Download - Net Neutrality WNET NEUTRALITY WITH COMPETING INTERNET platformsith Competing Internet Platforms

NET NEUTRALITY WITH COMPETING INTERNETPLATFORMS*

MARC BOURREAU†

FRAGO KOURANDI‡

TOMMASO VALLETTI§

We propose a two-sided model with two competing Internet platforms,and a continuum of Content Providers (CP’s). We study the effect of anet neutrality regulation on capacity investments in the market forInternet access, and on innovation in the market for content. Under thealternative discriminatory regime, platforms charge a priority fee tothose CP’s which are willing to deliver their content on a fast lane. Wefind that under discrimination, investments in broadband capacity andcontent innovation are both higher than under net neutrality. Totalwelfare increases, though the discriminatory regime is not always ben-eficial to the platforms as it can intensify competition for subscribers.As platforms have a unilateral incentive to switch to the discriminatoryregime, a prisoner’s dilemma can arise. We also consider the possibilityof sabotage, and show that it can only emerge, with adverse welfareeffects, under discrimination.

I. INTRODUCTION

SHOULD WE CONTINUE TO TREAT all types of Internet traffic equally, that is,with no discrimination with respect to the type of content, service orapplication and the identity of the data transmitter, or should we insteadallow Internet platforms (Internet Service Providers, ISP’s) to discriminatethe traffic they carry? This question over the ‘net neutrality’ has generatedhot discussions since the Federal Communications Commission (FCC)changed the classification of Internet transmissions from the category of

*We thank Bruno Jullien, Michał Grajek, Jan Krämer, Andre Veiga, and the participantsat the Conference on the Economics of ICT (Paris, 2012), the International Conference onManagement and Economics of ICT (Munich, 2012), the Workshop on the Economics ofICT’s (Oporto, 2012), CRESSE (Crete, 2012), CRETE (Milos, 2012), and EARIE (Rome,2012). We acknowledge funding from the Orange ‘Innovation and Regulation’ Chair atTelecom ParisTech/Ecole Polytechnique.

†Authors’ affiliations: Telecom ParisTech, Department of Economics and Social Sciences,Paris, France and CREST-LEI.e-mail: [email protected]

‡Athens University of Economics and Business, Department of Economics, Athens,Greece.e-mail: [email protected]

§Imperial College London, London, England; University of Rome II and CEPR.e-mail: [email protected]

THE JOURNAL OF INDUSTRIAL ECONOMICS 0022-1821Volume LXIII March 2015 No. 1

© 2015 The Editorial Board of The Journal of Industrial Economics and John Wiley & Sons Ltd

30

mailto:[email protected]



‘telecommunications services’ to the category of ‘information services’ inthe U.S. in 2005, making ISP’s no longer explicitly subject to the principleof net neutrality.

This debate has been exacerbated by the fact that, over the last few years,the volume of Internet traffic has grown drastically, requiring ISP’s toupgrade their network capacity. In 2005, AT&T, later followed by othermajor telephone and cable operators, proposed to charge content providers(CP’s) premium prices for preferential access to broadband transmissionservices. Comcast, the largest cable operator in the U.S., was also accusedof interfering with users’ access to file-sharing services such as BitTorrent.There have been other cases reported in the popular press of ISP’s blockingor degrading the quality of content. ISP’s argue that these practices arenecessary to manage Internet traffic efficiently and ensure a sufficientquality of service, especially for content, services and applications that arevery sensitive to delays, such as VoIP services or video conferencing.However, even if this view seems now widely accepted, which trafficmanagement techniques will be allowed is still discussed. In particular,policy-makers argue that it is crucial to prevent ISP’s from adopting dis-criminatory practices for reasons unrelated to traffic management.1

The net neutrality issue turns out to be highly contested among policy-makers and industry players. Opponents to net neutrality argue that a netneutrality regulation would reduce ISPs’ incentives to invest in broadbandcapacity, and lead to less entry of CP’s.2 Proponents of net neutrality, onthe other hand, contend that the Internet has been neutral since its incep-tion, and should be kept free and open to everyone. They further argue thata departure from the net neutrality regime would reduce innovation inInternet services (entry of CP’s),3 and that ISP’s will continue to invest inbroadband capacities whatever the traffic regime, since this is the only wayto keep their demand high. Finally, end users are concerned about thesubscription fees that they pay to ISP’s, the variety of Internet content, andthe quality of their Internet connection. The aim of this paper is to proposea formal analysis of the impact of a transition from the net neutralityregime to a discriminatory regime, in a model with competing ISP’s and acontinuum of heterogeneous CP’s.

It has indeed been argued that spurring competition between ISP’s cansolve the net neutrality problem, making a discriminatory regime less

1 On September 23, 2011, the FCC released an Order on ‘Preserving the Open Internet’(FCC 10-201, ‘In the Matter of Preserving the Open Internet, Broadband Industry Practices’),where it adopts three basic protections: transparency, no blocking, and no unreasonablediscrimination. This is currently challenged in courts. Some countries have adopted non-binding guidelines on net neutrality, such as Norway and Canada, while Chile was the firstcountry to address directly the principle of net neutrality in its legislation (Holland was thesecond).

2 See, for example, Yoo [2005].3 See Van Schewick [2006].

NET NEUTRALITY WITH COMPETING INTERNET PLATFORMS 31


threatening (in terms of blocking, sabotage, etc.) to the extent that ISP’srace against each other.4 For example, the European Commission statedthat ‘the significance of the types of problems arising in the net-neutralitydebate is correlated to the degree of competition existing in the market.’5 Inthe U.S., the FCC exempted mobile networks from most of the net neu-trality rules,6 on the grounds that they face stronger capacity constraintsthan fixed networks, and that competition warrants net neutrality or atleast mitigates the negative effects of a departure from it.7

Despite its apparent relevance in the policy context, the competitionaspect has been overlooked by the literature, as most papers assume amonopolistic market structure at the ISP level. Though it is always benefi-cial for a monopolist ISP to depart from the net neutrality regime, since itcan extract part of the CPs’ revenues by charging them for priority and stillserve all end users, it is less clear that a switch to the discriminatory regimewould benefit competing ISP’s. Moreover, in a monopolistic framework,consumer surplus is not affected by a departure from net neutrality if theISP can fully extract the surplus from the consumption of content and theconsumer market is fully covered. As the ISP additionally extracts part ofthe CPs’ profits under discrimination, a departure from net neutrality thenmechanically increases welfare when it is profitable for the ISP, as the ISPinternalizes total welfare more. An important question is whether this isstill true when there is competition between Internet platforms.

We build a two-sided model where two horizontally differentiated Inter-net platforms compete to bring together the two sides of the Internet, theCP’s and the end users. We then compare the pricing, investment andinnovation incentives under the net neutrality and the discriminatoryregimes. Innovation in services takes place when CP’s enter the market andoffer advertising-supported content to end users. CP’s are heterogeneouswith respect to their congestion sensitivity and may single-home, multi-home, or stay out of the market. For the most congestion-sensitive CP’s (e.g.,those who offer streaming or VoIP applications) delays in data transmis-sions are harmful, since such delays make end users less likely to clickon ads, and hence, reduce advertising revenues. By contrast, the less

4 See, e.g., Becker et al. [2010].5 Communication from the Commission to the European Parliament on 19 April 2011.6 In particular, the rules allow mobile operators to discriminate or to block specific appli-

cations. However, mobile networks have the same obligation as fixed networks to publiclydisclose their network management practices (‘transparency’ rule). See Maxwell and Brenner[2012] for a comparison of the net neutrality rules for fixed and mobile networks in the U.S.and in Europe. Choi et al. [2013] show that net neutrality rules may be harmful when thenetwork capacity is highly limited (as on mobile broadband networks), because it hindersentry from highly congestion-sensitive CP’s.

7 In its Order, the FCC explains the different rules for fixed and mobile networks by statingin particular that ‘most consumers have more choices for mobile broadband than for fixed(particularly fixed wireline) broadband’ (paragraph 95).

MARC BOURREAU, FRAGO KOURANDI, TOMMASO VALLETTI32


congestion-sensitive CP’s (e.g., those who supply e-mail account services)are hardly affected by congestion. Under net neutrality, CP’s that areconnected to the same ISP are treated equally, and experience the same levelof congestion. Under discrimination, by contrast, ISP’s offer two differen-tiated traffic lanes to CP’s, a priority (fast) lane and a non-priority (slow)lane. CP’s have to pay a priority fee to their ISP to access the fast lane, whilethe slow lane remains free-of-charge. Finally, end users—who value thevariety of content, but dislike network congestion—choose one ISP tosubscribe to.

Our first result is that a switch from the net neutrality regime to thediscriminatory regime would be beneficial in terms of investments, innova-tion and total welfare. First, when ISP’s offer differentiated traffic lanes,investment in broadband capacity increases. This is because the discrimi-natory regime allows ISP’s to extract additional revenues from CP’sthrough the priority fees. Second, innovation in services also increases:some highly congestion-sensitive CP’s that were left out of the marketunder net neutrality enter when a priority lane is proposed. Overall, dis-crimination always increases total welfare, though the impact of a switch tothe discriminatory regime on each type of agent (ISP’s, CP’s, end users) isgenerally ambiguous.

Our second result is that ISP’s might be trapped in a prisoners’ dilemmawith regards to the choice of a traffic regime. Indeed, we find that each ISPalways has a unilateral incentive to adopt the discriminatory regime, eventhough the two ISPs’ profits might be reduced if they both switch todiscrimination.

We extend our baseline model to account for the possibility that ISP’sengage in quality degradation or ‘sabotage’ of CPs’ traffic. We find thatsabotage never arises endogenously under net neutrality. By contrast,under the discriminatory regime, ISP’s may have an incentive to sabotagethe non-priority lane to make the priority lane more valuable, and hence, toextract higher revenues from the CP’s that opt for priority. Any level ofsabotage is detrimental for total welfare, and therefore, a switch to thediscriminatory regime would still require some regulation of traffic quality.Our qualitative results are robust when we account for the existence ofsmall and large CP’s, in which case prioritization is likely to hurt the smallCP’s more than the large ones. Finally, our qualitative results are alsorobust when we restrict our attention to one ISP; however, the monopolistis always (at least weakly) better off under discrimination since it canreplicate the net neutrality outcome under discrimination.

Related literature. While the possibility of a departure from net neutralityhas generated rich policy debates, few academic papers have addressed thisissue. Choi and Kim [2010] and Cheng et al. [2011] study models with amonopolistic ISP and a fixed number of CP’s (two) who can access a fastlane by paying a priority fee and the ISP invests in capacity. Krämer and



Wiewiorra [2012] extend this framework by considering a continuum ofheterogeneous congestion-sensitive CPs.

These contributions concern models of monopoly. In our work weprovide a setting with both investment in capacity, innovation by CP’s andISPs’ competition, and study whether the policy concerns surrounding thenet neutrality debate are alleviated when there is competition betweenInternet platforms.8

A small number of works have considered the question of net neutralityin a model with competing ISP’s. Economides and Tåg [2012] propose sucha model but in a static framework, which ignores the congestion problemand the investment decisions of the ISP’s. Njoroge et al. [2013] build up amodel with two competing ISP’s which can invest in quality, however theydo not study analytically the impact of traffic prioritization, which is at thecore of the net neutrality debate. Choi et al. [2012] analyze a static modelwith competing and interconnected ISP’s and a fixed continuum of hetero-geneous CP’s. They do not address the investment issue, and focus on thetermination fees charged by the ISP’s to the CP’s and on the interconnec-tion fees charged between ISP’s. By contrast, we focus on the impact of thetraffic regime (net neutrality vs. discrimination) on investment and inno-vation incentives, in a setting with competing ISP’s.

Our paper is also related to the literature on two-sided markets,9 andmore specifically to the stream of literature that analyzes investment andinnovation strategies in two-sided markets (Farhi and Hagiu [2008]). Inparticular, Belleflamme and Peitz [2010] study the impact of two competingplatforms’ intermediation mode (for-profit versus free-access) on sellers’investment, in a model where sellers’ investment increases the buyers’ utilityof joining a platform. They show that for-profit intermediation may lead tooverinvestment.

