EFFECTS OF COMPETITION AMONG INTERNET SERVICE PROVIDERS AND CONTENT PROVIDERS ON THE NET NEUTRALITY DEBATE1

EFFECTS OF COMPETITION AMONG INTERNET SERVICE PROVIDERS AND CONTENT PROVIDERS ON THE NET NEUTRALITY DEBATE1

Supporters of net neutrality have often argued that more competition among Internet service providers (ISPs) is beneficial for an open Internet and that the market power of the ISPs lies at the heart of the net neutrality debate. However, the joint effects of the competition among ISPs and among content providers (CPs) have yet to be examined. We study the critical linkage between ISP competition and CP competition, as well as its policy implications. We find that even under competitive pressure from a rival ISP, an ISP always has the incentive and the ability to enforce charging CPs for priority delivery of content. Upending the commonly held belief that when facing direct competition CPs will always support the preservation of net neutrality, we find that, under certain conditions, it is economically beneficial for the dominant CP to reverse its stance on net neutrality.

1

Keywords: Net neutrality, Internet service provider competition, content provider competition, packet discrimination, social welfare

1Sulin Ba was the accepting senior editor for this paper. Zhengrui Jiang served as the associate editor.

The appendices for this paper are located in the “Online Supplements” section of the MIS Quarterly’s website (http://www.misq.org).

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Introduction

The Federal Communications Commission’s (FCC) path to enforce net neutrality rules to preserve an open Internet has been complicated and controversial. In its 2010 Open Internet Order, the FCC proposed net neutrality rules consisting of four core principles: transparency, no blocking, no unreason- able discrimination, and reasonable network management (FCC 2010). These rules were later struck down by the U.S. Court of Appeals for the District of Columbia Circuit, which assessed that the FCC only has limited regulatory options for broadband as an information service (Nagesh and Sharma 2014). During a five-month period in 2014, the FCC solicited public comments on the net neutrality issue and received nearly four million comments, which makes it the most commented-upon issue in the agency’s history. In February 2015, the FCC introduced its new open Internet rules (FCC 2015), but was soon challenged again in court (Risen 2015).

Proponents of net neutrality have long opined that a lack of effective competition in the local broadband market enables Internet service providers (ISPs) to act as gatekeepers of con- tent, and thus to be in a position to charge content providers (CPs) for priority delivery of their data packets.2 The appeals court made the same argument as part of its ruling:

If end users could immediately respond to any given broadband provider’s attempt to impose restrictions on edge providers by switching broadband provid- ers, this gatekeeper power might well disappear…. For example, a broadband provider like Comcast would be unable to threaten Netflix that it would slow Netflix traffic if all Comcast subscribers would then immediately switch to a competing broadband provider (U.S. Court of Appeals 2014, pp. 39).

Supporters of net neutrality have often argued that more competition among ISPs is beneficial for an open Internet (Dunbar 2014; Glaser 2014) and that the market power of the ISPs lies at the heart of the net neutrality debate (McMillan 2014; Winegarden 2014). They argue that competition among ISPs would prevent them from gaining the market power that currently allows them to charge consumers supra-competitive prices for Internet access and to potentially charge CPs for preferential delivery. In fact, there have been several calls to remove the barriers to a competitive broadband market (Szoka et al. 2013).

In this paper, we investigate whether the presence of competi- tion in local broadband markets would indeed remove the

incentives of ISPs to charge online CPs for preferential delivery. Our analysis builds upon the extant research of Cheng et al. (2011) and Choi and Kim (2010) , who examined the net neutrality issue for a monopoly ISP. One contribution of our research is to show that, even under competitive pressure from a rival ISP, an ISP always has the incentive and the ability to enforce charging CPs for priority delivery of content. This result contrasts with some prior finding in the literature, for example, Bourreau et al. (2015), who find that competing ISPs may not always prefer packet discrimination and sometimes prefer to stay with net neutrality, when CPs are not in competition with each other.

The issue of competition among CPs has thus far taken a back seat in the net neutrality debate. CPs have been among the strongest proponents of net neutrality (Internet Association 2014). Recent developments, however, show some deviations from this stance. Manjoo (2014) observed that in contrast to the recent grassroots movements over the ongoing discussions regarding net neutrality regulation, the large Internet com- panies “have not joined online protests, or otherwise moved to mobilize their users in favor of new rules.” Google has been questioned for its stance on net neutrality after its entry into the broadband market through Google Fiber (Singel 2013). Two important issues remain unaddressed: to wit, how competitive pressures drive CPs to pay for preferential delivery and how their choices affect the ISPs’ incentives to manage their traffic.

We investigate the impact of CP competition in the presence of ISP competition. One question that is of particular interest is whether sufficient market power of the CP encourages it to abandon its support for net neutrality (Choi and Kim 2010). Jointly examining both ISP competition and CP competition enables us to make a unique contribution to the literature by studying the critical linkage between ISP competition and CP competition, as well as its policy implications. We find that a dominant CP may be better off without net neutrality given sufficient market power relative to that of the ISPs. Our findings suggest that the impact of net neutrality regulation on the incentives of CPs depends critically on the market power of the competitors both within the local ISP market and within the content market.

Apart from these policy prescriptions, this paper makes an important contribution in extending the traditional multi- dimensional spatial-competition literature. The proposed model captures the relevant characteristics of data transmis- sion in the net neutrality debate. Generally, the modeling framework can be used to analyze the competition between two sets of firms providing complementary products that are consumed together to constitute the total end-user experience (e.g., computer hardware platforms and the software on those platforms).2This paid prioritization is also referred to as packet discrimination.

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The paper is organized as follows: In the next section, we review the related literature and discuss the contributions of this paper. We then propose a game-theoretical model of Internet data transmission in the presence of both ISP compe- tition and CP competition. Following that, we analyze the outcomes under both net neutrality and packet discrimination regimes with a focus on the impact of ISP competition and CP competition. The paper concludes with theoretical, mana- gerial, and policy implications.

Literature Review

In this section, we first review the fast-growing literature of economic analysis of net neutrality. The issue of net neu- trality focuses on “last-mile” ISPs3 that provide Internet access services to their local consumers. Existing models make different assumptions about market conditions of Inter- net data transmission within the last mile and find a variety of results on key economic outcomes such as ISP profit, CP profit, social welfare, etc. Here we focus on market condi- tions that are most related to our paper (i.e., ISP competition and CP competition). For a broader review of the network neutrality literature, see Krämer et al. (2013). Figure 1 illustrates the context of our paper with respect to the related literature.

From the perspective of modeling ISP competition, most extant models (such as Cheng et al. 2011; Choi and Kim 2010; Krämer and Wiewiorra 2012) consider a monopoly ISP, although Economides and Tåg (2012) and Hermalin and Katz (2007) extend their models to consider the effects of ISP com- petition and in either case find results similar to the monopoly case. Bourreau et al. (2015) extend the model proposed in Krämer and Wiewiorra (2012) to allow ISP competition. They find that the packet discrimination regime results in higher infrastructure investment, more content innovation, and higher overall social welfare. The ISPs, however, may be worse off under the packet discrimination regime, due to intensified competition in the consumer market. Bykowsky and Sharkey (2014) study the welfare effects of the zero-price rule under various conditions of the ISPs’ market power. They find that the zero-price rule is welfare enhancing if and only if the ISP’s ability to establish competitive prices for the CPs exceeds its ability to establish such prices for consumers. Broos and Gautier (2015) look at the issue of ISPs excluding certain apps on their network, and their research indicates that in the presence of duopoly ISPs, the app may be offered only

by one firm. However, prohibiting the exclusion of the app does not improve social welfare.

From the perspective of modeling CP competition, most papers (such as Bourreau et al. 2015; Economides and Tåg 2012; Krämer and Wiewiorra 2012) assume that CPs are the sole providers of their own content and do not compete for consumers. As a result, these models are unable to capture the competitive pressure on the CPs to pay for preferential delivery service under a packet discrimination regime. Other papers (Cheng et al. 2011; Choi and Kim 2010; Guo et al. 2010; Guo et al. 2013) consider the competition for con- sumers between two CPs, but assume that the service of delivering the content is provided by a monopolist ISP. Cheng et al. (2011) and Choi and Kim (2010) find that the ISP’s incentive to expand infrastructure capacity is higher under net neutrality. Guo et al. (2010) find that without net neutrality, when the ISP integrates with a CP, social welfare may decrease in certain cases, or increase at the expense of the competing pure-play CP in other cases. Furthermore, the vertically integrated ISP does not always degrade, and some- times even prioritizes, the competing content. Guo et al. (2013) find that given the freedom to engage in non-neutral traffic management on both the CP side and the consumer side of the market, the ISP does not always discriminate both sides.

Most of the articles suggest that if packet discrimination were permitted, the ISP would be better off while most CPs would be worse off,4 due to the ISP’s added flexibility in network management. Hermalin and Katz (2007) find that net neu- trality reduces the set of available content and thus leads to lower content innovation. Economides and Tåg (2012) con- clude that there are more active CPs under net neutrality when the value of an additional consumer to the CPs exceeds the value of an additional CP to the consumers. Guo et al. (2012) find that packet discrimination can hinder the ability of start- ups to compete against established rivals and thus reduce content innovation at the edge. Krämer and Wiewiorra (2012) model congestion-sensitive CPs with differing congestion- sensitivity distributions and find that content innovation is lower under net neutrality for less congestion-sensitive CPs and higher for more congestion-sensitive CPs. Guo and Easley (2016) find that net neutrality may result in higher content innovation because of the existence of a pro bono innovation zone.

3Studies in network interconnection (Armstrong 1998; Chiang and Jhang-Li 2014; Laffont et al. 2003; Tan et al. 2006) focus on the issues of inter- connection settlements among backbone network providers.

4In the existing literature of economics of net neutrality, there are papers that have identified that some CPs may benefit from packet discrimination ( Bourreau et al. 2015; Hermalin and Katz 2007; Krämer and Wiewiorra 2012). For example, Bourreau et al. and Krämer and Wiewiorra find that the most congestion sensitive CPs are better off under packet discrimination in the long run. However, in all such models, the CPs do not directly compete against each other. Most papers that do model CP competition (Cheng et al. 2011; Guo et al. 2010; Guo et al. 2013) find that CPs are worse off under packet discrimination.

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Figure 1. Context of Our Paper with Respect to the Related Literature

Table 1. Assumptions and Findings in the Related Literature

Related Papers Modeling

Assumptions* Related Findings

Choi and Kim (2010) • No ISP competition• Competing CPs • Results for ISP profit, CP profit, and social welfare are mixed

Cheng et al. (2011) • No ISP competition• Competing CPs

• The monopoly ISP’s profit is always higher under PD • The competing CPs’ profits are always lower under PD • Social welfare is higher under PD

Krämer and Wiewiorra (2012)

• No ISP competition • No CP competition

• The monopoly ISP’s profit is always higher under PD • All CPs’ profits are lower under PD in the short run; the most con-

gestion sensitive CPs’ profits are higher under PD in the long run • Social welfare is higher under PD

Economides and Tåg (2012)

• No ISP competition in the main model and competing ISPs in the extended model

• No CP competition

• Results for ISP profit, CP profit, and social welfare are mixed

Bourreau et al. (2015) • Competing ISPs• No CP competition

• The competing ISPs’ profits are sometimes lower under PD • The most congestion sensitive CPs’ profits are higher under PD • Social welfare is higher under PD

Our paper • Competing ISPs• Competing CPs

• The competing ISPs’ profits are always higher under PD • The dominant CP’s profit may be higher under PD while the

economically less successful CP’s profit is always lower under PD • Social welfare is higher under PD

*As with any economic model, these papers also make a host of other assumptions. Here we list only the ones that are related to market structures.

The results are mixed when it comes to evaluating the impact of the potential net neutrality regulation on social welfare. Some papers (Bourreau et al. 2015; Cheng et al. 2011; Guo and Easley 2016; Guo et al. 2012; Krämer and Wiewiorra 2012) find that net neutrality results in lower social welfare

compared to packet discrimination, while others (Choi and Kim 2010; Economides and Hermalin 2012; Economides and Tåg 2012; Hermalin and Katz 2007) obtain mixed welfare results. Table 1 compares the assumptions and findings of the related literature and highlights the contribution of this paper.

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This paper is among the first to examine the joint effects of the competition among CPs and among ISPs in the context of net neutrality. Brito et al. (2013) study the competition among CPs and ISPs and find that the ISPs prefer to sell the highest quality of service to CPs with the highest advertising revenue. In their paper, consumers’ choice of ISP and CP are modeled as independent decisions and, therefore, the interac- tion between the competition among CPs and ISPs cannot be examined. Kourandi et al. (2015) investigate the impact of the net neutrality regulation on Internet fragmentation through exclusivity contracts between ISPs and CPs. They find that the zero-price rule on traffic termination is neither sufficient nor necessary to prevent Internet fragmentation. They study the competition among CPs and ISPs in the context of Internet fragmentation, an extreme case of non-neutral Internet when some content is not delivered by all ISPs. For example, if Comcast and Netflix enter an exclusivity contract, then Netflix’s content will be available only to Comcast sub- scribers and nobody else. In contrast, our paper studies a less severe case of non-neutral Internet—that of paid fast lanes, which is what the net neutrality debate has mostly been con- cerned with. This paper fills the research gap by studying the linkage between the markets of Internet access services and digital content in the context of paid fast lanes. Given the different roles of CPs and ISPs, it is important to investigate the impact of the competition among both these types of players on the outcomes. If one of the two markets is modeled as a monopoly, then that monopolist has greater market power to influence the outcomes of the other market. This is different from what is observed in reality, where the effects of competition in one market mediate the effects of competition in the other market. We find that the impact of net neutrality on some key outcomes such as the CPs’ profit critically depends on the relative strength of the ISP compe- tition and the CP competition.

This paper also extends the literature of multidimensional spatial competition with horizontal differentiation in both dimensions. There have been various efforts to extend the analysis of product competition from single dimension to two- or multidimensional product competition (Caplin and Nale- buff 1986). Matutes and Regibeau (1988) model two firms each producing two complementary components that are horizontally differentiated. They find that the firms choose full compatibility for their systems, which leads to higher prices. Tabuchi (1994) considers a two-dimensional setting and finds that maximum differentiation arises along one dimension, while minimum differentiation arises along the other dimension. Ansari et al. (1998) and Irmen and Thisse (1998) extend Tabuchi’s model to multiple horizontal dimen- sions and find that firms maximize differentiation on one dimension while minimizing differentiation along all others. Von Ehrlich and Greiner (2013) adapt two-dimensional spatial-competition models to the context of media markets

and analyze two media outlets providing both online and offline platforms. They find that maximum differentiation may occur in both dimensions.

We modify the existing models of multidimensional spatial- competition to capture the unique features of the net neutrality debate. First, we analyze two interrelated markets with com- plementary products (the markets of Internet access services and digital content) as opposed to multiple product attributes in the same market, which has been considered in prior studies. In the existing multidimensional spatial-competition models, consumers choose between two firms based on multiple product attributes, for example, between two com- puter printer manufacturers based on their products’ speed, noise, and clarity of output (Caplin and Nalebuff 1986). However, the two dimensions in our model represent two different but complementary duopoly markets. Consequently, consumers have to choose between two ISPs as well as between two CPs (i.e., choose among four ISP-CP combin- ations). Second, since the ISPs and the CPs know the mechanism of the consumers’ decision-making process, the competition between the CPs moderates the competition between the ISPs (and vice versa). In addition, we allow for different unit fit costs for the two different markets of Internet access services and digital content. In other words, the two markets differ in terms of competition intensity. Third, in the existing multidimensional spatial-competition models, a con- sumer’s choice of firm does not affect other consumers’ choices. In our model, a consumer’s choice of a particular ISP-CP combination does affect the choices of other con- sumers. The market shares of the ISPs and the CPs are determined by the consumers’ choices among the four ISP-CP combinations. The ISP-CP combination that a consumer finally chooses depends on the waiting times, which in turn depend on the market shares and the CPs’ delivery service choices. The CPs’ delivery service choices in turn depend on the expected waiting times at the ISPs. These interconnected variables (the market shares of the ISP-CP combinations, the waiting times, and the CPs’ delivery service choices) are simultaneously determined in our model. The above three features are key characteristics of the Internet data- transmission process, which is crucial to modeling the net neutrality issue.

Model

Modeling Framework

We consider two competing ISPs, C and D, providing Internet access services to a unit mass of consumers and content delivery services to two competing CPs, Y and G. This market structure is illustrated in Figure 2.

