, and acheve a wn-wn stuaton. There are some other works studyng how a monopoly provder uses a supplementary network technology to 1. Although Lee et al. [16] consdered varous prcng schemes, the proposed usage-based prcng does not apply to our WF servces.

3 3 mprove the exstng one e.g., usng WF networks to offload heavy data traffc from cellular networks to avod congeston e.g., [1], []. Unlke those studes, our study focuses on the publc WF servce market, and tres to understand the ssue of servce prcng and collaboraton/competton locally and globally. 1. Taxonomy The followng terms wll be used throughout ths paper. Local provder: A WF provder who deploys APs to provde servce to a sngle regon. For example, PCCW serves the Hong Kong market only, and AT&T serves the USA market only. Global provder: A WF provder who serves multple local markets, by usng the network nfrastructure APs of the correspondng local provders. For example, the Skype WF servce covers many countres wth collaboratons wth local provdes, but Skype does not own any physcal WF APs. Local market: A market that s served by one or multple local provders and possbly by a global provder. There are a set I = {1,,...,I} of dsjont local markets. Intally we wll assume that each local market has a sngle local provder. In Secton 7, we wll further look at the case where there are multple local provders n the same market. Local user: A user who lves n a partcular local market as a long-term resdent. There are N local users n each local market I. Traveler: When a user travels to a market other than hs own local market, he becomes a traveler. We use the parameter α j [0,1] to denote the percentage of users n a local market j who are wllng to pay short-term vsts to local market, and thus the total travelers from market j to s α j N j. USAGE-BASED PRICING FOR LOCAL WIFI We wll frst study how a local provder n a local market optmzes the prce to maxmze the revenue, assumng that he chooses the usage-based prcng. In Secton 3, we wll derve the optmal prcng term should the local provder choose to use the flat-fee prcng. In Secton 4, we wll compare these two cases, and show that flatfee prcng always brngs more revenue than the usagebased prcng n the local WF servce. We consder a two-stage dynamc game between a local provder and a group of N local users. In Stage I, the provder announces the prce p per unt of usage tme to maxmze hs revenue. In Stage II, users decde whether and how much to use the servce to maxmze ther payoffs. As there are two stages n ths game and the provder s the only leader followed by users, ths s also a Stackelberg game. At a Subgame Perfect Equlbrum SPE, or smply equlbrum of the game, the provder and users wll not have ncentves to change ther prcng and usage choces. Next we wll analyze the equlbrum of the game usng the backward nducton [4]. We wll frst study the users decsons n Stage II for any gven prce, and then look at how the provder should optmze the prce n Stage I by takng the users decsons nto consderaton..1 Stage II: Users Usage Choces Due to the lmted number of APs, a local WF provder typcally cannot provde a complete coverage n a regon. Let us denote the local provder s WF s coverage as G M 0,1, where M s the total number of deployed APs. In ths paper, we wll assume that M s fxed, and thus wll smply wrte G M as G. Notce that today s WF technologes support hgh data throughput and the comng WF technology IEEE 80.11ac further offers a much larger throughput up to Mbt/s per user [1]. Hence, the network congeston s usually not a major ssue n such WF networks. Furthermore, the FCC has decded to dramatcally expand the unlcensed spectrum for use by WF devces and hence wll effectvely mtgate possble WF congeston n the near future [13]. Note that the WF deployment cost s fxed and s related to G, and the optmal prcng decsons are not affected by the cost, as long as the maxmum revenue can compensate the cost. When a local user n market s n the WF coverage, we denote hs usage level as d [0, 1], whch represents the percentage of Internet connecton tme over the whole tme n WF coverage. For example, d = 1 means that the user always stays onlne whenever WF s avalable. Dfferent users may demand dfferent usage levels as they have dfferent valuatons towards Internet connecton. We characterze such a valuaton by a type parameter θ. Unlke d, the parameter θ s not a decson varable. A largerθ mples the user s hgher valuaton of the Internet access tme. Lke many other studes n ths feld, we assume that θ follows a unform dstrbuton n [0, 1] for analyss tractablty and the relaxaton to more general dstrbutons s unlkely to change the man engneerng nsghts e.g., [16], [17], [5]. We further assume that a type-θ user s utlty uθ,d s lnearly ncreasng n θ and concavely ncreasng n d. The concavty assumpton s to represent hs dmnshng return n Internet access tme. One commonly used utlty functon satsfyng our requrement s 3 uθ,d = θln1+kd, 1 where the parameter k > 0 represents the elastcty of demand,.e., the rato between the percent change of demand and the percent change of prce [8]. In economcs and marketng, the usual way to obtan the value. We assume that moble users tme-varyng locatons follow Posson pont process PPP, and thus each user has the same expected total tme normlzed by G wthn the WF coverage durng a perod of tme e.g., one month. Each user s total WF actual connected tme s hence G f the demand level d = The logarthmc utlty s wdely used n the networkng lterature to model elastc applcatons e.g., [6], [7].

