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Network Competition: I. Overview and Nondiscriminatory PricingAuthor(s): Jean-Jacques Laffont, Patrick Rey, Jean TiroleSource: The RAND Journal of Economics, Vol. 29, No. 1 (Spring, 1998), pp. 1-37Published by: Blackwell Publishing on behalf of The RAND CorporationStable URL: http://www.jstor.org/stable/2555814Accessed: 10/05/2010 12:01

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RAND Journal of Economics

Vol. 29, No. 1, Spring 1998

pp. 1-37

Network competition: I. Overview and nondiscriminatory pricing

Jean-Jacques Laffont*

Patrick Rey**

and

Jean Tirole***

We develop a model of unregulated competition between interconnected networks and analyze the mature and transition phases of the industry in this deregulated environment. Networks pay (negotiated or regulated) access charges to each other and compete in prices for customers. We show that a competitive equilibrium may fail to exist for large access charges or for large network substitutability, and that freely negotiated access charges may prevent effective competition in the mature phase of the industry and erect barriers to entry in the transition toward competition. Last, we examine the meaning and impact of policies such as the efficient component pricing rule.

1. Introduction

* The developing competition in the telecommunications industry is likely to pro- duce a substantial change in the way the industry operates. Most observers predict that decades of regulatory scrutiny will give way in the near future to a competitive mar- ketplace from which detailed regulation will withdraw. Legislators, regulators,' and antitrust authorities all envision a transitional period followed by the substitution of competition policy for regulatory supervision. This view is, for example, expressed in the United States in the 1996 Telecommunications Act, which will facilitate entry (including by the long-distance companies) into the regional Bell companies' territories in order to enhance competition in local phone service while allowing the latter to

* IDEI, GREMAQ (UMR 5603 CNRS), and Institut Universitaire de France, Toulouse; laffont @ cict. fr.

** IDEI, GREMAQ (UMR 5603 CNRS), LEESP, University Toulouse I, Toulouse, and CEPR,

London; prey @ cict.fr. *** IDEI and GREMAQ (UMR 5603 CNRS), Toulouse, CERAS (URA 2036 CNRS), Paris, and MIT;

vaissade @acict.fr.

The authors are grateful to Michael Davies, Alain de Fontenay, Michael Riordan, Michel Le Breton, and three referees for helpful suggestions and comments. A research grant from BellSouth New Zealand is also gratefully acknowledged.

1 See, e.g., Oftel's consultative document of December 1994 entitled "A Framework for Effective Competition."

Copyright (? 1998, RAND 1

2 / THE RAND JOURNAL OF ECONOMICS

enter the long-distance market once "sufficient competition has developed in the local phone market," and in the bills passed by the U.S. Congress prior to this act:

The House and Senate have passed competing bills to promote competition and deregulation in telecommunications, both of which drew broad, bipartisan support. The two proposals (HR 1555-H Rept 104-204 Part I; S 652-S Rept 104-23) have the same goal: to allow all telecommunications companies to compete head to head in one another's markets, with as little government regulation as possible.2

In this respect New Zealand may be a test laboratory for the future of the industry. The regulatory authority has been abolished, and the dominant firm (Telecom) and the entrants (Clear, BellSouth New Zealand) are subject only to general antitrust provisions on the abuse of dominant position and on vertical restraints. New Zealand's "light- handed" regulatory regime relies on private negotiations between competitors to secure interconnection agreements. Section 36 of the Commerce Act may be invoked to limit access charges that a vertically integrated dominant operator can set for the essential input. But in the aftermath of bitter disputes between the incumbent and the entrants, it is widely perceived that satisfactory, freely negotiated interconnection agreements may not come about easily. A wide-ranging consultation has been launched with the aim of promoting competition with minimal state intervention.

While laudable, the current vision of unregulated head-to-head competition between networks can be criticized for its lack of a conceptual framework in which the resulting industry can be analyzed. Open network architecture requirements, motivated by the existence of substantial network externalities, imply that networks are and will remain interconnected. Interconnection, however, requires cooperation among competitors, who must agree on its mode and especially on its price. Unconstrained interconnection negotiations raise two concerns. First, it is often suggested that during the transition toward competition, entrants may be handicapped by the incumbent's reluc- tance to provide access to its network on a reciprocal basis and at a reasonable price. Second, some wonder whether, in the mature phase, established networks could not use their interconnection agreements to enforce collusive behavior. The extent to which competition for end users is sufficient to discipline both access and retail prices thus remains uncertain.

