Net Neutrality with Competing Internet Service Providers

Transcription

1 Net Neutrality with Cometing Internet Service Providers Marc Bourreau, Frago Kourandi y, Tommaso Valletti z December 1, 011 Abstract We roose a two-sided model with two cometing Internet Service Providers (ISPs) and a continuum of heterogeneous Content Providers (CPs), and study the e ect of a net neutrality regulation on investment and innovation in the market for Internet access. Under the discriminatory regime, ISPs charge a riority fee to CPs, which are willing to deliver their content on a fast lane. We nd that, under discrimination, the investment of the ISPs in broadband caacity and the entry of CPs are higher than in the net neutrality regime. ISPs manage more e ciently their tra c, and achieve a lower level of congestion. Total welfare increases, though the discriminatory regime is not always bene cial to the ISPs. We also consider the ossibility of sabotage, and show that it may decrease total welfare under discrimination. Keywords: Net neutrality; Two-sided market; Duooly cometition; Investment; Innovation. JEL Codes: L13; L51; L5; L96. Telecom ParisTech, Deartment of Economics and Social Sciences, and CREST-LEI, Paris, France. marc.bourreau@telecom-aristech.fr. y Telecom ParisTech, Deartment of Economics and Social Sciences, Paris, France. kourandi@aueb.gr z Imerial College Business School and CEPR, UK, Imerial College London, London SW7 AZ, UK. t.valletti@imerial.ac.uk 1

2 1 Introduction The debate on net neutrality started in 005, when the Federal Communications Commission (FCC) changed the classi cation of Internet transmissions from the category of "telecommunications services" to the category of "information services". After this change, Internet Service Providers (ISPs) were no longer exlicitly subject to the rincile of net neutrality. Under net neutrality, all tyes of the Internet tra c are treated equally, that is, there is no discrimination with resect to the tye of content, services or alications and the identity of the uloader or downloader. Moreover, ISPs charge no fees to the Content Providers (CPs) for the data transferred through their networks. Much of the debate has centered around tra c management, since over the last years the volume of the data transferred through the Internet has grown u drastically, demanding a signi cant amount of bandwidth caacity. 1 In fall 005, AT&T, later followed by other major telehone and cable oerators, roosed to charge CPs remium rices for referential access to broadband transmission services. Comcast, the largest cable oerator in the United States, was also accused of interfering with users access to le-sharing services such as BitTorrent. There have been many other cases reorted in the oular ress of ISPs blocking or degrading the quality of content. ISPs argue that these ractices are necessary to e ciently manage their tra c on the Internet. It tends to be widely acceted that network oerators need to adot some tra c management ractices to ensure a su cient quality of service, esecially for content, services and alications that are very sensitive to delays, such as VoIP services or video conferencing. However, even if this view is acceted widely, the way that this tra c management is realized is very imortant. In articular, it is crucial, for olicymakers, to revent ISPs from adoting some discrimination ractices for reasons unrelated to tra c management. Recently, on Setember 3rd, 011, the FCC released a rule on "Preserving the Oen Internet; Final Rule", where it adots three basic rotections: transarency, no blocking and no unreasonable discrimination. Broadband roviders should disclose information about their ractices, their erformance and the terms and conditions of their services o ered. ISPs may not block lawful content, alications or services and may not unreasonably discriminate in transferring lawful network 1 Transarency is also an imortant art of the net neutrality debate. End users are able to make informed choices when they are adequately informed about the restrictions and the tra c management ractices followed by the ISPs they are connected to. In this aer, we focus on the tra c management ractices. Comcast s big victory against the FCC was due to no legal net neutrality obligations.

3 tra c. The Euroean Commission (EC) launched a ublic consultation on "The oen Internet and net neutrality in Euroe" (30 June - 30 Setember 010) to collect the oinions of the various arties involved in the Internet market and clarify the issue of net neutrality. The EC may assess, under the laws concerning the collusive behavior or the abuse of dominant osition, any behavior related to tra c management that may restrict or distort cometition. Other countries have adoted non-binding guidelines on net neutrality, such as Norway and Canada, and Chile was the rst country to address directly the rincile of net neutrality in its legislation (the Netherlands is the second). Therefore, net neutrality turns out to be a very debated issue by olicymakers and arties involved in the market. The ISPs argue that net neutrality reduces their incentives for investment in broadband caacity and that this leads to less entry by CPs. On the other hand, CPs argue that Internet has been neutral since its incetion, and that it should be ket free and oen to everyone. They argue that the CPs that will not be able to ay for riority will be worse-o, comared to the current situation, and they state that ISPs will continue their investments in broadband caacities, since this is the only way to kee their demand high. Finally, end users are concerned about the subscrition fees that they should ay, the roduct variety in the market and the quality of the Internet services. The aim of this aer is to address these issues in a model with cometing ISPs and a continuum of heterogeneous CPs. We adot a two-sided model where two latforms (ISPs) bring together the two sides of the Internet: the CPs and the end users. More seci cally, we study the "last-mile" of an Internet service market with two cometing ISPs and we examine the ricing, investment and innovation incentives of the layers under net neutrality and under discrimination. CPs are heterogeneous with resect to their congestion sensitivity, and they may either single-home or multi-home. For the more congestion-sensitive CPs, for examle the CPs that rovide streaming or VoIP alications, delay in the data transmissions is very imortant, since it can deteriorate a lot the end users exerience. However, for the less congestion-sensitive CPs, for examle account online services, delays are not such a concern. Finally, end users single-home, and they value innovation in the market, but dislike the congestion in the network they connect to. Under net neutrality, all CPs connected to the same ISP are treated equally, and have the same average level of congestion. However, under discrimination, the ISPs o er multile lanes and the CPs may choose to deliver their content on the riority lane by aying a riority fee to an ISP. The ISPs are horizontally di erentiated and comete for end users, with rices and caacity levels 3