4 4 of k s through extensve market survey and statstcal analyss [9]. As t s dffcult and costly to track each user s demand elastcty, t s common to examne users aggregate behavor and use an dentcal k for all users to represent the average elastcty. Unlke k, t s relatvely easy to estmate the dstrbuton of wllngness to pay.e., θ n marketng. When usng the servce, a user needs to pay lnearly proportonally to hs usage tme and the unt prce p. Ths s motvated by the fact that many provders charge based on connecton tme nstead of data volume. As the user s usage and payment are only meanngful when he s wthn the WF coverage, hs overall payoffv s lnear n the coverage G, 4 v θ,p,d = G θln1+kd p d. Maxmzng payoff v over d leads to the optmal usage level θ d θ,p = mn max 1 p k,0,1, 3 whch s ncreasng n the user s ndvsual type θ and the common elastcty parameter k, and s decreasng n prce p. Furthermore, only users wth θ p /k wll have a postve usage.e., subscrbe to the servce. Next we explot how users optmal usage levels change wth the prce p. By assumng that the two terms n the mn operaton n 3 are equal at θ = 1, we can derve the followng prce threshold: p th = k k When the prce p s less than p th, some hgh valuaton users wll choose dθ,p = 1. Otherwse, all users wll request a usage level less than 1 can be zero f θ s very small. We wll dscuss these two scenaros n Stage I.. Stage I: The Local Provder s Prcng Choce..1 Low prce regme: p < k/k +1./01$&"%&/. "#$%&#'#*+,#-&,,#*+ 0 p 1 p1 k 1 k k Fg. 1. Users WF usage choces n the low prce regme Fgure 1 summarzes users optmal usage levels n ths case. There are three categores of users based on the type parameterθ: a user wth a small type θ [0,p /k wll not subscrbe to the WF servce, a user wth a medum type θ [p /k,p 1+k/k wll subscrbe wth a partal usage level.e., d θ,p = θ/p 1/k < 1, and a user wth a hgh type θ [p 1+k/k,1] wll have 4. A moble user wll start to consder hs network usage level d after detectng the WF sgnal.e., nsde the coverage of G from tme to tme, and wll not decde a total usage level G d beforehand. Thus we model the user s utlty as G θln1+kd n, where the lnear term G can be vew vewed as the tme frequency to use d. " the maxmum usage.e., d θ,p = 1. The provder s total revenue collected from the latter two user categores s pk+1 k π p = N G p p k = N G p p θ 1 1 dθ + 1dθ p k p k+1 k k By checkng the frst and second order dervatves of π p, we can show that π p s concave n p. Thus the optmal prce that maxmzes the revenue n the low prce regme s p L = k k +. 6 The provder s maxmum revenue n the low prce regme s π p L = N k G k Hgh prce regme: p k/k +1,-./$&"%&-, "#$%&#'#*+ 0 1 p 1 k Fg.. Users WF usage choces n the hgh prce regme Fgure summarzes users optmal usage n ths case. There are two categores of users under such a prce: a user wth a low typeθ [0,p /k wll not subscrbe to the WF servce, and a user wth a hgh type θ [p /k,1] chooses to subscrbe the WF servce wth a partal usage level.e., d θ,p = θ/p 1/k < 1. The provder s total revenue collected from the second user category s π p = N G p 1 p k θ p 1 k The frst order dervatve of 8 over p s dπ p dp dθ = N G 1 p k + p k 8 = N G p k k. 9 Notce that to obtan a postve revenue, the provder should set the prce such that the hghest type user s wllng to subscrbe,.e., d 1,p = 1/p 1/k > 0. Ths means p < k, whch mples 9 s negatve. Thus the optmal prce n the hgh prce regme s p H = k k +1, whch s the boundary case of the low prce regme. Summarzng the results from both prce regmes, we have the followng result. Proposton 1: The provder s equlbrum usage-based prce that maxmzes hs revenue s p = k k +, 10.

