Network Neutrality and Competition on Advertising Markets -Preliminary-

Transcription

1 Network Neutrality and Competition on Advertising Markets -Preliminary- Anna D'Annunzio Antonio Russo 0 March 013 Abstract We investigate the eects of removing network neutrality regulation on the distribution of contents in the Internet. We model a two-sided market, where consumers and advertisers interact through Content Providers (CPs), and CPs and consumers through Internet Service Providers (ISPs). We consider two CPs, and we rst model a monopolist ISP and then two duopolist ISPs. An ad on multiple contents browsed by the same consumer is partially wasted, so advertisers' willingness to pay for a slot on a CP decreases in the number of multiple impressions on a single consumer. Under network neutrality, CPs can connect to ISPs for free, while in the unregulated regime, an ISP allows access to its network to a CP conditional on the payment of a fee. We show that switching to the unregulated regime makes universal distribution of contents less likely, specically when repeated impressions of an ad rapidly lose value and consumers care for content availability to a relatively small extent. The unregulated regime is never superior from a welfare point of view to the net neutrality regime. Consumer and advertiser surplus are weakly higher under net neutrality. ISPs are unambiguosly better o in the unregulated regime, while CPs are unambiguosly worse o. University of Rome Sapienza and Toulouse School of Economics European University Institute 1

2 1 Introduction Traditionally, the Internet has been subject to net neutrality regulation, that refers to the principle that all Internet trac is treated equally according to the principle of rst-come- rst-served. However, there is an ongoing debate on the eects of removing net neutrality, that counts many proponents and many opponents. Net neutrality regulation has dierent practical implications. In particular, Schuett (010) assesses that net neutrality implies a zero-price rule and a non-discrimination rule, and these are the two main aspects that have been studied by the literature. 1 In this paper, we consider the former feature of net neutrality, namely the fact that Interner Service Providers (hereafter, ISPs) are not allowed to impose fees to Content Providers (hereafter, CPs) in order to deliver their contents to nal users. charge a fee to a CP willing to access its customers base. 3 This entails that, when net neutrality is removed, an ISP may In this paper we are interested to study the competitive eects of removing net neutrality. In particular, we investigate whether an ISP that can charge an access fee to CPs may have incentives to restrict its oer of contents for consumers, fragmenting the Internet and departing from the end-to-end principle that has gouverned the Internet till now. In our paper, the rationale for doing so is to increase the eectiveness of the ads on a given CP, hence its market power and the revenues collected on the advertisers market, so as to increase the prots the ISPs can extract from CPs through the access fee. In our model, we take into consideration the stilized fact that the value of an ad impression on a consumer decreases with the number of impressions on that consumer. 4 Indeed, an ad that reaches a consumer that is already informed could be (at least partially) wasted, since the consumer could elicit no more information from the ad and could have already decided wether to buy the advertised product. Hence, we consider the rst ad impression on a consumer to be the most valuable since it allows consumers to know about the product and to decide to buy it, if they are interested. Following impressions are still valuable for advertisers, since they can still induce some consumers to purchase or remind them about the product, but they have less impact than the rst one. 5 Under net neutrality, CPs decide whether to access an ISP or not. When we consider a monopoly ISP, both CPs always connect to it, since a CP has no incentives to stay out of the market and no instrument to exclude the rival CP. Under duopoly, we nd that, since 1 For further details, see the literature review is in section. Actually, CPs pay some small fee to ISPs, but here we consider these fees to be zero under net neutrality. 3 The AT&T CEO, Edward Whitacre, said that he does not want content providers to use my lines for free. 4 See Calvano and Jullien (011), Anderson, Foros and Kind (011). 5 See Athey, Calvano and Gans (011).

3 access is free, there still always exists an equilibrium where CPs access both ISPs, hence where there is universal distribution of content. Indeed, CPs do not take into consideration the externalities they impose on each other and they are not able to coordinate on their preferred conguration of the network. CPs are in a prisoner dilemma situations. Hence, ISPs have to compete strongly for attracting consumers (low dierentiation) and CPs to attract ads. When the value of the second impression is very low, we nd a second equilibrium, where CPs can nd protable to share the market and to join dierent ISPs, leading to a total segmented network. Indeed, when one CP is connected exclusively to an ISP, it oers only high quality customers to advertisers, since consumers connected to that ISP can be reached only by buying ads from that CP. This increases the price that a CP can impose for its advertising space, and could increase their total revenues. When net neutrality is removed, an ISP can impose an access fee for its network. This access fee could be low, so that all CPs choose to access the market, or it could be as high as only one CP nds ptoitable to join one platform. Under this scenario, an ISP thinks as an editor, who cares about the protability of the contents it carries. With a monopolist ISP, we nd that both CPs access the network when the value of the second impression is high enough, while one CP is excluded when the value of the second impression is low. In this case an equilibrium always exists and for each value of the parameters this equilibria is unique. With dupoly ISPs, we nd two pure-strategy equilibria: universal distribution of contents exists when the value of the second impression is high enough, while total fragmentation exists when the value of the second impression is low enough. Indeed, when the value of rst impressions of ads on consumers are high enough, ISPs prefer to restrict the access to their network. In this way, they allow CPs to increase their prots, since they are monopolist of consumers' attention, and then they extract CPs' prots trough the access fee. We never nd multiple equilibria. However, for intermediate values of the second impression, we do not nd any pure strategy equilibrium, since each ISP tries to deviate from an equilibrium conguration in order to have some exclusive relations with the CPs. Hence, comparing the two regulatory regimes, we nd that the region where universal distribution of contents occurs in the unregulated regime shrinks. Moreover, we nd that the region where universal dustribution occurs never intersects the one where total fragmentation occurs under the net neutrality regime. It can easily be shown that universal distribution is benecial for consumers, advertisers and total welfare. Indeed, universal distribution of contents creates a higher gross surplus both on the consumers' side of the market (consumers enjoy more contents and stand less transportation costs) and on the advertisers' side of the market (more consumers' attention is provided to advertisers). Hence, we can conclude that removing net neutrality might entail 3

