Net Neutrality with Competing Internet Platforms

Transcription

1 Net Neutrality with Cometing Internet Platforms Marc Bourreau y, Frago Kourandi z, Tommaso Valletti x March 21, 2013 Abstract We roose a two-sided model with two cometing Internet latforms, and a continuum of Content Providers (CPs). We study the e ect of a net neutrality regulation on caacity investments in the market for Internet access, and on innovation in the market for content. Under the alternative discriminatory regime, latforms charge a riority fee to those CPs which are willing to deliver their content on a fast lane. We nd that under discrimination investments in broadband caacity and content innovation are both higher than under net neutrality. Total welfare increases, though the discriminatory regime is not always bene cial to the latforms as it can intensify cometition for subscribers. As latforms have a unilateral incentive to switch to the discriminatory regime, a risoner s dilemma can arise. We also consider the ossibility of sabotage, and show that it can only emerge, with adverse welfare e ects, under discrimination. Keywords: Net neutrality; Two-sided markets; Platform cometition; Investment; Innovation. JEL Codes: L13; L51; L52; L96. We thank Bruno Jullien, Micha Grajek, Jan Krämer, Andre Veiga, and articiants at the Conference on the Economics of ICT (Paris, 2012), the International Conference on Management and Economics of ICT (Munich, 2012), the Worksho on the Economics of ICTs (Oorto, 2012), CRESSE (Crete, 2012), CRETE (Milos, 2012), and EARIE (Rome, 2012). We acknowledge funding from the Orange Innovation and Regulation Chair at Telecom ParisTech/Ecole Polytechnique. y Telecom ParisTech, Deartment of Economics and Social Sciences, and CREST-LEI. marc.bourreau@telecom-aristech.fr z Telecom ParisTech, Deartment of Economics and Social Sciences. kourandi@aueb.gr x Imerial College London, University of Rome II and CEPR. t.valletti@imerial.ac.uk

2 1 Introduction Should we continue to treat all tyes of Internet tra c equally, that is, with no discrimination with resect to the tye of content, service or alication and the identity of the data transmitter, or should we instead allow Internet latforms (Internet Service Providers, ISPs) to discriminate the tra c they carry? This question over the net neutrality has generated hot debates since the Federal Communications Commission (FCC) changed the classi cation of Internet transmissions from the category of telecommunications services to the category of information services in the US in 2005, making ISPs no longer exlicitly subject to the rincile of net neutrality. This debate has been exacerbated by the fact that, over the last few years, the volume of Internet tra c has grown u drastically, requiring ISPs to ugrade their network caacity. In 2005, AT&T, later followed by other major telehone and cable oerators, roosed to charge content roviders (CPs) remium rices for referential access to broadband transmission services. Comcast, the largest cable oerator in the US, was also accused of interfering with users access to le-sharing services such as BitTorrent. There have been other cases reorted in the oular ress of ISPs blocking or degrading the quality of content. ISPs argue that these ractices are necessary to manage Internet tra c e ciently and 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 seems now widely acceted, which tra c management techniques will be allowed is still discussed. In articular, olicy-makers argue that it is crucial to revent ISPs from adoting discriminatory ractices for reasons unrelated to tra c management. 1 The net neutrality issue turns out to be very contested among olicy-makers and industry layers. Oonents to net neutrality argue that a net neutrality regulation would reduce ISPs incentives to invest in broadband caacity, and lead to less entry of CPs. 2 Proonents of net neutrality, on the other hand, contend that the Internet has been neutral since its incetion, and should be ket free and oen to everyone. They further argue that a dearture from the net neutrality regime would reduce innovation in Internet services (entry of CPs), 3 and that ISPs will 1 On Setember 23rd, 2011, the FCC released a rule on Preserving the Oen Internet where it adots three basic rotections: transarency, no blocking, and no unreasonable discrimination. The Euroean Commission also launched a ublic consultation on The oen Internet and net neutrality in Euroe in 2010 to collect the oinions of the various arties involved in the Internet market, and clarify the issue of net neutrality. Some countries have adoted non-binding guidelines on net neutrality, such as Norway and Canada, while Chile was the rst country to address directly the rincile of net neutrality in its legislation (Holland was the second). 2 See, for examle, Yoo (2005). 3 See Van Schewick (2006). 1

