Demand-side Spillovers and Semi-collusion in the Mobile Communications Market #

Transcription

1 1 Demand-sde Spllovers and Sem-colluson n the Moble Communcatons Market # Øysten Foros, Bjørn Hansen and Jan Yngve Sand Abstract: We analyze roamng polcy n the market for moble telecommuncatons. Frms undertake nvestments n network nfrastructure to ncrease geographcal coverage, capacty n a gven area, or functonalty. Pror to nvestments, roamng polcy s determned. We show that under colluson at the nvestment stage, frms' and a benevolent welfare maxmzng regulator's nterests concde, and no regulatory nterventon s needed. When nvestments are undertaken non-cooperatvely, frms' and the regulator's nterests do not concde. Contrary to what seems to be the regulator s concern, frms would decde on a hgher roamng qualty than the regulator. The effects of allowng a vrtual operator to enter are also examned. Furthermore, we dscuss some mplcatons for competton polcy wth regard to network nfrastructure nvestment. Keywords: Moble communcatons, roamng, competton, vrtual operators JEL classfcaton: L13, L51, L96 # Ths work has been carred out as part of a research project at Telenor R&D - DN The authors are grateful to the edtor and an anonymous referee for comments. Furthermore we thank Kåre P. Hagen, Lars Sørgard, Lars Mathesen and Derek Clark, partcpants at the 19 th Annual Conference on the "Compettve challenge n network ndustres", May 2000, Lake George, New York, EUNIP 2000, December 2000, Tlburg, Netherlands, Helsnk Conference on Ant-trust Issues n Network Industres 2001, and EARIE 2001, Dubln, Ireland, for comments and dscussons. Norwegan School of Economcs and Busness Admnstraton and Telenor R&D, Norway. Correspondng address: Norwegan School of Economcs and Busness Admnstraton, Department of Economcs, Hellev. 30, N-5045 Bergen, Norway. E-mal: oysten.foros@nhh.no. Telenor R&D, Norway. Unversty of Tromso and Telenor R&D, Norway.

2 2 1 Introducton We analyze competng moble telephony provders ncentves to nvest n, and share nfrastructure. Furthermore, we analyze whether the regulator should ntervene nto the frms sharng agreements, and whether the regulator should allow the frms to coordnate ther nvestments. The nfrastructure nvestment we have n mnd s upgradng of the moble networks from second generaton (2G) to thrd generaton (3G) systems. Agreements on sharng nfrastructure are called roamng n moble markets. The man mprovement of 3G networks (e.g. UMTS) compared to the current 2G moble networks (e.g. GSM) s to ncrease the speed of communcaton n the access network and thereby gve access to new servces and new functonalty for exstng servces. Investments wll consequently ncrease consumers wllngness to pay for moble access. The basc mechansm drvng our results s that nvestments carred out by one frm ncrease the value of the servce provded by other frms when there s a roamng agreement between the frms. An analyss of consequences of coordnatng nvestments and nfrastructure sharng seems to be more relevant n 3G as compared to 2G networks. Frst, whle the provders of 2G networks (GSM) made ther nvestment non-cooperatvely, we now see that several provders of UMTS are coordnatng ther nvestments n nfrastructure (e.g. n Sweden and Germany). There has been a heated debate whether the regulator should allow the frms to cooperate at the nvestment stage. Second, the beneft from sharng agreements through roamng seems to be hgher n 3G than 2G networks. In current 2G networks the consumers have access to a gven capacty (9.6 kbt/s), whle n 3G the avalable capacty for data transmsson may be allocated n a more dynamc way. If there are free resources n the network, a consumer may be gven a capacty of up to 2 megabt/s. However, as the number of users n a gven area at a gven tme ncreases, each user wll have less capacty avalable. Ths may ncrease the value of nfrastructure sharng agreements. There are n general potental gans from sharng network capacty when the load n two networks s not perfectly correlated. Let us llustrate ths by a smple example. At a gven tme, operator A has no free capacty n ts network whereas operator B has dle capacty. Suppose now that a subscrber of A tres to download a huge amount of content and needs 2 megabt/s. If there s no capacty sharng agreement between A and B, the customer wll not be able to access such servces at that tme. However, f a sharng agreement s establshed between the operators, the servce wll be avalable to the

3 3 consumer. In ths stuaton, t s obvous that an nvestment n capacty by B wll ncrease the wllngness to pay for subscrptons from frm A. We analyze a stylzed mult-stage model where the frms frst agree on roamng qualty, second choose ther nvestment non-cooperatvely or cooperatvely, and fnally compete à la Cournot. We nvestgate whether t s welfare mprovng to let the frms sem-collude by choosng ther nvestment cooperatvely before they compete n the downstream market. Alternatvely we may have sem-colluson where the frms compete at the nvestment stage and collude n the retal market such as n Brod and Shwakumar (1999), Fershtman and Gandal (1994), and Steen and Sørgard (1999). More generally the latter form of semcolluson seems realstc snce the frms typcally wll collude on the most observable varable. Usually ths wll be the prce n the retal market. However, our motvaton s that we observe colluson at the nvestment stage n the market we consder, and the effects of allowng such colluson are what we want to nvestgate. Therefore, we do not consder colluson n the fnal product market. 1 In our basc model we assume that there are two symmetrc faclty-based frms. If the nvestments are set non-cooperatvely we show that voluntary roamng leads the frms to agree on a too hgh roamng qualty compared to the socal optmum. Moreover, the nvestments are strategc complements, and frms wll then nvest less wth voluntary than mandatory roamng. In contrast, f the nvestments are set cooperatvely, the frms choces on the roamng qualty concde wth the regulator s nterests. We show that the frms should be allowed to sem-collude n the way descrbed above, snce ths yelds the hghest welfare. In an extenson of the basc model we assume that there s a non-faclty-based frm, or a vrtual operator, n addton to the two faclty-based frms. Whether the vrtual operator should be allowed to enter the market and to whch extent the presence of such an operator wll affect the ncentves to nvest n nfrastructure has been a hot topc n the ndustry and amongst regulators. Ths debate started when the Scandnavan vrtual moble operator Sense Communcaton attempted to get access to the faclty-based moble operators networks. The 1 See Busse (2000) and Parker and Röller (1997) for analyss of tact colluson n the moble market.