4 and, under discrimination, they also comete for the CPs that choose the riority lane. Under net neutrality, the subscrition fees aid by the end users and the ro ts obtained by the ISPs are higher comared to the standard one-sided model of horizontal di erentiation. In the two-sided model, under the net neutrality regime, cometitive ressure is less intense comared to the standard Hotelling (199) model, since an increase in the subscrition fee by an ISP decreases its demand but, additionally, decreases the congestion in its network and fosters the innovation of the CPs, which, in turn, a ects ositively the demand. However, in the two-sided model with discriminatory lanes, cometitive ressure between the ISPs may be less or more severe comared to the standard one-sided model. The result is ambiguous. An increase in the subscrition fee by an ISP decreases directly its own demand and its own congestion in the network, but it also a ects the number of CPs that ot for riority. If an increase in the subscrition fee by an ISP increases the number of CPs that ay for riority in this ISP, then the cometitive ressure is less imortant comared to the one-sided market. But in the oosite case, the result on the nal demand and the ISP s ro ts is ambiguous. When comaring the net neutrality regime to the discriminatory regime, we obtain the following results. When the ISPs o er multile lanes, investment in broadband caacity increases, since the ISPs incentives to invest increase as they may now aroriate art of the CPs ro ts through the riority fees charged. Some highly congestion-sensitive CPs enter the market in the riority lane, while they stay out of the market under net neutrality. Thus, innovation under discrimination increases. Moreover, with multile lanes, the ISPs allocate the tra c more e ciently in their networks and decrease the average congestion level. However, we nd that it is not always ro table for the ISPs to follow the discriminatory regime, in contrast to the case of a monoolistic ISP. Under discrimination, the ISPs comete on the basis of the CPs that buy riority and this might lead to lower ro ts. The e ect of a deviation from the net neutrality regime on the CPs ro ts and the end users utility is also ambiguous. However, the discriminatory regime always a ects ositively the total welfare in the market. Extending the aer to study the case of quality degradation or "sabotage" rovides additional insights into the roblem. ISPs are o ered an extra instrument that reduces costlessly the revenues of the CPs. We nd that the ISPs will never sabotage the CPs under the net neutrality regime, however, their incentives to start sabotage in the non-riority lane may be increased under discrimination. This could be a way to make the riority lane more valuable and extract more ro ts by the CPs. The e ect of a small ositive sabotage rate would be detrimental for the total welfare. 4

5 Related literature. While the net neutrality regulation has been discussed a lot by both the roonents and the oonents of the net neutrality, only few academic aers have been written on this issue. Choi and Kim (010) and Cheng et al. (011) study a model with a monoolistic ISP and two CPs where riority fees are aid for the fast lane. Krämer and Wiewiorra (011) extend these aers by adding a continuum of heterogeneous congestion sensitive CPs that may ot for the riority lane. A dynamic model with a big CP and a fringe of smaller CPs delivering their content through a monoolistic ISP is examined by Reggiani and Valletti (011). In contrast, we introduce cometition at the ISP level to study the investment, innovation and ricing decisions in a duoolistic framework with strategic interaction. By adding cometition in the ISP level, it is not any more clear and certain that a regime with multile riority lanes is always referred by the ISPs as it haens in the case with a monoolistic latform. Moreover, the cometing ISPs do not extract the whole surlus from the end users and the consumers surlus analysis becomes richer. Njoroge et al. (010) examine the case of two interconnected ISPs who invest in quality and the ISPs charge, under not net neutrality, the CPs a fee to have access to the end users (on- and o -network fees). However, this aer does not deal with the tra c rioritization. Economides and Tag (011), also analyze a model where the CPs have to ay access fees to the ISPs to reach the end users, initially with a monoolistic ISP sector and then with a duooly but in a static framework, that is, without endogenizing the investment decisions of the ISPs. Recently also, Choi et al. (011) analyze a static model with cometing and interconnected ISPs with a xed continuum of heterogeneous CPs, but they focus on the termination fees charged by the ISPs. Instead, we deart from interconnected ISPs and termination fees and focus on the investment and innovation incentives of the rms when multi lanes can be o ered by the ISPs. In Hermalin and Katz (007), rms under roduct line restrictions should roduce a single quality of the roduct (net neutral regulation), but under no regulation rms are allowed to roduce more than a single quality. In their model, this exibility either increases the variety in the market or the cometition between the rms. In a similar framework with heterogeneous consumers concerning the taste for quality, Alexandrov and Deb (011) examine the investments in quality and the ricing decisions of the rms when they are allowed (or not) to rice discriminate. In our model, the decisions on the level of quality a ect the market structure since they a ect the number of CPs entering the market. Also, in our aer, there i correlation between the di erent quality levels due to the constrained caacity levels. Finally, our aer is related to the literature on two-sided markets. This strand of the literature contains many in uential aers and it is too 5

