INTERCONNECTION INCENTIVES OF A LARGE NETWORK. David A. Malueg Marius Schwartz WORKING PAPER August 2001 revised January 2002

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1 INTERCONNECTION INCENTIVES OF A LARGE NETWORK David A. Malueg Marius Schwartz WORKING PAPER 0 05 August 200 revised January 2002 Georgetown University Department of Economics 580 Intercultural Center Washington, DC Tel: (202) Fax: (202)

2 INTERCONNECTION INCENTIVES OF A LARGE NETWORK * by David A. Malueg and Marius Schwartz January, 2002 Abstract This paper builds on Cremer, Rey and Tirole s analysis of the possible incentives of a firm with the largest share of installed-base customers, in a market characterized by strong network externalities, to degrade or refuse interconnection with its smaller rivals in order to gain a relative quality advantage in competing for new customers. We extend their model to allow any number of smaller rivals. We show that degrading interconnection can lead to tipping of the market away from the largest network even if its share of the installed base exceeds one half; for a given initial share of the largest network, such tipping becomes more likely as the number of rivals increases. We examine the minimal market share required for the largest network to prefer degradation (considering both tipping and non-tipping equilibria), as a function of the model s key parameters. Besides the number of rivals, key parameters include firms common marginal cost and the size of the installed-base relative to potential additional demand. Lower values of these parameters make profitable degradation less likely. In the case of the Internet, plausible parameter values suggest that degradation is not likely to be profitable unless the largest network commands significantly more than fifty percent of the installed customer base. JEL: Keywords: L3, L4, L86, L96 Interconnection, Network Externalities, Exclusion * We wish to thank Bob Majure, Michael Pelcovits, and Daniel Vincent for helpful comments and to acknowledge support from WorldCom for this research. The views in this paper and any errors, however, are ours. Department of Economics and the A.B. Freeman School of Business, Tulane University, New Orleans, LA 708; <david.malueg@tulane.edu>. Department of Economics, Georgetown University, Washington, DC 20057; <schwarm2@georgetown.edu>.

3 INTERCONNECTION INCENTIVES OF A LARGE NETWORK Table of Contents Summary I. Introduction II. Oligopoly with Competing Networks: Extending the CRT Framework A. The Model. Firms and Their Installed-Base Customers 2. Interconnection Quality 3. Demand by Potential New Subscribers a. Benefits from Subscribing to a Network b. Individual Subscription Decisions and Inverse Demands 4. Interconnection Choices and Competition for Subscribers B. Cournot Equilibria. The Interior Equilibrium 2. Tipping Equilibria C. Output Constraints and Their Interpretation D. Bounds on Plausible Values of the Parameters β, c, and v III. Global Degradation of Interconnection A. CRT s Result on Degradation in Duopoly B. Evaluating the Likelihood of Global Degradation. Duopoly: A Single Rival to Firm 2. Oligopoly: Two or More Rivals to Firm 3. Plausible Values of the Parameters c and v: Further Discussion 4. Summary: the Scope for Global Degradation IV. Targeted Degradation of Interconnection A. CRT s Example of Profitable Targeted Degradation B. Evaluating the Likelihood of Targeted Degradation. Restrictions Required for Profitable Targeted Degradation 2. Summary: the Scope for Targeted Degradation V. Conclusion References Appendix. Consumer Preferences Over Tipping Equilibria Appendix 2. Decomposing the Effects of β and c on the Largest Network s Incentives for Global Degradation Appendix 3. Targeted Degradation that Leaves Firm 3 Active Appendix 4. Reformulating CRT s Model So Output Constraints Never Bind A. The Reformulated Model B. Global Degradation C. Targeted Degradation D. Summary: the Scope for Degradation

4 Summary This paper builds on the analysis by Cremer, Rey and Tirole (2000) of possible incentives for a large Internet Backbone Provider to degrade interconnection with smaller rivals so as to curb their ability to share in network externalities, thus placing them at a quality disadvantage. CRT establish the following main results. Depending on the other parameters, a firm with more than fifty percent of the installed-base (locked-in) customers may profit by degrading interconnection when facing a single rival. When facing two smaller rivals, a market share of over fifty percent is again necessary for the largest network to profit from degrading interconnection with both rivals global degradation (CRT do not identify sufficient conditions for global degradation to be profitable). However, a fifty-percent share (and, by continuity, also somewhat lower shares) can make it profitable to degrade interconnection with one of the two equally-sized, smaller rivals targeted degradation. Within CRT s framework, we attempt to evaluate whether profitable degradation is not only possible, but also whether it is likely. In CRT s model, firms differ only in the size of their installed bases, and compete for new subscribers. A network s quality rises with the number of perfect links it offers. The key parameters are β, the total installed base relative to potential future demand (whose size is normalized to ); c, the marginal cost of serving new customers; and v, the strength of network externalities. If the network with the largest installed base, firm, degrades interconnection with a smaller rival, both their qualities decline but the smaller network s quality falls by more. Degradation could lead to an interior equilibrium in which all firms acquire new customers, or a tipping equilibrium in which only one firm acquires new customers. We extend CRT s model by allowing firm to face any number n of smaller rivals. This extension is especially important for assessing the scope for tipping away from firm if it degrades interconnection. In addition, we consider which parameter values can be viewed as plausible within the model as applied to the Internet, and ask if such parameter values support profitable degradation. One restriction on plausible parameter values is based on the fact that CRT s equilibrium formulas are only valid in parameter regions where the number of customers added in various equilibria does not exceed the pool of potential customers. Because it does seem reasonable that not all potential customers are likely to be served in oligopoly equilibria, we confine attention to parameters that predict some unserved potential customers (i.e., satisfy the output constraint ). (As a complementary approach, we present a reformulated model in which the pool of potential customers is large enough that, for any parameter values, some potential customers remain unserved. That alternative formulation reaches qualitative results similar to those described below.) In addition, for the Internet it is reasonable to suppose that future potential growth is large relative to the current customer base; within the model, this implies β. Other arguments described shortly suggest additional limits on plausible values of (c, v). i

