Asymmetric Neutrality Regulation and Innovation at the Edges: Fixed vs. Mobile Networks

Transcription

1 TSE 521 August 2014 Asymmetric Neutrality Regulation an Innovation at the Eges: Fixe vs. Mobile Networks Jay Pil Choi, Doh Shin Jeon an Byung Cheol Kim

2 Asymmetric Neutrality Regulation an Innovation at the Eges: Fixe vs. Mobile Networks Jay Pil Choi Doh-Shin Jeon Byung-Cheol Kim August 31, 2014 Abstract We stuy how net neutrality regulations affect a high-banwith content provier s (CP) investment incentives in quality of services (QoS). We fin that the effects crucially epen on network capacity levels. With limite capacity, as in mobile networks, prioritize elivery services are complementary to the CP s investments an can facilitate entry of congestion-sensitive content; however, this creates more congestion for other existing content. By contrast, if capacity is relatively large, as in fixe-line networks, prioritize services reuce QoS investment as they become substitutes, but improves traffic management. These results are qualitatively robust to the extension of the ISP s enogenous choice of network capacity. JEL coes: D4, K2, L1, L5, O3 Key wors: Net neutrality, asymmetric regulation, quality of service, investment incentives, queuing, congestion, mobile/fixe networks We thank Marc Bourreau, Jane Choi, Jeroen Hinloopen, Bruno Jullien, Martin Peitz, Wilfrie San- Zantman, Glenn Woroch, an seminar participants at 2014 EEA-ESEM at Toulouse, 2014 IIOC at Northwestern Univ., 2014 NET Conference at UC Berkeley, 2014 ICT Conference Paris at Telecom ParisTech, 2013 Miwest Economic Theory Conference at Univ. of Michigan, an Georgia Institute of Technology for helpful comments. We gratefully acknowlege financial support from the NET Institute ( through the 2013 summer grant program. An earlier version of this paper was circulate as NET Institute Working Paper # The usual isclaimer applies. School of Economics, University of New South Wales, Syney, NSW 2052, Australia an Department of Economics; Michigan State University, 220A Marshall-Aams Hall, East Lansing, MI choijay@msu.eu. Toulouse School of Economics an CEPR, Manufacture e Tabacs, 21 allees e Brienne Toulouse, France. ohshin.jeon@gmail.com. School of Economics, Georgia Institute of Technology, 221 Bobby Do Way, Atlanta, GA byung-cheol.kim@econ.gatech.eu.

3 1 Introuction Net neutrality is the principle that all packets on the Internet must be treate equally in their elivery without iscrimination an charges regarless of its content source, estination, an type. The ebate on net neutrality has been the most important an controversial regulatory agena since the inception of the Internet. The open Internet orer in aopte by the U.S. Feeral Communication Commission (FCC) has playe as a focal guieline for neutrality regulations. One well-known controversy surrouning this orer has been whether the FCC has legitimate statutory authority to impose any regulatory obligations over the Internet. While the FCC has legitimate regulatory authority over telecommunication services uner Title II of the Communications Act regaring common-carriers, the Internet is currently categorize as information services, an thereby consiere a non-common carrier; the FCC s powers are consierably limite in the information services governe by Title I of the Act. 2 As a result, some Internet broaban access proviers such as Comcast, Verizon Communications, an Metro PCS have challenge the legality of the FCC s orer. The Unite States Court of Appeals for the District of Columbia Circuit rule on the case Comcast Corp. v. FCC (600 F.3 642) on April 6, 2010 that the FCC oversteppe its authority when it impose anti-iscrimination rules on Comcast, which blocke BitTorrent applications in the summer of For the case Verizon v. FCC (740 F.3 623), the same D.C. Circuit foun on Jan. 14, 2014 that the FCC s Orer that prevente eals between Verizon an content proviers for faster elivery is not legitimate, while at the same time stating that the Commission oes have some basic authority to promulgate rules governing broaban proviers treatment of Internet traffic. After all, the vericts were mixe. The current regulatory stance on net neutrality is also flui with mixe messages. The FCC recently announce that it woul propose new rules that allow major content proviers like Google, Netflix, an Disney to pay Internet service proviers for preferential treatment of their content 3 whereas the FCC Chairman, Tom Wheeler, mae a strong statement in his speech (April 30, 2014) at the National Cable & Telecommunications Association that he woul consier reclassifying the 1 FCC , In the Matter of Preserving the Open Internet, Broaban Inustry Practices (the FCC Orer ), publishe in Fe. Reg. Vol. 76, No. 185, Sept. 23, 2011, went into effect on November 20, For more etails on reclassification an relate issues, we refer to Net neutrality is on trial in Washington. Here s what you nee to know by Timothy B. Lee in The Washington Post on Sept. 10, Netflix recently struck such a eal with Comcast. For a relate newspaper article, see F.C.C. in a Shift, Backs Fast Lanes for Web Traffic by Ewar Wyatt in The New York Times on April, 24,

