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1 August, 999 &RPSHWWRQDQG&RPSDWEOW\DPRQJ,QWHUQHW6HUYFH 3URYGHUV By: Øystein Foros and Bjørn Hansen ** Telenor Research and Development $EVWUDFW We consider a two stage game between two competing Internet Service Providers (ISPs). The firms offer access to the Internet. Access is assumed to be a differentiated service. Our model exhibits network externalities. In the first stage the two ISPs choose the level of compatibility (i.e. quality of a direct interconnect link between the two networks). In the second stage the two ISPs compete á-la Hotelling. We find that the ISPs can reduce the stage competitive pressure by increasing compatibility due to the network externality. The firms will thus agree upon a high compatibility at stage. This result is not altered, as vertical differentiation is included in the model. When it is costly to invest in compatibility, we find that the firms overinvest, as compared to the welfare maximising investment level..h\zrugv Compatibility, Internet, Competition, Duopoly -(/FODVVIFDWRQ: 3; 96; 4 * We are grateful to Ragna Brekke, Hans Jarle Kind, Tore ilssen, Björn Rupp and Seminar participants at the nd Berlin Internet Economics Workshop for very useful discussions and comments. ** Address for correspondence: Telenor Research and Development, Instituttvn 3, -07 Kjeller, orway. bjorn.hansen@telenor.com

2 ,,QWURGXFWRQ We consider competition between two ISPs (Internet Service Providers) operating in the same geographic area. The product from these service providers is basically access to the Internet, and the ISPs operate their own network (backbone). Internet access is assumed to be a horizontally differentiated service from the customer s point of view. Furthermore we assume that there are positive consumption externalities. We consider ISP competition in a two stage game where two competing ISPs in the first stage determine the quality of interconnection (i.e. the quality of off-net traffic). This choice of interconnection quality can be considered as a choice of compatibility between the networks. In the second stage, for given compatibility, the two firms compete à la Hotelling in attracting customers. The motivation for the paper is the observation that ISPs competing in the same geographic area typically offer higher quality for on-net communication as compared to off-net communication. Roughly, on-net communication refers to traffic between computers/customers connected to the same ISP, while off-net communication is between computers/customers connected to different networks, e.g. communication between customers subscribing to competing ISPs. There are two possible causes for the quality differential between off- net and on-net traffic. The first cause is related to coordination problems between independent firms. The technology for measuring both traffic and quality of service (e.g. delay) between ISPs may be hard to implement. The second cause is that ISPs may have strategic incentives to degrade the interconnection quality for off-net traffic to a competing ISP. In this paper we focus on the second cause, i.e. to what extent do ISPs have incentives to degrade interconnection quality.

3 The majority of the literature on Internet economics focuses on the US-market. In contrast, our paper is motivated by the situation for competing ISPs outside USA. Previously, the attention in the ISP-markets outside USA has been directed to the quality of the connection to the US. The quality of local communication between competing ISPs was rather unimportant since the majority of the Internet content was in the US. The situation is, however, altered, and the portion of the Internet-traffic where both the sender and the receiver are located in the same area is increasing. This tendency is probably due to new customer-types and new services in the Internet. In non-english speaking countries content intended for the mass-market must be produced locally or translated. Furthermore, for new interactive services, such as telemedicine, tele-education, and video conferencing, a larger portion of the communication are probably between customers in the same geographical area than what is the case for conventional Internet services such as web-browsing. Thus, the quality of local interconnection is more important seen from the consumer s point of view, and accordingly, the importance of local interconnection as a strategic variable has increased. Utility from network participation depends on the number of potential communication partners and the quality of this communication. For given market shares, the customer s willingness to pay is increasing in interconnection quality. It is not obvious, however, that competing firms will choose a high quality. In the presence of network externalities, customers will FHWHUVSDUEXV consider it more advantageous to choose the larger ISP if the chosen quality of interconnection is reduced. A large ISP may accordingly choose a low interconnection quality in order to increase its market share. See Mueller et al. (997) 3

