When can bundling help adoption of network technologies or services?

Transcription

1 When an bundlng help adopton of network tehnologes or serves? Steven Weber Dept. of ECE, Drexel U. Roh Guérn Dept. of CSE, WUSTL Jaudele C. de Olvera Dept. of ECE, Drexel U. ABSTRACT Network tehnologes (and serves) often beome more valuable as more users adopt them, e.g., Metalfe s law. The flp sde of ths phenomenon s that many potentally valuable network tehnologes never take off, as ther ost exeeds ther ntal value (when few are usng them). Ths s often blamed for the slow adopton of IPv6 and seurty extensons to popular protools suh as DNSSEC and BGP-SEC. Developng approahes to overome those early adopton hurdles s, therefore, of nterest. Bundlng tehnologes so as to appeal to a larger set of early adopters s a possble opton, but t s hard to predt why and when t may sueed,.e., help both tehnologes. Our goal s to develop prnpled nsght and answers to ths queston, and n partular how t s affeted by orrelaton n how users value eah tehnology. The paper outlnes a possble modelng approah, and ponts to potental dfferenes wth how orrelaton has tradtonally been found to mpat bundlng s effay. Categores and Subjet Desrptors 5 [Networks]: Network eonoms; [Networks]: Publ Internet Keywords Internet serves, adopton, user valuaton, orrelaton. INTRODUCTION Many Internet tehnologes and serves have value that nreases wth the sze of ther user base,.e., they exhbt postve externaltes or network effets (Metalfe s law s often mentoned as one of the frst aknowledgments of ths effet n modern ommunaton networks [5, p.7]). Externaltes are well-known [] to have dual effets on adopton patterns. Adopton rapdly aelerates after passng a rtal threshold (untl the market starts saturatng), but reahng ths rtal level of adopton s often slow and dffult. In prate, tehnologes that fal often fal durng ths early stage, as many potental adopters see a ost that exeeds the (low) ntal value of the tehnology. Ths s ommonly mentoned as an explanaton for the lmted or stalled adopton of many Internet seurty protools [], and s also partly responsble for IPv6 slow adopton, e.g., see [9] for a related dsusson. IAB ITAT Cambrdge, UK Copyrght s held by author/owner(s). A ommon approah (see agan []) to overome ths ntal hurdle s to bundle tehnologes, n the hope that the bundle has broader appeal and s, therefore, able to overome early adopton nerta. The man unknown s the extent to whh dependenes (as measured by a jont dstrbuton) or orrelaton n how users value the ndvdual tehnologes nfluenes ther adopton deson for the bundle. We llustrate ths next by way of two examples; one nvolvng two dstnt Internet tehnologes that offer aess to very dfferent funtonaltes, the other nvolvng a ommon famly of serves that are dfferentated solely by how ndvdual users value them.. Anonymous ommunatons and seure dstrbuted storage Anonymous ommunaton systems have been avalable for some tme, e.g., see [7] for a reent survey, but n spte of a reent rse n profle [], they reman relatvely margnal,.e., have not yet attrated a large user-base. Ths an affet ther robustness and ther ablty to delver strong anonymty guarantees (mxng traff from more users and tappng nto the resoures ontrbuted by those users an mprove both anonymty and robustness, at least n PP based mplementatons of suh systems). Overomng the lmted appeal (to users) of anonymous ommunatons and nreasng the number of users suh a system an tap nto, an be realzed by bundlng t wth another serve. Ideally, ths other serve should exhbt tehnal synerges wth anonymous ommunatons so as to faltate a jont mplementaton. Seure dstrbuted storage s a possble anddate. It enables the automat and enrypted bakup of loal fles over a dstrbuted set of network peers (see BuddyBakup for an example), and shares wth anonymous ommunatons a relane on ryptograph prmtves and protools, as well as a value that grows wth ts number of adopters (more users lkely means a more relable system). The man queston s whether ombnng those two serves an nrease adopton for both. The answer depends on the ost versus value of the bundle. The ost of the bundle onssts of the ommunaton (bandwdth), proessng, and storage osts of the two serves, wth anonymous ommunatons allng mostly for bandwdth and proessng resoures, and seure dstrbuted storage requrng prmarly storage resoures and to a lesser extent proessng and ommunaton resoures. Beause the two serves have mostly ndependent needs, those osts should be approxmately addtve. The value a user assgns

