THE standard based wireless local area network

Transcription

1 1056 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 14, NO. 5, MAY 015 Prcng for Local and al W-F Marets Lngje Duan, Member, IEEE, Janwe Huang, Senor Member, IEEE, and Byng Shou Abstract Ths paper analyzes two prcng schemes commonly used n W-F marets: 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 maret, as long as the W-F capacty s abundant, the flat-rate prcng leads to more revenue. Second, we study how a global provder (e.g., Sype) collaborates wth ths monopolst n each local maret to provde a global W-F 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 maret to determne the global W-F servce prce and revenue sharng agreement. In Stage II, local users and travelers choose local or global W-F 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 maret 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 maret 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 W-F marets, flat-rate prcng, usage-based prcng, Nash barganng, collaboraton and competton Ç 1 INTRODUCTION THE standard based wreless local area networ technology, also nown as W-F, s one of the most successful stores n modern wreless communcatons []. Operatng n the unlcensed.4 GHz and 5 GHz spectrum band, W-F networs 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 W-F access ponts (APs) [3]. Furthermore, APs n W-F networs are nexpensve and can be easly deployed and mantaned [4]. These explan why the annual revenue n the W-F 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 W-F 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 W-F APs n ther local marets. For example, Pass has set up more than 1. mllon publc W-F venues, and hs revenue eeps growng 14 percent quarter-overquarter (reachng $0.3 mlllon n the second quarter of 013) [6]. In the Hong Kong maret alone, PCCW has L. Duan s wth Engneerng Systems and Desgn Pllar, Sngapore Unversty of Technology and Desgn, Sngapore. E-mal: lngje_duan@sutd.edu.sg. J. Huang s wth the Networ Communcatons and Economcs Lab, Department of Informaton Engneerng, The Chnese Unversty of Hong Kong, Hong Kong. E-mal: jwhuang@e.cuh.edu.h. B. Shou s wth the Department of Management Scences, Cty Unversty of Hong Kong, Hong Kong. E-mal: byng.shou@ctyu.edu.h. Manuscrpt receved 10 Feb. 014; revsed 9 June 014; accepted 15 July 014. Date of publcaton 1 July 014; date of current verson 30 Mar For nformaton on obtanng reprnts of ths artcle, please send e-mal to: reprnts@eee.org, and reference the Dgtal Object Identfer below. Dgtal Object Identfer no /TMC ncreasngly rolled out more than 1;000 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 W-F 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 W-F servces). Generally, cellular data servces and W-F 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], [9], [10]), where a user pays a fxed amount per month ndependent of the actual usage. Ths motvates us to as the frst ey queston n ths paper: Why does a local W-F provder prefer to charge hs local users a flat fee nstead of a usage-based fee? Notce that a W-F 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, Sype has poneered n provdng a global W-F servceunderthebandnameofsype W-F, throughcollaboratng wth many local W-F provders who own a total of more than 1 mllon W-F APs worldwde [11]. Once a user subscrbes to the Sype W-F servce, he can useanyoftheassocatedw-fapwthhssypeaccount, and pays accordng to usage wth hs Sype Credt (.e., onlypaysforthetmeyouareonlne,assypeputst). Such flexble Sype W-F servce provdes great convenence for travelers, but also ntroduces competton wth local W-F provders among local users. In order to ß 014 IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

2 DUAN ET AL.: PRICING FOR LOCAL AND GLOBAL WI-FI MARKETS 1057 promote such cooperaton, Sype needs to share part of the revenue wth the local W-F provders who provde the physcal W-F APs. Thus, the local W-F provders wll have ncentves to collaborate wth Sype and share ther nfrastructure only f they can also gan from ths new servce. Ths motvates us to as the second ey queston n ths paper: Why does a global provder choose usagebased prcng for hs global W-F servce, and how should he share the benefts wth the local W-F provders? To answer the frst ey queston, we focus on a local maret wth a monopolstc local W-F provder and a group of local users. We model ther nteractons as a two-stage Stacelberg 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 usagebased prcng for such a monopolstc local provder. To answer the second ey queston, we study how the global provder may provde a global W-F servce by cooperatng wth local provders, gven the local provders optmal flatfee based prcng. We formulate the problem as a two-stage dynamc game. In Stage I, the global provder negotates wth each local provder about the global W-F 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 W-F servce. Our ey results and contrbutons are as follows: Flat-fee prcng domnates the local W-F marets. 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 W- F 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 W-F provder prefers the usagebased 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 marets), and hence ncreases the total revenue n the maret. When the revenue s shared properly, the global provder and each local provder acheve a wn-wn stuaton. Nash barganng on the global W-F prce and revenue sharng. In Secton 6, we decompose the nteractons among dfferent local marets 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 marets ncreases, the global provder has a larger barganng power and gves away less revenue. Impact of local maret competton. In Secton 7, we extend the analyss n the monopolstc local maret to a compettve maret. We analytcally show that the local provder competton reduces the maret 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 Wor The recent lterature on W-F 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 W-F s lmted coverage and the users movements across dfferent W-F marets. 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 W-F AP owner, who charges vstors for usng hs AP s resources (e.g., [17], [18], [19]). The ey desgn challenge here s the asymmetrc nformaton,.e., vstors now more about ther own utlty functons than the AP owner. The thrd category studed wreless socal communty networs, where W-F 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 W-F marets. We consder several ey and practcal features of W-F networs (e.g., W-F s lmted coverage and users movement across dfferent W-F marets), 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 W-F servce provder (such as Sype) may cooperate wth local provders, negotate prcng and revenue sharng schemes, and acheve a wn-wn stuaton. There are some other wors studyng how a monopoly provder uses a supplementary networ technology to mprove the exstng one (e.g., usng W-F networs to offload heavy data traffc from cellular networs to avod congeston) (e.g., [1], []). Unle those studes, our study focuses on the publc W-F servce maret, 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 W-F provder who deploys APs to provde servce to a sngle regon. For example, PCCW serves the Hong Kong maret only, and AT&T serves the USA maret only. 1. Although Lee et al. [16] consdered varous prcng schemes, the proposed usage-based prcng does not apply to our W-F servces.