5 5 whch s ncreasng n the elastcty parameter of demand k and s ndependent of coverage G. The provder s maxmum revenue under the equlbrum usage-based prcng s π p = N k G k The ndependence of p n G s due to the fact that a user only pays when he uses the servce n the WF coverage area../01$&"%&/. "#$%&#'#*+,#-&,,#*+ 0 1 k 1 k 1 k 1 Fg. 3. Users WF usage choces at the equlbrum usage-based prcng Fgure 3 summarzes all users usage behavors at the equlbrum. The flexblty of usage-based prcng attracts the majorty of users to the servce, snce the threshold type p /k = 1/k + < 1/. As the elastcty parameter k ncreases, the type threshold wll decrease and more users wll jon the servce. Users total usage level, however, s D p = N G p 1+k k p k θ p 1 k " 1 dθ + p 1+k k 1dθ = N G /, 1 whch s ndependent of k. 3 FLAT-RATE PRICING FOR LOCAL WIFI Smlar to Secton, n ths secton we also consder a two-stage Stackelberg game played by the provder and N users. The dfference s that the provder wll announce a flat-fee n Stage I, and users decde whether to subscrbe to the servce n Stage II. Snce a user s payment s ndependent of hs usage level, he wll always choose the maxmum usage tme d = 1.e., stay onlne whenever the user s n the WF coverage area whenever he subscrbes. Next we derve the game equlbrum by usng the backward nducton. 3.1 Stage II: Users Subscrpton Choces In Stage II, by jonng the flat-rate prce plan, a type-θ user s payoff s v θ,p = G uθ,1 P = G θln1+k P. 13 Notce that the flat fee P s ndependent of usage, and thus s also ndependent of whether the user s n the WF coverage area. In other words, once a user subscrbes to the WF servce, he wll be charged a flat fee at the end of that month. Ths means that the effectve prce consderng the lmted coverage s P := P /G > P. It s clear that only users who have hgh valuatons of moble Internet access would subscrbe to the WF servce and obtan a postve payoff. The mnmum type parameter θ among the actve users s θ th P = P G ln1+k Stage I: The Local Provder s Prcng Choce In Stage I, the provder wants to maxmze hs revenue by collectng payment from users wth θ [θ th P,1],.e., max π P = N P 1 P 0 P. 15 G ln1+k It s easy to verfy that π P s concave n P, and we can derve the optmal prce as follows. Proposton : The provder s equlbrum flat-rate prce that maxmzes hs revenue s P = G ln1+k/, 16 whch s ncreasng n the coverage G and elastcty parameter k. The provder s maxmum revenue wth the equlbrum flat fee s π P = N 4 G ln1+k, 17 whch s ncreasng n G and k. *+'&,'-.%/0%+* "#$%"&"&'# Fg. 4. Users WF usage choces at the equlbrum flatfee prcng Fgure 4 summarzes users usage behavors at the equlbrum. Comparng wth Fgure 3, the nflexblty of the flat-fee prcng scheme attracts fewer users 1/ nstead of k+1/k+ than the usage-based scheme. Intutvely, a better WF coverage and a larger elastcty parameter encourage more users to jon the WF servce, and the provder can charge more. Users total usage s D P = N G, 18 whch s the same as n the usage-based prcng case n 1. Ths s because users consume more on average wth the flat-fee prcng. 4 FLAT-RATE OUTPERFORMS USAGE-BASED PRICING FOR LOCAL WIFI SERVICE Now we are ready to compare the two prcng schemes and see whch one leads to a larger provder revenue. Let us defne the rato between the equlbrum revenues of the flat-rate prcng scheme and the usage-based prcng scheme as r := π P /π p. Based on 11 and 17, we can rewrte the rato as a functon of k,.e., rk = k +ln1+k. 19 k

6 6 The frst order dervatve of rk over k s drk dk = kk +/k +1 ln1+k k, 0 and we can show that such a dervatve s postve for all postve values of k. Usng L Hosptal law, we can show that lm k 0 rk = ln1+k+k +/k +1 = 1. k=0 Ths means that rk > 1 for any k > 0. Thus, we have the followng result. Theorem 1: A local provder can obtan a larger revenue wth the flat-rate prcng than wth the usagebased prcng. The revenue gap ncreases n the elastcty parameter k. Theorem 1 s consstent wth the current ndustry practce, where most WF provders offer flat-rate prcng nstead of usage-based prcng n local markets e.g., Orange n UK [9], AT&T n US [10], and PCCW n Hong Kong [8]. Another beneft of the flat-rate prcng that s not explctly modeled here s that t s easy to mplement wth lttle overhead for bllng, whle the usagebased prcng requres the provder to record users moble traffc for payment calculaton and collecton over tme [30]. 4.1 Impact of WF Congeston When a large number of users try to access the same WF network, they may experence network congeston, whch wll reduce some of ther nterests to jon the local WF servce. In the followng, we take the congeston nto account n our local WF model and evaluate the mpact of congeston on the prcng choce. Let us denote the WF congeston coeffcent cb, whch s related to the WF bandwdth B and models the congeston cost for one unt of WF demand. We also denote the mnmum type parameter θ among the WF subscrbers as θ th, and users wth θ [θ th,1] wll subscrbe Usage-based prcng under congeston We frst analyze users best decsons n Stage II and then solve the provder s problem n Stage I by predctng users best responses. By ncorporatng the congeston cost nto, the payoff of a user wth θ θ th by demandng a usage level d s 1 v θ,p,d = G θln1+kd p d cn d θ,p dθ, θ th 1 where d θ,p s the optmal demand of user type-θ. As each WF subscrber s nfntesmal non-atomc n contrbutng to the congeston term n 1, hs optmal demand as long as hs payoff s non-negatve s not affected by the congeston and s the same as 3. That s, d θ,p = mnmaxθ/p 1/k,0,1. As the user wth type θ = θ th s ndfferent n choosng between WF and not, hs normalzed optmal payoff by G s zero. Thus, we can derve the unque soluton θ th accordng to the followng equaton: v θth θ th,p /G = θ th ln 1+kmn max 1 p k,0,1 θth p mn max 1 1 p k,0,1 cn d θ,p dθ = 0, θ th We can see that θ th here becomes larger because of congeston, and fewer users wll subscrbe. As θ th depends on the servce prce p, we rewrte t as θ th p. By predctng ths, the provder s revenue-maxmzaton problem s 1 maxπp = p N G mn p θ th p θ max 1 p k,0,1 dθ. 3 We can show that Problem 3 has no closed-form soluton, but can be solved effcently and numercally through an one-dmensonal exhaustve search about prce p Flat-rate prcng under congeston A WF subscrber does not care about hs contrbuton to the congeston and t s stll optmal for hm to demand a full usage level d = 1. Under network congeston, a type-θ user s payoff s changed from 13 to 1 v θ,p = G θln1+k cn 1dθ P, 4 θ th whch s zero for the ndfferent user wth θ = θ th. Then user partton threshold for subscrpton s θ th P = P /G +cn ln1+k+cn, whch depends on the flat-rate prce P and s larger than 14 due to congeston. In Stage I, the provder s optmzaton problem s max P π P = P N 1 P /G +cn, ln1+k+cn whch s a concave functon np and ts optmal soluton P = G ln1+k/. Ths s the same as 16 and s ndependent of congeston level. The resultant revenue s π P N G ln1+k = 41+cN /ln1+k, 5 whch s decreasng n congeston coeffcent c. Now we are ready to compare the provder s optmal revenue under the two prcng schemes. As there s no closed-form soluton to Problem 3, we rely on numercal results. Fgure 5 shows the provder s optmal revenue rato π p /π P between usage-based and flat-rate prcng. As the congeston coeffcent c ncreases or the local user populaton N ncreases, the network congeston n the WF servce ncreases and flat-rate prcng not adaptve to congeston level wll eventually lose ts advantage over the usage-based prcng.