2 to the bundle depends on her level of use of anonymous ommunatons and relane on seure dstrbuted storage as a means of preservng and aessng her personal data. Ths value wll hange as more users adopt the bundle (t mproves the qualty and relablty of both serves), but the desons of early adopters depends prmarly on how they ntrnsally value aess to anonymous ommunaton and seure dstrbuted storage. For llustraton purposes, assume that wthn a gven user populaton the stand-alone values of both serves are unformly dstrbuted. However, to reflet the fat that seure dstrbuted storage should be attratve to most users whle anonymous ommunatons wll lkely have more lmted appeal, we assume that the stand-alone values of the former are n [a, ], < a <, whle they span the full [, ] range for the latter. In other words, most users vew seure dstrbuted storage as useful (valued at > a), whle fewer assgn a smlar value (n the range [a, ]) to anonymous ommunatons. Under those assumptons, orrelaton n user valuatons learly affets the number of early adopters the serve bundle wll attrat. For example, t s relatvely easy to show that the ost threshold beyond whh there are no early adopters for the bundle s under perfet postve orrelaton, but only a+ under perfet negatve orrelaton.. Onlne dsusson forums Consder next the ase of an onlne dsusson forum dedated to a partular top. Partpatng n suh a forum has some ntrns value, e.g., from aess to promotons and dsounts on related produts, but ts ore value often omes from the answers and adve t provdes n response to users questons. To sueed, a forum must, therefore, aumulate a large enough knowledge-base and onsequently aheve a rtal mass of users. Ths an be hallengng, as the added value from Q&A s s essentally absent n the early stages, and promotons and dsounts alone may be nsuffent to attrat enough early adopters. Combnng the tops of multple forums under a ommon umbrella s one way to address ths hallenge. The stand-alone value of suh a bundled forum, e.g., promotons and dsounts that now extend aross more produts, may appeal to a broader user base, and allow t to sueed where ndvdual forums would not have. The queston we seek to answer s agan when and why ths may be the ase? As wth anonymous ommunatons and seure dstrbuted storage, whether a bundled forum attrats more early adopters, and therefore mproves ts odds of suess, depends on ts ntal ost-beneft rato relatve to that of ndvdual forums. The ost of jonng a bundled forum, e.g., the amount of tme needed to extrat useful nformaton, s typally hgher than that of more foused, sngle-top forums. Its ombned stand-alone value arguably depends on many fators, but a reasonable frst approxmaton s agan to assume that t s the sum of the stand-alone values of the ndvdual forums t ombnes. As n the prevous example, whether ths sum exeeds the ost of jonng the forum, whh determnes the number of early adopters, depends to a large extent on the jont dstrbuton of user valuatons for the ndvdual forums; an mportant measure of whh s ther orrelaton. For purpose of llustraton, onsder a senaro where we ontemplate mergng two dsusson forums, whose stand- Smlar arguments hold for other systems of a lke rowdsourng nature, e.g., reommender systems. alone values (value of produt promotons and dsounts) follow dental unform dstrbutons when measured aross a populaton of users. Assume further that for a gven user, the values she sees n the two forums are ether perfetly postvely or perfetly negatvely orrelated,.e., equal or dametrally opposte. Under perfet postve orrelaton, the stand-alone value that any user derves from the bundled forum s then smply twe the value she sees n ether of the ndvdual forums. If we also assume that the ost of jonng the bundled forum s also twe that of jonng a sngle-top forum,.e., t takes twe as long to fnd relevant nformaton, then t s easy to show that bundlng has no mpat on early adopton, and the bundled forum sees the same number of potental early adopters as ether of the orgnal forums. In ontrast, when values are perfetly negatvely orrelated, all users now see the same (average) value from jonng the bundled forum. In ths ase ether no user or all users wll be early adopters, dependng on whether ths average value s above or below the bundle s ost. Hene, unlke the ase of perfet postve orrelaton, bundlng an now have a sgnfant mpat