Finally, our paper is linked to the literature that analyzes the welfareeffects of price discrimination in oligopoly markets. In line with this litera-ture (e.g., Corts [1998]; Armstrong [2008]), in our model discrimination canmake competition between Internet platforms either softer or tougher.10

Alexandrov and Deb [2012] examine the investment incentives and thepricing decisions of the firms when they are allowed (or not) to pricediscriminate. Price discrimination increases investments in their one-sidedmodel, as it does in our two-sided setting.

The remainder of the paper is as follows. Section II sets up the model.Section III derives the equilibrium under net neutrality. The equilibriumunder discrimination is studied in Section IV. Section V compares the two

8 Other monopoly models of net neutrality with investments exist, e.g., Economides andHermalin [2012] and Reggiani and Valletti [2012]. See Schuett [2010] for a review of recentliterature.

9 See, for example, Rochet and Tirole [2006] and Armstrong [2006].10 See also Liu and Serfes [2013].



regimes. In Section VI we extend the model to allow for the possibility ofsabotage, while in Section VII we discuss the case of small and large CP’s.Section VIII concludes.

II. THE MODEL

Two horizontally-differentiated Internet service providers (ISP’s), denotedas A and B, bring together two sides of the Internet, respectively contentproviders (CP’s) and end users. CP’s provide free content to end users viathe broadband networks of the ISP’s and derive revenues from advertis-ing,11 while ISP’s sell broadband access to end users. The CP’s are global,thus, they are not provided Internet access by ISP A or ISP B.12

Under net neutrality, ISP’s do not charge CP’s for access to their broad-band network. However, due to capacity constraints, networks can sufferfrom congestion, which both CP’s and end users dislike. We therefore studythe effect of an alternative to the net neutrality regime, the discriminatoryregime.13 Under the discriminatory regime, each ISP offers two differenti-ated traffic lanes to CP’s, the priority (fast) and non-priority (slow) lanes.ISP’s charge CP’s to access their priority lane, whereas they offer free accessto the non-priority lane.

II(i). Content Providers

There is a continuum of non-competing and congestion-sensitive CP’s thatderive revenues from advertising. At each level of congestion sensitivityh ∈ [0, ∞), there is a mass 1 of CP’s. Each CP may connect to no ISP, to asingle ISP, or to both ISP’s; that is, we allow CP’s to single-home or tomulti-home. If it connects to ISP i, a CP has access only to the end usersconnected to that ISP.

CP’s receive advertising revenues as follows. When a CP of type h connectsto ISP i, it receives λxi visits, where xi is the number of end users subscribingto ISP i and λ is the constant number of visits per user, which is the same forall web sites. Visitors of CP h click on ads with a click-through rate of(1 − hwi), where wi denotes the congestion on ISP i’s network. The click-through rate represents the proportion of the CP’s visitors who actually clickon ads. Finally, clicks generate advertising revenues of aλxi(1 − hwi) for CPh, where a denotes the fixed per-click advertising revenue.

11 This corresponds to the typical business model for CP’s on the Internet. Moreover,although some (typically large) CP’s charge consumers for content, they often offer a free andad-supported version of their service as well.

12 We focus on the ‘last-mile’ market for Internet access, taking as given a competitivebackbone that connects global CP’s to residential-access ISP’s. The debate on net neutralitycenters around traffic management at the last-mile level; thus, we take the peering agreementsbetween the networks at the backbone as given.

13 Note that we first consider each regime separately. In Section V we will however discussan ISP’s incentive to switch unilaterally to the discriminatory regime.



With this formulation, a CP with a high congestion sensitivity (e.g., a CPwhich offers live streaming) suffers a lot from network congestion, as itsclick-through rate is sharply reduced. This is because, when there is con-gestion, end users primarily consume the content, and are less likely tospend enough time on the service to click on ads.14 By contrast, a CP witha very low congestion sensitivity (e.g., a CP that provides e-mail accounts)is hardly affected by congestion. Since its service requires limited band-width, end users can use it with a similar comfort as if there were nocongestion, and are therefore almost as likely to click through on ads.

Under net neutrality (N), as no payment is due to the ISP’s, the profit ofCP h is

ΠhN

AN

AN

BN

BNa x hw a x hw

a=

−( ) + −( )λ λ

λ

1 1 it connects to both ISP’s

xx hw iiN

iN1

0

−( )⎧

⎨⎪⎪

⎩⎪⎪

if it connects only to ISP

otherwise.

Under net neutrality, all the CP’s that are active at ISP i are treatedequally and face the same average level of congestion wi

N. By contrast,under the discriminatory regime, a CP may choose to pay a fixed fee fi toISP i to benefit from a priority lane where congestion is lower.15 The profitof CP h under discrimination (D) is then given by

ΠhD

AD

AP

A BD

BP

Ba x hw f a x hw f

=

−( ) − + −( ) −λ λ1 1 priority at both ISP’ss

priority only at ISPa x hw f a x hw i

a x

iD

iP

i jD

jNP

A

λ λ

λ

1 1−( ) − + −( )DD

ANP

BD

BNP

iD

hw a x hw

a x

1 1−( ) + −( )λ

λ

if non-priorityat both ISP’s

11

1

−( ) −

−(

hw fi

j

a x hw

iP

i

iD

iNP

priority at ISPno entry at ISP

,

λ ))

⎧

⎨

⎪⎪⎪⎪⎪⎪

non-priority at ISPno entry at ISP

otherwise

ij

,

,0⎩⎩

⎪⎪⎪⎪⎪⎪

14 For example, videos on Youtube come bundled with advertisements that viewers canskip after a few seconds, or view until the end. With a slow connection, it is more likely thatthese ads will be skipped as the viewer would have to waste quite some time to download andsee them in full. In the limit, some applications (e.g., video conferencing) may literally notwork with a slow connection, and hence no advertising revenues would be possible at all.

15 Since each CP receives the same number of visits, having a fixed fee for priority is withoutloss of generality in our setting, and could be replaced by a variable fee based on datatransferred, without affecting our results. If instead CP’s generated different amounts oftraffic, ISP’s could implement non-linear pricing schemes. See Jullien and Sand-Zantman[2012] for a monopoly model along these lines.



where wiP and wi

NP denote the congestion at ISP i under priority (P) andnon-priority (NP), respectively, with w wi

PiN< , as we further detail below.

Our model thus intends to capture an elastic supply of CP’s. Note thatthe CP’s with a high congestion sensitivity do not enter the market. Wedenote by hi

N and hiD the marginal CP which is indifferent between con-

necting to ISP i and not connecting to it, in the net neutrality and discrimi-natory regimes, respectively (see an example in Figure 1). Underdiscrimination, the CP’s that enter the market choose either to buy accessto the priority lane or to use the non-priority lane for free. We denote by�hi the CP which is indifferent between the priority lane and the non-priority

lane at ISP i. In the paper, we refer to the number of CP’s that enter themarket, hi

N and hiD, as the level of innovation in content and services.16

The connection of an extra end user (keeping the total number of CP’sconstant) has two opposite effects on CPs’ profits. First, there is a demandeffect; a larger customer base for ISP i implies larger advertising revenuesfor the CP. Second, a higher number of consumers for the ISP increasescongestion, which decreases the CP’s click-through rate and thereforeits profit. Overall, the connection of an extra user increases the profit ofCP h if and only if17

hh xi i i

i<

−( )μ λμ

2

,

that is, if the CP’s congestion sensitivity is not too large.

16 In the debates around net neutrality, content innovation is often interpreted as the entryof new CP’s, which is what we model. Our definition of innovation on the content side ignoressome other important dynamic aspects of innovation by content providers, and in particularby incumbent content providers, who could improve the quality of an existing service and/orintroduce additional services.

17 This condition is the same under both regimes, and we therefore drop the superscriptshere for simplicity.

Figure 1Demand of CP’s for ISP i



Two remarks are important about this setting. First, we assume that thead revenue per click, a, is constant. If we endogenize the advertising price(e.g., if a depends on the number of CP’s at a given ISP), our results undernet neutrality are unchanged. This is because the number of CP’s that enterthe market does not depend on a.18 Under discrimination, the total numberof CP’s is also unchanged, while the number of CP’s that buy priorityincreases with the advertising price. To the extent that the advertising pricedecreases with the number of CP’s, this reduces ISPs’ investment incentives,compared to our setting with a fixed advertising price. Second, in our modelthere are no entry costs for the CP’s to connect to a platform. It is possibleto account for CPs’ fixed entry costs. This extension, that we have solved,does not lead to any qualitative change in our main results, and we willcomment below only where the analysis is affected.

II(ii). Internet Service Providers

The two ISP’s are located at the extremities of a linear city of length one,with ISP A located at point 0 and ISP B located at point 1.19 Each ISP icharges a subscription fee pi to the end users connected to its network, andinvests in broadband capacity μi. The investment cost C(μi) is increasingand convex in μi (i.e., we have C′ > 0 and C″ > 0).

Under net neutrality, the profit function of ISP i is

ΠiN

iN

iN

iNp x C= − ( )μ .

Under discrimination, ISP i also charges a fixed fee fi to the CP’s that optfor the priority lane, and makes profit

ΠiD

iD

iD

iD

i i iDp x h h f C= + −( ) − ( )� μ ,

where h hiD

i− � is the total number of CP’s that buy priority at ISP i, in thediscriminatory regime.

II(iii). Congestion

Due to capacity constraints, traffic from the content providers to the endusers might suffer from congestion. Congestion is measured by the waiting

18 See eq. (9) further below.19 Apart from the standard brand differentiation interpretation, horizontal product differ-

entiation may reflect the different types of services offered by the ISP’s. For example, one ISPmight target ‘techie’ consumers with high computer skills, and offer them flexibility in tuningtheir Internet connection (e.g., for setting the latency of their broadband connection), whilethe other ISP might target ‘non-techie’ users with low computer skills, and offer them abroadband service already embedded with the average desirable characteristics of a broad-band connection.



time for end users when they request content from CP’s. As it is standardin the literature, we adopt the M/M/1 queuing model to determine theaverage level of congestion as a function of network capacity and traffic.20

Under the net neutrality regime, the average level of congestion for ISP i is

(1) wh xi

N

iN

iN

iN

=−

1

μ λ.

Note that the level of congestion wiN decreases with the level of capacity

μiN , while it increases with the number of visits per user λ, the total number

of end users of the ISP xiN , and the total number of CP’s hi

N that connect

to ISP i. We refer to h xiN

iNλ as the total traffic of ISP i.

Under discrimination, each ISP sorts CP’s into two traffic lanes, thepriority lane and the non-priority lane. The congestion for the priority lane(P) operated by ISP i is given by

(2) wh h x

iP

iD

iD

i iD

=− −( )

1

μ λ� ,

whereas the congestion for the non-priority lane (NP) is given by

(3) wh x

wiNP i

D

iD

iD

iD i

P=−

μμ λ

.

Note that the average congestion under discrimination, wiD , satisfies

(4) w b w b wh xi

Di i

Pi i

NP

iD

iD

iD

= + −( ) =−

11

μ λ,

where b h hi i iD= −1 � is the share of CP’s that buy priority from ISP i. If

capacities and total traffic volumes are the same under net neutrality anddiscrimination, the average level of congestion is also the same under bothregimes (i.e., we have w wi

NiD= ), which is a well-known property of the

M/M/1 queuing model.

II(iv). 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 netneutrality, a user located at xj on the unit interval and who subscribes toISP A, obtains utility

20 On the M/M/1 model, see Choi and Kim [2010] and the references cited therein.



(5) U R vhd

wp txj A

N

AN A

Nj= + + − − ,

where R is a fixed utility obtained from Internet access, v represents theconsumers’ preference for product variety supplied by CP’s, d is a param-eter which measures the preference for the speed of the connection (as wA

N

is congestion in some time units, 1 wAN represents the speed of the Internet

connection), and finally, t is the standard Hotelling unit transportationcost.

Similarly, under discrimination, the end user located at xj obtains utility

(6) U R vhd

wp txj A

D

AD A

Dj= + + − − ,

if she subscribes to ISP A. Similar expressions are obtained if the end usersubscribes to ISP B. We assume that R is sufficiently high so that themarket is covered in equilibrium in both regimes.

To see how the connection of an extra CP affects the utility of the enduser (keeping the total number of end users at ISP i constant), replace wA

N

from (1) into (5) in the net neutrality regime, and wAD from (4) into (6) in the

discriminatory regime. In both regimes, the end user’s utility can then berewritten as

U R v d x h d p txj i A i A j= + −( ) + − −λ μ .