3 1058 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 14, NO. 5, MAY 015 al provder. A W-F provder who serves multple local marets, by usng the networ nfrastructure (APs) of the correspondng local provders. For example, the Sype W-F servce covers many countres wth collaboratons wth local provdes, but Sype does not own any physcal W-F APs. Local maret. A maret that s served by one or multple local provders (and possbly by a global provder). There are a set I¼f1; ;...; Ig of dsjont local marets. Intally we wll assume that each local maret has a sngle local provder. In Secton 7, we wll further loo at the case where there are multple local provders n the same maret. Local user. A user who lves n a partcular local maret as a long-term resdent. There are N local users n each local maret I. Traveler. When a user travels to a maret other than hs own local maret, he becomes a traveler. We use the parameter a j ½0; 1Š to denote the percentage of users n a local maret j who are wllng to pay short-term vsts to local maret, and thus the total travelers from maret j to s a j N j. USAGE-BASED PRICING FOR LOCAL WI-FI We wll frst study how a local provder n a local maret 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 flat-fee prcng always brngs more revenue than the usage-based prcng n the local W-F 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 Stacelberg 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 bacward nducton [4]. We wll frst study the users decsons n Stage II for any gven prce, and then loo at how the provder should optmze the prce n Stage I by tang the users decsons nto consderaton..1 Stage II: Users Usage Choces Due to the lmted number of APs, a local W-F provder typcally cannot provde a complete coverage n a regon. Let us denote the local provder s W-F s coverage as G ðm Þð0; 1Þ, wherem s the total number of deployed APs. In ths paper, we wll assume that M s fxed, and thus wll smply wrte G ðm Þ as G. Notce that today s W-F technologes support hgh data throughput and the comng W-F technology IEEE 80.11ac further offers a much larger throughput (up to Mbt/s) per user [1]. Hence, the networ congeston s usually not a major ssuensuchw-fnetwors.furthermore,thefcchas decded to dramatcally expand the unlcensed spectrum for use by W-F devces and hence wll effectvely mtgate possble W-F congeston n the near future [13]. Note that the W-F 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 maret s n the W-F coverage, we denote hs usage level as d ½0; 1Š, whch represents the percentage of Internet connecton tme over the whole tme n W-F coverage. For example, d ¼ 1 means that the user always stays onlne whenever W-F 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 u. Unle d, the parameter u s not a decson varable. A larger u mples the user s hgher valuaton of the Internet access tme. Le many other studes n ths feld, we assume that u follows a unform dstrbuton n ½0; 1Š for analyss tractablty and the relaxaton to more general dstrbutons s unlely to change the man engneerng nsghts (e.g., [16], [17], [5]). We further assume that a type-u user s utlty uðu;dþ s lnearly ncreasng n u 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 uðu;dþ¼u lnð1 þ dþ; (1) where the parameter >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 maretng, the usual way to obtan the value of s through extensve maret survey and statstcal analyss [9]. As t s dffcult and costly to trac each user s demand elastcty, t s common to examne users aggregate behavor and use an dentcal for all users to represent the average elastcty. Unle, t s relatvely easy to estmate the dstrbuton of wllngness to pay (.e., u) n maretng. 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 W-F coverage, hs overall payoff v s lnear n the coverage G, 4 v ðu;p ;dþ¼g ðu lnð1 þ dþp dþ: (). We assume that moble users tme-varyng locatons follow Posson pont process (PPP), and thus each user has the same expected total tme (normalzed by G ) wthn the W-F coverage durng a perod of tme (e.g., one month). Each user s total W-F actual connected tme s hence G f the demand level d ¼ The logarthmc utlty s wdely used n the networng lterature to model elastc applcatons (e.g.,[6], [7]). 4. A moble user wll start to consder hs networ usage level d after detectng the W-F 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 u lnð1 þ dþ n (), where the lnear term G can be vew vewed as the tme frequency to use d.

4 DUAN ET AL.: PRICING FOR LOCAL AND GLOBAL WI-FI MARKETS 1059 Fg. 1. Users W-F usage choces n the low prce regme. Maxmzng payoff v over d leads to the optmal usage level d ðu;p Þ¼mn max u 1 p ; 0 ; 1 (3) whch s ncreasng n the user s ndvsual type u (and the common elastcty parameter ), and s decreasng n prce p. Furthermore, only users wth u p = 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 u ¼ 1, we can derve the followng prce threshold: p th ¼ þ 1 : (4) When the prce p s less than p th, some hgh valuaton users wll choose dðu;p Þ¼1. Otherwse, all users wll request a usage level less than 1 (can be zero f u 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 <=ðþ1þ Fg. 1 summarzes users optmal usage levels n ths case. There are three categores of users based on the type parameter u: () a user wth a small type u ½0;p =Þ wll not subscrbe to the W-F servce, () a user wth a medum type u ½p =; p ð1 þ Þ=Þ wll subscrbe wth a partal usage level (.e., d ðu;p Þ¼u=p 1= < 1), and () a user wth a hgh type u ½p ð1 þ Þ=; 1Š wll have the maxmum usage (.e., d ðu;p Þ¼1). The provder s total revenue collected from the latter two user categores s Z pðþ1þ u p ðp Þ¼N G p 1 du þ p p ¼ N G p p 1 þ 1 Z 1 p ðþ1þ 1du! : (5) By checng the frst and second order dervatves of p ðp Þ, we can show that p ðp Þ s concave n p. Thus the optmal prce that maxmzes the revenue n the low prce regme s p L ¼ þ : (6) The provder s maxmum revenue n the low prce regme s Fg.. Users W-F usage choces n the hgh prce regme. wth a low type u ½0;p =Þ wll not subscrbe to the W-F servce, and () a user wth a hgh type u ½p =; 1Š chooses to subscrbe the W-F servce wth a partal usage level (.e., d ðu;p Þ¼u=p 1= < 1). The provder s total revenue collected from the second user category s p ðp Þ¼N G p Z 1 p u 1 p The frst order dervatve of (8) over p s dp ðp Þ dp 1 du ¼ N G p þ p : (8) ¼ N G p : (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 ð1;p Þ¼1=p 1= > 0. Ths means p <, whch mples (9) s negatve. Thus the optmal prce n the hgh prce regme s p H ¼ þ 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 ¼ þ ; (10) whch s ncreasng n the elastcty parameter of demand and s ndependent of coverage G. The provder s maxmum revenue under the equlbrum usage-based prcng s p p ¼ N G ð þ Þ : (11) The ndependence of p n G s due to the fact that a user only pays when he uses the servce n the W-F coverage area. Fg. 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 = ¼ 1=ð þ Þ < 1=. As the elastcty parameter ncreases, the type threshold wll decrease and more users p ðp L Þ¼N G ð þ Þ : (7).. Hgh Prce Regme: p =ð þ 1Þ Fg. summarzes users optmal usage n ths case. There are two categores of users under such a prce: () a user Fg. 3. Users W-F usage choces at the equlbrum usage-based prcng.