on the number of early adopters the bundled forum attrats. As the above examples hopefully llustrated, orrelaton n how users value dfferent serves and/or tehnologes (and more generally ther jont dstrbuton) an have a sgnfant effet on whether ombnng them n a bundle s benefal. Explorng ths ssue n a systemat fashon s our man goal. In Seton, we outlne an arguably stylzed ntal model that aptures fundamental aspets of the role orrelaton plays n determnng when and why bundlng tehnologes s benefal or not. Many enhanements and extensons to ths bas model are learly possble, but n spte or maybe beause of ts smplty, t helps llustrate how models an help buld nsght and offer a bass on whh to develop a more prnpled understandng of when bundlng network tehnologes an be benefal. Before ntrodung the bas model we rely on, we brefly revew pror works n two areas most relevant to our nvestgaton, namely, produt adopton models and haraterzaton of optmal (produt) bundlng strateges.. RELATED WORK The top ths paper dsusses s at the nterseton of two major lnes of work; produt and tehnology dffuson, and produt and serve bundlng. Modelng how produts, tehnologes, and serves dffuse through a populaton of potental users,.e., are beng adopted by users, s a top of longstandng nterest n marketng researh wth [] offerng a reent revew of avalable models and tehnques. The models most relevant to our nvestgaton are those based on the approah ntrodued n [] and extended n many subsequent works, whh explore produt dffuson n the presene of externaltes usng an adopton deson proess that reflets the utlty of ndvdual users. However, and exept for a few reent works that we revew below, the aspet of bundlng had not been norporated n those nvestgatons. There has obvously been a sgnfant lterature devoted to bundlng as a stand-alone top (see [6] for a reent revew). The man goal of most of those works has typally been the development of optmal bundlng and prng strateges, and prng s a dmenson that s largely absent from our nvestgaton as tehnology adopton osts are as-

3 sumed gven and exogenous. Instead, our fous s mostly on how the jont dstrbuton n tehnology valuaton aross users (as measured throuhg ther orrelaton oeffent), determnes whether the adopton level of a tehnology bundle an exeed those of separate tehnology offerngs. Correlaton n how users value dfferent tehnologes and the mpat ths has on bundlng strateges s n tself a top that several pror works have expltly taken nto aount, e.g., [5,, ]. In general, negatve orrelaton n demand mproves bundlng s benefts over separate offerngs, although hgh margnal osts (ompared to the average value of the bundle) an negate ths effet. Conversely, a hgh postve orrelaton tends to yeld the opposte outome,.e., favor separate (pure omponent) offerngs. As we shall see, when promotng adopton s the goal, the outome appears to be somewhat dfferent wth some level of postve orrelaton typally needed to produe favorable outomes (see Seton for detals). Furthermore, none of the early works on bundlng norporated externaltes, whh are lkely also ontrbutng to the dfferent effet of orrelaton. There are to-date only three works we are aware of [,, 6] that have nvestgated the problem of bundlng tehnologes or serves wth externaltes, and we brefly revew how these papers dffer from our fous. Frst and as has been the norm n the bundlng lterature, all three papers seek optmal prng strateges, whle we assume exogenous osts (pres),.e., the ost of adoptng a new tehnology s typally not easly ontrolled. Seond and more mportantly, the mpat of value orrelaton s absent from those three pror works. Spefally, [] fouses on optmal prng whle assumng ndependent valuatons for two serves. [] explores the jont offerng of a produt and a omplementary serve, where the latter exhbts postve externaltes. As n [], users valuatons for the produt and ts omplementary serve are assumed ndependent, and there s no nvestgaton of the mpat of orrelaton. [6] s ast n the ontext of a two-sded market (the two market sdes reate externaltes), where the platform provder seeks to dede how to bundle and pre new ontent wth the platform t offers, gven the exstene of an nstalled based of users that already own the platform and ontent developers that ontrbute to ts popularty through the ontent theydevelop. The fous s agan on optmal prng strateges and bundlng desons, and there s no orrelaton between the value of new ontent and older ontent.. MODEL OVERVIEW