An extra CP has two effects on the end user’s utility: a variety effect and acongestion effect. The net effect is positive (i.e., consumers value the pres-ence of CP’s) if the term into brackets is positive, that is, v − dλxi > 0.Although it will not be invoked until we extend the model to account forpossible sabotage, we already assume that in the symmetric equilibrium endusers value content sufficiently compared to the disutility they suffer fromcongestion. Therefore, it must be that

(7) v d> λ 2.

In (5) and (6), consumer utility depends only on the average waitingtime. With this formulation, we take an ‘average’ approach, whichshould be viewed as an approximation. As the delay experienced byeach CP is the same within a given traffic lane, and consumers careonly about total available content and not about specific content oradvertising, consumer utility depends only on the average speed of theconnection and is independent of the congestion-sensitivity of eachspecific CP.21

21 See Choi et al. [2013] for an analysis of the differential effect of specific content onconsumer utility, within a simplified model with a monopolistic ISP and two types of CP’s.



III. NET NEUTRALITY

In the net neutrality regime, there is a unique lane for Internet transmis-sions and CP’s pay no fee to the ISP’s. We study the following two-stagegame:22

1. The two ISP’s choose their capacities, μAN and μB

N , and set thesubscription fees to the end users, pA

N and pBN .

2. The CP’s choose which ISP(s) to connect to (if any), and the end userschoose which ISP to subscribe to.

We proceed backwards to solve for the symmetric subgame perfectequilibrium.

III(i). Stage 2: Content Providers’ 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 congestionsensitivity h connects to ISP i if and only if 1 0−( ) ≥hwi

N , that is, if h hiN≤ ,

where

(8) hw

i A BiN

iN

= =1, , .for

Replacing for wiN , as given by (1), into (8) and solving for hi

N , we find thatthe type of the marginal CP is

(9) hxi

N iN

iN

=+μλ1

.

Given our model assumptions, the number of subscribers affects thenumber of CP’s only through the level of congestion. As a higher numberof subscribers implies more congestion on ISP i’s network, there is lessentry of CP’s on that ISP.23

Simultaneously, at Stage 2, each consumer chooses whether to subscribeto ISP A or ISP B. The indifferent consumer �xN is given by

22 For expositional simplicity, we adopt a timing where capacities and prices are set simul-taneously at the first stage of the game. We also solved for the three-stage sequential game,where ISP’s first decide on capacity prior to setting their prices, and found similar qualitativeresults. The proof is available online in the Supplementary material on the Journal of Indus-trial Economics website.

23 Using (9), we find that an extra end user increases CP h’s profit iff h h xiN

iN< +( )1 λ .

Since h x hiN

iN

iN1+( ) <λ , the most congestion sensitive CP’s would benefit from ISP i serving

less end users.



(10) R vhd

wp tx R vh

d

wp t xA

N

AN A

N NBN

BN B

N N+ + − − = + + − − −( )� �1 .

Replacing for hAN and hB

N into (10), we find that the indifferent consumeris defined implicitly from

(11) F x p p d vx x

NAN

BN

AN

BN B

N

NAN

N�

� �, , , ,μ μ

μλ

μλ

( ) ≡ +( )+ −( ) −

+

⎛

⎝⎜⎞

⎠⎟

−

1 1 1

tt x p pNBN

AN1 2 0−( ) − −( ) =� ,

and, therefore, we have � �x x p pN NAN

BN

AN

BN= ( ), , ,μ μ . The number of end

users of ISP A and ISP B are then x xAN N= � and x xB

N N= −1 � , respectively.

III(ii). Stage 1: ISPs’ Decisions

At the first stage of the game, the two ISP’s compete by choosing aninvestment in capacity, and by setting a subscription fee to theend users. The maximization problem of ISP i can be expressed asfollows

max ,,p

iN

iN

iN

iN

iN

iN

p x Cμ

μΠ = − ( )

where x x p piN

iN

AN

BN

AN

BN= ( ), , ,μ μ . The two first-order conditions are

(12)∂∂

= +∂∂

=Πi

N

iN i

NiN i

N

iNp

x px

p0,

and

(13) ∂∂

=∂∂

− ′( ) =Πi

N

iN i

N iN

iN i

Npx

Cμ μ

μ 0.

We obtain the following result.24

Proposition 1. Under net neutrality, in the symmetric equilibrium, thecapacity level, the subscription fee, the number of CP’s and the averagelevel of congestion are given by:

24 With some abuse of notation, in the symmetric equilibrium, we drop the subscriptsi = A, B for the two ISP’s. For example, we denote by μN the equilibrium level of investmentof each ISP. Furthermore, for expositional simplicity, we do not put asterisks to denote theequilibrium values.



μλ

λμλ

μλλ

N

NN

NN

N

Cd v

p td v

h

w

= ′( ) ++

⎛⎝⎜

⎞⎠⎟

= + +( )+( )

=+

= +

−1

2

2

4

2

22

,

,

,

22

2μN.

Proof. Since we do not have an explicit solution for market shares xiN , we

apply the Implicit Function Theorem to equation (11) in order to determinethe derivatives ∂ ∂x pi

NiN and ∂ ∂xi

NiNμ , which are then used in the FOC’s

of Stage 1. Define

KF

xt d v

x x

NN

BN

BN

AN

AN

≡ ∂∂

= + +( )+( )

++( )

⎛

⎝⎜⎜

⎞

⎠⎟⎟

>�

21 1

02 2

λμ

λ

μ

λ.

We obtain

∂∂

= −∂ ∂∂ ∂

= − <∂∂

= −∂ ∂∂ ∂

= +

x

p

F p

F x K

x F

F x

d v

AN

AN

AN

N NAN

AN

AN

N� �1

0 andμ

μ

110

+( ) >λx KA

N N.

Similarly,

∂∂

= >∂∂

= − ++( ) <

x

p K

x d v

x KAN

BN N

AN

BN

BN N

10

10and

μ λ.

By replacing for these derivatives in the first-order conditions (12) and (13),and by imposing symmetry, we obtain the symmetric equilibrium levels ofinvestment in capacity and the subscription fees, as reported in the Propo-sition. We assume that the investment cost function C(μ) is sufficientlyconvex so that the candidate equilibrium corresponds to a maximum of theprofit function. See Appendix A for the condition on C″(·).

In the symmetric equilibrium, the two ISP’s share the market equally(i.e., we have x xA

NBN= = 1 2). After replacing for the equilibrium values

into the profit functions of the ISP’s and of the CP’s, we obtain the equi-librium profits for each ISP and for each CP,



Π

Π

NN

N

hN N

N

t d vC

ah

h h

= + +( )+( )

− ( )

=− +( )⎛

⎝⎜⎞⎠⎟

≤

22

2

12

2

0

2

λμλ

μ

λ λμ

,

if

iif h h N>

⎧⎨⎪

⎩⎪.

The total profits of CP’s are equal to

ΣΠ ΠhN

hNh N

dhaN

= =+∫0 2

λμλ

.

Finally, we determine consumers’ surplus and total welfare in the netneutrality regime.25 The net utility of end user j located at xj ≤ 1/2 is

U Rd v

t xjN

N

j= + −( ) +( )+( )

− +( )2 2

21

2

μ λλ

.

By summing up the net surplus of all end users, we obtain the consumers’surplus,

CS U dx Rt d vN

jN

j

N

= = − + −( ) +( )+( )∫2

54

2 2

20

12

2

μ λλ

.

The total welfare WN is defined as the sum of ISPs’ profits, CPs’ profits andconsumers’ surplus. We find that

(14) W CS Rt a d v

CN NhN N

NN= + + = − + + +( )( )

+− ( )2

42

22Π ΣΠ λ μ

λμ .

III(iii). Equilibrium Properties

Under net neutrality, the equilibrium subscription fee is higher than the feethat would prevail in the standard Hotelling setting (i.e., p = t). This is dueto congestion and to the presence of network externalities in our setting. An

25 The analysis of consumer surplus in our set-up with competitive ISP’s is richer and morerelevant compared to the case of a monopolistic ISP, which can fully extract the surplusobtained by consumers from content consumption due to the lack of competition. If weignore the Hotelling part, consumer surplus would always be zero, with or without neutrality,under a monopolist ISP. This would not be true if either the market of consumers were notfully served, or if consumers were heterogenous with respect to the utility obtained fromcontent.



increase in ISP i’s subscription fee decreases directly its demand, but it alsoleads to a reduction in the congestion on its network, which increasesdemand. At the same time, less congestion leads to an increase of thenumber of CP’s at the ISP, which in turn affects positively the demand fromthe end users who benefit from more content. The total effect of a priceincrease on ISP i’s demand is negative, but it is less negative than in aone-sided market, which induces ISP’s to set a higher price than in astandard Hotelling model.

The equilibrium converges to a standard Hotelling game in the limitingcases where either there is no traffic (λ → 0), or investment in capacity goesto zero (μN → 0). In particular, when μN → 0, the equilibrium subscriptionfee and the ISPs’ equilibrium profits converge to those of the Hotellingmodel (i.e., pN → t and ΠN → t/2), whereas the equilibrium congestion goesto infinity (i.e., wN → ∞) and the number of CP’s goes to zero (i.e.,h N → 0). However, this degenerate case never arises in equilibrium as thecapacity is always positive (μN > 0), otherwise there would be no market forInternet access.

Finally, we provide some intuitive comparative statics. We find thatwhen the number of visits per user λ increases, the investments in capac-ity and the number of active CP’s decrease, whereas congestion increases.The effect of an increase in λ on the subscription fee and the ISP’sprofit is generally ambiguous and depends on the value of λ. Whenλ is low enough, congestion is not so important, and hence, an increasein λ increases the subscription fees and the ISPs’ profits becauseof the competition-dampening effect from the network externalitythat we described above. By contrast, when λ is high enough, congestionbecomes substantial: the prevailing effect comes from a reduction ofcontent, so that prices and ISPs’ profits decrease with further increasesin λ.

When the preference for speed d and/or the preference for productvariety v increase, ISP’s can extract more rents from consumers,which leads to higher subscription fees, and therefore higher invest-ments in capacity, higher entry by the CP’s, and lower congestion.The CPs’ profits and the total welfare increase too. Finally, the per-clickadvertising revenue a only enters the CPs’ profits, and hence, boththe CPs’ profits and the total welfare are positively affected by an increasein a.

IV. DISCRIMINATION

In the discriminatory regime, each ISP offers a priority lane and a non-priority lane to CP’s. The CP’s that opt for priority at ISP i pay a fixedfee fi, whereas the non-priority lane is offered for free. We modify ourtwo-stage game accordingly:



1. The two ISP’s choose their capacities, μAD and μB

D, set their subscriptionfees to the end users, pA

D and pBD, as well as the fees for their priority

lanes, fA and fB.2. The CP’s choose which ISP(s) to connect to (if any) and whether

to pay for priority, and the end users choose which ISP to subscribeto.

IV(i). Stage 2: Content Providers’ 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 topay for priority. The CP’s which are the most congestion-sensitive opt forthe priority lane. A CP of type h connects to the priority lane at ISP i ifh hi

D≤ , where hiD solves

(15) a x h w fiD

iD

iP

iλ 1 0−( ) − = .

Furthermore, the CP of type �hi which is indifferent between the prioritylane and the non-priority lane at ISP i is defined by

(16) a x h w f a x h wiD

i iP

i iD

i iNPλ λ1 1−( ) − = −( )� � .

From (15) and (16), the total number of CP’s that pay for priority at ISP iis max ,h hi

Di−{ }� 0 .

Equation (16) implies that

f a x h w wi iD

i iNP

iP= −( )λ � ,

and replacing for this expression into (15), we obtain

1 0− −( ) +( ) =h h w h wiD

i iP

i iNP� � .

By dividing the latter expression by hiD and using wi

D which is defined in(4), we find that the type of the marginal CP that enters at ISP i ish wi

DiD= 1 , which can be rearranged as

(17) hxi

D iD

iD

=+μλ1

.