4 There are to our knowledge few papers explicitly considering ISP competition, but Crémer, Rey and Tirole (999), Dangguyen, and Penard (999) and Baake and Wichmann (998) are notable examples. The strategic effect of interconnect quality does however have many similarities with the strategic effect of interconnect price (for given quality) in telephony networks, see affont, Rey and Tirole (998a, 998b) and Armstrong (998). As argued above, network externalities result in a strategic effect of interconnect quality. Such externalities were first given a theoretical treatment by Rohlfs (974). The strategic effect of network externalities on competition was recognized by Katz and Shapiro (985), who analyze the strategies of choosing compatibility. As pointed out by Katz and Shapiro, externalities and the choice of compatibility are closely related. Matutes and Regibeau (988) do however demonstrate that in a mix and match model, compatibility is of significance even in the absence of network externalities. Following several recent studies of the competition in the telecommunication market, e.g. affont, Rey and Tirole (998a, 998b), we assume that firms offer horizontally differentiated goods. The motivation for this horizontal differentiation is receiving little attention in the literature. In our setting, product differentiation in the horizontal dimension may be given several interpretations. Customers of ISPs are typically buying some complementary products to the Internet access. Private customers connect to the ISP via the telephone, television cable or wireless telephone. Most ISPs are owned by, or, are in co-operation with a certain supplier of local access, such as cable-tv or local telephony operators. This is one source of horizontal differentiation, since e.g. cable-tv-access suppliers can offer the best incoming capacity, while local telephony companies have more experience with switching technologies and two-way communications. Customers with preferences for mobility choose wireless access Matutes and Regibeau (996) argue that the literature on compatibility can be divided into two categories, namely the network externality approach (e.g. Katz and Shapiro 985) and the mix and match approach (e.g. Matutes and Regibeau, 988). 4

5 although the capacity is lower than for e.g. cable-tv access. Another source of horizontal differentiation is the alliances between ISPs and content providers. The ISPs may choose to specialize in offering high quality of some services and thus attracting customers preferring these services. Our assumption of horizontal differentiation is in contrast to the assumption applied by Crémer, Rey and Tirole (999) and Baake and Wichmann (998). In these papers the suppliers have an installed base and they are engaged in Cournot-type competition where the providers compete in attracting new consumers. Crémer HWDO. (999) find that the firms may have incentives to degrade interconnection quality under market sharing equilibrium. They show that the firm with the larger installed base may have lower incentives to increase the interconnection quality as compared to the smaller one. Moreover, the dominating network may have a strategic motivation for interconnection quality reduction, even absent cost of interconnection quality. Baake and Wichmann (998) present a model concerning ISPs that are in Cournot competition. They do not derive any unambiguous effects from increasing interconnection quality trough a direct bilateral agreement in a Cournot duopoly. However, they show that certain conditions are more favorable for such agreements than others. Our paper is organized as follows. In section II we present a stylized network structure. In particular we describe how the firms can affect the interconnect quality. In section III we present our model with horizontal product differentiation and price competition. In section IV, the model of section III is extended by introducing vertical differentiation. Finally, in section V we conclude.,,$vw\o]hgqhwzruvwuxfwxuh Suppose that for communication between own customers (on-net traffic) ISP $ is offering a quality guarantee of. If ISP $ s customers are communicating with ISP 5

6 % s customer (off-net traffic), no such quality guarantee is given. et the quality of off-net traffic be (where ). The technical explanations may be that internal traffic is organized and routed by ISP $through its own infrastructure (ISP $ s own backbone and router $, see figure ). Traffic to ISP % or other destinations in the Internet are sent out of ISP $ s network. Such interconnect points between networks are often denominated Internet exchanges (IX). We examine such an IX that links several ISPs in the same area (e.g. a country) and, furthermore, this IX is connected to the Internet Backbone in the US. We denominate this IX as RIX (Regional Internet exchange), and we assume that this interconnection point is administrated and controlled by a non-commercial third party. 3 The quality level at the RIX is assumed to be outside the control of both ISP $ and ISP % 4 In figure, below, we have illustrated a situation where ISP $ and ISP % only are connected through the RIX. Even if the ISPs have the opportunity to invest in the quality of the RIX, the free-rider problem will tend to lower an independent ISP s incentives for such investments in the open RIX. This is due to the fact that both ISPs connected directly to the RIX, and other ISPs connected indirectly via the Internet, will take advantage from such an investment. Other ISPs can accordingly free-ride and increase their traffic, and this will in turn erode the revenue from the investment. The RIXs have also been considerable bottlenecks and sources of congestion in several European and Asian countries. 3 Bailey and McKnight (997) described four interconnection models where exchange point described here refers to what they called Third-Party Administrator. The other categories are Peer-to Peer Bilateral, Hierarchical Bilateral, and Co-operative Agreement. 4 Mueller, Hui and Cheng (997) give a detailed description of the local regional interconnection point in Hong Kong. The Hong Kong Internet exchange (HKIX) serves as a neutral, non-commercial interconnection point between ISPs in Hong Kong. HKIX is administrated by the Chinese University of Hong Kong. The context is comparable with the situation in many European countries, and the marketcontext is simplified in figure. Mueller HWDO (997) analyse the factors that affect the incentives for ISPs to use the HKIX or break apart and form a private IX. The economic issues facing the HKIX are analogous to the situation we analyse. 6