6 vast to survey here. 3 Thus, we have only focused on the aers closely related to our work on net neutrality. The remainder of the aer is as follows. Section sets u the model. Section 3 derives the equilibrium under net neutrality and studies its roerties. The equilibrium under discrimination is studied in Section 4. Section 5 comares the two regimes. The model is extended to study the ossibility of quality degradation in Section 6. Section 7 concludes. The Model Two horizontally di erentiated Internet service roviders (ISPs) bring together two sides of the Internet, content roviders (CPs) and end users. CPs rovide free content to end users via the broadband networks of the ISPs, and derive revenues from advertising. ISPs sell broadband access to end users. Under net neutrality, ISPs do not charge CPs for access to their broadband network. 4 However, due to caacity constraints, networks can su er from congestion, which CPs and end users both dislike. We study the e ect of an alternative to the net neutrality regime, namely, the discriminatory regime. Under the discriminatory regime, the ISPs o er two di erentiated tra c lanes to CPs, the riority (fast) and non-riority (slow) lanes. ISPs charge CPs to access the riority lane, while there is free access to the non-riority lane..1 Content roviders There is a continuum of congestion-sensitive CPs that derive revenues from advertising. Each CP is characterized by its congestion sensitivity h, where h is distributed over [0; 1), with density 1. Each CP may connect to no ISP, to a single ISP or to both ISPs, that is, we allow CPs to singlehome or to multi-home. If it connects to ISP i, a CP has access only to the end users connected to that ISP. CPs generate advertising revenues as follows. When a CP of tye h connects to ISP i, it receives x i visits, where x i is the number of users of ISP i and is the constant number of visits er user, which is the same for all web sites. 5 Visitors of CP h s web site click on ads with a click-through rate of (1 hw i ), where w i denotes the waiting time on ISP i. The click-through rate reresents 3 See, for examle, Rochet and Tirole (003, 006), Armstrong (006) and Valletti and Cambini (005) among others. 4 In other words, we do not introduce termination fees charged by the ISPs to the CPs when they rovide access to the end users. 5 The same assumtion is made by Krämer and Wiewiorra (011). 6

7 the roortion of the CP s visitors who actually click on ads. Finally, clicks generate advertising revenues of ax i (1 hw i ) for CP h, where a denotes the er-click advertising revenue. With this formulation, a CP with a high congestion sensitivity (e.g., a CP which o ers live streaming) su ers a lot from network congestion, because its click-through rate is sharly reduced. In contrast, a CP with a very low congestion sensitivity (e.g., a CP that rovides accounts) is hardly a ected by congestion. Under net neutrality (N), the ro t of CP h is therefore 8 >< N h = >: ax N A 1 hwn A + ax N B 1 hwb N ax N i 1 hwi N 0 otherwise if he connects to both ISPs if he connects only to ISP i : Whereas under net neutrality the CPs that are active at ISP i s face the same average waiting time w N i, under the discriminatory regime, a CP may choose to ay a xed fee f i to ISP i to bene t from a riority lane where congestion is lower (i.e., w P i discrimination (D) is then given by < w N i ). The ro t of CP h under 8 >< D h = >: ax D A (1 hwp A ) f A + ax D B (1 hwp B ) f B riority at both ISPs ax D i (1 hwp i ) f i + ax D j ax D A (1 (1 hwnp j ) riority only at ISP i hwnp A ) + axd B (1 hwnp B ) if non-riority at both ISP ax D i (1 hwp i ) f i riority at ISP i, no entry at ISP j ax D i (1 hwnp i ) non-riority at ISP i, no entry at ISP j 0 otherwise, where w P i resectively. and w NP i denote the congestion at ISP i s under riority (P) and non-riority (NP), Note that the CPs with a high congestion sensitivity do not enter the market. We denote by h N i and h D i the marginal CP which is indi erent between connecting to ISP i and not connecting to it, in the net neutrality and discriminatory regimes, resectively (see an examle in Figure 1 below). Under discrimination, the CPs that enter the market choose either to buy access to the riority lane or to use the non-riority lane for free. We denote by e h i the CP which is indi erent 7

8 between the riority lane and the non-riority lane at ISP i s. enter do not enter 0 h i N enter with no riority enter with riority do not enter 0 Ê h i h i D Figure 1: Demand of CPs for ISP i. Internet Service Providers Two ISPs, ISP A and ISP B, rovide broadband connections to CPs and to end users. The two ISPs are located at the extremities of a linear city of length one, with ISP A located at oint 0 and ISP B located at oint 1. 6 Each ISP i charges a subscrition fee i to the end users connected to its network, and invests in broadband caacity i. The investment cost C( i ) is increasing and convex in i (i.e., C0 > 0 and C 00 > 0). Under net neutrality, the ro t function of ISP i is N i = N i x N i C( N i ). Under discrimination, ISP i also charges a xed fee f i to the CPs that ot for the riority lane, and makes ro t D i = D i x D i C( D i ) + (h D i where h D i is the total number of active CPs at ISP i s, and h D i buy riority at ISP i s, in the discriminatory regime. e hi )f i, e hi is the total number of CPs that 6 For examle, one ISP might target consumers with high comuter skills, and o er them exibility in tuning their Internet connection (e.g., for setting the latency of their broadband connection), while the other ISP might target users with low comuter skills, and o er them a broadband service without such exibility. 8

9 .3 Congestion Due to caacity constraints, tra c from the content roviders to the end users might su er from congestion. Congestion is measured by the waiting time for end users when they request content from CPs. As it is standard in the literature, we adot the M/M/1 queuing model to determine the average waiting time as a function of network caacity and tra c. Under the net neutrality regime, the average waiting time for ISP i is w N i = 1. (1) N i h N i x N i Note that the waiting time w N i decreases with the level of caacity N i, while it increases with the number of visits er user, the total number of end users of the ISP x N i, and the total number of CPs h N i that connect to ISP i. We refer to h N i x N i as the tra c of ISP i. Under discrimination, each ISP discriminates CPs according to two tra c lanes, the riority lane and the non-riority lane. The waiting time for the riority lane (P) served by ISP i is given by w P i = D i h D i 1 e hi x D i, () whereas the waiting time for the non-riority lane (NP) is given by w NP i = D i D i h D i x D i w P i. (3) Note that the average waiting time under discrimination, w D i, satis es w D i = b i w P i + (1 b i )w NP i = D i 1 h D i x D i, (4) where b i = 1 e hi =h D i is the share of CPs that buy riority from ISP i. If caacities and tra c volumes are the same under net neutrality and discrimination, the average waiting time is also the same under both regimes (i.e., we have wi N = wi D ), which is a well known roerty of the M/M/1 queuing model. 9