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Figure 2. Market Structure

Table 2. List of Notations Subscript a ISP a = C or D Subscript b CP b = Y or G

Subscript i Outcome i = N (Neither CP pays), Y (only Y pays), G (only G pays), and B (Both CPs pay)representing CPs’ content delivery choices on ISP C

Subscript j Outcome j = N (Neither CP pays), Y (only Y pays), G (only G pays), and B (Both CPs pay)representing CPs’ content delivery choices on ISP D Fa{ij} Fixed fee ISP a = C or D charges consumers for Internet access service in outcome ij pa{ij} Usage-based fee ISP a = C or D charges CPs for preferential delivery in outcome ij V Consumers’ gross valuation for each ISP-CP combination Iab{ij} Indicator function to represent whether CP b pays ISP a for preferential delivery in outcome ij uab{ij}(x, z) Utility of the ISP-CP combination ab for consumer (x, z) in outcome ij U{ij}(x, z) Utility of the preferred ISP-CP combination for consumer (x, z) in outcome ij Nab{ij} Market share of the ISP-CP combination ab in outcome ij Na{ij} Market share of ISP a = C or D in outcome ij and Na{ij} = NaY{ij} + NaG{ij} Nb{ij} Market share of CP b = Y or G in outcome ij and Nb{ij} = NCb{ij} + NDb{ij} t Unit fit cost for content k Unit fit cost for Internet access service rb Revenue rate per packet of CP b = Y or G d Consumers’ unit delay cost (unit congestion cost) wab{ij} Expected waiting time (expected delay) for consumers who choose ISP a and CP b in outcome ij λ Poisson arrival rate of content requested by each consumer, expressed in packets per unit of time μ Capacity that the ISPs provide to the consumers, expressed in packets per unit of time πa{ij} Profit of ISP a = C or D in outcome ij πb{ij} Profit of CP b = Y or G in outcome ij CS{ij} Consumer surplus in outcome ij SW{ij} Social welfare in outcome ij

Figure 2 also demonstrates payments the ISPs receive from consumers and potentially from CPs. In the net neutrality regime, the ISPs charge consumers fixed fees FC and FD, respectively, for Internet access, which are their only revenue source. In the packet discrimination regime, in addition to fixed fees (FC and FD) from consumers, the ISPs may also

charge the CPs usage-based fees pC and pD, respectively, for preferential delivery of their content. In other words, the ISPs have two revenue sources in the packet discrimination regime: Internet access fees from consumers and preferential delivery fees from CPs. Table 2 provides a list of all notations.

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We use a two-dimensional spatial-competition model to cap- ture consumers’ heterogeneous preferences for both content and Internet access service, and firm competition in these two markets. Specifically, consumers, characterized by their preference for content (x) and preference for Internet access service (z), are uniformly distributed on a unit square. Without loss of generality, we assume that the horizontal axis represents consumers’ preference for content (CP Y located at 0 and CP G located at 1); the vertical axis represents consumers’ preference for Internet access service (ISP C located at 0 and ISP D located at 1). Consumers have four choices (i.e., the four ISP-CP combinations CY, CG, DY, and DG), represented by the four corners of the unit square.

Let V be consumers’ gross valuation for each ISP-CP combin- ation. We denote the unit fit cost for content and Internet access service as t and k, respectively, and use the weighted box topology distance measure to calculate the fit cost in consumers’ utility functions. As shown in Figure 3, when choosing the ISP-CP combination of CY, the consumer located at (x, z) incurs a fit cost for content of tx and a fit cost for Internet access service of kz. Similarly, consumer (x, z)’s fit costs for the other three ISP-CP combinations can be calculated by multiplying the unit fit cost (t or k) by the corresponding (horizontal or vertical) distance between the consumer and the ISP-CP combination.

Both CPs may decide whether to pay for preferential delivery of their content for each ISP. As a result, there are four outcomes for each ISP based on the two CPs’ delivery service choices: outcome N (Neither CP pays for preferential delivery), outcome Y (only Y pays), outcome G (only G pays), and outcome B (Both CPs pay). Thus, there are 16 outcomes in all, based on the CPs’ delivery service choices for the two ISPs, represented by outcome ij, with i, j = N, Y, G, B (outcomes NN, NY, NG, NB, YN, YY, YG, YB, GN, GY, GG, GB, BN, BY, BG, and BB). These outcomes are summarized in Table 3.

Following prior work (Cheng et al. 2011; Choi and Kim 2010; Krämer and Wiewiorra 2012), we model the content delivery systems offered by the two ISPs as two independent M/M/1 queuing systems under net neutrality, one for each ISP. Let μ denote the capacity of the ISPs and λ denote the consumers’ rate of requests for content. These two queuing systems are interrelated through the traffic that they receive from con- sumers. Since the total consumer base is normalized to 1, the total consumer traffic is λ, which is divided between the two ISPs based on their market shares. Under packet discrim- ination, the content delivery systems offered by the two ISPs are modeled as two priority M/M/1 queuing systems with two priority classes. In the packet discrimination regime, if only one CP pays for preferential delivery, then its data packets

will be transmitted with higher priority compared to data packets from the other CP. However, if both CPs pay for preferential delivery, then all data packets will receive equal priority.

We denote the expected waiting time (expected delay) for consumers who choose ISP a and CP b in outcome5 ij as wab{ij}. Under outcome NN, neither CP pays for preferential delivery for both ISPs and hence receive the same priority, that is,

w wCY NN CG NN N NCY NN CG NN{ } { } { } { }= = − − 1

μ λ λ and

w wDY NN DG NN N NDY NN DG NN{ } { } { } { } .= = − − 1

μ λ λ Under outcome BG, both CPs pay ISP C for preferential delivery and hence receive the same priority on C with

w wCY BG CG BG N NCY BG CG BG{ } { } { } { } ,= = − − 1

μ λ λ

while only G pays D for preferential delivery and hence receives higher priority than Y on D. As a result, the waiting time of Y’s consumers is higher than that of G’s consumers on ISP D, that is,

( )( )w

w

DY BG N N N

DG BG N

DG BG DY BG DG BG

DG BG

{ }

{ }

{ } { } { }

{ } .

=

> = − − −

μ μ λ μ λ λ

μ λ 1

Appendix A presents the details of how we compute the delays within the 16 outcomes under packet discrimination. Note that outcome NN, where neither CP pays for preferential delivery even with the option to do so, is essentially equivalent to the net neutrality regime.

In summary, the consumers’ utility functions for the four ISP- CP combinations are

(1)

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

u x z V tx kz d w F

u x z V t x kz d w F

u x z V tx k z d w F

u x z V t x k z d w F

CY ij CY ij C ij

CG ij CG ij C ij

DY ij DY ij D ij

DG ij DG ij D ij

{ } { } { }

{ } { } { }

{ } { } { }

{ } { } { }

,

,

,

,

= − − − −

= − − − − −

= − − − − −

= − − − − − −

λ λ λ

λ

1

1

1 1

where d represents the consumers’ unit delay cost (unit congestion cost).

5We put the outcomes in brackets in the subscripts throughout the paper to visually distinguish the 16 outcomes, e.g., {BG}, from the four ISP-CP combinations, e.g., CY.

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Figure 3. Consumer Choice

Table 3. The 16 Potential Outcomes Neither CP pays D Y pays D G pays D Both CPs pay D

Neither CP pays C Outcome NN Outcome NY Outcome NG Outcome NB Y pays C Outcome YN Outcome YY Outcome YG Outcome YB G pays C Outcome GN Outcome GY Outcome GG Outcome GB Both CPs pay C Outcome BN Outcome BY Outcome BG Outcome BB

Each consumer compares the four ISP-CP combinations based on the corresponding utilities specified in equation (1) and chooses the option that yields the highest utility. We denote the market share of the ISP-CP combination ab in outcome ij as Nab{ij}, for example, NDG{BG} represents the market share of DG when both CPs pay ISP C but only G pays ISP D.

Outline of the Analysis Process

In this subsection, we present an overall structure of the solution process that we employ for analyzing this game. Figure 4 presents a schematic of the flow of content from the CPs to the consumers through the ISPs. For the purposes of illustration, we show the priority of content from the CPs Y and G that would flow through the ISPs C and D in outcome BG. Recall that in outcome BG, both Y and G pay priority delivery fees to ISP C, and therefore neither CP is at an advantage with respect to the other. Thus, the waiting time of consumers for both Y and G on ISP C is the same (i.e., wCY{BG} = wCG{BG}). However, on ISP D, only G pays the priority delivery fee, and as a result, the waiting time of consumers of G on ISP D is lesser than the waiting time of consumers of Y on ISP D (i.e., wDG{BG} < wDY{BG}).

In order to solve for the equilibrium, we start with deriving the market shares (i.e., NCY, NCG, NDY, and NDG). To derive these market shares, we need to determine the consumers who are indifferent between choosing a particular ISP-CP com-

bination and another ISP-CP combination (the indifferent consumers between CY and CG, between CY and DY, between CY and DG, between CG and DY, between CG and DG, and between DY and DG). As a result, we have six curves of indifferent consumers, which partitions the market into four segments. We can then determine the market shares by calculating the sizes of these segments.

The indifferent consumers, say between the ISP-CP combina- tions of CY and DG, is derived by equating the utilities of the consumers when they access their content from CY and from DG. These utilities in turn are dependent on the waiting times of these consumers on CY and DG respectively (a higher waiting time leads to a lower utility).

We model that the content is delivered through a queueing mechanism (one queue for each ISP). The number of con- sumers in a particular “queue” (e.g., NCY and NCG for the queuing system of ISP C) affects the waiting time for the consumers within that queue (an increased market share leads to a higher waiting time). However, if a CP pays an ISP for priority delivery while its rival does not (for example, in outcome BG, G pays ISP D while Y does not), consumers of that CP will enjoy decreased waiting times and therefore more consumers will move over to that CP on that particular ISP. In outcome BG, where only G pays ISP D, the extra consumers of G on ISP D will come from three sources: (1) some consumers of Y on ISP D who now prefer G (CP switching); (2) the consumers of G on ISP C who would now

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Figure 4. Schematic of the Flow of Content in Outcome BG

rather access G on ISP D (ISP switching); and (3) consumers of Y on ISP C who would now access G on ISP D (simul- taneous ISP and CP switching).

However, this increased market share of G on ISP D degrades the experience of these consumers (by increasing their waiting times). These two opposing effects (increasing waiting times from larger market shares and decreasing waiting times by paying the priority delivery fee) finally balance out in equili- brium. Note that this “balancing” needs to be done across all four ISP-CP combinations simultaneously in order to deter- mine the equilibrium market shares in an outcome. Thus, the waiting times (and therefore the market shares) for consumers within a particular ISP-CP combination is affected by the waiting times (and therefore market shares) of every ISP-CP combination, as well as the CPs’ payment choices on each ISP, and in equilibrium, all these effects need to be simul- taneously balanced. The surfeit of variables and parameters makes this process extremely complicated. The equilibrium market shares cannot be obtained using ordinary algebra, and hence we resort to group theory. These consumer demand patterns are summarized in Lemma 1.

The solution process is further complicated by the fact that in the ISPs’ profit maximization problem for each of the 16 outcomes, there are six incentive compatibility constraints for the two CPs. These incentive compatibility constraints make the different outcomes intertwined with each other. For example, in order for outcome BG to be an equilibrium, both CPs Y and G have to calculate their profits from three other possible outcomes each and then find that the delivery service choices in outcome BG are their preferred choices. These different incentive compatibility constraints are summarized in Appendix B.

We then eliminate all of the dominated outcomes to derive the possible equilibrium outcomes, which are summarized in Lemma 2. Finally, within the universe of possible parameter values, we find out the market conditions under which each of the remaining outcomes is the equilibrium. This enables us to characterize the different equilibria for changing parameter values. The equilibrium results are summarized in Lemma 3 (and graphically in Figure 7). Based on these equilibrium results, we present our main findings in Propositions 1, 2, 3, and 4. In the next subsection, we formally describe the decision problems for the CPs and the ISPs. Following that, in the next section, we solve for the equilibrium under both the net neutrality and packet discrimination regimes.

Formulation of the Decision Problems of the CPs and the ISPs

CPs decide whether to pay ISP C, ISP D, or both. The profit of CP b = Y or G is

(2) ( )π λ λ

λ b ij Cb ij Db ij b Cb ij Cb ij C ij

Db ij Db ij D ij

N N r I N p

I N p { } { } { } { } { } { }

{ } { } { }

= + − −

where rb is the revenue rate per packet of CP b. The CPs’ profit is their revenue generated from consumers served by both ISPs, net of their payments to the ISPs for preferential content delivery. Without loss of generality, we assume that rG $rY , or CP G is more effective in generating revenue from its customer base than is CP Y. The indicator functions (ICY{ij}, ICG{ij}, IDY{ij}, IDG{ij}) represent the CPs Y and G’s delivery service choices for the ISPs C and D, respectively. Consider outcome BG as an example, in our notation, the first

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letter (B) refers to the fact that both CPs pay ISP C for prefer- ential delivery, and the second letter (G) refers to the fact that only G pays ISP D for preferential delivery. In other words, ICY{BG} = 1, ICG{BG} = 1, IDY{BG} = 0, and IDG{BG} = 1.

As shown in equation (3), ISPs make their pricing decisions as follows. ISP a = C or D selects its prices Fa{ij} and pa{ij} to maximize its profit πa{ij}. To ensure that all consumers adopt the Internet access service, we need to consider the con- sumers’ participation constraint. In other words, consumers choose the ISP-CP combination that yields the highest net utility and we assume that all consumers have nonnegative net utility. This full-market-coverage assumption is commonly made not only in the literature of economics of net neutrality that considers competition among CPs (Cheng et al. 2011; Choi and Kim 2010; Guo et al. 2010; Guo et al. 2013), but also generally in the literature of economics of telecommu- nications (Armstrong 2002) to achieve analytical closure. To ensure that neither CP has any incentive to deviate from outcome ij, we need to consider the CPs’ incentive com- patibility constraints. In other words, given the other CP’s delivery service choice, the profit for a CP in outcome ij needs to be higher than that with its alternative choices. For any outcome, given G’s delivery service choice, Y has three options to deviate from his current choice: change his delivery service choice on C only; change his delivery service choice on D only; or change his delivery service choice on both ISPs. Y’s profit under these three options are denoted by

and respectively, and the incentiveπY i j{ } ,1 1 πY i j{ } ,2 2 πY i j{ } ,3 3 compatibility constraints ensure that Y’s profit by employing its strategy in outcome ij is at least equal to what it would be if he had decided to deviate from his strategy (which he could have done in the three aforementioned ways). Similarly, given Y’s delivery service choice, G also has three options to deviate from his current choice: change his delivery service choice on C only; change his delivery service choice on D only; or change his delivery service choice on both ISPs. G’s profit under these three options are denoted by πG i j{ } ,4 4

and respectively, and the incentive compa-πG i j{ } ,5 5 πG i j{ } ,6 6 tibility constraints ensure that G’s profit by employing his strategy in outcome ij is at least equal to what it would be if he had decided to deviate from its strategy (which he could have done in the three aforementioned ways).

Formally, the decision problem of ISP a can be formulated as

( ) ( )

max { } { },

{ } { } { } { }

{ } { } { } { } { }

F p a ij aY ij aG ij a ij

aY ij aY ij aG ij aG ij a ij

a ij a ij

N N F

I N I N p

π

λ

= +

+ +

subject to

( ) ( ) { } ( ){ ( ) ( )}

U x z u x z u x z

u x z u x z

ij CY ij CG ij

DY ij DY ij

{ } { }

{ } { }

, max , , , ,

, , ,

=

≥ 0

(3)π π π πY ij Y i j Y i j Y i j{ } { } { } { }, ,≥ 1 1 2 2 3 3

π π π πG ij G i j G i j G i j{ } { } { } { }, ,≥ 4 4 5 5 6 6 The ISPs’ profit consists of two components: payment from consumers for Internet access service and payment from CPs for preferential content delivery. The first set of constraints are the consumers’ participation constraints. A consumer (x, z) compares the net utility of four ISP-CP combinations, that is, and selects( )u x zCY ij{ } , , ( )u x zCG ij{ } , , ( )u x zDY ij{ } , , ( )u x zDG ij{ } , , the ISP-CP combination that yields the highest net utility, that is, As a result, the consumer market gets divided( )U x zij{ } , . into four segments (corresponding to the four ISP-CP combinations) and we end up with four consumer partici- pation constraints, one for each segment. The full-market- coverage assumption ensures that this utility is( )U x zij{ } , nonnegative for all consumers. The last two sets of con- straints are the CPs’ incentive compatibility constraints. In response to the prices (Fa{ij} and pa{ij}) set by the ISPs, the CPs choose whether to pay for preferential delivery and their choices of content delivery services determine the outcomes ij, where i and j take the values N (Neither CP pays), Y (only Y pays), G (only G pays), and B (Both CPs pay), and represent the CPs’ content delivery choices on ISP C and D respectively.