7 )JXUH ISP A Internet Backbone ISP B Computer B Computer A RIX Computer A Router A Router B Computer B In this diagram (figure ), traffic within a single ISP never reaches an external router such as the RIX. Traffic between computer $ and computer $ is served by router $ and the quality level is. Router $ will send all non-internal traffic to the RIX. Then the quality is. Traffic with destination in the network of ISP % will be routed to Router %. All other traffic is sent to the Internet Backbone. ISP $ and ISP % do, however, have the opportunity to invest in a direct link between their networks, i.e. they can invest in a direct interconnect point (a private Internet exchange (IX)). If they do, the quality level related to communication between ISP $ and ISP % is, where. The direct private IX between the two ISPs ensures better quality of the communication between the competing ISPs. Figure illustrates the context when there is a direct interconnection router (IX) between ISP $ and ISP %: 7

8 )JXUH ISP A Internet Backbone ISP B Computer B Computer A RIX Computer A Router A IX Router B Computer B The routing structure in this diagram (figure ) is the same as above, with one exception. ISP $ and ISP % have invested in a direct interconnection (IX)which serves traffic between ISP $ s customers and ISP % s customers. The quality level for this traffic is in the interval,. The aim of this paper is to analyze the incentives competing ISPs have to implement such direct interconnection. 5 In the ISP-markets in the European countries competing ISPs have been reluctant to implement direct interconnection links between their networks in order to enhance the quality of off-net traffic to ISPs in the same area. Thus, they operate in a context more like figure than figure. 6 5 As in the formal model in the next section, since both users and suppliers of Internet services have preferences for interconnection quality, we do not make a distinction between the two customer groups in the ISP market. The distinction is furthermore technologically arbitrary, since each computer can act both as supplier (host) and user (client) of content. 6 Take orway as an example: The three dominating ISPs: Telenor, Telia and Tele are managing their own networks, off-net traffic between the competing ISPs are routed through the orwegian Internet exchange (IX). The IX is non-commercial and managed by a third party administrator at the University of Oslo, such as the RIX in the figures above. It has been argued that the IX constitutes a bottleneck that gives rise to lower quality (delay) for communication between the ISPs, e.g. Telenor and Telia, than for on-net traffic. However, private IXes are now more common both in the US and in the rest of the world, see Chinoy and Solo (997) and Cawley (997). 8

9 In addition to a third party interconnection point, such as the RIX, ISPs outside USA usually have a direct link to one or several Internet Backbone Providers (IBPs) in the US. Thus, another possible path for traffic between competing ISPs located in the same area is via USA. Analogous to traffic via a congested RIX a detour via USA implies lower quality for off-net traffic than for on-net traffic. For Internet services like this is not an important problem. However, for interactive services like video-conferencing, such delays are not tolerated. In such contexts, "death of the distance" is not only a buzzword, it is even false. Moreover, the connection to the US is by expensive private leased circuits. Baake and Wichmann (999) and Mueller HW DO. (997) emphasise that the cost-reduction from setting up a local interconnection point, instead of sending local traffic via USA, may be substantial. 7 We have used the quality-term in a rather generic way. However, the quality of interconnection could be given several interpretations in our setting. As mentioned above, the key notion is that customers have preferences for high quality and that quality degradation of interconnection prevents them from communications with offnet customers with the same quality as communications with on-net customers. otice also that the motivation for degrading the quality of an interconnect arrangement in the ISP market may be analogous to the price discrimination between on-net and offnet traffic we observe particularly in the mobile telephony market. In the mobile market, we see that the operators charging different prices for calls terminating on-net and calls terminating on a competing network (off-net). Price discrimination between on-net and off-net calls may squeeze an operator with a small market share, and creating a GHIDFWRdegradation of interconnection. The current Internet offers a single quality called EHVWHIIRUWVHUYFHV where the bitstream is served after the principle first come, first served. There is no guarantee for 7 Baake and Wichmann (998) give an analogous description of the ISP market in Germany, and, as mentioned in a footnote above, Mueller HWDO. (997) describe the situation in Hong Kong. 9

