Surplus extraction by network providers: Implications for net neutrality and innovation

ARTICLE IN PRESS Telecommunications Policy 32 (2008) 545–558

Contents lists available at ScienceDirect

Telecommunications Policy URL: www.elsevierbusinessandmanagement.com/locate/telpol

Surplus extraction by network providers: Implications for net neutrality and innovation Gireesh Shrimali  Indian School of Business, Room 6115, Gachibowli, Hyderabad 500032, India

a r t i c l e in fo

Keywords: Net neutrality Surplus extraction Innovation Dynamic effects Internet Stackelberg game

abstract This paper looks at surplus extraction by network providers who control the medium of information transfer between application developers and consumers, and addresses the following questions: is net neutrality beneficial to society? and does providing network providers flexibility in pricing stunt innovation in the long run? To answer the first question, it looks at a market consisting of a monopoly network provider and two application providers with non-substitutable products, using a simple single period model. It shows that net neutrality is necessary to ensure maximal benefit to the society. To answer the second question, the paper shows that a monopoly network provider, if allowed complete flexibility in pricing, does not necessarily stunt innovation. Looking at a market that consists of one network provider and one application provider, and using a simple multi-period model, it shows that given maximum flexibility the network provider not only encourages innovation when the potential benefits are sufficiently high but also maximizes surplus. This paper takes the view that the topic of net neutrality is not only controversial but also complicated, and suggests that policy makers use a balanced approach based on sound analysis. & 2008 Elsevier Ltd. All rights reserved.

1. Introduction In the Internet, the network is (the infrastructure) used to transfer the actual data used to run applications, such as the web, that the users are interested in. These applications are developed by application providers who, in most cases, are separate from the network providers. Due to their control over the critical infrastructure element, the network providers may be tempted to extract as much surplus as possible from the consumers and, in particular, from the application providers. There is widespread concern that such behavior from the network providers may not only result in reducing social surplus but also in stunting innovation due to reduced surplus for the application providers. This brings up the important policy question of whether the network providers should be restricted in pricing the consumers as well as the application providers. Net neutrality (Wikipedia, 2007) has become a controversial issue in recent times. There are various definitions in the literature, ranging from absolute non-discrimination (Wu, 2003) to limited discrimination without QoS tiering (Dorgan, 2007) to limited discrimination and tiering (Lee, 2006a, 2006b). Similar to its definitions, the literature on net neutrality is extensive. Proponents argue in favor of net neutrality based on property rights (Lessig, 2004; Wu, 2003) as well as on lack of benefits from abandoning the principle of standardized, open communications network (Roycroft, 2006). Opponents argue against net neutrality not only because it may not be necessary in the absence of clear harm (McTaggart, 2006;  Tel.: +91 40 2318 7155.

E-mail address: [email protected] 0308-5961/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.telpol.2008.06.005

ARTICLE IN PRESS 546

G. Shrimali / Telecommunications Policy 32 (2008) 545–558

Thierer, 2004), but also because it may amount to price regulation resulting in reduced investment incentives (Ford, Koutsky, & Spiwak, 2006; Hahn & Wallsten, 2006). Finally, Peha (2006) and Weitzner (2006) argue that a balanced approach regarding net neutrality is required since it is clearly a two-edged sword. Before proceeding further, given numerous definitions in literature, it is critical to clarify what is meant by net neutrality in the context of this paper. It is defined as non-discriminatory pricing (Dorgan, 2007; Lee, 2006a, 2006b; Wikipedia, 2007; Wu, 2003). A distinction between network quality (of service) and product quality is necessary to explain this further. Network quality is defined as the performance guarantees available at the network level, whereas product quality is defined as the quality of the product as perceived by the customers (it may or may not depend on network quality). For example, network quality may be reflected in bandwidth guarantees provided by network providers. It is assumed that network providers do not discriminate based on quality of network service and application providers share the same network with the same network quality of service, also known as best effort service. The application providers can then differentiate themselves based on the quality of their products. For example, Yahoo! and Google may differentiate themselves based on search engines running on the best effort network provided by AT&T. Then, net neutrality simply means that network providers do not discriminate between application providers that potentially provide different quality products on the shared network infrastructure. There are two dimensions to price regulation. The first dimension is related to investigating the effects of differential access pricing across application providers. The second dimension is related to investigating surplus extraction and its effects on innovation. This paper is then mainly interested in the following questions: first, if a network provider is in a monopoly position, would allowing it complete freedom in pricing be bad from the perspective of the society? and second, would a monopoly network provider, if allowed complete freedom in pricing, stunt innovation in the long run? Note that the first question assumes that the issue of net neutrality is relevant only when a network provider is in a monopoly position and it can discriminate among application providers. In this situation, when an application provider with a higher-quality product makes higher profits, the network provider may want a share of the same (Wikipedia, 2007). This is indeed the case—Section 3.2 verifies that net neutrality is a non-issue when there is competition in the network market. In this context, it becomes important to perform economic analysis of the interaction between consumers, network providers, and application providers to provide insights into the impact of price regulation imposed on network providers. The topic is controversial and the policy makers need to expose themselves to arguments on both sides. This paper takes the view that using a balanced approach based on sound analysis may be the way to go. To do so, the interaction among consumers, application providers and network providers is studied using a simple model where the application providers charge consumers for using the applications and the network providers charge the application providers for accessing the network. Various combinations of the application and network market structures are modeled and important structural properties are investigated. Since the primary focus is on the behavior of the network providers, it is assumed that1 Assumption 1. The application provider is a monopoly in the market where it sells its product. To answer the first question, Section 3.1 examines whether net neutrality is beneficial in a static setting, using a single period model of a market with one network provider and two application providers providing non-substitutable products. Non-differential pricing (where the network provider is not allowed to discriminate among application providers) is shown to result in a higher social surplus compared with the case where the network provider is allowed to use price discrimination. That is, net neutrality is beneficial for the society. However, Section 3.2, argues that net neutrality is a nonissue in markets with multiple network providers since, due to price competition, the network providers have no control over the extraction of social surplus. To answer the second question, Section 4 looks at a simple market with one network provider and one application provider in a realistic multi-period model that takes market dynamics into account by allowing the product quality in later stages to depend on the application provider’s profits in earlier stages. It is shown that, given maximum flexibility (i.e., the ability to optimize over multiple periods by charging different access prices), the network provider, acting in self-interest (it maximizes long-term discounted profits), sets the access charges in the non-terminal periods lower than they would be in the presence of various restrictions. By doing so, it passes more of the social surplus to the application provider, encouraging higher investment in product quality. That is, in a dynamic setting, the network provider promotes innovation. In particular, Propositions 3 and 4 establish that, given maximum flexibility, the network provider completely subsidizes the application provider by charging zero access prices in all but the last period, provided the potential benefits are sufficiently high. By doing so, in the non-terminal periods, it passes the whole social surplus to the application provider. In addition, comparing various profits and social surplus, Propositions 7, 8, and 9 establish that allowing maximum flexibility to the network provider is preferred not only by the society as a whole but also by the application provider. The model in this paper (Section 2) is influenced by Farrell (2007), who examines separate network and application markets and shows that, though an unregulated monopoly network provider has ex ante incentives to organize service innovation efficiently, this incentive breaks down ex post. However, the similarities end at the level of the model since 1 The results are robust with respect to this assumption. Similar results can be obtained for the case when there is perfect competition within distinct application markets with different quality products.