4 Internet as a telecommunication service to enable the regulation of the Internet uner Title II. With a split vote of 3-2, the FCC ecie to open up for public ebate regaring new rules for the open Internet (May 15, 2014). Net neutrality thus still remains a contentious regulatory issue. Another issue of importance, which appears to have been somewhat ignore, is that the FCC s Orer treate mobile network operators more leniently than fixe wireline network operators. More specifically, its first two rules, namely, (i) transparency an (ii) no blocking are commonly applie to both types of network operators, but the thir rule (iii) no unreasonable iscrimination appertains only to fixe line operators: A person engage in the provision of fixe broaban Internet access service, insofar as such person is so engage, shall not unreasonably iscriminate in transmitting lawful network traffic over a consumer s broaban Internet access service. Reasonable network management shall not constitute unreasonable iscrimination. (47 of CFR 8.7, italics ae) Maxwell an Brenner (2012) escribe such asymmetric treatment of fixe an mobile networks as by far the most controversial aspect of the FCC s orer insofar as it is esigne to prohibit pai prioritization arrangements between an Internet access provier an upstream content, application or service proviers. Importantly an interestingly, this asymmetric regulatory approach is in sharp contrast to the European approach to the same issue; European regulatory stanars, the 2002 EC Directives on electronic communications an its revisions in 2009, 4 have no such istinction between fixe an mobile networks. The uniform treatment reflects one of the European regulatory principles, technological neutrality, which allows no ifferential treatment across all types of networks incluing cable, mobile, an fixe wireline networks. 5 Nevertheless, to our knowlege, no rigorous analysis has been one on the sharp contrast in regulatory approaches between the US an EU; our stuy fills this voi. We stuy when mobile networks woul call for asymmetric regulation an when uniform treatment may be justifie. Our stuy is not only motivate by regulatory ifferences, but also by the implications of 4 Directive 2002/22/EC of the European Parliament an of the Council ( Universal Service Directive ) an Directive 2002/21/EC ( Framework Directive ); amenments were mae uner 2009/1140/EC (the Better Regulation Directive ) an Directive 2009/136/EC (the Consumer Rights Directive ). 5 For a specific example, the Netherlans enacte net neutrality law in 2011 that prohibite mobile network operators from charging extra fees to customers on certain applications, which is opposite to the US FCC s rather lenient treatment of mobile network operators. Krämer, Wiewiorra, an Weinhart (2013) offer a comprehensive literature review on recent progress of net neutrality issues. 2

5 neutrality regulation on innovation incentives at the eges. The extant literature on network neutrality has mainly focuse on the expansion of Internet service proviers (ISPs) network capacity as innovation at the core. 6 However, the ISPs capacity expansion making bigger pipelines is not the only solution to resolving the congestion problem in the moern Internet ecosystem. In fact, major content proviers such as Google, Netflix, an Amazon have evelope various measures to improve the quality of service (QoS) for their content an applications, inepenent of the ISP s network infrastructure. For example, they have pursue alternative technological solutions such as content istribution (or elivery) networks (CDN) 7 an avance compression technology to ensure a sufficient quality of service, without asking for preferential treatment of their own content (Xiao, 2008). 8 From an en user s perspective, the funamental goal is to enjoy highest quality of service at a minimum fee; the channel through which this is achieve, either through ISP s capacity investment or CP s CDN investments, is of little interest to en users. Researchers have selom stuie how these new technological changes relate to regulatory ecisions, yet regulators an policy-makers nee to unerstan how the network regulations woul affect the content proviers investments in alternative technology solutions to ensure their quality of services, inepenent of the ISPs (Maxwell an Brenner, 2012). Reflecting technology avances at the eges of the Internet, we evelop a theoretical moel to analyze the effects of net neutrality regulation on innovation incentives of major content proviers. To be consistent with the FCC s interpretation, we characterize neutrality regulation as not allowing for pai prioritization uner which the ISPs can allocate some traffic into a prioritize lane for a premium charge. In this setting, we fin that the effects of net neutrality regulation substantially epens on the relative size of the ISPs network capacity vis-à-vis major content proviers banwith usage. The intuition is as follows. With a limite network capacity, the pai prioritization can facilitate the entry of a congestion-sensitive content provier while the entry is not mae uner neutral 6 Networks constitute the core of the Internet while content, applications, an evices are at the ege. See Reggiani an Valletti (2012) for more iscussion on this. 7 CDN is to cache frequently accesse content in various geographical locations, an reirect access request of such content to the closer place. (... ) [B]y moving content closer to en users, CDN can ramatically reuce elay, elay variation, an packet loss ratio for users applications an thus their perception of network QoS (Xiao, 2008 p.117). 8 It is well known that the innovative vieo compression technologies have contribute to better content elivery for live-streaming vieo applications. In aition, thir-party commercial CDN proviers such as Akamai an Internap have rapily expane their businesses to provie a high QoS for content proviers. 3

6 networks because the content provier may fin it too costly to invest up to its esire QoS. For this case, the prioritization complements innovation at the eges. The newly available content woul generate aitional value to the network, which resonates with the rationale given by the FCC for its ifferential treatment between fixe an mobile networks: Mobile broaban is an earlier-stage platform than fixe broaban, an it is rapily evolving. Mobile broaban spees, capacity, an penetration are typically much lower than for fixe broaban. (... ) In aition, existing mobile networks present operational constraints that fixe broaban networks o not typically encounter. (FCC Orer, par ) The FCC appears to believe that its lenient non-neutral treatment facilitates the availability of innovative content an applications in the early-stage mobile network. However, the entry of new content oes not necessarily result in higher welfare. This is because the new content will consume a substantial portion of the existing network capacity, which increases the congestion for other content. Such a negative externality of congestion becomes more pronounce with a limite capacity network such as mobile. Inee, the surplus from new content can be outweighe by the efficiency loss from the elevate congestion for other content when the negative externality is not internalize in the content provier s entry ecision. In contrast, if the network capacity is large enough, prioritize elivery an QoS investment turn into substitutes. Consier a high network capacity case in which the entry of new content is no longer a focal issue. That is, suppose that the high-banwith content proviers enter even without the prioritize service. The prioritization then presents a ifferent type of trae-off. On the positive sie, the prioritization results in more efficient traffic management by assigning the faster elivery service to the more elay-sensitive content, which is referre to as the traffic management effect. The prioritization thus enhances static efficiency. However, the availability of the prioritize service may ampen content proviers incentives to invest in QoS because the pai prioritization can provie an alternative technological solution to achieve their esire level of QoS. We refer to this uner-investment problem as the QoS investment effect. In other wors, the prioritization may yiel a negative effect on social welfare by weakening ynamic incentives for QoS investment. 9 The social welfare epens on the relative magnitue of these two forces, an we consier it applicable 9 Consistent with this insight, Xiao (2008) claims that major content proviers have increase their pursuit of quality of service through technological solutions rather than prioritization after the FCC s intensive efforts to apply network neutrality regulations. 4