Let us illustrate formulation (3) with an example, by con- sidering outcome BG, where both CPs pay ISP C and only G pays ISP D. For outcome BG to be an equilibrium, there are three incentive compatibility constraints for each CP. Given that G pays both ISPs in outcome BG, Y has three options to deviate from his current choice (of paying C but not D): (1) not pay either ISP (i.e., change his delivery service choice on C only, and since G would continue to pay both ISPs, this would correspond to outcome GG); (2) pay both ISPs (i.e., change his delivery service choice on D only, which would correspond to outcome BB); or (3) not pay ISP C but pay ISP D (i.e., change his delivery service choice on both ISPs, which would correspond to outcome GB). Similarly, given Y’s delivery service choice in outcome BG (he pays C but not D), G also has three options to deviate from his current choice (of paying both ISPs): (1) not pay C but pay D (i.e., change his delivery service choice on C only, which would correspond to outcome YG); (2) pay C but not pay D (i.e., change his delivery service choice on D only, which would correspond to outcome BN); or (3) not pay either

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Figure 5. Timing of the Game

ISP (i.e., change his delivery service choice on both ISPs, which would correspond to outcome YN). Formally, πY{BG} $ πY{GG}, πY{BB}, πY{GB}, and πG{BG} $ πG{YG}, πG{BN}, πG{YN}. Similarly, we arrive at the CPs’ incentive compatibility con- straints for all the other outcomes, the details of which are presented in Appendix B.

Figure 5 shows the timing of the game. In stage 1, ISP a = C or D sets the fixed fee Fa for end consumers and potentially set a priority price of pa per packet for the CPs. In stage 2, CP b = Y or G decides to pay or not to pay the ISPs C and D for preferential delivery of his content. In stage 3, consumers choose their preferred CP and ISP.

Analysis of Net Neutrality and Packet Discrimination Regimes

Consumers compare the four ISP-CP options and choose the option that yields the highest utility. In order to derive the market shares for each option, we need to calculate the six curves of indifferent consumers based on the pairwise com- parisons among them. Figure 6 demonstrates the various possibilities of how consumers are distributed among the four options. Solving for the exact market shares under each ISP- CP combination is difficult and the market shares under each ISP-CP option could look very different (demonstrated by the dotted lines in Figure 6).

In order to solve this problem, we utilize the symmetry of the corresponding market shares when the CPs interchange their decisions on paying for preferential delivery of their content. Interchanging the CPs’ delivery service choices induces what is called a Z2 × Z2 (or the Klein 4-group) action in group theory. We use the symmetry associated with this group action to solve for the demand distributions. The details of this symmetry analysis can be found in the appendices. The results of the consumer demand patterns (market shares) are summarized in Lemma 1. All proofs are relegated to the appendices.

Lemma 1 (Consumer Demand Patterns): Depending on the ISPs’ pricing decisions and the CPs’ delivery service choices, there are 16 possible outcomes. These outcomes can be grouped into four classes with similar consumer demand patterns under both symmetric and asymmetric equilibria.

The details of the consumer demand patterns can be found in Appendix C for the symmetric equilibrium case and Appendix E for the asymmetric equilibrium case.

Lemma 2 (Possible Equilibrium Outcomes): There are four possible (symmetric or asymmetric) equilibrium outcomes—only G pays both ISPs (outcome GG); both CPs pay ISP C and only G pays ISP D (outcome BG); only G pays ISP C and both CPs pay ISP D (outcome GB); both CPs pay both ISPs (outcome BB).

Lemma 2 shows that under both symmetric and asymmetric equilibria, the ISPs would have the incentive to deviate from the net neutrality outcome (which corresponds to the outcome NN in the PD regime), leading to four possible equilibrium outcomes, all of which involve packet discrimination. Note that with rG $ rY, any outcome that has only Y paying either ISP is not a possible equilibrium. For any given price p, if Y could afford to pay, then G would also have the incentive and the ability to pay. In other words, G has no reason to allow for Y’s content to be prioritized over its own content on either ISP, since not only G gains from an added customer, it gains more from the customer as compared to Y. Therefore, there is no feasible p that can induce any outcome involving only Y pays. Due to the technical complexity of asymmetric equilibrium analysis, there is no closed-form analytical expression for the separating market conditions for these four possible asymmetric equilibria and we explore them numeri- cally in Appendix K.6 We henceforth focus on the symmetric equilibrium results in the rest of the analysis.

6The numerical analysis of the asymmetric equilibria shows qualitatively the same results as the symmetric equilibria and is therefore not included in the main text.

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Figure 6. General Demand Distribution

Lemma 3 (ISPs’ Strategy): Depending on market condi- tions, there are four possible symmetric equilibrium pricing strategies (i.e., the F and p choices) for the ISPs: (a) when rG $ max{α1, β1rY, α2 + β2rY}, the equilibrium is outcome GG, where only G pays for priority delivery on both ISPs; (b) when β3rY # rG < α1 and rY # α3, the equilibrium is outcome BG (and equivalently, equilibrium GB), where G pays for priority delivery on both ISPs, while Y pays for priority delivery on only one ISP; and (c) otherwise, the equilibrium is outcome BB, where both CPs pay for priority delivery on both ISPs.

We diagrammatically show the results of Lemma 3 in Figure 7. The results of Lemma 3 is under the assumption of rG $ rY, which correspond to the upper half of the first quadrant above the rG = rY line in Figure 7. The equilibrium results assuming rG $ rY can be easily generalized to the case when rG < rY (the lower half of the first quadrant below the rG = rY line in Figure 7). Equilibria BG and GB (similarly BY and YB) are equiva- lent because of symmetric ISPs considered in this model.7

In general, ISPs will charge higher prices to CPs when only one pays for priority delivery than when both CPs pay for priority delivery. Consumers, however, are charged less, indicating that as the revenue generation rate rG increases, the relative contribution to ISPs’ profit gradually switches from the consumers to the CPs. This leads to our first proposition.

Proposition 1 (Competing ISPs always have an incentive to deviate from net neutrality): The competing ISPs’ profit is weakly higher under packet discrimination than under net neutrality, that is, π π π πC

PD D PD

C NN

D NN= ≥ = .

Proposition 1 shows that the competing ISPs are always better off under packet discrimination even in the presence of ISP

competition and thus have the incentive to deviate from net neutrality. In other words, when it comes to the net neutrality debate, ISPs will prefer abolishing net neutrality, even in the presence of ISP competition. This is a result that has been shown to be true when the ISP is a monopoly and it continues to hold with ISP competition. This finding is different from that of Bourreau et al. (2015), where the authors do not model the competition between CPs and find that competing ISPs do not always prefer packet discrimination. In Bourreau et al., the effect of competition faced by the ISPs is exaggerated due to the absence of CP competition. In contrast, when CPs are also under competitive pressure as considered in this paper, the effect of competition faced by the ISPs is moderated by CP competition and Proposition 1 shows that competing ISPs always prefer packet discrimination when CPs also compete with each other. Our analysis provides an explanation for the public stance of the ISPs in the ongoing net neutrality debate, as they continue to lobby for abolishing net neutrality. This result mirrors the results of Gans (2015), even though he does not explicitly model the effects of ISP competition.

Content providers, however, have supported the preservation of net neutrality. Would they continue to support net neu- trality when there is competition between ISPs? Our next result (Proposition 2) shows that under certain conditions, it is economically beneficial for the dominant CP to reverse its stance on net neutrality. In other words, some CPs might be better off when net neutrality is abolished in the presence of competition between ISPs. This is a crucial and, in some ways, a surprising result. Ever since the issue of net neu- trality has been publicly debated, prominent CPs like Google, Yahoo!, Microsoft, Netflix, and others have publicly sup- ported net neutrality, and so far, the economic analyses have mirrored the public stances of the various parties in the debate: when facing direct competition, CPs are worse off when net neutrality is abolished, while the ISPs are better off. Proposition 2 shows that under ISP competition, the support for net neutrality from CPs—and, specifically, from the dominant CPs—might not be so forthcoming.

7In Appendix L, we numerically explore asymmetric ISPs with different capacities and show that the main findings still hold true.

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Outcome BB: Both CPs pay both ISPs Outcome GG: Only G pays both ISPS Outcome BG: Both CPs pay C; only G pays D Outcome GB: Only G pays C; both CPs pay D Outcome YY: Only Y pays both ISPs Outcome BY: Both CPs pay C; only Y pays D Outcome YB: Only Y pays C; both CPs pay D

Figure 7. Equilibrium Outcomes

Proposition 2 (CP G may be better off under packet discrimination): When CP G is sufficiently dominant, its profit is higher under packet discrimination (corresponds to equilibrium GG) than that under net neutrality if the intensity of competition in the ISP market relative to that in the CP market is greater than a threshold. Formally,

if the ratio of t/k is higher than a thres-π π πG PD

G GG G NN= >{ }

*

hold and the ratio of rG/rY is higher than a threshold.

Proposition 2 shows that under certain conditions, CP G might in fact do better than it could under net neutrality. When rG and rY are similar and the corresponding equilibrium outcome is BB (both CPs decide to pay the two ISPs), CP G is definitely worse off under packet discrimination than under net neutrality. As rG becomes larger relative to rY, however, and the equilibrium shifts to outcome GG (where only G prefers to pay the two ISPs), G’s profit is at least as great as that under net neutrality. Specifically, the comparison result of G’s profit depends on the relative magnitude of the inten- sity of competition in the ISP and CP markets. We can think of the unit fit costs t and k as the strengths of the consumer loyalties within the CP market and within the ISP market, respectively. A more differentiated market corresponds to a higher level of consumer loyalty. Thus, t and k can be inter- preted as the reverse measures of the intensity of competition in the two markets, and the ratio of t/k measures the relative magnitude of the intensity of competition in the ISP market to that in the CP market. When the intensity of competition between the CPs is relatively low compared to that between the ISPs, such that t/k is greater than a threshold, the more efficient CP is actually better off under packet discrimination. In practice, it can be argued that the consumer loyalty in the CP market is relatively high compared to that in the ISP market, because digital content is more differentiated than Internet access service, which raises the possibility that this condition is likely to hold within markets for certain types of digital content.

To explain the intuition behind this result, it is instructive to first consider the effects of the CP competition between Y and G: when rG and rY are comparable, both CPs Y and G may end up in a Prisoner’s Dilemma—both CPs are forced to pay for priority delivery due to competitive pressure. Neither CP would like to pay, but is forced to, since otherwise they would be much worse off due to competition. But when rG is much higher than rY, both ISPs find it preferable to charge a high p such that only G can afford to pay. There are also indirect effects: because of the higher delays associated with the consumers of Y, the marginal consumer has lesser net utility, which leads to a lower fixed fee F. Due to ISP competition, although the ISPs would like to extract the surplus from the CPs as much as possible, their abilities to do so are limited by competition (i.e., ISP C’s ability to charge a high p is moderated by its competition with ISP D, and vice versa). Therefore, while they do stand to gain by extracting a part of G’s additional surplus, they cannot extract it fully. As a result, G ends up with a higher surplus than what it would have had under net neutrality even after paying for priority delivery. In other words, G would want to pay for priority delivery to marginalize its competitor (Y) in both the ISP markets. Consequently, the competition between the ISPs and the competition between the CPs will have moderating effects on each other. Which party has the upper hand in this scenario will depend on the relative magnitude of the intensity of competition in the two markets, in other words, the ratio of t/k.

This result is extremely significant. In the presence of ISP competition, a dominant CP (in our case, G, with rG being relatively large compared to rY) might no longer be concerned with preserving net neutrality. In fact, G might actually eke out a higher profit under packet discrimination, since its pay- ments to the ISP for priority delivery might pay off in terms of the additional revenue garnered from consumers that have switched from a rival CP.

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In the net neutrality debate thus far, CPs have generally been supportive of net neutrality (Internet Association 2014). This stance has been vindicated in the literature (Cheng et al. 2011; Guo et al. 2010; Guo et al. 2013), where it has been shown that when facing direct competition CPs are never better off under packet discrimination. Those results, however, have been derived under the assumption that there is no compe- tition among ISPs. Indeed, a monopoly ISP can extract all the rent from a CP that gains market share by paying for priority delivery. But when there is competition among ISPs, while they do increase their profits by deviating from net neutrality, they cannot extract the entire surplus from the CP that decides to pay for priority delivery of its content. The effect of competition moderates an ISP’s ability to extract the surplus from the CPs, and in such situations, a dominant CP can indeed be better off when ISPs deviate from net neutrality. In such cases (for example, in the mobile broadband market where there is effective ISP competition), we can expect the dominant CPs to be less supportive of the need for net neutrality.

In fact, such a shift in stance might already be underway. As Manjoo (2014) observed,

Large Internet businesses have written a few letters to regulators in support of the issue and have parti- cipated in the back-channel lobbying effort, but they have not joined online protests, or otherwise moved to mobilize their users in favor of new rules.

He further goes on to speculate on the reason why the large Internet businesses have taken such a stance: “They may be too big to bother with an issue that primarily affects the smallest Internet companies,” and they “would escape rela- tively unscathed” by paid prioritization. Our research shows that not only would some of these large Internet companies escape relatively unscathed from paid prioritization, they might actually prosper from such an arrangement.

Proposition 3 (CP Y is always worse off under packet discrimination): CP Y’s profit is lower under packet dis- crimination than under net neutrality, that is, π πY

NN Y PD≥ .

Proposition 3 reminds us that although the dominant CP may be better off under the packet discrimination regime, the economically less successful CP (e.g., a startup in a market with an established market player) is always worse off. In such situations, packet discrimination (e.g., the option of a paid fast lane) can act as a disincentive to entry for newer entrants in a marketplace with well-established incumbents. From a policymaker’s perspective, in the long term, this can have a debilitating effect on content innovation. The impact of net neutrality and packet discrimination on content inno-

vation has been studied from different perspectives, such as the entry of CPs (Bourreau et al. 2015; Guo and Easley 2016; Krämer and Wiewiorra 2012), the investment of CPs (Choi and Kim 2010), and the profitability of CPs (Guo et al. 2012). Our analysis contributes to this discussion. It shows that even in the presence of ISP competition, we do not have a level playing field since the dominant CP can still marginalize a less efficient or newer rival, to the extent that it (the dominant CP) might be better off without net neutrality. So, in a way, the dominant CP can leverage the competition among ISPs to become even more dominant by taking advantage of the flexible traffic management options under the packet discrimination regime.

As Manjoo observed, recently it is the smaller Internet firms that have been most vocal in the net neutrality debate. Companies like Etsy, where consumers can shop directly from people around the world, “would not have been able to pay for priority access if broadband companies ever created a fast lane online.” Etsy’s public policy director went on to com- ment that “Delays of even fractions of a second result in dropped revenue for our users.” Our result in Proposition 3 shows that this concern is justified because the smaller firms will certainly be negatively affected by paid prioritization.

Prior studies with a monopolist ISP and competing CPs (Cheng et al. 2011; Choi and Kim 2010) show that all CPs will be united in their stance in preserving net neutrality. With both ISP competition and CP competition, however, our findings suggest that under certain market conditions, it will be just the smaller CPs that will support net neutrality.

Next, we study the welfare effect under net neutrality and pac- ket discrimination regimes. Consumer surplus is defined as

( )CS U x z dxdzij ij=  ,0 1

0

1

and social welfare is defined as

SW CSij Cij Dij Yij Gij ij= + + + +π π π π .

Proposition 4 (Comparison of Social Welfare under Net Neutrality and Packet Discrimination): Social welfare is weakly higher under packet discrimination than under net neutrality, that is, SW SWPD NN≥ .

Proposition 4 indicates that packet discrimination with flexible network management options is welfare enhancing compared to the net neutrality regime. This result supports findings in prior studies (Bourreau et al. 2015; Cheng et al. 2011; Guo et al. 2012; Guo and Easley 2016; Krämer and Wiewiorra 2012).

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Concluding Remarks

Theoretical Implications

We have proposed a modeling framework that captures the dynamics of two interrelated markets—that of Internet access service and that of digital content—providing complementary products. Duopolists compete for consumers in each market (ISPs C and D in the Internet access service market and CPs Y and G in the digital content market). Therefore consumers choose their preferred option among four product combin- ations (CY, CG, DY, and DG). Furthermore, user experiences are jointly determined by the ISPs’ pricing decisions and the CPs’ delivery service choices. We show that the interactions between the two markets and the relative market power of the agents in the two markets play a critical role in determining the equilibrium outcomes.