3 continue to invest in broadband caacities whatever the tra c regime, since this is the only way to kee their demand high. Finally, end users are concerned about the subscrition fees that they ay to ISPs, the variety of Internet content, and the quality of their Internet connection. The aim of this aer is to roose a formal analysis of the imact of a transition from the net neutrality regime to a discriminatory regime, in a model with cometing ISPs and a continuum of heterogeneous CPs. It has indeed been argued that surring cometition between ISPs can solve the net neutrality roblem, making a discriminatory regime less threatening (in terms of blocking, sabotage, etc.) to the extent that ISPs race against each other. 4 For examle, the Euroean Commission (2011) stated that the signi cance of the tyes of roblems arising in the net-neutrality debate is correlated to the degree of cometition existing in the market. 5 In the US, the FCC exemted mobile networks from net neutrality regulation, on the grounds that cometition warrants net neutrality or at least mitigates the negative e ects of a dearture from it. Desite its aarent relevance in the olicy context, the cometition asect has been overlooked by the literature, as most aers assume a monoolistic market structure at the ISP level. Though it is always bene cial for a monoolist ISP to deart from the net neutrality regime, since it can extract art of the CPs revenues by charging them for riority and still serve all end users, it is less clear that a switch to the discriminatory regime would bene t cometing ISPs. Moreover, in a monoolistic framework, total welfare mechanically increases with a dearture from net neutrality when the ISP can fully extract consumer surlus. An imortant question is whether this is still true when there is cometition between Internet latforms. We build a two-sided model where two horizontally-di erentiated Internet latforms comete to bring together the two sides of the Internet, the CPs and the end users. We then comare the ricing, investment, and innovation incentives under the net neutrality and the discriminatory regimes. Innovation in services takes lace when CPs enter the market and o er advertisingsuorted content to end users. CPs are heterogeneous with resect to their congestion sensitivity and may single-home, multi-home, or stay out of the market. For the most congestion-sensitive CPs (e.g., those who o er streaming or VoIP alications) delays in data transmissions are harmful, since such delays make end users less likely to click on ads, and hence, reduce advertising revenues. By contrast, the less congestion-sensitive CPs (e.g., those who suly account services) are hardly a ected by congestion. Under net neutrality, CPs that are connected to the same ISP are 4 See, e.g., Becker et al. (2010). 5 Euroean Commission, , Communication from the Commission to the Euroean Parliament. 2

4 treated equally, and exerience the same level of congestion. Under discrimination, by contrast, ISPs o er two di erentiated tra c lanes to CPs, a riority (fast) lane and a non-riority (slow) lane. CPs have to ay a riority fee to their ISP to access the fast lane, while the slow lane remains free-of-charge. Finally, end users who value the variety of content, but dislike network congestion choose one ISP to subscribe to. Our rst result is that a switch from the net neutrality regime to the discriminatory regime would be bene cial in terms of investments, innovation, and total welfare. First, when ISPs o er di erentiated tra c lanes, investment in broadband caacity increases. This is because the discriminatory regime allows ISPs to extract additional revenues from CPs through the riority fees. Second, innovation in services also increases: some highly congestion-sensitive CPs that were left out of the market under net neutrality enter when a riority lane is roosed. Overall, discrimination always increases total welfare, though the imact of a switch to the discriminatory regime on each tye of agent (ISPs, CPs, end users) is generally ambiguous. Our second result is that ISPs might be traed in a risoners dilemma with regards to the choice of a tra c regime. Indeed, we nd that each ISP always has a unilateral incentive to adot the discriminatory regime, even though the two ISPs ro ts might be reduced if they both switch to discrimination. We extend our baseline model to account for the ossibility that ISPs engage in quality degradation or sabotage of CPs tra c. We nd that sabotage never arises endogenously under net neutrality. By contrast, under the discriminatory regime, ISPs may have an incentive to sabotage the non-riority lane to make the riority lane more valuable, and hence, to extract higher revenues from the CPs that ot for riority. Any level of sabotage is detrimental for total welfare, and therefore, a switch to the discriminatory regime would still require some regulation of tra c quality. Our qualitative results are robust when we account for the existence of small and large CPs, in which case rioritization is likely to hurt the small CPs more than the large ones. Finally, our qualitative results are also robust when we restrict our attention to one ISP; however, the monoolist always is better of under discrimination since it can extract the whole consumer surlus. Related literature. While the ossibility of a dearture from net neutrality has generated rich olicy debates, few academic aers have addressed this issue. Choi and Kim (2010) and Cheng et al. (2011) study models with a monoolistic ISP and a xed number of CPs (two) who can access a fast lane by aying a riority fee and the ISP invests in caacity. Krämer and Wiewiorra (2012) extend this framework by considering a continuum of heterogeneous congestion-sensitive CPs. 3