7 to the fixe network where the entry of content proviers has not been treate as a serious concern. We exten the moel to allow for the ISP s investment in network capacity prior to the entry of the major CP. This extension confirms an even strengthens the main insight obtaine for a given capacity. When a major CP s entry critically epens on the ISP s network capacity, the ISP s incentive to inuce entry by investing in capacity is suboptimal regarless of the neutrality regulation regime. Intuitively, this problem is much more severe uner neutral networks in which the ISP s incentive oes not epen on the surplus create by the major CP than uner nonneutral networks in which the ISP partially internalizes the surplus. Provie that the entry occurs, however, the ISP invests less uner non-neutrality to enhance its bargaining position to such an extent that the major CP fins its entry unprofitable without purchasing a prioritize elivery service from the ISP. By contrast, uner neutral networks the ISP s investment is simply to reuce waiting time for non-major CPs. Overall, these finings suggest that for mobile networks neutrality regulation can be averse to the entry of major CPs, whereas for fixe networks non-neutrality may reuce the ISP s incentive to invest in capacity. Our stuy makes two primary contributions to the ebate of net neutrality regulations. First, we provie a novel theoretical moel of major content proviers QoS investment. Consiering the importance of innovations at the eges of the Internet, we think it critical to offer a formal theory to unerstan innovation incentives an associate externalities across ifferent network capacities. Secon, our moel provies a useful framework through which one can comprehen the contrasting neutrality regulations between the US FCC, which treats mobile networks more leniently than fixe networks, an the EU which treats both networks uniformly. The remainer of our paper is organize as follows. After reviewing relate literature, we present our moel in Section 2 incluing a generalize queuing moel which escribes how prioritization an QoS investment affects congestion. In Section 3, we first show that the first-best outcome is characterize by iscrimination across content types with ifferent sensitivities to elay. This implies that net neutrality regulation can be justifie only as a secon-best policy when a social planner cannot irectly control content proviers entry an investment ecisions. After the first-best, we analyze the QoS investment ecisions by the major content proviers uner neutral an non-neutral network regimes. We show how mobile networks an fixe networks can be ifferentiate epening on network capacity. In Sections 4 an 5, we provie our main analysis for mobile an fixe networks, respectively. In Section 6, we analyze the ISP s capacity choice. Section 7 presents two extensions of our moel with consumer heterogeneity an iscrete QoS. We wrap up with concluing remarks in Section 8. Lengthy mathematical proofs are relegate to the Appenix. 5

8 1.1 Relate Literature Several survey articles such as Lee an Wu (2009), Schuett (2010), Lee an Hwang (2011), an Krämer, Wiewiorra, an Weinhart (2012) have offere comprehensive reviews on the literature of net neutrality. So, we here briefly mention notable works in relation to this paper. The main focus of the extant stuies has been investment incentives for the ISPs (at the core) an content proviers (at the eges). One major issue in the net neutrality ebate is Internet access service proviers investment incentives on its last mile network capacity. In particular, proponents an opponents of the regulation collie hea-to-hea on whether the content proviers allege free-riing woul have a chilling effect on the ISPs incentives to upgrae their pipelines. Economic research on this issue inclues Musacchio, Schwartz, an Walran (2009), Choi an Kim (2010), Cheng, Banyopahyay an Guo (2011), Economies an Hermalin (2012), Krämer an Wiewiorra (2012), an Njoroge et al. (2013). A relate issue is the content proviers hol-up concern that may result in no entry or less investment in content. This concern arises because investments by high-value content proviers may be expropriate ex post by Internet service proviers who can play as gatekeepers with pai prioritization services. For stuies along this avenue, we can refer to Banyopahyay, Guo, an Cheng (2009), Choi an Kim (2010), Grafenhofer (2010), Reggiani an Valletti (2012), an Bourreau, Kourani, an Valletti (2012). Beyon investment incentives, economists have stuie how network neutrality woul affect consumer an social welfare from various perspectives. Hermalin an Katz (2007) analyze network neutrality from the perspective of prouct line restrictions in a vertical ifferentiation moel. Economies an Tåg (2012) regar neutrality regulation as a zero-pricing regulation on the content sie in a two-sie market. Mialon an Banerjee (2013) stuy how the effects of net neutrality on Internet access (or subscription) price an social welfare crucially epens on the market structure of the content sie. Choi, Jeon, an Kim (2013) evelop a moel of secon-egree price iscrimination in a two-sie market to stuy how the business moels of content proviers affect social welfare with an without the regulation. Jullien an San-Zantman (2013) examine the net neutrality issues in the context of information transmission such as signaling an screening. We fin Peitz an Schuett (2014) more closely relate to our paper though they consier a ifferent type of externality to the network erive from content proviers. They consier socalle congestion control techniques that ecrease packet losses uring elivery to users with an inflation of traffic by sening multiple reunant packets. This practice may be privately optimal but aggravates the congestion problem on the network. They introuce the tragey of common 6