Modeling both ISP competition and CP competition enables us to make unique contributions to the literature of economic analysis of net neutrality. Prior models with no ISP compe- tition (Cheng et al. 2011; Choi and Kim 2010; Krämer and Wiewiorra 2012) find that the monopolist ISP always prefers packet discrimination. When considering ISP competition but no CP competition, Bourreau et al. (2015) show that com- peting ISPs may not always prefer packet discrimination. Our results show that when CPs are also under competitive pressure, competing ISPs always prefer packet discrimination. In addition, the coexistence of both ISP and CP competition may also reverse the dominant CP’s stance on net neutrality. Prior models with CP competition (Cheng et al. 2011; Guo et al. 2010; Guo et al. 2013) find that CPs are worse off under packet discrimination. Our results show that the dominant CP may be better off under packet discrimination.

This modeling framework is not restricted to the Internet data transmission process and can be applied to a wide range of other contexts, where consumers derive their utility from a pair of complementary products. For example, in the ongoing hardware battle between competing hardware platforms (e.g. the Apple Macintosh versus the PC), a critical factor is soft- ware compatibility and functionality. While computer makers do not compete directly with software manufacturers, the competition between the computer hardware platforms never- theless attenuates the competition between the software manufacturers, since consumers need to “consume” both the hardware and the software for their computing needs. When making their purchase decisions, users simultaneously con- sider the specifications of the device and the compatibility and ease-of-use of the corresponding software. The competi- tion between firms in both the computer hardware and soft- ware markets interacts with each other and jointly determine the experiences of the end-users.

Managerial and Policy Implications

Our findings have important managerial implications. We find that net neutrality regulation (or conversely, the potential packet discrimination mechanisms) affects CPs differently. Moreover, this impact on the CPs’ incentives and conse- quently content innovation critically depends on the market power of the CP and the relative magnitude of the intensity of competition between the markets of Internet access service and digital content. In practice, CPs strive to improve their profit margin through lowering the cost of generating new content or licensing existing content. It has been observed in several online markets that the dominant CPs often get more dominant over time. Our findings suggest that packet dis- crimination in the presence of ISP competition will sometimes amplify the competitive advantage of the more efficient CP, even to the extent that the more efficient CP is better off with paid prioritization compared to the outcome under the net neutrality regime. At the same time, we note that packet discrimination will ensure that a majority of consumers will benefit from getting their preferred content faster, leading to higher social welfare. However, this will also lead to margin- alizing the smaller content providers, including startups that will find it more difficult to gain a foothold against a well- established incumbent.

Our findings also have important policy implications for net neutrality. Our results show that ISP competition may not substitute for net neutrality regulation, especially in the presence of CP competition. Without net neutrality regula- tion, the competing ISPs always have the incentive to charge CPs for preferential delivery, and in the presence of CP competition, they have the ability to induce CPs to pay for packet prioritization. Contrary to popular belief, we find that some advantaged CPs may benefit from paid prioritization because such arrangements further enforce their dominance in the content market. Paid prioritization, however, always hurts the disadvantaged CPs. In order to protect and encourage content innovation, the policy makers are advised to evaluate the specific market conditions (such as revenue generation ability of CPs and competition intensity) of individual markets of ISPs and CPs.

Limitations and Future Research

In this paper, we assume that the entire consumer market is covered. If we relax this assumption, we postulate that under net neutrality the ISPs will choose to cover the whole market if consumers’ valuation of the Internet access service is higher than a threshold, and only part of the market if consumers’ valuation is low. In the packet discrimination regime, the ISPs’ decision whether to serve the whole consumer market

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should be similar. Intuitively, the threshold value under packet discrimination should be lower than that under net neutrality, since the ISPs have the option to subsidize end consumers from the payments collected from CPs and there- fore have a higher incentive to serve more consumers. That is, the ISPs could cover more market without net neutrality. As a result, it is possible that social welfare is higher under packet discrimination than under net neutrality. In other words, we expect our social welfare result to continue to hold when the full-market-coverage assumption is relaxed. An- other possible result of not enforcing the full-market-coverage constraint is that under certain conditions, in the absence of net neutrality, the disadvantaged CP Y might be completely marginalized, especially when both the ISPs find it profitable to prioritize only G’s content. This is more likely to occur when rG is substantially greater than rY. In such a scenario, consumers of Y that are being served by either ISP will find it advantageous to switch to G or stay out of the market, so much so that Y is completely driven out of the market.

We study a short-run problem where the ISPs’ capacity is fixed, and focuses on the interaction between ISP competition and CP competition. In a long-run problem with competing ISPs having the option to expand their capacity, we envisage that individually, they would not like to invest in capacity expansion, but they would stand to lose a lot of customers (on both sides of the platform) if their competitor expands capacity. Consequently, the competition between the ISPs and the competition between the CPs will have moderating effects on each other. In other words, both CPs might be forced to pay for priority delivery and end up with the same congestion as they would have had when neither pays, thanks to the competition between CPs in the short run. This result will be alleviated by a higher bandwidth in the long run because the ISPs might be forced to expand capacity due to the competition between the ISPs.

We assume that the CPs generate their revenue based on an advertisement-supported model. In real life, some CPs (e.g., Netflix) charge consumers a subscription fee for accessing their content. If the consumers pay the CPs for content, the equilibrium results will be slightly different: for example, the Internet access fee charged by the ISP will presumably be lower, because consumers now have to pay the additional subscription fee for content. But the dynamics of the compe- tition between CPs will still remain the same. Under the subscription-fee-based revenue model for CPs, we expect that with this additional pricing instrument (i.e., the subscription fee from consumers) the dominant CP8 would be even more

dominant in competing with the other CP in the absence of net neutrality. In other words, our main result regarding the dominant CP being better off in the absence of net neutrality would be further amplified.

Another assumption in our model is that consumers only visit one of the two available competing CPs (i.e., consumers single-home CPs). In real life, consumers visit various web- sites (i.e., consumers multi-home CPs). A consumer can be considered to multi-home CPs when she accesses email on Gmail and watches videos on YouTube. Gmail and YouTube represent two different types of content and they do not directly compete for consumers. This type of multi-homing behavior exacerbates the degree of network congestion. The more multi-homing behavior, the more burden on the net- work. Since the focus of this paper is competition, this type of multi-homing different content types (where CPs do not compete with each other) is beyond our model. It is also possible that a consumer might split her attention between different competing contents of the same type (e.g., she might allocate some of her time from watching videos on YouTube to watching videos on Vimeo, with no change in her overall consumption). The content consumption of these “split” consumers is still captured by the market shares of the com- peting CPs in our model. A variant of this situation is where the consumer watches more videos on Vimeo on top of what she was already watching on YouTube (with an increase in her overall consumption). This type of consumption could be an extension of our model. It reduces the intensity of compe- tition between the two CPs somewhat, but does not qualitatively change the insights of the paper.

Another interesting direction for further research is extending the market structure. In this paper, we consider that CPs and ISPs operate independently and explore the role of packet discrimination in the last mile. If a CP and an ISP merge, this type of firm integration would somewhat change the dynamics of competition in both the ISP and the CP markets. It might well be possible that under some conditions, when one ISP integrates with the less efficient CP, the integrated firm may even prioritize the rival CP’s content to profit from charging for priority delivery. CPs may pay ISPs in order to effectively move their content closer to the edge through paid peering, thereby reducing the latency of content. There is no con- sensus so far as to whether this arrangement violates the principles of net neutrality, but regardless, we believe that it will be an exciting area for further research.

Future studies may explore whether the various strands of literature on the economics of net neutrality can be brought together. Given the complexity of the issue, different streams of literature have looked at different aspects of the problem, and it is an open question whether those different streams can be reconciled through a unified model.

8Note that under the subscription-fee-based revenue model for CPs, a CP can become dominant as a result of a lower marginal cost of production (e.g., a CP like Netflix might enjoy lower costs in terms of acquiring or producing content).

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About the Authors

Hong Guo is an associate professor and Robert and Sara Lumpkins Associate Professor of Business Analytics in the Department of Information Technology, Analytics, and Operations at the Univer- sity of Notre Dame. She received her Ph.D. in information systems from the University of Florida in 2009. Hong studies economic analysis of IT policy issues such as net neutrality and public safety networks. She is also interested in characterizing key design features of emerging information systems (e.g., consumer review systems, mobile platforms, digital games, etc.) and examining firms’ corresponding strategies.

Subhajyoti Bandyopadhyay is an associate professor and George W. and Lisa O. Etheridge, Jr. Professor of Management in the Department of Information Systems and Operations Management at the University of Florida. He received his Ph.D. in MIS from Purdue University in 2002. His work has been published in several journals in the areas of Information Systems, Operations Manage- ment, and Marketing. His current research interests include econo- mics of information systems and public policy, especially in the area of net neutrality, national broadband policy, and health informatics.

Arthur Lim is a professor of the Practice of Mathematics at the University of Notre Dame. He received his Ph.D. in Mathematics from the University of Utah in 2001. His research interest lies in the areas of mathematical analysis and its applications. He has pub- lished papers in representation theory and combinatorial matrix analysis. Arthur is also an award-winning mathematics teacher. He enjoys employing an eclectic mix of pedagogical methods and technology to create an enhanced learning experience.

Yu-Chen Yang is an assistant professor in the Department of Information Management in the College of Management at National Sun Yat-sen University in Taiwan. Prior to joining National Sun Yat-sen University, he received his Ph.D. in Information System from the University of Florida in 2013. He served in the Air Force of the Republic of China for two years and won the distinguished service award. He teaches managerial math, electronic commerce and supply chain management. Yu-Chen won the Teaching Excellent Award of National Sun Yat-sen University in 2013 and 2014. His research interests include e-commerce, economics of information systems, and cloud computing.

Hsing Kenneth Cheng received his Ph.D. in computers and information systems from William E. Simon Graduate School of Business Administration, University of Rochester in 1992. He is John B. Higdon Eminent Scholar at the Department of Information Systems and Operations Management of Warrington College of Business Administration, University of Florida. Prior to joining UF, he served on the faculty of The College of William and Mary from 1992 to 1998. His research interests focus on analyzing the impact of Internet and information technology on software development and marketing, and information systems policy issues, in particular, the national debate on network neutrality. He has served on the pro- gram committee of many information systems conferences and workshops. He is a program cochair for the 2003 Workshop on E- Business, and conference cochair for the 2012 Workshop on E- Business.

370 MIS Quarterly Vol. 41 No. 2/June 2017

RESEARCH ARTICLE

EFFECTS OF COMPETITION AMONG INTERNET SERVICE PROVIDERS AND CONTENT PROVIDERS ON

THE NET NEUTRALITY DEBATE Hong Guo

Mendoza College of Business, University of Notre Dame, Notre Dame, IN 46556 U.S.A. {hguo@nd.edu}

Subhajyoti Bandyopadhyay Warrington College of Business Administration, University of Florida

Gainesville, FL 32611 U.S.A. {shubho.bandyopadhyay@warrington.ufl.edu}

Arthur Lim Department of Mathematics, University of Notre Dame,

Notre Dame, IN 46556 U.S.A. {arthurlim@nd.edu}

Yu-Chen Yang College of Management, National Sun Yat-sen University, Kaohsiung 80424, TAIWAN {ycyang@mis.nsysu.edu.tw}

Hsing Kenneth Cheng Warrington College of Business Administration, University of Florida, Gainesville, FL 32611 U.S.A. {kenny.cheng@warrington.ufl.edu}

School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai, China

Appendix A Delays under Packet Discrimination

Under outcome NN, both CPs receive the same priority on both ISPs. Thus, and w wCY NN CG NN N NCY NN CG NN{ } { } { } { }= = − − 1

μ λ λ

w wDY NN DG NN N NDY NN DG NN{ } { } { } { } .= = − − 1

μ λ λ

Under outcome NY, both CPs receive the same priority on C and Y receives higher priority on D. Thus,

and w wCY NY CG NY N NCY NY CG NY{ } { } { } { } ,= = − − 1

μ λ λ wDY NY NDY NY{ } { } ,= − 1

μ λ ( )( )wDG NY N N NDY NY DY NY DG NY{ } { } { } { } .= − − − μ

μ λ μ λ λ

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A2 MIS Quarterly Vol. 41 No. 2─Appendices/June 2017

Under outcome , both CPs receive the same priority on and receives higher priority on . Thus, { } = { } = { } { } , { } = { } { } { } , and { } = { } .

Under outcome , both CPs receive the same priority on both ISPs. Thus, { } = { } = { } { } and { } ={ } = { } { } . Under outcome , receives higher priority on and both CPs receive the same priority on . Thus, { } = { } , { } =

{ } { } { } , and { } = { } = { } { } . Under outcome , receives higher priority on both ISPs. Thus, { } = { } , { } = { } { } { } , { } = { } , and { } = { } { } { } . Under outcome , receives higher priority on and receives higher priority on . Thus, { } = { } , { } =

{ } { } { } , { } = { } { } { } , and { } = { } . Under outcome , receives higher priority on and both CPs receive the same priority on . Thus, { } = { } , { } =

{ } { } { } , and { } = { } = { } { } . Under outcome , receives higher priority on and both CPs receive the same priority on . Thus, { } =

{ } { } { } , { } = { } , and { } = { } = { } { } . Under outcome , receives higher priority on and receives higher priority on . Thus, { } = { } { } { } , { } = { } , { } = { } , and { } = { } { } { } . Under outcome , receives higher priority on both ISPs. Thus, { } = { } { } { } , { } = { } , { } = { } { } { } , and { } = { } . Under outcome , receives higher priority on and both CPs receive the same priority on . Thus, { } =

{ } { } { } , { } = { } , and { } = { } = { } { } . Under outcome , both CPs receive the same priority for both ISPs. Thus, { } = { } = { } { } and { } ={ } = { } { } . Under outcome , both CPs receive the same priority on and receives higher priority on . Thus, { } = { } =

{ } { } , { } = { } , and { } = { } { } { } . Under outcome , both CPs receive the same priority on and receives higher priority on . Thus, { } = { } =

{ } { } , { } = { } { } { } , and { } = { } . Under outcome , both CPs receive the same priority for both ISPs. Thus, { } = { } = { } { } and { } ={ } = { } { } .

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MIS Quarterly Vol. 41 No. 2─Appendices/June 2017 A3

Appendix B CPs’ Incentive Compatibility Constraints Under outcome , CPs’ incentive compatibility constraints are { } ≥ { }, { }, { } and { } ≥ { }, { }, { }. Under outcome , CPs’ incentive compatibility constraints are { } ≥ { }, { }, { } and { } ≥ { }, { }, { }. Under outcome , CPs’ incentive compatibility constraints are { } ≥ { }, { }, { } and { } ≥ { }, { }, { }. Under outcome , CPs’ incentive compatibility constraints are { } ≥ { }, { }, { } and { } ≥ { }, { }, { }. Under outcome , CPs’ incentive compatibility constraints are { } ≥ { }, { }, { } and { } ≥ { }, { }, { }. Under outcome , CPs’ incentive compatibility constraints are { } ≥ { }, { }, { } and { } ≥ { }, { }, { }. Under outcome , CPs’ incentive compatibility constraints are { } ≥ { }, { }, { } and { } ≥ { }, { }, { }. Under outcome , CPs’ incentive compatibility constraints are { } ≥ { }, { }, { } and { } ≥ { }, { }, { }. Under outcome , CPs’ incentive compatibility constraints are { } ≥ { }, { }, { } and { } ≥ { }, { }, { }. Under outcome , CPs’ incentive compatibility constraints are { } ≥ { }, { }, { } and { } ≥ { }, { }, { }. Under outcome , CPs’ incentive compatibility constraints are { } ≥ { }, { }, { } and { } ≥ { }, { }, { }. Under outcome , CPs’ incentive compatibility constraints are { } ≥ { }, { }, { } and { } ≥ { }, { }, { }. Under outcome , CPs’ incentive compatibility constraints are { } ≥ { }, { }, { } and { } ≥ { }, { }, { }. Under outcome , CPs’ incentive compatibility constraints are { } ≥ { }, { }, { } and { } ≥ { }, { }, { }. Under outcome , CPs’ incentive compatibility constraints are { } ≥ { }, { }, { } and { } ≥ { }, { }, { }. Under outcome , CPs’ incentive compatibility constraints are { } ≥ { }, { }, { } and { } ≥ { }, { }, { }.