In ths seton, we provde a bref desrpton of the type of models we rely on to explore when and why bundlng network tehnologes may be benefal when t omes to mprovng ther adopton. We onsder a model for the adopton of multple (two) tehnologes (or serves) by a heterogeneous populaton of potental users. The pereved utlty V (x (t)) of tehnology {, } by a (random) user gven that a fraton e.g., the tme needed to deploy a new protool, nstall a new software, or more generally the resoures requred by a new serve. Note that ths does not mean that there are no benefts to nvestgatng adopton s senstvty to hanges n ost. The models we propose an be readly used for suh purpose. x (t) [, ] of the populaton has already adopted the tehnology at tme t norporates three omponents: ) the user s affnty for the tehnology (apturng users heterogenety n how they value the tehnology), ) the network externalty ted to the adopton level of the tehnology, and ) the tehnology adopton ost. Spefally: V (x (t)) = U + e x (t), {, }, () where ) U s the user s (random) affnty for tehnology ; ) e s the strength of the externalty ontrbuton 5 for tehnology ; and ) s the ost of adoptng tehnology. Smlarly, when the two serves are bundled, the utlty V (x(t)) that a random user pereves from adoptng the bundle s of the form V (x(t)) = V (x(t)) + V (x(t)) = U + ex(t). () Here, x(t) s the (ommon) adopton level of the bundled tehnologes. Note that the assumpton of addtve values for the two tehnologes,.e., V (x(t)) = V (x(t)) + V (x(t)), mples that they are nether substtute nor omplement. Under suh an assumpton, U = U + U s the aggregate ntrns value of the bundled tehnologes, e +e s the aggregate fore of the externalty, and s the aggregate ost, whh for smplty s also assumed to satsfy = +. Extendng the models to aount for nstanes where the two tehnologes are partal omplements (U U + U and/or e e +e ) or substtutes (U U +U and/or e e +e ), or for possble eonomes of sope n the ost of the bundle ( + ) s ertanly of nterest. Suh extensons an be norporated n the models, but at the ost of added omplexty. Users adopt a tehnology f they derve postve utlty from dong so. In the presene of ndependent tehnologes,.e., that are nether omplements nor substtutes, adopton desons for the two tehnologes are deoupled. However, the value an ndvdual user assgns to one tehnology may be oupled to the value she assgns to the other tehnology,.e., the par of random varables (U, U ) may be orrelated. Ths wll affet whether she adopts the tehnologes when they are bundled. In partular, the number of users whh derve postve utlty from adoptng the bundle depends on the jont dstrbuton of U and U, and n partular ther orrelaton. Our goal n developng models and ther solutons s to nform an answer to the general queston of How do adopton equlbra (x, x ) under bundlng ompare wth adopton equlbra (x, x ) when network tehnologes (or serves) are offered separately, and what parameters affet the outome? An explt answer for an arbtrary jont dstrbuton of U and U s dffult and furthermore relatvely opaque,.e., the expressons that an be derved offer lttle nsght nto the mpat of ndvdual parameters. However, t s possble to nvestgate smple ases that an be expltly solved, and whh more mportantly allow us to dretly assess the mpat of varous parameters and n partular orrelaton n users valuatons for the two tehnologes. We desrbe 5 The assumpton of lnear externalty affords analytal tratablty, and typally does not qualtatvely affet the nature of the fndngs,.e., they hold for dstrbutons wth CDF F (u), whh share wth the unform dstrbuton a nondereasng hazard-rate funton F (u)/ ( F (u)) [, 8].

4 r h (x ) x h (x ) x h (x ) x h (x ) e = ( ) x next a very smple onfguraton (some may even argue smplst), whh nevertheless norporates some of the bas effets we want to apture,.e., heterogenety n how users value tehnologes, and the possblty of orrelaton n how an ndvdual user values dfferent tehnologes.. A bas model We onsder a settng where users ether lke or don t lke a tehnology. In other words, a user s affntes for the two tehnologes (the values t assgns to the tehnologes) an be modeled as a par of Bernoull random varables (U, U ) {, } wth jont dstrbuton parameterzed by p [, ] as follows: (e) h x (x ) U \U ( p)/ p/ / l () r p/ x ( p)/ / + h(x) / / / (f) h The user populaton x (x ) + then onssts of four types: + negatve affntes /e /e for both tehnologes (, ), postve affntes for l m r x both