7 7 Proft rato between usage and flat rate prcng N =100 N =150 N = Congeston coeffcent c Fg. 5. The optmal proft rato π p /π P between usage-based and flat-rate prcng 5 GLOBAL WIFI SERVICE Now let us look at the WF servce n a global market by nvestgatng the fact of Skype s global WF operaton. If one company wants to provde a global WF servce, he can ether densely deploy APs worldwde or cooperate wth many local WF provders. The former approach typcally requres an extremely large nvestment, whle the latter approach s more feasble. In fact, today a global provder e.g., Skype uses the latter approach to provde a global WF servce called Skype WF, whch nvolves more than 1 mllon APs deployed by many local provders worldwde e.g., Best Western n US, BT Openzone n UK, and PCCW n Hong Kong. To motvate the cooperaton of local provders, Skype shares some of hs WF revenue wth these cooperators [31]. Here s what each sde wll gan and lose durng ths cooperaton. Skype s gan: Skype can gan extra revenue by provdng WF servce. Skype used to be just a software provder wthout any physcal WF nfrastructure. Wth the cooperaton and a usage-based prcng, Skype s able to serve travelers who are not wllng to sgn a long-term contract wth local provders. Furthermore, Skype can attract some low-valuaton local users who do not subscrbe to the flat-fee local WF servce, or prefer usage-based prcng to the flat-fee prcng. Durng ths process, Skype needs to share part of the revenue wth the local WF provders to acheve a wn-wn stuaton. Local provder s beneft and loss: When Skype starts to provde WF servce n a local market, the local provder wll experence new market competton and a reduced number of subscrbers. However, as Skype reles on the local provder s WF nfrastructure, the provder has the market power to negotate wth Skype on Skype WF s prce to avod severe competton. 5 Furthermore, he can share part of the Skype s revenue to compensate hs loss and potentally ncrease hs total revenue. The slogan of Skype WF s only pay for the tme you re onlne usage-based prcng. Note that Skype has the followng three advantages over many local provders to mplement a usage-based prcng. Exstng mechansm to record users traffc: Skype can use the same traffc recordng system n Skype WF as n the exstng Skype Internet Call Servce. Trustworthy global bllng system: Skype has bult a reputable global bllng platform wth hs exstng servces. As Skype has successfully cooperated wth many local telecommuncaton companes on offerng the Skype Internet Call Servce, t s easy for Skype to convnce local WF provders to be new collaborators. Hgh market penetraton and brand vsblty: Skype has a more than 600 mllon users and can easly advertse the Skype WF servce globally, whle many local provders have lttle brand vsblty outsde ther local markets. Even wth these advantages, one may stll wonder why Skype does not choose the flat-fee prcng, as what the local provders are dong for local WF servces. Our analyss shows that one key reason s for Skype to avod severe competton wth local provders n order to reach a wn-wn stuaton. To make the dscusson more concrete, let us frst look at the users choces. After Skype s entry, a user n hs own local market can choose between the local WF servce and Skype WF servce. When the user travels to a dfferent market, he wll only choose Skype WF as he does not want to pay a monthly flat fee n a dfferent market. Now consder the possblty of Skype adoptng the flat-rate prcng scheme for the global WF servce. Ths can further nclude two varatons: a market-dependent flat-rate prcng and a market-ndependent one. In the market-dependent scheme, a user needs to pay a separate flat-rate prce for each market ether local or foregn he mght enter. In ths way, Skype WF s just replcatng many local servces at a global scale. Ths leads to drect competton wth local provders n each local market e.g., all local users n a market wll choose Skype WF f hs flat-fee s lower than the correspondng local provder s prce. Furthermore, such a scheme s not attractve to a user who travels n many markets, as more markets means a hgher total payment. In the market-ndependent scheme, a user subscrbng to Skype WF only needs to pay a sngle flat fee to receve servces n all markets. Then many users no longer need to use the local WF servce. To summarze, n each of 5. For smplcty, we assume that a local provder wll stll charge the same flat fee P n 16 after Skype s entry. In practce, a local provder may not be able to change the flat-rate prce very often due to the reputaton ssue [6].