4 4 faclty-based frms were reluctant to grant Sense Communcaton access. 2 A much more frendly recepton was gven to Vrgn Moble n the UK. The roamng qualty between the entrant and the two-faclty-based frms n our model s assumed to be weakly lower than the roamng qualty between the two faclty-based frms. We show that when the nvestments are set non-cooperatvely between the faclty-based frms an ncrease n the roamng qualty of the ncumbents may now ncrease the nvestments. Ths s n contrast to the basc model. We analyze a type of sem-colluson where the frms may collude at the nvestment stage and compete n the retal market. Our model s an extenson of the multple stage models of d'aspremont and Jacquemn (1988) and Kamen et al. (1992) consderng R&D nvestment. Through the roamng agreements the nvestments n nfrastructure gve rse to spllover effects smlar to those consdered n models of strategc R&D nvestments. In the majorty of these models, the externalty s exogenous. In our model, we focus on the stuaton where the level of the externalty s endogenously determned. 3 Furthermore, n contrast to the majorty of the R&D lterature we ntroduce asymmetry between the frms. That s, there are frms that nvest n nfrastructure and frms that do not nvest. 4 We also make some other key assumptons n our model. Frst, for the sake of smplcty we gnore the ssue of nterconnecton (agreements that gve access to rvals customer bases) and focus on roamng only. We gve roamng a wder nterpretaton than pure geographcal coverage. Roamng agreements extend avalablty, such that () subscrbers can make and receve calls va the nfrastructure coverage of a rval operator, () when there s congeston a customer may take advantage of the nfrastructure of the rval, and () gve access to new functonalty/servces n the rvals network. 2 Sense wanted to ssue ther own SIM cards, but the Scandnavan faclty-based operators refused ths. Sense fled a complant to all natonal regulators, but only the Norwegan regulator supported t. Telenor s appeal to the Norwegan regulator was stll pendng when Sense fled for bankruptcy n March 1999 (Matthews, 2000). Now, Sense Communcaton, along wth several other vrtual operators, has an agreement wth Telenor to resell artme. 3 Katsoulacos and Ulph (1998a,b) ntroduce endogenous levels of spllovers between frms. Contrary to ther models we assume that the nvestments undertaken by frms result n product nnovaton wth probablty one. Furthermore, our focus s on a context where frms (or a regulator), n the termnology of Katsoulacos and Ulph, choose the degree of nformaton sharng and not research desgn. We are accordngly examnng nvestments wth frms operatng n the same ndustry, but pursue complementary research. 4 See e.g. De Bondt (1997) for a survey of the R&D lterature of strategc nvestments.

5 5 Second, to smplfy we make the assumpton that there s no sde payments between frms engaged n roamng. If frms have the ablty to wrte complete contracts n all dmensons of the nfrastructure sharng (roamng), all external effects from the nvestment can n prncple be nternalzed through the prce mechansm. Then, the problem of spllovers through roamng analyzed n ths paper may vansh. Snce sharng agreements n the next generaton systems should ensure a dynamc capacty allocaton, t s however rarely possble to wrte complete contracts n all dmensons. Thus, even f a prce mechansm for roamng s mplemented, t wll not be able to nternalze all external effects. Ths s smlar to what we see n the Internet, where nfrastructure sharng of backbones s common (Crémer, Rey and Trole, 2000). Note that regulaton may also constran the frms' ablty to nternalze external effects through prcng. In partcular, ths wll be mportant n the nteracton between the faclty-based frms and the non-faclty based frm (vrtual operators). Thrd, we make the smplfyng assumpton that consumers only pay for subscrpton, not for usage. On the one hand ths s evdently a restrctng assumpton snce moble provders typcally employ varous types of nonlnear prcng. On the other hand, t s far from evdent what the alternatve s, and n partcular, whether moble provders wll choose to prce dscrmnate between calls orgnated off-net and calls orgnated on-net. 5 The focus n our model s however on how avalablty n varous dmensons (capacty, speed etc.) affects the choce of suppler. Consequently, our focus s on demand for subscrptons, not usage and then t s suffcent to consder prcng as a fxed per perod fee. Fourth, we assume Cournot competton n the retal market. We nterpret the quantty frms dump n the retal market as the number of subscrptons they sell. A justfcaton for assumng Cournot competton s that, due to the fact that the amount of rado spectrum avalable s scarce, there are both physcal and technologcal lmts to capacty. Furthermore, the frms must choose a capacty level whch s bult (or rented) n both the backbone network and the access network (number of base statons) pror to the competton n the retal 5 In addton to the prcng ssues, by ntroducng a call volume dmenson we wll have to model the cost structure for calls orgnatng and termnatng on the same net by a subscrber of that network. Under such a generalzaton of our model t would also be natural to relax assumpton 2 and ntroduce a volume prce on roamng (as well as a volume prce on nterconnecton). A proper modelng of all these prcng and cost components wll lead to a very complex model. By dsregardng both the revenue and the cost sde of traffc we also avod the so-called bll and keep fallacy.

6 6 market. 6 Ths wll be more mportant wth 3G systems where the capacty needed ncreases. However, as shown by Kreps and Schenkman (1983), strong assumptons are requred to ensure that a capacty constraned prce game result n dentcal results as a Cournot game. Nevertheless, ths seems more approprate than assumng a Bertrand game wthout capacty lmts. The rest of the paper s organzed as follows: In secton 2, the model wth only faclty-based frms s presented and analyzed. In secton 3, we provde an extenson to the basc model by ntroducng a vrtual operator. In secton 4, some concludng remarks are made. 2 The model In our basc model we wll look nto a duopoly case where we assume the followng threestage game: Stage 1: Stage 2: Stage 3: Ether the frms or the regulator determnes roamng qualty The frms determne nfrastructure nvestments ether non-cooperatvely or cooperatvely Cournot competton There are four dfferent varants of the game dependng on the stage 1 and stage 2 strateges: Stage 2: Investments Compettve Collusve Stage 1: Roamng Voluntary Game 1 Game 3 Mandatory Game 2 Game 4 Fgure 1 The four varants of the game 6 The basc structure n a moble network s that coverage n a gven area s acheved through a number of base statons coverng gven areas (cells). Hence, a moble network conssts of a net of such cells. The spectrum band allocated for moble use lmts the total bandwth a cell can handle at a gven pont of tme. Thus total capacty measured s lmted and one bandwth hungry user occupyng 2 Mbt/s s crowdng out approxmately 200 ordnary voce calls. In stuatons wth capacty problems t s possble to nvest n hgher capacty through what s called cell splttng. Cell splttng mples that a gven area s served wth a hgher number of smaller cells.