The type of the marginal CP hiD is independent of the priority fee and takes

an expression similar to the total number of CP’s at ISP i in the netneutrality regime (which is given by (9)). Note that two conflicting effectsare at play here: a demand effect and a congestion effect. On the one hand,a higher number of subscribers increases CPs’ profits, and hence, entry



(demand effect). On the other hand, it increases congestion, which reducesentry (congestion effect). We find that the congestion effect alwaysdominates the demand effect, which is why the number of CP’s at ISP idecreases with the number of subscribers on this platform. In addition, wehave

(18) �hf

x x a x f

f

x a x fhi

iD

i

iD

iD

iD

i

i

iD

iD

iiD=

+( ) −( ) =−( )

μλ λ λ λ λ1

.

Simultaneously, at Stage 2, each consumer chooses whether to subscribeto ISP A or ISP B. The indifferent consumer �xD is given by

(19) R vhd

wp tx R vh

d

wp t xA

D

AD A

D DBD

BD B

D D+ + − − = + + − − −( )� �1 .

By replacing for hAD and hB

D into (19), the indifferent consumer satisfies

(20) d vx x

t x p pBD

DAD

DD

BD

AD+( )

+ −( ) −+

⎛

⎝⎜⎞

⎠⎟− −( ) − −( ) =

μλ

μλ1 1 1

1 2 0� �

� ,

and, therefore, we have � �x x p pD DAD

BD

AD

BD= ( ), , ,μ μ . The number of users of

ISP A and ISP B are then x xAD D= � and x xB

D D= −1 � . Note that equation(20) for the discriminatory regime is similar to equation (11) for the netneutrality regime, and that �xD is independent of the priority fees.

IV(ii). Stage 1: ISPs’ Decisions

At the first stage, the two ISP’s choose simultaneously their capacities,subscription fees and priority fees. The maximization problem of ISP i canbe expressed as follows

max ,, ,p f

iD

iD

iD

iD

i i iD

iD

iD

i

p x h h f Cμ

μΠ = + −( ) − ( )�

where x x p piD

iD

AD

BD

AD

BD= ( ), , ,μ μ . The corresponding first-order conditions

are

(21)∂∂

= + +∂ −( )( )

∂

⎛

⎝⎜

⎞

⎠⎟

∂∂

=Πi

D

iD i

DiD i

Di i

iD

iD

iDp

x ph h f

x

x

p

�0,

(22)∂∂

= +∂ −( )( )

∂

⎛

⎝⎜

⎞

⎠⎟

∂∂

− ′ ( ) +∂Πi

D

iD i

D iD

i i

iD

iD

iD i

D iD

ph h f

x

xC

h

μ μμ

� −−( )( )∂

=�h fi i

iDμ

0,



(23)∂∂

=∂ −( )( )

∂=

ΠiD

i

iD

i i

if

h h f

f

�0.

We obtain the following result.

Proposition 2. Under discrimination, in the symmetric equilibrium, thecapacity level, the priority fee, the subscription fee, the number of CP’s andthe levels of congestion are given by:

μλ

λλ

λλ

D Cd v a

fa

= ′( ) ++

++ −( )+( )

⎛

⎝⎜⎜

⎞

⎠⎟⎟

= −+

⎛⎝⎜

⎞⎠⎟

−1

2

2

2 2 2

2 2

21

2

2

,

,,

,

,

p td v a

h h

DD D

DD

= + +( )+( )

−+ −( )

+( )

=+

=

4

2

2 2 2 2

2

22

2

2 2

λμλ

λ μ λ

λ

μλ

λ� ++ −⎛⎝⎜

⎞⎠⎟

= + = +( ) = +

2 2

2 2

2

2 2

4

2

2

32

λ

λμ

λμ

λμ

h

w w w

D

PD

NPD

DD

,

, , .

Proof. We proceed as in the net neutrality regime, by applying theImplicit Function Theorem to (20) in order to determine the derivatives∂ ∂x pi

DiD and ∂ ∂xi

DiDμ . We find that

∂∂

= − <∂∂

= >∂∂

= ++( ) >

∂

x

p K

x

p K

x d v

x K

x

AD

AD D

AD

BD D

AD

AD

AD D

10

10

10, , ,

μ λ

AAD

BD

AD D

AD

A

AD

B

D

d v

x K

x

f

x

fK d v

∂= − +

+ −( )( ) <

∂∂

=∂∂

= ≡ +

μ λ1 10

0

,

, where (( )+ −( )( )

++( )

⎛

⎝⎜⎜

⎞

⎠⎟⎟

+ >λμ

λ

λμ

λBD

AD

AD

ADx x

t1 1 1

2 02 2

.

By replacing for these derivatives in the three first-order conditions, and byimposing symmetry, we obtain the symmetric equilibrium levels of invest-ment in capacity, the subscription fees and the priority fees, as reported inthe Proposition. Provided that the investment cost function is sufficientlyconvex, the candidate equilibrium corresponds to a maximum of the profitfunction. See Appendix A for details.



In the symmetric equilibrium, the market is equally shared between thetwo ISP’s (i.e., we have x xA

DBD= = 1 2). The equilibrium profits for an ISP

and a CP are

ΠDD

D

D

t d v

aC

= + +( )+( )

++ − +( ) − + −( )( )

+( )−

22

2

2 2 2 2 2 2

2

2

2

2

λμλ

μ λ λ λ λ

λμ(( ),

and

Π

Π

ΠhD

hNP

D

hP

D

a h h h

ah

=

= − +( )⎛

⎝⎜⎜

⎞

⎠⎟⎟

≤

=+

− +

λ λμ

λλ

λμ

12 2

4

2

21

2

2

32

if �

⎛⎛⎝⎜

⎞⎠⎟

< <

≥

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪

if

if

�h h h

h h

D

D0

,

respectively. The total profits of the CP’s are

ΣΠ Π ΠhD

hNPh

hP

h

hD

dh dhaD

D

D

= + =+ −( )

+∫ ∫0

2 2 2 2

2

�

�

μ λλ

.

Finally, the utility of end user j located at xj ≤ 1/2 is

U Rd v a

t xjD

D

j= ++( ) −( ) + + −( )( )

+( )− +( )

2 2 2 2 2

21

2

μ λ λ λ

λ,

which is used to determine consumers’ surplus and total welfare,

CS U dx Rt d v a

DjD

j

D

= = − ++( ) −( ) + + −( )( )

+( )∫254

2 2 2 2 2

20

12

2

μ λ λ λ

λ,

and

(24) W CS

Rt d v a

C

D DhD D

DD

= + +

= − ++( ) + + − +( )( )

+− ( )

2

4

2 2 2 2

22

Π ΣΠ

λ λ μλ

μ .



IV(iii). Equilibrium Properties

The comparison between the equilibrium subscription fee under discrimi-nation and the fee in the standard Hotelling model (i.e., t) depends onthe values of the parameters. When a is low enough (i.e., lower than2 2 2 2d v+( ) + −( )λ ), the equilibrium fee for end users in the discrimi-natory regime is higher than the Hotelling equilibrium price (i.e., p ti

D > ).The intuition is as follows. To begin with, if there were no fee for thepriority lane, we already know from the analysis under net neutrality thatan increase in the subscription fee pi

D of ISP i would decrease its owndemand, but this effect is less severe than in the Hotelling model. Besides,under discrimination, there is an additional effect: revenues from the pri-ority lane are partly passed on to end users, which tend to push the pricedown. Since more revenues are made from priority fees when CP’s earnhigh advertising revenues, that is, when a is high enough, the second effectcan prevail over the former.

Finally, we present some comparative statics. We find that when thenumber of visits per user λ increases, the priority fee increases, since thepriority lane is valued more as more advertising revenues are made.However, the effect of an increase in λ on all the other equilibrium valuesis ambiguous and depends on the effect of λ on investment in capacity (i.e.,on ∂ ∂μ λi

D ). This latter effect is not always negative, as it is the case undernet neutrality, since in the discriminatory regime, the ISP’s may now havean incentive to increase their capacity when λ becomes higher to obtainhigher revenues from the CP’s that are willing to pay for priority.

An increase in the preference for speed d and an increase in the pref-erence for variety v both affect positively investment in capacity, the totalnumber of CP’s, CPs’ profits and total welfare. Moreover, congestiondecreases with d and v. In contrast to the net neutrality regime, anincrease in the per-click advertising revenue a affects positively capacityinvestment, the number of CP’s and the pricing decisions of the firms.This is because, under discrimination, ISP’s can extract part of the CPs’profits through the priority fees. When a increases, the ISP’s chargehigher priority fees and increase their investment in broadband capacity.Congestion is reduced and entry of CP’s is fostered. Therefore, totalwelfare increases with a.

The comparison between the net neutrality regime and the discrimina-tory regime is examined in more detail in the next section.

V. NET NEUTRALITY VS. DISCRIMINATION

We now turn to the main question of this paper. We compare the twoalternative regimes, net neutrality and discrimination, to investigate theeconomic effects of a departure from net neutrality. First, we comparecapacity investments and innovation in services in the two regimes. Second,



we compare congestion, subscription fees and profits. Finally, we compareend users’ utility and total welfare.

V(i). Effect on Investment and Innovation

In this subsection, we compare the investment in capacity and the numberof CP’s that enter the market, that is, innovation in Internet services, underthe net neutrality and the discriminatory regimes. Using Proposition 1 andProposition 2, we have the following result.

Proposition 3. Investment in broadband capacity and innovation in ser-vices are higher under the discriminatory regime than under the net neu-trality regime, that is, μD > μN and h hD N> .

Proof. Since C″ > 0, (C′)−1 is an increasing function, and therefore, fromPropositions 1 and 2, we have μD > μN, as λ λ+ ≥ +4 2 2 2 for all λ ≥ 0.

This, in turn, implies that h hD N> .

An increase in ISP i’s capacity increases its demand and its investmentcost under both regimes, but in the discriminatory regime it also affectspositively the revenues that ISP i can extract from the CP’s that opt forpriority. Therefore, under discrimination, ISP’s have larger investmentincentives.

Under net neutrality, ISP i’s incentive to invest in capacity is given by thechange in its profits due to a marginal increase of the capacity level, that is,

(25)∂∂

=∂∂

− ′( )ΠiN

iN i

N iN

iN i

Npx

Cμ μ

μ ,

where ∂ ∂ >xiN

iNμ 0 and C′ > 0. In the discriminatory regime, we have

(26)∂∂

=∂∂

− ′( ) +∂ −( )

∂+

∂ −( )∂

ΠiD

iD i

D iD

iD i

D iD

i

iD

iD

i

iD

px

Ch h h h

xμ μμ

μ

� � ∂∂∂

⎛

⎝⎜

⎞

⎠⎟

xfi

D

iD iμ

,

where ∂ ∂ >xiD

iDμ 0. For given levels of subscription fees and

capacities, the terms p x CiN

iN

iN

iN∂ ∂( ) − ′ ( )μ μ are equal to the terms

p x CiD

iD

iD

iD∂ ∂( ) − ′ ( )μ μ . We further obtain that ∂ −( ) ∂ >h hi

Di i

D� μ 0,

∂ ∂ <h xiD

iD 0 and ∂ ∂ <�h xi i

D 0, but the sign of ∂ −( ) ∂h h xiD

i iD� is ambigu-

ous. Nevertheless, we have proved that the parenthesis in (26) is positive,which implies that the marginal revenue of an increase in the capacity levelis higher under the discriminatory regime.26

26 One alternative view of net neutrality would be to state that ISP’s cannot prioritize trafficor differentiate the quality of service to CP’s, while being able to charge CP’s to terminate



Since the ISP’s invest more in capacity under discrimination, the totalnumber of CP’s that are active under discrimination is also higher thanunder net neutrality. Innovation in services is increased when there is a fastlane, as congestion-sensitive CP’s that could not enter under net neutralitynow enter by buying access to the priority lane.

Note that as the total number of CP’s under discrimination is alwayshigher than the total number of CP’s under net neutrality, h D is located toright of h N . It is also interesting to compare the number of CP’s that enterthe market under net neutrality, h N , to the CP of type �h that is indifferentbetween buying priority and using the non-priority lane in the discrimina-tory regime (see Figure 1). We obtain that �h h N> if and only if

(27) μμ

λλ

D

N>

+ −2 2 2.

where μN and μD are the equilibrium capacity levels defined in Proposi-tion 1 and 2, respectively. Since μD increases in a while μN is independentof it, for a general functional form C(·) satisfying our assumptions, theratio μD/μN increases with a. Therefore, a sufficient condition for condi-tion (27) to hold is that the per-click advertising revenue is high enough.In this case, innovation in services under discrimination is so importantthat all CP’s that buy priority were not active under net neutrality.A simple revealed preference argument implies then that all CP’s arebetter-off in the discriminatory regime, independently from the lane theyend up choosing.