Appendix C Proof of Lemma 1: The Symmetric Equilibrium Case Consumers have four choices of ISP-CP combinations: , , , and . Consumer demands for these four ISP-CP combinations can be derived by analyzing the curves of indifferent consumers. There are six curves of indifferent consumers based on the pairwise comparisons among the four ISP-CP combinations. For a given outcome , where , = (Neither CP pays), (Only pays), (Only pays), and (Both CPs pay), these six curves of indifferent consumers can be characterized by four points { }, { }, { }, and { }: consumers located on = { } are indifferent between and ; consumers located on = { } are indifferent between and ; consumers located on = { } are indifferent between and ; consumers located on = { } are indifferent between and ; consumers located on the line that goes through points { }, { } and { }, { } are indifferent between and ; and consumers located on the line that goes through points { }, { } and { }, { } are indifferent between and .

Comparing consumers’ utility functions for the corresponding pairs of ISP-CP combinations yields { } = + { } { } , { } =+ { } { } , { } = + + { } { } , and { } = + + { } { } . Considering symmetric

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equilibrium with = , we have { } = + { } { } and { } = + { } { } . We observe that the sign of { } −{ } is the same as the sign of { } − { }. In particular, { } = { } if and only if { } = { }. Each outcome is determined by the ISPs’ pricing decisions and the corresponding content providers’ delivery service choices. We use indicator functions { }, { }, { } and { }, which take values of 0 or 1, to represent whether content providers and would pay for preferential delivery on ISPs and . To be consistent with the four ISP-CP combinations on the unit square, we denote outcome by

the matrix { } { }{ } { } . We introduce two types of actions (horizontal and vertical flips) to explore the connections among the 16 outcomes: Horizontal Flip: Decisions of and are simultaneously interchanged on ISPs and . Specifically, horizontal flip changes outcome

dictated by { } { }{ } { } to outcome ’ ’ dictated by { } { }{ } { } , where ’ = ,, if =if =,, if =if = and ’ = ,, if =if =,, if =if = .

Vertical Flip: Decisions of and are simultaneously interchanged across ISPs and . Specifically, vertical flip changes outcome

dictated by { } { }{ } { } to outcome dictated by { } { }{ } { } . Among the 16 outcomes, some outcomes permute amongst themselves when horizontal flip or vertical flip is applied and therefore can be grouped together into four invariant classes: (a) outcomes , , , and ; (b) outcomes and ; (c) outcomes and ; (d) outcomes , , , , , , , and . In the following discussion, we give precise description of the changes to the indifferent customers when horizontal flip or vertical flip is applied to an outcome.

Applying Horizontal Flip: The decisions of on the two ISPs are interchanged with the decisions of in a given outcome. Horizontal flip

changes outcome dictated by { } { }{ } { } to outcome ’ ’ dictated by { } { }{ } { } . That is we have { } = { }, { } ={ }, { } = { }, and { } = { }. When the decisions in outcome are changed to ’ ’, the decisions of on and and the decisions of on and are interchanged. The queuing priorities are interchanged on ISPs and . This simultaneously interchanges the waiting times and market demand on and according to the new queuing priorities. We note that fees for all customers are equal so the redistribution is dependent solely on waiting times. Interchanging waiting times on ISPs and yields { } = { }, { } =

{ } , { } = { } , and { } = { } . This gives { } + { } = + { } { } + + { } { } = +{ } { } + − { } { } = 1, which implies { } = 1 − { }. Similarly, we have { } = 1 − { }, { } = { }, and { } = { }. We note that the positions of these curves of indifferent consumers relative to the line of = or = remain the same according to the decisions of and . Applying Vertical Flip: The decisions of and on are interchanged with their decisions on in a given outcome. Vertical flip changes

outcome dictated by { } { }{ } { } to outcome dictated by { } { }{ } { } . That is we have { } = { } , { } = { } , { } = { }, and { } = { }. When the decisions in outcome are changed to , the decisions of and on are swapped with the decisions of and on . The queuing priorities are interchanged on ISPs and . This simultaneously interchanges the waiting times and market demand on ISPs and according to the new queuing priorities. We note that fees for all customers are equal so the redistribution is dependent solely on waiting times. Interchanging waiting times on ISPs and yields { } = { }, { } = { }, { } ={ } , and { } = { } . This gives { } = + { } { } = + { } { } = { } . Similarly, { } = { } . We also have { } + { } = + { } { } + + { } { } = − { } { } + + { } { } = 1, which implies { } = 1 − { }. Similarly, { } = 1 − { }. Next we apply the above results of horizontal and vertical flips to each of the classes (a) through (d) to characterize the demand distribution under each outcome.

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(Class a) Outcomes , , , and Under outcomes , , , and , all customers have equal queuing priorities. Therefore applying horizontal flip or vertical flip to these outcomes will not change the queuing priorities. Hence the indifferent consumers remain unchanged when horizontal flip or vertical flip is applied. From horizontal flip relations, we have { } = 1 − { }, { } = 1 − { }, { } = 1 − { }, { } = 1 − { }, { } =1 − { } , { } = 1 − { } , { } = 1 − { } , and { } = 1 − { } . That is { } = { } = { } = { } = and { } = { } = { } = { } = . From vertical flip relations, we have { } = 1 − { }, { } = 1 − { }, { } = 1 −{ } , { } = 1 − { } , { } = 1 − { } , { } = 1 − { } , { } = 1 − { } , { } = 1 − { } . That is { } ={ } = { } = { } = and { } = { } = { } = { } = . Therefore, as shown in Figure C1, the market demand for , , , and are equal under outcomes , , , and . That is { } = { } = { } = { } = , { } = { } = { } = { } = , { } = { } = { } ={ } = , and { } = { } = { } = { } = .

Figure C1. Demand Distribution of Class a (outcomes , , , and )

(Class b) Outcomes and Under outcome , only pays for preferential delivery on both ISPs. Under outcome , only pays for preferential delivery on both ISPs. Thus, { } − { } > 0, { } − { } > 0, { } − { } < 0, and { } − { } < 0. Vertical flip does not change the decisions of and on and in outcomes and . Therefore we have { } = { } > , { } =1 − { } ⟹ { } = , { } = 1 − { } ⟹ { } = , { } = { } < , { } = 1 − { } ⟹ { } = , and { } =1 − { } ⟹ { } = . Moreover, horizontal flip applied to outcome gives outcome and vice versa. This gives { } = 1 −{ } = { } = 1 − { }. Thus, we simplify the notations to { } = { } = { } > and { } = { } = { } < . Therefore, as shown in Figure C2, the demands for , , , and in outcomes and are related such that { } = { } = { } ={ } = { } and { } = { } = { } = { } = { } . In other words, ISPs and have the same market share, i.e., { } = { } = { } = { } = . Within each ISP, the paying CP gets more customers than the non-paying CP, i.e., { } ={ } = { } = { } > > { } = { } = { } = { }.

1 2⁄ 1 2⁄

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Outcome Outcome Figure C2. Demand Distribution of Class b (outcomes and )

(Class c) Outcomes and Under outcome , only pays for preferential delivery on and only pays for preferential delivery on . Under outcome , only pays for preferential delivery on and only pays for preferential delivery on . Thus { } − { } > 0, { } − { } < 0, { } − { } < 0, and { } − { } > 0. Therefore we have { } > > { } and { } < < { }. Since the sign of { } − { } is the same as the sign of { } − { } for any outcome , we have { } > { }, and { } < { }. Observe that both horizontal flip and vertical flip applied to outcome gives outcome and vice versa. Through the connection of horizontal flip, we have { } = 1 − { }, { } = 1 − { }, { } = { }, and { } = { }. Through the connection of vertical flip, we have { } = { }, { } = { }, { } = 1 − { }, and { } = 1 − { }. Combining the two set of equalities gives { } = 1 − { } , { } = 1 − { } , { } = 1 − { } , and { } = 1 − { } . Since { } > { } and { } < { } , the last set of equalities says that { } > > { } and { } < < { }. This says that the indifferent consumers { } and { } (as well as { } and { }) are symmetrically positioned on either side of = . Likewise, { } and { } (as well as { } and { }) are symmetrically positioned on either side of = . Therefore the demands for , , , and in outcomes and are related such that { } = { } = { } = { } and { } = { } = { } = { }. As shown in Figure C3, ISPs and have the same market share, i.e., { } = { } = { } = { } = . Within each ISP, the paying CP gets more customers than the non-paying CP, i.e., { } = { } = { } = { } > > { } = { } = { } ={ }.

1 2⁄ 1 2⁄

{ } 1 2⁄{ } 1 2⁄

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Outcome Outcome Figure C3. Demand Distribution of Class c (outcomes and )

(Class d) Outcomes , , , , , , , and Based on CPs’ delivery service choices in outcomes , , , , , , , and , we know that { } − { } = { } −{ } = 0 , { } − { } = { } − { } = 0 , { } − { } > 0 , { } − { } < 0 , { } − { } > 0 , and { } − { } < 0. Therefore we have { } = { } = , { } = { } = , { } > > { }, and { } > > { }. Since the sign of { } − { } is the same as the sign of { } − { } for any outcome , we have { } < { } and { } > { }. Likewise, we have { } > { } and { } < { }. Successive applications of horizontal flip and vertical flip connect outcomes , NG, , and as follows:

Outcome Horizontal Flip Outcome Vertical Flip ↑|↓ ↑|↓ Vertical Flip

Outcome Horizontal Flip Outcome Through horizontal flip, we have { } = 1 − { } = , { } = 1 − { } < , { } = { } , { } = { } , { } = 1 −{ } < , { } = 1 − { } = , { } = { }, and { } = { }. Through vertical flip, we have { } = { } > , { } ={ } = , { } = 1 − { }, { } = 1 − { }, { } = { } < , { } = { } = , { } = 1 − { }, and { } = 1 −{ } . Therefore the demand for , , , and in outcomes , , , and are related such that { } = { } ={ } = { } , { } = { } = { } = { } , { } = { } = { } = { } , and { } = { } ={ } = { }. The demand analysis for outcomes , , , and is the same as that in outcomes , , , and since both CPs receive the same queuing priority when they both pay for preferential delivery. Therefore, the demand for , , , and in outcomes , ,

, and are related such that { } = { } = { } = { }, { } = { } = { } = { }, { } = { } ={ } = { }, and { } = { } = { } = { }. If and make identical decisions on any ISP ( or ), consumers on that ISP will receive the same queuing priority. For example, under outcomes NG and BG, indifferent consumers of all four ISP-CP combinations are the same, which leads to identical demand distribution for

, , , and . That is { } = { }, { } = { }, { } = { }, and { } = { }. By the same arguments above, we obtain the pairings with identical demand distribution for , , , and : outcomes and , outcomes and , and outcomes and .

1 2⁄{ } { } 1 2⁄ { }

{ }

1 2⁄ { }

{ }

1 2⁄{ }

{ }

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As shown in Figure C4, outcomes in class d reveal particularly interesting demand patterns. For example, in outcome BG, although both CPs pay for preferential delivery on ISP , gets fewer consumers than from ISP , i.e., { } > { }.

Outcomes and Outcomes and

Outcomes and Outcomes and Figure C4. Demand Distribution of Class d (outcomes , , , , , , , and )

Summarizing the above analysis for the symmetric equilibrium case, we conclude that the 16 outcomes can be grouped into four classes, within which all outcomes are invariant under horizontal and vertical flips with similar consumer demand patterns.

Appendix D Proof of Lemma 2: The Symmetric Equilibrium Case We derive the possible symmetric equilibria in the packet discrimination regime by the following steps: step 1, prove that all outcomes involving only pays for priority delivery are infeasible; step 2, derive properties of the equilibrium fixed fee ; step 3, eliminate dominated outcomes.

Step 1: Prove that all outcomes involving only pays for priority delivery are infeasible In step 1, we show that there is no feasible for any outcome involving only pays. Therefore such outcomes ( , , , , , , and ) cannot be an equilibrium. Since some outcomes are infeasible for similar reasons, we group them together.

1 2⁄ 1 2⁄

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1 2⁄

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Outcomes and Here we focus on showing that there is no feasible for outcome , as the analysis for outcome is similar. For outcomes to be feasible, all the CPs’ incentive compatibility constraints need to be satisfied: (1) { } − { } ≥ 0 ; (2) { } − { } ≥ 0 ; (3) { } − { } ≥ 0; (4) { } − { } ≥ 0; (5) { } − { } ≥ 0; and (6) { } − { } ≥ 0. Inequality (2) is − { } + { } − { } − { } + { } ≥ 0 . Since { } + { } > and { } +{ } = , inequality (2) can be reduced to ≤ { } { } ⁄{ } . Inequality (5) is { } + { } − { } + { } − { } ≥ 0 . Since { } = , { } + { } = , and { } + { } < , inequality (5) can be reduced to ≥ ⁄ { } { }⁄ .

We know that − { } − { } = { } + { } − , { } > , and ≥ . Thus we have { } { } ⁄{ } <⁄ { } { }⁄ . Therefore (2) and (5) are inconsistent. Hence there is no feasible for outcome . Outcomes and

Outcomes and are infeasible for similar reasons. Outcome is not feasible since the following incentive compatibility constraints are inconsistent: (1) { } − { } ≥ 0 and (2) { } − { } ≥ 0.

Inequality (1) can be reduced to ≤ { } { } { } { }{ } { } . Note that we have { } + { } − { } − { } ={ } + { } − + − { } − { } . Since { } + { } − = − { } − { } , we have { } + { } −{ } − { } = 2 { } + { } − = 2 − { } − { } . Thus inequality (1) can be simplified to ≤⁄ { } { }{ } { } ⁄ .

Inequality (2) can be reduced to ≥ ⁄ { } { }⁄ { } . Note that we have { } + { } + { } + { } = 1. But { } <{ }. Thus we have { } { } > − { }. Therefore ≥ ⁄ { } { }⁄ { } > ⁄ { } { }{ } { } ⁄ .

In addition, we know ≥ . Thus we have ⁄ { } { }⁄ { } > ⁄ { } { }{ } { } ⁄ ≥ ⁄ { } { }{ } { } ⁄ . Therefore inequalities (1) and (2) are inconsistent. Hence outcome is infeasible.

Outcomes and Outcomes and are infeasible for similar reasons. Outcome is feasible provided { } − { } ≥ 0, i.e., − { } +{ } + { } − ≥ 0. Note that { } + { } = . This gives − { } ≥ 0. Since { } > , we have ≤ 0. Hence there is no feasible for outcome .

Outcome Outcome is not feasible since the following incentive compatibility constraints are inconsistent: (1) { } − { } ≥ 0 and (2) { } − { } ≥ 0. Inequality (1) is { } − { } − + { } − { } ≥ 0. Note that { } + { } = . Thus we have { } −{ } − = − { } − { } = −2 { } < 0. Therefore inequality (1) can be reduced to ≤ − { }{ } . Inequality (2) can be reduced to ≥ 1 − 4 { } .

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Recall that { } = { } , { } = { } , and { } + { } = . Thus inequality (1) may be re-written as ≤ 1 − { } and inequality (2) may be re-written as ≥ 4 { } 1 − { } . Since ≤ and 4 { } > 1, inequality (1) implies

that ≤ 1 − { } < but inequality (2) implies that ≥ 4 { } 1 − { } > . Therefore inequalities (1) and (2) are inconsistent and there is no feasible for outcome . To summarize the above, there is no feasible for outcomes , , , , , , and , and therefore, they cannot be an equilibrium.