7 7 The choce of whether frms cooperate when determnng ther nvestment levels wll depend on whether such cooperaton s approved by the competton authortes. Regardng stage 2 and 3 the structure n our model s farly smlar to Kamen et al. (1992) and d Aspremont and Jacquemn (1988). The generc feature of the nvestment s that t leads to product nnovaton ncreasng the qualty of the servce. One nterpretaton of the tmng n our model s that roamng polcy may be part of the lcenses to the operators n the case where the degree of roamng s mandatory, and therefore chosen pror to nvestments takng place. When roamng s voluntary, we assume that frms can commt to a polcy on roamng pror to undertakng the nvestments. Indeed, the tmng of the roamng qualty decson relatve to nfrastructure nvestments can obvously be dfferent. To be more specfc, the nfrastructure nvestment may be decded pror to a decson on roamng qualty. Such tmng may nvolve problems wth nvestment hold-ups, but ths wll not be our man focus. Thus, n our choce of tmng we mplctly assume that the frms/the regulator can credbly commt to a gven polcy on roamng. As far as the regulator s concerned, the ssued lcenses may serve as a commtment devce, whereas the commtment problem under voluntary roamng s solved, e.g. f a gven roamng polcy s embedded n the network desgn (e.g. type of nterfaces) The demand sde When frm nvests n ts nfrastructure t mpacts on the qualty of the servces ts own customers are offered, but there may also be an mpact on the qualty of the servces offered by the rval frm j, and vce versa. Gven a roamng polcy ϒ and nvestment decsons x, we can now wrte the total qualty offered to consumers by frm : a ΖaΗx Ηϒxj (1) where x s network nvestment undertaken by frm, and x j ndcates the nvestment by the rval. We assume that ϒ 01, s a parameter ndcatng the degree of roamng. Ths 7 Poyago-Theotoky (1999) consders a model of R&D where the degree of spllover s endogenous. In her model, the tmng of the game s dfferent from ours, n that the R&D nvestment decson (whch s equvalent to our nfrastructure nvestment decson) s made pror to the decson on how much nformaton to share wth compettors. In addton, she allows frms to choose dfferent levels of spllover. In our model, the degree of spllover (nterpreted as roamng qualty) s recprocal, n that the degree of spllover s dentcal n both drectons. When frms choose R&D cooperatvely they choose to fully dsclose ther fndngs, whereas when there s competton n R&D frms choose mnmal dsclosure. The latter result s very dfferent from what we fnd n our model.

8 8 parameter measures the externalty effect from sharng nfrastructure. If ϒ = 1, there s an agreement on full roamng, whle ϒ = 0 mples mnmum roamng qualty. The nverse demand functon faced by frm : p Ζa ϑq ϑqj The prce, p, s the subscrpton fee for avalablty (.e., a monthly fee). The externalty ntroduced above s such that when frm nvests n nfrastructure, the margnal wllngness to pay for the fnal products produced by both frms s ncreasng. 2.2 The supply sde We assume a lnear cost functon n the fnal stage for frm, gven by C Ζ cq. The cost c s the drect cost assocated wth access connecton of one user. We assume that frms face 2 quadratc (network nfrastructure) nvestment costs, gven by TC Εx Φ Ζ x / 2, where > 4/3. We wll later demonstrate that the restrcton on ensures a unque and stable equlbrum. Overall proft for frm s then: Ζ ( p ϑ c) q ϑ x 2 / 2 (2) 2.3 Welfare We assume that the regulator maxmzes welfare gven by the sum of producer and consumer surplus: W Ζ CS Η 1 Η 2 (3) Snce frms are symmetrc and the nverse demand functons are lnear wth dentcal slopes, we can wrte consumer surplus as each frm. 2 CS Ζ 2q, where q s the symmetrc producton level of 2.4 Cournot-competton (stage 3) At stage 3, frm maxmzes the proft functon: condtons for the two frms we obtan equlbrum quanttes: b g b g a c x x q j Ζ ϑ Η 2ϑ ϒ Η 2 ϒ ϑ1 3 Ζ ( p ϑ c ) q. Combnng the frst order

9 9 Note that n a symmetrc equlbrum ( a Ζ a ), the equlbrum quantty s gven by j q Z( a Jc) 3. 8 Ths quantty s monotonously ncreasng n a Ζ a, and ths mples that consumer surplus s monotonously ncreasng n a. Frm obtans stage 3 equlbrum profts j gven by q Ζ ( ) Infrastructure nvestment (stage 2) When frms nvest n nfrastructure at stage 2 of the game, they take nto account the effect such nvestments has on the stage 3 equlbrum Non-cooperatve soluton At stage 2, the frms maxmze the proft functon (2), subject to Cournot equlbrum quanttes at stage 3, whch mples that the (symmetrc) equlbrum nvestment s gven by: a c x ( 4J2ϒ )( J ) nc Z 9 J2( 2Jϒ)( 1Hϒ) In equlbrum, frms' profts are non-negatve for all permssble parameter values, and consequently frms wll partcpate n the game. Furthermore, the symmetrc equlbrum s the unque equlbrum. 9 Our result s analogous to d Aspremont and Jacquemn (1988) and Kamen et al. (1992), and s summarzed n the followng lemma: Lemma 1 If ϒ [ 1/ 2, then x and j Reversng the nequalty makes x and nc x are strategc complements; that s, ( x ) [ 0. x j strategc substtutes. x j When one frm nvests n ts nfrastructure, the equlbrum quantty of the other frm may or may not ncrease as a result of the spllover through the roamng agreement. As ponted out by Kamen et al. (1992), the spllover externalty (or nvestment externalty) s postve f and only f ϒ [ 1/ 2. In other words, the spllover externalty s postve only when x and strategc complements. (4) x j are 8 As t turns out, the unque equlbrum n nvestment s ndeed the symmetrc equlbrum. 9 2 The second-order condton requres that 2Ε2 ϑ ϒ Φ ϑ9 Ψ 0. In order to have a stable equlbrum the slope of the reacton functon has to have an absolute value below unty. It s straghtforward to demonstrate that ths condton s fulflled for > 4/3. Hence, the second order condton s also fulflled when we have assumed that >4/3. Fnally, t can be shown that the symmetrc equlbrum s ndeed unque.

