Network interconnection with competitive transit

Transcription

1 Information Eonomis and Poliy 16 (2004) INFORMATION ECONOMICS AND POLICY Network interonnetion with ompetitive transit David Gilo a, *, Yossi Spiegel b a Buhman Faulty of Law and Reanati Graduate Shool of Business Adminstration, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel b Reanati Graduate Shool of Business Adminstration, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel Available online 5 Marh 2004 Abstrat We examine the interation between two interonneted networks (e.g., two loal exhange arriers (LECs)) and a third network (e.g., an interexhange arrier (IXC)) seeking aess to their ustomer base. The IXC ould either interonnet with both LECs or interonnet with only one LEC and transit alls to the other LEC via the first LECÕs network. We show that there is a wide set of ases in whih ompetitive transit ould justify partial or even omplete deregulation of aess to a networkõs ustomer base. Ó 2004 Elsevier B.V. All rights reserved. JEL lassifiation: L51; L96 Keywords: Interonnetion; Aess priing; Transit; Teleommuniation; Bill and keep 1. Introdution As network industries ontinue to open up to ompetition around the world, the terms under whih various networks interonnet have inreasingly beome the subjet of publi and regulatory debate. Interonnetions are partiularly important in the teleommuniations industry where ompetition has developed faster than in other network industries. In the US, urrent regulation of interonnetion among teleommuniation arriers may be lassified into interonnetions among ompeting loal exhange arriers (LECs) and interonnetions between LECs and interexhange * Corresponding author. addresses: gilod@post.tau.a.il (D. Gilo), spiegel@post.tau.a.il (Y. Spiegel) /$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi: /j.infoeopol

2 440 D. Gilo, Y. Spiegel / Information Eonomis and Poliy 16 (2004) arriers (IXCs). The first type of interonnetions is, pursuant to the 1996 Teleommuniations At, mandatory, and requires LECs to negotiate reiproal ompensation rates for alls made by subsribers of one LEC to subsribers of another LEC. The seond type of interonnetions is regulated pursuant to a series of Federal Communiations Commission (FCC) orders and rules. These orders and rules mandate interonnetion between LECs and IXCs while plaing a ap on the interonnetion fees that LECs harge IXCs. Strit regulation of aess to a networkõs subsriber base also haraterizes other network industries suh as able TV and eletriity. 1 The idea behind the reforms in network industries was to replae regulation with ompetition. In the ase of teleommuniations, US ourts and the FCC have stressed CongressÕs diretive that the [FCC] replae regulation with ompetition to the greatest extent possible onsistent with the publi interest...ompetitive markets are far better than regulatory agenies at alloating resoures and servies effiiently for the maximum benefit of onsumers. 2 At the same time, regulators remain onerned that ompetitive fores would not suffie to restrain the rates and onditions that networks set for granting other networks aess to their ustomer base. This paper examines a simple and extremely effetive market fore that ould justify (either partial or omplete) deregulation of interonnetions: The ability of one network, seeking aess to another networkõs ustomer base, to transit traffi to and from the other network via a third network. For example, when two LECs are interonneted, an IXC an transit long-distane alls to and from the subsribers of one LEC via the other LECÕs network. Likewise, an ISP an reah the ustomer base of one LEC or able arrier via another LEC or able arrier with whih the first arrier is interonneted. 3 1 For example, the FCC has been onsidering requiring able operators to furnish nondisriminatory able transmission apaity to unaffiliated Internet Servie Providers (ISPs) (See In re inquiry onerning high-speed aess to the Internet over able and other failities, FCC Reord, vol. 17, p. 4798, 7 (Delaratory Ruling and Notie of Proposed Rulemaking) (2002)). Similarly, in the ourse of restruturing the US eletriity markets, the Federal Energy Regulatory Commission (FERC) reinfored open aess and unbundling requirements to insure undisriminatory aess to publi utilitiesõ transmission failities by independent retailers and generators of eletriity. For a reent disussion of suh regulation, see See Southwestern Bell Telephone Company v. Federal Communiations Commission, 153 F.3d 523, 547, 549 (8th Cir. 1998). 3 The pratie of sending traffi to one network via another network is very ommon and is often referred to as least ost routing. Transit arrangements are ommon between Internet bakbones: when bakbone A purhases transit aess from bakbone B, it typially gains aess to all bakbones interonneted with bakbone B (see Cremer et al., 2000; Kende, 2000). Transit arrangements are also ommon in international teleommuniation. Two ountries an interonnet by transiting alls through a third ountry (see, e.g., FCC Releases 1996 International Traffi Data, 1998 FCC LEXIS 363, *12 13, 1998). Transit also exists in loal teleommuniation markets (see, e.g., In re Developing a Unified Interarrier Compensation Regime, CC Doket No , 2001 FCC LEXIS 2339 (Notie of Proposed Rulemaking, 2001) albeit it is not ommon in the ontext of interonnetion with IXCs, presumably beause diret interonnetion between LECs and IXCs is mandated under regulated rates. Transit urrently exists in ases where a network, typially a ellular or paging network, does not have diret interonnetion with a ertain LEC, see e.g., Texom, In. v. Bell Atlanti Corp., FCC Reord, vol. 17, p (2002) (disussing a dispute between a ellular network and a LEC that transited alls flowing between the ompeting LEC and the ellular network).