10 .4 End users There is a unit mass of users uniformly distributed along the unit interval. Each end user subscribes to only one ISP (i.e., single-homes). Under net neutrality, a user located at x j on the unit interval and who subscribes to ISP A, obtains utility U j = R + vh N A + d w N A N A tx j, where R is a xed utility obtained from Internet access, v reresents the consumers reference for roduct variety, d is a arameter which measures the reference for the seed of the connection (as w N A is a waiting time in seconds, 1=wN A reresents the seed of the Internet connection), and nally, t is the transortation cost. Similarly, under discrimination, the end user located at x j obtains utility U j = R + vh D A + d w D A D A tx j, (5) if she connects to ISP A. We assume that R is su ciently high so that the market is covered in equilibrium. Relacing for w D A into (5), the end user s utility can be rewritten as U j = R + v dx D i h D A + d D i D A tx j. From this exression, for consumers to value the resence of CPs, it must be that v dx D i > 0. In articular, in a symmetric equilibrium, it must be that v > d=. We assume that the latter inequality holds. 7 3 Net Neutrality In the net neutrality regime, there is a unique lane for Internet transmissions and CPs ay no fee to the ISPs. We study the following two-stage game: 1. The two ISPs choose their caacities, N A and N B, and set the subscrition fees to the end users, N A and N B. 7 The same reasoning alies in the net neutrality regime and gives the same condition. 10

11 . The CPs choose which ISP(s) to connect to (if any), and the end users choose which ISP to subscribe to. We roceed backwards to solve for the symmetric subgame erfect equilibrium. 3.1 Stage : Content roviders and end users decisions At the second stage, each CP decides whether to multi-home, to single home, or to stay out of the market. A CP with congestion sensitivity h connects to ISP i if and only if 1 hw N i 0, that is, if h h N i, where h N i = 1 w N i, for i = A; B. (6) Relacing for w N i into (6) and solving for h N i, we nd that the tye of the marginal CP is N i h N i = 1 + x N i. (7) Simultaneously, at stage, each consumer chooses whether to subscribe to ISP A or ISP B. The indi erent consumer ex N is given by R + vh N A + d w N A N A tex N = R + vh N B + d w N B N B t 1 ex N : (8) By relacing for h N A and h N B into (8), the tye of the marginal consumer solves F (ex N ; N A ; N B ; N A ; N N B B ) = (d + v) 1 + (1 ex N ) N A 1 + ex N t(1 ex N ) ( N B N A ) = 0, (9) and, therefore, we have ex N = ex N ( N A ; N B ; N A ; N B ). The number of users of ISP A and ISP B are then x N A = exn and x N B = 1 exn. 3. Stage 1: ISPs decisions At the rst stage of the game, the two ISPs comete by choosing an investment in caacity, and by setting a subscrition fee to the end users. The maximization roblem of ISP i can be exressed as follows: max N N i = N i x N i C N i i ;N i, 11

12 where x N i = x N i N A ; N B ; N A ; N B. The two rst-order conditions N N i = x N i + N N N i = 0, (10) N N i = N N N i C 0 N i = 0. (11) Since we do not have an exlicit solution for x N i, we use the Imlicit Function Theorem to determine the N i =@N i N i =@N i from equation (9). We then look for the symmetric subgame-erfect Nash equilibrium. We obtain the following result. 8 Proosition 1 Under net neutrality, in the symmetric equilibrium, the caacity level, the subscrition fee, the number of content roviders and the average waiting time are given by: Proof. We nd that C 0 ( N ) = d + v +, N = t + 4N (d + v) ( + ), h N = N +, w N = + N. K = t + (d + N N B 1 + x N + B N A! 1 + x N > 0, A and, therefore, we can aly the Imlicit Function Theorem. We N N A N = 1 K N < 0 N A N = d + v 1 + x N > A K N 0, and N N B = 1 K N > 0 A N B d + v 1 + x N < B K N 0, By relacing for these derivatives in the rst order conditions (10) and (11), and by imosing 8 By abuse of notation, in the symmetric equilibrium, we dro the subscrits i = A; B for the ISPs. For examle, we denote by N the equilibrium level of investment of each ISP. Furthermore, for exositional simlicity, we do not ut asterisks to the equilibrium values. 1

13 symmetry, we obtain the symmetric equilibrium levels of investment in caacity and the subscrition fees. The candidate equilibrium corresonds to a maximum of the ro t function (i.e., the Hessian matrix is negative de nite) if and only if C 00 () > 4 (d + v). ( + ) t ( + ) + 4 (d + v) We assume that C () is su ciently convex so that this condition holds. In the symmetric equilibrium, the two ISPs share the market equally (i.e., we have x N A = xn B = 1=). After relacing for the equilibrium caacity and subscrition fee into the ro t functions of the ISPs and of the CPs, we obtain the equilibrium ro ts for each ISP and for each CP: N = t + N (d + v) ( + ) C( N ), and 8 < N h = : a 1 h(+) N if h h 0 if h > h. The total ro ts of CPs is equal to: N h Z N h = 0 N h dh = an + : Finally, we determine the consumers surlus and the total welfare in the net neutrality regime. After relacing for the equilibrium values of the subscrition fee, the number of content roviders and the level of congestion into the utility of end user j located at x j 1=, we obtain: U N j = R + N ( ) (d + v) ( + ) t (1 + x j ) : By summing the net surlus of all end users, we obtain the consumers surlus, Z 1 CS N = Uj N dx j = R 0 5t 4 + N ( ) (d + v) ( + ) : The total welfare W N is de ned as the sum of ISPs ro ts, CPs ro ts and consumers surlus. 13