5 These contributions concern models of monooly. In our work we rovide a setting with both investment in caacity, innovation by CPs and ISPs cometition, and study whether the olicy concerns surrounding the net neutrality debate are alleviated when there is cometition between Internet latforms. 6 A small number of works have considered the question of net neutrality in a model with cometing ISPs. Economides and Tåg (2012) roose such a model but in a static framework, which ignores the congestion roblem and the investment decisions of the ISPs. Njoroge et al. (2012) build u a model with two cometing ISPs which can invest in quality, however they do not study analytically the imact of tra c rioritization, which is at the core of the net neutrality debate. Choi et al. (2012) analyze a static model with cometing and interconnected ISPs and a xed continuum of heterogeneous CPs. They do not address the investment issue, and focus on the termination fees charged by the ISPs to the CPs and on the interconnection fees charged between ISPs. By contrast, we focus on the imact of the tra c regime (net neutrality vs. discrimination) on investment and innovation incentives, in a setting with cometing ISPs. Our aer is also related to the literature on two-sided markets, 7 and more seci cally to the stream of literature that analyzes investment and innovation strategies in two-sided markets (Farhi and Hagiu, 2008). In articular, Belle amme and Peitz (2010) study the imact of a monooly latform s intermediation mode (for-ro t versus free-access) on sellers investment, in a model where sellers investment increases the buyers utility of joining the latform. They show that for-ro t intermediation may lead to overinvestment. Finally, our aer is linked to the literature that analyzes the welfare e ects of rice discrimination in oligooly markets. In line with this literature (e.g., Corts, 1998; Armstrong, 2008), in our model discrimination can make cometition between Internet latforms either softer or tougher. 8 Hermalin and Katz (2007) roose a model where rms subject to a roduct line restriction should roduce a single quality (which is tantamount to a net neutrality regulation), whereas in the absence of regulation they can roduce more than a single quality. In a similar framework, Alexandrov and Deb (2012) examine the investment incentives and the ricing decisions of the rms when they are allowed (or not) to rice discriminate. Price discrimination increases investments in their one-sided model, as it does in our two-sided setting. 6 Other monooly models of net neutrality with investments exist, e.g., Economides and Hermalin (2012) and Reggiani and Valletti (2011). See Schuett (2010) for a review of recent literature. 7 See, for examle, Rochet and Tirole (2006) and Armstrong (2006). 8 See also Liu and Serfes (2012). 4

6 The remainder of the aer is as follows. Section 2 sets u the model. Section 3 derives the equilibrium under net neutrality. The equilibrium under discrimination is studied in Section 4. Section 5 comares the two regimes. In Section 6 we extend the model to allow for the ossibility of sabotage, while in Section 7 we discuss the case of small and large CPs. Section 8 concludes. 2 The Model Two horizontally-di erentiated Internet service roviders (ISPs), denoted as A and B, bring together two sides of the Internet, resectively 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, 9 while ISPs sell broadband access to end users. The CPs are global, thus, they are not rovided Internet access by ISP A or ISP B. 10 Under net neutrality, ISPs do not charge CPs for access to their broadband network. However, due to caacity constraints, networks can su er from congestion, which both CPs and end users dislike. We therefore study the e ect of an alternative to the net neutrality regime, the discriminatory regime. 11 Under the discriminatory regime, each ISP o ers two di erentiated tra c lanes to CPs, the riority (fast) and non-riority (slow) lanes. ISPs charge CPs to access their riority lane, whereas they o er free access to the non-riority lane. 2.1 Content roviders There is a continuum of non-cometing and congestion-sensitive CPs that derive revenues from advertising. At each level of congestion sensitivity h 2 [0; 1), there is a mass 1 of CPs. Each CP may connect to no ISP, to a single ISP, or to both ISPs; that is, we allow CPs to single-home or to multi-home. If it connects to ISP i, a CP has access only to the end users connected to that ISP. CPs receive 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 end users subscribing to ISP i and is the constant number of visits er user, which is the same for all web sites. Visitors of CP h click on ads with a clickthrough rate of (1 hw i ), where w i denotes the congestion on ISP i s network. The click-through 9 This corresonds to the tyical business model for CPs on the Internet. Moreover, although some (tyically large) CPs charge consumers for content, they often o er a free and ad-suorted version of their service as well. 10 We focus on the last-mile market for Internet access, taking as given a cometitive backbone that connects global CPs to residential-access ISPs. The debate on net neutrality centers around tra c management at the last-mile level; thus, we take the eering agreements between the networks at the backbone as given. 11 Note that we rst consider each regime searately. In Section 5 we will however discuss an ISP s incentive to switch unilaterally to the discriminatory regime. 5