3 D. Gilo, Y. Spiegel / Information Eonomis and Poliy 16 (2004) Our model fouses on an IXC that faes two interonneted LECs and needs to pay them interonnetion fees for long-distane alls that either originate or terminate at their networks. Contrary to the urrent regime, in whih interonnetion between LECs and IXCs is heavily regulated, interonnetion between the LECs and the IXC in our model is ompletely deregulated. This is beause we are interested in finding out whether ompetitive transit an replae regulation. An important feature of the model is that the IXC need not interonnet diretly with both LECs; instead it an interonnet with a single LEC and transit alls to and from the other LEC via the first LEC. Antiipating their dealings with the IXC, the LECs negotiate either a positive or a negative reiproal aess fee for transited traffi that flows between their networks so as to boost their aess revenue from dealing with the IXC. 4 We therefore examine how, if at all, the reiproal aess fee that the two LECs negotiate should be regulated in order to restrain the interonnetion fees that LECs harge the IXC with no need for further regulatory intervention. We show that if the volumes of inbound and outbound long-distane traffi are equal, both LECs will voluntarily interonnet with the IXC at no harge, irrespetive of the value of the reiproal aess fee that the LECs have negotiated before dealing with the IXC. Interestingly, this outome is equivalent to that under mandatory interonnetion with a bill and keep regime whih was reently proposed by the FCC. Under this regime, all LEC interonnetion harges are regulated down to zero, unless the interonneting networks agree otherwise. 5 Transit has the obvious advantage that it leads to voluntary interonnetion at no harge without a need for any regulatory intervention. In ontrast, when the volumes of inbound and outbound long-distane traffi are unequal, the two LECs would strategially set the reiproal aess fee for transited long-distane traffi so as to fore the IXC to offer them higher interonnetion fees. This strategi behavior on the LECsÕ part may fore the IXC to pay the two LECs exessively high interonnetion fees. Nonetheless, we show that it is still possible to ahieve the same outome as in a bill and keep regime by mandating that the LECs will transit long-distane alls to one another at no harge. Given this requirement, the two LECs will voluntarily agree to interonnet with the IXC at no harge without a need for diretly regulating their interonnetion with the IXC. We also show that when the IXC an prie disriminate between diret and transited long-distane alls (and has all the bargaining power vis-a-vis the two LECs) then the IXC will be able to interonnet with both LECs at ost without a need for any type of regulation. The literature on aess priing is relatively new but is rapidly growing (see Armstrong, 2002; for a omprehensive literature survey). Eonomides et al. (1996a,b) examine ompetition between interonneted networks and find that a dominant network an prie squeeze an entrant by setting a higher prie for off-net alls than for 4 Throughout the paper we refer to the prie that the LECs pay one another for transited long-distane traffi as aess fee and refer to the pries that the IXC pays the two LECs as interonnetion fees. 5 For details, see Interarrier Compensation Proposal FCC Reord vol. 16, p. 9610, (2001). The FCCÕs Proposal is based mainly on two FCC working papers: Atkinson and Barnekov (2000) and DeGraba (2002).

4 442 D. Gilo, Y. Spiegel / Information Eonomis and Poliy 16 (2004) on-net alls. But, when aess harges must be reiproal, the prie differene between on-net and off-net alls disappears and monopoly beomes less likely. Armstrong (1998) and Laffont et al. (1998a) show that whenever networks ompete with one another by setting uniform per-all pries, an above-ost reiproal aess fee an be used as an instrument of tait ollusion. The reason for this is that an above-ost aess fee indues eah network to raise its per-all prie above its rivalsõ prie in order to indue its subsribers to make fewer off-net alls than they reeive and thereby ensure that the network enjoys an aess surplus. Laffont et al. (1998a,b) show that this onlusion no longer holds when networks an either use nonlinear pries and/or prie disriminate between on-net and off-net alls. Carter and Wright (2003) extend the Laffont et al. (1998a,b) model and onsider the ase of asymmetri networks. They show that under two-part tariffs, the larger network will always prefer a reiproal aess fee equal to ost, while the smaller network may prefer an above-ost reiproal aess fee for moderate levels of asymmetry. Valletti and Cambini (2003) endogenize the potential asymmetry between the networks by introduing a preliminary stage in whih the networks invest in their quality of servie. Sine in their model subsribers make more alls when the networkõs quality is higher, an aboveost reiproal aess fee will give the higher quality network an aess defiit vis-a-vis the lower quality network. As a result, the networks prefer to set an above-ost aess fee in order to soften the ompetition between them in the investment stage. Peitz (in press) shows that regulating aess pries to ensure that only an entrant enjoys an aess markup enhanes the likelihood of entry and, given entry, makes ompetition between the entrant and inumbent more intense. None of these papers, however, studied the interation between two interonneted networks and a third network whih is the main fous of our paper. Moreover, in our paper, the reiproal aess fee does not affet ompetition between the interonneted networks but rather affets their interation with a third network that seeks aess to their subsribers. The losest papers to ours are Carter and Wright (1999) and Wright (2002). They onsider two networks that ompete for ustomers and set aess fees that a third network must pay them for aess. They show that when the ompeting networks set unilateral aess fees and use two-part retail tariffs, they both wish to raise their aess fees and use the resulting revenue as a way to subsidize their fixed retail harges in an attempt to attrat more subsribers and boost their respetive market share. This will lead to esalation of the unilateral aess fees. This esalation an be mitigated or even ompletely eliminated if the two networks must agree on a ommon aess fee. These papers, however, do not onsider the possibility of ompetitive transit, whih is the main fous of our paper. Finally, Gilo (2003) disusses the legal and regulatory impliations of relying on transit as a market fore that ould restrain aess harges. The paper is organized as follows. Setion 2 presents the basi framework. Setion 3 derives the interonnetion fees that the IXC would offer and haraterizes the reiproal aess fee that the two LECs would hoose in antiipation of the IXCÕs offer. Aess prie disrimination is examined in Setion 4 and the ase in whih the LECs offer interonnetion fees to the IXC is examined in Setion 5. Conluding remarks appear in Setion 6.