14 We obtain: Z N h W N = N + 0 N h dh + Z Equilibrium roerties 0 U N j dx j = R t 4 + (a + (d + v)) N + C( N ). In the net neutrality regime, we nd that the equilibrium subscrition fee is higher than the fee that would revail in a standard Hotelling setting (i.e., = t). This is due to the resence of network externalities. An increase in ISP i s subscrition fee decreases directly its demand, but it also leads to a reduction in the congestion of its network and, thus, to an increase of the number of CPs, which in turn a ects ositively the demand of the CP. Overall, the total e ect of a rice increase on ISP i s demand is negative, but is less severe than in a one-sided market. In the words, the cometitive ressure is reduced in the two-sided model and the ISPs ro ts are higher than in the standard Hotelling model. 9 Furthermore, note that when the investment in caacity goes to zero (i.e., N! 0), the equilibrium subscrition fee and the ISPs equilibrium ro ts converge to the equilibrium rice and ro t in the Hotelling model (i.e., N! t and N! t=), whereas the equilibrium waiting time goes to in nity (i.e., w N! 1) and the number of CPs goes to zero (i.e., h N! 0). However, the caacity is always ositive ( N > 0), otherwise, there would be no market for Internet access. Finally, we rovide some comarative statics. We nd that when the number of clicks er user increases, the investments in caacity and the number of active CPs decrease, whereas congestion increases. The e ect of an increase in on the subscrition fee and the ISP s ro t deends on the value of. When is low enough, congestion is not so imortant, and hence, an increase in increases the subscrition fees and the ISPs ro ts. In contrast, when is high enough (i.e., > ), congestion becomes substantial, and rices and ISPs ro ts decrease. An increase in the reference for seed d and an increase in the reference for roduct variety v lead to higher investments in caacity, higher subscrition fees, higher entry by the CPs, and to lower congestion. The CPs ro ts and the total welfare increase too. Finally, an increase in the er-click advertising revenue a only a ects ositively the CPs ro ts, and hence, the total welfare. 9 Formally, under net neutrality, we N i =@ N i = x N i + N N i =@ N i, N i =@ N i H i =@ H i = 1=(t), H i =@ H i is the e ect of a rice increase on demand in the standard Hotelling model. In our model, the negative e ect of an increase of the subscrition fee on ISP i s demand is less intense. 14

15 4 Discrimination In the discriminatory regime, each ISP o ers a riority lane and a non-riority lane to CPs, and the CPs that ot for riority at ISP i s ay a xed fee f i. The two-stage game becomes: 1. The two ISPs choose their caacities, D A and D B, set their subscrition fees to the end users, D A and D B, and the riority fees for the riority lane, f A and f B.. The CPs choose which ISP(s) to connect to (if any) and whether they ay for riority, and the end users choose which ISP to subscribe to. We roceed backwards to solve for the symmetric subgame erfect equilibrium. 4.1 Stage : Content roviders and end users decisions At the second stage, each CP decides whether to multi-home, to single home or to stay out of the market and, if it enters the market, whether to ay for riority. The CPs which are the most congestion-sensitive ot for the riority lane. A CP of tye h connects to the riority lane at ISP i s if h h D i, where h D i solves ax D i (1 h D i w P i ) f i = 0: (1) Furthermore, the CP of tye e h i which is indi erent between the riority lane and the non-riority lane at ISP i s is de ned by ax D i (1 e hi w P i ) f i = ax D i (1 e hi w NP i ): (13) From equations (1) and (13), the total number of CPs that ay for riority at ISP i s is h D i e hi. Equation (13) imlies that f i = ax D i e h i w NP i w P i, and relacing for this exression into (1), we obtain 1 h D i e hi wi P + e h i wi NP = 0. By dividing the latter exression by h D i and by rearranging, we nd the tye of the marginal CP 15

16 that enters at ISP i s h D i = 1 w D i, (14) where w D i is de ned in (4). Since w D i is indeendent of the subscrition fees, (14) can be rewritten as h D i = D i 1 + x D i, (15) which is also indeendent of the subscrition fees. Note that the total number of CPs at ISP i s in the discriminatory regime (which is given by (15)) is analogous to that in the net neutrality regime (which is given by (7)). In addition, we have 10 e hi = x D i D i f i 1 + x D = i ax D i f i f i x D i ax D i f i h D i : Simultaneously, at stage, each consumer chooses whether to subscribe to ISP A or ISP B. The indi erent consumer ex D is given by R + vh D A + d w D A D A tex D = R + vh D B + d w D B D B t 1 ex D. (16) By relacing for h D A and h D B into (16), the tye of the marginal consumer solves D B (d + v) 1 + (1 ex D ) D A 1 + ex D t 1 ex D D B D A = 0, (17) and, therefore, we have ex D = ex D ( D A ; D B ; D A ; D B ). The number of users of ISP A and ISP B are then x D A = exd and x D B = 1 exd. Note that equation (17) for the discriminatory regime is analogous to equation (9) for the net neutrality regime, and that ex D is indeendent of the riority fees. 10 We have e h i > 0 and h D i e hi > 0 if x D i ax D i f i f i > 0. This inequality is always satis ed in equilibrium. 16