10 success, and some packets are delayed while others never arrive. The minimum quality level may be interpreted as EHVWHIIRUWVHUYFHV. Different services and different users place different demands related to networks resources. and file transfers can easily tolerate delay, while real time services as interactive video only tolerate minor delays. Thus, with the quality level, it may well happen that real time services cannot be provided. Interactive services may be among the most profitable services in the Internet, in which case the ISPs will possibly want to serve their customers with connection sufficient to transfer such services. 8 The standard protocols TCP/IP in the Internet are more suited for services that tolerate delays than for interactive services 9. This means that new standards have to be implemented in the Internet in order to serve customers demanding interactive services. For on-net traffic the ISP has opportunities to offer sufficiently high quality, i.e. to provide real-time interactive services. This can be done by several mechanisms for resource reservation. However, such mechanism for resource reservation or guarantees seem to be easier to implement internally in a network (on-net traffic) than by several independent networks (off-net traffic). Thus, even if there is no coordination and engineering problems in increasing the quality level of off-net traffic to the level of on-net traffic, it may happen that ISPs in an unregulated oligopoly environment are reluctant to improve off-net quality. Indeed, there may be strategic incentives to degrade the quality for traffic to the competitors, even if increasing the interconnection quality implies no cost. 8 One reason for the profitability of interactive services is that they are less prone to personal arbitrage and reselling than services tolerating some delays (Choi HWDO., 997). Another reason is that customers have higher willingness to pay for new information. This will be especially true for strategic information such as stock exchange rates (Shapiro and Varian, 998). 9 IP manages the addressing in the Internet, while the TCP breaks a message into packets, and sends the packet to the IP network. At the destination the TCP waits until all packets constitute e.g. an are arrived before reassembling the message and send it to the receiver. 0

11 ,,,7KHPRGHO The preferences of customers are assumed to be distributed uniformly with density on a line of length. The two firms (Dand E) are located at the extremes of this unit line, firm D is at [ D = 0 and firm E is at [ E =. The unit cost for each firm is F, and the customers have unit demands. The location of preferences on the unit line indicates the most preferred network type for each customer. Since there are only two networks available located at the ends of the line most customers will have to choose a network different from their most preferred type. et utility for a customer located at [ connected to supplier is accordingly: 8 = Y W [ [ + Q + Q S β 3 8 M The first term is a fixed advantage Y of being connected to a network. The second term is the disutility from not consuming the most preferred network type (the transportation cost in the standard Hotelling model). A customer located at [ is accordingly incurring a transportation cost equal to W[ [ when connecting to a supplier located at [ ( = DE). The third term is a utility term depending upon the number of on-net and off-net customers ( Q and Q M respectively) equal to β 3Q + Q M8, where β > 0 and, 0. The parameter can be interpreted as a measure of the quality of the interconnect arrangement. When the quality of interconnect equals unity, customers are indifferent as to the distribution of off-net and on-net customers since on- and off-net traffic have identical quality. This is opposed to a situation where <. Then, all other things being equal, a customer will 0 We are here following Crèmer, Rey and Tirole (999) by modelling network externalities such that consumers benefit from an increase in network size. They are also assuming that the additional utility stemming from an increase in on net network members is larger than if the number of off net networks members increase. We are thus assuming network externalities and furthermore, that the utility from network size is linear. In appendix A we show that this formulation can be derived in a slightly more general model.

12 prefer a network with many customers. When = the quality equals, the quality available via the Internet (or the RIX in figure ), whereas! implies that the two ISPs have agreed upon establishing an interconnect arrangement (the IX in figure ) with superior quality. The fourth term, S is the per period price charged for ISP subscription. The customers utility functions are linear in consumption of the network service and money. $VVXPSWRQ: We assume that each of the customers along the interval 0, value the products sufficiently high such that they always prefer to subscribe to one or the other network. Thus, they will buy the subscription from either firm D or firm E, i.e. the fixed advantage Y of being connected to a network is sufficiently large. $VVXPSWRQ: In order to exclude the possibility of market cornering we assume that the magnitude of the network externality βdoes not exceed the transportation cost W This condition is fulfilled if W > β 6. Assumption is perhaps unfamiliar and it may deserve a comment: Consider a symmetric case where the two suppliers charge the same price. Assume that almost all customers along the unit line, for some reason, are connected to supplier D. The marginal customer with the longest distance to travel to supplier D will compare the offer from the two suppliers and he will choose supplier D(and the market will accordingly be characterised by cornering) if: β + 0 W > β 0 + W < β Assumption is thus ruling out the possibility of market cornering in such symmetric cases. We define α as the market share of firm D. Assumption, and are then implying that 6 for Q D = α, Q E = α. For a given price vector, the location of preferences [ 0,