5 Global Degradation We convert CRT s condition for profitable degradation when firm faces a single rival into a more interpretable condition specifying the minimal installed-base market share needed by, as a function of the parameters, β, c, and v, and we illustrate the condition graphically. We then allow firm to face an arbitrary number n of smaller rivals and analyze the outcome if firm were to degrade interconnection with all rivals while they remain interconnected among themselves. An interesting finding concerns the effect of increasing the number of rivals. Holding s share of the installed base ( m ) constant even at high levels such as 70% an increase in n expands monotonically the set of parameter values for which, if firm pursued global degradation, the unique equilibrium would be tipping away from firm. Global degradation clearly is unprofitable if it leads to tipping away from firm, but can also be unprofitable because of the reduction in overall market demand if it results in an interior equilibrium. For given values of β, n, and m, we show how the (c, v) parameter space is divided into three regions describing firm s choice of interconnection: Degradation in this region degradation leads to either a more profitable interior equilibrium for firm or, elsewhere in this region, a tipping equilibrium to firm ; No Degradation in this region degradation would lead to either a less profitable interior equilibrium for firm or a tipping equilibrium away from firm ; Ambiguous in this region either of the above tipping equilibria is possible following degradation. For given values of β and n, we explore which values (c, v) may be plausible for the Internet by computing what they would imply about two ratios: α price relative to marginal cost; and M the valuation of the median new subscriber relative to price (assuming in both cases Cournot equilibrium with four interconnected firms). Illustrative calculations suggest that the (c, v) values in the Degradation or Ambiguous regions for a market share of firm reaching well over fifty percent imply rather low α and M, values that appear at odds with actual conditions in the Internet. That is, parameter values needed for firm to profit from global degradation would imply a small markup of price above marginal cost (which is inconsistent with the presence of significant fixed costs that must be covered in long-run equilibrium), and an unrealistically low consumer surplus to Internet subscribers. To illustrate, consider β = 0.5, firm s market share at 70%, and three rivals (n = 3); to believe that (c, v) would lie in the Degradation or Ambiguous regions, one must also believe that the implied M would be below.73 and that α would be below.27. Furthermore, it would be quite risky for firm to pursue degradation in the Ambiguous region, because tipping might be away from. This risk is magnified by our finding that, under most parameter values plausible for the Internet, consumers would prefer the tipping equilibrium away from firm, and hence might naturally coordinate on this outcome. If firm thus would forgo degradation in the Ambiguous region, then the set of values (c, v) for which degradation is chosen will shrink, and the implied maximal values of M and α consistent with degradation become even lower. (In the above example of β = 0.5, m = 70%, and n = 3, the threshold α falls from.27 to.3, and the threshold M falls from.73 to.39.) ii

6 Overall, our analysis suggests that in CRT s framework the largest Internet backbone provider is unlikely to find global degradation profitable unless its share of existing subscribers is well above fifty percent. Targeted Degradation CRT s analysis of targeted degradation consists of an example where the largest firm has a market share of fifty percent and faces two rivals that split equally the remaining installed base. We first illustrate the necessary conditions graphically. As CRT point out, the value of the network-externalities parameter v must be high enough for degradation to exclude the targeted firm, but also not too high, for otherwise firm would lose too many customers to the non-degraded third firm that maintains good interconnection with all. The above requirements, together with restrictions required by the output constraint noted earlier, are rather stringent. Most (c, v) combinations that seem plausible for the Internet, based on their implied values for price relative to marginal cost and for the size of consumer surplus, do not satisfy the conditions for profitable targeted degradation. These findings persist when we extend CRT s analysis to targeted degradation that results in only partial rather than complete exclusion of the targeted firm from the market for new customers. We therefore conclude that in the example analyzed by CRT, targeted degradation is unlikely. iii