5 1060 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 14, NO. 5, MAY 015 wll jon the servce. Users total usage level, however, s 0 1 D p u ¼ N G p 1 Z du þ 1duA Z p ð1þþ p p ð1þþ ¼ N G =; (1) whch s ndependent of. 3 FLAT-RATE PRICING FOR LOCAL WI-FI Smlar to Secton, n ths secton we also consder a twostage Stacelberg 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 ¼ 1 (.e., stay onlne whenever the user s n the W-F coverage area) whenever he subscrbes. Next we derve the game equlbrum by usng the bacward nducton. 3.1 Stage II: Users Subscrpton Choces In Stage II, by jonng the flat-rate prce plan, a type-u user s payoff s v ðu;p Þ¼G uðu; 1ÞP ¼ G u lnð1 þ ÞP : (13) Notce that the flat fee P s ndependent of usage, and thus s also ndependent of whether the user s n the W-F coverage area. In other words, once a user subscrbes to the W- F 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 :¼ P =G >P. It s clear that only users who have hgh valuatons of moble Internet access would subscrbe to the W-F servce and obtan a postve payoff. The mnmum type parameter u among the actve users s ðp Þ¼ P G lnð1 þ Þ : (14) 3. Stage I: The Local Provder s Prcng Choce In Stage I, the provder wants to maxmze hs revenue by collectng payment from users wth u ½ ðp Þ; 1Š,.e., max p P ðp Þ¼N P 1 : (15) P 0 G lnð1 þ Þ It s easy to verfy that p ðp Þ 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 ¼ G lnð1 þ Þ=; (16) whch s ncreasng n the coverage G and elastcty parameter. The provder s maxmum revenue wth the equlbrum flat fee s p P N ¼ 4 G lnð1 þ Þ; (17) whch s ncreasng n G and. Fg. 4. Users W-F usage choces at the equlbrum flat-fee prcng. Fg. 4 summarzes users usage behavors at the equlbrum. Comparng wth Fg. 3, the nflexblty of the flat-fee prcng scheme attracts fewer users (1/ nstead of ð þ 1Þ=ð þ Þ) than the usage-based scheme. Intutvely, a better W-F coverage and a larger elastcty parameter encourage more users to jon the W-F servce, and the provder can charge more. Users total usage s D P N ¼ 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 FORLOCALWI-FI 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 :¼ p ðp Þ=p ðp Þ. Based on (11) and (17), we can rewrte the rato as a functon of,.e., rðþ ¼ ð þ Þ lnð1 þ Þ : (19) The frst order dervatve of rðþ over s drðþ d ð þ Þ=ð þ 1Þlnð1 þ Þ ¼ ; (0) and we can show that such a dervatve s postve for all postve values of. Usng L Hosptal law, we can show that lm!0 þ ÞþðþÞ=ðþ1Þ rðþ ¼lnð1 ¼ 1: ¼0 Ths means that rðþ > 1 for any >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 usage-based prcng. The revenue gap ncreases n the elastcty parameter. Theorem 1 s consstent wth the current ndustry practce, where most W-F provders offer flat-rate prcng nstead of usage-based prcng n local marets (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 usage-based prcng requres the provder to record users moble traffc for payment calculaton and collecton over tme [30].

6 DUAN ET AL.: PRICING FOR LOCAL AND GLOBAL WI-FI MARKETS Impact of W-F Congeston When a large number of users try to access the same W-F networ, they may experence networ congeston, whch wll reduce some of ther nterests to jon the local W-F servce. In the followng, we tae the congeston nto account n our local W-F model and evaluate the mpact of congeston on the prcng choce. Let us denote the W-F congeston coeffcent cðbþ, whch s related to the W-F bandwdth B and models the congeston cost for one unt of W-F demand. We also denote the mnmum type parameter u among the W-F subscrbers as, and users wth u ½ ; 1Š 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 u by demandng a usage level d s v ðu;p ;dþ¼g ðu lnð1 þ dþp d cn Z 1 d ðu 0 ;p Þdu 0 Þ; (1) where d ðu 0 ;p Þ s the optmal demand of user type-u 0.As each W-F 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 ðu;p Þ¼ mnðmaxðu=p 1=; 0Þ; 1Þ. As the user wth type u ¼ s ndfferent n choosng between W-F and not, hs normalzed optmal payoff by G s zero. Thus, we can derve the unque soluton accordng to the followng equaton: v uth ð ;p Þ=G ¼ ln 1 þ mn max 1 p ; 0 ; 1 uth p mn max 1 p ; 0 ; 1 cn Z 1 d ðu 0 ;p Þdu 0 ¼ 0; () We can see that here becomes larger because of congeston, and fewer users wll subscrbe. As depends on the servce prce p, we rewrte t as ðp Þ. By predctng ths, the provder s revenue-maxmzaton problem s Z 1 max pðp Þ¼p N G mn max u 1 p ðp Þ p ; 0 ; 1 du: (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 W-F subscrber does not care about hs contrbuton to the congeston and t s stll optmal for hm to demand a full usage level (d ¼ 1). Under networ congeston, a type-u user s payoff s changed from (13) to Fg. 5. The optmal proft rato p ðp Þ=p ðp Þ between usage-based and flat-rate prcng. Z! 1 v ðu;p Þ¼G u lnð1 þ ÞcN 1du P ; (4) whch s zero for the ndfferent user wth u ¼. Then user partton threshold for subscrpton s ðp Þ¼ P =G þ cn lnð1 þ ÞþcN ; 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 ðp Þ¼P N 1 P =G þ cn ; P lnð1 þ ÞþcN whch s a concave functon n P and ts optmal soluton P ¼ G lnð1 þ Þ=. Ths s the same as (16) and s ndependent of congeston level. The resultant revenue s p P N G lnð1 þ Þ ¼ 4ð1 þ cn = lnð1 þ ÞÞ ; (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. Fg. 5 shows the provder s optmal revenue rato p ðp Þ=p ðp Þ between usage-based and flat-rate prcng. As the congeston coeffcent c ncreases or the local user populaton N ncreases, the networ congeston n the W-F servce ncreases and flat-rate prcng (not adaptve to congeston level) wll eventually lose ts advantage over the usage-based prcng. 5 GLOBAL WI-FI SERVICE Now let us loo at the W-F servce n a global maret by nvestgatng the fact of Sype s global W-F operaton. If one company wants to provde a global W-F servce, he can ether densely deploy APs worldwde or cooperate wth many local W-F provders. The former approach typcally requres an extremely large nvestment, whle the latter approach s more feasble. In fact, today a global provder