13 the consumer satisfying 8 = 8 is determining the market shares. The market shares of the two firms are accordingly: S S D E α = ( W β( ) S S E D α = ( W β( ) D 6 6 E otice that if =, the expression for market shares are identical to what we obtain in a standard Hotelling model (i. e. a model without network externalities). By defining 67 we can write the market shares: σ = W β α= σ( S S ) D E α= σ( S S ) E D σ is a function of k where σ ( ) > 0, σ () = W, σ ( ) < 0. otice that assumption assures that σ > 0. The expression for market shares in our model is similar to the one we obtain in a standard Hotelling model with unit demand. In the standard Hotelling model, the parameter σ is interpreted as a measure of product substitutability. The products become closer substitutes if the transportation cost, W, between the two products is reduced. From our definition of σ it also follows that the products become closer substitutes, in the eyes of the consumers, if the quality of the link between the two networks is reduced. We can accordingly expect that an increase in the cost of transport and an increase in the quality of the link between the two networks to have similar effects upon prices and profits. $WZRVWDJHJDPH We model a two-stage game. In the first stage the two ISPs set the interconnection quality such that prices for a given.. In the second stage, the two ISP simultaneously set their 3

14 Stage In stage of the game the quality of interconnect is given and thus the measure of substitutability σ. The firms set their prices simultaneously, and firm is choosing S so as to maximize profits given by: M π = S F α = S F σ S S The first order condition for profit maximization is: π S S + F M = 0 = σ S S σ S F S = + M 4σ Combining the first order conditions for firm and M yields: S = + F σ and α = By inserting equilibrium prices and market shares in the profit function we obtain: π 6 = 4σ6. From this profit function we can directly see that profit is a function 67 of the level of product substitutability σ = W β 3 8 and thus of the interconnection quality. Inserting for σ and rearranging the profit function yields: W β π 6= ( = ( ) 4σ (.) When =, this profit function is identical to the one we obtain in a conventional Hotelling model with unit demand. Stage At stage of the game the two firms decide whether to set up an interconnect arrangement or not. As already stated, stage profit is a function of the quality of interconnection Direct differentiation of the profit function (.) with respect to yields: 4

15 π 6 = β (.) We readily see that the firms does not have conflicting interests with respect to network compatibility, i.e. π = π, implying that the two firms M always agree upon the optimal interconnection quality-level. Consequently, there is no need for an assumption that ensures that the firm with the lowest incentives for quality has a veto in setting The effect upon profits from changing interconnect quality can be decomposed into a price and a market share (or volume) effect by differentiating: π = α S F6: 6 π = α + α S F S The first term is the market share effect and the second term is the price effect. Consider first the price effect. By differentiating the equilibrium price we obtain: S = β The price effect of an increase in interconnect quality is accordingly always positive. In the symmetric case considered in this section, market shares are unaffected by interconnect quality. In the following we will apply the expression above to discuss the equilibrium quality of interconnect under various sets of assumption. &RVWIUHHQWHUFRQQHFWRQTXDOW\ We will first consider a situation where it is costless to improve the quality of interconnect. From (.) we have π = β > 0 and thus the firms have no incentives to damage the quality of the link between the two networks. Furthermore, if possible, they have a mutual interest in improving the quality of this link. Then, both on-net and off-net traffic have the same quality level = =. 5

16 Prices and profits increasing in the quality of the link between the two networks are due to two effects. The obvious effect is that for given market shares willingness to pay is increasing from all customers as the quality is increased. Furthermore, when the quality of the link is increased the competition between the two suppliers becomes less aggressive. This is due to the fact that if the quality of the link is low, then a firm will get a large increase in profits by increasing its market share since it leads to a strong infra-marginal effect. The infra-marginal effect stems from the fact that willingness to pay from existing customers increase more when market share increase when the quality of the link is poor as compared to the situation where the quality of the link equals (perfect interconnectivity). When the quality of the link equals, existing customers are indifferent with respect to market share. When comparing the conventional Hotelling model with our model featuring network externalities, the argument can be put the other way around: When the networks offer less than perfect connectivity ( < ) then the firms will compete more aggressively than what the conventional Hotelling model predicts. otice that since the quality of interconnect in this case is costless the socially optimal quality evidently is =. In the case without investment costs the market will accordingly implement the first best solution. &RQYH[FRVWVRIQWHUFRQQHFWRQTXDOW\ We will now consider a case where it is costly to set up the interconnection arrangement. The cost of interconnect in this case is the sum of the cost of investing in the necessary technical facilities and the transaction cost of writing a contract and the cost of mutual monitoring. It is reasonable that the total investment cost is The best response functions ( reaction functions ) in stage of the game is: S = 53SM8= 3W β 6+ SM + F 8. An increase in will result in parallel shifts outwards for these best response functions and the firms does indeed become less aggressive as the quality of interconnect increase. We can furthermore see 5 = 0.5, we are thus considering a stable ash equilibrium. 6