9 property resources into the net neutrality iscussion an show that net neutrality regulation may lea to socially inefficient inflation of traffic whereas the socially optimal allocation can be achieve with tiere pricing. In contrast, our paper investigates the effects of net neutrality regulation on CPs investment incentives in CDN or compression technologies, which ecreases the packet size of iniviual content an generates a positive spillover to the network. Our paper eparts from the earlier literature in several respects. We focus on content proviers incentives to invest in alternative ways of reucing congestion beyon the ISPs network capacity. This is in line with the basic premise in the ebate that en-users quality of service must be the primary goal of a esirable network ecosystem (See Xiao (2008), Altman et al. (2012), an Guo, Cheng, an Banyopahyay (2013)). We show how these alternative mechanisms can be complements or substitutes to network capacity epening on the ISP s capacity limit. Our analysis captures the ifferences between fixe an mobile networks because mobile networks encounter technical an physical constraints in expaning capacity ue to the limite availability of spectrum. It highlights the FCC s asymmetric regulation between the two networks in contrast to the EU s uniform treatment The Moel 2.1 ISP, CPs, an Consumers We consier a monopolistic broaban Internet service provier (ISP) who is in charge of last mile elivery of online content to en-users. 11 Since we are primarily intereste in major content proviers inepenent investment incentives to improve quality of service, we consier two types of content proviers: one major content provier (henceforth, simply referre to as MCP ) such as Google, Netflix, Disney, an Amazon Instant Vieo, an a continuum of other non-major content proviers (simply, NCPs ) whose mass is normalize to one. This istinction allows us to focus on the MCP s investment ecision to improve QoS for a successful content business; the MCP s relatively large scale of operation justifies the costly investment. There is a continuum of homogeneous consumers whose mass is normalize to one. Each 10 See Rea (2012) an Hairong an Reggiani (2011) for the EU s regulatory framework. 11 In reality, the Internet is a network of networks with multiple network service proviers. It is not uncommon that an originating ISP may not be the same as a terminating ISP for complete elivery of content, with several interconnecte network proviers being involve along a transit route. Choi, Jeon, an Kim (2013) aresses the equivalence in network quality choices between interconnecte ISPs an a monopoly ISP. 7

10 consumer emans both the MCP s an NCPs content. When a consumer receives the MCP s content with average waiting time of w, the consumer earns utility u(w) = v kw. (1) where parameter v represents the consumer s intrinsic utility from receiving the MCP s content. The corresponing utility from the NCPs content with an average waiting time of W is given by U(W ) = V W. (2) where V represents the consumer s intrinsic utility from receiving the NCPs aggregate content. Each consumer experiences a isutility from elays of content elivery ue to network congestion. We aopt an aitive utility specification in which the net surplus ecreases in the average waiting time for both types of content. The parameter k 1 measures the relative sensitivity of the MCP s content to elays compare to the NCPs. Since we assume that the mass of consumers is normalize to one, u(w) an U(W ) respectively represent the entire surplus from the MCP s content an the NCPs. We assume that the MCP can extract the entire surplus u(w) in the absence of a priority service uner net neutrality, but it negotiates with the ISP over the price of the priority service in a non-neutral network. 12 For the NCPs content, we introuce a parameter β [0, 1] to enote the ISP s share of the total surplus generate by the NCPs content elivery. In other wors, the ISP receives βu(w ) from proviing elivery services for the NCPs content; the rest of the surplus, (1 β)u(w ), is share among NCPs an en users. The parameter β can be seen as the ISP s ability to extract rent from NCPs an en users via connection fees. Alternatively, one may regar β as a measure of the extent to which the ISP internalizes any externality inflicte on the NCPs an en users by its ecisions. If β = 0, the ISP will not take into account any potential effects on the NCPs content traffic when the ISP eals with the MCP. By contrast, if β = 1, the ISP will fully internalize the externality. As will be clearer later, the parameter β plays an important role in assessing the welfare effects of net neutrality regulations. The private an the social planner s incentives coincie when β = 1 because the ISP fully internalizes any externality create in its ealing with the MCP. However, for any β < 1, there may be a iscrepancy between the ISP s optimal ecision an the social planner s, with the potential for iscrepancy more pronounce with 12 In Section 7.1, we relax the assumption of full rent extraction by the MCP an show that this simplification oes not change our results qualitatively. 8