5 2. The model D. Gilo, Y. Spiegel / Information Eonomis and Poliy 16 (2004) Consider two interonneted networks faing a third network that seeks aess to their ustomer base. For the sake of onreteness, we refer to the two interonneted networks as LECs and to the third network as an IXC although our analysis may also apply to other ases. For instane, the third network ould be an ISP or an internet bakbone seeking aess to the LECsÕ or to able arriersõ ustomer base, or an eletriity generator or retailer seeking aess to the transmission grids of interonneted eletri utilities. In order to fous on the interation between the two LECs and the IXC, we abstrat from ompetition in the loal exhange market and onsider the following three-stage game: In the first stage, the two LECs negotiate a reiproal per-all aess fee a for transited traffi that flows between their networks. 6 The aess fee a is paid by the sending network to the reeiving network. In the seond stage, the IXC offers the two LECs ontrats, ðp 1 ; bp 1 Þ and ðp 2 ; bp 2 Þ, where p 1 and p 2 are the per-all interonnetion fees that the IXC will pay the two LECs for inbound and outbound long-distane alls if both LECs interonnet with the IXC, and bp i is the per-all interonnetion fee for inbound and outbound alls that the IXC will pay LEC i ¼ 1; 2 if only LEC i interonnets with the IXC. In the third and last stage of the game, the two LECs simultaneously deide whether to aept or rejet the IXCÕs offer. If LEC j rejets the IXCÕs offer while LEC i aepts it, long-distane alls to and from LEC jõs ustomers will be transited via LEC iõs network. 7 If both LECs rejet the IXCÕs offers, the ustomers of the two LECs annot reeive or make longdistane alls (in equilibrium of ourse this is never the ase). Let Q 1 and Q 2 be the volumes of inbound long-distane alls that ustomers of LECs 1 and 2 reeive and mq 1 and mq 2 the orresponding volumes of outbound long-distane alls. That is, we assume that there is a onstant ratio, m P 0, between outbound and inbound long-distane alls and that this ratio is the same for both LECs. Although in general m is stritly positive, there are important ases in whih m ¼ 0 (i.e., no outbound traffi). Examples for suh one-way-aess situations inlude ISPs seeking aess to LECsÕ or able arriers ustomers base and eletriity generators or retailers seeking aess to eletri utilitiesõ transmission grids. To simplify matters, we assume that Q 1 and Q 2 are independent of the interonnetion fees that the IXC pays the two LECs. Admittedly, this assumption is restritive and should be relaxed in future researh. However, at least in the ase of the US, this assumption an be partly justified on the grounds that IXCs are required by the FCC to average their osts aross all of their subsribers regardless of the LEC they 6 In Mihigan Bell Telephone Company v. Chappelle, 222 F. Supp. 2d 905, (2002), the federal distrit ourt held that federal law does not deal with the issue of aess that a LEC provides for transited alls and that this issue is left to the state law governing the operations of the LEC. Hene, the aess fee a need not be equal to the aess fee that the LECs set for loal alls made between their respetive ustomers. 7 For all termination, the IXC an simply route the alls to LEC j via LEC iõs network. In the ase of all origination, the IXC an ask its LEC jõs ustomers to dial up a speial aess ode that routes their outbound alls via LEC iõs network.

6 444 D. Gilo, Y. Spiegel / Information Eonomis and Poliy 16 (2004) subsribe to. 8 Consequently, the interonnetion fees of one LEC, espeially if it is relatively small, will have only a small impat on the retail long-distane tariffs and hene on the volume of long-distane traffi. Without a loss of generality, we will assume that Q 1 P Q 2 : the volume of long-distane alls is greater in LEC 1 than in LEC 2. Aordingly, we will often refer to LEC 1 as the big LEC and LEC 2 as the small LEC. The LECs inur per-all osts for trunk transmission, o for all origination, and t for all termination. Hene, when a LEC is diretly interonneted with the IXC, the osts of originating and terminating long-distane alls, respetively, are þ o and þ t. When long-distane alls are transited, there is an additional trunk transmission ost sine the transited alls are routed through the networks of both LECs. Hene, transit is ineffiient. Yet, as we shall see, transit may arise if the aess fee, a, that the LECs negotiate for transited traffi that flows between their networks is relatively high. We now turn to the LECsÕ profits. The profit of LEC i when both LECs are interonneted with the IXC is p i ðy ; Y Þ¼Q i ðp i t ÞþmQ i ðp i o Þ: ð1þ The first term represents LEC iõs profit on inbound long-distane alls while the seond term represents its profit on outbound alls. In both ases, LEC i ollets from the IXC per-all interonnetion fee, p i, and bears the assoiated osts. If LEC i interonnets with the IXC while LEC j does not, then LEC iõs profit is p i ðy ;NÞ¼Q i ðbp i t ÞþmQ i ðbp i o ÞþQ j ðbp i a ÞþmQ j ðbp i þ a Þ: ð2þ In the opposite ase where only LEC j interonnets with the IXC, LEC iõs profit is p i ðn; Y Þ¼Q i ða t Þ mq i ða þ þ o Þ: ð3þ The first two terms in p i ðy ; NÞ represent LEC iõs profit on long-distane alls that terminate and originate at its own network, while the last two terms represent LEC iõs profit on alls that are transited to and from LEC jõs network. LEC i then pays LEC j a per-all aess fee a on inbound alls that terminate at LEC jõs network but reeives from LEC j a per-all aess fee a on outbound alls that originate at LEC jõs network. p i ðn; Y Þ has a orresponding interpretation. 3. Equilibrium To haraterize the (subgame perfet) equilibrium of the three-stage game desribed in the previous setion, we first solve the third stage of the game in whih the two LECs 8 See In re Poliy and Rules Conerning the Interstate, Interexhange Marketplae Implementation of Setion 254(g) of the Communiations At of 1934, as amended, CC Doket No , FCC Rd., vol. 11, p (Report and Order) (1996).

7 D. Gilo, Y. Spiegel / Information Eonomis and Poliy 16 (2004) simultaneously deide whether or not to aept the IXCÕs offer. We then turn to the seond stage of the game in whih the IXC makes offers to the two LECs in antiipation of their responses in the third stage. Finally we onsider the first stage of the game in whih the two LECs determine their reiproal aess fee, a, for transited traffi The interonnetion fees Given the IXCÕs offers, ðp 1 ; bp 1 Þ and ðp 2 ; bp 2 Þ, the payoff matrix in the third stage of the game is given by If the IXC wishes to interonnet with both LECs, it must indue a unique Nash equilibrium at (Aept, Aept). To this end, the IXCÕs offers ðp 1 ; bp 1 Þ and ðp 2 ; bp 2 Þ must satisfy the onditions (i) p 1 ðy ; Y Þ P p 1 ðn; Y Þ, (ii) p 2 ðy ; Y Þ P p 2 ðn; Y Þ, and either (iii) p 1 ðy ; NÞ > 0, or (iv) p 2 ðy ; NÞ > 0 (we assume that when indifferent, LECs aept the IXCÕs offer). Conditions (i) and (ii) ensure that (Aept, Aept) is a Nash equilibrium, while onditions (iii) and (iv) ensure that (Rejet, Rejet) is not a Nash equilibrium. Conditions (i) and (ii) require that p i P 1 m a; i ¼ 1; 2; ð4þ while onditions (iii) and (iv) require that bp 1 and bp 2 are suffiiently large. On the other hand, if the IXC wishes to interonnet exlusively with LEC 1, then it must indue a unique Nash equilibrium at (Aept, Rejet). Therefore, ðp 1 ; bp 1 Þ and ðp 2 ; bp 2 Þ must be suh that (i) p 2 ðy ; Y Þ < p 2 ðn; Y Þ, (ii) p 1 ðy ; NÞ P 0, and either (iii) p 1 ðy ; Y Þ P p 1 ðn; Y Þ, or (iv) p 2 ðy ; NÞ < 0. Conditions (i) and (ii) ensure that (Aept, Rejet) is a Nash equilibrium, while either onditions (iii) or (iv) ensures that (Rejet, Aept) is not a Nash equilibrium. Condition (i) and (iii) are equivalent to p 2 < a < p 1, ondition (iv) requires that bp 2 would be suffiiently small (say 0), and ondition (ii) is equivalent to bp 1 P bp 1 1 m þ K þð1 Þ a; ð5þ where K tþm o is a weighted average of the ost of all origination, o and all termination, t, and Q 1 Q 1 þq 2 is the share of long-distane alls that originate and terminate at LEC 1Õs network. The fee bp 1 is equal to the average ost of LEC 1 when it interonnets exlusively with the IXC. These average osts onsist of the