17 increasing in interconnect quality. Furthermore it may be reasonable to expect the cost to be convex, since, as interconnect quality increase, the complexity of the contract the two firms write becomes large. In particular the monitoring costs increase. As the quality of interconnect increase, the joint network of the two suppliers become more like a common facility where the firms have very many opportunities of opportunistic behavior. When the quality of interconnect is high, a firm may, for instance, route traffic to the international internet via the transportation network of the competing firm. In this way a firm can save infrastructure costs by congesting the competing network. Firms are, of course, not willing to agree upon interconnection unless the contract prohibit such opportunistic behavior. In order to observe and verify that the contract indeed is fulfilled, mutual monitoring is required. et the cost of investing in interconnect quality in order to increase the quality of 6 6 interconnect above be, =,,, > 0,, > 0, lim, =. Assume now that the two firms form an input joint venture where they equally share the cost of investing in interconnect quality. Each firm will then maximize the stage profit minus the share of the interconnect cost the firm has to pay in stage. Thus the two firms will solve identical optimization problems and agree upon a interconnect quality level G G characterized by: W β 6 = arg max, 6! Thus the investment join venture investment level is characterized by: 6 β = I k " $# We can compare this equilibrium quality level with the socially optimal quality. The first best interconnect quality,, is defined as the quality level that is maximizing customer gross surplus minus total production cost. Since the unit cost of serving customers in the two firms are identical and customers are distributed uniformly on the interval, first best is evidently characterized by sharing customers evenly among 7

18 the two firms. Then average distance from the most preferred brand is 0.5. Inserting this yields: * k = arg max v0 05. t k c I k β 6 6 The first best investment level is then characterized by: β = I k By comparing the first best investment level, we see that * < G (since β > 0.5 β). An input joint venture will thus choose a quality level of the interconnect arrangement exceeding the socially optimal level. The intuition behind this result is the following: There are two effects leading to the firms stage profits increasing in interconnect quality: The first effect is that for given market shares willingness to pay is increasing from all customers as the quality is increased. The second effect is that when the quality of the link is increased, the competition between the two suppliers becomes less aggressive. Only the first effect is a social gain. Thus the input joint venture is over investing in interconnect quality in order to reduce the stage competitive pressure.,97khvdphprghoihdwxuqjyhuwfdogiihuhqwdwrq The results obtained in the model above indicates that competing ISPs is always agreeing upon interconnect arrangements. In this section of the paper we will investigate whether this result stems from the strict symmetry in the model in the previous section. We will do this by introducing vertical differentiation into our model. Consider the following utility function: 8 = Y W [ [ + Q + Q S β 3 8 M 8

19 Where the only modification compared to the utility function in the previous section is that the fixed advantage Y DE, of being connected to network is allowed to differ among the two suppliers. Define θ = Y Y. Given that the two firms charge M identical prices the consumer with preferences located at the middle of unit line will strictly prefer supplier when θ > 0. Thus the firm selling the superior product will obtain a market share above 0.5 when the two firms charge the same price. In order to avoid corner solution we will have to add an additional assumption: $VVXPSWRQ: The valuation differential θ between products of the two firms is sufficiently low, such that there exist one customer located at [, where 0 < [ <, who is indifferent 67. between consuming the network service from the two firms i.e.: θ 3 W β It follows from assumption that the indifferent consumer located at α (0, ) derives a nonnegative surplus. Given the assumptions above the market shares of firm Dand E become: 6 θ S S D D E α = + ( W β( ) ( W β( ) 6 θ S S D E D α = ( W β( ) ( W β( ) By defining σ in the same way as in the previous section the market shares can be written: α= + σθ σ( S S ) D D E α= σθ σ( S S ) D E D The timing of the game we consider is identical to the game in the previous section. In the second stage, the two ISP simultaneously set their prices for a given and firm is choosing S so as to maximize profits given by: 9

20 M π = S F α = S F + σθ σ S S The first order condition for profit maximization is: π S S + θ + F M = 0 = σ S S + θ σ σ S F S = + M 4σ Combining the first order conditions for firm and M yields: S θ = + + F σ 3 σθ and α = + 3 Assumption 3 assures that the indifferent customer indeed does exist, i.e. α 0, 6 implying the parameter restriction: σθ θ α W β, 67 From assumption we have W β > 0 6, and then the condition above is fulfilled when assumption 3 is fulfilled. By inserting equilibrium prices and market shares in the profit function we obtain: θ σθ ( W β( ) θ θ πθ, 6= + + = + + 4σ ( W β( ) At stage of the game the two firms decide whether to set up an interconnect arrangement or not. Direct differentiation of the profit function above with respect to yields: 6 π θ, βθ = β 8( W β( ) By definition we haveθ M = θ, and thus we get: π = π M 0