8 8 the two cases, the local WF provder wll suffer from Skype s flat-fee prcng, and wll not have the ncentve to cooperate. Ths can explan why n practce Skype chooses the usage-based prcng scheme. 6 OPTIMAL USAGE-BASED PRICING SCHEME FOR GLOBAL WIFI PROVIDER Now we wll analyze the optmal usage-based prcng scheme for the global WF provder. We wll consder the market-dependent usage-based prcng scheme whch s Skype s current practce, where a user pays dfferent usage-based prces when he s n dfferent markets.the market-ndependent usage based prcng s a specal case of the market-dependent one. Under such a scheme, we can model the nteractons between the global provder, a local provder, and local users as well as travelers n market as a two-stage dynamc game. In Stage I, the global provder and the local provder jontly and the revenue sharng porton η as a compensaton of usng provder s network nfrastructure. In Stage II, each of the N local users chooses between the global provder s WF and the provder s local servce and the usage level f choosng global WF, and travelers decde ther usages of the global WF servce. As there s more than one leader the global and local provders n Stage I, ths game s no longer a Stackelber game but a twostage dynamc game. In the followng, we use backward nducton to examne Stage II frst. decde the global WF usage-based prce 6.1 Stage II: Local Users and Travelers choces Consder a total of I markets n the global market. A type-θ local user n the local market has two types of demands: Demand n hs local market: he can choose global WF s usage-based prce wth the optmal usage d θ, as n 3 or provder s flat-rate prce P n 16 wth the optmal maxmum usage d θ,p = 1. Demand when he travels n non-local markets: he wll only choose global WF s usage-based prces n other I 1 markets. The probablty for ths user travelng to a market j s α j < 1. By demandng a usage level d θ, j n market j as n 3, ths user s aggregate payoff n all non-local markets s α j G j u θ,d θ, j j d θ, j. j Apparently, the user s usage n non-local markets the second type of demand does not affect hs choce of servce n the local market the frst type of demand. To study a local user s local servce choce, we can smply compare hs optmal local payoff f usng global WF, v Glob = G θln1+kd θ, d θ, to the optmal payoff f subscrbng to the provder, v = G θln1+k P. Fg. 6. Local users usage n market wth a low global WF prce. All usage are wth the global WF. Fg. 7. Local users servce choces n market n the medum global WF prce regme. In the followng, we analyze the local users equlbrum behavors gven any possble value of. 6 To facltate analyss n ths secton, we assume the elastcty parameter of demand k = 1 and utlty uθ,d = θln1 + d. Smlar to Sectons, 3 and 4, our results here can be extended to the case wth any postve k value. Proposton 3: At Stage II, local users equlbrum decsons n market depend on the global WF prce as follows: Low prce regme ln/: no local users wll choose provder s local servce. Users wth types θ [,1] wll choose global WF. Ther equlbrum usage levels are llustrated n Fg Medum prce regme ln/ < 1/: both local provder and the global provder have postve numbers of local subscrbers. Fgure 7 llustrates local users servce subscrptons, where there are three categores of users dependng on ther valuatons: a user wth the type θ [0, wll not choose any servce, a user wth the type θ [,θ th wll choose global WF, and a user wth the type θ [θ th,1] wll choose local provder s servce. The threshold type θ th s the unque soluton to θ θ th th ln θ th + θ th 1 ln = 0, 6 whch satsfes θ th <.e., d θ th, < 1, and θ th s decreasng n. Provder s local servce targets at hgh-valuaton users, whereas global WF targets at low-valuaton users and none of global WF subscrbers request maxmum usage level. Hgh prce regme > 1/: no local users wll choose global WF. Users wth types θ [1/,1] choose Provder s servce as n Fg. 4. The proof of Proposton 3 s gven n Appendx A. We also provde all appendces n [?]. Note the thresholds ln/ and 1/ dentfy whether the global WF prce s low enough to attract all local users or hgh enough to 6. Note that the revenue sharng decson η n Stage I does not affect users decsons n Stage II. 7. The result n Fg. 6 s consstent wth Fg. 1, as here we set k = 1.