When the investment cost is quadratic, that is, C(μ) = μ2/2, condition (27)simplifies to

ad v+

> +

+ −( )2 2

2 2 22

λ

λ.

their traffic. We solved our model in this alternative scenario, where there is a single lane (asin our net neutrality regime), but ISP’s can charge (uniform) positive termination fees to CP’s.We found that capacity investments under this alternative regime are always (weakly) higherthan under our net neutrality regime. Therefore, if one compares our net neutrality regime (azero price to everybody) with this alternative regime with the same uniform price charged toeverybody, our main results still go through. Having an extra ‘instrument’ (a positive termi-nation price) is used by the ISP’s to invest more in capacity. However, if the comparison isdone between our discriminatory regime and the alternative uniform regime, capacity invest-ments under the alternative regime can be either lower or higher. This is because the com-parison is between a scenario with a uniform price to all CP’s and a single lane (under thealternative net neutrality regime) and one with a free slow lane and a paid-for fast lane (underthe discriminatory regime). In both cases, ISP’s have only one price they can charge, thoughunder discrimination the ISP’s can offer two different lanes. The computations for thealternative uniform regime are available online in the Supplementary material on the Journalof Industrial Economics website.



Since the right-hand side decreases with λ, we have �h h N> if a/(d + v)and/or λ are sufficiently high.

V(ii). Effect on Network Congestion

Discrimination increases capacity compared to net neutrality, but also totaltraffic grows as more CP’s enter the market. In principle, therefore, theeffect on average congestion could be ambiguous. However, as the equilib-rium number of CP’s under both regimes is h = +( )2 2μ λ , from the defi-nition of average congestion it then follows that 1 2 2 2w h= − = +( )μ λ μ λSince μD > μN, it is clear that the capacity expansion effect underdiscrimination prevails. We can thus state immediately the followingProposition.

Proposition 4. The average level of congestion is lower under discrimina-tion than under net neutrality, that is, wD < wN.

Even if the congestion on the non-priority lane is higher than the con-gestion in the net neutrality regime, the decrease of congestion on thepriority lane is high enough to overcome the increase of congestion on thenon-priority lane. In other words, the ISP’s manage Internet traffic moreefficiently when they can offer multiple lanes, and the more congestion-sensitive CP’s can opt and pay for priority.

Since from the properties of the M/M/1 queuing system, we havewP < wD < wNP, it follows immediately that the level of congestion under netneutrality, wN, is always higher than the level of congestion on the prioritylane, wP. After comparing the equilibrium level of congestion on the non-priority lane, wNP, to wN, we find that for sufficiently high values of the ratioμD/μN (i.e., higher than λ +( )2 2 ), congestion on the non-priority lane is

also lower. Note that λ λ λ+( ) < + −( )2 2 2 2 2 , hence (27) is sufficient

for this to be true.27 Sufficient conditions are then again that a is sufficientlyhigh in the general case, and that a/(d + v) and/or λ are relatively high witha quadratic cost function.

V(iii). Effect on Subscription Fees and Profits

We now compare the equilibrium subscription fees in the two regimes.Under net neutrality, the ISP’s obtain profits only from the end users,whereas under discrimination, the ISP’s can extract additional revenues bycharging for access to the priority lane. As we have already discussed, thepricing incentives between the two regimes differ, as

27 In other words, �h h N> implies that wNP < wN.



∂∂

= +∂∂

ΠiN

iN i

NiN i

N

iNp

x px

p,

whereas,

∂∂

= +∂∂

+∂ −( )

∂∂∂

ΠiD

iD i

DiD i

D

iD

iD

i

iD

iD

iD i

px p

x

p

h h

x

x

pf

�.

An increase in the subscription fee by ISP i, decreases the demandthat it obtains in both regimes, but it also affects indirectly the totalnumber of CP’s that opt for priority in the discriminatory regime (via theterm ∂ −( ) ∂ × ∂ ∂h h x x pi

Di i

DiD

iD� ). Whenever this latter effect is positive,

the incentives of the ISP’s to increase the subscription fees underdiscrimination are higher compared to the net neutrality regime. In thiscase, competition in subscription fees between the ISP’s is relaxed andthe end users pay higher prices under discrimination than under netneutrality.

Formally, we find that pD > pN if and only if

(28) d va D N

+ −⎛⎝⎜

⎞⎠⎟

> + −1

1 2 2 22μ μ

λ.

If this condition holds, subscription fees are higher under discriminationthan under net neutrality. The capacity expansion due to the introductionof multiple lanes is relatively high, which leads to a high number of activeCP’s and thus increases end users’ utility. The ISP’s extract this increasedutility via higher subscription fees. When a goes to zero, the first term in theLHS of (28) goes to infinity, while the second term goes to zero as the ratioμD/μN goes to 1. However, computing the Taylor series of the LHS at a = 0,we find that (28) holds at a = 0 if

d v

CN N

+′′ ( ) >

+( ) + +( )μ μ

λ λλ

2 2 2 2

2.

If this condition holds, then (28) is satisfied, in the general case, when a islow enough.

Under the quadratic investment cost function example, condition (28)simplifies to

ad v+

<+ −( ) −

+ −( )2 2 2 2 2

2 2 22

λ

λ.



This latter condition holds if end users value highly the variety and thespeed of the network (i.e., d + v is high), if the per-click advertisingrevenue a is low enough,28 and/or the number of visits per user λ is highenough.29

Now, we turn to the profits of the ISP’s and of the CP’s. The comparisonof the ISPs’ profits between the two regimes yields that ΠD > ΠN if and onlyif

2 0p p C C h h fD N D NiD

i i−( ) − ( ) − ( )( ) + −( ) >μ μ � .

ISP i obtains additional revenues under discrimination through the priorityfees, but the comparison depends also on the difference in the subscriptionfees and on the difference in the costs of capacity. When competition isrelaxed under discrimination, the term (pD − pN)/2 is positive, and hence,profits tend to be higher under discrimination. Moreover, the difference inthe investment costs is always positive (since μD > μN and C′ > 0), whichtends to decrease the profits under discrimination compared to the netneutrality regime. The final comparison depends on the levels of capacityand on the parameter values.30 We can conclude that

Proposition 5. A departure from the net neutrality regime is not alwaysbeneficial for the ISP’s.

In the case of a monopolistic ISP, a departure from the net neutralityregime is always profitable, since it can extract part of the CPs’ profitsthrough the priority fee and still serve the whole mass of end users.However, when there is competition at the ISP level, it is ambiguouswhether discrimination will improve or deteriorate the ISPs’ profits. Com-petition for the end users under discrimination might be more severe as thedemand of each ISP affects indirectly the profits obtained through thepriority lane.

Concerning the CP’s, we compare their total profits under the tworegimes. We find that ΣΠ ΣΠh

DhN> if and only if

(29)μμ

λλ

D

N>

+ −( )2 2 2 2.

28 When a increases, it is more likely that the ISP’s are willing to reduce their prices underdiscrimination to obtain a higher demand (the countervailing effect via the increase incongestion is less severe).

29 The expression 2 2 2 2 2 2 2 22

λ λ+ −( ) −( ) + −( ) is negative for λ < 2.5, hence in

this range we always have pD < pN. For higher values of λ, the expression is non-monotonic:it first increases, reaches a maximum of 1/2 at λ = 6, and then decreases with λ.

30 We discuss the quadratic case below in Figure 2.



For high values of the ratio μD/μN, the total profits of the CP’s underdiscrimination are higher, and hence, on average CP’s are better off. Notethat this condition is less stringent than (27) that described insteada Pareto improvement for CP’s.31 In the quadratic investment costexample, we have ΣΠ ΣΠh

DhN> if the ratio a/(d + v) and/or λ are suffi-

ciently high.Since CP’s in the non-priority lane only care about their congestion, wNP,

we obtain from wNP < wN that they all obtain higher profits compared to thenet neutrality regime for high values of μD/μN.32 On the other hand, theCP’s in the priority lane benefit from the reduction in the congestioncompared to the net neutral regime (wP < wN), but pay priority fees. Sincethis fee is fixed and each CP in the priority lane faces the same level ofcongestion, we conclude that the highly congestion-sensitive CP’s benefitmore from priority compared to the less congestion-sensitive CP’s. Still, theCP’s in the priority lane earn higher profits compared to the net neutralregime for high values of the ratio μD/μN, but this threshold is lower for themore congestion-sensitive CP’s.

V(iv). Effect on End Users’ Utility and Total Welfare

Now, we proceed with the comparison of the end users’ utility and the totalwelfare in the discriminatory and net neutrality regimes. For the consum-ers’ surplus, we have CSD > CSN if

(30)a

d v

D N

D N+ ( ) −> −

+ −( )μ μ

μ μλ

λ λ1

2

2 2 2.

On the one hand, discrimination affects positively the end users’ utility, sinceit increases innovation in services and reduces the average level of congestionin the network. On the other hand, discrimination may increase the subscrip-tion fees that the end users have to pay for Internet access. For sure, (30) issatisfied in the general case when a is high enough, as the first term on theLHS increases linearly with a, while the second term decreases with a but isbounded by 1 from below. It is also always true for low enough values of λ.We also note from (28) that when pD < pN, then CSD > CSN always holds.33

31 The right-hand side of (29) is just half the right-hand side of (27).32 The condition for Π Πh

NPhN> > 0 is again μ μ λD N > +( )2 2 .

33 From (28) we obtain that pD < pN if and only ifa

d v

D N

D N+ ( ) −>

μ μμ μ 1

+ −>

−+ −( )λ

λλ λ

2

2 2 2

2

2 2 2.



Therefore, when discrimination leads to more competitive pressure at theISP level with respect to the subscription fees, the end users are better off andthe ISP’s tend to be worse off. When μD/μN increases, it is less likely that theend users will pay lower subscription fees under discrimination, but it is morelikely that the profits of the ISP’s will be higher.34

In the quadratic investment cost example, condition (30) becomes

ad v+

>−( ) + −( ) −

+ −( )λ λ λ

λ λ

2 2 2 2 2

2 2 22

.

Since the right-hand side decreases down to zero when λ gets large, thiscondition holds if a/(d + v) and/or λ are sufficiently high.35

We finally turn to the question of which regime is to be preferredaccording to a welfare criterion.

Proposition 6. Total welfare under discrimination is higher than totalwelfare under net neutrality, that is, WD > WN.

Proof. Let

Δ μλ λ μ

λλ μ

λμ μ

( ) =+ − +( ) + +( )

+

− + +( )( )+

− ( ) − ( )( )

2 2 2 2

2

22

2

a d v

a d vC C

NN ..

The difference between the total welfare under discrimination andunder net neutrality is WD − WN = Δ(μD). We show that Δ(μD) > 0. Tosee that, first note that Δ(μN) > 0 as 2 2 2 2a d vλ λ+ − +( ) + +( ) >

2 0a d vλ + +( )( ) > . Second, we have μD > μN, and Δ′(μ) > 0 forμ ∈ [μN, μD] since the level of capacity that maximizes Δ(μ) is higher thanthe equilibrium level of capacity μD and Δ(·) is concave. Therefore,Δ(μD) > Δ(μN) > 0.

Total welfare is the sum of firms’ profits and end users’ utility. While theimpact of discrimination on each agent is generally ambiguous, the overalleffect on the aggregate economy is always positive: prioritization leads tomore efficient allocations.

34 Such an analysis is irrelevant in the monopolistic ISP set-up, since the monopolistic ISPcharges the monopoly price in both regimes to extract the entire consumers’ surplus (exceptfor the Hotelling part). Thus, consumers are indifferent between the two regimes undermonopoly.

35 The condition additionally holds if the right-hand side is negative, which happens forλ < + ≈5 13 8 61. .



Figure 2 shows the comparison between the ISPs’ profits, the CPs’profits, the total industry profits and the end users’ utility in the discrimi-natory and the net neutrality regimes, when the investment cost functiontakes the quadratic form C(μ) = μ2/2. The horizontal axis represents thenumber of visits per user λ, while the vertical axis represents the ratioa/(d + v). The lines represent the locus of points where there is no differencebetween the regimes. The arrows indicate in which direction, in the(λ, a/(d + v)) space, the profits or the end users’ utility are higher underdiscrimination than under net neutrality.