ARTICLE IN PRESS G. Shrimali / Telecommunications Policy 32 (2008) 545–558

547

Application providers p

a Network providers

Consumers Fig. 1. The model.

Farrell (2007) does not address the specific questions raised in this paper. Bauer (2006) is similar to this paper in that he asserts that a choice between different governance options should be based on a detailed evaluation of not only static but also dynamic efficiency implications, as performed in this paper. 2. The model The setup is introduced using a market with one network provider and one application provider. The interactions among various players are as depicted in Fig. 1. The application provider delivers an innovative product to consumers at quality q and price p, using the infrastructure provided by the network provider. The cost of providing the product is given by the function C(q). A consumer’s payoff is given by the quasilinear function V(p, q) ¼ U(q)p, where U(q) denotes consumer utility at quality q, with U0 (  )X0. The consumer demand takes the form X(V(p, q)) ¼ X(U(q)p), where X0 (  )X0. The network provider cost is given by N(X), with N0 (  )X0 and the network provider charges the application provider an access charge a.2 Here it is implicitly assumed that Assumption 2. The quality of product offered to the customer does not affect the network provider cost directly. However, it affects the network provider cost indirectly through the consumer demand. This is precisely what happens in the Internet today: for example, consumers access the Google search engine over the best effort AT&T network, and the cost to the network is due to the amount of traffic created by the consumers and not due to the quality of the Google search engine itself.3 Next, the baseline interaction between the market, the application provider and the network provider is investigated, with focus on provider profits. This will serve as the basis for the analysis in Sections 3 and 4. 2.1. The Stackelberg game The analysis is simplified by looking at linear forms of many of the functions defined above.4 In particular, it is assumed that Assumption 3. The consumer demand and network provider costs are linear functions. That is, XðUðqÞ  pÞ ¼ x½UðqÞ  p

(1)

NðXðUðqÞ  pÞÞ ¼ nx½UðqÞ  p,

(2)

where n; x 2 Rþ . 2

The network provider may also charge the consumers an access price, which turns out to be irrelevant in the analysis. This assumption may not hold in cases where the network services evolve beyond best effort and provide quality of service guarantees, which may directly impact the network provider cost. However, this assumption suffices for the purpose of this paper since it is assumed that the network provider does not discriminate based on network quality of service. 4 It is possible to use general, nonlinear forms. However, it would take significantly greater effort to extend the analysis. These linear forms, though simple, provide valuable insights. In addition, the linear approximation to network costs may be justified on the following grounds. The network costs are usually convex functions. In case of low network loads—a characteristic of networks today (Odlyzko, 2003)—the convex function is very closely approximated by a linear function. In general, convex functions can be approximated by piece-wise linear functions. Our linear form may also be taken as the approximation in the region of interest—for example, near the optimal operating point. 3

ARTICLE IN PRESS 548

G. Shrimali / Telecommunications Policy 32 (2008) 545–558

The profits of the application provider J and network provider M as well as the social surplus, denoted by pJ, pM and pS, respectively, can then be written as

pJ ¼ ðp  aÞXðUðqÞ  pÞ  CðqÞ ¼ x½UðqÞ  pðp  aÞ  CðqÞ

(3)

pM ¼ aXðUðqÞ  pÞ  NðXðUðqÞ  pÞÞ ¼ x½UðqÞ  pða  nÞ

(4)

pS ¼ UðqÞXðUðqÞ  pÞ  CðqÞ  NðXðUðqÞ  pÞÞ ¼ x½UðqÞ  p½UðqÞ  n  CðqÞ.

(5)

In order to ensure positive social surplus, it is also assumed that Assumption 4. U(q)4n. The following useful lemma is then obtained (the proofs of all the results are included in the Appendix). Lemma 1. Under monopolies in both application and network markets, and in presence of linear demand and network cost. UðqÞXpXaXn

(6)

The following sequence of decisions is examined. First, the network provider fixes a. Second, the application provider fixes p for a fixed q. q is assumed to be either fixed (as in the single period model) or a dependent variable (as in the multiperiod model). Finally, consumers respond to p to create demand X. Due to monopolies in the application and network markets, this interaction can be analyzed using the standard Stackelberg approach. The network provider chooses an a knowing how the application provider would fix p in response and the application provider chooses a p knowing how the consumer demand would pan out in response. Solving for the Stackelberg equilibrium, the following result is obtained. Proposition 1. Under monopolies in both application and network markets, the Stackelberg prices are given by aN ¼

½UðqÞ þ n 2

(7)

pN ¼

½3UðqÞ þ n . 4

(8)

In addition, the equilibrium profits and social surplus are given by   UðqÞ  n 2 pNJ ¼ x  CðqÞ 4

pNM ¼ 2x



UðqÞ  n 4

2

  UðqÞ  n 2  CðqÞ. 4

pNS ¼ 4x

(9)

(10)

(11)