7 I. Introduction In communications industries such as telephony and the Internet, and in other markets where the value of the service to any user rises with the total number of compatible users (positive network externalities), some cooperation among competing providers is needed to achieve good interconnection so that customers may enjoy greater benefits of network externalities. However, it is well recognized that a firm possessing a sufficiently large share of all customers in such a market may gain by denying good interconnection to its smaller rivals, so as to attain a relative quality advantage over them. This was a central concern, for example, in two prominent recent merger cases MCI with WorldCom and MCI WorldCom with Sprint. In each case, the merger partners were so-called large Internet Backbone Providers: suppliers of high-capacity and geographically broad links to smaller Internet service providers and large business customers. European and US competition authorities feared that the merged entity would command such a large share of Internet customers or traffic that it might have significant incentives to degrade or fail to enhance interconnection with smaller backbones. An influential contribution to the debate over both mergers was the theoretical work of Jacques Cremer, Patrick Rey, and Jean Tirole (hereinafter CRT). 2 Extending the framework advanced by Katz and Shapiro (985), CRT offer a formal analysis of the incentives of the network that has the largest share of installed-base customers to degrade interconnection with its rivals. CRT acknowledge that their model is highly stylized for example, the value of a network depends only on the total number of subscribers that can be reached through it. 3 Nevertheless, their analysis does capture the essential tradeoff facing the largest network if it degrades interconnection: a reduction in its own quality and thus in the absolute attractiveness of its service, but an increase in its attractiveness relative to the smaller rival, whose quality has suffered even more. That is, degradation of interconnection by the largest network reduces overall market demand but increases that network s equilibrium share of this new business. Moreover, this tradeoff arises not only in the Internet context the focus of CRT s analysis but also in other industries where network externalities are important. The MCI/WorldCom merger was concluded in 998 subject to divestiture of MCI s Internet operations, while MCI WorldCom/Sprint was abandoned in 2000 under pressure from the European Commission and U.S. Department of Justice. See European Commission (998; 2000), US DOJ (2000), and WorldCom and Sprint (2000). 2 Their article published in 2000 was available as a working paper by the same title issued in May 999, and some of their analysis circulated earlier in the MCI WorldCom merger. The 999 paper contains the Appendix, which will be forthcoming on the web site of the Journal of Industrial Economics, the journal in which CRT s 2000 article appeared. 3 Also, Internet Backbone Providers are viewed as directly controlling access to final customers, even though the two are often separated by Internet Service Providers that serve as intermediaries and control the immediate connection to consumers. - -

8 The present paper attempts to assess, within CRT s framework and a natural extension, the likelihood not just possibility that the largest network can gain by degrading interconnection. 4 CRT analyze two strategies for the largest network: global degradation of interconnection with all rivals, and targeted degradation of interconnection with only one rival. For profitable global degradation as considered by CRT (Propositions 2 and 5), a necessary condition is that the largest network has at least fifty percent of all installed-base subscribers. As CRT explain, if the largest firm s share is only fifty percent, then loss of interconnection yields it no competitive advantage (since the other interconnected rivals provide access to an equal total number of customers), but drastically reduces the product s quality and therefore overall demand by new subscribers. Indeed, this logic suggests that global degradation would be profitable only if the largest firm s share of subscribers is more than just slightly above fifty percent. However, it is difficult to determine directly from CRT s analysis what level of market share depending on the other parameters is sufficient for global degradation to be profitable. CRT provide a sufficient condition only under duopoly the largest network facing a single rival (for oligopoly, CRT s Proposition 5 provides only a necessary condition). Moreover, this sufficient condition (Proposition 2 and Appendix) is a complicated algebraic expression involving the model s various parameters. One cannot readily judge whether this condition is satisfied in a large subset of the model s parameter values, and whether values in this parameter subset seem plausible relative to real world data. Turning to targeted degradation, CRT s Proposition 6 shows that a fifty percent share (and, by continuity, some lower shares as well) can make it profitable for the largest firm to degrade interconnection with only one of its two symmetric rivals. Here, too, the relevant condition is not readily interpreted. We build on CRT s analysis to address the above issues. Our paper is organized as follows. Section II extends CRT s model by allowing the large network to face any number of smaller rivals. We also attempt to place some realistic bounds on values of the model s key parameters: the current market size relative to potential future demand, β; the marginal cost of providing service to new customers, c; and the strength of network externalities, v. In addition, CRT s equilibrium formulas implicitly assume that the number of customers served in the various equilibria does not exceed the total pool of potential customers. Because it indeed seems plausible that not all potential customers are likely to be served in oligopoly equilibria, we focus on the parameter values for which this output constraint does not bind. The output constraint generally imposes further restrictions on the admissible parameter values, beyond those based on our plausibility arguments noted above. As a check for robustness, Appendix 4 presents a reformulation of CRT s model, along the lines of Katz and 4 We do not address other interesting aspects of their paper, such as their description of the structure of the Internet and how degradation incentives are altered if some customers subscribe to more than one network ( multihoming )

9 Shapiro s (985) analysis, in which the potential pool of customers is large enough that the output constraint would never bind. That alternative formulation reaches similar qualitative results to those described below. Section III analyzes global degradation. We first convert CRT s condition for degradation under duopoly into a condition that specifies the minimal market share of existing customers that the large firm must have in order to find degradation profitable, as a function of the model s key parameters, β, c, and v. We illustrate this condition graphically, showing how the parameters interact to determine whether global degradation is profitable. We then extend CRT s analysis to oligopoly, where the largest network faces several smaller rivals. An important effect arises as the number of smaller rivals increases. Holding constant the largest firm s share of the installed base even at high levels such as seventy percent an increase in the number of rivals (themselves perfectly interconnected) expands the set of parameter values for which, if the largest firm pursued global degradation, it might obtain no new customers, i.e., the equilibrium could involve tipping away from the initially largest network. For plausible bounds on the size of the current market relative to its future potential, β, we can provide threshold levels of c below which the largest firm would not choose global degradation unless its market share of initial subscribers exceeds corresponding thresholds. Since c and v are difficult to measure directly, we approach the issue of plausible values of these parameters indirectly by examining other implications of the model. Our analysis suggests that, for plausible values of the parameters, the largest firm is unlikely to find global degradation profitable unless its market share of existing subscribers is well above fifty percent. Section IV examines CRT s example of targeted degradation. Here, too, we find that the set of parameters for which targeted degradation is profitable is relatively small. Section V presents our conclusions. II. Oligopoly with Competing Networks: Extending the CRT Framework The model developed in this section is a straightforward extension of CRT s duopoly framework: the largest firm faces n smaller rivals (n = is CRT s duopoly case). Unless otherwise stated, all other assumptions and parameters mentioned below track CRT s model. A. The Model. Firms and Their Installed-Base Customers All firms have constant marginal cost c of serving additional customers. Firms differ only in the size of their installed bases of existing subscribers. These subscribers are locked in - 3 -