7 106 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 14, NO. 5, MAY 015 (e.g., Sype) uses the latter approach to provde a global W- F servce called Sype W-F, 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, Sype shares some of hs W-F revenue wth these cooperators [31]. Here s what each sde wll gan and lose durng ths cooperaton. Sype s gan. Sype can gan extra revenue by provdng W-F servce. Sype used to be just a software provder wthout any physcal W-F nfrastructure. Wth the cooperaton and a usage-based prcng, Sype s able to serve travelers who are not wllng to sgn a long-term contract wth local provders. Furthermore, Sype can attract some low-valuaton local users who do not subscrbe to the flat-fee local W-F servce, or prefer usage-based prcng to the flat-fee prcng. Durng ths process, Sype needs to share part of the revenue wth the local W-F provders to acheve a wn-wn stuaton. Local provder s beneft and loss. When Sype starts to provde W-F servce n a local maret, thelocal provder wll experence new maret competton and a reduced number of subscrbers. However, as Sype reles on the local provder s W-F nfrastructure, the provder has the maret power to negotate wth Sype on Sype W-F s prce to avod severe competton. 5 Furthermore, he can share part of the Sype s revenue to compensate hs loss and potentally ncrease hs total revenue. The slogan of Sype W-F s only pay for the tme you re onlne (usage-based prcng). Note that Sype has the followng three advantages over many local provders to mplement a usage-based prcng. Exstng mechansm to record users traffc. Sype can use the same traffc recordng system n Sype W-F as n the exstng Sype Internet Call Servce. Trustworthy global bllng system: Sype has bult a reputable global bllng platform wth hs exstng servces. As Sype has successfully cooperated wth many local telecommuncaton companes on offerng the Sype Internet Call Servce, t s easy for Sype to convnce local W-F provders to be new collaborators. Hgh maret penetraton and brand vsblty. Sype has a more than 600 mllon users and can easly advertse the Sype W-F servce globally, whle many local provders have lttle brand vsblty outsde ther local marets. Even wth these advantages, one may stll wonder why Sype does not choose the flat-fee prcng, as what the local provders are dong for local W-F servces. Our analyss shows that one ey reason s for Sype to avod severe competton wth local provders n order to reach a wn-wn stuaton. 5. For smplcty, we assume that a local provder wll stll charge the same flat fee P n (16) after Sype 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]. To mae the dscusson more concrete, let us frst loo at the users choces. After Sype s entry, a user n hs own local maret can choose between the local W-F servce and Sype W-F servce. When the user travels to a dfferent maret, he wll only choose Sype W-F as he does not want to pay a monthly flat fee n a dfferent maret. Now consder the possblty of Sype adoptng the flatrate prcng scheme for the global W-F servce. Ths can further nclude two varatons: a maret-dependent flat-rate prcng and a maret-ndependent one. In the maret-dependent scheme, a user needs to pay a separate flat-rate prce for each maret (ether local or foregn) he mght enter. In ths way, Sype W-F s just replcatng many local servces at a global scale. Ths leads to drect competton wth local provders n each local maret (e.g., all local users n a maret wll choose Sype W-F 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 marets, as more marets means a hgher total payment. In the maret-ndependent scheme, a user subscrbng to Sype W-F only needs to pay a sngle flat fee to receve servces n all marets. Then many users no longer need to use the local W-F servce. To summarze, n each of the two cases, the local W-F provder wll suffer from Sype s flat-fee prcng, and wll not have the ncentve to cooperate. Ths can explan why n practce Sype chooses the usage-based prcng scheme. 6 OPTIMAL USAGE-BASED PRICING SCHEME FOR GLOBAL WI-FI PROVIDER Now we wll analyze the optmal usage-based prcng scheme for the global W-F provder. We wll consder the maret-dependent usage-based prcng scheme (whch s Sype s current practce), where a user pays dfferent usage-based prces when he s n dfferent marets.the maret-ndependent usage based prcng s a specal case of the maret-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 maret as a two-stage dynamc game. In Stage I, the global provder and (the local) provder jontly decde the global W-F usage-based prce and the revenue sharng porton h (as a compensaton of usng provder s networ nfrastructure). In Stage II, each of the N local users chooses between the global provder s W-F and the provder s local servce (and the usage level f choosng global W-F), and travelers decde ther usages of the global W-F servce. As there s more than one leader (the global and local provders) n Stage I, ths game s no longer a Stacelber game but a twostage dynamc game. In the followng, we use bacward nducton to examne Stage II frst. 6.1 Stage II: Local Users and Travelers Choces Consder a total of I marets n the global maret. A type-u local user n the local maret has two types of demands: Demand n hs local maret. He can choose global W- F s usage-based prce (wth the optmal usage d ðu; Þ as n (3)) or provder s flat-rate prce P n (16) (wth the optmal maxmum usage d ðu; P Þ¼1).