11 a lower β. 2.2 Network Congestion, CP s Investment an QoS Improvement Users initiate the Internet traffic through their clicks on esire content an become final consumers of the elivere content. As a micro-founation to moel network congestion, we aopt the stanar M/M/1 queuing system which is consiere a goo approximation to congestion in real computer networks. 13 Let µ enote the ISP s network capacity. Each consumer emans a wie range of content from both the MCP an NCPs. The content request rate follows a Poisson process, which represents the intensity of content eman. For the NCPs content, we normalize the arrival rate of the Poisson istribution an the size of packets for each content to one. Since the mass of the NCP is one, the overall eman parameter (i.e., the total volume of traffic) for the NCPs content is also normalize to one. By contrast, we envision the MCP as one iscrete player operating a content network platform that provies a continuum of content whose aggregate packet size is given by λ. 14 Then, we can interpret λ as the sheer volume of the MCP s content or a measure of the relative traffic volume of the MCP s content vis-à-vis the NCPs aggregate traffic volume. The total traffic volume for the ISP thus amounts to 1 + λ. Note that we nee the conition of µ > 1 + λ for a meaningful analysis of network congestion; otherwise, the waiting time becomes infinity. The MCP can make an investment of h 0 to enhance the quality of service in its content elivery. As iscusse earlier, the investment can take various forms, such as compression technology to reuce packet-size or content elivery networks (CDN) that shorten the elivery istance by installing content servers at local ata centers so that en-users emans are serve by the closest ata center. 15 The common objective of all such investments is to spee up content elivery to enhance the user experience. We thus moel them simply as an investment in a compression 13 Choi an Kim (2010), Cheong et al. (2011), Bourreau et al. (2012), Krämer an Wiewiorra (2012) aopt the M/M/1 queuing moel to analyze network congestion. 14 For instance, if the MCP s content mass is ξ an the packet size for each content is m, then we have λ = ξ m. 15 Accoring to Xiao (2008), there are at large three ifferent types of elays that account for the total elay from one en of the network to the other: (1) en-point elay, (2) propagation elay, an (3) link (or access) elay. Increasing spee of bottleneck links can be the most effective approach to aress (3), whereas caching or content elivery networks (CDN) helps to reuce (2). The ISP s capacity expansion at the last mile helps to reuce (1). While the total elay is collectively affecte by all these ifferent types of elays, en-users typically cannot istinguish what type of elay affecte their perceive quality of service. 9

12 technology that woul reuce the traffic volume of the major CP s content from λ to aλ, where a = 1 1+h (0, 1]; more investment leas to a smaller packet size for the MCP s content. Therefore, its elivery spee increases even without the ISP s capacity expansion. No investment (h = 0) correspons to a = 1. We assume that the investment cost is increasing an convex in the investment level, i.e., c (h) > 0 an c (h) > 0, an satisfies the Inaa conition of c(0) = 0 an c (0) = 0 with a fixe cost of investment F ( 0) for any positive investment h > 0. We consier two network regimes: neutral an non-neutral networks. Consistent with the literature an regulatory obligations, we take the availability of a pai prioritize service as the efining characteristic that istinguishes the two network regimes. In the neutral regime, there is no pai prioritization: all traffic is treate equally with every packet being serve accoring to the best-effort principle on a first come, first serve basis. In the non-neutral regime, ISPs are allowe to provie a two-tiere service with the pai priority class packets elivere first. In the neutral network, both the MCP s an NCPs content are elivere with the same spee. More specifically, each user in the M/M/1 queuing system faces the following total waiting time for the major CP s content: w n (a, µ) = 1 µ (1 + aλ) } {{ } waiting time per packet aλ }{{}. total packet size (3) The total volume of traffic (packet size) amounts to 1 + aλ (one for the NCPs content an aλ for the MCP s content with compression), an thus the average waiting time per packet is given by 1 µ (1+aλ) for both types of content. With the packet size of aλ for the major CP s content, the total waiting time is compute as (3). With no investment in the compression technology (h = 0, or a = 1), the average waiting time reuces to 1 µ (1+λ) as in the stanar M/M/1 queuing system. Similarly, for the non-major CP s content, we can erive the total waiting time as W n (a, µ) = because the total packet size for NCPs content is one (4) µ (1 + aλ) Without neutrality obligations, the ISP may aopt a pai prioritization in which the MCP can purchase the premium service at some price to sen its content ahea of the NCPs packets in queue so that the waiting time for the prioritize packets is given by w (a, µ) = 1 aλ. (5) µ aλ 10

13 The faster elivery of the prioritize packets is achieve at the expense of NCPs content. Once the priority service is introuce, the non-prioritize content is elivere at a slower spee; the waiting time for the basic service in the non-neutral network is given by W (a, µ) = µ 1 1. (6) µ (1 + aλ) µ aλ In what follows, when there is no confusion, we often suppress the epenence of a on h with w r (h, µ) = w r (a(h), µ) an W r (h, µ) = W r (a(h), µ), where r = n,. 2.3 Generalize Queuing System an Its Properties Using (3)-(6), we can erive the following set of properties that are not only intuitive but also serve collectively as an important micro-founation for our analysis. Property 1 The major content provier s investment to enhance its own quality of service generates positive spillover into other content in both neutral an non-neutral networks: i.e., W n h < 0 an W h < 0. Intuitively, less use of banwith from one content provier means more network capacity for other content in a given network capacity. Property 2 For a given pair of (a, µ), the prioritization makes the waiting time for prioritize major CP s content shorter, an the waiting time for non-major content longer than the respective ones in the neutral network: i.e., w (a, µ) < w n (a, µ) an W (a, µ) > W n (a, µ). Property 3 For a given pair of (a, µ), the total waiting time is equal regarless of the network regimes: i.e., w n (a, µ) + W n (a, µ) = w (a, µ) + W (a, µ). This result is an extene version of the waiting cost equivalence characterize in Choi an Kim (2010), Bourreau et al. (2012), Krämer an Wiewiorra (2012) in a more generalize queuing system that allows for a content provier s investment for QoS enhancement an its spillover effects. Intuitively, the total waiting time must epen on the network capacity an the total packet size to be elivere whether or not a subset of the packets is prioritize. 11