Three cases emerge. First, when there is a switch from net neutrality tothe discriminatory regime, the market profits may increase more than thereduction in the end users’ utility. This arises in the bottom-right part of theFigure (e.g., point A). Second, the end users’ utility may increase more thanthe reduction in the market profits. This arises in the left part of the Figure(e.g., point B). Third, both market profits and the end users’ utility mayincrease under discrimination. This is the case in the central, and in thetop-right part of the Figure (e.g., point C).

V(v). Incentives to Switch to the Discriminatory Regime

So far, we have considered that the traffic regime (either net neutrality ordiscrimination) was given exogenously, and hence, a departure from netneutrality meant that both ISP’s adopted the discriminatory regime. Aninteresting question is however whether the ISP’s would endogenouslydecide to remain under net neutrality, or rather to implement the

Figure 2Discrimination vs. Neutrality when C(μ) = μ2/2



discriminatory regime. To analyze this question, we study an ISP’s unilat-eral incentives to depart from the net neutrality regime, at the first stage ofthe game. We obtain the following result:

Lemma 1. Each ISP has a unilateral incentive to adopt the discriminatoryregime.

Proof. Whenever the priority fees are equal to zero, the discriminatoryregime coincides with the net neutrality regime, since all CP’s connect to thepriority lane. Therefore, ISP i has a unilateral incentive to discriminate if itsprofit increases with the priority fee at fi = 0. By replacing (17) and (18) intoΠi

D , we find that, irrespective of fj,

∂∂

=−( ) − −( ) −( )

=

ΠiD

i f

iD

iD

iD

i i iD

i iD

i

iDf

x a x f f a x f a x f

xi 0

2

1

μ λ λ λ λ

λ ++( ) −( )

=+

>

=λ λ

μλ

x a x f

x

iD

iD

if

iD

iD

i

2

0

10.

This Lemma shows that each ISP has an incentive to switch from the netneutrality to the discriminatory regime, unilaterally and independently ofthe rival ISP, in an effort to extract part of CPs’ profits, and whatever therival does. With Proposition 5, we have shown that ISPs’ profits underdiscrimination can be lower than their profits under net neutrality, as aresult of more intense competition. We therefore obtain the followingresult.

Proposition 7. ISP’s can be trapped in a prisoner’s dilemma, with respectto the choice of the traffic regime.

In such a case, both ISP’s would prefer to remain under net neutrality toachieve higher profits,36 but each of them has a unilateral incentive toswitch to the discriminatory regime.37 In Figure 2, the prisoner’s dilemmaarises, for example, at point B.

All in all, in this section we have shown that a departure from the netneutrality regime increases total welfare in the market for Internet access.However, as we argue in the next section, policy-makers should be aware of

36 As a consequence, ISP’s would have an incentive to lobby jointly for net neutrality.However, since each ISP has a unitaleral incentive to adopt the discriminatory regime, eachISP would also have an incentive to deviate from the lobbying agreement, making such jointlobbying difficult to implement.

37 Note that this prisoner’s dilemma appears only in a setting with ISP competition. Witha monopoly at the ISP level, there is no strategic interaction, and the monopolistic ISP prefers(at least weakly) the discriminatory regime that always increases its profit compared to the netneutrality regime.



other practices that ISP’s could adopt in order to manipulate the traffic intheir networks and increase their profits, for example, sabotage.

VI. SABOTAGE

Up to now, we have examined the effect of a departure from the netneutrality regime by introducing a discriminatory regime where both ISP’soffer a paid-for priority lane and a free (best-effort) non-priority lane. Thedebates around net neutrality however also stress that ISP’s could betempted to adopt strategies to manipulate the traffic in their networks. Onesuch practice could be to degrade the quality of the CP’s that do not pay forpriority. As shown by Deneckere and McAfee [1996], damaging some oftheir goods may help firms to price discriminate. In our setting, such astrategy could work especially in the discriminatory regime to make thepriority lane more valuable relative to the best-effort lane. By doing so,ISP’s may appropriate a higher share of the CPs’ surplus via the priorityfee.

In this section, we study the case in which the ISP’s can endogenouslydecide on a level of sabotage, which reduces the click-through rate of theCP’s and thus their revenues. In what follows, we begin by studying theincentives of the ISP’s to undertake sabotage in the net neutrality regime,and then we analyze the incentives for sabotage in the discriminatoryregime.

VI(i). Sabotage in the Net Neutrality Regime

We extend the baseline analysis of the net neutrality regime, and supposenow that ISP’s may sabotage CP’s at no cost. The profit of CP h thenbecomes

ΠhN

AN

AN

AN

BN

BN

BN

a x s hw

a x s hw=

− +( )( )+ − +( )( )λ

λ1 1

1 1it connects too both ISP’s

if it connects only to ISPa x s hwiN

iN

iNλ 1 1− +( )( ) ii

0 otherwise,

⎧

⎨

⎪⎪

⎩

⎪⎪

where siN ≥ 0 is the level of sabotage imposed by ISP i in the net neutrality

regime, with i = A, B. The expression of the CP’s profit is the same as in ourbaseline model of Section II, except that the CP’s congestion sensitivity isincreased by the level of sabotage.

The timing of the game is modified as follows. At the first stage, ISP’sdecide on capacity levels, subscription fees, and sabotage levels simultane-ously and non-cooperatively. At the second stage of the game, CP’s decidewhich ISP(s) to connect to and end users choose an ISP.



The analysis is similar to the analysis of the baseline model in Section II.We obtain the following result.

Proposition 8. In the net neutrality regime, ISP’s never sabotage the CPs’,that is, si

N = 0, for i = A, B.

Proof. Solving backwards for the symmetric equilibrium, and followingthe same procedure as in the baseline model, we find that the profit func-tions of the ISP’s are decreasing with respect to the level of sabotage, thatis,

∂∂

= ∂∂

= − −( )+ +( ) + + +( )

<Πi

N

iN

i

iNs

px

s

v d p

t s d v ds

2

2 2 40

2

λ μλ λμ

,

where p p pAN

BN= = , μ μ μA

NBN= = and s s sA

NBN= = . Note that we invoke

(7) here, so that (2v −dλ) > 0. Therefore, in equilibrium, ISP’s set a zerolevel of sabotage.

Even if we allow the level of sabotage to be endogenous, the ISP’sdo not have any incentive to sabotage the CP’s in the net neutralityregime. Indeed, there is a unique lane to transfer the data. Anypositive level of sabotage would just reduce the revenues of the CP’s, andsubsequently the total number of active CP’s. ISP’s would then have tolower the subscription fees to the end users, since innovation in serviceswould be lower, which would result in lower profits for the ISP’s.Therefore, sabotage in the net neutrality regime is not an equilibriumoutcome.

VI(ii). Sabotage in the Discriminatory Regime

It is interesting to study the incentives of the ISP’s to sabotage the differentlanes in the discriminatory regime. We allow the model to be flexible, andassume that there could in principle be two different sabotage rates that theISP’s can set at no cost, one for the priority lane, denoted by si

P ≥ 0, andone for the non-priority lane, denoted by si

NP ≥ 0, with i = A, B.38 Sabotagelevels are chosen at the first period of the game, at the same time as capacitylevels and subscription fees. The analysis is then similar to the analysis ofthe baseline model in Section III, except that the profits of the CP’s are nowgiven by

38 Since ISP’s can damage their fast and slow lanes independently, it may happen that anISP damages one lane, but not the other. For this reason, the sabotage decision hereis not equivalent to the choice of a lower capacity, which would degrade both lanes in a similarway.



ΠhD

AD

AP

AP

A BD

BP

BP

B

a x s hw

f a x s hw f

=

− +( )( )− + − +( )( ) −λ

λ1 1

1 1priorityy at both ISP’s

a x s hw

f a x s hwiD

iP

iP

i jD

jNP

j

λλ

1 1

1 1

− +( )( )− + − +( ) NNP

AD

ANP

ANP

BD

i

a x s hw

a x

( )− +( )( )

+ − +

priority only at ISP

λλ

1 1

1 1 ss hw

a x s hw

BNP

BNP

iD

iP

( )( )− +( )

if non-priority at both ISP’s

λ 1 1 iiP

i

iD

iNP

iNP

f i j

a x s hw

( ) −

− +( )( )priority at no access at

no

,

λ 1 1nn-priority at

no access at

otherwise

ij

,

.0

⎧

⎨

⎪⎪⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪⎪⎪

We examine the local incentives of the ISP’s to implement sabotage. Inother words, we evaluate the ISPs’ incentives to decide on some positivelevel of sabotage in the symmetric case, starting from a baseline case withno sabotage. We find the following result.39

Proposition 9. Under discrimination, ISP’s have no incentive to sabotagetheir priority lanes, that is, si

P = 0. By contrast, ISP’s may have incentivesto sabotage the non-priority lane if the advertising rate issufficiently high.

Proof. By solving backwards and by the first-order conditions ofthe ISPs’ profits with respect to the sabotage rate in the priority andnon-priority lanes, evaluated at zero, under symmetry, we have

∂∂

= − −( )

+( )<

= =

ΠiD

iP

s ss

N v d

iP

iNP 0

52

2

20

μ λ

λ λ,

where

N

a

= +( ) − +( )+ + −( ) + + +( ) − +( )( ) >

2 2 2 2

2 2 2 2 2 4 2 2 2 02

λ λ

λ λ λ λ λ ,

and

∂∂

=+( ) − +( ) − + −( ) −( )( )

+(= =

ΠiD

iNP

s ss

a v d

iP

iNP 0

2 2 4 8 2 2 2 2

2

μ λ λ λ λ

λ λ ))32

,

39 Note that all our results are robust to the introduction of some ‘sabotage cost function’,as long as the marginal cost of sabotage at a zero level of sabotage is zero.



where μ μ μAD

BD= = , with

∂∂

>= =

ΠiD

iNP

s ssiP

iNP 0

0 if a v d> −( )2 λ

+ −( ) >2 2 2 2 0λ , implying siNP > 0. Note that we also invoke (7) here,

so that (2v − dλ) > 0.

This Proposition shows that a zero sabotage rate is still a candidateequilibrium for the priority lane, since the ISPs’ profits, at that point, aredecreasing with respect to the level of sabotage. However, for some param-eter values, ISP’s have now an incentive to sabotage the non-priority lane.Note that we only study the local incentives of the ISP’s to sabotage,without fully characterizing the equilibrium sabotage rates, as we just wantto highlight a possibility result.40

It is not profitable for the ISP’s to degrade the quality of the prioritylane, since this would reduce its attractiveness and lower the profitsobtained by the ISP’s through the priority fees. By contrast, we haveestablished that sabotage can emerge endogenously for the best-effortnon-priority lane. In particular, for sufficiently high values of theadvertising revenue a or sufficiently low values of the preference ofthe end users for innovation v, the ISP’s find it profitable to sabotage thenon-priority lane. Degrading the quality of the non-priority lane makesthe priority lane more attractive, and hence, the ISP’s can extract higherprofits from CP’s.41 The total number of CP’s decreases with sabotage atthe non-priority lane, but the total number of CP’s that opt for priorityincreases. Since innovation in services is reduced, the ISP’s have tocharge less for access to the end users. But when the preference for inno-vation v is low relative to the advertising revenue a, the revenue loss onthe end users’ side is more than compensated by the gains on the CPs’side.

It is important to examine now the effect of sabotage on welfare. Let usconsider a symmetric equilibrium where the ISP’s impose small but positivesabotage rates on the non-priority lane, that is, s s sA

NPBNP

iNP= = > 0.

Consequently, total welfare is a function of these rates, W s sDANP

BNP,( ). By

calculating the local effect of an increase of the sabotage rate on thenon-priority lane on total welfare, we obtain

40 Also, sabotage arises because there is still a ‘missing’ (zero) price for thenon-priority lane. If the ISP could charge for it, a price instrument will always do better thana non-price instrument such as sabotage. Nevertheless, the zero price for best-efforttraffic is a requirement of every legislation we are aware of, thus making sabotage a realpossibility.

41 Our finding is somewhat reminiscent of the result obtained by Choi and Kim [2010] thatan ISP might have incentives to limit capacity expansion because expanding capacity makespaying for priority less desirable.