10 by previous contracts, and will not switch to other networks; but firms compete for new customers. The total installed base of customers in the market is equal to β (> 0). The maximum number of new customers that potentially could be added in the next period is normalized to. Firm has the largest installed base, of size β. The remaining installed base, β β, is divided among the rivals, with firm i s installed base denoted β i, i = 2, 3,..., n +. Throughout the paper, a firm s market share refers to its share of the installed base. All firms compete for new customers in the next period. The number of subscribers added by firm i is denoted by q i. Any customer is equally likely to wish to reach any other, regardless of their choice of network. Thus, if interconnection between two firms is inferior to the quality of connection between subscribers of the same firm, then a firm with a larger installed base will have an advantage in competing for new customers, because its network gives better access to a larger number of users than does any smaller network. 2. Interconnection Quality The quality of interconnection between two networks is determined as the lesser of the qualities chosen by each network. Thus, if network i chooses high-quality interconnection with network j but j chooses low-quality, then the realized quality of interconnection between i and j will be low. In this section and in Section III, we consider global interconnection policies by the largest firm, that is, firm establishes the same interconnection quality with each of the rivals. This assumption is relaxed in Section IV, which addresses targeted degradation. The interconnection quality between firm and a rival network is denoted by θ, where θ [ 0.,] A value of θ = represents perfect interconnection (i.e., the same quality as between subscribers on the same firm s network), while θ = 0 represents no interconnection. Values of θ strictly between 0 and denote imperfect interconnection subscribers of firm can potentially reach those of the other network, but not as well as they can reach other subscribers on network (e.g., the connection between networks is less reliable or imposes longer delay). For simplicity, we adopt the modeling assumption invoked in most of CRT s analysis, that there is no extra cost of increasing the quality of interconnection (providing any level of θ entails the same cost). For this case of costless connectivity, CRT found that small backbones prefer the highest quality of interconnection. Accordingly, we model the interconnection among firms 2, 3,..., n + as perfect. The remaining choice of interconnection quality is between the largest firm,, and each of the smaller rivals

11 3. Demand by Potential New Subscribers a. Benefits from Subscribing to a Network Following CRT, if a new subscriber whose type is τ joins network i, that subscriber obtains gross benefit of τ + s i, where s i depends on the effective size of network i (explained shortly) and τ can be viewed as the value of basic access. New subscribers differ only in their values of τ. This parameter τ is uniformly distributed on the interval [0, ], with total mass equal to (i.e., the pool of potential new customers is of size ). 5 The term s i is given by s = vl, i i where v > 0 is a common taste parameter measuring the intensity of preferences for connectivity (hence, the strength of network externalities), and L i represents the effective size of network i, that is, the quality-adjusted total number of links offered by network i next period. The number L i includes the subscribers (installed-base and new ones) on network i as well as on other networks with which i interconnects. Because we have assumed that all smaller firms will be perfectly interconnected, a subscriber of firm i, i, can reach perfectly the subscribers of all the small firms. If the quality of interconnection between firm i and firm is θ, the quality-adjusted number of links offered by i is therefore given by () L = ( β β ) + q + θ( β + q ) i n+ j= 2 j. Thus, if firm i s interconnection with firm is perfect (θ = ), then a subscriber to i can reach all of the (next-period) subscribers in the market; but if interconnection with is degraded (θ < ), then the benefit of subscribing to firm i is reduced, as the number of subscribers to, β + q, accessible from firm i is discounted by θ. Similarly, the effective size of network is given by n+ (2) L = ( β+ q) + θ( β β + q j ). j= 2 b. Individual Subscription Decisions and Inverse Demands The net benefit to customer of type τ from subscribing to firm i at price p i is given by (3) τ + s p i i. Regardless of τ, all potential subscribers have the same ranking of various networks desirability. Therefore, in order for all firms to attract new customers, they must offer the same net benefit, 5 One could model parameter τ as uniformly distributed over [0, T], for T > 0. Our current results would carry through after slight reinterpretation. For example, τ would be replaced by τ/t and c would be replaced by c/t