14 Property 4 For a given pair of (a, µ), prioritizing the major CP s traffic reuces the total elay cost: i.e., kw n (a, µ) + W n (a, µ) > kw (a, µ) + W (a, µ) for any k > 1. This is because the major CP s content is assume to be more sensitive to congestion (k > 1) an the prioritization allocates more congestion-sensitive content to the faster lane. Formally, this property is prove by applying Properties 2 an 3: [kw n (a, µ) + W n (a, µ)] [kw (a, µ) + W (a, µ)] = (k 1)[w n (a, µ) w (a, µ)] > Decision an Bargaining Timings In the neutral network, the MCP s ecisions are straightforwar since it oes not involve a bargaining situation with the ISP. N-1. For a given ISP s network capacity µ, the major CP makes a ecision on whether to enter the market. If the MCP enters, it chooses its investment level h. N-2. For a given (µ, h), content is elivere to consumers an the payoffs are accoringly realize. In the non-neutral network, we nee an aitional stage in which the major CP an the ISP bargain over the price of the prioritize service. D-1. For a given µ, the CP an the ISP bargain over the price of the prioritize service. D-2. With an agreement on the price of the prioritize service, the MCP makes its entry an investment ecisions taking the prioritize service into account. Without a mutual agreement, the prioritize service is not introuce an, as in the neutral regime, all traffic is elivere without any preferential treatment uner the best effort principle. The MCP s entry an investment ecisions remain the same as in the neutral regime. D-3. Given (µ, h) an a priority class, content is elivere to consumers an the payoffs are realize. We assume that the MCP s investment is not contractible in that the MCP an the ISP can agree only on the priority price, but the investment ecision is solely left to the MCP. 3 Optimal QoS Investment an Network Regimes 3.1 Benchmark: First-best We first characterize the first-best outcome (given a network capacity µ) in which the social planner can control the MCP s entry an QoS investment ecisions as well as the network regime. In our 12

15 setup, the comparison of alternative network regimes is meaningful only when the MCP s entry is relevant. If there is no entry, the etermination of the network regime in the first-best outcome is vacuous because there is only one type of content provier. We thus focus on the case in which the social planner inuces the entry of the MCP. Denote the socially optimal QoS investment level in each network regime by h F B r for r = n, that is characterize as follows: h F B r Then, we can establish the following intuitive result. = arg min h r Ψ r (h) = kw r (h) + W r (h) + c(h). (7) Proposition 1 (First-Best Comparison) Suppose that the social planner inuces the entry of the major CP. Then, for k > 1, the first-best non-neutral network is always superior in welfare to the first-best neutral network. Proof. Ψ (h F B ) = kw (h F B < kw n (h F B n ) + W (h F B ) + W n (h F B n ) + c(h F B ) kw (h F B n ) + c(h F n B ) = Ψ n (h F n B ) ) + W (h F n B ) + c(h F n B ) The first line of the above proof is by a reveale preference argument. The secon inequality is base on Property 4. Proposition 1 tells us that the first-best outcome always entails a non-neutral network when the MCP s entry is socially esirable because it allows more efficient traffic management (Property 4). This result suggests that net neutrality regulation can be justifie only as a secon-best policy when the entry an the investment ecisions are left to the private parties. In fact, our subsequent analysis reveals that the secon-best neutral network can offer higher welfare than the secon-best non-neutral network. 3.2 Neutral Networks Let us consier a neutral network in which all packets are equally treate base on the first-comefirst-serve principle. As usual, we procee with backwar inuction an istinguish two subgames epening on whether or not the MCP has entere. provier s optimal choice of h is to maximize its profit: Assuming the MCP s entry, the content max h 0 π n = v kw n (h, µ) c(h) F, 13

16 where w n (h, µ) = λ (µ 1)(1+h) λ π n h from (3). The first orer conition with respect to h becomes = h n kλ(µ 1) [(µ 1)(1 + h) λ] 2 c (h) = 0, (8) for an interior solution h n. The marginal benefit of the investment ecreases in the ISP s network ) capacity, which is easily confirme by the cross-partial erivative < 0. Let π n (µ) π n (h n(µ), µ) enote the maximize profit of the MCP at the optimal investment level h n(µ) for a given network capacity µ. By the Envelope Theorem, we fin that the MCP obtains a higher profit as the network capacity increases: πn µ = π n µ = k w n(h n, µ) µ µ ( πn h λ(1 + h = k n) [(µ 1)(1 + h > 0. (9) n) λ] 2 This relationship implies that a threshol network capacity µ n exists such that π n(µ) 0 if an only if µ µ n. In other wors, the MCP makes an investment only when the ISP s capacity is above this threshol level. For a sufficiently low capacity µ < µ n, the investment cost is too high to justify entry into the content service market. Hence, there is a iscontinuity in the MCP s investment at the threshol value µ n : no investment for µ < µ n but h n > 0 for µ µ n. Furthermore, we analyze how the (interior) optimal investment h n changes with the capacity level for µ > µ n an establish the following lemma: Lemma 1 The MCP s QoS investment ecreases in the ISP s network capacity µ, i.e., h n µ < 0 for µ µ n. Proof. See the Appenix. We can illustrate the optimal QoS investment in the neutral network as in Figure 1: h n = 0 for µ < µ n an then h n > 0 an h n µ < 0 for µ µ n. 3.3 Non-neutral Networks Now let us consier the non-neutral network in which the MCP has an option to buy the prioritize elivery service at a negotiate price. One benefit of such an arrangement is that the MCP can achieve the same quality of service with a lower investment in the compression technology ue to a preferential treatment of its content elivery. The analysis for the non-neutral network procees similarly as in the neutral network. Suppose that the MCP an the ISP agree on a price of the prioritize service. We efine the MCP s profit gross of any payout for the priority as π u kw (h, µ) c(h) F, 14