8 DUAN ET AL.: PRICING FOR LOCAL AND GLOBAL WI-FI MARKETS 1063 Fg. 6. Local users usage n maret wth a low global W-F prce. All usage are wth the global W-F. Demand when he travels n non-local marets. He wll only choose global W-F s usage-based prces n other I 1 marets. The probablty for ths user travelng to a maret j s a j < 1. By demandng a usage level d ðu; j Þ n maret j as n (3), ths user s aggregate payoff n all non-local marets s X a j G j u u;d u; j6¼ j p j d u; j : Apparently, the user s usage n non-local marets (the second type of demand) does not affect hs choce of servce n the local maret (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 W-F, v ¼ G u ln 1 þ d u; p d u; to the optmal payoff f subscrbng to the provder, v ¼ G u lnð1 þ ÞP : 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 ¼ 1 and utlty uðu;dþ¼ulnð1 þ dþ. Smlar to Sectons, 3 and 4, our results here can be extended to the case wth any postve value. Proposton 3. At Stage II, local users equlbrum decsons n maret depend on the global W-F prce as follows: Low prce regme ( lnðþ=). No local users wll choose provder s local servce. Users wth types u ½ ; 1Š wll choose global W-F. Ther equlbrum usage levels are llustrated n Fg Medum prce regme (lnðþ= < 1=). Both local provder and the global provder have postve numbers of local subscrbers. Fg. 7 llustrates local users servce subscrptons, where there are three categores of users dependng on ther valuatons: () a user wth the type u ½0; Þ wll not choose any servce, () a user wth the type u ½ Þ wll choose global W-F, and () a user wth the type u ½ ; 1Š wll choose local provder s servce. The threshold type s the unque soluton to ln þ 1 lnðþ ¼0; (6) 6. Note that the revenue sharng decson h 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 ¼ 1. Fg. 7. Local users servce choces n maret n the medum global W- F prce regme. whch satsfes and < s decreasng n (.e., d ð ;p Þ < 1),. Provder s local servce targets at hgh-valuaton users, whereas global W-F targets at low-valuaton users and none of global W-F subscrbers request maxmum usage level. Hgh prce regme ( > 1=). No local users wll choose global W-F. Users wth types u ½1=; 1Š choose Provder s servce as n Fg. 4. The proof of Proposton 3 s gven n Appendx A, whch can be found on the Computer Socety Dgtal Lbrary at TMC We provde all proofs n our onlne techncal report [3]. Note the thresholds lnðþ= and 1= dentfy whether the global W-F prce s low enough to attract all local users or hgh enough to attract no local users, respectvely. Both thresholds are less than 1 as they cannot exceed the maxmum user type u ¼ 1. Proposton 3 shows that two servces wll coexst only n the medum global W-F prce regme, when the two prces are comparable to each other. When decreasesnthsregme, more local users wll swtch from the local provder to global W-F, resultng n a larger partton threshold. Moreover, only depends on and s ndependent of W-F coverage G, as both servces compete wth each other usng the same networ nfrastructure. 6. Stage I: Negotaton between al 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 maret, they are not lely 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 W-F prce n the medum prce regme (.e., lnðþ= < 1=) as long as the local user number s nontrval compared to the traveler number from other marets. 8 The proof Theorem s gven n Appendx B, avalable onlne. Next we focus on the medum prce regme and study 8. We rule out the extreme case where the local user number s trval compared to the traveler number (.e., N =ð P j6¼ a j N jþ!0), n whch case the global provder wll become the monopolst n maret 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 marets 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 W-F networ 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, avalable onlne.

9 1064 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 14, NO. 5, MAY 015 Fg. 8. Travelers usage choces n maret n global W-F n the medum prce regme. the revenues for both the global provder and Provder. h 0 lnðþ p ¼ mn 1; 4 N u th p 1 Pj6¼ a j N j 3ðp Þ u þ N th 0 B lnðþ 1 þ P j6¼ a j N j 4 N u th p þ N 3 11 ; 1 CC AA ; (7) Frst consder the global provder, who gans revenue by servng both local users and travelers n maret, but needs to share h porton of hs revenue from maret to local provder for usng the local W-F nfrastructure. al W- F s revenue from other marets s not related to local provder, and can be normalzed to 0 n the followng analyss. By servng local users wth types u ½ Þ, the global provder collects a total payment D h ; ¼ð1 h Þ Z uth N G d u; du: (8) wth d ðu; Þ¼u= 1. As for travelers n maret, 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 u ½0; usage, () travelers wth types u ½ Þ demand zero ; Þ demand ; 1Š partal usage, and () travelers wth types u ½ demand the maxmum usage. Smlar to (5), we can derve that the total payment collected by the global provder from the travelers n maret as D h ; Z ¼ð1h Þ X a j N jg j6¼ Z! 1 du þ 1du : u 1 (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 D h ; u th ¼ð1h ÞN G þð1h Þ X a j N jg j6¼ 3! (30) whch lnearly decreases n the revenue sharng porton h and ncreases n the number of travelers P j6¼ a j N j from the other marets. Notce that the number of travelers n maret s fxed, and (30) s ndependent of other local marets operatons. 9 Thus we can decompose the nteractons between dfferent local marets, 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 marets. Now we loo 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 u ½1= Š to global W-F. Compared wth provder s orgnal revenue n (17) wth ¼ 1, such competton reduces the revenue by Dp h ; lnðþ ¼ G N 1 < 0: On the other hand, the global provder wll share part of hs revenue wth local provder : h ; ¼ h : Dp D h 1 h ; Thus local provder s total revenue ncrease s Dp h ; ¼ Dp h ; þ Dp h ; ¼ lnðþ G N 1 þ h G u th N þ X a j N j 3!! j6¼ (31) whch lnearly ncreases n h and P j6¼ a j N j. Now we dscuss how the global provder bargans wth local provder on and h based on (30) and (31). We wll use the Nash barganng framewor 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 h ; ; D h ; subject to; 0 h 1; ln lnðþ Dp h ; 1 ; þ 1 lnðþ ¼0; (3) where the last constrant comes from (6). Notce that only depends on, and thus we can express t as Þ. Ths means that we need to solve the remanng ðp 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 maret ndvdually by presumng the global provder s collaboratons wth all other provders. 10. We can add dfferent weghts to each term n the product to reflect dfferent maret powers of the global provder and provder, but ths wll not change the ey nsghts of ths paper.

10 DUAN ET AL.: PRICING FOR LOCAL AND GLOBAL WI-FI MARKETS 1065 Fg. 9. Equlbrum prce of global W-F n maret. two varables h and n Problem (3). We can tae a sequental optmzaton approach: frst optmze over h gven a fxed, and then optmze over. We can show that the objectve functon of Problem (3) s strctly concave n h, whch leads to the followng result. Proposton 4. At the equlbrum, the global provder shares the majorty of hs revenue n maret wth local provder,.e., h > 1=. More specfcally, gven any feasble prce lnðþ= < < 1=, the unque optmal h ðp Þ s gven n (7), whch ncreases n the local user populaton N and decreases n the traveler populaton P j6¼ a j N j from other marets to maret. 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 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 maret decreases, and hence the global provder can eep more revenue (but stll less than half). Wth (7), we can smplfy Problem (3) nto the followng one varable optmzaton problem: max to; D h p Dp h lnðþ ;p p ;p 1 ; p p (33) where h ðp Þ s gven n (7) and ðp Þ (though not n closed-form) can be derved from (6). We can chec 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 [33]. 11 Next we hghlght some ey observatons of the solutons to Problem (33). 11. Here s an algorthm to solve Problem (33). We frst approxmate the contnuous feasble range ½lnðÞ=; 1=Š of through a proper dscretzaton wth gap D,.e., representng all possbltes by 1lnðÞ D equally spaced values (wth the frst and last values equal to lnðþ= and 1=, respectvely). By comparng ther correspondng objectve values, we then determne. The overall computaton complexty s Oð 1lnðÞ D Þ. In practce, the global provder wll not change p frequently, and there s no need to solve Problem (33) often. Fg. 10. Sharng porton h between Provder and the global provder. Observaton 1. At the equlbrum of maret, both the global W-F prce and revenue sharng porton h are ndependent of the local W-F coverage G. 1 As the local user populaton N decreases or the traveler populaton P j6¼ a j N j ncreases, both and h 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 ¼ 1, the prce of needs to be hgher than 1=3 to avod severe prce competton wth provder s local flat-rate prcng servce. When the traveler populaton P j6¼ a j N j ncreases or local user populaton N decreases, the global provder s ganng a maret power approachng a monopolst n servng the whole maret, and t s effcent for the global provder to lower the prce (and eventually approach the monopoly benchmar 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 h wth provder as shown n Fg. 10. global W-F Observaton. The equlbrum revenue ncreases of both provder and the global provder, D and Dp, are ncreasng n P j6¼ a 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 P j6¼ a 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 maret, as very few provders can afford the very hgh cost to deploy a large scale W-F 1. As both D n (30) and Dp n (31) are lnear n G, and s ndependent of G accordng to (6), the objectve of Problem (33) can be normalzed over G. Thus the optmal solutons p and h to the problem are also ndependent of G.