3. When is net neutrality necessary? This section looks at two different markets in a static, single-stage model. Section 3.1 shows that net neutrality is beneficial in a market with a monopoly network provider. Section 3.2 shows that net neutrality is not necessary in a market with competition in the network market. 3.1. One network provider and multiple application providers This section answers the following question: assuming that the network provider has the freedom to charge different access prices, among the various providers (network provider, application providers and the social planner), who prefers different access charges and who does not? To do so, it looks at a market with monopoly network provider M and application providers J1 and J2 providing products of quality q1 and q2, respectively. 3.1.1. Differential access pricing This subsection analyzes the case where the network provider M charges application providers J1 and J2 access prices a1 and a2, respectively. Since the application providers’ problem does not change, they charge consumers according to (40), i.e., pi ¼ ([U(qi)+ai]/2). M’s profits are now given by

pM ¼

2 2 X xX ðai X i  nX i Þ ¼ ½Uðqi Þ  ai ðai  nÞ. 2 i¼1 i¼1

ARTICLE IN PRESS G. Shrimali / Telecommunications Policy 32 (2008) 545–558

549

From the first-order conditions, similar to (7) and (8) aN i ¼

½Uðqi Þ þ n 2

(12)

pN i ¼

½3Uðqi Þ þ n , 4

(13)

for iA{1, 2}. Then, the provider profits and social surplus are given by, similar to (9)–(11) and (3)–(5)

pN;diff ¼ M

pN;diff ¼ S

2 xX ½Uðqi Þ  n2 8 i¼1 2 h X x i¼1

4

i fUðqi Þ  ng2  Cðqi Þ .

(14)

(15)

3.1.2. Same access pricing This subsection analyzes the case where the network provider charges the same access price a. Again, it is straightforward to obtain pi ¼ ([U(qi)+a]/2). M’s profits are given by

pM ¼

2 2 X xX ðai X i  nX i Þ ¼ ½Uðqi Þ  aða  nÞ, 2 i¼1 i¼1

and the first-order condition gives aN ¼

½Uðq1 Þ þ Uðq2 Þ þ 2n 4

(16)

pN i ¼

½5Uðqi Þ þ Uðqj Þ þ 2n . 8

(17)

The provider profits and social surplus are then given by, similar to (9)–(11)

pN;same ¼ M

pN;same ¼ S

2 x X x ½Uðq1 Þ þ Uðq2 Þ  2n2 ½3Uðqi Þ  Uðqj Þ  2n½Uðqi Þ þ Uðqj Þ  2n ¼ 32 i¼1 16 2 X ½xfUðqi Þ  pi gfUðqi Þ  ng  Cðqi Þ.

(18)

(19)

i¼1

3.1.3. Who prefers what From the previous two subsections, the following result is obtained. Proposition 2. Under monopolies in both application and network markets the higher-quality application provider and society prefer non-differential access pricing, whereas the lower-quality application provider and the network provider prefer differential access pricing. This result is significant because it shows that price discrimination, though preferred by the network provider (as expected) as well as the application provider with inferior quality product, is not preferred by the application provider with superior quality product and by the society as a whole. That is, net neutrality is beneficial to the society. 3.2. Multiple network providers Since the application providers are innovators and their products do not compete (Assumption 1), the analysis is independent of the number of application providers, and the focus can be on the case with one application provider. In this case, the network providers compete on prices and, due to Bertrand competition, a ¼ n, independent of the size of the consumer base. Then, the price set by the application provider would be given by, from (40), pN ¼ ((U(q)+n)/2). The equilibrium profits would then be given by     UðqÞ  n 2 UðqÞ  n 2 pNJ ¼ 4x  CðqÞ; pN pNS ¼ 8x  CðqÞ. M ¼ 0; 4 4 That is, compared with the case where both markets are monopolies, the profit of the application provider as well as social surplus are higher. In fact, if C(q) ¼ 0, these are four times and twice, respectively. This is due to elimination of double marginalization by Bertrand competition in the network market.

ARTICLE IN PRESS 550

G. Shrimali / Telecommunications Policy 32 (2008) 545–558

4. Dynamic effects: innovation and social surplus This section answers the following question: assuming that the provider interaction is dynamic and the innovator’s (application provider’s) future quality depends on current profits, what would be the impact of restricting access prices on the profits of various providers? To do so, various pricing options for the network provider are examined in a two period model in Sections 4.1–4.3. Three cases that capture the behavior of the network provider under the presence of various restrictions are examined. Section 4.1 looks at the case where the network provider is allowed to price differently over periods but is not allowed to optimize across periods. Section 4.2 looks ast the case where the network provider is allowed maximum freedom, i.e., it is allowed to optimize across periods as well as to price differently over periods. Section 4.3 looks the case where the network provider is allowed to optimize across periods but is not allowed to charge differently over periods. It is shown that, when allowed maximum freedom, the network provider may subsidize the application provider in the non-terminal periods by setting zero access prices, provided that the potential benefits are high enough (Propositions 3 and 4). Finally, these options are compared in terms of preferences of providers as well as of the society in Section 4.4. While the obvious result that the network provider prefers the most freedom (Proposition 7) is obtained, Propositions 8 and 9 show that even the application provider and the society may prefer non-myopic, non-differential pricing. For most of this section, the focus is on the following two period model. In each period, the network provider sets an access price ai followed by the application provider setting a consumer price pi. The quality of the product is denoted by q1 in the first stage and q2 in the second stage, with q2 ¼ q1 þ aq pN J;1 where a40 and pN J;1 is the application provider profit in stage 1. q1 is assumed to be exogenously determined, as in the rest of the paper. Due to the multiple-stage nature of the interaction, many (complicated) game forms are possible where the application and network providers both anticipate each other’s earlier stage behavior at later stages. In addition, the application provider may vary aq across stages in order to maximize its overall profit. However, since the focus is on determining the effects of allowing freedom to the network provider, it is assumed that Assumption 5. In any stage, the application provider responds to an access price independently of other stages. In addition, the parameter aq is exogenously determined. That is, the application provider does not optimize across stages and it controls only the prices charged to customers. Then, assuming linear functions of form (1) and (2) (Assumption 3), from (40), the application provider would set pi ¼ (U(qi)+ai)/2, iA{1,2} and, from (9)–(11) "  #  Uðq1 Þ  a1 2  Cðq1 Þ (20) q2 ¼ q1 þ aq x 2 with N

dpJ;1 aq x½Uðq1 Þ  a1  dq2 . ¼ aq ¼ 2 da1 da1

(21)