∂∂

= −

+( ) +( ) − +( )⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

+ + −

= =

W

s

a

D

iNP

s siP

iNP 0

322 4 2 2 2 2

2 2

μ λ λ λ

λ λλ λ

λ λ

+( ) −( )⎞⎠⎟

+( )<

2 2

20

2

v d,

where μ μ μAD

BD= = .

An increase of the sabotage rates on the non-priority lane fromzero to a positive level always decreases total welfare. The CP’s on thenon-priority lane and the end users are worse off: the CP’s that donot opt for priority obtain lower advertising revenues due to sabotage,and the end users face less variety in the market. However, the ISP’sbenefit from sabotage (for the range of the parameter values discussedabove).

To sum up, while in the baseline model the introduction of thepriority lanes and fees is always welfare-enhancing due to the moreefficient traffic management and the associated higher incentives toinvest, policy-makers should be aware of the additional practicesthat the ISP’s may adopt under discrimination. The implementationof sabotage by the ISP’s gives them an additional instrument toextract more profits, which could potentially decrease social welfare.Such a practice may reduce innovation in services, and thus excludesome CP’s from the Internet market. Therefore, the competitive pressureat the ISP level is not sufficient to eliminate the probability ofsabotage.

VII. SMALL AND LARGE CP’S

In the baseline model, we assumed that the advertising rate was identicalacross CP’s. However, some (small) CP’s may earn lower advertisingrates than other (large) CP’s. One concern expressed by the proponentsof net neutrality is that a departure from the neutral regime could hurtthese small CP’s, and even drive them out of the market. To study thisissue, we consider that, for each level of congestion sensitivity h, a pro-portion γ of the CP’s has a low advertising rate aL, while a proportion1 − γ has a high advertising rate aH, with aH > aL and γ ∈ (0, 1). Theformer are considered to be ‘small’ due to lower advertising revenues, andthe latter to be ‘large.’ We assume that γaL + (1 − γ)aH = a, which meansthat the average advertising rate is the same as in our baseline model.We keep assuming that each ISP charges a fixed fee for the priority lane,that is, does not seek to price discriminate between small and largeCP’s.



The equilibrium outcome under net neutrality for this extended setting isthe same as the one described in Proposition 1.42 When there is a uniquetraffic lane, advertising rates do not affect the equilibrium level of capacityinvestment, innovation in services, the subscription fees and network con-gestion.43 The only difference is that small CP’s obtain lower profits thanlarge CP’s. However, total welfare remains unchanged.

Under discrimination, we denote by hk i, the total number of CP’s enter-ing ISP i when they earn advertising rate ak, and by �hk i, the CP which isindifferent between the priority lane and the best-effort lane at ISP i, withk = L, H, and i = A, B. We solve the game in a similar way as for ourbaseline model, and obtain the same qualitative results. In particular, aswitch from the net neutrality regime to the discriminatory regime remainsbeneficial in terms of investments, innovation and total welfare.

However, a departure from the net neutrality regime hurts the small CP’smore often than the large CP’s. In particular, there might be cases wherelarge CP’s benefit from a switch to the discriminatory regime, while smallCP’s are hurt.44 This is due to the fact that large CP’s earn higher adver-tising revenues, and therefore, there is more entry from large CP’s thanfrom small CP’s, using the priority lane. Finally, for some parametervalues, for example, when the difference aH − aL is large enough, all smallCP’s are excluded from the priority lane, though they still can use thefree-of-charge non-priority lane.

To sum up, in this extension, a departure from the net neutrality regimeis still positive in terms of total welfare, but with a caveat, as small CP’s gethurt more than large CP’s.

VIII. CONCLUSION

We propose a model with two competing Internet platforms (ISP’s) thatbring together Internet users and a continuum of congestion-sensitiveadvertiser-supported content providers. The CP’s deliver content to the end

42 See Appendix B for the detailed analysis.43 The equilibrium is slightly affected by the introduction of a fixed cost for the CP’s who

connect to an ISP. We find that the equilibrium level of entry by CP’s increases with theadvertising rate. As a consequence, the entry of CP’s with high advertising rates is highercompared to the entry of CP’s with low advertising rates. Nevertheless, in this extension, westill obtain that entry under discrimination is higher compared to entry under net neutrality(due to higher capacity investments under discrimination). The proof is available online in theSupplementary material on the Journal of Industrial Economics website.

44 Recall that this result is obtained under the assumption that ISP’s cannot price discrimi-nate between small and large CP’s. If the ISP’s had the ability to price discriminate betweensmall and large CP’s for access to the priority lane, the effect of a departure from netneutrality on small CP’s could be different (e.g., it could be less negative if the small CP’s wereoffered a lower price).



users via the ISPs’ broadband networks. Under the net neutrality regime,CP’s pay no fees to the ISP’s for network access, whereas under the alter-native discriminatory regime, the CP’s who opt for an ISP’s fast lane haveto pay a priority fee to that ISP, while the other CP’s can use a best-effortslow lane at no charge.

We find that in the discriminatory regime, where the two ISP’soffer prioritized lanes, Internet traffic is managed more efficiently than inthe net neutrality regime. Consequently, the average level of congestionexperienced by end users is lower under discrimination than undernet neutrality. Moreover, ISP’s invest more in network capacity, sincethey can be partly compensated for their investments by the additionalrevenues that they can extract from the CP’s through the priorityfees. Innovation in services is also higher in the discriminatory regimecompared to the net neutrality regime. As traffic is managed moreefficiently, some highly congestion-sensitive CP’s are able to enter themarket when a prioritized lane is available, while they choose toremain out of the market when there is only one best-effort lane for allCP’s.

In this duopoly framework, ISP’s do not always benefit from a depar-ture from the net neutrality regime, as the introduction of multiple lanescan actually intensify competition between Internet platforms. However,ISP’s always have a unilateral incentive to adopt the discriminatoryregime, when they are allowed to. In such a case, the two competing ISP’smight be trapped in a prisoner’s dilemma, switching to the discriminatoryregime, even though it makes them worse-off. Finally, while the effect ofa departure from the net neutrality regime on the CPs’ profits and theend users’ utility is generally ambiguous, total welfare always increaseswhen there is a switch from the net neutrality to the discriminatoryregime.

Our findings in a setting with competing platforms are useful tosupport and qualify some policy statements. For example, the FCCexempted cellular operators from most of the net neutrality ruleson the grounds in particular that the cellular industry is typically morecompetitive than the fixed-line industry, suggesting that competitionmight itself bring net neutrality, without mandating it. Our resultssupport the idea that lifting net neutrality regulation on competing plat-forms is welfare-increasing. However, this is not because competitionreduces the ISPs’ incentives to discriminate. In fact, each operator has aunilateral incentive to introduce a priority lane, no matter what its rivaldoes.

Though welfare-enhancing, the discriminatory regime has some unde-sirable effects. When we distinguish between small and large CP’s, itturns out that a switch to the discriminatory regime hurts the small onesmore than the large ones. Besides, and perhaps more importantly,



the discriminatory regime might bring forth a risk of sabotage byISP’s of content providers’ traffic. Whereas this risk is absent under netneutrality—sabotage is never an optimal strategy for the ISP’s underthis regime—under the discriminatory regime, if the advertisingrevenue is sufficiently high, each ISP benefits from degrading the qualityof the non-priority lane in order to extract higher profits from the prioritylane.

If regulation of traffic quality is too complex and/or costly, keeping thecurrent net neutrality regime might be a solution to avoid sabotage of CPs’traffic. Otherwise, our analysis suggests that a switch to the discriminatoryregime would be welfare-improving, while still requiring some monitoringof traffic quality.

APPENDICES

Appendix A: Second-Order Conditions

Net Neutrality. The candidate equilibrium in Proposition 1 corresponds to amaximum of the profit function if the Hessian matrix is negative definite, which is thecase if

′′ ( ) >+( )

+( ) +( ) + +( )( )Cd v

t d vμ

λ λ λμ4

2 2 4

2

2 2 .

Discrimination. The candidate equilibrium in Proposition 2 corresponds to amaximum of the profit function if the Hessian matrix is negative definite. The Hessianmatrix is

H

p p p f

p f

i

i

i

i i

i

i i

i

i i

i

i

i

i i=

∂∂

∂∂ ∂

∂∂ ∂

∂∂ ∂

∂∂

∂∂ ∂

2

2

2 2

2 2

2

2

Π Π Π

Π Π Π

μ

μ μ μ∂∂∂ ∂

∂∂ ∂

∂∂

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥⎥

2 2 2

2

Π Π Πi

i i

i

i i

i

if p f fμ

.

In the symmetric equilibrium under discrimination, we have

∂∂

= −

+ + +( ) + +( ) + + +( )⎛⎝⎜

⎛⎝⎜

⎛⎝

2

2

3 2 32 2 2 2 2 2 2 16 8 16

Πi

i

i

p

t aλ λ λ μ λ λ λ λ⎜⎜

− + + + +( )) + +( ) +( )⎞⎠⎟⎞⎠⎟

+( ) +

2 2 10 20 16 2 2 2

2 2 4

3 232

2

λ λ λ λ λ λ

λ λμ

d v

t ii d v+( )( )<2 0,



∂∂ ∂

=∂

∂ ∂

=

+( ) +( ) − +( )⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎛

2 2

2 2522 2 2 2 2

Π Πi

i i

i

i ip p

t a

μ μ

λ λ λ λ λ⎝⎝⎜

+ +( ) +( ) +( )⎞⎠⎟⎞⎠⎟

+( ) +( ) + +( )( )

+

2 1 2

2 2 4

2 4

2

2 2 2

λ λ

λ λ λμ

μ

d v

t d vi

i dd v d v

a

+( ) +( ) +( ) +( )⎛⎝⎜

⎛⎝⎜

− +( ) +( ) − +( ) +

2 1 2

2 2 4 2 4

2

12

472

2

λ λ λ

λ λ λ λ λλ

λ λ λμ

+( )⎛⎝⎜

⎞⎠⎟⎞⎠⎟⎞⎠⎟

+( ) +( ) + +( )( )8

2 2 42 2 2t d vi

,

∂∂ ∂

=∂∂ ∂

= −+( ) +( ) − +( )⎛

⎝⎜⎞⎠⎟

+( )

2 2

322 2 2 2 4

2

Π Πi

i i

i

i i

i

p f f p t

μ λ λ λ

λ λ 22 2

2

2

2

40

2 2 2 2 2 2

+ +( )<

∂∂

= − ′′ ( ) −

+( ) +( ) − +(

λ μ

μμ

λ λ λ λ

i

i

ii

d v

C

d v t a

,

Π

))⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎛⎝⎜

+ +( ) +( )⎞⎠⎟⎞⎠⎟

+( ) +( ) + +

52

12

2

2

2 2

2 2 4

λ λ

λ λ λμ

d v

t d vi (( )( )

−

+( ) +( ) + + + +( )(((− + + +

2

3 2

2 3

2 2 2 2 4 16 16

2 20 6 1

d v d v aiμ λ λ λ λ

λ λ λ 66 2 2

2 2 4

2

2 2

( )) + +( )))+( ) +( ) + +( )( )

λ

λ λ λμ

d v

t d vi

,

∂∂ ∂

=∂∂ ∂

=+( ) +( ) − +( )⎛

⎝⎜⎞⎠⎟

+( )

2 2

32

2

4 2 2 4

2

Π Πi

i i

i

i i

i

f f

d v

tμ μ

μ λ λ

λ λ ++ +( )>

40

2λ μi d v,

and

∂∂

= −+

<2

2 2

4 2 20

Πi

i

i

f a

λ μλ

.

The Hessian matrix is negative definite if ∂ ∂ <2 2 0Πi ip , ∂ ∂ <2 2 0Πi iμ ,∂ ∂ <2 2 0Πi if , ∂ ∂( ) ∂ ∂( ) − ∂ ∂ ∂( ) >2 2 2 2 2 2

0Π Π Πi i i i i i ip pμ μ , and if the determinant of



the Hessian matrix is negative. The first and the third inequalities are always true, andthe rest holds if C(·) is sufficiently convex. This always holds when transportationcosts are high enough.