4 a loss in total, consumers and advertisers surplus, in the region where the equilibrium moves from total distribution under net neutrality to total fragmentation under the unregulated regime, since it restricts the access of nal users to contents. The unregulated regime is never superior to the net neutrality one from a welfare point of view. Moreover, when net neutrality is removed, ISPs are unambiguosly better o, while CPs are unambiguosly worse o. This paper is organized as follows. Section analyzes the relevant literature. Section 3 presents the basic model, that is solved in section 4 when we consider a monopoly ISP and in section 5 for dupoly ISPs. In each section we consider both regulatory regime, namely the net neutrality and the unregulated regime, we compare the two regimes and we derive welfare eects of removing net neutrality regulation. Then, section 6 concludes. All proofs are relegated to the Appendix. Literature There is a wide debate on net neutrality, that involves lawyers, engineers and economists. This debate tries to assess the consequencies of a change in the regulatory regime. Only recently this issue has been formally analized from an economic perspective. Choi and Kim (010) studies how both the incentives to invest of a monopolist ISP and of two horizontally dierentiated CPs change when net neutrality regulation is removed. They use the queuing theory to model scarce bandwidth, and in their model departing from net neutrality means allowing the platform to charge content providers in order to have priority on the net while best eort is assured for the others. In the short run, an ISP prefers to sell priority if the advertising margin for the content providers are high, since in this case it can impose a high price for the priority. If it has enough bargaining power, the content provider that receives the priority is better o in the discriminatory, while the content provider without priority is always worse o. As concerns total welfare, the result depends on the weight of the total margins for content providers and the total transportation costs for consumers, since both increase under the discriminatory regime. In the long run, an ISP can invest more or less under the discriminatory regime. Indeed, as the capacity of the network increases, the ISP can charge more for access to consumers. However, capacity expansion decreases the value of the scarce resource, i.e. the fast line. As concerns content providers, the incentive to invest of the high-speed contents depends on its ability to exploit the fast line and on its bargaining power, while the rival content always invests less under the discriminatory regime. In a related paper, Choi, Jeon and Kim (01) consider two interconnected ISPs and two 4

5 types of content providers that dier in their sensitivity to the delay in the network. They show that ISPs contract on reciprocal access charges as they were a monopoly bottleneck againts content providers. They nd that ISPs x a price for the content providers as if all the trac were o-net (this is the o-net principle established by Laont et al., 001). The advantage of net neutrality regulation crucially depends on the business model of the content providers. In particular, the quality provided to low-quality types is too distorted downwards under discrimination compared to the neutrality regime when the level of surplus extracted by content providers from consumers is positive but suciently small. Hermalin and Katz (007) consider a monopolist ISP and a continuum of content providers that dier in their attractiveness for consumers. 6 When the ISP is free to charge content providers for accessing the network and to oer dierent level of quality connections, it oers a menu of contract. At equilibrium, higher types purchase higher quality. The highest type buys the ecient quality, then quality is distorted downwards for other types. When net neutrality is imposed, the ISP is forced to oer a unique quality to all content providers. At equilibrium, low types are not anymore active, high types obtain less quality while intermediate types purchase higher quality. Compared to the unregulated model, welfare can increase or decrase under net neutrality: the rst and second eect pull down welfare, while the third one pulls it up. Even if the total eect is a priori ambiguous, the authors argue that the it is often negative. Also Bourreau, Kourandi and Valletti (01) gives the same interpretation of net neutrality: when it is removed, content providers can buy priority from the two competing ISPs. In a model that uses the queing theory, they show that the discriminatory regime is welfare superior to the net neutrality regime, since it allows a more ecient use of the network. Under discrimination, ISPs have larger investment incentives, more content providers are active and there is less congestion. However, they also show that under discrimination, ISPs could have the incentive to sabotate the best eort network, with adverse eects for welfare. Dierently from the previous papers, Economides and Tag (01) consider net neutrality to be a zero-price rule on the content side. They concentrated on the pricing issues linked to the two-sidedness of the market that could arise due to a depart from net neutrality. They consider both a model with a monopolist ISP and one with two horizontally dierentiated ISPs with single-homing consumers, and they show that results are not qualitatively aected. They nd that, when content providers value consumers more than consumers value contents, net neutrality is welfare enhancing compared to a situation where ISPs are allowed to charge a positive price to content providers. Indeed, only if this condition is veried, ISPs are willing to impose a positive price to content providers when net neutrality is removed. However, in 6 They consider an extension where ISPs compete, and the results of the basic model carry on. 5