10 Cooperatve soluton In the cooperatve case the two frms coordnate ther nfrastructure nvestments at stage 2, and compete à la Cournot at stage 3 n the same way as above. When determnng the proftmaxmzng choce of nvestments at stage 2, frm maxmzes the jont proft of the two frms (.e. ndustry profts): max µζ( q) Η( qj) ϑ ( x Ηxj) for j x 2 The followng frst-order condton yelds the equlbrum nvestment for a gven frm under colluson: 10 2 a c x ( J )( 1Hϒ ) c Z 2 9 J2( 1Hϒ) The cooperatve soluton yelds lower nfrastructure nvestment than the non-cooperatve, x Ψ, f and only f ϒ Y 1/ 2. Ths s equvalent to the results obtaned by d'aspremont and c x nc Jacquemn (1988) and Kamen et al. (1992). Observe furthermore that for ϒ Ψ 1/ 2, equlbrum quantty n the fnal stage of the game s lower under colluson relatve to the non-cooperatve case. Consequently, consumer surplus s, on the one hand, lower under colluson relatve to non-cooperaton f the roamng qualty s suffcently low. If, on the other hand, ϒ [ 1/ 2, consumers' surplus s hgher under colluson at the nvestment stage. In addton, frms' profts under colluson are always at least as large as under non-cooperaton. For ϒ Ζ1/ 2frms are ndfferent between colluson and noncooperaton at stage 2. Consequently, a welfare-maxmzng regulator would, provded that the roamng qualty s suffcently hgh (.e. ϒ [ 1/ 2 ), choose to allow colluson at stage 2 and such colluson would be n the frms' nterests. In the next secton we examne whch level of roamng qualty a welfare-maxmzng regulator would choose. (5) 2.6 Roamng qualty (stage 1) In ths secton, we extend the model by consderng the two cases where: 1) Frms decde roamng qualty (voluntary roamng) and 2) the regulator decdes roamng qualty (mandatory 10 In the same way as n game 1, the second-order condton, 2( 1Hϒ) 2 J9 Y0, s satsfed wth our parameter restrctons.

11 11 roamng). These two cases combned wth the two ways of determnng nvestments at stage 2 yelds four dfferent games (see Fgure 1). The analyss n ths secton can be seen as an extenson to the basc model wth exogenous R&D spllovers to examne endogenous spllovers Game 1, voluntary roamng when nvestments are determned non-cooperatvely Recall that equlbrum nfrastructure nvestment (under non-cooperaton) s gven by equaton (4). Drect dfferentaton of (4) yelds the followng result: Lemma 2 When frms determne the nvestments non-cooperatvely, the nfrastructure nvestment decreases as the roamng qualty ncreases snce x / ϒ Ψ 0. The ntuton behnd Lemma 2 s as follows: We are consderng the equlbrum wth recprocal spllover levels, mplyng that both frms fnal products ncrease n value to consumers by the same proporton (contrary to what s the case n secton 3). Hence, there s no product dfferentaton gan from nvestments for any of the frms. When frms do not cooperate at the nvestment stage, they do not nternalze the effect of the nvestment on the other frm s proft. An ncrease n the degree of roamng qualty s thus affectng the margnal revenue from nvestng n nfrastructure adversely, due to the fact that the nvestng frm s unable to capture the effect on the rval s proft. When examnng the stage 3 equlbrum we observe that equlbrum quanttes ncrease n both the degree of roamng qualty and the nvestment level. Snce quanttes are strategc substtutes, the rval frm wll ncrease ts producton f you reduce yours. Each frm wll then have to be more cautous and raton ts producton of the fnal product more than s the case f they collude n the nvestment stage. To acheve a substantal enough reducton, any gven frm wll have to lmt ts producton even more. Consequently, snce q ncreases when ϒ ncreases and Εq Η q j Φ ncreases when x ncreases, the nvestng frms can raton the fnal product market by reducng the level of nvestments when the degree of roamng qualty ncreases. The compettve equlbrum nfrastructure nvestment s gven by equaton (4); x nc nc Z x ( ϒ ). ' From Lemma 2 we know that x nc ( ϒ) Y 0. Usng the symmetry of the problem the equlbrum proft s accordngly: Z F HG I K J J 2 2 ah( 1Hϒ) xnc( ϒ) Jc ( xnc( ϒ)) 3 2 nc (7)

12 12 By dfferentatng equlbrum proft wth respect to ϒ, we fnd the roamng qualty preferred by the frms. c b g b ghc bgb g bgh bg 2 ' ' ajch 1Hϒ xnc ϒ xnc ϒ H 1Hϒ xnc ϒ J xnc ϒ Z0 9 It can be shown that the optmal ϒ for the frms s ndependent of (a-c). The soluton to equaton (8) wll be a functon of the convexty of the nvestment cost functon,.e. of the value for. The proft maxmzng choce wth respect to ϒ s ncreasng and concave n and strctly larger than 9/10. As an example; when Ζ 3 / 2 the expresson gven by equaton (8) s concave over the nterval where t s defned and the frst order condton s satsfed for ϒ Ζ If the frms determne roamng qualty, the frms wll accordngly agree on ϒ Ζ as the preferred level of roamng. However, there may be a commtment problem for the frms. After frms have chosen ther level of expendture on network nfrastructure (at stage 2), both frms have an ncentve to renegotate the roamng qualty between stages 2 and 3. The reason for ths s that for a gven level of x, the (stage 3) Cournot-equlbrum proft of both frms s strctly ncreasng n ϒ. If frms cannot commt to the roamng qualty chosen at stage 1 of the game, we may thus experence hold-up problems n network nfrastructure nvestments. 11 As ndcated earler, ths commtment problem s solved f roamng polcy s embedded n the network desgn, such that the frms cannot change roamng polcy after the nvestments have been made. Furthermore, n secton 3, we demonstrate brefly that the ntroducton of a vrtual operator can elmnate the potental commtment problem for the frms. (8) Game 2, mandatory roamng when nvestments are determned noncooperatvely In ths secton we nvestgate the roamng qualty a welfare-maxmzng regulator would choose, whch can ether be consdered as a benchmark case or as the chosen roamng qualty under mandatory roamng. We assume that the regulator maxmzes the objectve functon gven by equaton (3). Producer surplus s calculated above (equaton 7). Consder now the roamng qualty preferred by consumers. We know that the equlbrum s symmetrc n the 11 Snce the frms proft s ncreasng n roamng qualty for a gven level of nvestment, frms have ncentves to ncrease ϒ to ts maxmum after the nvestments are sunk. The hold-up problem arses because we know that when nvestments are made non-cooperatvely, the margnal revenue of the nvestments s reduced when ϒ ncreases. Thus, f frms know that, ultmately, roamng qualty s chosen to gve perfect roamng, they wll hold back on nvestments.