11 1066 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 14, NO. 5, MAY 015 Fg. 1. Local users choces between provders 1 and n maret : Fg. 11. Provder s normalzed equlbrum revenue ncrease by G. networ. In ths secton, we relax ths assumpton and consder two compettve provders 1 and n a local maret I. 13 We would le to understand how local competton affects local provders prcng strateges and the global provder s entry nto the local maret. 7.1 Duopoly Competton n W-F Prcng Let us denote the two local provders W-F coverages as G ;1 and G ;, and we can assume G ;1 G ; wthout loss of generalty. If a provder jð¼ 1; Þ announces a flat-fee prce P ;j, 14 then a type-u user s payoff by choosng provder j s v ;j ðuþ ¼uG ;j lnðþp ;j ;j¼ 1; : The user wll choose the provder that offers a larger payoff: j ðuþ ¼arg max v ;j ðuþ: (34) j¼1; 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 ¼ 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 W-F coverage G ;1 ¼ G ;, the unque equlbrum flat-rate prces are P;1 ¼ P ; ¼ 0. 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 13. As the general case of olgopoly (whch nvolves more than two local provders n the same local maret) 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 sp the detals here. In practce, we observe flat-rate prcng n most competton marets, as the usage-based prcng s complex and costly to manage. W-F servce, and the total demand n the maret s equally shared by the two provders. A type-u user obtans a payoff of u G lnðþ > 0, and each provder obtans a payoff of 0. Next we consder the asymmetrc case G ;1 >G ;. Lemma 1. Gven an asymmetrc W-F coverage G ;1 >G ;, the equlbrum prces ðp ;1 ;P ; Þ satsfy 0 < P ; G ; lnðþ < P ;1 G ;1 lnðþ < P ;1 P ; < 1; (35) ðg ;1 G ; Þ lnðþ and the local users subscrptons are shown n Fg. 1. The proof of Lemma 1 s gven n Appendx C, avalable onlne. Usng Lemma 1, we can derve two provders revenues: P ;1 P ; p ;1 ðp ;1 ;P ; Þ¼P ;1 N 1 ; (36) ðg ;1 G ; Þ lnðþ and P ;1 P ; p ; ðp ;1 ;P ; Þ¼P ; N ðg ;1 G ; Þ lnðþ P ; : (37) G ; lnðþ We can show that both p ;1 ðp ;1 ;P ; Þ n (36) and p ; ðp ;1 ;P ; Þ n (37) are jontly concave n P ;1 and P ;.By checng 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 ðp ;Þ ¼ ðg ;1 G ; Þ lnðþ þ P ; ; (38) P; ðp ;1Þ ¼ G ; P ;1 : (39) G ;1 By solvng (38) and (39) smultaneously, we obtan the unque prcng equlbrum as follows. Theorem 3. Gven an asymmetrc W-F coverage G ;1 >G ;, the unque equlbrum flat-rate prces are and P ;1 ¼ lnðþg ;1ðG ;1 G ; Þ 4G ;1 G ; ; (40) P ; ¼ lnðþg ;ðg ;1 G ; Þ 4G ;1 G ; : (41) Both equlbrum prces are lower than the monopoly prce ðg ;1 þ G ; Þ lnðþ= n (16), f we assume that the monopolst has a coverage of G ;1 þ G ;. 15 In the monopoly 15. One can also show that the two compettve prces are stll lower than the monopoly prce even f the monopolst only covers G ;1.

12 DUAN ET AL.: PRICING FOR LOCAL AND GLOBAL WI-FI MARKETS 1067 Such a competton has the followng postve and negatve mpacts on the global provder s maret entry: Fg. 13. Local users equlbrum choces between provders 1 and n maret. equlbrum, a monopolst wth the optmal flat-rate prcng can only serve 50 percent of users (see Fg. 4); n the duopoly case here, however, the two compettve provders together serve more than 75 percent of users, and provder 1 alone serves more than 50 percent of users (see Fg. 13). Intutvely, the local maret competton sgnfcantly drves the maret 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 mae 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 loo 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. Le Lemma 1 and Theorem 3, we can also show that provders wth dfferent coverages wll dfferentate and segment the maret. More provders wll further lower the equlbrum prces (below monopoly prce). 7. Impact of Local Competton on al W-F Nowwedscusstheentryoftheglobalprovderntoa compettve maret wth two provders, and evaluate the mpact of competton on the global provder s entry. We wll also consder the local monopoly benchmar, where a monopoly local provder has a coverage of G ;1 þ G ;, n whch case the global provder s decson has been dscussed n Secton 6 by assumng G ¼ G ;1 þ G ;.Snce any exstng local provder s coverage s relatvely small and ther W-F 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 maret 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. 16. 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 maret. 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.. Integraton of W-F coverage (see Theorem 4). By ntegratng the local provders W-F networs, the global provder s able to provde the best servce qualty n terms of W-F coverage, whch s mportant to hgh-valuaton users. Larger barganng power (see Theorem 5). As local provders equlbrum revenues are zero, they are more wllng to collaborate wth the global provder. Ths means that the global provder may share less revenue wth each of the local provder. Severe prce competton (see Theorem 4). The zero local W-F prce and full user subscrpton mae t dffcult for the global provder to charge a hgh prce to the local users. By usng bacward nducton, we have the followng result about the global provder s equlbrum usage-based prcng decson n Stage I (by consderng users responses n Stage II). Theorem 4. At the maret entry equlbrum wth two symmetrc coverage local provders, the global W-F usage-based prce s always n the low prce regme (.e., lnðþ=), whch s less than the prce n the local monopoly benchmar (see Theorem n Secton 6.). All local users wth a u ½ = lnðþ; 1Š wll use the global W-F servce and demand the full usage level. The proof of Theorem 4 s gven n Appendx D, avalable onlne. Even wth a lower prce comparng to the local monopoly benchmar, the global provder can stll mae a proft by provdng a better W-F servce n doublng local W-F coverage and attract hgh-end users. Next we derve the revenues for the global provder and both local provders. To serve local users and travelers, the global provder needs to share h ;j ð0; 1Þ to provder j f1; g. Due to the symmetrc W-F coverage, we wll focus on the symmetrc sharng case where h ;1 ¼ h ; ¼ h. Recall from Theorem 4 that the global provder wll serve local users wth u ½ = lnðþ; 1Š. Smlar to (30), (31), and the global maret decomposton n Secton 6., we can derve the revenue ncreases of the global provder and local provder j f1; g n maret as the summaton of revenue ncreases n servng local users and travelers,.e., D h ; ¼ð1h ÞG N 1 p þ X a m lnðþ N m 1 3p (4) ; m6¼ and for j f1; g Dp ;j h ; ¼ h G N 1 p þ X a m lnðþ N m m6¼ 1 3p : (43) Notce that both the global provder and the two local provders revenue ncreases are ncreasng n the number of travelers from other marets P m6¼ a m N m. Accordng to [34], the generalzed Nash (group) barganng n maret