8 446 D. Gilo, Y. Spiegel / Information Eonomis and Poliy 16 (2004) transmission ost,, plus a weighted average of K (the ost of originating and terminating alls) and a (the ost of aess), with the weights being equal to the proportion of alls that terminate in LEC 1Õs own network and the proportion of alls that are transited to LEC 2Õs network. Analogously, to interonnet exlusively with LEC 2, the IXCÕs offer must be suh that p 1 < a < p 2, bp 1 should be suffiiently small (say 0), and bp 2 should be suh that bp 2 P bp 2 1 m þð1 ÞK þ a; ð6þ where bp 2 is the average ost of LEC 2 when it interonnets exlusively with the IXC. Using (4) (6) we establish the following result: Proposition 1. (The interonnetion fees) The IXC will interonnet with both LECs and will pay them a per-all fee a if 1 m a 6 K þ : Otherwise, theixc will interonnet exlusively with LEC 1 and will pay it a per-all fee bp 1 < a. Proof. Sine the IXC wishes to minimizes its per-all aess harges, it will offer a if it wishes to interonnet with both LECs and bp i if it wishes to interonnet exlusively with LEC i. Using (5) and (6), bp 1 bp 2 ¼ ð2 1Þ K 1 m a : Sine Q 1 P Q 2, Q 1 Q 1 þq 2 P 1 2. Hene, bp 1 P bp 2 There are now two possibilities: if K P a and bp 1 < bp 2 otherwise. (i) If K P a, then the IXC will either interonnet with both LECs or will interonnet exlusively with LEC 2. But sine K P a, bp 2 1 m a ¼ þ ð1 Þ K 1 m a P 0; so the IXC will interonnet with both LECs and will pay them a. (ii) If K < a, then the IXC will either interonnet with both LECs or will interonnet exlusively with LEC 1. Noting that bp 1 a ¼ þ K a ; 1 m 1 m

9 D. Gilo, Y. Spiegel / Information Eonomis and Poliy 16 (2004) the IXC will either interonnet with both LECs and will pay them a if a 6 K þ but will interonnet exlusively with LEC 1 and will pay it bp 1 if a > K þ. h The intuition behind Proposition 1 is as follows. To interonnet with both LECs, the IXC needs to offer the two LECs an interonnetion fee a sine this is the net per-all aess revenue that eah LEC an reeive by rejeting the IXCÕs offer and transiting all inbound and outbound long-distane alls via the rival LECÕs network. 9 On the other hand, if the IXC wishes to interonnet exlusively with LEC i, then rejeting the IXCÕs offer means that neither LEC will be interonneted with the IXC. Hene, to indue LEC i to agree to an exlusive interonnetion, the IXC must offer LEC i an interonnetion fee bp i equal to LEC iõs average ost and ensures that the LEC just breaks even on long-distane alls. When a is small (or even negative), it is heaper to interonnet with both LECs than interonnet exlusively with one of them. But sine bp 1 and bp 2 inrease with a at a rate of less than 1, it is lear that as a inreases, there eventually exists a ritial value of a above whih an exlusive interonnetion with one LEC is heaper than interonnetion with both LECs. Noting that sine P 1 2, a reeives a smaller weight in bp 1 than in bp 2 (the volume of transit alls is smaller when the large LEC has to transit long-distane alls to the small LEC than vie versa), it follows that when a is relatively large, it is heaper for the IXC to interonnet exlusively with LEC 1. Proposition 1 has at least two important impliations. First, transit is ineffiient sine eah transited all is transmitted through the networks of both LECs and hene involves an additional trunk transmission ost of. Hene, Corollary 1. (Effiieny) The equilibrium is ex post effiient only when a 6 K þ. Otherwise, long-distane alls to and from LEC 2 s ustomers are ineffiiently transited via LEC 1 s network. Seond, as mentioned in Setion 1, the FCC has reently proposed a new bill and keep regime aording to whih all LECsÕ interonnetion harges will be regulated to 0 unless the interonneting networks agree otherwise. Proposition 1 shows that whenever m ¼ 1 (the volumes of inbound and outbound long-distane alls are equal), ompetitive transit indues the LEC to interonnet with the IXC at no harge without any need for regulatory intervention. Intuitively, if LEC i refuses to interonnet with the IXC, then its long-distane alls are transited via LEC jõs network. But sine m ¼ 1, the resulting aess revenue (on inbound alls if a > 0 and 9 Note that a ould be negative in whih ase the LECs pay the IXC for interonnetion rather than vie versa. a will be negative if either m > 1 (more outbound than inbound long-distane alls) and a > 0, or when m < 1 (more inbound than outbound long-distane alls) and a < 0.