13 13 sense that the two frms nvest n the same level of nfrastructure and that they offer the same quantty at stage 3 of the game. Let x and q denote the proft-maxmzng choces of nvestment and quantty, respectvely. In the equlbrum, we have the followng equlbrum prce: b g pζaη 1Ηϒ x ϑ2q Insertng for the non-cooperatve equlbrum nvestment gven by equaton (4), and ca f a f h 2baJcg Hb1Hϒgxncbϒg q Ζ aϑc Η 1Ηϒ x nc 3 the consumer surplus becomes: 2 CSnc Z (9) 9 By dfferentatng consumer surplus gven by equaton (9) wth respect to ϒ, we fnd that the frst order condton s satsfed for roamng qualty ϒ = Consequently, a roamng qualty determned at ϒ Ζ 05. s the consumer surplus maxmzng qualty level. 13 The roamng level maxmzng consumer surplus can be compared to the roamng qualty maxmzng profts for the frms, (equaton 8). In secton we demonstrated that the roamng level maxmzng producer surplus s strctly larger than 9/10. It s accordngly evdent that the frms prefer a roamng level exceedng the roamng level preferred by consumers. Snce welfare s the sum of consumer and producer surplus, the welfare maxmzng roamng level (game 2) s below the level preferred by the frms (game 1). Ths result s summarzed n Proposton 1: Proposton 1 Assume that nvestments are undertaken non-cooperatvely. Voluntary roamng nduces frms to choose a hgher level of roamng qualty relatve to the socal optmum. Consequently, n a voluntary roamng regme frms nvest less n network nfrastructure than n a mandatory regme. The ntuton behnd ths result s as follows: For a gven quantty of the fnal product, the consumers beneft from hgh levels of nfrastructure nvestments. Frms also beneft from hgh levels of nvestments, ceters parbus. However, the nvestng frms cannot capture all of the benefts from the nvestments (due to the spllover externalty through the roamng agreement) and, n addton, frms face convex costs of nvestng. Consequently, frms wll 12 The soluton that ϒ = 0.5 maxmzes consumers' surplus s also ndependent of the convexty of the nvestment cost functon,.e. of the value for. 13 The second-order condton for CS s satsfed for all permssble values of ϒ.

14 14 choose a lower level of nvestment compared to the level that maxmzes consumers surplus. Furthermore, from Lemma 2 we know that ncentves to nvest n nfrastructure are worse the hgher the degree of roamng qualty. In a stuaton wth hgh roamng qualty, each of the nvestng frms wll attempt to be a free rder on the other frm's nvestments. Consequently, the equlbrum nvestment level wll be lower. On the other hand, a welfare-maxmzng regulator wll be able to nternalze all the externaltes of roamng. Thus, when roamng s voluntary frms choose a hgh level of roamng qualty to reduce nvestment ncentves. When roamng s mandatory, a lower level of roamng qualty s chosen to nduce hgher levels of nvestment n network nfrastructure. If frms are not allowed to collude at the nvestment stage, regulatory nterventon may be needed. In ths case, frms would set a hgher roamng qualty than the socally optmal level. Consequently, frms would agree on more compatblty than what would be benefcal to consumers and socety as a whole. For consumers, an ncrease n roamng qualty has two potentally opposng effects. Increased roamng qualty mples (under non-cooperaton) that nvestment s reduced. Ths mples that the sze of the market s reduced (the nverse demand functon s shfted nwards). For a gven quantty, ths results n a reducton n the prce charged to consumers. Ths has a postve mpact on consumers' welfare. However, a reducton n nfrastructure results n a reducton n quanttes sold n the last stage of the game. Ths has a negatve mpact on consumers' welfare. The overall effect of ncreasng qualty s postve for low levels of roamng qualty, and negatve for hgh levels. For a suffcently hgh roamng qualty, an ncrease n roamng qualty reduces consumers' welfare. Frms, on the other hand, can by settng a hgh roamng qualty restrct the sze of the nfrastructure nvestments. As a result, the output of the fnal product n stage 3 of the game s also restrcted, wth an ncrease n equlbrum prce Game 3 and 4, voluntary and mandatory roamng when nvestments are determned cooperatvely Recall that the equlbrum nvestment as a functon of roamng qualty s gven by equaton (5). Drect dfferentaton yelds the followng result: Lemma 3 When frms collude at the nvestment stage, the nfrastructure nvestment ncreases as the roamng qualty ncreases snce x c / ϒ [ 0. Contrary to the case of non-cooperatve nvestment, the ncentves to nvest are n fact hgher when the roamng qualty s hgh. In ths case, frms acheve a better coordnaton due to the