7 rate reresents 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. 12 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, as its click-through rate is sharly reduced. This is because, when there is congestion, end users rimarily consume the content, and are less likely to send enough time on the service to click on ads. 13 By contrast, a CP with a very low congestion sensitivity (e.g., a CP that rovides accounts) is hardly a ected by congestion. Since its service requires limited bandwidth, end users can use it with a similar comfort as if there were no congestion, and are therefore almost as likely to click through on ads. Under net neutrality (N), as no ayment is due to the ISPs, the ro t of CP h is 8 >< N h = >: ax N A 1 hwn A + ax N B 1 hwb N ax N i 1 hwi N 0 otherwise. if it connects to both ISPs it connects only to ISP i Under net neutrality, all the CPs that are active at ISP i are treated equally and face the same average level of congestion wi N. By contrast, 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. 14 The ro t of CP h under discrimination (D) is then given by 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 ISPs 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 and w NP i denote the congestion at ISP i under riority (P) and non-riority (NP), 12 We model CPs ro ts in a similar way as Krämer and Wiewiorra (2012). 13 For examle, videos on Youtube come bundled with advertisements that viewers can ski after a few seconds, or view until the end. With a slow connection, it is more likely that these ads will be skied as the viewer would have to waste quite some time to download and see them in full. In the limit, some alications (e.g., video conferencing) may literally not work with a slow connection, and hence no advertising revenues would be ossible at all. 14 Since each CP receives the same number of visits, having a xed fee for riority is without loss of generality in our setting, and could be relaced by a variable fee based on data transferred, without a ecting our results. If instead CPs generated di erent amounts of tra c, ISPs could imlement non-linear ricing schemes. See Jullien and Sand-Zantman (2012) for a monooly model along these lines. 6

8 resectively, with w P i < w N i, as we further detail below. enter do not enter Net Neutrality 0 h i N Discrimination 0 enter at the non riority lane Ê h i enter at the riority lane h i D do not enter Figure 1: Demand of CPs for ISP i 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). 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 between the riority lane and the non-riority lane at ISP i. 2.2 Internet Service Providers 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 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., we have C 0 > 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, 15 Aart from the standard brand di erentiation interretation, horizontal roduct di erentiation may re ect the di erent tyes of services o ered by the ISPs. For examle, one ISP might target techie 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 non-techie users with low comuter skills, and o er them a broadband service already embedded with the average desirable characteristics of a broadband connection. 7

9 and makes ro t D i = D i x D i + (h D i e hi )f i C( D i ), where h D i e hi is the total number of CPs that buy riority at ISP i, in the discriminatory regime. 2.3 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 level of congestion as a function of network caacity and tra c. 16 Under the net neutrality regime, the average level of congestion for ISP i is w N i = 1. (1) N i h N i x N i Note that the level of congestion 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 total tra c of ISP i. Under discrimination, each ISP sorts CPs into two tra c lanes, the riority lane and the nonriority lane. The congestion for the riority lane (P) oerated by ISP i is given by w P i = D i h D i 1 e hi x D i, (2) whereas the congestion 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 congestion 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 total tra c 16 On the M/M/1 model, see Choi and Kim (2010) and the references cited therein. 8

10 volumes are the same under net neutrality and discrimination, the average level of congestion is also the same under both regimes (i.e., we have w N i = w D i ), which is a well-known roerty of the M/M/1 queuing model. 2.4 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 sulied by CPs, d is a arameter which measures the reference for the seed of the connection (as w N A is congestion in some time units, 1=wN A reresents the seed of the Internet connection), and nally, t is the standard Hotelling unit 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 subscribes to ISP A. Similar exressions are obtained if the end user subscribes to ISP B. We assume that R is su ciently high so that the market is covered in equilibrium in both regimes. Although it will not be invoked until we extend the model to account for ossible sabotage, we already further assume that end users value content su ciently comared to the disutility they su er from congestion. In articular, in a symmetric equilibrium, it must be that v > d=2: (6) To see why, relace w D A from (4) into (5) in the discriminatory regime.17 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. For consumers to value the resence of CPs, the bracket has to be ositive. Thus, v dx D i > 0, 17 The same reasoning alies in the net neutrality regime and gives the same condition. 9

11 which we assume to hold in a symmetric equilibrium with x D i = 1=2. 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: 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. 2. 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 2: 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. (7) Relacing for w N i, as given by (1), into (7) and solving for hn i, we nd that the tye of the marginal CP is N i h N i = 1 + x N i. (8) Given our model assumtions, the number of subscribers a ects the number of CPs only through the level of congestion. As a higher number of subscribers imlies more congestion on ISP i s network, there is less entry of CPs on that ISP. Simultaneously, at stage 2, 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. (9) 18 As we are interested in the long-run roerties of the two regimes, we consider that caacities and rices are set simultaneously at the rst stage. This sequence of events also allows us to derive analytical solutions. The three-stage sequential game, where the ISPs rst decide on caacity, and then set the end users rices, cannot be solved analytically, and is even extremely hard to solve numerically. 10