12 τ + s p = τ + s p i i j j, which implies that quality-adjusted prices must be equal: pi si = pj sj, for all networks i, j that acquire new subscribers. The marginal customer, τ, just obtains a net surplus of zero from subscription ( τ = p s i i ). All customers with values of τ greater than τ would subscribe to one of the networks, implying a total number of new subscribers equal to τ. Therefore, market clearing requires that, for each firm i, we have n+ (4) qj = ( pi si), j= so that, using (2) with s = vl in (4), the resulting inverse demand facing firm is (5) n+ p = + s q q j= 2 j n+ = + v( β + θ( β β )) ( v) q ( θv) q ; j= 2 j similarly, using (), the inverse demand facing any smaller firm i is (6) for i 2. p = + s q q i i i j j i = + v(( β β + v qi + qj v q j i ) θβ) ( ) ( θ ),, 4. Interconnection Choices and Competition for Subscribers Firms compete for new customers in two stages. In the first stage, each firm selects its desired quality of interconnection with its rivals. In the second stage, given the realized interconnection qualities, firms compete in a Cournot fashion for new subscribers: each firm chooses the number of customers it wishes to add, and firms prices adjust to yield the qualityadjusted price that clears the market, given the expected total number of new subscribers. As noted earlier, we draw on results provided by CRT to simplify our analysis by assuming that all firms other than firm will choose perfect interconnection among themselves. Their interconnection quality with firm will be determined by firm. Firm chooses this interconnection quality to maximize its profit in the subsequent Cournot competition for new subscribers. The profit function of any firm i is simply π i = ( p i c) q i, where the quality choice θ made by firm enters in the inverse demand function p i discussed earlier. (Like CRT, we - 6 -

13 ignore the profit on the locked-in base because that is assumed fixed by prior contracts.) In choosing its interconnection quality, firm faces a tradeoff. Decreasing θ makes all networks less attractive, thus attracting fewer new customers in total (market-contraction effect); but it also increases the quality advantage that firm, with its largest installed base, has over rivals, causing firm to capture an increased share of the new subscribers (quality-differentiation effect). B. Cournot Equilibria Two types of Cournot equilibria are possible. One is the standard interior Cournot-Nash equilibrium in which all firms obtain new customers. This is the outcome on which CRT focus. In addition, because of the network externalities in this market, tipping equilibria are also possible, and we shall study these in some detail. If firm chooses global degradation (θ = 0), then new subscribers essentially have the choice of two networks: firm s network, with installed base β ; or the network consisting of the perfectly interconnected smaller firms 2,..., n +, with total installed base β β. A tipping equilibrium arises when all new subscribers choose the same one of these two alternative networks.. The Interior Equilibrium Firm chooses its number of new customers, q, to maximize its profit π = ( p c) q (7) n+ = + v( β+ θ( β β)) ( v) q ( θv) qj c q. j= 2 Among the smaller backbones, firm i chooses its number of new customers, q i, to maximize π = ( p c) q i i i (8) = + v β β + θβ v qi + qj θv q c qi j i (( ) ) ( ) ( )., For the (interior) equilibrium in which each firm obtains new customers, the Cournot equilibrium outputs, given θ, are found in the typical fashion to be 6 6 Given the constant marginal cost and linear demand, for parameters β, c, v, n and θ such that (9) and (0) specify positive outputs for each firm, these outputs constitute the unique Cournot equilibrium. CRT restrict attention to parameters for which the interior equilibrium is stable. In our oligopoly setting, stability for all θ [ 0,] would require that v < /(n + ). In order to provide a complete depiction of equilibrium possibilities, we will analyze both interior equilibria (stable or unstable) and tipping equilibria

14 (9) and (0) * ( c)[ ( + n( θ )) v] q = 2( n+ )( v) n( θv) [ n( θ) θ( v)] v 2( n+ )( v) n( θv) c v q ( )[ ( 2 θ ) ] * i = 2( n+ )( v) n( θv) β ( θ)[( v) + n( 2 v θv)] v + β 2 2( n+ )( v) n( θv) 2 + [( 2 v) θ( θv)] v 2( n+ )( v) n( θv) ( θ)[ 3 ( 2+ θ) vv ] 2( n+ )( v) n( θv) β β, 2 2 for i = 2,..., n +. Note that firm s rivals all have the same number of new customers, regardless of their individual installed bases, because the rivals are perfectly interconnected hence offer the same quality. 2. Tipping Equilibria A tipping equilibrium toward firm if it refuses interconnection with all rivals is described as follows. Suppose that each potential new customer expects that any other customer will also choose firm (or no network at all). Given such expectations, firm chooses to add its monopoly number of new subscribers and obtains the corresponding price; and taking as given that this number of new customers will go to firm, no other rival can profitably attract any new customers, despite the fact that firm s price is above its marginal cost. 7 Such a tipping equilibrium to firm can be derived as follows. If q = L = =, then firm s optimal output (i.e., numbre of new customers) is () q 2 q n + 0 Tip ( c) + β v =. 2 ( v) This is simply firm s monopoly output firm s Cournot response to its rivals total new output of zero. Each of firm s rivals will indeed choose zero output if, given q Tip and zero output by the other smaller firms, the net price to firm i is nonpositive at any positive output for i: pi c 0, for any q i > 0, where the function p i is given by (6). At these candidate equilibrium outputs, q Tip and q 2 = L = q n + = 0, we indeed have pi c 0 if and only if (2) ( 2 ) ( ) 2( ) 2 v c v β + β β β v. 7 Because of presence of network externalities, entry on a small scale would deliver a low quality which would have to be compensated by a prohibitively lower price; and entry on a large scale yielding higher quality would require a large price cut to achieve the requisite market expansion, again driving price below marginal cost