6 this region, consumers are worse o under net neutrality. Indeed, the direct eect of a higher subscription fee for viewers overcome the indirect eect of higher content provision. Economides and Hermalin (01) gives the same denition as Economides and Tag (01) of net neutrality. They rst show that the preferred conguration from a welfare point of view is the one where more contents are delivered to consumers. This implies that welfare connot be enhanced by blocking contents. Departing from net neutrality through a tiering service can either increase or decrease total content sent, and then welfare. In particular, welfare increases when the delay times are shorter for content with greater elasticities of demand with respect to trasmission time than for contents with smaller elasticities. Remark that more time sensitive contents need not to be the contents with the highest elasticity. Thus, prioritizing these contents could entail a loss of welfare. They also show that, contrary to Choi and Kim (010), departing from net neutrality unambiguosly increases the incentives of the ISP to invest in the bandwidth. However, the net welfare eect, taking into account dynamic and static eects, is not a priori clear. The authors show that when consumer surplus weight a lot on total welfare, net neutrality is welfare-enhancing. In our paper, we consider net neutrality as a zero-price rule. Dierently from the previous paper, we are interested to analyse the segmentation issue that could arise when net neutrality is removed. Indeed, when a price is imposed for the access, ISPs have a stake in prots made by content providers, and this entails that they can nd protable to exclude some contents from their network in order to extract more prots from them through the access fee. Indeed, content providers can increase their prots when they oer the attention of some consumers as a monopolist. A similar issue is analysed in an independent paper by Kourandi, Kramer and Valletti (01), in a quite dierent model. Both papers analyse fragmentation of the Internet, in a setting with As we do, they consider two content providers and two ISPs. However, they consider exclusivity contracts among CPs and ISPs, while here we are interested to analyse exclusionary decisions made by the ISPs when net neutrality is removed. They consider that each ISP contracts sequentially with CPs for exclusivity. 7 Then, if no exclusive contract is signed, agents contract for non-exclusive provision. In our paper, we consider instead exclusionary fees. Namely, each ISP xes a fee that a CP has to pay if it wants access its network. This tari will be high if the ISP wants to exclude a CP and will be low if it wants to attract both CPs. In such a way, we simplify the negotiation stage, and we think to a negotiation process that could resemble a probable one in a big world like the Internet is. Moreover, they do not model how competition works on the advertisers market, and they just use a parameter to capture the protability of a given CP on the advertising market. Instead, in our model, we explicitely model competition between CPs on the advertising 7 First, an ISP contacts for exclusivity with a CP. Then, if no agreement is reached, with the other CP. 6

7 market. We model competition between CPs so as to capture the stylized fact concerning the decreasing value of multiple advertising impressions on viewers (see, among others, Calvano and Jullien, 011, and Anderson, Foros and Kind, 011). 3 The Model 3.1 Setup We consider a setting with two horizontally dierentiated Internet Service Providers (ISPs), indexed by i = A, B, and two identical Content Providers (CPs), indexed by j = 0, 1. An ISP is a platform connecting consumers to CPs, and a CP is a platform connecting consumers to advertisers. Obviously, a CP needs to be connected to at least one ISP in order to be able to reach consumers. Moreover, each CP reaches only the consumers of the ISP it is conncted to. We consider ISPs and CPs to be independent rms. We compare the connection choices made by rms under two alternative regulatory regimes: one in which network neutrality regulation is in place and one in which it is removed, referred to as the unregulated regime. In the former case, ISPs have to grant access to their network to all CPs for free. In the latter, ISPs impose an access fee to CPs. Internet Service Providers. ISPs are located at the extremes of a Hotelling line: ISP i = A is located at point 0 and ISP i = B at point 1. ISP i sets a subscription fee a i (which can be positive or negative) for consumers. In the unregulated regime, ISP i also xes an access fee F i (which can be positive or negative) for CPs. In the net neutrality regime, CPs can freely access both ISPs, hence F i = 0. Access fees F i are exclusionary: if a CP pays it, it can access ISP i's consumer base, otherwise it is excluded. All fees are non-discriminatory and non-contingent. The prot function of ISP i is π i = a i q i + F i I ij j=0,1 i = A, B where q i is the number of consumers connecting to ISP i and I ij is an indicator function, such that I ij = 1 if CP j acquires access to ISP i's consumers and I ij = 0 otherwise. More details on this function are provided below. Content Providers. Each CP provides free content to consumers but charges advertisers for ad spaces. A CP j charges a per-impression price p j to an advertiser if and only if a consumer is exposed to the ad while browsing content (an impression). We assume that 7

8 there is no cost of providing ad spaces and that CPs set a uniform price for all advertisers. We abstract from the issue of consumer targeting, assuming all consumers are equally valuable targets for all advertisers. Hence, each time a consumer visits a given content, she is impressed with all ads with probability one and all impressions are relevant. However, their eect may depend on how many times the consumer has already been impressed with the same ad, as we discuss below. We also assume that each avertiser can buy at most one ad space per content provider. 8 Given these assumptions, the volume of impressions for an ad put on CP j is equal to q j, which is the number of consumers connected to the ISPs distributing j's content, i.e. q j = q i I ij j = 0, 1 i=a,b The prot of CP j is π j = d j p j q j F i I ij j = 0, 1 i=a,b where d j is the number of advertisers on CP j. A CP can connect to either no ISP, only one or both. CPs make connection decisions by comparing prots under all network congurations, taking as given the couple (F A, F B ) and the decision of the rival CP. A given network conguration arises at equilibrium when no CP nds a protable unilateral deviation. Consumers. There is a mass of size one of consumers uniformely distributed on the Hotelling line on the interval [0, 1]. Consumers connect to one and only one ISP and visit all available contents. 9 The utility U i consumer x [0, 1] gets from connecting to ISP i and browsing contents available on it is U i (x) = Z + i t x l i a i i = A, B (1) where Z is the gross surplus from accessing the Internet, assumed large enough that all consumers connect to an ISP. t is the transportation cost on the Hotelling line, i.e. disutility for consumer x from not consuming its preferred specication of the content. l i represents the position of the ISP on the Hotelling line. a i is the subscription fee to access ISP i. i represents the utility consumers get from browsing contents available on ISP i. We 8 The results would not change if CPs could charge a dierent per-impression price depending on which ISP the consumer impressed is connected to. 9 The rst assumption implies single-homing consumers. This assumption could be linked to some technological constraint that prevents consumers from having multiple connections at home. Moreover, many players in the telecom sector are active both in the mobile and xed telephony markets, and bundle access to the Internet on mobile and landline, so that it could be advantageous for consumers to use the same operator for both services. The second assumption follows from the fact that we ignore costs of visiting content. the 8