4.1. Myopic differential access pricing If the network provider does not account for the influence of the first-stage access price on second-stage profits, it n=2 and pN would optimize for each stage profits independently to deliver, similar to (7)–(8) aN i ¼ ½Uðqi Þ þ P i ¼ ½3Uðqi Þ þ n=2, N with the equilibrium profits and social surplus, derived in a manner similar to (9)–(11), pJ ¼ 2i¼1 x½ðUðqi Þ  nÞ=42  Cðqi Þ, P P pNM ¼ 2i¼1 2x½ðUðqi Þ  nÞ=42 and pNS ¼ 2i¼1 4x½ðUðqi Þ  nÞ=42  Cðqi Þ. To further simplify analysis and to obtain valuable 5 insights it is also assumed that Assumption 6. Consumer utility is a linear function of quality. In addition, the application provider cost to develop the product is zero. That is, U(q) ¼ uq and C(q) ¼ 0. ~ ¼ w=4, the provider profits can be written as With this assumption in hand, denoting w ¼ uq1n, w    ua x 2    ua x 2 2 ua x q ~ ~ þ ~ ~2þ w ~ þ q w ~2 2þ q w w pNJ ¼ x w ¼ xw 4 2 4

(22)

5 Note that the linear utility assumption is in line with Assumption 3 and that any relaxation may require significant effort. The zero application cost assumption is not very crucial—similar results can be derived with C(q) ¼ cq instead of C(q) ¼ 0. However, again the underlying analysis gets complicated very quickly.

ARTICLE IN PRESS G. Shrimali / Telecommunications Policy 32 (2008) 545–558

551



ua x 2  uaq x q ~ þ ~ w w ¼ 2pJ 2 4

(23)



ua x 2  uaq x q ~ þ ~ w w ¼ 4pJ . 2 4

(24)

~2 2þ pNM ¼ 2xw ~2 2þ pNS ¼ 4xw

N N N That is, pN M ¼ pS =2 and pJ ¼ pS =4. Having established this baseline behavior of the network provider, the scenarios where the network provider accounts for the influence of the first-stage access price on second-stage profits are investigated next.

4.2. Non-myopic differential access pricing If M sets different access prices ai in the two stages, assuming the discount factor is 1

pM ¼

2 X

pM;i ¼ x

i¼1

2 X ½Uðq Þ  ai ðai  nÞ i

i¼1

2

with the necessary conditions, derived in a manner similar to (6) Uðqi ÞXpi Xai

(25)

Uðqi ÞXn,

(26)

iA{1,2}. Then the following result is obtained. Proposition 3. Under monopolies in both application and network markets

 if a~ wX2:48,6 the first period access price is set to zero, and  if a~ wp2:48, the first period access price satisfies sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð8  a~ wÞ 4w puq1  paN;2p 1 ð8  a~ wÞ 3a~ 2

uq1  2

(27)

where w ¼ ðuq1  nÞ, v~ ¼ ðuq1  a1 Þ=2, a~ 2 ¼ ðuaq xÞ2 X0, b ¼ a~ w  8, and g ¼ 2w. In addition, various profits are given by 2 !2 3 ~ v~ 2 w þ a 2 N 5 (28) pJ ¼ x4v~ þ 4 2

N M

p

w þ a~ v~ 2 ¼ x4v~ ð2v~  wÞ þ 2 4

!2 3 5

pNS ¼ 2pNJ þ pNM .

(29)

(30)

This result is instructive in the following way. When a~ wX2:48 the network provider sets the first-stage access price as zero. This essentially means incurring a loss of ðxuq1 nÞ=2 in the first stage. However, this is optimal for the network provider since, by doing so, it increases the profit of the application provider and encourages investment in subsequent stages. The network provider then extracts as much social surplus as possible in the second stage—which more than makes up for the first-stage loss, as shown in Proposition 7. Proposition 3 shows that the network provider would subsidize the application provider in the first period, provided the potential benefits are much higher than the application cost. It can be further extended to a more general k42 period case. If M sets different access prices ai in k stages, assuming the discount factor is 1

pM ¼

k X

pM;i ¼

i¼1

k xX ½Uðqi Þ  ai ðai  nÞ, 2 i¼1

with the necessary conditions, derived in a manner similar to (6) Uðqi ÞXpi Xai

(31)

Uðqi ÞXn,

(32)

iA{1, y, k}. Then the following result is obtained. 6

a~ wX2:48 is a combination of a~ wX8 and 2:48pa~ wp8.

ARTICLE IN PRESS 552

G. Shrimali / Telecommunications Policy 32 (2008) 545–558

Proposition 4. Under monopolies in both application and network markets, if a~ wX8 then the access prices for the first k1 stages are zero, where a~ and w are as defined in Proposition 3. This result is instructive in the following way. When a~ wX8, setting zero access prices and incurring losses in stages 1, y, k1 is optimal for the network provider. By doing so, it increases the profit of the application provider and encourages investment in subsequent stages—note that the quality grows super-exponentially in stages 2, y, k since qj ¼ qj1 þ j1 ððaq xu2 Þ=4Þq2j1 ; j 2 f2; . . . ; kg results in qj ¼ Yðq21 Þ; j 2 f2; . . . ; kg. The network provider then extracts as much social surplus as possible in the last stage—which more than makes up for the losses in the previous stages. 4.3. Non-myopic non-differential access pricing If M sets the same access price a in both stages, assuming the discount factor is 1, its profits can be written as   Uðq1 Þ þ Uðq2 Þ a , pM ¼ pM;1 þ pM;2 ¼ xða  nÞ 2 with the necessary conditions, derived in a manner similar to (6) Uðqi ÞXpi XaXn;

i 2 f1; 2g.

(33)

Then the following result is obtained. Proposition 5. Under monopolies in both application and network markets, the two period access price is given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b þ b2 þ 8aw , aN;2p ¼ uq1 

a

and various profits are given by  ua xv2  q pNJ ¼ xv2 2 þ uaq xv þ 2 

pNM ¼ xðw  2vÞv 2 þ

uaq xv 2

pNS ¼ 2pNJ þ pNM ,

(34)

(35)

(36) (37)

where w ¼ ðuq1  nÞ, v ¼ ðuq1  aÞ=2, a ¼ 3a~ ¼ 3uaq xX0, b ¼ ððawÞ=3Þ  8 ¼ a~ w  8, and g ¼ 2w. The following proposition is also obtained. Proposition 6. Under monopolies in both application and network markets, the access charge under non-myopic, nondifferential pricing is less than the access charges under myopic, differential pricing. In addition   w 2 w w max  ; pvp (38) 3 a 4 3 ! ! wðaw  6Þ ðuq1  nÞ2 wðaw þ 12Þ ðuq1  nÞ2 max ; ; pvðw  2vÞpmin . 9a 9a 12 6