9 9 Fg. 8. Travelers usage choces n market n global WF n the medum prce regme attract no local users, respectvely. Both thresholds are less than 1 as they cannot exceed the maxmum user type θ = 1. Proposton 3 shows that two servces wll coexst only n the medum global WF prce regme, when the two prces are comparable to each other. When decreases n ths regme, more local users wll swtch from the local provder to global WF, resultng n a larger partton threshold θ th. Moreover, θ th only depends on and s ndependent of WF coverage G, as both servces compete wth each other usng the same network nfrastructure. 6. Stage I: Negotaton Between Global and Local Provders As the low and hgh prce regmes n Proposton 3 wll drve ether local provder or the global provder out of the local market, they are not lkely to be vable choces for the negotaton n Stage I. In fact, we can prove that the medum prce regme s the only practcal choce for the whole game equlbrum. Theorem : In Stage I, the global provder and local provder wll only agree on a global WF prce n the medum prce regme.e., ln/ < 1/ as long as the local user number s nontrval compared to the traveler number from other markets. 8 The proof Theorem s gven n Appendx B. Next we focus on the medum prce regme and study the revenues for both the global provder and Provder. Frst consder the global provder, who gans revenue by servng both local users and travelers n market, but needs to share η porton of hs revenue from market to local provder for usng the local WF nfrastructure. Global WF s revenue from other markets s not related to local provder, and can be normalzed to 0 n the followng analyss. By servng local users wth types θ [,θ th π Glob, the global provder collects a total payment η,,θ th = 1 η θ th N G d θ, dθ We rule out the extreme case where the local user number s trval compared to the traveler number.e., N / j α j N j 0, n whch case the global provder wll become the monopolst n market wth the monopoly prce of 1/3 n the low prce regme and serve the travelers only. It s clear that n the majorty of markets the number of local users should be much larger at least comparable to the traveler number. Actually, a small number of local users cannot compensate the ntal deployment cost of a large-scale WF network and does not allow the exstence of a local provder n the frst place before the global provder s entry. However, for the purpose of completeness, we stll provde the analyss for ths extreme case n Appendx B. wth d θ, = θ/ 1. As for travelers n market, they can be dvded nto three categores dependng on ther valuatons and ndependent of where they come from as n Fg. 8: travelers wth types θ [0, demand zero usage, travelers wth types θ [, demand partal usage, and travelers wth types θ [, 1] demand the maxmum usage. Smlar to 5, we can derve that the total payment collected by the global provder from the travelers n market as π Glob η, p Glob,θ th =1 η α j N jg j θ 1 1 dθ + 1dθ. 9 By summng up 8 and 9, the global provder s revenue ncrease comparng wth the zero revenue f he does not cooperate by cooperatng wth local provder s π Glob η,,θ th =1 η θ th N G +1 η j α jn j G 3pGlob, 30 whch lnearly decreases n the revenue sharng porton η and ncreases n the number of travelers j α j N j from the other markets. Notce that the number of travelers n market s fxed, and 30 s ndependent of other local markets operatons. 9 Thus we can decompose the nteractons between dfferent local markets, and study each of them separately. Note that a local provder s revenue and the global provder s local revenue are stll dependent on the number of travelers from other markets. Now we look at the revenue ncrease of local provder through the cooperaton. As the global provder s entry wll result n servce competton, provder wll lose those users wth types θ [1/,θ th ] to global WF. Compared wth provder s orgnal revenue n 17 wth k = 1, such competton reduces the revenue by π η,,θ th = ln G N θ th 1 < 0. On the other hand, the global provder wll share part of hs revenue wth local provder : π η,,θ th = η π Glob η, 1 η,θ th. 9. At the equlbrum, each local provder wll jon the collaboraton wth the global provder and realze a wn-wn stuaton. Thus we can study each market ndvdually by presumng the global provder s collaboratons wth all other provders.

10 10 η pglob = mn 1, j α j N j ln 4 N θ th 3pGlob 1 θ +N th + max pglob j α j N j ln 4 N θ th 3pGlob 1 θ +N th pglob, 1, 7 Equlbrum local prce of Global WF p Glob* N =100 N =00 N = Σ α Nj j j Fg. 9. Equlbrum prce of global WF n market Equlbrum revenue sharng rato η * N =100 N =00 N = Σ α Nj j j Fg. 10. Sharng porton η between Provder and the global provder Provder s normalzed revenue ncrease Σ j α j Nj =100 Σ j α j Nj =10 Σ j α j Nj = N Fg. 11. Provder s normalzed equlbrum revenue ncrease by G. Thus local provder s total revenue ncrease s π η,,θ th = π η, = ln G N,θ th + π η, θ th 1 +η G θ N th + α j N j j,θ th 3pGlob whch lnearly ncreases n η and j α j N j., 31 Now we dscuss how the global provder bargans wth local provder on and η based on 30 and 31. We wll use the Nash barganng framework to resolve ths ssue. Accordng to [4], the Nash barganng equlbrum s Pareto effcent, symmetrc, and ndependent of rrelevant alternatves. It s the same as Zeuthen s soluton of a general barganng problem where two players could bargan for nfnte rounds. In our problem, the Nash barganng leads to the followng jont optmzaton problem of the revenue ncrease product, 10 max η,,θ th π Glob η,,θ th subject to, 0 η 1, ln π η, 1, θ θ th th ln θ th + θ th 1,θ th ln = 0, 3 where the last constrant comes from 6. Notce that θ th only depends on, and thus we can express t as θ thpglob. Ths means that we need to solve the remanng two varables η and n Problem 3. We can take a sequental optmzaton approach: frst optmze over η gven a fxed, and then optmze over. We can show that the objectve functon of Problem 3 s strctly concave n η, whch leads to the followng result. Proposton 4: At the equlbrum, the global provder shares the majorty of hs revenue n market wth local provder,.e., η > 1/. More specfcally, gven any feasble prce ln/ < < 1/, the unque optmal η pglob s gven n 7, whch ncreases n the local user populaton N and decreases n the traveler populaton j α j N j from other markets to market. It s nterestng to observe that the global provder always needs to gve away more than half of hs revenue to the local provder n order to provde enough ncentves for cooperaton. As the local user populaton N 10. We can add dfferent weghts to each term n the product to reflect dfferent market powers of the global provder and provder, but ths wll not change the key nsghts of ths paper.