15 15 fact that the effect on the other frm s profts s nternalzed. Thus, all benefts from the nvestments are credted to the nvestng frm, whch changes nvestment ncentves qualtatvely. There s no longer the problem that each of the nvestng frms wll have ncentves to free rde on the other frm's nvestments. If frms determne a hgh (low) level of roamng qualty, each frm's nvestment presents a large (mnor) postve external effect the frms jontly can nternalze. By nsertng for the collusve equlbrum nvestment, x c (gven by equaton 5), and thrd stage equlbrum quanttes, we obtan consumer surplus (under colluson), CS c : Εa ς cφε1 Τ ϒ Φ ς 2Ε1 Τ ϒ Φ 2 2 a ς c 2 CS c φ 2 Τ 2 3 3Ε9 Φ When frms decde on nfrastructure nvestments collusvely, consumer surplus gven by equaton (10) s ncreasng and convex n roamng qualty over the relevant nterval for ϒ. Consequently, the optmal ϒ for consumers s equal to unty (or maxmal roamng qualty). Quantty s ncreasng n roamng qualty both drectly and through the effect of roamng qualty on nvestment. Furthermore, consumer surplus s ncreasng n quantty. Thus, a hgher roamng qualty mples a hgher level of consumers' surplus. Frms maxmze ther equlbrum proft under colluson wth respect to ϒ, whch results n: (10) ϒ φ 2q c xc 3 1Τ ϒ xc Τ 3 ϒ ϑ x c xc ϒ (11) where q c s the stage 3 equlbrum quantty for each frm f frms collude at the nvestment stage. In the colluson case, the proft functon s ncreasng and convex n ϒ over the nterval [0,1]. Ths mples that the optmal roamng qualty for frms corresponds to the maxmal roamng qualty. We summarze our fndngs n Proposton 2: Proposton 2 Assume that frms collude at stage 2. The (unregulated) proft maxmzng choce of roamng qualty s dentcal to the choce of a regulator maxmzng welfare. Consequently, the level of nvestments n nfrastructure s dentcal n both the voluntary and mandatory roamng regmes. Snce frms' and consumers' nterests concde there s no reason for governmental nterventon and there s no need for consderng game 3 and 4 separately. As n the noncooperatve case, consumers beneft from hgh nvestments n nfrastructure for a gven producton level. However, to acheve hgh levels of nvestments, consumers now choose a

16 16 hgh level of roamng qualty. The man reason for the dfference n our result s that frms, when they are allowed to coordnate ther nvestments, are able to capture all benefts from the nvestments. Because of ths, frms nvestment ncentves are changed and they now seek hgh roamng qualty to nduce hgh levels of nvestments, whereas n the non-cooperatve case they seek hgh roamng qualty to nduce low levels of nvestments. 2.7 Collusve and compettve nvestments compared At stage 2 of the game the level of nvestment n the network nfrastructure s determned. As already stated, frms can ether compete (games 1 and 2) or they can collude when determnng the nvestment level (games 3 and 4). We may thnk of the decson to allow frms to collude or not as a decson taken by the competton authortes pror to commencement of the 3-stage game we analyze above. Assumng that roamng s voluntary we can compare equlbrum under collusve and compettve nvestments, respectvely (.e. we compare games 1 and 3), to determne whether the nvestng frms should be allowed to collude or not at the nvestment stage. Under voluntary roamng the frms set the ϒ so as to maxmze profts. Frms are evdently better off under colluson as compared to compettve nvestments. 14 Furthermore, t follows from the calculatons above that equlbrum consumer surplus s hgher under colluson (game 3 and 4) as compared to equlbrum consumer surplus under compettve nvestments and mandatory roamng (game 1). 15 The ntuton behnd ths result s as follows: Consumers' surplus ncreases, both n roamng qualty for gven nvestments and n nvestment for a gven roamng qualty. Snce we have demonstrated that roamng s at the hghest possble level under collusve nvestments and that nvestments are hgher under colluson provded that ϒ > 0.5, consumer surplus wll ndeed be hgher under colluson. In the fgure below we llustrate the welfare effects of chosen roamng polcy for a regulator under the two nvestment regmes for the parameter values a = 3, c = 1, and Ζ 3 / 2 [ 4 / 3 : 14 When frms collude they can always mmc the outcome under competton, f they choose to devate from ths outcome t s because they are better off. 15 Ths result s derved by frst observng that consumer surplus (CS) s hgher n game 2 as compared to game 1. Then a suffcent condton for demonstratng that CS s hgher n game 3 and 4 as compared to game 2 s to assume that the regulator n game 2 determne the roamng at the level maxmzng CS (ϒ = 0.5). Then we can compare CS under colluson, equaton (10), for ϒ = 1 and compare t CS under compettve nvestments, equaton (9), for ϒ = 0.5. Then we fnd that CS game 3 and 4 CS game 2 CS game 1.

17 17 Collusve Investments Compettve Investments Optmal roamng n game 2 Fgure 2 Welfare comparson of colluson versus non-cooperaton It s evdent from the fgure above that socal welfare s maxmzed when the regulator allows frms to collude at stage 2, provded that the qualty of roamng s suffcently hgh (.e. for ϒ hgher than 0.5). We know from the analyss above that a welfare maxmzng regulator ndeed wll set the qualty of roamng equal to unty when frms collude at the nvestment stage. The fgure s also llustratng the, perhaps, counter ntutve results that t s detrmental to welfare to determne mandatory roamng at too hgh a level under compettve nvestments. Consequently, the competton authortes (or a regulator) can never do worse than allowng colluson at the nvestment stage, provded that the frms/regulator can commt to a suffcently hgh roamng qualty. The reason s that allowng colluson allows the postve external effects to be nternalzed. 3 Entry of a non-faclty-based frm In ths secton we analyze a stuaton where there are two dfferent types of frms. One type s faclty-based and nvests n ts own nfrastructure. We assume that there are two ncumbents whch both are faclty-based as n the prevous secton. The other type s an entrant that s a vrtual operator. The tmng of the game s the same as n the above analyss, but t s of course only the faclty-based frms whch undertake nvestments at stage 2 and we assume that the faclty-based frms have all the barganng power n determnng the qualty of roamng for the vrtual operator.

18 18 The model s amended to ncorporate the fact that there are now two types of frms. In the case where the entrant s a vrtual operator we have: f a ZaHx Hϒ xj v a ZaHϒ ( x Hx ), v where subscrpt, j = 1,2, j j represents the two ncumbents, and subscrpt v represents the vrtual operator. 16 The parameter ϒ f represents the degree of the roamng qualty between the faclty-based frms, whle ϒ v s the roamng qualty from a faclty-based operator to a vrtual operator. We restrct the analyss to the case where ϒ f ϒ v. 17 The parameters ϒ v and ϒ f can also be nterpreted as the vrtual operator s and faclty-based operator s capabltes of transformng the nputs nto a fnal product of hgh qualty, respectvely. The proft functons of the facltes frms are equal to equaton (2), whle the proft of the vrtual operator s v Z( p v Jcq ) v. By combnng the stage 3 frst order condtons for the three frms we obtan the followng equlbrum quanttes: f v f v q Z[( ajc) H x ( 3Jϒ Jϒ ) H x ( 3ϒ Jϒ J1)] / 4 v f q Z[( ajc) H( x H x )( 3ϒ Jϒ J1)] / 4 v j j 3.1 Incumbents set the nvestments non-cooperatvely When the two faclty-based frms set ther nvestment non-cooperatvely, we use the symmetry between the two frms, and we fnd the equlbrum nvestment for each facltybased frm: 18 x f v ( ajc)( 3 Jϒ Jϒ ) Z f v f v 8 J2( 3Jϒ Jϒ )( 1Hϒ Jϒ ) (12) 16 Ceccagnol (1999) gves a smlar formulaton wth process nnovaton. In contrast to us he only focuses on the case where the R&D-nvestment s set non-cooperatvely. 17 Ths seems to be an approprate assumpton f the vrtual operator s smply a reseller of artme (e.g. Sense Communcaton n Scandnava). However, f the vrtual operator has a well known brand name and possesses detaled knowledge about certan segments of the market (e.g. Vrgn n the UK), t may be reasonable to assume that nvestments beneft the vrtual operator more than they beneft the ncumbents. 18 The second order condton s fulflled f > 9/8, whch also ensures stablty.