(39)

4.4. Who prefers what This subsection compares the three access pricing alternatives by numbering them one to three. The first one refers to myopic, non-differential pricing. The next two refer to non-myopic pricing (i.e., when the network provider decides access prices while keeping in mind the dependency of q2 on a1 through the first-stage profits): the second case refers to nondifferential pricing whereas the third case refers to differential pricing. Since dynamic programming using different access prices over periods allows the network provider maximum flexibility in extracting surplus, the following, somewhat obvious, result is obtained. Proposition 7. Under monopolies in both application and network markets, among the three cases, the network provider profits are the highest in the case where the network provider uses non-myopic, differential pricing. Comparing the various profits (surpluses) between the first and the third case, the following strong result establishes that, when the network provider charges different access prices over time periods, everybody (i.e., not only the network provider but also the application provider and the society) would be better off. That is, giving the network provider more flexibility in setting access pricing is better for everybody. Proposition 8. Under monopolies in both application and network markets, the application provider’s profits (as well as the social surplus) are higher under non-myopic, differential pricing compared to the same under myopic, differential pricing.

ARTICLE IN PRESS G. Shrimali / Telecommunications Policy 32 (2008) 545–558

553

Comparing the various profits (surpluses) between the second and the third case, the following result establishes that, when the network provider charges different access prices over time periods, it is possible for everybody (i.e., not only the network provider but also the application provider and the society) to be better off. That is, giving the network provider more flexibility in setting access pricing is better for everybody. Proposition 9. Under monopolies in both application and network markets, among the non-myopic pricing schemes, the application provider’s profits (and the social surplus) are higher if the network provider uses differential pricing and a~ wX2:48. 5. Conclusion This paper adds to the growing body of literature on the net neutrality debate. It provides an exploratory economic investigation into this controversial topic. It also looks at whether allowing a network provider freedom in pricing would discourage innovation and be detrimental to the society. It first looks at a static setting and shows that allowing the network provider to engage in differential pricing (i.e., no net neutrality) is detrimental for the society since such pricing results in a lower social surplus. It then looks at the dynamics of provider interaction and shows that allowing network provider freedom actually encourages innovation since the network provider subsidizes the application provider in all stages but the final one. The policy implications suggested by this paper are subtle. On the one hand, this paper indicates that net neutrality is desirable in the short term in order to maximize social surplus. On the other hand, it indicates that it may not be necessary to restrict a monopoly network provider in the long term since, due to its impact on long-term profits, it is in the best interests of the network provider to promote innovation and maximize social surplus. Therefore, this paper takes the view that the topic of net neutrality is not only controversial but also complicated, and suggests that policy makers use a balanced approach based on sound analysis. The analysis in this paper is based on many simplifying assumptions. These include linear forms of consumer demand and network provider cost (for all the results) as well as linear consumer utility and zero application cost (for Section 4). In order to broaden the scope of this analysis, it would be desirable to relax these assumptions and show that the results still hold.

Acknowledgment The author would like to acknowledge Prof. Sunil Kumar for his inputs on model formulation and the structure of the paper. Appendix

Proof of Lemma 1. The inequalities (from left to right) are necessitated by the individual rationality constraints (i.e., non-negative surplus) for the consumer, application provider, and network provider, respectively. & Proof of Proposition 1. The first-order condition for the application provider is x½ðUðqÞ  pÞ  ðp  aÞ ¼ 0; which gives p¼

½UðqÞ þ a 2

(40)

as well as 

pJ ¼ x

UðqÞ  a 2

2

 CðqÞ

dpJ ½2pJ þ CðqÞ ½UðqÞ  a ¼ ¼ x p0, 2 da ½UðqÞ  a

(41)

(42)

where the inequality follows from (6). The profit of M can be now written down as pM ¼ ðx½UðqÞ  aða  nÞÞ=2, and the firstorder condition is given by ðx½UðqÞ  a  a þ nÞ=2 ¼ 0. Eqs. (7) and (8) then follow in a straightforward manner and, using (3)–(5), so does (9)–(11). & Proof of Proposition 2. For the application providers, from (12)–(13) and (16)–(17), aN;same ¼ aN;diff  ½Uðqi Þ  Uðqj Þ=2. So, if i U(qi)4U(qj) then aN;same oaN;diff and, from (41)–(42), pN;same 4pN;diff . That is, since U0 (  )40, the higher-quality application i J;i J;i provider prefers the same access price. Similarly, it can be shown that the lower-quality application provider prefers different access prices. Next, look at the preference of the network provider M. Since 2abpa2+b2, [U(q1)+U(q2)2n]2 ¼ [U(q1)n]2+[U(q2)n]2+ P pðx=8Þ 2i¼1 ½Uðqi Þ  n2 ¼ 2[U(q1)n][U(q2)n]p2[U(q1)n]2+2[U(q2)n]2. That is, from (14)–(15) and (18)–(19) pN;same M N;diff pM , and the network provider prefers differential pricing.

ARTICLE IN PRESS 554

G. Shrimali / Telecommunications Policy 32 (2008) 545–558

Finally, the social planner prefers non-differential access pricing, as follows. Using (16)–(17) and (18)–(19), under nondifferential pricing Uðqi Þ  pi ¼

½Uðqi Þ  n ½Uðqi Þ  Uðqj Þ þ 4 8

as well as

pN;same ¼ S

2 h X x i¼1

¼

4

2 i xX fUðqi Þ  ng2  Cðqi Þ þ ½Uðqi Þ  n½Uðqi Þ  Uðqj Þ 8 i¼1

2 h X x i¼1

Thus, p

N;same S

N;diff S

p

4

i x fUðqi Þ  ng2  Cðqi Þ þ ½Uðq1 Þ  Uðq2 Þ2 8

¼ ðx=8Þ½Uðq1 Þ  Uðq2 Þ2 X0, and the society would prefer non-differential pricing.