tehnologes (, ), and mxed tehnology affntes (, ) and (, ). Note l that rexatly x half of the populaton has a = postve affnty for eah tehnology, regardless of p. Furthermore, (g) the orrelatonh ρ(x n ) a user s affntes for the two tehnologes, (U, U ), an be expressed as a smple funton + of p: x p E[UU] le[u]e[u] r x ρ = = = p, () Var(U)Var(U ) h x (x ) (h) whh ranges from ρ = for p = (all users have mxed 5 5 affntes) up to ρ = + for p = (all affntes are ether both postve or both l negatve). r x It = e s possble under ths smple model to haraterze adopton equlbra, both when tehnologes are offered separately and when they are offered as a bundle. Possble adopton equlbra are, /, and under separate offerngs, and, +ρ, ρ, and for a bundled offerng. Fg. llustrate the dfferent regons of the (, e ) and (, e) planes (for separate and bundled offerngs, respetvely) n whh eah equlbrum s realzed, assumng that when the two tehnologes or the bundle are frst offered, there are no adopters,.e., x () =, {, } and x() =. 5 5 e = e = ( ) + e = = = = ( ) + ( ) ( ) 5 (a) Separate Equlbra = ( ) + ( ) + + = ( ) + 5 (b) Bundled Equlbra Fgure : Regons of realzed adopton equlbra as a funton of adopton ost and externalty strength. By omparng Fg. (a) and Fg. (b), t s possble to determne when bundlng s benefal or not, e.g., when t results n wn-wn (WW) or lose-lose (LL) outomes, where both tehnologes realze a hgher, respetvely lower, level of adopton than when offered alone. For a gven ρ value, ths essentally amounts to overlayng Fg. (a) and Fg. (b) to dentfy how the bundled and separate equlbra regons overlap. In partular, we readly see that the boundares of the dfferent equlbra regons n the (, e) plane of Fg. (b) depend on the value of ρ. Hene, we an expet ρ to nfluene when WW (and LL) outomes arse. In the next seton, we revew some ntal nsght that emerges from omparng regons n Fg. (a) and Fg. (b).. INITIAL RESULTS AND INSIGHT The tradtonal wsdom n developng bundlng strateges, e.g., see [6], s that bundlng s typally most effetve n the presene of negatve orrelaton n user valuatons (reservaton pres). The ntuton s that bundlng redues heterogenety n users valuatons, whh faltates the seleton of a pre for a bundled offerng that results n an overall hgher proft (see [6, Seton.]). Ths s easly llustrated wth a smple two produts, X and Y, and two ustomers, A and B, example. Assume that A s wllng to pay p and p < p for produts X and Y, respetvely, whle B s wllngness to pay for X and Y s p, p, respetvely. In other words, A and B s valuatons for the two produts are perfetly negatvely orrelated. For the sake of llustraton, assume p = 5 and p =. It s then easy to see that the optmal pres p and p when the two produts are offered separately are both equal to for a total proft (assumng zero margnal osts) of. In ontrast the bundle s optmal pre s p = 8 for a total proft of 6 >. In ontrast, f the two users wllngness to pay had been perfetly postvely orrelated, then bundlng yelds no beneft over separate offerngs 6. There are obvously dfferenes between the proft maxmzaton goal of tradtonal bundlng strateges, and our goal of maxmzng adopton gven a fxed adopton ost (ths ost wll typally be dfferent from the pre that would optmze proft). The other mportant dfferene between our formulaton and that of tradtonal bundlng strateges s the presene of externaltes. Hene, we an expet both fators to ontrbute to possble dfferenes n outomes, wth the latter (presene of externaltes) lkely to have a stronger nfluene. In partular, t s relatvely easy to see from Eqs. () and () that n the absene of externaltes, assessng whether bundlng benefts adopton s straghtforward. Spefally, adopton levels when tehnologes are offered separately are equal to F ( ) and F ( ), where F (x) represents the CDF of users valuaton for tehnology. Conversely, the adopton level of the bundle s gven by F ( + ), where F (x) s the CDF of the random varable U = U + U that aptures the umulatve valuaton of the two tehnologes to a (random) user). Hene, n the absene of externaltes, whether bundlng s benefal or not s solely a funton of how the bundle s ost ompares to the ost of ndvdual tehnologes. On the other hand, more omplex and nterestng behavors emerge when externaltes are present. In partular, our ntal results ndate that bundlng s effetve n m- 6 In general t s possble for bundlng to lower proft by preventng users who may have bought ndvdual produts from purhasng the bundle.