19 19 We now examne how the equlbrum nvestment level x changes when f ϒ and v ϒ change: Proposton 3 When ntroducng a vrtual operator and the nvestments are made noncooperatvely by the faclty-based frms, ncreased roamng qualty between the nvestng f frms may result n a hgher equlbrum nvestment level;.e. x / ϒ [ 0 f and only f f v ϒ Ηϒ Ψ ϑ c h 2 3. Furthermore, ncreased roamng qualty to the vrtual operator reduces v nvestment ncentves, x / ϒ Ψ0. Proof: f v 2 x J( ajc)[8 J23 ( Jϒ Jϒ ) ] Z f f v f v ϒ [8 J23 ( Jϒ Jϒ )( 1Hϒ Jϒ )] f v 2 x J( ajc)[8 H23 ( Jϒ Jϒ ) ] Z v f v f v ϒ [8 J23 ( Jϒ Jϒ )( 1Hϒ Jϒ )] 2 2 Y 0 f v The frst expresson s postve f and only f [ 8 ϑ2( 3ϑϒ ϑϒ ) 2 ] Ψ0. Ths mples that f v f v ϒ Ηϒ Ψϑ3 2. Snce ϒ Η ϒ 02, the only root possbly satsfyng the nequalty s f v cϒ Ηϒ hψ2 ϑ3.qed. Recall the basc model wth only two faclty-based frms. Then, f nvestments were undertaken non-cooperatvely, the ncentves to nvest were lower the hgher the degree of roamng qualty was. For suffcently hgh values of the roamng qualtes we obtan a smlar result n the presence of a vrtual operator. We observe from Proposton 3 that, contrary to the basc model, the ncentves to nvest may n fact be mproved the hgher the roamng qualty s between the faclty-based frms. Ths wll be the case gven a combnaton of a f small sum of ( ϒ + v ϒ ) and suffcently large. In stage 1 of the game, ether the nvestng frms or the regulator choose the level of roamng qualty. Our fndngs suggest that f roamng s voluntary and nvestments are made noncooperatvely, the nvestng frms wll choose to set the roamng qualty between the nvestng f frms as hgh as possble ( ϒ Ζ 1). The roamng qualty between an nvestng frm and the v vrtual operator s set as low as possble ( ϒ Ζ 0 ). It may however be the case that proft for the vrtual operator s negatve n ths soluton. A suffcent condton for ensurng non-negatve profts for the vrtual operator s that the convexty of the nvestment cost functon s suffcently large (.e. for suffcently large). It can be shown that > 2 ensures non-negatve profts for the vrtual operator under

20 20 v f compettve nvestments. The ntuton behnd ths result s that when Ε3 ϑ ϒ ϑ1φ Ψ 0 ϒ any nvestments n nfrastructure undertaken by the faclty-based frms wll reduce the equlbrum output of the vrtual operator, and consequently, nfrastructure nvestments may be used to deter entry. If, however, the cost of nvestng s suffcently convex, then the equlbrum level of nvestment s low enough not to deter entry by the vrtual operator. We only consder the case where the faclty-based frms choose accommodaton of entry by the vrtual operator. In order to ensure ths we assume that the costs are suffcently convex (hgh value of ). As long as we have accommodaton of entry proposton 3 holds. However, for lower values of, t may be optmal for the faclty-based frms to nvest such that the vrtual operator s foreclosed from the market. In ths case, the hgher the f ϒ, the more the faclty-based frms have to nvest n order to deter entry. 19 v ϒ compared to When roamng s mandatory, a welfare-maxmzng regulator decdes the approprate levels. The regulator wll choose a roamng polcy that corresponds to the voluntary roamng case. Ths seems to correspond well to ntuton. By keepng v ϒ low and f ϒ hgh, frms have better ncentves to nvest n nfrastructure. Furthermore, a hgher level of nvestment leads to more output beng produced n the fnal product market, whch s a drect beneft to consumers. Consequently, there s lttle scope for regulatory nterventon n ths case. The man result n ths secton then suggests that the provson of the rght nvestment ncentves s of greater mportance than allowng the vrtual operator entry at equal terms to the ncumbents. 3.2 Incumbents set the nvestments cooperatvely When the faclty-based frms set nvestments cooperatvely they maxmze the jont proft, and by nsertng for optmal stage 3 quantty we obtan the followng equlbrum nvestment level: 20 x Ζ f ( a ϑ c)( 1 Η ϒ v ϑ ϒ ) f 4 ϑ 2( 1Η ϒ v 2 ϑ ϒ ) (13) 19 In a smlar context, the case where a faclty-based frm over-nvests to deter entry s analyzed by Foros (2000). 20 Note that for the equlbrum nvestment level to be postve, the nvestment cost needs to be suffcently convex; ths requres > 2.