17 Figure 1: Optimal QoS Investment in the Neutral Network where w (h, µ) = λ µ(1+h) λ. The first orer conition for the MCP s optimal investment ecision with the prioritize service (h ) yiels the following equation: π h = h kλµ [µ(1 + h) λ] 2 c (h) = 0. (10) As in the neutral network case, by efining π (µ) π (h (µ), µ), we can show that the maximize profit increases in the network capacity, i.e., π µ = π µ = k w (h, µ) µ λ(1 + h) = k [µ(1 + h) λ] 2 > 0, an the optimal investment ecreases in the capacity, h µ < 0.16 Note that while the investment ecision h is inepenent of β, the price of prioritization must be affecte by the level of β because the pai prioritization will make the ISP earn less from NCPs content ue to increase elay for non-prioritize content. The ISP woul ask for compensation from the MCP for the loss via the priority price. The ISP s incentive to provie the prioritize service woul be higher as β becomes smaller. In this section, we analyze the case of β = 0, in which the MCP s entry is facilitate to the maximum extent, an relegate the analysis of β > 0 to the next section. 17 In particular, if β = 0, the ISP an the major content provier will agree on some price of prioritization whenever π (µ) > 0. As the MCP s profit π (µ) strictly increases with µ as in the neutral network, there will be another threshol capacity µ such that π (µ) 0 if an only 16 The proof is omitte as it is similar to the process leaing to Lemma 1 in Section We formally erive this result in the next section (see Lemma 5). 15

18 if µ µ. Again, the MCP s investment iscretely jumps up at the threshol µ, then ecreases with µ for µ > µ. Because π (µ) > π n(µ) an π (µ) increases in µ, we must have µ n > µ. The last step neee to compare h n an h is to verify that the marginal benefit of the QoS investment is greater in the neutral network compare to that in the non-neutral network. The reason is that the marginal benefit from reucing the content elivery size increases with the severity of congestion in the network, as is shown below. π n h > π h because we have w n(h) = Consequently, we establish the following lemma: λ(µ 1) [(µ 1)(1 + h) λ] 2 > λµ [µ(1 + h) λ] 2 = w (h). Lemma 2 The major CP reuces its QoS investment with the purchase of the prioritization service, i.e., h n(µ) > h (µ), for all µ > µ n. 3.4 Mobile/Fixe Networks an QoS Investments Base on Lemmas 1-2, we can summarize the major CP s optimal investment ecisions for β = 0 in the following Proposition. Proposition 2 Suppose β = 0. (i) For a limite network capacity of µ [µ, µ n ), a pai prioritization an the MCP s investment are complements in that prioritization inuces the MCP to enter an make a positive investment, whereas the major CP oes not enter in the neutral network. (ii) For a larger capacity µ > µ n, prioritization an the MCP s investment are substitutes in that purchasing prioritization reuces the major CP s QoS investment, compare to the investment that woul be mae in the neutral network. We illustrate the optimal QoS investments in both network regimes in Figure 2. The upwar arrow for the range of µ < µ < µ n epicts the greater QoS investment uner the non-neutral network compare to the neutral network. The ownwar arrow when µ > µ n shows the smaller investment with the pai prioritization. Intuitively, the prioritization reuces the QoS investment incentives because it provies an alternative technological solution to achieve the esire level of QoS. Our analysis on the content provier s entry an investment ecisions offer a framework to assess the US FCC s asymmetric regulation across fixe an mobile networks. For mobile networks, 16

19 Figure 2: The QoS Investments an Mobile/Fixe Networks there is a heightene concern for congestion an the entry of high-banwith content an complex applications can be facilitate with the availability of the prioritize service. The mobile networks encounter technical an physical constraints in expaning capacity ue to the limite availability of spectrum whereas such constraints are not much of a restriction in fixe networks. In the remainer of the paper, we thus take the limite capacity case of µ (µ, µ n ) as a representation of mobile networks an the high capacity case of µ > µ n as a representation of fixe networks. 4 Mobile Networks In this section, we analyze the effects of net neutrality regulation on various participants in the mobile network with µ (µ, µ n ),with a particular focus on social welfare. As in the previous section, we characterize the mobile network as a limite capacity case in which the MCP makes no entry uner the neutral regime because π n(µ) < 0 for µ < µ n but is able to enter with pai prioritization in the non-neutral network (at least for β = 0). 4.1 Effects of MCP s Entry on NCPs Uner non-neutral network, the MCP s entry has two countervailing effects. On one han, the new content generates a surplus of π (µ) > 0, which can be share by the content provier an the ISP accoring to their respective bargaining powers. On the other han, the entry exacerbates the congestion in the existing non-major content traffic through the following two channels. The aitional banwith taken by the new MCP s content means more congestion for a given network 17