10 448 D. Gilo, Y. Spiegel / Information Eonomis and Poliy 16 (2004) outbound alls if a < 0) is just equal to the aess expenditure (on outbound alls if a > 0 and inbound alls if a < 0). That is, LEC i just breaks even on long-distane alls if it does not interonnet with the IXC. Consequently, the IXC an indue both LECs to interonnet with it at 0 interonnetion fee. By ontrast, when the volumes of inbound and outbound long-distane alls are unequal (i.e., m 6¼ 1), Proposition 1 shows that in general, the IXC will have to pay the LECs interonnetion fees that are different than 0. However, if the reiproal aess fee, a, is regulated to 0, then the two LECs would be willing to interonnet with the IXC at no harge. Again, the intuition for this is that by refusing to interonnet with the IXC, the net inome of eah LEC from long-distane alls (that are now transited through the network of the rival LEC) is 0. One again, it is possible to repliate the outome of a bill and keep regime for LEC IXC interonnetion without having to diretly regulate the interonnetion fees that the LECs harge the IXC. Corollary 2. (Repliating a bill and keep regime with ompetitive transit) The IXC will interonnet with both LECs at 0 fees if either the volumes of inbound and outbound long-distane alls are equal (i.e., m ¼ 1) or if the reiproal aess fee that the LECs harge one another, a, is equal to 0. In pratie, diret regulation of LEC IXC interonnetion should address not only the interonnetion fees that IXCs pay the LECs, but also an array of additional fators, suh as the quality of interonnetion, tehnial standards, and repair servies (see Gilo, 2003 for details). Corollary 2 suggests that in order to ahieve a bill and keep outome there is no need to regulate LEC IXC interonnetion: instead, it is enough to add an additional provision to the regulation of LEC LEC interonnetions (whih is regulated anyway for various reasons) stating that LECs should transit long-distane alls to one another at no harge. 10 Clearly then, ompetitive transit an lower the regulatory burden needed to enfore bill and keep outomes The hoie of the reiproal aess fee In this subsetion we turn to the first stage of the game in whih the two LECs negotiate their reiproal aess fee, a. Our main purpose is to examine the preferenes of the two LECs over a we will not postulate a partiular bargaining game and attempt to solve for a speifi value of a. Using Eq. (1) and Proposition 1, the profits of the two LECs, as funtions of a, are 10 In fat, the rates that inumbent LECs harge new LECs for transited alls are typially regulated anyway. See, e.g., US West Communiations v. TCG Seattle,1998 US Dist. Lexis 22271, at p. 9, 10; In re Petition of WorldCom, In. Pursuant to Setion 252(e)(5) of the Communiations At for Preemption of the Jurisdition of the Virginia State Corporation Commission Regarding Interonnetion Disputes with Verizon Virginia In., CC Doket No , 2003 FCC LEXIS 6879, at p. 76; Texom, In. v. Bell Atlanti Corp., FCC Reord, vol. 17 p (2002); and Mihigan Bell Telephone Company v. Chapelle, 222 F. Supp. 2d 905 (2002).

11 D. Gilo, Y. Spiegel / Information Eonomis and Poliy 16 (2004) ( p 1 ðaþ ¼ p 1ðN; Y Þ; if a 6 K þ ; 0; otherwise; ð7þ and p 2 ðaþ ¼p 2 ðn; Y Þ: ð8þ With Eqs. (7) and (8) in plae, we are ready to examine the preferenes of the two LECs for the reiproal aess fee, a. Proposition 2. (The LECs preferenes for the reiproal aess fee) If m ¼ 1, the two LECs are indifferent to the value of the reiproal aess fee, a. If m 6¼ 1, the big LEC, LEC 1 will prefer to set a suh that a ¼ K þ ; 1 m whih in turn indues the IXC to interonnet with both LECs at K þ =. By ontrast, the small LEC, LEC 2, will prefer to set a as negative as possible if m > 1 and as large as possible if m < 1. The equilibrium is effiient only if jaj 6 K þ. When theixc interonnets with both LECs, it offers them a per-all interonnetion fee a to ensure that the profit of eah LEC i is just equal to p i ðn; Y Þ whih is LEC iõs profit from rejeting the IXCÕs offer and transiting all inbound and outbound long-distane alls via LEC jõs network. As (3) shows, p i ðn; Y Þ is independent of a when m ¼ 1, implying that in this ase the LECs are indifferent to the value of a. When m > 1(m < 1), p i ðn; Y Þ is dereasing (inreasing) with a sine the LECÕs total expenditure on outbound alls is larger (smaller) than its total revenue from inbound alls. Hene, the two LECs wish to set a negative (positive) a to boost their profits from long-distane traffi. But, as jaj > K þ, the IXC offers interonnetion fees suh that LEC 2 refuses to interonnet with the IXC. In this ase, if LEC 1 rejets the IXCÕs offer as well, no LEC will interonnet with the IXC and LEC 1Õs profit will be 0. The IXC an therefore offer LEC 1 a fee bp 1 that leaves LEC 1 with a 0 profit. Obviously then, LEC 1 does not want jaj to exeed K þ. On the other hand, LEC 2 prefers to raise jaj as muh as possible. 11 Interestingly, Carter and Wright (2003) also find that a large network will prefer a low reiproal aess fee while the smaller network may prefer a high reiproal 11 Of ourse, if the demand for long-distane alls is prie elasti, then an inrease in jaj (that raises the interonnetion fees that the IXC pays the two LECs), will lead to higher retail pries for long-distane alls and hene will depress the demand for long-distane alls. Hene, even LEC 2 will wish to raise jaj only up to a ertain point.