&

Proof of Proposition 3. The network provider’s profit maximization problem can be solved using the standard dynamic programming approach. Looking at the second stage first, the first-order condition for the second-stage profits can be written as dpM;2 ½Uðq2 Þ  2a2 þ n ¼ 0. ¼x 2 da2 That is, a2 ¼ ½Uðq2 Þ þ n=2, where q2 is as defined in (20). The first-stage profit can now be written as "   # x Uðq2 Þ  n 2 , pM ða1 Þ ¼ ðUðq1 Þ  a1 Þða1  nÞ þ 2 2 and the first-order derivative with respect to a1 is   dpM x Uðq2 Þ  n 0 dq Uðq1 Þ  2a1 þ n þ U ðq2 Þ 2 . ¼ 2 2 da1 da1 Assuming U(q) ¼ uq, C(q1) ¼ 0 (Assumption 6), denoting ðuq1  a1 Þ X0 2

(43)

w ¼ ðuq1  nÞX0,

(44)

v~ ¼

where the inequalities follow from (25)–(26), and using (41)–(42), (21): dpM x x ¼ ½2ð4v~  wÞ  uaq xv~ ðuaq xv~ 2 þ wÞ ¼ ½a~ 2 v~ 3  bv~  g, 4 4 da1 where a~ 2 ¼ ðuaq xÞ2 X0, b ¼ ða~ w  8Þ, and g ¼ 2wX0. If bX0, since a~ 2 ; wX0 and v~ X0, it follows that ðdpM =da1 Þp0 for 0pa1 puq1. That is, the network provider’s profits are ¼ 0, which is below cost (since 0pn). The derivation of aN;2p is now straightforward. maximized at aN;2p 1 2 The case bp0 is more complicated. In this case, look at the solutions of f ðv~ Þ ¼ a~ 2 v~ 3 þ bv~ þ g ¼ 0.

(45) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Looking at f ðv~ Þ, note that it has two local optimas at f ðv~ Þ ¼ 3a~ v~ þ b ¼ 0, i.e., at v~ ¼  ðbÞ=3a~ ¼  ð8  a~ wÞ=3a~ 2 . Since f ð1Þ ¼ 1 and f ð1Þ ¼ 1, it must be that f ðv~ Þ is increasing for v~ Xv~ þ X0 and decreasing for v~ pv~  p0. Thus, f ðv~ Þ will have a form similar to the one shown in Figs. 2 and 3. Further,7 since a~ 2 X0 as well as gX0, the condition 0

bp03a~ wp8

2 2



(46)

results in two sign changes in the coefficients of (45) and, from Descartes’ sign rule, guarantees two positive roots (i.e., v~ X0).8 To determine the nature of the roots, look at the discriminant, given by

Dða~ wÞ ¼ 4a~ 2 b3 þ 27a~ 4 g2 ¼ 4a~ 2 ½ða~ w  8Þ3 þ 27ða~ wÞ2 . 7 The following discussion on the roots of (45) (which is in the standard or depressed form) cubic equation is based on Hall and Knight (1906) and Obrechkoff (2003). 8 Applying the rule to f(x) two sign reversals are obtained—hence a maximum of two (the other possibility being zero) positive roots and a minimum of one negative root. Similarly, applying the rule to f(x) one sign reversal is obtained—hence a maximum of one negative root and a minimum of two positive roots. Combining the two observations, it must be that (45) has exactly two positive and one negative roots.

ARTICLE IN PRESS G. Shrimali / Telecommunications Policy 32 (2008) 545–558

555

f(x)

x

Fig. 2. Graph of f ðxÞ ¼ a~ 2 x3 þ bx þ g when bp0 and DX0.

f(x)

x

Fig. 3. Graph of f ðxÞ ¼ a~ 2 x3 þ bx þ g when bp0 and Dp0.

Since D(0)p0, D0 (  )X0, and D(2.48) ¼ 0, ( X0 if 2:48pa~ wp8 D¼ . p0 if 0pa~ wp2:48

(47)

When DX0 (2:48pa~ wp8), (45) will have one real (negative) root and two complex conjugate roots with positive real parts (Fig. 2). That is, ðdpM =da1 Þp0 for 0pa1 puq1 (v~ X0), and this case results in the same behavior as when b ¼ ða~ w  8ÞX0. When Dp0 (0pa~ wp2:48), (45) has three real roots. Two of these are positive (Fig. 3) as dictated by the two sign reversals. This establishes that the two positive roots of f ðv~ Þ ¼ 0 must satisfy sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð8  a~ wÞ (48) 0pv1L p pv1H , 3a~ 2 2

a non-empty condition. However, v1H is ruled out due to the second-order condition (ðd pM =da21 Þp03  ðf ðv~ Þ=da1 Þp0). In 0 0 00 addition, since f ð0Þ ¼ g; f ð0Þ ¼ b and bpf ðv~ Þp0; f ðv~ ÞX0; v~ 2 ½0; v~ þ , it must be that v1L X  ðg=bÞ, and9 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2w ð8  a~ wÞ pv~ p (49) ð8  a~ wÞ 3a~ 2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð8  a~ wÞ 4w puq1  uq1  2 paN;2p 1 2 ð8  a~ wÞ ~ 3a

(50)

Finally, the provider profits are simply given by 2 2 X X uqi  aN;2p i p ¼ x ðuqi  pi Þðpi  ai Þ ¼ x 2 i¼1 i¼1 N J

pNM

!2

2 2

¼ x4v~ þ

2 !2 3 2 X ~ v~ 2 ðuqi  ai Þðai  nÞ w þ a 5 ¼ x4v~ ð2v~  wÞ þ 2 ¼x 2 4 i¼1

w þ a~ v~ 2 4

!2 3 5

(51)

(52)

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi It necessitates ð2w=8  a~ wÞp ðð8  a~ wÞ=3a~ 2 Þ3ða~ w  8Þ3 þ 12ða~ wÞ2 p03a~ wp3:11—a looser bound compared with a~ wp2:48. So, not an empty condition. 9

ARTICLE IN PRESS 556

G. Shrimali / Telecommunications Policy 32 (2008) 545–558

pNS ¼ x

2 2  X X uqi  ai 2 N N N N ðuqi  pi Þ2 þ pN þ pN J þ pM ¼ x J þ pM ¼ 2pJ þ pM : 2 i¼1 i¼1

&

(53)

Proof of Proposition 4. The proof is by induction. Since the sequence {qi} is non-decreasing by definition, the sequence wi ¼ uqi  n is too. This implies that if the above result is true for a k1 stage problem, then it is true for the stages 2, y, k in a k stage problem. That is aN;kp ¼ 0; i 2 f2; . . . ; k  1g. One only needs to show that aN;kp ¼ 0. 1 i By a reasoning similar to Propositions 3, the profit maximization objective in the first stage can be written as 2 3 k1 uq  n2 X x4 k 5 pM ¼ ðuq1  a1 Þða1  nÞ  nu q2 þ 2 2 j¼2 where qj ¼ qj1 þ aq xv2j1 ¼ q1 þ aq x

j1 X

v2i ;

j 2 f2; . . . ; kg

(54)

i¼1

vj ¼

uqj ; 2

j 2 f2; . . . ; k  1g.