Step 2: Derive properties of the equilibrium fixed fee In step 2, we derive properties of the equilibrium fixed fee . Here we first discuss some properties for all 16 outcomes and thus the subscript

is omitted in this discussion. Under the assumption of full market coverage, the profit maximizing fixed fee is such that the consumers of all four ISP-CP combinations ( , , , and ) with the lowest net utility will get zero net utility. We now define the global utility function ( , ) for the entire market [0,1] × [0,1]. First recall the definition of the demand distribution of each ISP-CP combinations characterized by the utility functions. = {( , ) ∈ [0,1] × [0,1]; ( , ) ≥ max{ ( , ), ( , ), ( , ) } } = {( , ) ∈ [0,1] × [0,1]; ( , ) ≥ max{ ( , ), ( , ), ( , )} } = {( , ) ∈ [0,1] × [0,1]; ( , ) ≥ max{ ( , ), ( , ), ( , )} } = {( , ) ∈ [0,1] × [0,1]; ( , ) ≥ max{ ( , ), ( , ), ( , )} } Note that each of the following inequalities reduces to regions on [0,1] × [0,1] dictated by the indifference customers between mutual pairs of ISP-CP combinations: ( , ) − ( , ) ≥ 0 ⟺ ≥ ( , ) − ( , ) ≥ 0 ⟺ ≥ ( , ) − ( , ) ≥ 0 ⟺ ≥ ( , ) − ( , ) ≥ 0 ⟺ ≥ ( , ) − ( , ) ≥ 0 ⟺ ≥ ( ) ( , ) − ( , ) ≥ 0 ⟺ ≥ ( ) Then the demand distributions can be written in terms of the indifference customers as follows: = {( , ) ∈ [0,1] × [0,1]; ≤ , ≤ , ≤ ( ) } = {( , ) ∈ [0,1] × [0,1]; ≤ , ≥ , ≥ ( ) } = {( , ) ∈ [0,1] × [0,1]; ≥ , ≤ , ≤ ( ) } = {( , ) ∈ [0,1] × [0,1]; ≥ , ≥ , ≥ ( ) } Define the global utility function ( , ) over the entire market [0,1] × [0,1]:

( , ) = ( , ),( , ), if ( , ) ∈if ( , ) ∈( , ),( , ), if ( , ) ∈if ( , ) ∈ By definition of the demand regions , , , and , the global utility function gives the maximal utility value for the consumer ( , ) according to its choice of ISP-CP combination. We also note that ( , ) is a continuous function over the set [0,1] × [0,1]. Indeed, first note that the functions ( , ), ( , ), ( , ), and ( , ) are linear functions in ( , ) and thus are all continuous. Since ( , ) is piecewise defined over demand regions , , , and , we only need to check that ( , ) is continuous at each point on the boundaries between mutual pairs of the demand regions , , , and . We check each boundary:

• Between and , the boundary is along the line = on which = . • Between and , the boundary is along the line = on which = . • Between and , the boundary is along the line = ( ) on which = . • Between and , the boundary is along the line = on which = . • Between and , the boundary is along the line = on which = . • Between and , the boundary is along the line = ( ) on which = .

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Since corresponding utility functions all matches along the boundaries between mutual pairs of the demand regions , , , and , the global utility function ( , ) is continuous over the entire set [0,1] × [0,1]. The global utility function ( , ) is a continuous function over the closed and bounded set [0,1] × [0,1]. Therefore ( , ) attains its maximum and minimum at some points in the set [0,1] × [0,1]. Under the assumption of full market coverage, the optimal fixed fees the ISPs charge consumers are such that the minimum of ( , ) equal to zero. In other words, the optimal fixed fee is the maximum fee such that all consumers get nonnegative utility. Since ( , ) is piecewise defined by linear functions, it has no critical points in the interior of each demand regions , , , and

. Therefore we only need to analyze the value of ( , ) along each mutual boundaries to capture the minimum of ( , ). Before we analyze the boundaries between , , , and , we recall that the demand distributions split into the three geometric types (i) =

and = ; (ii) < and < ; and (iii) > and > . The feasible outcomes , , , , and are of type (i), where the demand regions are all rectangular in shape. The feasible outcomes and are of type (ii), which have exactly two rectangles, and two pentagonal regions sharing a boundary along = ( ). And finally, the feasible outcomes and are of type (iii), which have exactly two rectangles, and two pentagonal regions sharing a boundary along = ( ). We organize the analysis into two cases (A): ≤ and ≤ and (B): ≥ and ≥ . Cases (A) and (B) overlaps in those of type (i) here the diagonal boundary on = ( ) or = ( ) collapses to the point of intersection of these lines. Case (A): ≤ and ≤ There are five boundaries including a segment on = ( ). (A1) Boundary between and . This boundary is along the horizontal line = and is the line segment joining (0, ) and the point ( , ). Since = on this boundary, along the boundary we may write for 0 ≤ ≤ , ( , ) = ( , ) = − − −− , or ( , ) = ( , ) = − − (1 − ) − − . In either formula, we see that on this boundary ( , ) is a decreasing function of . Therefore ( , ) minimizes at ( , ) on the boundary between and . (A2) Boundary between and . This boundary is along the horizontal line = and is the line segment joining ( , ) and the point (1, ). Since = on this boundary, along the boundary we may write for ≤ ≤ 1, ( , ) = ( , ) = − (1 −) − − − , or ( , ) = ( , ) = − (1 − ) − (1 − ) − − . In either formula, we see that on this boundary ( , ) is a increasing function of . Therefore ( , ) minimizes at ( , ) on the boundary between and . (A3) Boundary between and . This boundary is along the vertical line = and is the line segment joining ( , 0) and the point ( , ). Since = on this boundary, along the boundary we may write for 0 ≤ ≤ , ( , ) = ( , ) = − − −− , or ( , ) = ( , ) = − (1 − ) − − − . In either formula, we see that on this boundary ( , ) is a decreasing function of . Therefore ( , ) minimizes at ( , ) on the boundary between and . (A4) Boundary between and . This boundary is along the vertical line = and is the line segment joining ( , ) and the point ( , 1). Since = on this boundary, along the boundary we may write for ≤ ≤ 1, ( , ) = ( , ) = − − (1 −) − − , or ( , ) = ( , ) = − (1 − ) − (1 − ) − − . In either formula, we see that on this boundary ( , ) is a increasing function of . Therefore ( , ) minimizes at ( , ) on the boundary between and . (A5) Boundary between and . This boundary is along the line = ( ) and is the line segment joining ( , ) and the point ( , ). We parameterize the directed line segment as follows: For 0 ≤ ≤ 1, = (1 − ) + and = (1 − ) + . On this boundary the utility function is a function of the parameter . Since = on this boundary, along the boundary we may write for 0 ≤ ≤ 1 , ( ) = ((1 − ) + , (1 − ) + ) = − [(1 − ) + ] − [1 − (1 − ) − ] − − = +( − ) − − (1 − ) + ( − ) − − , or ( ) = ((1 − ) + , (1 − ) + ) = ( ) − [1 − (1 −) − ] − [(1 − ) + ] − − = ( ) − (1 − ) + ( − ) − + ( − ) − − . If = and = then ( ) is a constant not dependent on . However, in general we note that the slope of = ( ) is given by = , i.e., ( − ) = ( − ). Thus the values of ( ) reduces to the constant: ( ) = − − (1 − ) − − or ( ) = −(1 − ) − − − . From the analysis above, we could see that ( , ) minimizes on the points along the boundary on the line = ( ). In particular, ( , ) minimizes at ( , ) or ( , ) with the same value. Case (B): ≥ and ≥ There are five boundaries including a segment on = ( ).

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(B1) Boundary between and . This boundary is along the horizontal line = and is the line segment joining (0, ) and the point ( , ). Since = on this boundary, along the boundary we may write for 0 ≤ ≤ , ( , ) = ( , ) = − − −− , or ( , ) = ( , ) = − − (1 − ) − − . In either formula, we see that on this boundary ( , ) is a decreasing function of . Therefore ( , ) minimizes at ( , ) on the boundary between and . (B2) Boundary between and . This boundary is along the horizontal line = and is the line segment joining ( , ) and the point (1, ). Since = on this boundary, along the boundary we may write for ≤ ≤ 1, ( , ) = ( , ) = − (1 −) − − − , or ( , ) = ( , ) = − (1 − ) − (1 − ) − − . In either formula, we see that on this boundary ( , ) is a increasing function of . Therefore ( , ) minimizes at ( , ) on the boundary between and . (B3) Boundary between and . This boundary is along the vertical line = and is the line segment joining ( , 0) and the point ( , ). Since = on this boundary, along the boundary we may write for 0 ≤ ≤ , ( , ) = ( , ) = − − −− , or ( , ) = ( , ) = − (1 − ) − − − . In either formula, we see that on this boundary ( , ) is a decreasing function of . Therefore ( , ) minimizes at ( , ) on the boundary between and . (B4) Boundary between and . This boundary is along the vertical line = and is the line segment joining ( , ) and the point ( , 1). Since = on this boundary, along the boundary we may write for ≤ ≤ 1, ( , ) = ( , ) = − − (1 −) − − , or ( , ) = ( , ) = − (1 − ) − (1 − ) − − . In either formula, we see that on this boundary ( , ) is a increasing function of . Therefore ( , ) minimizes at ( , ) on the boundary between and . (B5) Boundary between and . This boundary is along the line = ( ) and is the line segment joining ( , ) and the point ( , ). We parameterize the directed line segment as follows: For 0 ≤ ≤ 1, = (1 − ) + and = (1 − ) + . On this boundary the utility function is a function of the parameter . Since = on this boundary, along the boundary we may write for 0 ≤ ≤ 1 , ( ) = ((1 − ) + , (1 − ) + ) = − [1 − (1 − ) − ] − [1 − (1 − ) − ] − − =+ ( − ) − (1 − ) − (1 − ) + ( − ) − − , or ( ) = ((1 − ) + , (1 − ) + ) = −[(1 − ) + ] − [(1 − ) + ] − − = − + ( − ) − + ( − ) − − . If = and = then ( ) is a constant not dependent on . However, in general we note that the slope of = ( ) is given by: − = , i.e., ( − ) = ( − ). Thus the values of ( ) reduces to the constant: ( ) = − (1 − ) − (1 − ) − − or ( ) =− − − − . From the analysis above, we could see that ( , ) minimizes on the points along the boundary on the line = ( ). In particular, ( , ) minimizes at ( , ) or ( , ) with the same value. Maximum Fees for Case A: The maximum fees occur when the minimum of the global utility function is zero. Therefore from the formulas in (A5), the maximum fees are given by: − − (1 − ) − − = 0 and − (1 − ) − − − = 0. This gives the maximum fees: = − 1 − − − and = − − 1 − − . Maximum Fees for Case B: The maximum fees occur when the minimum of the global utility function is zero. Therefore from the formulas in (B5), the maximum fees are given by: − (1 − ) − (1 − ) − − = 0 and − − − − = 0. This gives the maximum fees: = − − − and = − 1 − − 1 − − . We next solve for the optimal fixed fee for feasible outcomes in symmetric equilibrium when = = . Optimal for outcomes , , , and : All waiting times are the same and = = = = . Using the formulas for maximum fees above, we get { } = { } = { } = { } = − − − ⁄ . Optimal for outcome : In this outcome, { } = { } = and { } = { } < . We have four formulas for F which must be consistent. We verify that those in Case A and Case B both reduces to the following formula for : { } = − 1 − { } − −

{ } . Optimal for outcomes and : These outcomes have the same demand distributions and so the same indifferent customers and waiting times. We use the formulas for Case B for these outcomes: { } = { } = − 1 − { } − 1 − { } − { } . Optimal for outcomes and : These outcomes have the same demand distributions and so the same indifferent customers and waiting times. We use the formulas for Case A for these outcomes: { } = { } = − 1 − { } − { } − { } .

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Step 3: Eliminate Dominated Outcomes From step 1, we know that outcomes , , , , , , and can be eliminated from the equilibrium analysis due to no feasible

. Next, we further eliminate other dominated outcomes by comparing CPs’ profits. Recall that: { } = { } = { }; { } = { } and { } = { } + { }; { } = { } + { } and { } = { }; and { } = { } = { } + { }. For outcomes , , , and

, we have { } = { } = { } = { } and equal demand distributions amongst all ISP-CP combinations. Comparing pairs of these outcomes yields { } < { }, { } < { }, and { } < { }. Therefore, outcomes , , and are dominated and can be eliminated. Next, we compare outcomes , , , and . We know { } = { } = { } = { } , and the following demand distributions amongst all ISP-CP combinations: { } = { } = { } = { } , { } = { } = { } = { } , { } ={ } = { } = { }, and { } = { } = { } = { }. Recall that { } = { } + { } { }, { } ={ } + { } { } + { } { }, { } = { } + { } { } + { } { }, { } = { } + { } { }, { } = { } + { } { } + { } , { } = { } + { } { } + { } { }, { } = { } +{ } { } + { } { }, and { } = { } + { } { } + { } . Comparing pairs of these outcomes yields { } <{ } and { } < { }. Therefore, outcomes and are dominated and can be eliminated from the equilibrium analysis. Therefore, after eliminating all the dominated outcomes, we conclude that outcomes , , , and as the only four possible symmetric equilibria.

Appendix E Proofs of Lemma 1 and Lemma 2: The Asymmetric Equilibrium Case We derive the possible asymmetric equilibria in the packet discrimination regime by the following steps: in step 1, we characterize consumers demand patterns; in step 2, we derive properties of the equilibrium fixed fees and ; in step 3, we eliminate dominated outcomes and derive the only possible asymmetric equilibria. Without loss of generality, we assume = + ∆ , where ∆ ≥ 0. Step 1: Characterize Consumer Demand Patterns in Asymmetric Equilibrium Similar to the analysis of symmetric equilibrium, we compare consumers’ utility functions for the corresponding pairs of ISP-CP

combinations and derive { } = + { } { } , { } = + { } { } , { } = − + { } { } , and { } =− + { } { } . Note that the sign of { } − { } is the same as the sign of { } − { }. Each outcome is determined by the ISPs’ pricing decisions and the corresponding content providers’ delivery service choices. As in the

symmetric case, we denote outcome by the matrix { } { }{ } { } . When considering asymmetric equilibrium, horizontal flip still applies to permuting the outcomes while vertical flip no longer applies since ≥ . Among the 16 outcomes, we still have four invariant classes under horizontal flip: (a) outcomes , , , and ; (b) outcomes and

; (c) outcomes and ; (d) outcomes , , , , , , , and . Next we apply the horizontal flip to each of the classes (a) through (d) to characterize the demand distribution under each outcome.

(Class a) Outcomes , , , and Under outcomes , , , and , all customers have equal queuing priorities. Therefore applying horizontal flip to these outcomes will not change the queuing priorities. Hence the indifferent customers remain unchanged when horizontal flip is applied. From horizontal flip relations, we have { } = 1 − { }, { } = 1 − { }, { } = 1 − { }, { } = 1 − { }, { } =1 − { } , { } = 1 − { } , { } = 1 − { } , and { } = 1 − { } . That is { } = { } = { } = { } = and { } = { } = { } = { } = .

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Since the sign of { } − { } is the same as the sign of { } − { } for any outcome and = under outcomes , , , and , we have = . Next we prove that = ≤ by contradiction. First, suppose < − . Then < since ≥ . This

implies > which gives > . But we also have = − + ( ). Therefore − + ( ) < − which gives − < 0. A contradiction arises. Therefore, we must have ≥ − . Second, suppose > . Then <

which gives < . But we have ≥ . Therefore = + + ( ) < . A contradiction arises. Therefore we must have ≤ . Therefore, as shown in Figure E1, the market demands for and are equal, and the market demands of and are equal under outcomes , , , and . That is { } = { } = { } = { } = { } = { } = { } = { } < and { } = { } = { } = { } = { } = { } = { } = { } > .

Figure E1. Demand Distribution of Class a (outcomes , , , and )

(Class b) Outcomes and Based on symmetry under horizontal flip, we can obtain the demand distribution of by reflecting the demand distribution of outcome through the line = . Thus we may focus on deriving the demand distribution of outcome . We know from the analysis of symmetric equilibrium that when = , { } = { } < and { } = { } = . When > , we know that { } = + { } { } , { } = + { } { } , { } = − + { } { } , and { } = −+ { } { } . Since only pays for preferential delivery on both ISPs, { } − { } < 0, and { } − { } < 0. Thus, { } < and { } < .

Furthermore, { } − { } = { } { } { } { } = { } { }{ } { } { } −{ } { }{ } { } { } > 0 since { } > { } and { } + { } > { } + { }. Therefore, we have { } <{ } < . Since the sign of { } − { } is the same as the sign of { } − { } for any outcome , we have { } < { } . Furthermore, we know that { } < since { } + { } > { } + { }. Therefore, as shown in Figure E2, { } < { } < , { } < { }, and { } < . Based on horizontal flip, we know that { } =1 − { }, { } = 1 − { }, { } = { }, and { } = { }. Therefore, { } > { } > , { } < { }, and { } < .

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Outcome Outcome Figure E2. Demand Distribution of Class b (outcomes and )

(Class c) Outcomes and Based on symmetry under horizontal flip, we can obtain the demand distribution of by reflecting the demand distribution of outcome through the line = . Thus we may focus on deriving the demand distribution of outcome . Under outcome , only pays for preferential delivery on and only pays for preferential delivery on . Thus, { } − { } > 0 and { } − { } < 0. Therefore we have { } > > { }. Since the sign of { } − { } is the same as the sign of { } −{ } for any outcome , we have { } > { }. When > , we know that { } + { } > { } + { }. Therefore, we have { } < . Therefore, as shown in Figure E3, { } < < { }, { } < { }, and { } < . Based on horizontal flip, we know that { } =1 − { }, { } = 1 − { }, { } = { }, and { } = { }. Therefore, { } < < { }, { } < { }, and { } < .