9 assume that each CP connected to ISP i increases individual utility by a value δ > 0, hence i = j δi ij. 10 We assume that the market is covered and that the demand for each ISP is positive, i.e. q i = 1 and q i > 0 i. Net consumer surplus (CS ) can be computed as CS = ˆ x (Z + A tx a A ) dx + ˆ 1 0 x (Z + B t (1 x) a B ) dx where x is the marginal consumer, indierent between subscribing to ISP A or B. Consumers' surplus can be written as CS = Z + ( i a i ) q i + t tq B tqa i=a,b Advertisers. There is a mass of size one of advertisers interested in reaching consumers by means of CPs' content. V 1 denotes the gross advertiser surplus (e.g. the increase in the expected value of sales due to the consumer seeing the ad) produced by impressing the ad on a consumer for the rst time, while V the gross advertiser surplus produced by impressing the ad on a consumer for the second time. The consumer may, in particular, have already been impressed with the same ad by consulting the content of the rival CP. Recent literature on online advertising suggests that ads seen multiple times are partially wasteful (Calvano and Jullien, 011). This is because ads end up hitting already informed consumers and hence are wasted together with their attention. 11 As a response, internet platforms introduce tracking technologies that reduce within-outlet waste. However, when consumers have access to multiple platforms (as in the setup we study here), more attention gets wasted as there is no across-outlet tracking. Therefore, we make the following Assumption V 1 V 0 Advertisers can buy ad spaces from none, one or both CPs. Suppose an advertiser multihomes, buying ad space from both content providers. Its total surplus would be V 1 j=0,1 q j + V j=0,1 q j p j q j 10 We do not endogenize consumers' demand for content, hence we do not explicitely take into account nuisance cost of advertising. 11 Athey, Calvano and Gans (011) estimate that more than two thirds of the ads in large campaigns are wasted, hitting the same receivers more than 10 times. j=0,1 9

10 where j=0,1 q j denotes the mass of consumers accessing at least one contentand j=0,1 q j denotes the number of consumers that access both contents. Given the assumptions taken above, each consumer that access at least a CP ( j=0,1 q j) is impressed at least once by each ad. Consumers that access both CPs ( j=0,1 q j) are impressed twice. Suppose instead the advertiser single-homed, buying an ad space only from CP j. Then, its total surplus would be (V 1 p j ) q j j = 0, 1 Obviously, the surplus is zero if no ad space is bought. Taking as given the network conguration and the prices p j, the advertiser will choose the option that guarantees the highest surplus. We may therefore compute the total surplus for advertisers as follows AS = ( d sj (V 1 p j ) q j + d m V 1 q j + V q j ) p j q j j=0,1 where d sj is the number of advertisers that single-home on CP j and d m is the number of advertisers that multi-home. j=0,1 j=0,1 j=0,1 Social Welfare. We dene Social Welfare as the sum of consumer surplus, advertisers surplus and prots of ISP and CPs. Thus SW = CS + AS + π i + i=a,b j=0,1 It is intutive that social welfare coincides with the gross surplus generated by connections at the two ends of the market, i.e. with the sum of gross surplus for consumers and advertisers. Indeed, payments collected by ISPs and CPs are simply transfers from other agents and cancel out in the social welfare formula. Replacing CS, AS, i=a,b π i and j=0,1 π j in SW, we get SW = Z + i + t tq B tqa + ( ) d sj V 1 q j + d m V 1 q j + V q j i=a,b j=0,1 j=0,1 j=0,1 It is straightforward to conclude the following π j Lemma 1 The socially optimal market conguration is such that each CP connects to both ISPs and all advertisers multi-home. PROOF: The fact that each CP is connected to both ISPs implies that q j = 1 j, as 10

11 consumers have access to all contents, irrespectively of the ISP they subscribe to. It also implies that q A = q B = 1/, hence total transport cost t tq B tqa are minimized. SW is strictly increasing in i=a,b i, which is maximized when I ij = 1 i, j. It is also optimal to have advertisers buy all ad spaces, since SW increases in the number of ad impressions to consumers. Timing and denition of equilibrium. The timing of the game is as follows: 1. Under the unregulated regime, ISP A and B simultaneously set access fees F i. Under the net neutrality regime, F i is restricted to be zero. Having observed fees F i, CPs simultaneously decide which ISPs to connect to (if any).. ISP A and B simultaneously set subscription fees a i. CPs simultaneously set (perimpression) prices p j for their ad spaces. Advertisers buy ad spaces from CPs. 3. Consumers connect to their preferred ISP and visit the available CPs, getting exposed to the ads. A subgame perfect equilibrium of this game is a set of fees, prices, connection decisions and demands such that, at each stage, no player wants to deviate given what has been decided at the previous stages and the choice of other players at the given stage. We assume all agents have perfect foresight. 1 The model is solved by backward induction. A remark is in order at this point. In a standard two-sided market framework, one could expect ISPs to cut subscription fees in order to attract more consumers and exploit network externalities on the content side. The timing we assume rules this out, since price competition for consumers comes at a later stage with respect to competition for contents. Hence, ISPs take revenues collected on the content side as given when deciding on subscription fees. We believe this to be a reasonable simplication, justied by the fact that contracts between ISPs and CPs have generally a more long-run perspective and their connection decision is more rigid than that between ISPs and consumers. 1 At Stage 1, ISPs set their fees anticipating the possible network congurations that may arise considering incentive and partecipation constraints of CPs. Given a couple (F A, F B ), one or more network congurations (i.e. quadruples {I ij } i=a,b;j=0,1 ) may occur in equilibrium. We make the assumption that, when they are indierent between connecting or not to an additional ISP, CPs always choose to connect. 11