(55)

The first-order derivative with respect to a1 is k1 X dqj 4 dpM dq ¼ 2ðuq1  2a1 þ nÞ  2nu þ ðuqk  nÞu k . x da1 da da1 1 j¼2

To simplify, using (54)–(55), first write q2 ¼ q1 þ aq xv21    j1  Y a~ a~ qj ¼ qj1 þ aq xv2j1 ¼ qj1 1 þ uqj1 ¼    ¼ q1 1 þ uqi ; 4 4 i¼1

u

j Y dqj dqi ¼u da1 dqi1 i¼3

uqk ¼ uq1 þ a~

k1 X

!

v2j

 j1  Y dq2 a~ ¼ a~ v1 1 þ uqi ; da1 2 i¼2

~ v21

¼ q1 þ a

j¼1

þ

a~ 4

u2 q21

j 2 f3; . . . ; kg

j 2 f2; . . . ; kg

 2 k1 (Y )2 j1  aq xv21 X a~ 1þ 1 þ uqi q1 4 j¼2 i¼2

Then, for v1X0  j1  k1 Y X 4 dpM a~ ¼ 2ð4v1  wÞ þ 2na~ v1 1 þ uqi x da1 2 j¼2 i¼2 2 3  2 k1 (Y )2 kY  j1  1 ~ 2 2 ~ aq xv21 X a a a~ 2 4 5 1 þ uqi 1 þ uqi  a~ v1 w þ a~ v1 þ u q1 1 þ 4 q1 4 2 j¼2 i¼2 i¼2  j1  k1 Y X a~ 1 þ uqi 2 j¼2 i¼2 2 ( )2 3   2 j1 k1 2 X Y ~ 2 2 ~ a xv a a q 1 ð1 þ uqi Þ 5  a~ v1 4w þ u q1 1 þ 4 q1 4 j¼2 i¼2

p2ð4v1  wÞ þ 2na~ v1

p  2w  v1 ða~ w  8Þ  a~ v1



a~ 4

u2 q21  2n

X j1  k1 Y j¼2 i¼2

1þ

a~ 2

uqi



a~ 4

 u2 q21  2n p0,

Qk1 where the first inequality uses the facts that each term in ðuqk  nÞuðdqk =da1 Þ is positive and that i¼2 ð1 þ ða~ =2Þuqi ÞX1; the last inequality comes from ð1 þ ða~ =4Þuqi Þ2 Xð1 þ ða~ =2Þuqi Þ, ða~ w  8ÞX0 and ðða~ =4Þu2 q21  2nÞX½ða~ =4Þðn þ ð8=a~ ÞÞ2  2nX0. ¼ 0. & That is, the network provider’s profits are maximized at aN;kp 1 Proof of Proposition 5. The first-order condition for the network provider can be written as    0  dpM Uðq1 Þ þ Uðq2 Þ U ðq2 Þðdq2 =daÞ  a þ xða  nÞ  1 ¼ 0. ¼x 2 2 da

ARTICLE IN PRESS G. Shrimali / Telecommunications Policy 32 (2008) 545–558

557

That is     dq dq a U 0 ðq2 Þ 2  4  n U 0 ðq2 Þ 2  2 þ ½Uðq1 Þ þ Uðq2 Þ ¼ 0. da da Assuming U(q) ¼ uq, C(q1) ¼ 0 (Assumption 6), and using (21) " # dpN J;1 þ pN Þ  2½2ða  uq1 Þ þ ðuq1  nÞ ¼ 0. uaq ða  nÞ J;1 da Defining v¼

ðuq1  aÞ X0 2

(56)

w ¼ ðuq1  nÞX0,

(57)

where the inequalities follow from (33), and using (41)–(42), uaq ½ðw  2vÞxv þ xv2   2½w  4v ¼ 0, which can be simplified to

av2  bv  g ¼ 0, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 where a ¼ 3a~ ¼ 3uaq xX0, b ¼ ðaw=3Þ  8 ¼ a~ w  8, and g ¼ 2w. Then, v ¼ ðb  b þ 8awÞ=2a with vþ ¼ ðb þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b2 þ 8awÞ=2a and v ¼ ðb  b2 þ 8awÞ=2a. Now, since wX0 (56)–(57), b2 þ 8awXb, and since vX0 (56)–(57), v is ruled out. The only remaining possibility is v ¼ v+. Since the two period access charge is given by a2p ¼ uq1  2v, it is straightforward to obtain (34). In addition, various profits are given by  2 2 X uqi  aN;2p x 2 i¼1 i¼1  ua xv2  h i uaq x 2 2 q v Þ ¼ xv2 2 þ uaq xv þ ¼ x v2 þ ðv þ 2 2

pNJ ¼

2 X

xðuqi  pi Þðpi  aN;2p Þ ¼



pNM ¼ xðw  2vÞ 2v þ pNS ¼

2 X

uaq xv2 2



 uaq xv ¼ xðw  2vÞv 2 þ 2

N xðuqi  pi Þ2 þ pN J þ pM ¼

i¼1

as in (35)–(37).