Outcome Outcome Figure E3. Demand Distribution of Class c (outcomes and )

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{ } { }

{ }

{ }

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(Class d) Outcomes , , , , , , , and The demand analysis for outcomes , , , and is the same as that in outcomes , , , and since both CPs receive the same queuing priority when they both pay for preferential delivery. Based on symmetry under horizontal flip, we can obtain the demand distribution of by reflecting the demand distribution of outcome through the line = . Similarly, we can obtain the demand distribution of by reflecting the demand distribution of outcome through the line = . Thus, we may focus on deriving the demand distribution of outcomes and . In outcome , neither CP pays on and only pays on . Thus, { } − { } = 0 and { } − { } < 0. Therefore, we have { } < { } = . Since the sign of { } − { } is the same as the sign of { } − { } for any outcome , we have { } < { }. When > , we know that { } + { } > { } + { }. Therefore, we have { } < . Therefore, as shown in Figure E4, { } < { } = , { } < { }, and { } < . Based on horizontal flip, we know that { } =1 − { }, { } = 1 − { }, { } = { }, and { } = { }. Therefore, { } < { } = , { } < { }, and { } < . Similarly, in outcome , only pays on and neither CP pays on . Thus, { } − { } < 0 and { } − { } = 0 . Therefore, we have { } < { } = . Since the sign of { } − { } is the same as the sign of { } − { } for any outcome , we have { } < { } . From the analysis of symmetric equilibria, we know that when = , { } < . Thus, when > , have { } < . Therefore, as shown in Figure E4, { } < { } = , { } < { }, and { } < . Based on horizontal flip, we know that { } =1 − { }, { } = 1 − { }, { } = { }, and { } = { }. Therefore, { } = < { }, { } < { }, and { } < . The demand patterns for outcomes , , , and are identical to that for outcomes , , , and respectively.

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Outcomes and Outcomes and

Outcomes and Outcomes and

Figure E4. Demand Distribution of Class d (Outcomes , , , , , , , and )

Step 2: Derive Properties of the Equilibrium Fixed Fees and in Asymmetric Equilibrium As shown in step 2 in Appendix D, the equilibrium fixed fees and take two different forms: in Case (A) when ≤ and ≤ , we have = − 1 − − − and = − − 1 − − ; in Case (B) when ≥ and ≥ , we have = − − − and = − 1 − − 1 − − . Among the 16 outcomes, outcomes , , , and are contained in both Case (A) and Case (B); outcomes , , , , , and are contained in Case (A); outcomes , , , , , and are contained in Case (B). Based on the results in step 1, we know the demand patterns and waiting times are related across different outcomes by horizontal flip. Therefore, we can compare the equilibrium fixed fees and for the following groups of outcomes.

Outcomes , , , and For outcomes , , , and , we have { } = { } = { } = { } = { } = { } = { } = { } = and { } = { } = { } = { } = { } = { } = { } = { } < . In addition, we know that { } = { } = { } ={ } = { } = { } = { } = { } and { } = { } = { } = { } = { } = { } = { } ={ }. Therefore, we know that { } = { } = { } = { } and { } = { } = { } = { }.

1 2⁄ 1 2⁄ { }

{ }

{ }{ }

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{ } { }

{ } { }

1 2⁄ 1 2⁄

{ } { }

{ }

{ }

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{ } { }

{ }

{ }

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Outcomes , , , and For outcomes , , , and , we have { } = { } = { } = { } = , { } = 1 − { } = 1 − { } = { } , { } = { } = { } = { }, and { } = { } = { } = { }. In addition, we know that { } = { } = { } ={ } and { } = { } = { } = { } . Therefore, we know that { } = { } = { } = { } and { } ={ } = { } = { }.

Outcomes , , , and For outcomes , , , and , we have { } = { } = { } = { } = , { } = 1 − { } = 1 − { } = { } , { } = { } = { } = { }, and { } = { } = { } = { }. In addition, we know that { } = { } = { } ={ } and { } = { } = { } = { } . Therefore, we know that { } = { } = { } = { } and { } ={ } = { } = { }. Outcomes and For outcomes and , we have { } = 1 − { }, { } = 1 − { }, { } = { }, and { } = { }. In addition, we know that { } = { } and { } = { }. Therefore, we know that { } = { } and { } = { }.

Step 3: Eliminate Dominated and Infeasible Outcomes in Asymmetric Equilibrium Next we compare groups of outcomes and eliminate the dominated outcomes from further analysis of asymmetric equilibrium.

Outcomes , , and are dominated In outcome , the ISPs’ profit functions are { } = { } + { } { } and { } = { } + { } { } . In outcome , the ISPs’ profit functions are { } = { } + { } { } and { } = { } + { } { } + { } . In outcome , the ISPs’ profit functions are { } = { } + { } { } + { } and { } = { } + { } { } . In outcome , the ISPs’ profit functions are { } = { } + { } { } + { } and { } ={ } + { } { } + { } . Based on the results in step 1, we know that { } = { } = { } = { } ={ } = { } = { } = { } and { } = { } = { } = { } = { } = { } = { } = { } . Based on the results in step 2, we know that { } = { } = { } = { } and { } = { } = { } = { }. Comparing pairs of these outcomes yields { } < { }, { } < { }, and { } < { }. Therefore, outcomes , , and are dominated and can be eliminated from further analysis of asymmetric equilibrium.

Outcome is dominated by outcome The feasible region of { } and { } is determined by the six incentive compatibility constraints: { } − { } ≥ 0 , { } −{ } ≥ 0, { } − { } ≥ 0, { } − { } ≥ 0 , { } − { } ≥ 0, and { } − { } ≥ 0. These constraints respectively imply { } + { } − { } − { } + { } { } + { } − { } { } ≥ 0 , { } + { } − −{ } { } ≥ 0, { } + { } − { } + { } + { } { } − { } { } ≥ 0, { } + { } − +{ } { } ≥ 0 , { } + { } − + { } { } ≥ 0 , and { } + { } − { } − { } +{ } { } + { } { } ≥ 0. The feasible region of { } and { } is determined by the six incentive compatibility constraints: { } − { } ≥ 0 , { } −{ } ≥ 0, { } − { } ≥ 0, { } − { } ≥ 0, { } − { } ≥ 0, and { } − { } ≥ 0. These constraints respectively imply { } + { } − + { } { } ≥ 0 , { } + { } − + { } { } ≥ 0 , { } + { } −{ } − { } + { } { } + { } { } ≥ 0 , { } + { } − { } − { } + { } { } +

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{ } − { } { } ≥ 0 , { } + { } − − { } { } ≥ 0 , and { } + { } − { } − { } + { } { } − { } { } ≥ 0. The feasible region of { } and { } contains the feasible region of { } and { } since ≥ and the demand patterns across outcomes are related by horizontal flip. Based on the results in step 2, we know that { } = { } and { } = { }. In outcome , the ISPs’ profit functions are { } = { } + { } { } and { } = { } + { } { } + { } { } . In outcome , the ISPs’ profit functions are { } = { } + { } { } and { } = { } + { } { } +{ } { }. Therefore, outcome is dominated by outcome since { } ≤ { }. Outcomes is dominated by outcome The feasible region of { } and { } is determined by the six incentive compatibility constraints: { } − { } ≥ 0 , { } −{ } ≥ 0 , { } − { } ≥ 0 , { } − { } ≥ 0 , { } − { } ≥ 0 , and { } − { } ≥ 0 . These constraints respectively imply { } + { } − − { } { } + { } − { } { } ≥ 0 , { } + { } − + { } −{ } { } − { } { } ≥ 0 , { } + { } − { } − { } − { } { } − { } { } ≥ 0 , { } + { } − { } − { } − { } { } ≥ 0, { } + { } − + { } − { } { } + { } { } ≥ 0, and { } + { } − { } − { } − { } { } + { } { } ≥ 0. The feasible region of { } and { } is determined by the six incentive compatibility constraints: { } − { } ≥ 0 , { } −{ } ≥ 0 , { } − { } ≥ 0 , { } − { } ≥ 0 , { } − { } ≥ 0 , and { } − { } ≥ 0 . These constraints respectively imply { } + { } − { } − { } − { } { } ≥ 0 , { } + { } − + { } − { } { } +{ } { } ≥ 0 , { } + { } − { } − { } − { } { } + { } { } ≥ 0 , { } + { } −{ } − { } − { } { } + { } − { } { } ≥ 0 , { } + { } − + { } − { } { } −{ } { } ≥ 0, and { } + { } − { } − { } − { } { } − { } { } ≥ 0. The feasible region of { } and { } contains the feasible region of { } and { } since ≥ and the demand patterns across outcomes are related by horizontal flip. Based on the results in step 2, we know that { } = { } and { } = { }. In outcome , the ISPs’ profit functions are { } = { } + { } { } + { } and { } = { } + { } { } +{ } { }. In outcome , the ISPs’ profit functions are { } = { } + { } { } + { } and { } = { } + { } { } + { } { }. Therefore, outcome is dominated by outcome since { } ≤ { }. Outcomes is dominated by outcome In outcome , the ISPs’ profit functions are { } = { } + { } { } and { } = { } + { } { } +{ } { } . In outcome , the ISPs’ profit functions are { } = { } + { } { } + { } and { } ={ } + { } { } + { } { }. Based on the results in step 1, we know that { } = { } and { } = { }. Based on the results in step 2, we know that { } = { }. Therefore, outcome is dominated by outcome since { } ≤ { }.

Outcomes is dominated by outcome The feasible region of { } and { } is determined by the six incentive compatibility constraints: { } − { } ≥ 0 , { } −{ } ≥ 0 , { } − { } ≥ 0 , { } − { } ≥ 0 , { } − { } ≥ 0 , and { } − { } ≥ 0 . These constraints respectively imply { } + { } − − { } { } ≥ 0 , { } + { } − { } − { } + { } − { } { } +{ } { } ≥ 0, { } + { } − { } − { } − { } { } + { } { } ≥ 0, { } + { } − +{ } { } ≥ 0 , { } + { } − { } − { } + { } { } ≥ 0 , and { } + { } − { } − { } + { } { } + { } { } ≥ 0. The feasible region of { } and { } is determined by the six incentive compatibility constraints: { } − { } ≥ 0 , { } −{ } ≥ 0, { } − { } ≥ 0, { } − { } ≥ 0, { } − { } ≥ 0, and { } − { } ≥ 0. These constraints respectively imply { } + { } − + { } { } ≥ 0 , { } + { } − { } − { } + { } { } ≥ 0 ,

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{ } + { } − { } − { } + { } { } + { } { } ≥ 0 , { } + { } − − { } { } ≥ 0 , { } + { } − { } − { } + { } − { } { } + { } { } ≥ 0 , and { } + { } −{ } − { } − { } { } + { } { } ≥ 0. The feasible region of { } and { } contains the feasible region of { } and { } since ≥ and the demand patterns across outcomes are related by horizontal flip. Based on the results in step 2, we know that { } = { } and { } = { }. In outcome , the ISPs’ profit functions are { } = { } + { } { } + { } { } and { } = { } + { } { } . In outcome , the ISPs’ profit functions are { } = { } + { } { } + { } { } and { } = { } + { } { }. Therefore, outcome is dominated by outcome since { } ≤ { }.

Outcomes is dominated by outcome The feasible region of { } and { } is determined by the six incentive compatibility constraints: { } − { } ≥ 0 , { } −{ } ≥ 0 , { } − { } ≥ 0 , { } − { } ≥ 0 , { } − { } ≥ 0 , and { } − { } ≥ 0 . These constraints respectively imply { } + { } − − { } { } + { } − { } { } ≥ 0 , { } + { } − + { } −{ } { } − { } { } ≥ 0 , { } + { } − { } − { } − { } { } − { } { } ≥ 0 , { } + { } − + { } { } + { } − { } { } ≥ 0, { } + { } − { } − { } − { } { } ≥ 0, and { } + { } − { } − { } + { } { } − { } { } ≥ 0. The feasible region of { } and { } is determined by the six incentive compatibility constraints: { } − { } ≥ 0 , { } −{ } ≥ 0 , { } − { } ≥ 0 , { } − { } ≥ 0 , { } − { } ≥ 0 , and { } − { } ≥ 0 . These constraints respectively imply { } + { } − + { } { } + { } − { } { } ≥ 0 , { } + { } − { } − { } −{ } { } ≥ 0 , { } + { } − { } − { } + { } { } − { } { } ≥ 0 , { } + { } − −{ } { } + { } − { } { } ≥ 0 , { } + { } − + { } − { } { } − { } { } ≥ 0 , and { } + { } − { } − { } − { } { } − { } { } ≥ 0. The feasible region of { } and { } contains the feasible region of { } and { } since ≥ and the demand patterns across outcomes are related by horizontal flip. Based on the results in step 2, we know that { } = { } and { } = { }. In outcome , the ISPs’ profit functions are { } = { } + { } { } + { } { } and { } = { } + { } { } +{ } . In outcome , the ISPs’ profit functions are { } = { } + { } { } + { } { } and { } = { } + { } { } + { } . Therefore, outcome is dominated by outcome since { } ≤ { }.

Outcomes is dominated by outcome In outcome , the ISPs’ profit functions are { } = { } + { } { } + { } { } and { } = { } + { } { } . In outcome , the ISPs’ profit functions are { } = { } + { } { } + { } { } and { } ={ } + { } { } + { } . Based on the results in step 1, we know that { } = { } and { } = { }. Based on the results in step 2, we know that { } = { }. Therefore, outcome is dominated by outcome since { } ≤ { }.

Outcomes and are infeasible Here we focus on showing that there is no feasible for outcome , as the analysis for outcome is similar. For outcomes to be feasible, all the CPs’ incentive compatibility constraints need to be satisfied: (1) { } − { } ≥ 0 ; (2) { } − { } ≥ 0 ; (3) { } − { } ≥ 0; (4) { } − { } ≥ 0; (5) { } − { } ≥ 0; (6) { } − { } ≥ 0. Inequality (3) is { } + { } − { } − { } + { } − { } ≥ 0. Since { } + { } = , inequality (3) can be reduced to ≥ { }{ } + { } { }{ } .

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Inequality (6) is { } + { } − { } − { } + { } − { } ≥ 0. Since { } + { } = , inequality (6) can be reduced to ≤ { }{ } + { } { }{ } .

Based on the result in step 1, we have − { } − { } = { } + { } − > 0. This gives { } { }{ } > 0 and { } { }{ } < 0. Next we show that { }{ } > { }{ } . We first note that { } = { } and { } = { } . Thus, { }{ } > { }{ } ⟺ { }{ } > { }{ } ⟺ { }{ } > { }{ } . Since { } > { } and { } > { }, we have { }{ } > 1 > { }{ } . Thus, we also have { }{ } > { }{ }. Then (3) and (6) implies that and are both negative. Therefore, outcome is infeasible. Similarly, we can show that there is no feasible p for outcome . Therefore, both outcomes and are infeasible.

Outcomes is infeasible For outcomes to be feasible, all the CPs’ incentive compatibility constraints need to be satisfied: (1) { } − { } ≥ 0; (2) { } −{ } ≥ 0; (3) { } − { } ≥ 0; (4) { } − { } ≥ 0; (5) { } − { } ≥ 0; (6) { } − { } ≥ 0. Inequality (3) is { } + { } − { } − { } − { } − { } ≥ 0. Since { } + { } = , inequality (3) can be reduced to { } + { } − ≥ { } + { } . Inequality (6) is { } + { } − { } − { } + { } + { } ≥ 0. Since { } + { } = , inequality (6) can be reduced to { } + { } ≥ − { } − { } . Based on the result in step 1, we have { } = { }, { } = { } and − { } − { } = { } + { } − . We also know that ≥ . Thus, { } + { } = { } + { } ≥ { } + { } , which implies { } − { } + { } − { } ≤ 0. Since pays for priority delivery on both and , we know that { } > { } and { } > { }, i.e., { } − { } > 0 and { } − { } > 0. Thus, (3) and (6) imply that either or is negative. Therefore, outcome is infeasible. Therefore, after eliminating all the dominated and infeasible outcomes, we conclude that outcomes , , , and as the only four possible asymmetric equilibria.

Appendix F Proof of Lemma 3 From Lemma 2, we know that outcomes , , , and as the only four possible equilibria. Here we conduct symmetric equilibrium analysis ( = = and = = ) and derive the ISPs’ equilibrium pricing strategies and the corresponding equilibrium outcomes in the packet discrimination regime in the following two steps.