12 Relacing for h N A and h N B into (9), we nd that the indi erent consumer is de ned imlicitly from 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 2ex N ) ( N B N A ) = 0, (10) and, therefore, we have ex N = ex N ( N A ; N B ; N A ; N B ). The number of end users of ISP A and ISP B are then x N A = exn and x N B = 1 exn, resectively. 3.2 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 ; i = N i x N i C N i N i 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, (11) N N i = N N N i C 0 N i = 0. (12) We obtain the following result. 19 Proosition 1 Under net neutrality, in the symmetric equilibrium, the caacity level, the subscrition fee, the number of CPs and the average level of congestion are given by: d + v N = (C 0 ) 1, + 2 N = t + 4N (d + v) ( + 2) 2, h N = 2N + 2, w N = N. 19 With some abuse of notation, in the symmetric equilibrium, we dro the subscrits i = A; B for the two 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 denote the equilibrium values. 11

13 Proof. Since we do not have an exlicit solution for market shares x N i, we aly the Imlicit Function Theorem to equation (10) in order to determine the N i =@N i N i =@N i, which are then used in the FOCs of Stage 1. De ne K = 2t + (d + N N B 1 + x N 2 + B N A! 1 + x N 2 > 0. A We N N A N = 1 K N < 0 N A N = d + v 1 + x N > A K N 0. N N B = 1 K N > 0 N N = B d + v 1 + x N < B K N 0. By relacing for these derivatives in the rst-order conditions (11) and (12), and by imosing symmetry, we obtain the symmetric equilibrium levels of investment in caacity and the subscrition fees, as reorted in the Proosition. We assume that the investment cost function C () is su - ciently convex so that the candidate equilibrium corresonds to a maximum of the ro t function. See Aendix A for the condition on C 00 (). In the symmetric equilibrium, the two ISPs share the market equally (i.e., we have x N A = xn B = 1=2). After relacing for the equilibrium values 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 2 + 2N (d + v) ( + 2) 2 C( N ), 8 < N h = : a 1 h(+2) 2 N if h h N. 0 if h > h N The total ro ts of CPs are equal to N h Z N h = 0 N h dh = an + 2. Finally, we determine consumers surlus and total welfare in the net neutrality regime. 20 The 20 The analysis of consumers surlus in our set-u with cometitive ISPs is richer and more relevant comared to the case of a monoolistic ISP, which can extract the entire consumers surlus due to the lack of cometition. 12

14 net utility of end user j located at x j 1=2 is U N j = R + 2N (2 ) (d + v) ( + 2) 2 t (1 + x j ). By summing u the net surlus of all end users, we obtain the consumers surlus, Z 1 CS N 2 = 2 Uj N dx j = R 0 5t 4 + 2N (2 ) (d + v) ( + 2) 2. The total welfare W N is de ned as the simle sum of ISPs ro ts, CPs ro ts and consumers surlus. We nd that W N = 2 N + N h + CSN = R 3.3 Equilibrium roerties t 4 + (a + 2 (d + v)) N + 2 2C( N ). (13) Under net neutrality, the equilibrium subscrition fee is higher than the fee that would revail in the standard Hotelling setting (i.e., = t). This is due to the resence of network externalities in our setting. An increase in ISP i s subscrition fee decreases directly its demand, but it also leads to a reduction in the congestion on its network and, thus, to an increase of the number of CPs, which in turn a ects ositively the demand from the end users who bene t from more content. The total e ect of a rice increase on ISP i s demand is negative, but it is less negative than in a one-sided market, which induces ISPs to set a higher rice than in a standard Hotelling model. The equilibrium converges to a standard Hotelling game in the limiting cases where either there is no tra c (! 0), or investment in caacity goes to zero ( N! 0). In articular, when N! 0, the equilibrium subscrition fee and the ISPs equilibrium ro ts converge to those of the Hotelling model (i.e., N! t and N! t=2), whereas the equilibrium congestion goes to in nity (i.e., w N! 1) and the number of CPs goes to zero (i.e., h N! 0). However, this degenerate case never arises in equilibrium as the caacity is always ositive ( N > 0), otherwise there would be no market for Internet access. Finally, we rovide some intuitive comarative statics. We nd that when the number of visits 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 is Consumer surlus would always be zero, with or without neutrality, under a monoolist ISP. 13