12 4 ISP monopoly In order to understand the forces at work in the model, it is instructive to start by a simplied scenario in which only one ISP (say, A) is active. We simply disregard the presence of ISP B, so A acts as a monopolist. To describe in a concise way the network congurations that may arise in equilibrium, we now introduce some notation. In the following, network conguration (0A, 1A) means that both 0 and 1 connect to A (i.e. I Aj = 1 j); (0A, 1N) means that 0 connects to A and 1 does not (i.e. I A0 = 1 I A1 = 0); (0N, 1N) means that no CP connects to the ISP. 4.1 Stage 3 At Stage 3, consumers decide whether to connect to ISP A or stay out of the market. Indeed, only consumers with a low x participate to the market, while consumers with a high x prefer not to, since their transportation cost are too high. We calculate the marginal consumer x who is indierent between conecting to ISP A and not accessing the Internet at all. Solving for x equation U A (x) = 0, we nd x = Z + A a A t Demand for ISP A is given by all consumers who get positive utility from connecting to this ISP, that is q A = x Stage At Stage, ISP A decides its subscription fee a A maximizing its prots. ISP A's prots are π A = q A a A + j F Aj. By solving the rst order condition π A a A a Amon = Z + A By substitution, we obtain equilibrium demand and prot: = 0 i = A, B, we nd q Amon = Z + A t π Amon = (Z + A) 4t + j F Aj We nd that both subscription fee and demand are increasing in A. Hence, taking access fees j F Aj as given, prots are increasing in A. 13 In this special case, we relax the assumption that all market is covered. Hence, x 1. 1

13 Pricing of advertising spaces. At Stage, CPs also choose the price for advertising spaces. In order to understand how prices are formed, it is useful to start with a description of how much ad slots are worth to advertisers. Suppose an advertiser puts ads only on a single content provider, say, CP0. All consumers reached by 0 would be impressed once. The value of impressing a consumer with an ad for the rst time (a rst impression) is V 1. Consider now the possibility that the advertiser bought an ad space also from CP 1. The value of such additional space depends on whether consumers reached by CP1 have already been reached by CP0 or not. If a consumer browsing CP1 already browsed CP0, she would be exposed to the ad for a second time. Therefore, the additional ad space is worth V, i.e. the value of a second impression. If instead CP1 is the only outlet to reach the consumer, she will be exposed to the ad for the rst time. Hence, the additional ad space is worth V 1. If content providers are gatekeepers of their customers' attention they can always insist on charging the monopoly price for an impression. On the contrary, multi-homing on CPs by consumers introduces substitutability between platforms. As the fraction of consumers reached by multiple outlets goes up, strategic externalities become relevant, as in a standard Bertrand oligopoly model. These induce lower equilibrium prices (Ambrus, Calvano and Reisinger, 011, and Anderson, Foros and Kind, 011). To illustrate, assume to be in the universal distribution conguration: equilibrium prices are such that CPs charge a per-impression price V to all advertisers. To see why, consider that a higher price could protably be undercut by the rival CP, winning it the entire market. This is because advertisers would optimally single-home on the cheapest outlet. On the other hand, there is no point in charging less than V. This is because advertisers multi-home, since the price per impression is lower or equal than the value of a second impression V. 14 Consequently, when two CPs are connected to the same ISP, they charge p j = V j = 0, 1. Suppose, instead, a CP were the only one available to subscribers at a given ISP. Intuitively, it can act as a monopolist and set a per-impression price equal to p j = V 1, capturing the entire advertiser gross surplus. The above discussion introduces us to Lemma, presenting CPs' prots at Stage. We provide in its proof a more formal and complete description of how ad space prices are determined. Lemma In equilibrium, advertisers buy ad slots from all CPs that have access to consumers. Advertising prots π j for each CP, conditionally on its connection status, are as reported in the following table 14 If multi-homing was not possible, the equilibrium price would be equal to the marginal cost of providing ad spaces, which is zero by assumption. 13

14 π 1 π 0 A No A No V q mon ++ F A 0 V q mon ++ F A V 1 q mon + F A V 1 q mon + F A where q ++ mon = Z+δ t and q + mon = Z+δ t PROOF: We consider each possible market conguration in turn. Consider rst the universal distribution case. Thus, q j = q A j = 0, 1. Suppose an advertiser put ads on both CPs. Its total surplus would be (V 1 + V (p 0 + p 1 )) q A. Suppose instead the advertiser decided to put ads only on CP j. Its total surplus is (V 1 p j ) q A since, in this case, consumers are exposed only to rst impressions. This implies that, if it is already putting ads on, say, CP 0, an advertiser will also put them on CP 1 if and only if p 1 V. We now prove that p j = V j = 0, 1 is the unique equilibrium price for advertising spaces. Suppose p j V : as long as p j V advertisers would optimally multi-home and put ads on both CPs. Hence, it is optimal for CP j to set p j = V. Suppose instead that p j > V : then, it is optimal for j to set p j = p j ε. By so doing, all advertisers would single-home and buy only ad slots from j, leaving the other CP with zero revenues. It follows that the only equilibrium prices (mutual best response) are such that p j = V j = 0, 1. It is easily seen that, in such equilibrium, all advertisers multi-home. Finally, each CP makes a prot equal to V q A F i. Suppose now the market conguration involved full fragmentation, i.e. either (0A,1N) or (0N,1A). For instance, consider conguration (0A,1N). If an advertiser puts ads on both CPs, its total surplus is (V 1 p 0 p 1 ) q A. If ads are put only on CP 0, the surplus is (V 1 p 0 ) q A. If instead ads are put only on CP 1, the surplus is 0 p 1. We now prove that CPs set the following equilibrium prices: p 1 = 0 and p 0 = V 1. Indeed, as CP 1 does not provide any surplus to advertisers (since it is not able to reach consumers), they never join its platform for any positive price. Instead, CP 0 has no incentive to x any price lower than V 1, since advertisers join this platform for a price up to this value. Hence, CP 1's prots are π 1 = 0 and CP 0's prots are π 0 = V 1 q A F A. Trivially, when no CP is connected, no advertising takes place. Hence, all prots are zero. 4.3 Stage 1 At Stage 1, ISP A sets the access fee F A and CPs decide whether to connect to its platform or not. This decision determines, in turn, the network conguration. We now present the 14