21 21 Hence we have the followng results: Proposton 4 When faclty-based frms nvest n nfrastructure cooperatvely, the nvestment level s unambguously ncreasng n the degree of roamng qualty between the cooperatng f frms, x / ϒ [ 0, and decreasng n the roamng qualty between faclty-based frm and v the vrtual operator, x / ϒ Ψ0. The proof s straghtforward and hence omtted. Smlar to our fndngs when nvestment s undertaken non-cooperatvely, we observe that the equlbrum nvestment level s reduced whenever the roamng qualty between the nvestng frms and the vrtual operator ncreases. The ntuton s the same as n the non-cooperatve case. One mportant reason for nvestng n nfrastructure s to dfferentate ts product from that of the compettor. If the roamng qualty between the nvestng frms and the vrtual operator s suffcently hgh, the mportance of the dfferentaton effect dmnshes. As mentoned above, the degree of roamng qualty may be nterpreted ether as the qualty of the access provded to the vrtual operator or as the vrtual operator s capablty of transformng the product nnovaton resultng from the nvestment made by the faclty-based frms nto hgh qualty fnal products. Consequently, our fndngs suggest that any ncrease n the qualty of nput or n the vrtual operator s capabltes reduces the faclty-based frms ncentves to nvest n nfrastructure. Our results for both voluntary and mandatory roamng when nvestments are undertaken cooperatvely suggest that there s lttle scope for regulaton. Ths s also the case when nvestments are undertaken non-cooperatvely. Both the nvestng frms nterests and the nterests of a welfare-maxmzng regulator concde. When the faclty-based frms cooperate f v at the nvestment stage, they maxmze jont proft wth respect to Εϒ, ϒ Φ, whereas a f v welfare maxmzng regulator chooses Εϒ, ϒ Φ to maxmze the sum of profts and consumers' surplus. The soluton n both cases yelds maxmum roamng qualty between the faclty-based frms and mnmal roamng qualty between faclty-based frms and the vrtual operator. In order to ensure nonnegatve profts for the vrtual operator when ϒ v = 0 we must however make further restrctons on the convexty of the nvestment cost functon. A suffcent condton s that > 4. For a gven nvestment level, an ncrease n the degree of roamng qualty to the vrtual operator s a socal beneft and adds to consumers' surplus. However, ncreasng the roamng

22 22 qualty to the vrtual operator adversely affects the faclty-based frms' ncentves to nvest n nfrastructure, and hgher levels of nvestments s also a beneft to consumers. When a vrtual operator s allowed to enter and nvestments are undertaken collusvely the trade-off s the same as when nvestments are undertaken non-cooperatvely, and the nvestment ncentves domnate. 3.3 Some remarks on entry of a vrtual operator One remanng queston s whether the competton authortes (or a regulator) should allow a vrtual operator to enter or not. It s reasonable to assume that such entry should be encouraged f the entry mples that welfare s hgher than s the case n the absence of a vrtual operator. We assume that the decsons to allow entry by a vrtual operator and whether to allow colluson are taken pror to commencement of the three-stage game analyzed above. Wthout gong nto detals, t can be shown that welfare s hgher f colluson at the nvestment stage s allowed (as s also the case wthout a vrtual operator), and the reason s agan that the postve externalty can be nternalzed more easly under colluson. Furthermore, t can also be shown that welfare s ndeed hgher when entry of a vrtual operator s allowed when colluson s allowed. Snce we know that welfare under colluson s hgher than n the non-cooperatve case, we need to show that welfare under collusve nvestments wth a vrtual operator s hgher than wthout the vrtual operator. Then, we have essentally proven that the subgame-perfect equlbrum polcy for the government s to allow entry by a vrtual operator and allow faclty-based frms to cooperate at the nvestment stage. 21 Furthermore, we have seen that the optmal roamng polcy mples that the vrtual operator s only gven mnmal roamng qualty, whch means that the entry for the vrtual operator s not on partcularly generous terms. A fnal pont to be made s that the ntroducton of a vrtual operator can elmnate the commtment problem for frms. Note that frms choose the roamng qualty pror to undertakng nvestments, and n the absence of a vrtual operator frms may have ncentves to change the qualty of roamng after nvestments have been sunk. When a vrtual operator s allowed to enter, ths commtment problem s elmnated, and frms have no ncentves to change the qualty of roamng after nvestments are sunk. 21 The proof of ths result nvolves messy, but straghtforward algebrac manpulatons.

23 23 4 Concludng remarks We have dscussed roamng polcy (both voluntary and mandatory), and we have also brefly dscussed some competton polcy aspects related to sharng nfrastructure n the moble communcatons market. In partcular, we have focused on the nteracton between roamng polcy and nvestment ncentves n the thrd generaton moble networks (e.g. UMTS). We have shown that all nvolved are better off under colluson provded that roamng qualty s set suffcently hgh. Furthermore, n our model, the chosen level of roamng qualty s ndeed suffcently hgh n all cases. Ths mples that when a regulator or competton authorty chooses whether colluson at the nvestment stage should be allowed, they know that n whatever polcy they choose wth respect to roamng, they can never do worse than allowng colluson. In some of the Nordc countres, major players n the moble communcatons market have decded to cooperate n the process of settng up the next generaton moble networks, whch corresponds to the colluson case n our model. In danger of stretchng our model a lttle too far, we have shown that such colluson s actually benefcal n terms of welfare. Consequently, competton authortes should not nterfere wth such cooperaton. When we ntroduce a vrtual operator nto the game relyng on the faclty-based frms for nfrastructure access, we fnd that the relatonshp between roamng qualty and nvestment ncentves s qualtatvely dfferent. Furthermore, our fndngs suggest that there s lttle scope for regulaton of roamng qualty when there s a vrtual operator present, both under cooperatve and non-cooperatve nvestments. Ths s also dfferent from the case wthout the vrtual operator present, where the socal optmum does not correspond to the unregulated outcome f nvestments are undertaken non-cooperatvely. References Brod, A. and Shvakumar, R., Advantages of Sem-Colluson, The Journal of Industral Economcs, vol. 47, pp Busse, M., Multmarket contact and prce coordnaton n the cellular telephony Industry, Journal of Economcs & Management Strategy, vol. 9, pp Cave, M. and Vallett, T., Competton n the UK moble communcatons, Telecommuncaton Polcy, vol. 22, pp Ceccagnol, M. The Effects of Spllovers and Rvalry among Frms wth Heterogeneous Technologcal Capabltes on R&D Efforts, Mmeo, Crémer, J., Rey; P. and Trole; J., Connectvty n the commercal nternet, The Journal of Industral Economcs, vol. 48, pp d Aspremont, C. and Jacquemn, A., Cooperatve and Noncooperatve R&D n Duopoly wth Spllovers, Amercan Economc Revew, vol. 78, pp