13 1068 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 14, NO. 5, MAY 015 nvolvng three partes can be formulated as the followng jont optmzaton problem: max D Dp ;1 Dp ; ; h ; subject to; 0 h 1; 0 lnðþ=: (44) Ths above problem formulaton assumes that the global provder and the two local provders would engage n the barganng smultaneously. In [3], we also show that all the results derved from solvng Problem (44) stll hold even when the global provder bargans wth each provder ndvdually and smultaneously. Notce that the objectve functon n Problem (44) can be rewrtten as D Dp ;1 Dp ; ¼ h ð1 h Þ G 1 3p þ X m6¼ a m N m N 1 p lnðþ 3 whch s quas-concave n h, as t s ncreasng n h ½0; 1=3Þ and decreasng n h ð1=3; 1Š for any fxed value of. Then we have the followng result. Theorem 5. At the maret entry equlbrum wth two symmetrc coverage local provders, the global provder equally shares the revenue among the two provders and hmself (.e., h ¼ 1=3). Recall that n a monopoly local maret, the global provder needs to gve up most of hs revenue to the monopoly local provder, n order to compensate the local provder s loss of maret share and revenue due to the global provder s competton (see Proposton 4). However, wth severe competton, the two operators revenues are already zero and cannot be further reduced after the global provder s entry. Hence the global provder can decde a smaller revenue sharng rato wth each of the local provder. However, the total revenue rato shared by the global provder to both provders (h ¼ =3) can be larger than the revenue sharng n the local monopoly benchmar (see Fg. 10). After determnng h ¼ 1=3, Problem (44) becomes a sngle-varable optmzaton problem and can be easly solved through an effcent one-dmensonal exhaustve search algorthm. Next we provde some nterestng numercal results. Observaton 3. The equlbrum revenue ncreases of the global provder and the local provders are ncreasng n G, N and P m6¼ a m N m (see Fg. 14 for the global provder s case). Compared to the local monopoly benchmar, the global provder obtans a larger revenue ncrease n the competton case when there are a large number of local users N (hence there are a lot of hgh-valuaton users to attract), e.g., N 500 when P m6¼ a m N m ¼ 400. Such a beneft dmnshes when there are more travelers, e.g., the threshold of N ncreases from 500 to 700 when P m6¼ a m N m changes from 400 to 600, meanng fewer travelers allow the global provder to better explot the beneft of local competton. Fg. 14. The global provder s equlbrum revenue ncreases n monopoly and competton local marets as a functon of traveler populaton P m6¼ a m N m and local user populaton N. Intutvely, the local competton enables the global provder to easly enter and domnate the maret ncludng local users; however, the global provder can only charge a low prce due to local competton and he also needs to share revenue wth more provders. Compared to monopoly scenaro, the global provder s revenue may decrease when local user number does not domnate traveler number. Note that the analyss n ths subsecton can be extended to olgopoly case, by consderng M local provders n maret wth dentcal coverage G =M. Wecan stll show the low prce regme holds for the global W-F servce, as n Theorem 4. Followng ths, the Nash barganng n (44) extends to have M rather than local revenue ncreases n the objectve, where the global provder shares h revenuewtheachprovderandleaves1mh proton for hmself. Smlar to Theorem 5, the barganng outcome s h ¼ 1=ðM þ 1Þ. 8 CONCLUSION Our study n ths paper s motvated by the dfferent prcng practces of local W-F provders such as AT&T n USA and PCCW n Hong Kong as well as a new nd of global W-F provder represented by Sype W-F. We frst show that n a local maret, gven abundant W-F capacty, flat-rate prcng leads to hgher revenue for a local provder than usagebased prcng. We further study how a global W-F provder (e.g., Sype) cooperates wth many local provders n usng ther W-F nfrastructures to provde a global W-F servce. We explan why the global provder adopts usagebased prcng and gves away the majorty of hs revenue to the local provder. There are some possble drectons to extend our results. Frst, we can consder a user s traffc model s nelastc rather than elastc n the current model. For example, we can use a Sgmod functon to model a user s utlty n usng vdeo conferencng, and the analyss wll