12 450 D. Gilo, Y. Spiegel / Information Eonomis and Poliy 16 (2004) aess fee. Their model however only onsiders traffi between the two networks: there are no alls to and from a third network as in our model. Proposition 2 has several interesting impliations. First, at LEC 1Õs ideal a, the IXC interonnets with both LECs and pays them an interonnetion fee of K þ per-all. This fee dereases with whih is the share of long-distane traffi that originates and terminates at the big LEC, LEC 1. To the extent that a low ideal a for LEC 1 will translate to a low a, we an draw the following onlusion: Corollary 3. (The effet of the shares of the two LECs in the long-distane traffi) The IXC is better-off as the gap between the sizes of the two LECs grows. Seond, up to now we have impliitly assumed that transit is mandatory. A natural question to ask is what happens if the two LECs an refuse to transit alls to one another? To address this question, note that absent transit, the IXC needs to interonnet with both LECs so the profit of eah LEC i is given by p i ðy ; Y Þ (see Eq. (1)). To indue LEC i to interonnet, the IXC needs to offer LEC i an interonnetion fee suh that p i ðy ; Y Þ P 0. The lowest fee that ensures LEC i a nonnegative profit is K þ. With transit, the LECs lose money on long-distane alls if m ¼ 1 sine by Proposition 1, the IXC interonnets with both LECs at no harge. Hene, the two LECs are better-off ommitting not to transit long-distane alls to one another. In ontrast, if m 6¼ 1, then the two LECs make a positive profit on long- distane alls if they agree to transit alls and set jaj ¼ K þ. This reiproal aess fee indues the IXC to offer both LECs an interonnetion fee of K þ whih, given that < 1, exeeds the interonnetion fee absent transit, K þ. Consequently, both LECs an benefit from transit. Moreover, unless m ¼ 1, the small LEC, LEC 2, would like to raise jaj as muh as possible, whereas the big LEC, LEC 1, would like to raise jaj only up to K þ. But, if transit is not mandatory (eah LEC an refuse to transit alls to the rival LEC), then LEC 1 an threaten LEC 2 that if jaj > K þ, LEC 1 will refuse to transit long-distane alls to LEC 2. This threat is redible sine whenever jaj > K þ, the IXC offers LEC 1 an interonnetion fee bp 1 suh that LEC 1 just breaks even on long-distane alls and hene gains nothing from transiting alls to LEC 2. In ontrast, if transit is mandatory, then (at least in priniple) LEC 2 might be able to fore LEC 1 to agree to set jaj above K þ. Hene, Corollary 4. (Voluntary transit) If m ¼ 1 then the LECs are better-off ommitting not to transit long-distane alls to one another. If m 6¼ 1, then both LECs an benefit from agreeing to transit long-distane alls to one another. Moreover, allowing LEC 1 to refuse to transit long-distane alls to and from LEC 2 enables LEC 1 to fore LEC 2 to agree to set the aess fee, a, equal to ðk þ Þ whih is LEC 1 s ideal aess fee when m 6¼ 1.

13 D. Gilo, Y. Spiegel / Information Eonomis and Poliy 16 (2004) To the extent that it is soially desirable to keep jaj (and thereby the interonnetion fees) low, Corollary 4 suggests that it may be a poor idea to fore the LECs to transit long-distane alls to eah other: under mandatory transit, the reiproal aess fee may be set suh that jaj > K þ, in whih ase the IXC will ineffiiently interonnet exlusively with LEC 1. By ontrast, when LEC 1 an refuse to transit long-distane alls to LEC 2, jaj 6 K þ and the IXC interonnets with both LECs. 4. Aess prie disrimination In this setion we onsider the ase in whih the IXC an offer the LECs interonnetion fees that depend on whether alls originate or terminate at a LECÕs network or are transited to and from the rival LEC. That is, we onsider the ase where the IXC an prie disriminate between alls depending on their destination. Speifially, let p 11 and p 22 be the interonnetion fees that the IXC offers the two LECs for alls that originate or terminate at their own networks, and p ij be the interonnetion fee that the IXC offers LEC i for alls that originate or terminate at LEC j and are transited via LEC iõs network. Let bp ii and bp be the orresponding interonnetion fees when only LEC i aepts the IXCÕs offer. Proposition 3. (Prie disrimination) Suppose that the IXC an prie disriminate between long-distane alls that terminate in a LEC s network and alls that are transited to the rival LEC. Then, the two LECs will set a reiproal aess fee a ¼ ðk þ Þ and the IXC will interonnet with both LECs and will pay eah LEC an interonnetion fee K þ per-all. Proof. We begin by onsidering the IXCÕs offer to the two LECs given the reiproal aess fee a that the two LECs have negotiated in stage 1. If a < K þ, the IXC offers p 11 ¼ p 22 ¼ a, bp 11 ¼ bp 22 ¼ K þ, and bp 12 ¼ bp 21 ¼ a þ. If both LECs aept the offer, then the profit of LEC i is Q i ðp ii t Þþ mq i ðp ii o Þ. If LEC i rejets the offer, then LEC j will surely aept it sine with bp jj ¼ K þ and bp ji ¼ a þ, LEC jõs profit is 1 m 1 m Q j ðk t ÞþmQ j ðk o ÞþQ i a a þ mq i a þ a ¼ 0; exatly as in the ase where LEC j rejets the IXCÕs offer as well (in whih ase no LEC is interonneted with the IXC); we assume that when indifferent, a LEC aepts the IXCÕs offer. Sine LEC j aepts the IXCÕs offer, LEC i will reeive its longdistane alls via LEC jõs network and its profit is given by p i ðn; Y Þ (see Eq. (3)). Equating Q i ðp ii t ÞþmQ i ðp ii o Þ and p i ðn; Y Þ reveals that p ii ¼ a is the minimal interonnetion fee that will indue both LECs to aept the IXCÕs offer.

14 452 D. Gilo, Y. Spiegel / Information Eonomis and Poliy 16 (2004) If a P K þ, then the IXC would onede rents to the LECs if it were to make the above offers. Therefore, the IXC an modify its offer by setting p 11 ¼ p 22 ¼ K þ and bp 12 ¼ bp 21 ¼1. Now, if a LEC refuses to interonnet with the IXC, its profit will be 0 sine with bp 12 ¼ bp 21 ¼1, the IXC will never transit alls to this LEC via the rival LECÕs network. With p 11 ¼ p 22 ¼ K þ, both LECs will aept the IXCÕs offer sine at these interonnetion fees, they both break even on long-distane alls. Given the IXCÕs offer, the LECs lose money on long-distane alls if a < K þ and break even otherwise. Hene the two LECs will set a ¼ K þ in the first stage of the game, or a ¼ ðk þ Þ. In the resulting equilibrium, the IXC will interonnet with both LECs and will pay an interonnetion fee K þ on eah all. h Proposition 3 shows that under aess prie disrimination, the interonnetion fees that the IXC pays the two LECs are equal to those that would obtain in the absene of transit. The idea behind this result is as follows. To indue a LEC to interonnet with the IXC at minimal fees, the IXC must offer eah LEC i an interonnetion fee that leaves LEC i as well off as in the ase where it rejets the IXCÕs offer. If a < K þ, LEC i would lose money by refusing to interonnet with the IXC and transiting all long-distane alls via LEC jõs network. The minimal interonnetion fee that the IXC needs to offer LEC i in this ase is a, whih by design, leaves LEC i with a loss on eah long-distane all. However when a P K þ, transiting long-distane alls via LEC jõs network is not a losing proposition anymore for LEC i. Hene, if transit is an option, the IXC must offer eah LEC i an interonnetion fee that leaves the LEC a positive rent. But, when the IXC an prie disriminate between diret and transited long-distane alls, it an redibly ommit not to send or reeive suh alls by raising the interonnetion fee on transited alls to a prohibitive level. 12 As a result, a LEC an offer its ustomers aess to long-distane alls only if it interonnets diretly with the IXC: transit is not a viable option anymore. Sine the IXC an make take-it-or-leave-it offers to the two LECs, it an offer them interonnetion fees that just over their osts but leave them no rent. A similar strategy is impossible in the no disrimination ase sine the IXC must set the same interonnetion fee for diret and transited long-distane alls and therefore has no way of redibly ommitting to blok transited alls. The two LECs an therefore take advantage of that and set up a high jaj that fores the IXC to offer them higher interonnetion fees. By revealed preferenes, it is not surprising that the ability to prie disriminate between diret and transited alls benefits the IXC. Proposition 3 shows however 12 Alternatively, if a LEC an unilaterally refuse to transit alls, then the IXC an offer a prie of 0 on suh alls in whih ase, it will not pay a LEC to transit alls to and from a rival LEC and the same outome will emerge.