 2 2 X uqi  aN;2p N N N x þ pN J þ pM ¼ 2pJ þ pM , 2 i¼1

&

Remark. Eq. (33) ensures that the second-order necessary conditions (Luenberger, 1984) for profit maximization are met, i.e., 2

2

U 0 ðq2 Þðd q2 =da21 Þ uaq xv uaq x d pM U 0 ðq2 Þðdq2 =da1 Þ  1  ða  nÞ p0  1 þ ða  nÞ ¼ 1 þ ¼ 1  2 2 4 2 2 da Proof of Proposition 6. Under the one period model, since q2Xq1 gives aN;1p ¼ ðuq2 þ nÞ=2Xðuq1 þ nÞ=2 ¼ aN;1p , it suffices 2 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 N;1p N;2p N;1p N;2p N;1p pa1 ¼ a . Start by writing a a ¼ ððaw=2Þ  ðb þ b þ 8awÞÞ=a. Since aX0, the polarity of to show that a qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 aN;2p  aN;1p is determined by the numerator, i.e., ððaw=2Þ  bÞ  b þ 8aw, and aN;2p  aN;1p p0 iff 2

ððaw=2Þ  bÞ2 pðb þ 8awÞ. When w ¼ ðuq1  nÞX0, it must be that ððaw=2Þ  bÞ ¼ ððaw=6Þ þ 8ÞX0 as well as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b2 þ 4awXb. The condition ððaw=2Þ  bÞ2 pðb2 þ 8awÞ simplifies to bXððaw=4Þ  8Þ, which is always true when wX0. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 Next, since b þ 8aw ¼ ððaw=3Þ  8Þ2 þ 8aw ¼ ðaw=3Þ2 þ ð8aw=3Þ þ 64, ððaw=3Þ þ 4Þp b þ 8awpððaw=3Þ þ 8Þ as well as ðw=3Þ  ð2=aÞpvpðw=3Þ and ðwðaw  6Þ=9aÞpvðw  2vÞpðwðaw þ 12Þ=9aÞ, where the second set of relations directly follow from the first one. In addition, vXw/4 is obtained as the following. aN;2p paN;1p 3ððuq1 þ n  2aN;2p Þ=2ÞX03vXðw=4Þ finally, using w w ðuq1 þ 2nÞ ðuq1 þ nÞ ð2uqi þ nÞ ð3uqi þ nÞ pvp 3 paN;2p p 3 ppi p 4 3 3 2 3 4 the following inequality is obtained: ððuq1  nÞ2 =12Þpvðw  2vÞpððuq1  nÞ2 =6Þ:

&

(58)

ARTICLE IN PRESS 558

G. Shrimali / Telecommunications Policy 32 (2008) 545–558

Proof of Proposition 7. The profit maximization problems for case two and three are the same except for the additional constraint a1 ¼ a2 for the second case. Thus, the problem in case two may be considered as a constrained version of the problem in case three and, from Luenberger (1984), the profits in case two would be lower. Similarly, the profit maximization problem in case one optimizes a function different from the actual profit and, by definition, the profits in case one would be lower. & ~ þ ða~ =4Þv~ 2 Þ2 Xx½w ~ 2þ Proof of Proposition 8. From Proposition 7, (28)–(29) and (22)–(24), one needs to show x½v~ 2 þ ðw ~ þ ða~ =4Þw ~ 2 Þ2 , and the proof is complete if v~ Xw. ~ This is true when a~ wX2:48 since then v~ ¼ ððuq1 Þ=2ÞXððuq1  nÞ=4Þ ¼ w; ~ ðw ~ and also when a~ wp2:48 since then v~ X  ðg=bÞ ¼ ð2w=8  a~ wÞXw. & ~ þ ða~ =4Þv~ 2 Þ2 Xx½v2 þ Proof of Proposition 9. From Proposition 7, (28)–(29) and (35)–(37), one needs to show x½v~ 2 þ ðw 2 2 ðv þ ða~ =2Þv Þ . When a~ wX2:48, using Proposition 3 and vpðw=3Þ (38)–(39), get v~ ¼ ðuq1 =2ÞXðw=2ÞXð3=2Þv, and write  2  2 a~ 9 9 2 27 3 81 2 4 a~ v2 ~ þ v~ 2 X v2 þ v þ a~ v þ a~ v Xv2 þ v þ v2 þ ð2a~ 2 v2  5a~ v þ 26Þ v~ 2 þ w 4 16 32 256 4 2 32 The proof is complete since 2a~ 2 v2  5a~ v þ 26X0 for vX0 (it attains its minimum of E23 at a~ v ¼ 5=4).

&

References Bauer, J. M. (2006). Dynamic effects of network neutrality. In 34th research conference on communication information and Internet policy, Alexandria, VA, September–October. Dorgan, B. L. (2007). A bill to amend the Communications Act of 1934 to ensure net neutrality. Library of Congress Bill S.215, introduced 1/9/2007. Farrell, J. (2007). Integration and independent innovation on a network. UC Berkeley working paper no. CPC03-37. Ford, G. S., Koutsky, T. M., & Spiwak, L. J. (2006). Network neutrality and industry structure. Phoenix Center Policy Paper no. 24. Hahn, R., & Wallsten, S. (2006). The economics of net neutrality. Economists voice, Berkeley Electronics Press. Hall, H. S., & Knight, S. R. (1906). Higher algebra: A sequel to elementary algebra for schools. London: McMillan and Co. Lee, T. B. (2006a). Net neutrality. Available at /http://dig.csail.mit.edu/breadcrumbs/node/132S. Lee, T. B. (2006b). Net neutrality: This is serious. Available at /http://dig.csail.mit.edu/breadcrumbs/node/144S. Lessig, L. (2004). Coase’s first question. Regulation, Fall. Luenberger, D. (1984). Linear and nonlinear programming. Berlin: Springer. McTaggart, C. (2006). Was the Internet ever neutral. In 34th research conference on communication information and Internet policy, Alexandria, VA, September–October. Obrechkoff, N. (2003). Zeros of polynomials. Marin Drinov Academic Publishing House. Odlyzko, A. M. (2003). Data networks are lightly utilized, and will stay that way. Review of Network Economics, 2(3), 210–237. Peha, J. M. (2006). The benefits and risks of mandating network neutrality, and the quest for a balanced policy. In 34th Research conference on communication information and Internet policy, Alexandria, VA, September–October. Roycroft, T. R. (2006). Economic analysis and network neutrality: Separating empirical facts from theoretical fiction. Roycroft Consulting Issue Brief, June. Available at /http://www.roycroftconsulting.orgS. Thierer, A. D. (2004). Net neutrality: Digital discrimination or regulatory gamesmanship in cyberspace? Cato Institute Policy Analysis no. 507. Weitzner, D. J. (2006). The neutral Internet: An information architecture for open societies. Available at /http://digg.csail.mit.edu/2006/06/neutralnet.htmlS. Wikipedia. (2007). Network neutrality. Available at /http://en.wikipedia.org/wiki/Network_neutralityS. Wu, T. (2003). Network neutrality, broadband discrimination. Journal of Telecommunications and High Technology Law, 2, 141.