15 subgame perfect equilibria of the game. We begin from the benchmark case of net neutrality, where the access fee is constrained to zero. Next, we consider the unregulated scenario, in which ISP A freely sets F A. In the following, we denote with superscript N the equilibrium variables under net neutrality, and with superscript U the ones under the unregulated regime Benchmark: net neutrality regime In the Network Neutrality case, prots for ISPs are simply given by revenues collected from subscription fees πamon N = (Z + A) since FA N = 0 4t We now study CPs connection decisions, and derive the corresponding conguration of the network. We assume that, when CPs are indierent between connecting or not, they choose to connect. Elaboration from the table provided in Lemma leads to the following Proposition 1 In the net neutrality regime there exists a unique subgame perfect equilibrium where the market conguration is (0A,1A). It is such that a N Amon = Z + δ q N A = q N j = Z + δ t p N j = V I N Aj = 1 j PROOF: The proposition is easily proved using Lemma, showing that, when F i = 0, this equilibrium exists and is the only one. Under net neutrality, the network conguration in which all CPs connect to A is always an equilibrium. When signing up to an additional ISP, a CP produces a negative externality on the rival, eliminating the possibility to charge the monopoly price V 1 for ad slots. Each CP would be better o if the rival was excluded from the market. Since connection is free, however, there is no mechanism to internalize this external eect. Nonetheless, the equilibrium is ecient from society's perspective Unregulated regime In the unregulated regime, ISP A is allowed to impose an access fee F A to CPs. The following Proposition presents the subgame perfect equilibria in this regulatory regime: Proposition In the unregulated regime: 15

16 ) if and only if the value of second ad impressions is high enough, i.e. V (V (Z+δ) (Z+δ), 4t 4t there exists a subgame perfect equilibrium where the market conguration is (0A,1A). It is such that F U A = V a U A = Z + δ q U A = q U j = Z + δ t p U j = V I U Aj = 1 j if and only if the value) of second ad impressions is low enough, i.e. if 0 < V < 1 (V 1 + (Z+δ) (Z+δ), there exists a subgame perfect equilibrium where the market 4t 4t conguration is (0A,1N) or (ON,1A). It is such that F U A = V 1 a U i = Z + δ q U A = q U j = Z + δ t p U j = V 1 IAj U = 1 j j=0,1 PROOF: see Appendix. When setting the access fee at Stage 1 the ISP essentially makes a choice between two alternative network congurations. If the access fee is suciently low, both content providers connect to the platform. If instead the fee is high, only one will do it. This is because, as shown in Lemma, if both connect the protability of ad spaces is reduced. Hence, as long as one CP connects, the other will not nd paying worthwile. As a consequence, the ISP faces a trade-o between obtaining a relatively large fee from a single content provider, while also renouncing to a share of consumers (who subscribe to its platform only if multiple content are available), and obtaining smaller fees from both CPs, while also maximising prots on the consumer side of the market. This is the reason why the equilibrium access fee depends crucially on the relation between the value of rst and second ad impressions, V 1 and V, as well as on the attractiveness of content for consumers δ. When V and/or δ are high enough, the monopolist ISP is better o attracting both content providers. This is because CPs have a substantial willingness to pay for connection even if they cannot sell access to consumers' attention as monopolists. Hence, they are both willing to pay a high access fee. Moreover, the loss of consumer base when excluding a content is too strong. If instead V and/or δ are low enough, the monopolist ISP prefers to ask for a high access fee, thereby excluding one CP. This is because attracting both content providers would require renouncing to a large share of prots on the content side, while the gains on the consumer side would be insucient. 16

17 4.4 Comparison of the two regulatory regimes Let us now compare network congurations in the two regulatory regimes. While CPs are always universally distributed under net neutrality, one might be excluded from the network under the unregulated regime. This happens when there is a large premium for being the only available advertising outlet. The ISP can then nd protable to exclude a CP in order to boost advertising revenues of the remaining one and recoup them through the high access fee. Let us now look at welfare implications. Consumers are always better o under the (0AB,1AB) conguration that under the (0i,1 i) conguration, since they have access to more contents. Advertisers are also better o under universal distribution, since the number of ad impressions increases, while their price goes down. CPs are clearly better o under net neutrality, since they have positive prots, while all their prots are extracted by the ISP under the unregulated regime. On the contrary, the ISP is better o under the unregulated regime, since it can extract prots from CPs. 5 ISP duopoly Let us now move to the fully-edged version of the model, with both ISPs active on the market. Following the notation introduced in Section 4, network conguration (0AB, 1AB) will here mean that 0 connects to both A and B and 1 connects to both A and B (i.e. I ij = 1 i, j); (0A, 1B) means that 0 connects only to A and 1 connects only to B (i.e. I A0 = I B1 = 1 I A1 = I B0 = 0); (0N, 1AB) means that 0 connects to no ISP and 1 connects to both A and B, (I A1 = I B1 = 1 I A0 = I B0 = 0). Similar notation is used for all other congurations. 5.1 Stage 3 At Stage 3, consumers choose which ISP to connect, maximizing U, taking as given the CPs available at each ISP and subscription fees a i. In order to compute demands, we determine the marginal consumer x who is indierent between the two ISPs. Equalizing U A (x) = U B (x) and solving for x we nd x = 1 + ( A B ) (a A a B ) t The demand for ISP A is given by all consumers to the left of x on the Hotelling line, while that for ISP B is given by all consumers to its right. That is, q A = x and q B = 1 x. 17