5 . x Ρ. x Ρ. x Ρ. x Ρ. x Ρ Fgure : Impat of value orrelaton (ρ) on bundle adopton (x ) for dfferent tehnology ombnatons. Tehnology : = /, e = / so that x = /. Tehnology : = / and (left to rght) e =, /,, 5/,, so that x =. provng network tehnology adopton, and n partular reate wn-wn outomes, when the tehnologes beng bundled have postvely orrelated valuatons, although too strong a orrelaton wll often mtgate ths beneft. The model reveals that wn-wn outomes,.e., the bundled tehnologes realze a hgher level of adopton than f offered alone, often arse when one tehnology has a hgh adopton ost ompared to ts ntrns value together wth a hgh externalty fator, whle the other tehnology enjoys mddlng osts, values, and externalty fator. In suh ases, the frst tehnology ould be tremendously suessful, f only t managed to aqure enough of a user base to unleash the substantal value ts strong externalty fator an delver. Unfortunately, ts hgh adopton ost and relatvely low ntrns value make ths nearly mpossble. Hene, when offered alone, ths tehnology never takes off. In ontrast, the relatvely low adopton ost of the other tehnology enables t to make rapd ntal progress even when offered alone. Its ntal adopton spurt, however, qukly subsdes as ts externalty ontrbutons do not progress fast enough to keep attratng more users. Ths translates n nether tehnology experenng meanngful suess when offered alone. Bundlng an, however, hange ths. When the two tehnologes are bundled, the seond beomes the engne that drves ntal adopton untl enough of a user-base has been bult to allow the frst tehnology to ross ts rtal adopton threshold. At that pont, the roles reverse and the frst tehnology beomes the man drver for ontnued adopton, as ts strong externalty ontrbuton s now suffent to attrat more users. The bundle s adopton then takes off, possbly reahng full penetraton. In the proess, the seond tehnology also reahes a level of adopton t would never have realzed on ts own. In summary, externaltes play a major role n reatng suh a wn-wn outome, although as we shall see next, orrelaton n valuatons an have a sgnfant nfluene on the outome. We use Fg. to demonstrate the subtle role that orrelaton aross tehnology valuatons an play. Spefally, the fgure plots the adopton levels of two bundled tehnologes; one that alone would only aheve average penetraton (beause of a ombnaton of low ost, = /, and margnal externalty, e = /, so that x = /), and the other whh by tself would never take off n spte of ts strong potental (ts hgh ost, = /, prevents t from reahng the rtal mass t needs for ts hgh externalty, e > /, to kk n, and ts stand-alone adopton, therefore, remans at x = ). The fgure shows the adopton equlbrum of the bundled tehnologes as a funton of ther (value) orrelaton oeffent ρ [, ]. The fve plots n the fgure show the bundled equlbrum as a funton of ρ for dfferent values of the externalty fator e of the seond tehnology, whh vares (from left to rght) from average (e = ) to very hgh (e = ). When the externalty fator of the seond tehnology s not hgh enough (e = ) to ompensate for ts hgh ost (left-most plot), bundlng the two tehnologes s detrmental, ndependent of the value of ρ,.e., the bundled equlbrum s below the adopton level (/) of the frst tehnology offered alone. As the externalty fator of the seond tehnology nreases (e / four rght-most plots), the value t an delver as adopton nreases beomes hgh enough that t an leverage the ntal adopton spurt of the frst tehnology, and bundlng beomes benefal to both tehnology (x > /). Ths ross-over ours one orrelaton exeeds a ertan threshold. Ths s beause early adopters of the bundle are drven prmarly by the frst tehnology, and under hghly negatve orrelaton n tehnology valuatons, the seond tehnology ontrbutes added ost but lttle or no added value to those early adopters. Hene, adopton stops qukly at a level below that of the frst tehnology offered alone. As orrelaton nreases, the number of early adopters that experene a postve utlty from adoptng the bundle nreases to a pont that t an reah enough of a rtal mass to allow the externalty effet of the seond tehnology to beome effetve and nrease adopton beyond what tehnology would have realzed f offered alone. Note though that further nreases n orrelaton do not yeld addtonal mprovements. As a matter of fat, nreasng ρ beyond the threshold an lower adopton (seond and thrd plots from the left). Ths s beause as orrelaton nreases, the potental adopton base of the bundle narrows (both tehnologes appeal to an nreasngly smlar set of users). Ths effet perssts untl the externalty fator of the seond tehnology s strong enough to allow the bundle to reah full adopton (fourth plot from the left for e = 5/). One the externalty fator of the seond tehnology exeeds that level, ts strength s now suffent to preserve full adopton as long as ρ remans wthn some range (see agan fourth plot from the left). Further nreasng ρ beyond that range results n the adopton level of the bundle droppng agan, unless the externalty fator of the seond tehnology s so strong that the range of ρ values for whh no delne n bundle s adopton ours extends all the way to ρ =. Ths s llustrated n the rght-most plot of Fg. for e =. The followng bundlng gudelne emerges from the above dsusson. Bundlng gudelnes: When seletng tehnology bundles to foster adopton, t s best to hoose tehnologes that. Are heterogeneous n ther ost-beneft struture,.e., low ost & externalty vs. hgh ost & externalty;. Are suffently orrelated n how users value them, but not too muh.