15 Therefore, q Tip and q 2 = L = q n + = 0 constitute an equilibrium with tipping to firm if the parameters satisfy condition (2). Next consider a tipping equilibrium away from firm, toward its n rivals, which are themselves perfectly interconnected. This corresponds to the following outcome. Suppose each potential new customer expects that no other new customer will choose firm. The n rivals add the symmetric Cournot-equilibrium number of new customers; taking this number as given, firm cannot profitably attract any new customers, despite the fact that it has a larger share of the installed base than the rivals collectively. Suppose q = 0. The Cournot equilibrium outputs among the remaining (perfectly interconnected) firms are, for each firm, (3) q Tip i = ( c) + ( β β ) v, ( n+ )( v) i = 2,..., n +. These proposed outputs indeed constitute a Cournot equilibrium if p c 0, a condition equivalent to [ ] (4) ( n+ ) v c β ( n ) v ( β n βn 2β n) v. Tip Therefore, q = 0 and qi = qi, i = 2,..., n +, form a tipping equilibrium away from firm if condition (4) is satisfied. It can be shown that for any firm j, its profit at the interior or tipping equilibria is simply * = ( v)( q * ) 2, where q * j denotes firm j s corresponding equilibrium output. Therefore, in the π j j first stage firm chooses its interconnection quality to maximize its equilibrium output. C. Output Constraints and Their Interpretation Because the total number of potential new customers in CRT s model is fixed at, CRT s equilibrium formulas and analysis are valid only if the implied total number of new customers does not exceed. However, for some ( cv, ) [,] 0 [, 02 / ] these formulas imply a total output exceeding. One resolution would involve recalculating equilibria for parameters at which the total output implied by CRT s formulas exceeds. However, such a treatment of this output constraint would have to recognize that when all potential customers are served in equilibrium, there will generally be multiple equilibria. 8 Such multiplicity makes it problematic to evaluate the profitability of degradation. Rather than considering multiple equilibria arising when the output constraint binds, we focus, as did CRT, on the parameter regions in which the output constraint does not bind. At 8 The following example illustrates the problem of multiple equilibria arising when the standard Cournot equilibrium output would exceed maximal market demand. Two firms, and 2, each with marginal cost equal to zero face the following market demand function: Q(p) = 2 p, for p 2; and Q(p) =, for p. With q i denoting firm i s output, i =, 2, the set of Cournot equilibria includes {(q, q 2 ) such that q 0, q 2 0, and q + q 2 = }

16 least in the case of the Internet, it seems reasonable to expect as implicitly assumed by CRT s analysis that in a Cournot oligopoly equilibrium (even with perfect interconnection and low marginal cost) at least a few potential customers would not subscribe. Thus, we rule out as ex ante implausible those parameter regions in which the model predicts that all potential customers would actually be served. (In Appendix 4 we provide an alternative formulation, following Katz and Shapiro (985), for which the number of potential customers is so large that for any parameters some customers will remain unserved. Our findings for that model track the ones described in the rest of this paper.) To convert this output-constraint argument into a restriction on the admissible parameter values, we must specify a particular equilibrium in which not all customers would be served. As did CRT, we find that firm chooses either perfect interconnection (θ = ) or total degradation (θ = 0), not intermediate interconnection qualities. Therefore, four types of equilibria are possible: under accommodation (θ = ), (i) the interior Cournot equilibrium; or, under degradation (θ = 0), (ii) the interior equilibrium, (iii) tipping to firm, or (iv) tipping away from firm. The total equilibrium output is greatest in case (i) and is given by 9 (5) ( n+ )( c+ vβ ). ( n+ 2)( v) Therefore, the condition that some potential customers are unserved in a perfect-interconnection, interior equilibrium is given as + ( n+ ) c (6) v < ( n+ 2) + ( n+ )β. If one considers only parameters for which the total output in this equilibrium does not exceed, then total output under the other equilibrium configurations (with degraded interconnection) also will not exceed. 0 In the case of top-level Internet backbone providers, it seems reasonable to include at least five major firms. Therefore, throughout Section III we consider n = 4 as our benchmark case we restrict attention to those parameters for which some potential customers would be left 9 See (9) with θ =, or simply (20) below. 0 As explained in Section II.B.3, it is also sensible to restrict attention to (,) cv [, 0] [,.] 0 5. Condition (6) on v, which is equivalent to the condition that the output in (5) not exceed, leaves intact much of the parameter space (,) cv [, 0] [,.] 0 5. The least restrictive output constraint, corresponding to setting β = 0 and n = in (6), would eliminate (c, v) lying above v= ( + 2c)/ 3. The most restrictive constraint consistent with β is given by v c/2 (found with β =, as n ), which still leaves half of the parameters (,) cv [, 0] [,.] 0 5. In its decision, the European Commission (2000, Section V.D) analyzed the market for top-level connectivity as including at least five firms: MCI WorldCom, Sprint, AT&T, Cable & Wireless, and GTE, all having a position stronger than all the others ( 04). In another analysis, the Commission considered a universe of 7 networks (or groups of) participating in the market for top level Internet connectivity ( 05)