21 This means that in a shared market equilibrium, the two firms will always agree upon the interconnection quality-level even when the market share of the two firms differ. By rearranging the differentiated profit function we obtain: 6 π θ, θ = β 9 W β 67 6 The condition for having a shared market equilibrium is θ 3W β 7. This condition implies that the bracket above is positive. Thus in any shared market equilibrium profits of both firms increase in interconnect quality. As in the previous section it can be useful to decompose the effect of changing interconnect quality by considering the price- and the market share (or volume) effect. We recall that: 6 (3.) π = α + α S F S Consider first the price effect. By inserting the definition of σ in the equilibrium price and differentiating with respect to we obtain: S = β. The price effect under vertical differentiation is positive and it is identical to the price effect in the symmetric case. This is opposed to the market share effect. Under vertical differentiation market shares become a function of interconnect quality. By substituting for σ in the equilibrium market shares and differentiating we obtain: α θ β = 6 W β 67 (4.) The market share effect is positive for the firm selling the inferior service and thus it is negative for the firm selling the superior service. The negative market share effect for the firm selling the superior product is however dominated by the positive price effect as demonstrated above.

22 Although one of the firms has an advantage and a bigger market share, due to vertical differentiation, the incentives for interconnection quality do not differ between the firms. This result is in contrast to the results in e.g. Katz and Shapiro (985), Baake and Wichmann (998) and Crèmer, Rey and Tirole (999). In those papers, the dominating firm may have lower incentives to increase compatibility (interconnection quality) than the smaller firm. Crèmer, Rey and Tirole (999) assume that the firm preferring the lower has the privilege to determine the quality of interconnection 3 In contrast to our model, where the difference in market shares stems from vertical differentiation, the difference in market shares in Crèmer, Rey and Tirole (999) is due to differences in the exogenous given installed bases. &RVWIUHHQWHUFRQQHFWRQTXDOW\ The differentiated profit function is everywhere increasing in for both firms. Thus the firms have no incentives to damage the quality of the link between the two networks and furthermore, if possible, they have a mutual interest in improving the quality of this link. Then, both on-net and off-net traffic have the same quality level = =. Thus when interconnect arrangements are cost free, a shared market equilibrium is characterised by the best possible interconnection quality. In the same way as in the previous section the chosen quality of off-net traffic is then identical to the quality of on-net traffic and the first best interconnect quality is chosen. &RQYH[FRVWVRIQWHUFRQQHFWRQTXDOW\ Consider now the case with convex interconnect costs, i.e. we assume:, =, 6,, > 0,, > 0 and lim, 6 =. Since the firms do not have conflicting interest with respect to the optimal interconnect quality, it is reasonable to keep the assumption of 3 Assume the quality of the common interconnect arrangement is exceeding the quality level preferred by firm. Then firm has he opportunity of unilaterally degrading the quality of interconnect by manipulating the interface between network and the interconnect facility. The firm preferring the lower interconnection quality can accordingly make a take it or leave it offer in negotiations over interconnection quality.

23 an input joint venture where the cost of interconnect is shared equally among the two firms. In market equilibrium the firms invest in an interconnect arrangement of quality: 6 67 G = arg max π θ,,. The first order condition for optimal investments is then: βθ i βθ i β I 0 β 6 k = I 6 k = 8 t β( k) 9 t β( k) 6 6 In appendix A we show that this interconnect investment exceeds the socially optimal investment. 9&RQFOXVRQ In this paper we have considered the incentives for an Internet Service Provider (ISP) to strategically degrade the interconnection quality with the competitors. We have modeled this in a game where two firms choose the quality of interconnection before they compete over market shares á la Hotelling. In the case where there is no vertical differentiation, the firms split the market equally, and they have no incentives to degrade interconnection quality. Moreover, when interconnection is costly the firms will over invest in interconnection quality as compared to the first best quality level. We have also demonstrated that if the products from the two firms also are vertically differentiated, then the firm providing the superior product will have the larger market share. As far as interconnection quality is concerned, the results are however not changed. When the necessary conditions for a shared market equilibrium is fulfilled, the firms will agree upon an optimal interconnection quality. Furthermore, if interconnection quality is costly, the firms will agree upon a quality of interconnect exceeding the welfare maximizing quality level. 3

24 These results are derived in a quite simple model inspired by pricing structures and the type of competition observed in the current Internet. ISPs traditionally charge a monthly subscribing fee and no usage-sensitive price. Horizontal differentiation may be more likely here than in the market for conventional telecommunication services. Furthermore, the ISPs may have more flexibility to manipulate quality as compared to other telecommunications firms since ISPs operate in a more unregulated environment. As pointed out in the introduction, in European countries competing ISPs have been reluctant to implement direct interconnection between their networks. This may seem to contradict the results from our model. One interpretation of European ISP behavior is however that the condition for a shared market equilibrium is not fulfilled and thus that the ISP market is moving towards monopolization. 4