Step 1: Solve for the Equilibrium Fixed Fee and Preferential Delivery Fee for the Candidate Outcomes In step 1, we solve for the equilibrium fixed fee and preferential delivery fee for the candidate outcomes one by one. Among the four candidate equilibria, outcome and outcome are symmetric. Thus, we focus on outcomes , , and in this analysis.

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Outcome The preferential delivery fee for outcome is determined by the following two CPs’ incentive compatibility constraints: { } ≥ { } yields { } ≤ ⁄ { } { }⁄ { } ; { } ≥ { } yields { } ≤ ⁄ { } { }⁄ . Therefore, { }∗ = { } , where { } =min ⁄ { } { }⁄ { } , ⁄ { } { }⁄ . In addition, we know from the results in Lemma 2 that { }∗ = − − − ⁄ . Outcome The preferential delivery fee for outcome is determined by the following three CPs’ incentive compatibility constraints: { } ≥{ } yields { } ≤ { } { } { } { }{ } ; { } ≥ { } yields { } ≥ ⁄ { } { }⁄ { } ; { } ≥ { } yields { } ≤ { } { } ⁄{ } { } ⁄ . Thus, there exists a feasible { } if and only if ⁄ { } { }⁄ { } ≤min { } { } { } { }{ } , { } { } ⁄{ } { } ⁄ , which can be reduced to ≥ { } { } ⁄⁄ { } and ⁄ { } { }⁄ { } ≤ { } { } { } { }{ } . When these feasible conditions hold, we obtain { }∗ = min { } , { } , where { } = { } { } { } { }{ } and { } = { } { } ⁄{ } { } ⁄ . We know that in a symmetric equilibrium, { } = { } , i.e., { } + { } { } + { } { } = { } +{ } { } + { } . Thus, { }∗ = { } { } { } { }∗{ } { } { } { }. Note that since { } + { } > { } and { }∗ ≥ 0, we have { } + { } > { } + { }. Outcome The preferential delivery fee for outcome is determined by the following three CPs’ incentive compatibility constraints: { } ≥{ } yields { } ≥ { } { } { } { }{ } ; { } ≥ { } yields { } ≥ ⁄ { } { }⁄ ; { } ≥ { } yields { } ≤ { } { } ⁄{ } { } ; { } ≥ { } yields { } ≤ { } { } { } { }{ } { } { } . Let { } = max { } { } { } { }{ } , ⁄ { } { }⁄ and { } =min { } { } ⁄{ } { } , { } { } { } { }{ } { } { } . Thus, there exists a feasible { } if and only if { } ≤ { } . Here we note that { } ≥ ⁄ { } { }⁄ and { } ≤ { } { } ⁄{ } { } . So we have { }{ } ≥ ⁄ { } { }⁄{ } { } ⁄{ } { } = { } { }⁄ > 1. When these feasible conditions hold, we obtain { }∗ = { } . In addition, we know from the results in step 2 in the proof of Lemma 2 that { }∗ =− 1 − { } − − { } ⁄ . We note here that the solution of price in outcomes , , and form three non-overlapping intervals. Specifically, we have { } ≤{ } ≤ ⁄ { } { }⁄ { } ≤ { } ≤ min { } , { } ≤ { } ≤ { } ≤ { } . The non-overlapping solution reflects the fact that incentive criteria for content providers in outcomes , , and are mutually exclusive. Observe also that the endpoints of the non-overlapping intervals are given by constant multiples of the revenue rates and .

Step 2: Compare the Candidate Outcomes and Derive Equilibrium Outcomes In step 2, we compare the ISPs’ profits in outcomes , , and to determine the equilibrium outcomes. Since ISPs and have the same profit level in a given outcome, we simplify the notations to { } = { } = { } , { } = { } = { } , and { } ={ } = { }. Outcome is the equilibrium provided all the following inequalities are satisfied: { } ≤ { } , { } ≥ { }, and { } ≥ { }. These reduces to the following inequalities: ≥ { }{ } ≡ , ≥ { } { } { }{ } { } + { } { } { } { }⁄{ } { } ≡

, and ≥ { } { } { } + { } { }{ } { } ≡ + . Outcome (or outcome ) is the equilibrium provided all the following inequalities are satisfied: ≥ { } { } ⁄⁄ { } ≡ , { } > { }, and { } ≥ { }. These reduces to the following inequalities:

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≥ , < , and ≤ { } { } { }{ } − { } { } { } { }{ } ≡ . When the above market conditions are not satisfied, outcome is the equilibrium. Summarizing the above analysis yields Lemma 3.

Appendix G

Proof of Proposition 1

Since the net neutrality regime is essentially equivalent to outcome , where neither CP pays for preferential delivery even though they

have the option to do so. Based on the results from Lemma 2, we know that in the net neutrality regime, = = { }∗ = { }∗ . In addition, there are four possible equilibria in the packet discrimination regime, i.e., = = { }∗ = { }∗ { }∗ { } , or == { }∗ = { } { }∗ + { }∗ = { }∗ = { } { }∗ + { }∗ , or = = { }∗ = { }∗ { }∗ . From the results in step 3 in the proof of Lemma 2, we know { }∗ ≥ { }∗ . Therefore, we get = ≥ { }∗ ≥ { }∗ = = . Appendix H Proof of Proposition 2 In the net neutrality regime, we know that = { }∗ = . In the packet discrimination regime, there are three possible equilibria – outcomes , , and . The corresponding profit for content provider is: { }∗ = { } + { } − { }∗ , { }∗ ={ } + { } − { }∗ , and { }∗ = { }∗ . Next we focus on comparing { }∗ and { }∗ . Recall that { }∗ = { } , where { } = min { } { } ⁄{ } { } , { } { } { } { }{ } { } { } . If { } = { } { } ⁄{ } { } , then { }∗ = { } + { } − { } { } ⁄{ } { } = = { }∗ . If { } = { } { } { } { }{ } { } { } , then { }∗ = { } + { } − { } { } { } { }{ } { } { } = { } { } { }{ } { } { } ≥ = { }∗ . Thus, CP ’s profit in outcome is higher than that in outcome if and only if { } { } { } { }{ } { } { } < { } { } ⁄{ } { } , which can be simplified to { } + { } { } > { } { } { }. From the proof of Lemma 1, we know { } + { } = 1 − { }, { } = { }, and − { } = { } − { } . This gives: { } = 1 − { } 1 − { } − { } − { } − { } = 1 − { } 1 − { } − { } − { } .

Substituting these equations into the { } + { } { } > { } { } { } yields 1 − { } { } > 1 − { } −1 − { } 1 − { } + { } − { } . Rearranging this inequality gives > { } { }{ } { } { } . Therefore, if the ratio of is higher than a threshold, { }∗ > { }∗ .

In general, comparisons of { }∗ , { }∗ , and { }∗ show that CP ’s profit may be lower, unchanged or higher in the packet discrimination regime than that in the net neutrality regime. Specifically, it is lower under equilibrium BB, but is unchanged or higher under equilibrium , i.e., { }∗ ≥ { }∗ ≥ { }∗ .

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Appendix I Proof of Proposition 3 In the net neutrality regime, we know that = { }∗ = . In the packet discrimination regime, there are three possible equilibria – outcomes , , and . The corresponding profit for content provider is: { }∗ = { } , { }∗ = { } − { } { }∗ , and { }∗ = { }∗ . We compare ’s profit in the three possible equilibria in the packet discrimination regime to its profit in the net neutrality regime one by one. We first note that { }∗ ≥ { }∗ . Furthermore, since { } ≤ , we get that { }∗ ≥ { }∗ . Lastly, since { }∗ ≤ { }∗ , { }∗ ≥ { } + { } − { } { }∗ ≥ { } + { } − { } { }∗ = { }∗ . Summarizing the above, we conclude that ’s profit is higher in the net neutrality regime than that in all three possible equilibria in the packet discrimination regime. Therefore, ≥ .

Appendix J Proof of Proposition 4 Substituting the equilibrium prices into the social welfare formula = + + + + ( , ) , we get that, in the net neutrality regime, = { } = − − ⁄ + ( ). In the packet discrimination regime, there are three possible equilibria – outcomes , , and . The corresponding social welfare is: { } = − − { } − − { } ⁄ + { } +1 − { } , { } = { } + ( ) + ( ) 2 − { } − { } − { } + { } + { } + { } − +{ } − + { } + { } − { } + { } + { } − { } + − { } + { } − { } −+ 2 { } − { } − + 2 { } { } − { } , and { } = − − ⁄ + ( ). We first note that { } = { }. Furthermore, since { } ≤ , we get that { } ≥ { }. Lastly, we compare { } and { }. Let ∆ = { } − { }. We can show that ∆ ≥ 0 and ∆ = 0 at = . Therefore, { } ≥ { }. Summarizing the above, we conclude that social welfare is weakly higher in all three possible equilibria in the packet discrimination regime than that in the net neutrality regime. Therefore, ≥ .

Appendix K Numerical Analysis of the Asymmetric Equilibrium In this appendix, we numerically explore the asymmetric equilibrium. There are eight parameters ( , , , , , , , and ) in our model. Note that not all the parameters need to be changed independent of the other parameters. For example, with respect to the parameters and

, what is important is not their absolute values but the utilization rate of the service queue, i.e., / , and hence we set = 0.5 and varied the value of to achieve a wide range of utilization rate. Specifically, ∈ (0.5,5] in our numerical analysis, which resulted in a range for the utilization rate of [0.1,1). In addition, parameters , , , and can theoretically vary within an infinite range and they all affect the consumer’s utility. Thus, one of these parameters can be kept fixed relative to the others and here we normalized = 1. We then conducted the numerical analysis on a wide range of the other three parameters ∈ [1,5], ∈ [0.5,3], and ∈ [0.5,3]. Finally, recent empirical

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evidence1 shows that the revenue rates (measured by the average revenue per user, i.e., ARPU) vary widely2. Therefore, we chose a reasonable range of revenue rates ∈ (0,5] and ∈ (0,5]. In summary, the total number of exploration points for the entire parameter space was 1,593,750, which generated 38.8 GB of data. We implemented this asymmetric equilibrium analysis in Mathematica 10 and ran the solution procedure on clusters hosted by the High Performance Computing facility at a university. The total running time for all the simulations was around 180 hours. Figure K1 shows the result of the symmetric equilibria for parameters = 3, = 2, = 1, = 1, = 0.5, and = 1. Results for other parameter values are qualitatively the same. These numerical results validate the analytical results (all the lemmas and propositions for the symmetric equilibrium) that we present in the paper.

Figure K1. Types of Symmetric Equilibria Notes:

• The separating lines between the regions for different equilibria may shift based on different parameter values. • For symmetric ISPs (with the same capacity levels), outcome – where both CPs pay ISP and only pays ISP –

is equivalent to outcome . Thus, a set of parameter values that result in outcome can also (equivalently) result in outcome . Similarly, outcome is equivalent to outcome .

Next, we consider the asymmetric equilibria results with symmetric ISPs. As we show in Figure K2, the results show a somewhat more complex set of possible equilibrium outcomes. There are some regions which correspond to a single type of dominating outcomes (for example, the regions in green corresponding to the dominating equilibrium outcome , or similarly if ≥ , or the region in blue corresponding to the outcome ), and there are others that correspond to regions where there are two possible types of equilibrium outcomes (e.g., the region in red corresponding to either outcome or outcome ).

1 http://www.forbes.com/sites/tristanlouis/2013/08/31/how-much-is-a-user-worth/ 2 The ARPU for four popular websites are $1.63 (Facebook), $1.53 (LinkedIn), $1.81 (Yahoo), and $10.09 (Google).

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Figure K2. Types of Pareto Frontiers for Asymmetric Equilibria Notes: • The separating lines between the regions for different equilibria may shift based on different parameter values. • For symmetric ISPs (with the same capacity levels), outcome is equivalent to outcome . Similarly, outcome is

equivalent to outcome .

To understand why we may have multiple possible types of asymmetric equilibrium outcomes for a certain combination of and , it is instructive to look at the Pareto frontier of the asymmetric equilibria. Figure K3 shows two examples of the Pareto frontier results with different values of and . In Figure K3, every point on the curve corresponds to the profit of ISP (on the -axis) and the profit of ISP (on the -axis), such that if

and choose the corresponding ( , ) and ( , ) that results in these profits, such a strategy choice is not dominated by any other strategy in the strategy space of and forming a Pareto frontier. Thus, for a certain combination of and , there may be multiple asymmetric strategy choices contained in the Pareto frontier. Consider the example on the left in Figure K3 (with = 3 and = 3), all such strategy choices result in the equilibrium outcome , i.e., both and pay both ISPs. However, in the example on the right in Figure K3 (with = 0.5 and = 4), for some strategy choices of and , the equilibrium outcome is , but for other strategy choices, the equilibrium outcome is .

= 3 and = 3 = 0.5 and = 4 Figure K3. Examples of Pareto Frontier of Asymmetric Equilibria

or

or

or

or

only or

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Note that under these asymmetric strategy choices, the profits of and are different, which means that one of them is engaging in predatory pricing, with the intent of getting higher profits. In real life, such an action will likely result in a retaliatory action from the other ISP, which is harmful to both firms in the long run. As Farrell (1987)3 showed, it is very easy for symmetric firms who can engage in asymmetric equilibria to signal their intent at a very little cost to the other firm (in the words of Farrell, by engaging in “cheap talk”) and thereby arrive at the mutually beneficial symmetric equilibrium. Furthermore, our numerical results show that the main findings for the symmetric equilibrium case still hold for the asymmetric equilibrium case. We have already shown analytically in Lemma 3 that ISP competition does not substitute for net neutrality regulation even considering the asymmetric equilibria. In addition, our numerical analysis for the asymmetric equilibria confirms that the dominant CP still sometimes benefits in the absence of net neutrality. While we cannot develop similar generalized “conditions” with numerical analysis, we find however that when the ratio of ⁄ is high and the ratio of ⁄ is high (in other words, when the conditions of Proposition 2 hold), CP is better off under packet discrimination. The case is different however if the ISPs are asymmetric with respect to their capacities. In such situations, the asymmetric equilibrium is not just a theoretical exercise but can actually occur. We numerically explore the details of the asymmetric equilibria for asymmetric ISPs with different capacities in Appendix L.

Appendix L Numerical Analysis of the Asymmetric ISPs In this appendix, we numerically explore the asymmetric equilibria for asymmetric ISPs with different capacities. Without loss of generality, we assume ≥ . As compared to the symmetric equilibrium or the asymmetric equilibrium with symmetric ISPs, the equilibrium outcomes with asymmetric ISPs is more complicated with more possible types of strategy choices (as shown in Figure L1). For example, for a certain combination of and , there can be three or even four outcomes that are part of the Pareto frontier, i.e. and can choose three or four different types of pricing strategies.

3 Farrell, J. 1987. “Cheap Talk, Coordination, and Entry,” RAND Journal of Economics (18:1), pp. 34-39.

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Red “+”: , , or ( , , or ) Green “ − ”: , , , or ( , , , or ) Orange “∗”: , , or ( , , or ) Blue “⋅”: only Pink “ ”: , , or ( , , or ) Black “~”: or ( or )

Figure L1. Types of Pareto Frontiers for Asymmetric Equilibria with Asymmetric ISPs Notes: • Figure L1 is generated based on parameter values = 5, = 1, = 3, = 1, = 1, = 1, and = 0.5. • The separating lines between the regions for different equilibria may shift based on different parameter values. • Unlike the equilibria with symmetric ISPs, with asymmetric ISPs, the equilibrium outcomes and are not equivalent.

Similarly, outcomes and are not equivalent for the asymmetric ISP case.

Figure L1 shows that when and are somewhat comparable, the equilibrium outcome is . Also, when is much greater than , the equilibrium outcome is either just or it also includes the outcome or as part of the Pareto frontier. For intermediate values of and , the strategy choices for the two ISPs and the CPs get more varied. Figure L2 shows two examples of the Pareto frontier with two sets of and values ( = 3, = 3 and = 1, = 3). The Pareto frontier is no longer symmetric as for symmetric ISPs (Figure K3) because ISP has a higher capacity than ISP .

= 3 and = 3 = 1 and = 3 Figure L2. Examples of Pareto Frontier of Asymmetric Equilibria with Asymmetric ISPs

only , , or

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Furthermore, just as shown in Appendix K, our numerical analysis for asymmetric ISPs show that the main findings for the symmetric ISP case still hold for the asymmetric ISP case. For example, our numerical analysis for asymmetric ISPs confirms that ISP competition does not substitute for net neutrality regulation even for ISPs with different capacity levels as in the symmetric ISP case (Lemma 3). In addition, the dominant CP still sometimes benefits in the absence of net neutrality.

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