15 D. Gilo, Y. Spiegel / Information Eonomis and Poliy 16 (2004) that aess prie disrimination may also be welfare enhaning by leading to lower interonnetion fees and by ensuring that the IXC will eventually interonnet with both LECs. The reason why prie disrimination leads to a lower reiproal aess fee, a, is that if the LECs would try to set a high jaj as in the no disrimination ase, the IXC would set a prohibitively high fee on transit alls and would thereby ommit not to send or reeive suh alls. This lowers the disagreement payoffs of the two LECs and would fore them to aept lower interonnetion fees. 5. The LECs make offers Thus far, we have assumed that the IXC has all the bargaining power vis-a-vis the two LECs and an make them take-it-or-leave-it offers. In this setion we examine the opposite polar ase in whih the LECs have all the bargaining power vis-a-vis the IXC. Let ðr 1 ; br 1 Þ and ðr 2 ; br 2 Þ be the ontrats that the two LECs offer the IXC, where r i is the per-all interonnetion fee that LEC i demands in ase eah LEC reeives its long-distane alls diretly from the IXC, and br i is the per-all interonnetion fee if the IXC interonnets exlusively with LEC i. We assume that the LECs do not prie disriminate between diret and transited alls. 13 The IXC an either aept or rejet eah offer. If it aepts both offers, its total expenditure on interonnetion fees is ðþðq 1 r 1 þ Q 2 r 2 Þ, while if it interonnets only with LEC i, its total expenditure is ðþðq 1 þ Q 2 Þbr i. Realling that Q 1 Q 1 þq 2, it follows that the IXC will interonnet with both LECs if and only if r 1 þ ð1 Þr 2 6 min fbr 1 ; br 2 g: ð12þ If (12) fails, the IXC will interonnet exlusively with the LEC that demands the minimum between br 1 and br 2.Ifbr 1 ¼ br 2, the IXC will pik one of the two LECs at random and will interonnet exlusively with that LEC. Consequently, LEC iõs expeted profit is >< p i ¼ 8 Q i ðr i t ÞþmQ i ðr i o Þ; if ð12þ holds; Q i ðbr i t ÞþmQ i ðbr i o Þ þq j ðbr i a ÞþmQ j ðbr i þ a Þ; if ð12þ fails and br i < br j ; ðq i ðbr i t ÞþmQ i ðbr i o Þ þq j ðbr i a ÞþmQ j ðbr i þ a ÞÞ=2; if ð12þ fails and br j ¼ br i ; >: Q i ða t Þ mq i ða þ þ o Þ; if ð12þ fails and br i > br j : ð13þ 13 In a previous version of this paper we showed that when the LECs have all the bargaining power vis-avis the IXC, the LECsÕ ability to prie disriminate between diret and transited long-distane alls is immaterial in the sense that the results do not hange in the presene of prie disrimination.

16 454 D. Gilo, Y. Spiegel / Information Eonomis and Poliy 16 (2004) Using (13) we now haraterize the equilibrium offers of the two LECs and the IXCÕs response. Proposition 4. (The interonnetion fees when the LECs make offers to the IXC) Suppose that the LECs an simultaneously make offers totheixc. Then the equi- librium offers, ðr1 ; br 1 Þ and ðr 2 ; br 2Þ will be suh that a 6 r1 6 a þ, a 6 r2 6 a þ, and br 1 ¼ br 2 ¼ r 1 þð1 Þr 2. The IXC will aept both offers and will transfer long-distane alls diretly to eah LEC. The resulting equilibrium will therefore be effiient. Proof. First note that in equilibrium, (12) must hold with equality, otherwise eah LEC i an make more money by raising r i slightly. Seond, note that (12) annot fail: if it does and br i < br j, then LEC i an make more money by raising br i slightly. If (12) fails and br 1 ¼ br 2, then LEC iõs expeted profit is given by the expression in the third line of (13). If this expression falls short of the expression in the fourth line of (13), it pays LEC i to raise br i. If the expression in the third line of (13) is at least as large as that in the fourth line of (13), then it pays LEC i to lower br i slightly. Hene, in equilibrium, (12) must hold with equality and LEC iõs profit is given by the expression in the top line in (13). Sine (12) holds with equality, we will restrit attention to ases in whih br 1 ¼ br 2 ¼ br, where (12) implies that br ¼ r 1 þð1 Þr 2. We do so beause given r 1 and r 2, there exists a ontinuum of equilibria that differ only with respet to the value of maxfbr 1 ; br 2 g. But sine all of these equilibria are payoff equivalent, it is natural to fous on symmetri ases in whih br 1 ¼ br 2 ¼ br. Now, note that raising r i and br i will violate (12); sine br i will exeed br, the IXC will interonnet exlusively with LEC j so LEC iõs profit will beome Q i ða t Þ mq i ða þ þ o Þ. To ensure that this deviation is unprofitable, it must be that in equilibrium, Q i ðri t ÞþmQ i ðri o Þ P Q i ða t Þ mq i ða þ þ o Þ; i ¼ 1; 2; or equivalently, r1 P a and r2 P a. Likewise, lowering br i slightly will violate (12) and indue the IXC to interonnet exlusively with LEC i, in whih ase its profit will be almost Q i ðbr t ÞþQ j ðbr a Þ. To ensure that this deviation is unprofitable, it must be that in equilibrium Q i ri t þ mqi ri o P Q i ðbr t ÞþmQ i ðbr o ÞþQ j ðbr a ÞþmQ j ðbr þa Þ ¼ Q i ri t þ mqi ri o þ Qj rj a þ mq j rj þ a ; ð14þ where the last equality follows beause (12) holds with equality. Inequality (14) requires that rj 6 a þ, j ¼ 1; 2. We omplete the proof by showing that any triplet ðr1 ; r 2 ; br Þ suh that a 6 r1 6 a þ, a 6 r2 6 a þ, and br ¼ r1 þð1 Þr 2 an be