14 DUAN ET AL.: PRICING FOR LOCAL AND GLOBAL WI-FI MARKETS 1069 be more complcated. Second, ths paper focuses on the steady state about users servce choces, and t s also nterestng to study users dynamcs n networ selecton durng the adopton process (as n [35], [36]). Thrd, we can further nvestgate the cellular data servces possble competton wth local W-F servces. For example, we can ntroduce a reservaton payoff for each user, and a user wll choose the W-F servce only f hs payoff s larger than ths reservaton payoff. Our man results should hold, and a larger reservaton payoff encourages the W-F provder to charge a smaller W-F prce to attract the subscrbers. Fnally, one may study how the networ congeston affects the competton between two local provders. Dfferent from Secton 7.1, we beleve that the congeston can help dfferentate the servce qualtes of dfferent provders, and even wth the same coverage, t s unlely to result n current non-proftable outcome (as n Proposton 5). One provder caters to the hgh-type users whle the other covers many low-type users. ACKNOWLEDGMENTS Part of the results appeared n IEEE INFOCOM 013 [1]. Ths wor 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 41511) establshed under the Unversty Grant Commttee of the Hong Kong Specal Admnstratve Regon, Chna. Ths wor s also partally supported by the Hong Kong General Research Fund (Project No. CtyU 14981) and grants from Cty Unversty of Hong Kong (Project No and ). REFERENCES [1] L. Duan, J. Huang, and B. Shou, Optmal prcng for local and global WF marets, n Proc. IEEE Conf. Comput. Commun. (INFOCOM), Turn, Italy, Apr. 013, pp [] WF (wreless fdelty). [Onlne]. Avalable: org [3] W. Lehr and L. W. McKnght, Wreless nternet access: 3G vs. WF, Telecommun. Polcy, vol. 7, pp , 003. [4] M. H. Manshae, J. Freudger, M. Felegyhaz, P. 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Shou, Investment and prcng wth spectrum uncertanty: A cogntve operator s perspectve, IEEE Trans. Moble Comput., vol. 10, no. 11, pp , Nov [8] A. Mas-Colell, M. D. Whnston, and J. R. Green, Mcroeconomc Theory, vol. 1. New Yor, NY, USA: Oxford Unv. Press, [9] C. S. Bell. On the elastcty of demand at retal, Amer. J. Econ. Soc., vol. 0, pp. 63 7, [30] L. DaSlva, Prcng for QoS-enabled networs: A survey, IEEE Commun. Surveys Tuts., vol. 3, no., pp. 8, Second Quarter 000. [31] Sype. Sype launches WF hotspot operator partnershp program wth leadng WF provders. [Onlne]. Avalable: about.sype.com/press/011/0/wf.html [3] L. Duan, J. Huang, and B. Shou. Prcng for local and global WF marets. Tech. Rep., (014). [Onlne]. Avalable: abs/ [33] A. Ruszczyns, Nonlnear Optmzaton. Prnceton, NJ, USA: Prnceton Unv. Press, 011. [34] J. C. Harsany, Ratonal Behavour and Barganng Equlbrum n Games and Socal Stuatons. Cambrdge, U.K.: Cambrdge Unv. Press, [35] D. Nyato and E. 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15 1070 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 14, NO. 5, MAY 015 Lngje Duan (S 09-M 1) receved the PhD degree from The Chnese Unversty of Hong Kong n 01. He s an assstant professor of Engneerng Systems and Desgn Pllar, Sngapore Unversty of Technology and Desgn. Durng 011, he was a vstng scholar n the Department of EECS at the Unversty of Calforna at Bereley. Hs research nterests nclude networ economcs and game theory networ optmzaton and resource allocaton, and energy harvestng and management. He authored a boo "Cogntve Moble Vrtual Networ Operator Games", and hs other wors are hghly cted. He s the TPC co-char of INFOCOM 014 Worshop on GCCCN and the ICCS 014 program co-char of specal ssue on Economc Theory and Communcaton Networs. He s also a TPC member for multple top-ter conferences (e.g., ICC, GLOBECOM, WCNC, ICNC, VTC, PIMRC, MobArch, and Smart- GrdComm). He s a member of the IEEE. Byng Shou receved the BE degree from Tsnghua Unversty and the MS and PhD degree from Northwestern Unversty. She s an assstant professor of management scences at the Cty Unversty of Hong Kong. Her man research nterests nclude operatons and supply chan management, game theory, and economcs of wreless networs. She has publshed n leadng journals ncludng Operatons Research, Producton and Operatons Management, Naval Research Logstcs, and IEEE Transactons on Moble Computng. " For more nformaton on ths or any other computng topc, please vst our Dgtal Lbrary at Janwe Huang (S 01-M 06-SM 11) receved the PhD degree n electrcal and computer engneerng from Northwestern Unversty n 005. He s an assocate professor n the Department of Informaton Engneerng at The Chnese Unversty of Hong Kong. He receved the IEEE Marcon Prze Paper Award n Wreless Communcatons 011, and the Best Paper Awards from IEEE WOPT 014 and 013, IEEE SmartGrdComm 01, WCON 011, IEEE GLOBECOM 010, and APCC 009. He receved the IEEE ComSoc Asa-Pacfc Outstandng Young Researcher Award n 009. He co-authored three boos: Wreless Networ Prcng, Monotonc Optmzaton n Communcaton and Networng Systems, and Cogntve Moble Vrtual Networ Operator Games. He s the co-author of four ESI Hghly Cted Papers, whch are among the 1% top papers n terms of ctatons wthn the feld of Computer Scence accordng to Web of Scence. He has served as the Edtor of the IEEE Journal on Selected Areas n Communcatons Cogntve Rado Seres, Edtor of the IEEE Transactons on Wreless Communcatons, Guest Edtor of the IEEE Journal on Selected Areas n Communcatons specal ssue on Economcs of Communcaton Networs and Systems, Lead Guest Edtor of the IEEE Journal of Selected Areas n Communcatons specal ssue on Game Theory n Communcaton Systems, and Lead Guest Edtor of the IEEE Communcatons Magazne Feature Topc on Communcatons Networ Economcs. He has served as the Edtor (01-013) and Assocate Edtor-n-Chef (014) of the IEEE Communcatons Socety Technology News, the Vce Char (010-01) and Char (01-014) of IEEE Communcatons Socety Multmeda Communcatons Techncal Commttee, a Steerng Commttee Member of the IEEE Transactons on Multmeda (01-014) and IEEE Internatonal Conference on Multmeda & Expo (01-014), Char of Meetng and Conference Commttee (01-013) and Vce Char of Techncal Affars Commttee ( ) of IEEE ComSoc Asa-Pacfc Board. He has served as the TPC Co-Char of NetGCoop 014, IEEE SmartGrdComm Demand Response and Dynamc Prcng Symposum 014, IEEE GLOBECOM Selected Areas of Communcatons Symposum 013, IEEE WOpt 01, IEEE ICCC Communcaton Theory and Securty Symposum 01, IEEE GlOBECOM Wreless Communcatons Symposum 010, IWCMC Moble Computng Symposum 010, and GameNets 009. He s a frequent TPC member of leadng conferences such as INFOCOM and MobHoc.