17 unserved in equilibrium when there are four rivals to firm (n = 4, for a total of five firms) and interconnection is perfect among all five firms. (Higher values of n would restrict the set of plausible parameters even further.) Thus, when discussing global degradation by firm (Section III), we view as plausible model parameters only those for which c (7) v < β. D. Bounds on Plausible Values of the Parameters β, c, and v We now consider some additional bounds on plausible parameter values, beyond the restrictions needed to satisfy the output constraint. First, consider β. Recall that the pool of potential new customers is normalized to. Thus, β equal to, say, is interpreted to mean that the current number of customers is equal to the maximal number of new customers; β = thus would imply that, even if price were zero, the additional new subscribers could cause the network only to double. A salient feature of the Internet the industry on which CRT and we focus is that over the foreseeable future it is expected to grow rapidly, due to projected increases in penetration in developed countries, mass extension to developing countries, and increased number of Internet-enabled devices per person. While growth projections vary widely, their thrust is that the potential increase in users is quite large relative to the current user base. 2 Therefore, when specific values are needed in Sections III and IV, we assume β. 3 2 Accurate data on the number on Internet users are difficult to obtain. The most reliable counts arguably come from surveys of member countries and carriers conducted by the International Telecommunication Union (200a and 200b). According to the ITU, in 995 there were about 34 million Internet users worldwide, while by 2000 the user count grew to 35 million. For the period 995 to 2000, the year-to-year annual growth rates were 60%, 67%, 66%, 55% and 36% respectively. A linear extrapolation of these figures over five years yields a decreasing annual growth rate that reaches about 5% in the last year; even with such declining growth, the number of users would exceed one billion by (This is consistent with a recent estimate by the consulting firm IDC. See Wall Street Journal, Has Growth of the Net Flattened? July 6, 200.) The projected increase in users by 2005 thus represents more than 2.2 times the number of users in Furthermore, for at least two reasons, these figures are likely to significantly understate the number of potential additional users. First, they do not include an expansion in the number of wireless Internet-enabled devices per person, such as cell phones and personal digital assistants, which is expected to be substantial (Cerf, 2000). (For competitive analysis, different devices used by the same person can be regarded as different users, since a different Internet connectivity provider may serve each device.) Second, the above discussion regards actual subscribers, whereas β is measured relative to the number of potential new subscribers, which includes users that would only join at a zero price. 3 The discussion of the previous footnote can be adapted (albeit roughly) to CRT s two-period framework as follows. Consider the time path of additional users implied by the growth rates computed by extrapolating ITU data and compute its discounted present value over, say, a five-year horizon. Now calculate the constant stock of additional users over the same period that would yield the same present value. For any reasonable interest rate (0 to 30%/year), the implied constant stock is more than twice the initial number, implying β <. Recalling that the above growth figures consider only actual (not potential) subscribers, and no increase in the number of devices per person, they therefore imply an overestimate of β the size of the installed base relative to the potential additional users. Thus, the actual value of β is likely to be comfortably below. - -

18 One must restrict v < to guarantee that the demand for backbone services is downwardsloping. 4 Following CRT, we focus on the range v < /2. Doing so illustrates all the relevant possibilities; in addition, our later discussion (see Section III.B.3) suggests that for purposes of applying this model to the Internet, plausible values of v are less than /2. Also, we restrict c to ensure that at least some new customers are added, no matter how small the values of v or β. Among the potential new subscribers, the highest willingness to pay under perfect interconnection, for example, is at least + vβ, no matter how many new subscribers are added. Therefore, this is sure to exceed marginal cost only if c. III. Global Degradation of Interconnection A. CRT s Result on Degradation in Duopoly CRT s Proposition assumes that the cost of providing a given quality level θ is given by a function F( θ ), which is nonnegative and weakly increasing (expanding quality cannot reduce cost); CRT show that the larger firm always prefers a quality level no greater than (but possibly the same as) that desired by the smaller rival. Given the minimal restrictions on the cost function F, CRT s Proposition obviously can provide no indication of the magnitude of the differences in quality levels preferred by the two firms. However, under the assumption that expanding interconnection quality is costless ( F( θ ) = 0 for all θ), CRT s Proposition 2 shows that the two firms may disagree in the extreme about their preferred interconnection quality. 5 CRT s Proposition 2: Suppose n = and let β β2 denote firm s advantage in the size of its installed base, relative to firm 2. Suppose also that providing higher quality of interconnection is costless. Then the smaller backbone always wants perfect interconnection ( θ = ), and (i) the equilibrium quality of interconnection is either 0 or (whichever is preferred by firm ); (ii) for a given installed base β, there is a threshold * such that firm chooses perfect interconnection ( θ = ) if < *, and no interconnection ( θ = 0) if > *. This threshold * increases as β increases, and decreases as either c or v increases. Specifically, CRT show that ( 2v) (8) * [ 2 ( c) + ( 3 v) β ]. 3 ( v)( 3 2v) 4 To see this, consider perfect interconnection. Suppose at price p the marginal subscriber has personal connection value equal to τ. If τ more subscribers are to be added, then the connection value of the marginal subscriber must fall by τ (since τ is uniformly distributed over [0,]). The quality of the expanded network, however, rises by v τ, so that the overall value of subscription to the marginal subscriber (which determines the market price) would fall by just ( v) τ. In order for price actually to fall as the number of subscribers increases, it is necessary that v <. 5 We have slightly rephrased CRT s Proposition