15 generally ambiguous and 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 because of the cometition-damening e ect from the network externality that we described above. By contrast, when is high enough, congestion becomes substantial: the revailing e ect comes from a reduction of content, so that rices and ISPs ro ts decrease with further increases in. When the reference for seed d and/or the reference for roduct variety v increase, ISPs can extract more rents from consumers, which leads to higher subscrition fees, and therefore higher investments in caacity, higher entry by the CPs, and lower congestion. The CPs ro ts and the total welfare increase too. Finally, the er-click advertising revenue a only enters the CPs ro ts, and hence, both the CPs ro ts and the total welfare are ositively a ected by an increase in a. 4 Discrimination In the discriminatory regime, each ISP o ers a riority lane and a non-riority lane to CPs. The CPs that ot for riority at ISP i ay a xed fee f i, whereas the non-riority lane is o ered for free. We modify our two-stage game accordingly: 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, as well as the fees for their riority lanes, f A and f B. 2. The CPs choose which ISP(s) to connect to (if any) and whether to ay for riority, and the end users choose which ISP to subscribe to. 4.1 Stage 2: 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 if h h D i, where h D i solves ax D i (1 h D i w P i ) f i = 0. (14) Furthermore, the CP of tye e h i which is indi erent between the riority lane and the non-riority lane at ISP i is de ned by ax D i (1 e hi w P i ) f i = ax D i (1 e hi w NP i ): (15) 14

16 From (14) and (15), the total number of CPs that ay for riority at ISP i is maxfh D i e hi ; 0g. Equation (15) imlies that f i = ax D i e h i w NP i w P i, and relacing for this exression into (14), 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 using w D i which is de ned in (4), we nd that the tye of the marginal CP that enters at ISP i is h D i = 1 w D i, which can be rearranged as h D i = D i 1 + x D i. (16) The tye of the marginal CP h D i is indeendent of the riority fee and takes an exression similar to the total number of CPs at ISP i in the net neutrality regime (which is given by (8)). Note that two con icting e ects are at lay here: a demand e ect and a congestion e ect. On the one hand, a higher number of subscribers increases CPs ro ts, and hence, entry (demand e ect). On the other, it increases congestion, which reduces entry (congestion e ect). We nd that the congestion e ect always dominates the demand e ect, which is why the number of CPs at ISP i decreases with the number of subscribers on this latform. In addition, we have 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. (17) Simultaneously, at stage 2, 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. (18) By relacing for h D A and h D B into (18), the indi erent consumer satis es D B (d + v) 1 + (1 ex D ) D A 1 + ex D t 1 2ex D D B D A = 0, (19) 15

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 (19) for the discriminatory regime is similar to equation (10) for the net neutrality regime, and that ex D is indeendent of the riority fees. 4.2 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 + h D i i e hi f i C D i, where x D i = x D i (D A ; D B ; D A ; D B ). The corresonding 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, (20) D D e + i hi )f i ) = 0, D D i e i hi )f i ) = 0. i We obtain the following result. Proosition 2 Under discrimination, in the symmetric equilibrium, the caacity level, the riority fee, the subscrition fee, the number of CPs and the levels of congestion are given by: D = (C 0 ) 1 d + v a f = a 2 1! 2, + 2 D = t + 4D (d + v) ( + 2) 2 2a D h D = 2D + 2 ; e h = w P = D, w NP = 2! , 2 ( + 2) ( + 2) 2,! h D, 3 2 ( + 2) 2 4 D, w D = D. Proof. We roceed as in the net neutrality regime, by alying the Imlicit Function Theorem to 16

18 (19) in order to determine the D i =@D i D i =@D i. We nd D D A = 1 K D < D = 1 B K D > D = A d + v 1 + x D > A K D D = B d + v x D A K D < D A B = 0, where K D (d + v) D B x D 2 + A D A! 1 + x D 2 +2t > 0. A By relacing for these derivatives in the three rst-order conditions, and by imosing symmetry, we obtain the symmetric equilibrium levels of investment in caacity, the subscrition fees and the riority fees, as reorted in the Proosition. Provided that the investment cost function is su ciently convex, the candidate equilibrium corresonds to a maximum of the ro t function. See Aendix A for details. In the symmetric equilibrium, the market is equally shared between the two ISPs (i.e., we have x D A = xd B = 1=2). The equilibrium ro ts for an ISP and a CP are D = t 2 + 2D (d + v) a D ( + 2) ( + 2) 2 C( D ); and 8 >< D h = >: NP h 3 = a 1 h 2(+2) 2 4 D P h = 2a +2 1 h +2 2 D if if h e h e h < h < h D 0 if h h D, resectively. The total ro ts of the CPs are D h = Z eh D 0 NP h Z D h dh + Finally, the utility of end user j located at x j 1=2 is e h D P h dh = 2aD U D j = R + 2D (d + v) (2 ) + a ( + 2) 2 t (1 + x j ), which is used to determine consumers surlus and total welfare,. Z 1 CS D 2 = 2 Uj D dx j = R 0 5t 4 + 2D (d + v) (2 ) + a ( + 2) 2, 17