11 11 ncreases, the negatve mpact of competton ncreases, hence the global provder needs to gve away more revenue. On the other hand, as more travelers comng, the relatve mportance of the local market decreases, and hence the global provder can keep more revenue but stll less than half. Wth 7, we can smplfy Problem 3 nto the followng one varable optmzaton problem: max π Glob ηp Glob,,θ th π η pglob,,θ th pglob ln subject to, 1, 33 where η pglob s gven n 7 and θ th though not n closed-form can be derved from 6. We can check that the objectve of Problem 33 may not be concave n and Problem 33 s not a convex optmzaton problem. Despte ths, we can stll use an effcent one-dmensonal exhaustve search algorthm to fnd the global optmal soluton [3]. 11 Next we hghlght some key observatons of the solutons to Problem 33. Observaton 1: At the equlbrum of market, both the global WF prce and revenue sharng porton η are ndependent of the local WF coverage G. 1 As the local user populaton N decreases or the traveler populaton j α j N j ncreases, both and η decrease see Fgs. 9 and 10. Note that the global provder s the monopolst for travelers, whereas both the global provder and provder are competng n servng local users. Compared to the monopoly usage-based prce 1/3 n 10 wth k = 1, the prce of global WF needs to be hgher than 1/3 to avod severe prce competton wth provder s local flat-rate prcng servce. When the traveler populaton j α j N j ncreases or local user populaton N decreases, the global provder s ganng a market power approachng a monopolst n servng the whole market, and t s effcent for the global provder to lower the prce and eventually approach the monopoly benchmark of 1/3 as shown n Fg. 9. Meanwhle, local provder s loss of revenue due to the global provder s competton s smaller, and the global provder only needs to share a smaller porton η wth provder as shown n Fg. 10. Observaton : The equlbrum revenue ncreases of both provderand the global provder, π Glob and π, 11. Here s an algorthm to solve Problem 33. We frst approxmate the contnuous feasble range [ln/,1/] of through a proper dscretzaton wth gap,.e., representng all possbltes by 1 ln equally spaced values wth the frst and last values equal to ln/ and 1/, respectvely. By comparng ther correspondng objectve values, we then determne. The overall computaton complexty s O 1 ln. In practce, the global provder wll not change pglob frequently, and there s no need to solve Problem 33 often. 1. As both π Glob n 30 and π n 31 are lnear n G, and θ th s ndependent of G accordng to 6, the objectve of Problem 33 can be normalzed over G. Thus the optmal solutons pglob and η to the problem are also ndependent of G. are ncreasng n j α j N j and G, but are decreasng n N see Fg. 11. Intutvely, a larger coverage G mproves the qualty of both two servces, and a larger j α j N j provdes a larger cooperaton beneft between the global provder and local provder. However, a larger populaton N ncreases the competton between the global and local provders and thus reduces the cooperaton beneft. 7 IMPACT OF LOCAL MARKET COMPETITION In prevous sectons, we have assumed that there s a sngle local provder n each local market, as very few provders can afford the very hgh cost to deploy a large scale WF network. In ths secton, we relax ths assumpton and consder two compettve provders 1 and n a local market I. 13 We would lke to understand how local competton affects local provders prcng strateges and the global provder s entry nto the local market. 7.1 Duopoly competton n WF prcng Let us denote the two local provders WF coverages as G,1 and G,, and we can assume G,1 G, wthout loss of generalty. If a provder j= 1, announces a flat-fee prce P,j, 14 then a type-θ user s payoff by choosng provder j s v,j θ = θg,j ln P,j, j = 1,. The user wll choose the provder that offers a larger payoff: j θ = arg max j=1, v,j θ. 34 If payoffs obtaned from both provders are the same, the user wll randomly choose one provder wth a probablty of 1/. Gven users preferences, two provders wll optmze ther prces n order to acheve an equlbrum, where each provder s maxmzng hs revenue gven the prce of the other provder. Next we wll characterze the equlbrum flat-fee prces. We frst consder the symmetrc case G,1 = G,. By showng that each provder wants to reduce hs prce to be lower than hs compettor and any reasonable prce should be non-negatve, we have the followng result. Proposton 5: Gven a symmetrc WF coverageg,1 = G,, the unque equlbrum flat-rate prces are P,1 = P, = As the general case of olgopoly whch nvolves more than two local provders n the same local market s qute challengng to analyze, we focus on the case of duopoly whch already provdes sgnfcant engneerng nsghts for our problem. 14. Another possble scenaro can be that one provder uses flat-rate prcng and the other provder uses usage-based one, as at least one provder wants to use the effcent flat-rate prcng. Ths scenaro can be analyzed n a smlar way as the local competton between the global provder and a provder n Secton 6, hence we skp the detals here. In practce, we observe flat-rate prcng n most competton markets, as the usage-based prcng s complex and costly to manage.