17 4. Stage 1: ISPs decisions At the rst stage, the two ISPs choose simultaneously their caacities, subscrition fees and riority fees. The maximization roblem of ISP i can be exressed as follows: max D D i ;D i ;f i = D i x D i C D i i = D i x D i C D i + h D i e hi f i + 1 f i x D i ax D i f i! D i f i 1 + x D i ; where x D i = x D i (D A ; D B ; D A ; D B ). The three rst-order conditions D D D D i = x D i + D i i = D i D D i! e hi )f i )! e hi )f i D D D D i C 0 = 0, (18) D D e + i hi )f i ) = 0, D D i e i hi )f i ) = 0. i As in the net neutrality regime, we cannot obtain an exlicit solution for x D i, and hence, we use the Imlicit Function Theorem to determine the D i =@D i D i =@D i from equation (17). We then solve for the symmetric subgame-erfect Nash equilibrium. We obtain the following result. Proosition Under discrimination, in the symmetric equilibrium, the caacity level of each ISP, the riority fee, the subscrition fee, the number of CPs and the levels of congestion are given by: C 0 D = d + v + + a where D = D A = D + B; f = a! 1, + D = t + 4D (d + v) a D + ( + ) ( + ),! h D = D + ; e + h = h D, 3 + ( + ) w P = D, w NP = 4 D, w D = + D. 17

18 Proof. Similar to the net neutrality regime, we nd that K D (d + v) D B x D + A D A! 1 + x D +t > 0, A and, therefore, we can aly the Imlicit Function Theorem. We D D A = 1 K D < D D B = 1 K D > D D A = d + v 1 + x D > A K D D = B d + v x D A K D < D A B = 0, By relacing for these derivatives in the rst order conditions, and by imosing symmetry, we obtain the symmetric equilibrium levels of investment in caacity, the subscrition fees and the riority fees. In the symmetric equilibrium, the market is equally shared between the two ISPs (i.e., we have x D A = xd B = 1=). The equilibrium ro ts for an ISP and a CP are D = t + D (d + v) ( + ) + D a (3 + 4) ( + ) C D, and 8 >< D h = >: P h = a + 1 h + = a 1 h NP h D 3 (+) 4 D if h ( e h; h D ) if h e h 0 if h h D, resectively. The total ro ts of the CPs is D h = Z eh D 0 NP h Z D h dh + e h D P h dh = a D + +. Finally, we determine the consumers surlus and the total welfare in the discriminatory regime. In the symmetric equilibrium, the utility of end user j, located at x j 1=, is Uj D = R + D ( ) (d + v) + a + ( + ) t (1 + x j ). 18

19 By summing u the net surlus of all end users, we obtain the consumers surlus, Z 1 CS D = 0 Uj D dx j = R 5 4 t + D ( ) (d + v) + a + ( + ) : The total welfare W D is de ned as the sum of ISPs ro ts, CPs ro ts and consumers surlus. We nd that Z eh D W D = D Equilibrium roerties NP h Z D h dh + e h D P h dh + Z 1 0 U D j dx j = R t 4 + a d + v D + C D. The comarison between the equilibrium subscrition fee under discrimination and the fee in the standard Hotelling model (t) deends on the values of the arameters. When a= (d + v) < = +, the equilibrium end user fee in the discriminatory regime is higher than the Hotelling equilibrium rice (i.e., D i the subscrition fee D i > t). The intuition is as follows. To begin with, an increase in of ISP i decreases its own demand, though this e ect is less severe than in the Hotelling model. Besides, under discrimination, there is an additional e ect. 11 D i An increase in a ects indirectly the number of CPs that buy riority at ISP i s. The reduction in the demand of ISP i reduces the congestion on its network and leads to an increase in the total number of CPs that connect to ISP i (h D i ). However, the number of CPs that ot for riority at ISP i s may be a ected either negatively or ositively. The increase in h D i tends to increase the number of CPs that ay for riority, since the new entrants are more congestion-sensitive and connect to the riority lane, but due to the reduction in the congestion some CPs that were connected to the riority lane might switch now to the non-riority lane. Therefore, the e ect of an increase in D i on the number of CPs that ot for riority is ambiguous, which also makes ambiguous the comarison between the subscrition fee and ISP s ro ts under discrimination to the resective values of the standard Hotelling model. Of course, when an increase in the subscrition fee increases the number of CPs that buy riority, the cometitive ressure under discrimination is less intense comared to the Hotelling model. 11 By direct di erentiation of the ro t function, we have: < 0, < 0; but the sign h D i eh i is D D e h D D D D i = x D i + D D D i h D D i eh D D i f i, D i < 0, 19

20 Finally, we resent some comarative statics. We nd that when the number of clicks er user increases, the riority fee increases, since the riority lane is valued more. However, the e ect of an increase in on all the other equilibrium values is ambiguous and deends on the e ect of on investment in caacity (i.e., D i =@). This latter e ect is not always negative, as it is the case under net neutrality, since in the discriminatory regime, the ISPs may now have an incentive to increase their caacity with an increase in to obtain higher revenues from the CPs that are willing to ay for riority. An increase in the reference for seed d and an increase in the reference for variety v both a ect ositively investment in caacity, the total number of CPs, CPs ro ts and total welfare. Moreover, congestion decreases with d and v. In contrast to the net neutrality regime, an increase in the er-click advertising revenue a a ects caacity investment, the number of CPs and the ricing decisions of the rms. This is because, under discrimination, ISPs can extract art of the CPs ro ts through the riority fees. When a increases, the ISPs charge higher riority fees and increase their investment in broadband caacity. Congestion is reduced, entry of CPs is fostered and the number of CPs that buy riority increases too. Therefore, total welfare increases with a. The comarison between the net neutrality regime and the discriminatory regime is examined searately in the next section. 5 Net Neutrality vs. Discrimination We now comare the two alternative regimes, net neutrality and discrimination, to investigate the e ect of a dearture from net neutrality on the decisions of the various layers in the market for Internet access. First, we comare investment and innovation incentives in the two regimes. Second, we comare congestion, subscrition fees and ro ts. Finally, we resent the comarison of end users utility and total welfare in the two regimes. 5.1 E ect on investment and innovation In this subsection, we comare the investment in caacity and the number of CPs that enter the market, that is, the innovation or roduct variety, under net neutrality to the equilibrium results under discrimination by taking the relevant exressions from Proosition 1 and Proosition, resectively. We nd the following. Proosition 3 Investment in broadband caacity and innovation under the discriminatory regime 0