19 CRT s Proposition 2 thus shows that, even without realizing any cost savings, the larger network may find it profitable to degrade interconnection with its single rival under certain conditions involving the model s three key parameters: the size of the total installed base (relative to the future potential demand) β, marginal cost c, and the value of connectivity v. However, the conditions as stated are not easy to interpret empirically. 6 Nor is it clear how the likelihood of degradation changes if firm, for a given installed-base advantage, faces more than a single rival. We now turn to these issues. B. Evaluating the Likelihood of Global Degradation The discussion proceeds as follows. We begin with CRT s Proposition 2, which pertains to duopoly (a single rival). We first transform their condition on * into one in terms of the minimal market share of the installed base that firm must have in order to prefer degradation, as a function of the parameters β, c, and v. We then allow the number of rivals to firm to increase beyond one. If firm degrades interconnection with all its rivals ( global degradation ), several types of Cournot equilibria may be possible: a) the interior equilibrium in which all firms are active; b) a tipping equilibrium to firm (only obtains new customers); and c) a tipping equilibrium away from ( obtains no new customers). As noted earlier, CRT focus on stable interior equilibria. CRT state that by assuming that the value of the network externalities parameter v is below a certain level, they have stack[ed] the deck against the possibility of the extension of market dominance [through degradation of interconnection], as greater values of v yield tipping equilibria. 7 The suggestion 6 Note that * is the absolute (not percentage) difference in the installed bases of firms and 2 that makes indifferent between perfect interconnection and none. The intuition for the effects in part (ii) of the proposition can thus be understood as follows. (a) Why * increases as β increases: A higher total installed base β magnifies the demand-reduction effect to firm (and 2) from choosing no interconnection since, holding constant, a potential new subscriber to firm is denied access to a larger number of installed-base customers of 2 than if β were lower. For firm to remain indifferent between θ = 0 and θ =, it must therefore obtain a greater quality-differentiation advantage from refusing interconnection, which in turn requires a larger installed-base advantage,. (b) Why * decreases as c increases: The demand-reduction effect (i.e., the decrease in total equilibrium output) from choosing no interconnection instead of perfect interconnection, is smaller the higher is c, while (in duopoly) the competitive advantage from degradation is unaffected by c (see Appendix 2, which also shows going beyond duopoly that the increase in competitive advantage to firm from degradation is smaller the lower is c). Consequently, when c is higher, a smaller quality-differentiation effect (hence a smaller ) will suffice to leave firm indifferent between θ = and θ = 0. (c) Why * decreases as v increases: A higher valuation of connectivity, v, magnifies both the demand-contraction effect and the quality-differentiation effect from firm s refusing interconnection. However, for CRT s particular model, the impact on the quality-differentiation effect is stronger. 7 The relevant paragraph reads as follows (CRT, 2000, p. 455): A couple of assumptions stack the deck against the possibility of the extension of market dominance. First, we have imposed an upper bound on the magnitude of network externalities [i.e., on the size of v] by requiring equilibria to be stable. Larger network externalities would give rise to tipping effects and make it more likely that the industry would be monopolized

20 is that for higher values of v, firm would choose degradation more often. But this need not be the case, since continuing to assume that s market share exceeds 50% tipping can be away from firm. 8 Indeed, in some cases this would be the only equilibrium following degradation. Such prospects may make degradation a risky strategy for firm. Overall, as in duopoly, we find for oligopoly that if c is not too high, then degradation is not a profitable strategy for firm.. Duopoly: A Single Rival to Firm We first convert CRT s condition in Proposition 2, > *, into an equivalent condition on the market share of the installed base that firm must have for it to prefer no interconnection: * β (9) > * > * β ( β β) m > m +. β 2 2β Thus, firm will refuse interconnection with its rival only if s market share m exceeds the threshold m, which is a function of the parameters β, v, and c (since * is such a function). Figure illustrates the equilibrium possibilities when β = 0.5 and firm s share of the installed base is 70%. The figure is interpreted as follows. The thick upward-sloping line identifies the boundary of the set of plausible parameters all (c, v) parameters below this line lead to an equilibrium in which some consumers are unserved when there are five perfectly interconnected firms active in the market. (Throughout Section III, the thick upward-sloping line depicts the parameters for which (7) holds with equality. Points (c, v) above this line are ruled out as implausible, as described earlier.) The curve labeled m = 07. is the set of (c, v) pairs for which firm is just indifferent between degradation and accommodation when its share of the installed base is 70%. 9 To the left of this curve, firm strictly prefers accommodation, as the interior equilibrium with accommodation is more profitable than the interior equilibrium with degradation. Just to the right of such a curve, firm strictly prefers the interior equilibrium under degradation to that under accommodation. And even farther to the right (higher c) the equilibrium may be tipping toward firm, which firm also prefers over the interior equilibrium with accommodation. 20 Because * approaches 0 as v approaches 0.5, CRT s Proposition 2 seems to imply that firm will find degradation profitable if v is sufficiently close to 0.5, no matter how small is firm s installed-base advantage. But this implication is no longer valid once the constraint on total equilibrium output is recognized. In Figure, if one rules out the region of ex ante implausible 8 Tipping away from firm can occur also in duopoly, but only for some values of v exceeding /2. 9 For β = 0.5 and β = 035. (70% share), the contour labeled m =. 7 is the set of (c, v) for which firm s output is the same under degradation as under accommodation. The negative slope of this curve arises because (from condition (9) above) the critical share needed for degradation, m, is decreasing in both c and v. 20 The lower contour of the tipping equilibrium region is found where (2) holds with equality, given β = 0.5 and β =