17 an equilibrium. In equilibrium, LEC iõs profit is given by the top line of (14). Fixing LEC jõs offer, letõs onsider possible deviations for LEC i. Raising both r i and br i will indue the IXC to interonnet exlusively with LEC j, so LEC iõs profit will be given by the fourth line in (13); sine ri P a, suh a deviation does not inrease LEC iõs profit. Raising r i while lowering br i below br will indue the IXC to interonnet exlusively with LEC i. The resulting profit of LEC i will be less than the expression in the middle line of (14) and hene is unprofitable. Raising r i while keeping br i ¼ br will indue the LEC to pik one of the LECs at random and interonnet exlusively with that LEC. The resulting expeted profit of LEC i is half of the expression in the middle line of (14), and hene is unprofitable as well. Hene, it never pays LEC i to hange r i : But if r i is onstant, then raising br i above br does not affet the equilibrium, while lowering br i below br will indue the IXC to interonnet exlusively with LEC i, so LEC iõs profit will be given one again by the expression in the middle line of (14). h Comparing Propositions 1 and 4 reveals that the LECs benefit when they have all the bargaining power vis-a-vis the IXC in the sense that they end up reeiving higher interonnetion fees from the IXC: when the IXC has all the bargaining power, the interonnetion fees are at most a, while ifthe two LECs have the bargaining power, the interonnetion fees are at least a. Moreover, Proposition 4 shows that when the LECs have all the bargaining power, the IXC will effiiently interonnet diretly with both LECs implying that the potential ex post ineffiieny identified in Corollary 1 is ompletely eliminated. Proposition 4 has several interesting impliations. First, the interonnetion fees depend only on the reiproal aess fee, a, the ost of transmission,, and the ratio of outbound to inbound traffi, m, but are independent of the shares of the two LECs in the long-distane traffi, and 1, and the osts of all termination, t, and all origination, o. The fat that the interonnetion fees are independent of the LECsÕ osts of originating and terminating long-distane alls is akin to the off-net-ost priing priniple of Laffont et al. (2003). Aording to this priniple, internet bakbones set their retail prie as if their onnetions were entirely off-net. Here the relevant pries are not retail pries but rather interonnetion fees that the IXC pays; nonetheless, these fees are set as if all traffi was transited to the rival LEC (i.e., on the basis of the off-net osts, þ a). Seond, theequilibrium payoff of eah LEC i is given by the top line of (14) with a 6 ri 6 a þ. Hene, as in the ase where the IXC makes offers, the D. Gilo, Y. Spiegel / Information Eonomis and Poliy 16 (2004) LECs an strategially use a as a way to boost their profits at the IXCÕs expense. However, unlike in the ase where the IXC makes offers, here there is no onflit of interest between the two LECs: both wish to raise jaj as muh as possible Again, if the demand for long-distane alls is prie elasti, the two LECs will wish to raise a only up to a ertain point.

18 456 D. Gilo, Y. Spiegel / Information Eonomis and Poliy 16 (2004) Corollary 5. (The LECs preferenes over the reiproal aess fee when they make offers to the IXC) If the two LECs an simultaneously make offers to the IXC, then they will both prefer to raise jaj as muh as possible. Third, and again unlike the ase where the IXC makes offers, now the two LECs mutually prefer to ommit not to transit alls to and from one another. Absent transit, eah LEC beomes a monopolist with respet to alls that originate and terminate at its own network and an harge the IXC appropriate interonnetion fees. 15 Transit introdues ompetition between the two LECs and hene weakens their bargaining power vis-a-vis the IXC. By ontrast, when the IXC makes offers, transit boosts the LECs bargaining power vis-a-vis the IXC sine it allows them, when m 6¼ 1, to get a revenue of at least a on transited alls. Note, however, that so long as transit an be done on a unilateral basis (i.e., it does not require the mutual onsent of both LECs), then there does not exist an equilibrium in whih both LECs refuse to transit alls to one another. To see why, suppose otherwise and suppose that the monopoly prie of LEC i is equal to or below the monopoly prie of LEC j. Then, LEC i would offer the IXC an exlusive interonnetion at a prie whih is slightly below the monopoly prie of LEC j. The IXC will aept the offer (this arrangement lowers the IXCÕs ost of sending and reeiving long-distane alls to and from LEC j), thus upsetting the putative equilibrium. Consequently, Corollary 6. (Voluntary transit) Transit makes both LECs worse off relative to the ase where they an refuse to transit long-distane alls. However, absent a binding agreement that prohibits transit, the LECs will be unable to ommit not to transit alls to and from one another. Finally, Proposition 4 implies that if the LECs are required to interonnet with eah other at no harge (a ¼ 0) or if the long-distane alling pattern is balaned (m ¼ 1), then the equilibrium will be suh that r ¼ br 2½0; Š. Consequently, both LECs will at best reover their ost of transmission,, but not their osts of all termination, t, or all origination, o. This result is striking sine it implies that the ability to transit alls via a ompeting LEC at no harge (when m ¼ 0 the aess harges anel out so the situation is similar to that under a ¼ 0) indues both LECs to interonnet with the IXC at below-ost rates, even though the LEC IXC interonnetion is not regulated and the LECs have all of the bargaining power vis-a-vis the IXC Carter and Wright (1999) argue that if the LECs ompete with one another and use two-part tariffs, they will use their profits from long-distane aess harges as a way to subsidize their respetive retail fixed line harges in an attempt to inrease their respetive market shares and thereby boost their profits from long-distane aess harges. This would lead to an esalation of the long-distane aess fees (whih in their model are set by the LECs) until the long-distane market will vanish. 16 It should be stressed however that the LECs need not lose money on long-distane alls as they may be able to reover the remaining ost of all origination and termination from their own ustomers. Indeed, this is one of the main justifiations for mandating bill and keep regimes.