12 ,$*+-*.#&/0&$1 "#$%&'#*+*#* "#$%&'#"*+*#* "#$ "#" "#" ""#$ " # %&'$ %&'$ #$ ##" '##" "##$%&'$ Fg. 1. Local users choces between provders 1 and n market,$*+-*.#&/0&$1"#$%&'#*+*#* 0 G,1 G, 1 G,1 G, 1 1 4G G 4 4G G,1,,1, "#$%&'#1*+*#* Fg. 13. Local users equlbrum choces between provders 1 and n market Proposton 5 s the same as the non-proftable prcng equlbrum n the classc Bertrand model of perfect competton [8]. At the equlbrum, all users wll subscrbe to the WF servce, and the total demand n the market s equally shared by the two provders. A type-θ user obtans a payoff of θ G ln > 0, and each provder obtans a payoff of 0. Next we consder the asymmetrc case G,1 > G,. Lemma 1: Gven an asymmetrc WF coverage G,1 > G,, the equlbrum prces P,1,P, satsfy P, 0 < G, ln < P,1 G,1 ln < P,1 P, G,1 G, ln < 1, 35 and the local users subscrptons are shown n Fg. 1. The proof of Lemma 1 s gven n Appendx C. Usng Lemma 1, we can derve two provders revenues: π,1 P,1,P, = P,1 N 1 P,1 P,, 36 G,1 G, ln and P,1 P, π, P,1,P, = P, N G,1 G, ln P,. G, ln 37 We can show that both π,1 P,1,P, n 36 and π, P,1,P, n 37 are jontly concave n P,1 and P,. By checkng the frst-order condtons, we can derve each provder s best response prce.e., the prce that maxmzes hs revenue gven hs compettor s prce,.e., and P,1 P, = G,1 G, ln + P,, 38 P, P,1 = G, G,1 P,1. 39 By solvng 38 and 39 smultaneously, we obtan the unque prcng equlbrum as follows. Theorem 3: Gven an asymmetrc WF coverage G,1 > G,, the unque equlbrum flat-rate prces are and P,1 = lng,1g,1 G, 4G,1 G,, 40 P, = lng,g,1 G, 4G,1 G,. 41 " Both equlbrum prces are lower than the monopoly prce G,1 +G, ln/ n 16, f we assume that the monopolst has a coverage of G,1 + G,. 15 In the monopoly equlbrum, a monopolst wth the optmal flat-rate prcng can only serve 50% of users see Fg. 4; n the duopoly case here, however, the two compettve provders together serve more than 75% of users, and provder 1 alone serves more than 50% of users see Fg. 13. Intutvely, the local market competton sgnfcantly drves the market prce down and attracts more users. Under asymmetrc servce qualtes represented by coverages, two provders can stll dfferentate ther prces to cater to dfferent groups of users and make profts. However, under a symmetrc servce qualty, the severe competton wll brng ther profts down to zero. 16 It should be ponted out that though we only look at duopoly case, the analyss n ths subsecton can be extended to olgopoly case. For example, by showng that each provder wth dentcal coverage wll reduce prce to be lower than hs compettors, we have the same result about non-proftable prcng as n Proposton 5. Lke Lemma 1 and Theorem 3, we can also show that provders wth dfferent coverages wll dfferentate and segment the market. More provders wll further lower the equlbrum prces below monopoly prce. 7. Impact of Local Competton on Global WF Now we dscuss the entry of the global provder nto a compettve market wth two provders, and evaluate the mpact of competton on the global provder s entry. We wll also consder the local monopoly benchmark, where a monopoly local provder has a coverage of G,1 +G,, n whch case the global provder s decson has been dscussed n Secton 6 by assumng G = G,1 +G,. Snce any exstng local provder s coverage s relatvely small and ther WF hotspots are often deployed at dfferent locatons, we assume the aggregate coverage G 1. To analytcally characterze the prcng decsons wth the global provder s market entry and the mpact of local competton, we focus on the symmetrc coverage settng,.e., provders 1 and each covers G /. 17 Accordng to Proposton 5, all users are served by provders 1 and at the same zero prce before the global provder enters. Such a competton has the followng 15. One can also show that the two compettve prces are stll lower than the monopoly prce even f the monopolst only covers G, We want to remnd the readers that the zero proft result can be best understood qualtatvely.e., the profts are very small, as our model does not capture all factors that may affect the provders profts n a real market. In fact, most analytcal results n ths paper should be understood smlarly. 17. The asymmetrc coverage settng can be analyzed n a smlar way. Compared to symmetrc coverage case, n ths case, prce competton mtgates wth non-zero prces n Theroem 3 and the global provder s prce should be hgher compared to Theorem 4. Dfferent from Theorem 5, The global provder wll also decde dfferent revenue sharng portons wth the two dfferentated provders. One can vew the asymmetrc coverage case as a partal competton scenaro between the monopoly n Secton 6 wthout competton and perfect competton n Secton 7.. 1