21 is higher comared to the net neutrality regime, that is, we have D > N and h D > h N. The roof is straightforward. Since C 0 D > C 0 N and C 0 > 0, we have D > N. Then, since D > N, we also have h D > h N. The equilibrium level of investment in caacity in each regime is given by equating the marginal revenue from investing in caacity to the marginal cost of this investment. Here, the equilibrium marginal revenue of investing in caacity is always higher under discrimination. An increase in ISP i s caacity increases its demand and its investment cost under both regimes, but in the discriminatory regime it also a ects ositively the revenues that ISP i can extract from the CPs that ot for riority. Therefore, under discrimination, ISPs have larger caacity investment incentives. Analytically, under net neutrality, ISP i s incentive to invest is given by the change in its ro ts with a marginal increase of the caacity level, that N N i = N N N i C 0 N i, (1) N i =@N i > 0 and C 0 > 0. In the discriminatory regime, we D D i = D D D i C 0 D i h D D i e hi h D D i e D D i 1 A f i, () D i =@D i > 0. For given levels of the subscrition fees and the caacities, the term N i (@xn i =@N i ) C0 N i is equal to the term D i (@x D i =@D i ) C0 D D i. We further i e hi )=@ D i > D i =@x D i < 0 e h i =@x D i < 0, but the sign D e i hi )=@x D i is ambiguous. Nevertheless, we have roved that the arenthesis in () is ositive, which roves that the marginal revenue of an increase in the caacity level is higher under the discriminatory regime. 1 Since the ISPs invest more in caacity under discrimination, the total number of CPs that are active under discrimination is also higher than under net neutrality. Innovation or roduct variety is increased when there is a fast lane, as more congestion-sensitive CPs that could not enter under net neutrality now enter by buying access to the riority lane. It is also useful to comare the number of CPs that enter the market under net neutrality, h N, to the CP e h that is indi erent between buying riority or using the non-riority lane in the 1 Under symmetry (i.e., j = i and x i = 1=), we have ( i(4fi ( )(+) 4f ia( 4)+a 4 )(d+v)+t(+) ((a f i ) 4f i )(a f i )) > 0. (+)(a f i ) (t(+) +4 i h D D i eh i h D D i eh D D i = 1

22 discriminatory regime. We obtain that e h > h N for D N > +. For high values of the ratio D = N, innovation under discrimination is so high that all CPs that buy riority were not active under net neutrality. Figure resents the ossible cases. Note that as the total number of CPs under discrimination is always higher than the total number of CPs under net neutrality, h D is located to right of h N. However, h N might be located either to the left or to the right of e h. When the investment in caacity under discrimination exands a lot, h N is located to the left of e h. h N Ê 0 h h D Figure : Equilibrium number of CPs 5. E ect on network congestion The level of congestion under net neutrality, w N, is always higher than the level of congestion on the riority lane, w P, otherwise CPs would never connect to the riority lane. After comaring the equilibrium level of congestion on the non-riority lane, w NP, to the level of congestion in the net neutrality regime, w N, we nd that for high values of the ratio D = N (i.e., higher than + =), congestion on the non-riority lane is lower. Caacity exansion under discrimination is high enough to reduce the waiting time in both the riority and the non-riority lane. Finally, the e ect of discrimination on the average waiting time is summarized in the following result: Proosition 4 The average level of congestion under discrimination is lower than congestion under net neutrality, that is, we have w D < w N. Even if congestion on the non-riority lane is higher than the congestion in the net neutrality regime, the decrease of congestion on the riority lane is high enough to overcome the increase in the waiting time on the non-riority lane. In other words, the ISPs manage the tra c more

23 e ciently, when they can o er multile lanes, and the more congestion-sensitive CPs can ot and ay for riority. 5.3 E ect on subscrition fees and ro ts Following the same analysis as in the revious subsections, we comare the equilibrium subscrition fees between the two regimes and we obtain D > N for d + v a 1 N D > +. Under net neutrality the ISPs obtain ro ts only by the end users, however, under discrimination the ISPs extract additional revenues by charging the riority lane. As already discussed in Subsection 3.3 and Subsection 4.3, the ricing incentives between the two regimes di er, N N i = x N i + N N N i D i = x D i + D D D i h D D i e D D i f i. An increase in the subscrition fee by ISP i, decreases the demand that it obtains in both regimes (@x N i =@N i D i =@D i < 0 for given levels of subscrition fees and caacities), but it additionally a ects indirectly the total number of CPs that ot for riority in the discriminatory regime (@(h D e i hi )=@x D D i =@D i ). Whenever this latter e ect is ositive, the incentives of the ISPs to increase the subscrition fees under discrimination are higher comared to the net neutrality regime. Therefore, in these cases, the cometition in subscrition fees between the ISPs is relaxed and the end users are charged higher rices under discrimination. For high values of the ratio D = N, the subscrition fees under discrimination tend to be higher. The caacity exansion, with the introduction of the multile lanes, is relatively high which leads to a high number of total active CPs and, thus, increased utility for the end users. The ISPs extract this increased utility via higher subscrition fees. This result is emhasized when the end users value more the variety and the seed in the network (high d+v) and when the er-click advertising revenues are low (low a). When a increases, the ISPs are willing to reduce their rices under discrimination (@ D i =@a < 0) to obtain higher demand (the countervailing e ect via the increase in congestion is less severe). The results are reversed and cometition between the ISPs is more intense, under discrimination, for relatively low values of the ratio D = N. Now, let us turn to the ro ts of the ISPs and the CPs. The comarison of the ISPs ro ts 3