18 5. Stage At stage, ISPs simultaneously set subscription fees a i, maximising their prots. They do so taking as given access fees F i as well as CPs connection decisions (set at Stage 1), and anticipating consumers' behavior at stage 3. Equilibrium fees are obtained as the solution to the system of rst order conditions π i a i = 0 i = A, B. The result, for any network conguration, is a i = t + ( i i ) 3 i = A, B i i Replacing a i in q i and π i, we get demands and prots 15 q i = 1 + ( i i ) 6t π i = (3t + i i ) 18t + I ij F i i = A, B i i j=0,1 To describe in a brief way the equilibrium demands conditional on the values of i i, we introduce some additional notation, summarized in the following table i i q i dened as 1 δ 6t q δ 6t q + 1 δ 6t q ++ CPs set prices for ad spaces in the same way as in the monopoly case of Section 4. However, we can now nd situations where a CP is the unique gatekeeper only for a part of consumers connected to the Internet (the remaining part being reached by the other CP). In this case, the price of an ad space is a weighted average of the value of rst impression V 1 and of the second impression V, the weights being respectively the demand of subscribers who visit only one CP and the demand of subscribers who visit both CPs. Lemma 3 presents CP prots at Stage. Lemma 3 All advertisers multi-home at equilibrium. Prots π j for each CP, conditional on the network conguration, are as reported in the following table 15 Since we have assumed q i = 1 and q i > 0 i, this implies that we need δ 6t < 1 18

19 π 1 π 0 A&B A B None A&B A B None V F i V F i V q + + V 1 q F i V q + F A V q + + V 1 q F i V q + F A V 1 F i 0 V q + F A V q + + V 1 q F i V q + F B V q + + V 1 q 0 F i V 1 F i 0 V q ++ V F 1 A F B V q ++ F A V 1 F A V 1 q + F A V 1 F A V q++ F B 0 V 1 F B V q ++ F B V 1 q + F B V 1 q + F A V 1 q + F B PROOF: We consider each of the possible market congurations in turn. First, consider universal distribution. The discussion concerning this conguration is the same as the one in the proof of Lemma. Suppose now the market conguration involves partial fragmentation. For instance, consider the case (0AB,1A). If an advertiser puts ads on both CPs, its total surplus would be (V 1 p 0 ) q + (V 1 + V p 0 p 1 ) q +. If instead ads are put only on CP 0, the surplus is V 1 p 0. Finally, if ads are put only on CP 1, its surplus is (V 1 p 1 ) q +. We now prove that ISPs set the following equilibrium prices: p 1 = V and p 0 = V 1 q + V q + and that advertisers multi-home. Let us start by describing the best response function for CP 0. Suppose p 1 V. In that case, advertisers would buy ad spaces from CP 1, irrespectively of whether they have already bought ads from CP 0 or not, since price is surely below the value of a repeated impression. If they put ads on CP 1, however, they will also put them on CP 0 only if p 0 is low enough, i.e. only if (V 1 p 0 ) q + (V 1 + V p 0 p 1 ) q + (V 1 p 1 ) q + which results in p 0 V 1 q + V q +. It follows that the best response for CP 0 is to set p 0 = V 1 q + V q + (otherwise, CP 0 would not be able to sell any ad space). Suppose now p 1 > V : in that case, advertisers putting ads on CP 0, would never put them on CP 1, the price being too high. This rules out multi-homing, so all advertisers put ads either on CP 0 or CP 1. Clearly, CP 0 is better o being the player capturing all the market. This happens if and only if (V 1 p 0 ) (V 1 p 1 ) q + holds. As a consequence, the best response is p 0 = V 1 q + p 1 q +. 19