19 and W D = 2 D + D h +CSD = R t (d + v) + a D + 2 2C D : (23) 4.3 Equilibrium roerties The comarison between the equilibrium subscrition fee under discrimination and the fee in the standard Hotelling model (i.e., t) deends on the values of the arameters. When a is low enough (i.e., lower than 2 (d + v) = ), the equilibrium fee for end users in the discriminatory regime is higher than the Hotelling equilibrium rice (i.e., D i > t). The intuition is as follows. To begin with, if there were no fee for the riority lane, we already know from the analysis under net neutrality that an increase in the subscrition fee D i of ISP i would decrease its own demand, but this e ect is less severe than in the Hotelling model. Besides, under discrimination, there is an additional e ect: revenues from the riority lane are artly assed on to end users, which tend to ush the rice down. Since more revenues are made from riority fees when CPs earn high advertising revenues, that is, when a is high enough, the second e ect can revail over the former. Finally, we resent some comarative statics. We nd that when the number of visits er user increases, the riority fee increases, since the riority lane is valued more as more advertising revenues are made. 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 when becomes higher 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 ositively 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 and entry of CPs is fostered. Therefore, total welfare increases with a. The comarison between the net neutrality regime and the discriminatory regime is examined 18

20 in more detail in the next section. 5 Net Neutrality vs. Discrimination We now turn to the main question of this aer. We comare the two alternative regimes, net neutrality and discrimination, to investigate the economic e ects of a dearture from net neutrality. First, we comare investment and innovation incentives in the two regimes. Second, we comare congestion, subscrition fees and ro ts. Finally, we comare end users utility and total welfare. 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, innovation in Internet services, under the net neutrality and the discriminatory regimes. Using Proosition 1 and Proosition 2, we have the following result. Proosition 3 Investment in broadband caacity and innovation in services are higher under the discriminatory regime than under the net neutrality regime, that is, D > N and h D > h N. Proof. The roof is straightforward. Since C 00 > 0, (C 0 ) 1 is an increasing function, and therefore, from Proositions 1 and 2, we have D > N, as for all 0. This, in turn, imlies that h D > h N. 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 investment incentives. 21 Under net neutrality, ISP i s incentive to invest in caacity is given by the change in its ro ts due to a marginal increase of the caacity level, that N N i = N N N i C 0 N i, (24) 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, (25) 21 Note that the analysis of the short run case where caacity levels are exogenous can be obtained easily by setting D = N = in Proositions 1 and 2. 19

21 D i =@D i > 0. For given levels of subscrition fees and caacities, the terms N i (@xn i =@N i ) C 0 N i are equal to the terms D i (@x D i =@D i ) C0 D D i. We further obtain e i 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 (25) is ositive, which imlies that the marginal revenue of an increase in the caacity level is higher under the discriminatory regime. 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 in services is increased when there is a fast lane, as congestion-sensitive CPs that could not enter under net neutrality now enter by buying access to the riority lane. 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. It is also interesting to comare the number of CPs that enter the market under net neutrality, h N, to the CP of tye e h that is indi erent between buying riority and using the non-riority lane in the discriminatory regime (see Figure 1). We obtain that e h > h N when D N > (26) For high values of the ratio D = N, innovation in services under discrimination is so high that all CPs that buy riority were not active under net neutrality. In this case, a simle revealed reference argument imlies that all CPs are better-o in the discriminatory regime, indeendently from the lane they end u choosing. 5.2 E ect on network congestion Discrimination increases caacity comared to net neutrality, but also total tra c grows as more CPs enter the market. In rincile, therefore, the e ect on average congestion could be ambiguous. However, as the equilibrium number of CPs under either regime is h = 2=( + 2), from the de nition of average congestion it then follows that 1=w = h=2 = 2=( + 2): Since D > N, it is clear that the caacity exansion e ect under discrimination revails. immediately the following Proosition. We can thus state Proosition 4 The average level of congestion is lower under discrimination than under net neutrality, that is, w D < w N. 20