Appendix B: Small and Large CP’s

Net Neutrality. The equilibrium outcome under net neutrality with small and largeCP’s is the same as the equilibrium described in Proposition 1, with the total numberof CP’s now being equal to γ γh h hL

NHN N+ −( ) =1 . In equilibrium, the ISPs’ profits,

the consumers’ surplus and total welfare remain unchanged, whereas the CPs’ profitsare now given by

Π

Π

hN L

LN L L

N

L LN

hN H

L

H

ah

h h

h h

a

=−

+( )⎛⎝⎜

⎞⎠⎟

≤

>

⎧⎨⎪

⎩⎪

=

λ λμ

12

2

0

if

if

and

λλ λμ

12

2

0

−+( )⎛

⎝⎜⎞⎠⎟

≤

>

⎧⎨⎪

⎩⎪

hh h

h h

HN H H

N

H HN

if

if

.

Discrimination. At the second stage, a CP of type hk, with k = L, H, connectsto the priority lane at ISP i if h hk k i

D≤ , , where hk iD, solves a x h w fk i

Dk iD

iP

iλ 1 0−( ) − =, ,while the CP of type �hk i, , which is indifferent between the priority andnon-priority lanes at ISP i, is defined by a x h w f a x h wk i

Dk i i

Pi k i

Dk i i

NPλ λ1 1−( ) − = −( )� �, , ,

where

wh h h h x

w

iP

i L iD

L i H iD

H i i

iNP i

i

=− −( ) + −( ) −( )( )

=−

1

1μ γ γ λ

μμ γ

, , , ,,� �

hh h xw

L iD

H iD

iiP

, ,.

+ −( )( )1 γ λ

Similar to our baseline model, from these expressions we obtain that

ha a x f

x a a x a a a f

h

L iD i H L i i

i H L i L H L i

L i

,

,

,=−( )

+( ) − + −( )( )( )μ λ

λ λ γ1

� ==+( ) − + −( )( )( )

=

μλ λ λ γ

μ λ

i H i

i i H L i L H L i

H iD i L H

a fx x a a x a a a f

ha a x

1,

,ii i

i H L i L H L i

H ii L i

i

fx a a x a a a f

ha f

x

−( )+( ) − + −( )( )( )

=+

1

1

λ λ γμ

λ λ

,

,�

xx a a x a a a fi H L i L H L i( ) − + −( )( )( )λ γ.



Simultaneously, at stage 2, each consumer chooses whether to subscribe to ISPA or ISP B. The indifferent consumer �xD is given by

R v h hd

wp tx

R v h h

L AD

H AD

AD A

D D

L BD

H BD

+ + −( )( ) + − −

= + + −( )(

γ γ

γ γ

, ,

, ,

1

1

�

)) + − − −( )d

wp t x

BD B

D D1 � ,

where w h h xiD

i L iD

H iD

i= − + −( )( )( )1 1μ γ γ λ, , . By replacing for hk iD, into the expression

for the indifferent consumer, we find that �xD satisfies equation (20) as in the baselinemodel.

At the first stage, the two ISP’s choose simultaneously their capacities, subscriptionfees and priority fees. The maximization problem of ISP i can be expressed asfollows

max, ,

, , , ,p f

iD

iD

iD

L iD

L i H iD

H iiD

iD

i

p x h h h hμ

γ γΠ = + −( ) + −( ) −( ) −� �1 CC iDμ( ),

where x x p piD

iD

AD

BD

AD

BD= ( ), , ,μ μ . Solving for the first-order conditions ∂ ∂ =Πi

DiDp 0,

∂ ∂ =ΠiD

iDμ 0, ∂ ∂ =Πi

Dif 0, we obtain the capacity level, the priority fee, the sub-

scription fee, the number of CP’s and the levels of congestion in the symmetricequilibrium:

μλ

λλ γ

D H L

L H LC

d v a a

a a a

f

= ′( ) ++

++ −( )

+( ) + −( )( )

⎛

⎝⎜⎜

⎞

⎠⎟⎟

−1

2

2

2 2 2

2 2,

==+ −( )( )

−+

⎛⎝⎜

⎞⎠⎟

= ++( )

+( )−

λγ λ

λμλ

λ

a aa a a

p td v a

H L

L H L

DD

21

2

2

4

2

22

,

HH LD

L H L

LD H H L

a

a a a

ha a a

μ λ

λ γ

γ λ

2 2 2

2

2 1 2 2

2

+ −( )+( ) + −( )( )

=− −( ) −( ) +

,

(( )+( ) + −( )( )

=+ −( )

+( ) + −( )

μλ γ

λ μλ λ γ

D

L H L

LH

D

L H L

a a a

ha

a a a

2

2 2 2 2

2

,

�(( )

=+ −( ) +( )

+( ) + −( )( )=

+

,

,ha a a

a a ah

aHD L H L

D

L H LH

L2 2 2

2

2 2 2γ λ μλ γ

λ� −−( )+( ) + −( )( )

=+

=+( ) =

2

2

2 22

2 24

3 2

μλ λ γ

λμ

λμ

λ

D

L H L

PD

NPD

D

a a a

w w w

,

, ,++ 2

2μD .

The proof is similar to the one provided in the main text forProposition 2. The resulting equilibrium profits, consumers’ surplus and total welfareare



ΠDD

DH L

t d v

a a

a

= ++( )

+( )

++ − +( ) − + −( )( )

+( )

22

2

2 2 2 2 2 2

2

2

2

2

λμλ

μ λ λ λ λ

λ LL H L

D

hD

hNP

L L D

a aC

a h h

L

L

+ −( )( )− ( )

=

= −+( )⎛

⎝⎜⎞⎠⎟

γμ

λ λμ

,

Π

Π 12 2

4

3 2

if LL L

hP L

H

H L

L H LL

h

a

a

a aa a a

hL

≤

=+

− −( )−( ) +

+ −( )( )−

+

�

Π2

2

2 1

2 22

2λλ

γ

λγ

λ(( )⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

< <

≥

⎧

⎨

⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪

=

2

0

μD L L LD

L LD

hD

h h h

h h

H

if

if

� ,

Π

ΠΠ

Π

hNP

H H D H H

hP H

L

H

H

a h h h

a

a

= −+( )⎛

⎝⎜⎞⎠⎟

≤

=+

+

+

λ λμ

λλ

λ

12 2

4

2

2

2 2

3 2

if �

222

22

γγ

λμ

a aa a a

h h h hH L

L H LH D H H H

−( )+ −( )( )

−+

⎛

⎝

⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟

< <if� DD

H HD

DD

h h

CS Rt

d va

0

54

2

222

if ≥

⎧

⎨

⎪⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪⎪

= − ++( )

+( ) −( ) +

,

μλ

λHH L

L H L

D D

a

a a a

W Rt d v

λ λγ

μλ

λ λγ

2 2 2

42

2

2 2 1

+ −( )+ −( )

⎛

⎝⎜

⎞

⎠⎟

= − ++( )

++

+

,

−−( ) −( ) −( )+ +( )

+( ) + −( )( )

⎛

⎝

⎜⎜⎜⎜⎜

γ

λλ γ

a a a a

a aa a a

H L H L

H L

L H L

2 4

4 22 2

⎞⎞

⎠

⎟⎟⎟⎟⎟

− ( )2C Dμ .

Comparisons. Direct comparisons of the equilibrium levels of investment, innova-tion and total welfare in the net neutrality and discriminatory regimes yield thatμD > μN, γ γ γ γh h h hL

DHD

LN

HN+ −( ) > + −( )1 1 and WD > WN. Moreover, there are

parameter values such that ΣΠ ΣΠhD

hN

H H> while ΣΠ ΣΠh

DhN

L L< . The set of parameter

values where all CP’s are hurt by prioritization is smaller than the set of parameterswhere only the small CP’s are hurt.

Finally, the previous analysis is valid for the parameter values such thath hL

DL− >� 0, i.e., when there exists some small CP’s that opt for priority. However,

when the difference aH − aL is large enough, all small CP’s are excluded from thepriority lane, though they still can use the free-of-charge non-priority lane.



REFERENCES

Alexandrov, A. and Deb, J., 2012, ‘Price Discrimination and Investment Incentives,’International Journal of Industrial Organization, 30, pp. 615–623.

Armstrong, M., 2006, ‘Competition in Two-Sided Markets,’ RAND Journal of Econom-ics, 37, pp. 668–691.

Armstrong, M., 2008, ‘Price Discrimination,’ in P. Buccirossi (ed.), Handbook of Anti-trust Economics (MIT Press, Boston, Massachusetts, U.S.A.)

Becker, G.; Carlton, D. and Sider, H., 2010, ‘Net Neutrality and Consumer Welfare,’Journal of Competition Law & Economics, 6, pp. 497–519.

Belleflamme, P. and Peitz, M., 2010, ‘Platform Competition and Seller InvestmentIncentives,’ European Economic Review, 54, pp. 1059–1076.

Cheng, H.; Bandyopadhyay, S. and Guo, H., 2011, ‘The Debate on Net Neutrality: APolicy Perspective,’ Information Systems Research, 22, pp. 1–27.

Choi, J.P. and Kim, B.-C., 2010, ‘Net Neutrality and Investment Incentives,’ RANDJournal of Economics, 41, pp. 446–471.

Choi, J.P.; Jeon, D.-S. and Kim, B.-C., 2012, ‘Net Neutrality, Business Models andInternet Connection,’ American Economic Journal: Microeconomics, forthcoming.

Choi, J.P.; Jeon, D.-S. and Kim, B.-C., 2013, ‘Asymmetric Neutrality Regulation andInnovation at the Edges: Fixed vs. Mobile Networks,’ NET Institute working paperno. 13–24 (http://www.netinst.org/NET_Working_Papers.html).

Corts, K., 1998, ‘Third-Degree Price Discrimination in Oligopoly: All-Out Competitionand Strategic Commitment,’ RAND Journal of Economics, 29, pp. 306–323.

Deneckere, R.J. and McAfee, R.P., 1996, ‘Damaged Goods,’ Journal of Economics &Management Strategy, 5, pp. 149–174.

Economides, N. and Hermalin, B., 2012, ‘The Economics of Network Neutrality,’RAND Journal of Economics, 43, pp. 602–629.

Economides, N. and Tåg, J., 2012, ‘Net Neutrality on the Internet: A Two-Sided MarketAnalysis,’ Information Economics and Policy, 24, pp. 91–104.

Farhi, E. and Hagiu, A., 2008, ‘Strategic Interactions in Two-Sided Market Oligopo-lies,’ Harvard University Strategy Unit working paper 08-011, (Harvard BusinessSchool, Boston, Massachusetts, U.S.A.).

Jullien, B. and Sand-Zantman, W., 2012, ‘Congestion Pricing and Net Neutrality,’ IDEIworking paper no. 375 (Institut d’Économie Industrielle, allée de Brienne, Universitéde Toulouse, Toulouse, France).

Krämer, J. and Wiewiorra, L., 2012, ‘Network Neutrality and Congestion SensitiveContent Providers: Implications for Content Variety, Broadband Investment andRegulation,’ Information Systems Research, 23, pp. 1303–1321.

Liu, Q. and Serfes, K., 2013, ‘Price Discrimination in Two-Sided Markets,’ Journal ofEconomics & Management Strategy, 22, pp. 768–786.

Maxwell, W.J. and Brenner, D.L., 2012, ‘Confronting the FCC Net Neutrality Orderwith European Regulatory Principles,’ The Journal of Regulation, 2, pp. 72–87.

Njoroge, P.; Ozdaglar, A.E.; Stier-Moses, N.E. and Weintraub, G.Y., 2013, ‘Investmentin Two-Sided Markets and the Net Neutrality Debate,’ Review of Network Economics,12(4), pp. 355–402.

Reggiani, C. and Valletti, T., 2012, ‘Net Neutrality and Innovation at the Core and atthe Edge,’ School of Economics discussion paper 1202 (University of Manchester,Manchester, England).

Rochet, J.-C. and Tirole, J., 2006, ‘Two-Sided Markets: A Progress Report,’ RANDJournal of Economics, 35, pp. 645–667.



http://www.netinst.org/NET_Working_Papers.html

Schuett, F., 2010, ‘Network Neutrality: A survey of the Economic Literature,’ Review ofNetwork Economics, 9, pp. 1–13.

Van Schewick, B., 2006, ‘Towards an Economic Framework for Network NeutralityRegulation,’ Journal on Telecommunications & High Technology Law, 5, pp. 329–392.

Yoo, C., 2005, ‘Beyond Network Neutrality,’ Harvard Journal of Law & Technology, 19,pp. 1–77.

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