20 Let us now describe the best response function for CP 1. Suppose rst that p 0 V 1 q + V q +. Advertisers multi-home if and only if p 1 V. Otherwise, they all converge on one of the two CPs. However, if p 1 > V, this CP is 0, as condition (V 1 p 0 ) (V 1 p 1 ) q + is holds. It follows that the best response is p 1 = V. Suppose now that p 0 > V 1 q + V q +.p 0 is suciently high for CP 1 to be able to capture all the market while still setting a higher price than V. Indeed, it can easily be veried that condition (V 1 p 0 ) (V 1 p 1 ) q + holds as long as p 1 p 0 V 1 q. The threshold on the right hand side of the inequality is q + strictly higher than V as long as p 0 > V 1 q + V q +. Hence, by setting p 1 = p 0 V 1 q > V q +, CP 1 is able to capture all the market. Hence, the best response is p 1 = p 0 V 1 q. q + We are now in a position to describe the equilibrium. It is quite easy to see that the only mutual best response is such that p 1 = V and p 0 = V 1 q + V q +. This implies that CPs' prots are π 1 = V q + F A and π 0 = V 1 q + V q + F i and that advertisers multi-home. A similar reasoning applies when the conguration is (0A,1AB), (0B,1AB) and (0AB,1B). Consider now a conguration with all CPs being distributed by only one ISP, i.e. either (0A,1A) or (0B,1B). With a reasoning similar to that of the case of universal connection, one can prove that the only equilibrium is such that p 0 = p 1 = V so that CPs' prots are π 1 = π 0 = V q ++ F A. Again, advertisers multi-home. Consider a market conguration involving full segmentation, i.e. either (0A,1B) or (0B,1A). In this case, each CP would be a monopolistic outlet for the consumers it reaches. It is quite intuitive (we omit the proof) that equilibrium prices are p 0 = p 1 = V 1 and prots π 1 = π 0 = V 1 F i. It is again the case that, in equilibrium, advertisers multi-home. Consider now a conguration with one CP being distributed by both ISPs, while the other CP being distributed by no ISP. Take, for example, the case (0AB,1N). No advertiser puts an ad on CP 1 since no consumer can reach it. If an advertiser puts ads on CP 0, its total surplus is V 1 p 0. Thus, quite simply, the only equilibrium is such that p 0 = V 1. Hence, CPs' prots are π 1 = 0, π 0 = V 1 F i. In this case, advertisers single-home, since they have no benet from advertising on CP 1. A similar reasoning applies to conguration (0N,1AB). Finally, consider a conguration with one CP being distributed by one ISP, with the other CP being distributed by none, such as (0A, 1N). No advertiser puts an ad on CP1 since no 0

21 consumer is reached. If an advertiser puts ads on CP 0, its total surplus is (V 1 p 0 ) q +. Thus, p 0 = V 1. Hence, CPs' prots are π 1 = 0, π 0 = V 1 q + F A. A similar reasoning applies when the conguration is (0N,1A), (0N,1B) and (0B.1N). 5.3 Stage 1 At Stage 1, ISP i sets the access fee F i and CPs decide to which ISP they want to connect, if any. Our objective is now to determine the subgame perfect equilibria of the game. We begin from the benchmark case of net neutrality, where access fees F i are constrained to zero. Next, we consider the unregulated scenario, in which ISPs freely set F i. As in Section 4, we denote with superscript N the equilibrium variables under net neutrality, and with superscript U the ones under the unregulated regime Benchmark: net neutrality regime In the net neutrality case, prots for ISPs are simply given by revenues collected from subscription fees π i (F i = 0) = (3t + i i ) i = A, B 18t We now check which conguration of the network occurs at equilibrium, by studying CPs' choices of connection, given F i = 0. Elaboration from the table provided in Lemma 3 leads to the following Proposition 3 In the net neutrality regime: there always exists a subgame perfect equilibrium where the market conguration is (0AB,1AB). It is such that a N i = t q N i = 1 p N j = V q N j = 1 I N ij = 1 i, j if and only if the value of second impressions of advertisements is low enough, i.e. V V 1 ( δ 6t+δ ), there also exists a subgame perfect equilibrium where the market conguration is (0A,1B) or (0B,1A). It is such that a N i = t q N i = 1 p N j = V 1 q N j = 1 Iij N = 1 Iij N I ij N i, j j=0,1 1

22 PROOF: The proposition is easily proved using the table in Lemma 3, and showing that, when F i = 0, the equilibria are the only ones to exist. Under net neutrality, the network conguration in which all CPs connect to both ISPs is always an equilibrium. Interestingly, this is not necessarily the most desirable outcome from the perspective of CPs. More precisely, when the price of ad spaces is strongly reduced due to competition between multiple CPs, each could make higher prots if the network were fully segmented. This is because, if a single CP can act as a gatekeeper for advertisers interested in reaching consumers, it can charge monopoly prices for ad spaces. As in the monopoly case of Section 4, when connecting to an additional ISP, each CP produces a negative strategic externality on its rival, eliminating the possibility to charge the full price V 1 for ad slots. Since connection is free, this strategic externality is uninternalized, so the equilibrium with universal connection is always possible. Hence, when V is low compared to V 1, the game between CPs is a typical prisoner's dilemma. Nevertheless, quite inuitively, the equilibrium is ecient from society's perspective as availability of content is maximised and price of ad spaces are competitive. There also exists the possibility of a second equilibrium, characterized by the (0A,1B) or (0B,1A) market conguration. This is possible when the value of the second impression is suciently small. This is more likely to happen when consumers value contents to a large extent. 16 To get the intuition, suppose (0A,1B) to be the market conguration. Consider the problem of a content provider, say 0, deciding whether to connect also to ISP B or not. If it does not connect to B, the price it can charge for ad spaces is V 1, given that it is the only outlet for advertisers wanting to reach A's consumers. If CP 0 connects to B as well, its consumer base is enlarged but the price it can charge for ad spaces is the weighted average V 1 q + V q +. This is because part of its audience would already be reached by the rival content. Although connection to B is free and gives the possibility to reach more consumers, there is an implicit cost for CP 0. The quantity of eyeballs it monopolizes shrinks: when connecting also to B, CP 0 induces part of A's consumers to migrate to B. Hence, if the eect of content availability on consumers' demand is high enough and/or the relative value of second ad impressions is small, the implicit cost of an additional connection for CP 0 is too high. It follows that the CP may prefer not to connect to the extra ISP, even if it can ( do so for free. The above also implies that if V V δ ) 1 6t+δ, multiple equilibria exist Indeed, observe that the threshold V 1 ( δ 6t+δ ) is strictly increasing in δ. 17 One could use a given selection criterion to eliminate one of the two. We nd that the equilibrium where the market conguration is (0A,1B) ( ) or (0B,1A) payo-dominates the one where the market conguration is (0AB,1AB) when V V 1. We also nd that the equilibrium that induces δ (0AB,1AB) 6t+δ