20 capacity. In aition, the prioritize elivery of the MCP s content means a slower elivery for NCPs content that is now relegate to the non-prioritize, slow lane. Formally, we examine the ifference in waiting time for the non-major CPs content with the introuction of a two-tiere service, W, that can be ecompose into two parts. W W (h (µ), µ) W n(φ, µ) = [W n (h (µ), µ) W n(φ, µ)] + [W } {{ } (h (µ), µ) W n(h (µ), µ)], } {{ } (+) ue to new content entry (+) ue to ifferent priority classes (11) where φ stans for no entry by the MCP. The first brackete term in (11) measures the increase in elivery time even in the absence of prioritization ue to increase traffic volume with the entry of the major CP the Internet pipe now nees to be share with the major CP. The secon one captures the non-major content s waiting time increase ue to the prioritization for a given QoS investment h. On both accounts, NCPs suffer from longer elivery time, i.e., W > 0. We confirm this intuition formally by showing that W = a [ λ (2µ a λ 1) µ (1 + a λ) ] (µ a λ) (µ 1) > 0 for any a (0, 1]. 4.2 Effects of Prioritization on the ISP an Social Welfare We now examine the ISP s incentives to provie the prioritize service in the non-neutral regime an the overall welfare effects of prioritization. The prioritize service will be provie to the MCP an its price will be agree upon between the ISP an the MCP if their joint profits increase with the service. The joint profits uner the neutral regime will be given by Π n (φ, µ, β) = β[v W n (φ, µ)] in the mobile network because there is no entry by the MCP. With the priority service in the non-neutral network, their joint profits are given by Π (h, µ, β) = π (h, µ) + β[v W (h, µ)]. The change in joint profits ue to introuction of the prioritization can be written as follows: 18 Π m (µ, β) Π (h (µ), µ, β) Π n(φ, µ, β) = π (µ) β W (µ), (12) where the superscript m in Π m stans for the mobile network. Expression (12) clearly shows the trae-off associate with the prioritization in the mobile network. The MCP s entry generates the value of π (µ) but the ISP must bear the loss of β W (µ) ue to the negative effects on the NCPs. Note that Π m (µ, 1) captures the change in social welfare from the major CP s entry uner the non-neutral network. One immeiately sees that private incentives to introuce prioritize service 18 Note that W oes not epen on β because h is inepenent of β. 18

21 are thus excessive from a social planner s point of view. The iscrepancy between the private an social incentives can be represente by (1 β) W (µ), which is inversely relate to β. If β = 1, the ISP completely internalizes the effects on consumers an NCPs, with the private an social incentives coinciing. Recognizing that the welfare effects of prioritization an private incentives to provie prioritization crucially epen on the network capacity (µ), we nee to examine how Π m (µ, β) changes with µ for a given β. First, we analyze the effects of a higher network capacity on congestion. Consier the effect of network capacity (µ) on the waiting time for the MCP s content in the non-neutral network (w ). w (h (µ), µ) µ = w (h (µ), µ) µ + w (h (µ), µ) h h µ. (13) A higher network capacity has irect positive effects on the quality of service, which is represente by the first term on the RHS in (13). However, there are also inirect negative effects which counteract the irect effects on the waiting cost: the major CP respons to a higher network capacity by reucing its QoS investment. Nonetheless, we establish in Lemma 3 that the positive irect effects ominate the negative inirect effects. Lemma 3 The waiting time in the non-neutral network ecreases as the network capacity increases regarless of the priority class: (i) w (h (µ), µ) µ < 0; (ii) W (h (µ), µ) µ < 0. Proof. See the Appenix. We now analyze the private incentives to introuce prioritize service in the non-neutral network. From (12) an Lemma 3(i), it is clear that Π m (µ, β) strictly increases in µ for β = 0 for any k 1, an by continuity this result hols for small enough β. Even if β is not sufficiently small, we can still establish that the private incentives to introuce prioritize service increase with network capacity if k, the elay sensitivity parameter for the MCP s content, is sufficiently large. Lemma 4 There exists k(µ, β) such that for k k(µ, β), Π m (µ, β) strictly increases in µ. Proof. See the Appenix. The basic intuition for Lemma 4 is that as k increases, the ability to access the fast lane by the MCP s content offers a greater benefit of allocating more congestion-sensitive content to the faster 19

22 lane while the negative externality on NCP s content is inepenent of k. In aition, because only a proportion β of the externality is internalize by the ISP, if β is small enough, the ISP an the major CP are not much affecte aversely by the prioritization. In such a case, the prioritize service will be provie an the MCP will enter even when k is close to one. Now let us efine µ (β) as the cutoff capacity above which the MCP enters an below which there is no entry: the cutoff capacity efine for β = 0 in Section 4 is enote by µ (0) = µ. The MCP s investment h (µ) oes not epen on β, given its entry. Because [W (h (µ); µ) W n(φ; µ)] < 0 is a constant (inepenent of β), the joint surplus conitional on the MCP s entry strictly ecreases with β for a given µ, which yiels the following: Lemma 5 Suppose k k(µ, β). Then, µ (β) strictly increases with β. Any entry uner µ < µ (1) is socially harmful, an Lemma 5 tells us that for β < 1, such excessive entry can occur. This is because the coalition of the ISP an the major CP oes not fully internalize the negative externality of increase congestion onto the non-major content. Using Lemmas 4-5, we obtain the following Proposition. Proposition 3 (Mobile Networks) Consier the mobile network with µ [µ, µ n ). k k(µ, β). Suppose (i) Given β, the pai prioritization with two-tiere service inuces the MCP s entry with congestionsensitive content as long as µ µ (β), where µ (β) strictly increases with β an µ (0) = µ. (ii) If µ (1) < µ n, the MCP enters ue to the prioritization though the entry is not socially esirable for µ (µ (β), µ (1)). But, the entry is socially efficient for µ (µ (1), µ n ). 19 Figure 3: Social Efficiency an Private Entry Decision 19 If µ n < µ (1), there is no socially efficient entry ue to the prioritization. 20