24 between the two regimes yields D > N for D N = C D C( N ) + h D i e hi f i > 0: ISP i obtains additional revenues under discrimination through the riority fees, but this comarison deends also on the di erence in the subscrition fees and the di erence in the cost of the investment in caacity. When cometition under discrimination is relaxed, the term D N = is ositive, thus, ro ts tend to be higher under discrimination. Moreover, the di erence in the cost of investment is always ositive (since D > N and C 0 > 0) which tends to decrease the ro ts under discrimination comared to the net neutrality regime. The nal comarison deends on the levels of caacity and the arameter values. 13 We can conclude that: Proosition 5 A dearture from the net neutrality regime is not always bene cial for the ISPs. In the case of a monoolistic ISP, a dearture from the net neutrality regime is always ro table for the ISP, since it can extract art of the CPs ro ts through the riority fees and still serving the whole mass of the end users. However, when there is cometition in the ISP level, it is ambiguous whether discrimination will imrove or deteriorate the ISPs ro ts. It deends on the caacity levels, the values of the arameters and the convexity of the investment cost function. The cometition for the end users under discrimination might be more severe as the demand of each ISP a ects indirectly the ro ts obtained through the riority lane. Note that regulation in our set-u is exogenous. The ISPs face either the net neutrality regime or a dearture from it, meaning the discriminatory regime. Concerning the CPs, we comare the total market ro ts to take into account the extra CPs that enter the market under discrimination. We nd D h > N h for D N > + : For high values of the ratio D = N the total ro ts of the CPs under discrimination are higher, thus, on average CPs are better o. We have further roved that the CPs in the non-riority 13 Analytically, we obtain: D > N for ad (3 + 4) + (d + v) D N ( + ) > C D C( N ): 4

25 lane obtain higher ro ts comared to the net neutrality regime for high D = N. 14 When caacity exansion is high enough, congestion in the non-riority lane is lower than congestion under net neutrality which leads to increased ro ts. 5.4 E ect on end users utility and total welfare Now, we roceed to the comarison of the end users utility and the total welfare between discrimination and net neutrality. For the consumers surlus, we obtain CS D > CS N for a D d + v D N > + : On the one hand, discrimination a ects ositively the end users utility, since it increases the roduct variety and reduces the average level of congestion in the network. However, on the other hand, discrimination may increase the subscrition fees that the end users have to ay for Internet access. Therefore, when discrimination leads to more cometitive ressure in the ISP level with resect to the subscrition fees, the end users are better o and the ISPs tend to be worse o. We may rewrite (a=(d + v) D =( D N ) as a=(d + v) 1=(1 N = D ). Thus, when D = N increases, it is less ossible for the end users to ay lower subscrition fees under discrimination, but it is more ossible the ro ts of the ISPs and the CPs to be higher. When we comare the equilibrium levels of total welfare, we conclude that: Proosition 6 Total welfare under discrimination is higher than total welfare under net neutrality, W D > W N. Proof. The di erence between the total welfare under discrimination and net neutrality is given by W D W N = a d + v D + (a + (d + v)) N + C D C( N ) : Since a d + v > (a + (d + v)) > 0, D > N and due to the convexity of the investment cost function, we rove our result. 14 Comaring the ro ts of a CP h that is active in both regimes, we nd: NP h > N h > 0 if D + > : N 5

26 Total welfare is the sum of the market s ro ts and the end users utility. Under discrimination, either market ro ts increase more than the reduction in the end users utility or the end users utility increases more than the reduction in the market s ro ts. The e ect of a dearture from the net neutrality is ositive for the total welfare in the market for Internet access, but, as discussed in the next section, the olicy makers should be aware of other ractices adoted by the ISPs in order to manage the tra c in the network and gain higher ro ts. 6 Sabotage Thus far we have examined the e ect of a dearture from the net neutrality regime, by introducing multile congestion lanes where the CPs that ot for riority ay a xed fee to the ISPs. The debate on net neutrality lies also on the concern that the ISPs may adot additionally ractices to maniulate the tra c in the network. One such ractice could be to degrade the quality of the CPs that do not ay for riority. This could make the riority lane more valuable and, thus, ISPs may aroriate a higher share of the CPs surlus. In this section, we study the case where the ISPs can endogenously decide on the level of the sabotage rate, a rate that reduces the click-through ratio of the CPs. A ositive level of sabotage reduces the revenues obtained by the CPs. First, we study the incentives of the ISPs to do sabotage in the net neutrality regime and, then, we introduce sabotage in the discriminatory regime. 6.1 Sabotage in the net neutrality regime In contrast to our analysis of the net neutrality regime thus far, suose now that the ISPs may sabotage the CPs costlessly. The ro t of the CP h becomes 8 >< N h = >: ax N A sn A hw N A + ax N B s N B hw N B ax N i s N i hw N i 0 otherwise, if he connects to both ISPs if he connects only to ISP i where s N i is the level of sabotage imosed by ISP i, with i = A; B. The remaining exressions are the same as in our basic model in Section. The decision of the level of sabotage is made in the rst stage of the game, where the ISPs also decide on the caacity levels and the subscrition fees of the end users. From the otimization roblem, we obtain: Proosition 7 In the net neutrality regime, the ISPs never sabotage the CPs, s N i = 0; i = A; B. 6