25 Appendix A A utility function featuring a linear network externalities term. The utility function applied in the paper is: 8 = Y W [ [ + Q + Q S 0 β 3 8 M Members of a network do not have preferences over network size per se, but rather have preferences over communication with other network members. Assume that the utility from initiating T units of communication (measured in packets or information content) is XT 6, where X is increasing and strictly concave. Within the Internet it is usually time consuming to send or receive packets. Thus if Internet users incur a cost when waiting, then the marginal price of packets is strictly positive. In the network competition literature it is common to assume a balanced calling pattern (e.g. in affont et al., 998b and Armstrong 998). This implies that if the marginal price of usage is the same for communication with any network segment, then traffic is evenly distributed over all possible communication partners. If a customer is facing differentiated prices such that traffic to segment and M have marginal prices S and S M, then the assumption of balanced calling pattern implies that when two segments are of size α and α M the customer will derive gross utility: α XT 6 + α MXT 38 M from sending and receiving packets. A subscriber connected to the network will then solve: * % &K M 38 M M 38 M 'K YS 6 α YS 3 8 FOC S X T T ' S max α XT + α XT α ST α ST = = M M M M M T, T * M S = X T T = ' S We can now define an indirect utility function: YS X'S S'S. And total indirect utility 4 becomes: α M M +. Without loss of generality we can assume that the subscriber under consideration is member of network segment. Since the quality of on-net traffic is superior to off net traffic we have that S S M, thus YS 6> YS 3 M8. For given on- and off-net quality (and thus waiting time) we can define constants β and such that we obtain utility functions of the type applied in the paper: βα + α α α M Y S + MY SM Y S β = YS 6, β = YS 3 M8 = YS 3 M8 6 The focus of the paper is the parameter, the quality of the interconnect arrangement. The function above is illustrating that this quality affects customer utility via the cost of waiting. Since S S M we have Y(S M ) Y(S ) and thus [0,], as assumed in the paper. 4 All results in affont et al. (998b) are based on this particular indirect utility function. 5

26 Appendix A Welfare maximizing interconnect investments under vertical differentiation Consumers with preferences to the left of some point α join network D Since the individual transport cost is W[ and the distribution of consumers is uniform along the line, the sum of travelling costs for all consumers joining the networks are α W and of the game the social welfare function is: α6 W for network D and E respectively. In stage 6 > D 67 C 6 E 6 6 < A : = max α Y αw+ β α + α F+ α Y α W+ β α + α F α The welfare maximizing market share α * is thus: θ α * D = + W β 67 It can be shown that the market share of the firm selling the superior product will be to small in market equilibrium as compared to the welfare maximising market share. In special cases, the welfare maximising solution is to let the firm selling the superior product serve the entire market whereas both firms are active in the market equilibrium otice that this results not is specific to our model featuring network externalities. With the parameter value β = 0, the model does not exhibit network externalities (and thus there is no effect upon utility by improving interconnect quality). Then the welfare maximising market share is: α * = + α * = + θ D 6 W θ D W whereas market equilibrium is characterised by:, Thus the market share of the firm selling the superior product is accordingly to small. The stage socially optimal investment level is: 6 67 * = arg max :, FoC: : =, By applying the envelope theorem on :(): 3 8 : * * * * β βθ D βα α βα α = = = D E W β 67 In cases where the welfare maximizing network is characterized by market sharing, the following condition is fulfilled: W β > θ D 6. Both the numerator and denominator are then positive and in such cases welfare is everywhere increasing in interconnect quality. The welfare maximising * interconnect quality is found by solving: = arg max: 6, 6 7. The first order condition is accordingly: 6 : β βθ D, = 0 W β 67 6 =, The input joint venture will accordingly overinvest in interconnect quality when: 6

27 βθ β βθ β β > + βθ β β D 9 W ( ) W W β 9 W β( ) A sufficient condition is then that the large bracket is positive. This is the case since: W β < 9 W β( ) 0< 7W 0βW + β = 7W 0βW 8β + 9β 0< W β 7W + 4β + 9β > 0 It is only socially optimal to set up a direct link between the two networks if both networks have a positive market share, this is the case when W β > θ D 67. Thus the first bracket has to be positive. An input joint venture will accordingly over invest in interconnect quality under product differentiation as well as in the absence of vertical differentiation. 7

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