22 Even if the 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 congestion on the non-riority lane. In other words, the ISPs manage Internet tra c more e ciently when they can o er multile lanes, and the more congestion-sensitive CPs can ot and ay for riority. Since from the roerties of the M/M/1 queuing system, we have w P < w D < w NP, it follows immediately that the level of congestion under net neutrality, w N, is always higher than the level of congestion on the riority lane, w P. After comaring the equilibrium level of congestion on the non-riority lane, w NP, to w N, we nd that for su ciently high values of the ratio D = N (i.e., higher than ( + 2)=2), congestion on the non-riority lane is also lower. In this case, caacity exansion under discrimination is high enough to reduce congestion on both the riority and the non-riority lanes. 5.3 E ect on subscrition fees and ro ts We now comare the equilibrium subscrition fees in the two regimes. We nd that D > N if and only if a D = N d + v ( D = N ) 1 < 2. (27) Under net neutrality, the ISPs obtain ro ts only from the end users, whereas, under discrimination, the ISPs can extract additional revenues by charging for access to the riority lane. As we already discussed, the ricing incentives between the two regimes di er, N N i = x N i + N N N i, D 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, but it also a ects indirectly the total number of CPs that ot for riority in the discriminatory regime (via the 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. In this case, cometition in subscrition fees between the ISPs is relaxed and the end users ay higher rices under discrimination than under net neutrality. 21

23 For high values of the ratio D = N, the subscrition fees under discrimination tend to be higher. 22 The caacity exansion, due to the introduction of multile lanes, is relatively high, which leads to a high number of active CPs and thus increases end users utility. The ISPs extract this increased utility via higher subscrition fees. This result is stronger when the end users value more the variety and the seed of the network (high d + v), and when the er-click advertising revenue (a) is lower. When a increases, it is more likely that the ISPs are willing to reduce their rices under discrimination to obtain a 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 su ciently low values of the ratio D = N. Now, we turn to the ro ts of the ISPs and of the CPs. The comarison of the ISPs ro ts between the two regimes yields that D > N if and only if D N =2 C D C( N ) + h D i e hi f i > 0: ISP i obtains additional revenues under discrimination through the riority fees, but the comarison deends also on the di erence in the subscrition fees and on the di erence in the costs of caacity. When cometition is relaxed under discrimination, the term D N =2 is ositive, and hence, ro ts tend to be higher under discrimination. Moreover, the di erence in the investment costs 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 on the arameter values. 23 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, since it can extract art of the CPs ro ts through the riority fee and still serve the whole mass of end users. However, when there is cometition at the ISP level, it is ambiguous whether discrimination will imrove or deteriorate the ISPs ro ts. 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. 22 To see that, it is useful to rearrange condition (27) as d+v 23 Analytically, we have D > N if and only if a 1 1 > D = N 2 (2( D N )(d + v) + a D (( ) 2 ( )))= ( + 2) 2 > C( D ) C( N ): 22

24 Concerning the CPs, we comare their total ro ts under the two regimes. We nd that D h > N h if and only if D N > For high values of the ratio D = N the total ro ts of the CPs under discrimination are higher, and hence, on average CPs are better o. Note that this condition is less stringent than (26) that described instead a Pareto imrovement for CPs. Since CPs in the non-riority lane only care about their congestion, w NP, we obtain from w NP < w N that they obtain higher ro ts comared to the net neutrality regime for high values of D = N. 24 On the other hand, the CPs in the riority lane bene t from the reduction in the congestion comared to the net neutral regime (w P < w N ), but they ay riority fees. Since this fee is xed and each CP in the same lane faces the same level of congestion, we conclude that the highly congestion-sensitive CPs bene t more from riority comared to the less congestion-sensitive CPs. Still, the CPs in the riority lane earn higher ro ts comared to the net neutral regime for high values of the ratio D = N, but this threshold is lower for the more congestion-sensitive CPs. 5.4 E ect on end users utility and total welfare Now, we roceed with the comarison of the end users utility and the total welfare in the discriminatory and net neutrality regimes. For the consumers surlus, we have CS D > CS N if a D = N d + v ( D = N ) 1 > 2 2. (28) On the one hand, discrimination a ects ositively the end users utility, since it increases innovation in services and reduces the average level of congestion in the network. On the other hand, discrimination may increase the subscrition fees that the end users have to ay for Internet access. 25 Therefore, when discrimination leads to more cometitive ressure at the ISP level with resect to the subscrition fees, the end users are better o and the ISPs tend to be worse o. When D = N increases, it is less likely that the end users will ay lower subscrition fees under discrimination, but it is more likely that the ro ts of the ISPs will be higher The condition for NP h > N h > 0 is again D = N > ( + 2)=2. 25 From (27) we obtain that D < N if and only if a d+v D = N ( D = N ) 1 > Note that this condition is more stringent than (28) that describes the more general condition for CS D > CS N to hold. 26 Such an analysis is irrelevant in the monoolistic ISP set-u, since the monoolistic ISP charges the monooly rice in both regimes to extract the entire consumers surlus. Thus, consumers are indi erent between the two 23