6 The seond gudelne basally states that one the goal of reatng a suffent rtal mass of early adopters has been reahed (whh requres a ertan mnmum level of orrelaton n how users value the bundled tehnologes), there s no beneft n seletng tehnologes that exhbt hgher levels of orrelaton (and there ould be dsadvantages). 5. CONCLUSION The paper presents an ntal nvestgaton amed at developng a better understandng of when bundlng networkng tehnologes or serves an be benefal,.e., result n hgher adopton levels than when they are offered separately. The queston s of relevane n many pratal settngs as networkng tehnologes ommonly fae early adopton hurdles untl they aqure a large enough user-base to start delverng suffent value. Bundlng tehnologes an offer an effetve soluton to overome those early adopton hallenges, but t s often hard to predt whether t wll sueed or not. Of partular mportane n determnng the outome s orrelaton n how users value the ndvdual tehnologes beng bundled. The paper proposes smple models that an help explore ths queston n a prnpled manner, and llustrates the type of nsght they provde through a few smple examples. There are obvously many extensons that are desrable to the bas models desrbed n the paper and n ther ablty to realstally apture how tehnologes nterat, e.g., the extent to whh they are omplements or substtutes, or whether they exhbt eonomes of sope. The methodology outlned n the paper, however, offers a frst step towards developng a fundamental understandng of the role that bundlng an play n helpng network tehnologes overome ntal adopton hurdles. 6. REFERENCES [] C. Arthur. NSA sandal: what data s beng montored and how does t work? The Guardan,. Avalable at [] Y. Bakos and E. Brynjolfsson. Bundlng nformaton goods: Prng, profts, and effeny. Management Sene, 5(), Deember 999. [] H. K. Bhargava and V. Choudhary. Eonoms of an nformaton ntermedary wth aggregaton benefts. Informaton Systems Researh, 5(): 6,. [] L. Cabral. On the adopton of nnovaton wth network externaltes. Mathematal Soal Senes, 9:99 8, 99. [5] M. Castells. The rse of the network soety, volume I. Wley-Blakwell, nd edton,. [6] Y. Chao and T. Derdenger. Mxed bundlng n two-sded markets n the presene of nstalled base effets. Management Sene, 57(), Marh. [7] L. Fernández Frano. A survey and omparson of anonymous ommunaton systems: Anonymty and seurty. Unverstat Oberta de Catalunya - Insttutonal Repostory, June. Avalable at [8] D. Fudenberg and J. Trole. Game Theory. MIT Press., Cambrdge, MA, 99. [9] R. Guérn and K. Hosanagar. Fosterng IPv6 mgraton through network qualty dfferentals. ACM SIGCOMM Computer Communaton Revew, ():8 5, July. [] R. MAfee, J. MMllan, and M. Whnston. Multprodut monopoly, ommodty bundlng, and orrelaton of values. The Quarterly Journal of Eonoms, (), May 989. [] A. Ozment and S. Shehter. Bootstrappng the adopton of Internet seurty protools. In Pro. WEIS, 6. [] M.-S. Pang and H. Etzon. Analyzng prng strateges for onlne serves wth network effets. Informaton Systems Researh, (), Deember. [] R. Peres, E. Muller, and V. Mahajan. Innovaton dffuson and new produt growth models: A rtal revew and researh dretons. Internatonal Journal of Researh n Marketng, 7,. [] A. Prasad, R. Venkatesh, and V. Mahajan. Optmal bundlng of tehnologal produts wth network externalty. Management Sene, 56(), Deember. [5] R. Shmalensee. Gaussan demand and ommodty bundlng. Journal of Busness, 57(), 98. [6] R. Venkatesh and V. Mahajan. The desgn and prng of produt bundles: A revew of normatve gudelnes and pratal approahes. In V. Rao, edtor, Handbook of Prng Researh n Marketng, pages 57. Edward Elgar Publshng, 9.