We propose such a framework for modelling competition, both in linear pricing and nonlinear pricing (e.g., two-part tariffs), between two interconnected networks. Our starting point is that consumers face the discrete-choice problem of picking which network they will belong to. An extension for our discrete-choice model would allow consumers to belong to several networks. In practice, however, consumers often belong to a single network either because this minimizes their transaction costs or because the networks charge two-part tariffs to reflect the costs (connection, billing, servicing) of serving a customer or for price-discrimination purposes.4 We set up a tractable discrete- choice model for the telecommunications industry.5 In our framework, networks are differentiated as they offer different functionalities that appeal to different consumers.

2 Congressional Quarterly (1995, p. 6). An agreement between President Clinton, who threatened to veto the reconciliation bill, and the Congress was reached in December 1995. See Schwartz (1997) and the 1996 Economic Report of the President for good accounts of the debate on telecommunications reform in the United States.

3 See the joint document of the New Zealand Ministry of Commerce and Treasury (1995). 4 Note, however, that fixed fees or transaction costs are not needed to generate an exclusive relationship

with a network; in this article, consumers would still choose to belong to a single network as long as fixed fees are not negative.

5This setup builds on the multiunit Hotelling model: see in particular Anderson, De Palma, and Nes- terov (1995).

LAFFONT, REY, AND TIROLE / 3

This product differentiation takes the form of a Hotelling relative benefit of being connected to a given network. (The differentiation is thus horizontal, but the framework could be extended to allow for vertical differentiation to depict cases in which a network is superior in all respects to the rival network.) The consumers further derive a gross surplus from consuming telephone services and optimize over their consumption given the price(s) charged by the network they select.

Two key assumptions affect the networks' access deficit or revenue:

Balanced calling pattern. The percentage of calls originating on a network and com- pleted on the same network ("on-net calls") is equal to the fraction of consumers subscribing to this network. Statistically, a consumer has an equal chance of calling a given consumer belonging to her network and another given consumer belonging to the rival network. The balanced calling pattern assumption implies that for equal marginal prices, flows in and out of a network are balanced-even if market shares are not. Of course, the actual inflow/outflow balance depends on the prices charged by the networks. With an elastic demand, a network charging a lower price than its rival generates more calls, and its outflow exceeds its inflow. This fact will play an important role in our analysis.

It is easy to think of cases in which this calling pattern is violated. For example, cab companies or pizza parlors mainly receive calls, while phone-marketing companies principally originate calls: If one network prices aggressively in order to sign up cab companies while the other network is dominant in the phone-marketing segment, the flow between networks is unbalanced even if they charge identical usage fees, with the former network receiving an access contribution from the latter. Similarly, telecommunications entrants tend to initially build a higher market share in the business segment than in the residential segment and in cities than in rural areas. To the extent that businesses tend to call customers more than they are called, and that cities similarly tend to call rural areas, the entrants often face an access deficit vis-a-vis the incumbent (which gives the incumbent an incentive to insist on high access charges). We think that the balanced calling pattern assumption is a good first approximation, but we understand that it must be refined in specific instances.

Reciprocal access pricing. For most of the article we assume that there is no discrimination in the interconnection charge: A network pays as much for termination of a call on the rival network (an "off-net call") as it receives for completing a call orig- inated on the rival network.6 This assumption is made mainly for convenience, but it is worth noting that regulators and antitrust authorities are likely in the future to insist on the reciprocity of access charges. For example, Oftel, in its December 1995 consultative document (p. 42), leans toward reciprocal pricing.7 The interconnection charge agreement for the termination of local calls signed in April 1995 by Telstra (the dominant Australian operator) and Optus (a large entrant) also specifies reciprocal access pricing, while the February 1996 Telecommunications Act in the United States and the August 1996 FCC Report and Order mandate reciprocal interconnection pricing between incumbent local exchange carriers and competitive local exchange carriers (as

6 More generally, reciprocity means that the difference between access prices reflects only the differ- ential in the cost of giving access. Note also that the type of network interconnection considered here is called "transport and termination" in the United States. The term "access pricing" is also used in practice in a broader sense, which includes the one-way interconnection charges paid by the interexchange carriers to the local exchange companies.

7The March 1996 consultative document on "Communications Services from 1997" states that "Oftel favors the principle of reciprocal payments, but does not intend to impose it. It proposes to leave call termination rates on other networks [networks other than BT] to be decided in negotiation between operators. "


long as there is no rebuttal of the presumption of symmetry). Note that a balanced calling pattern together with reciprocal access pricing imply that monetary flows, and not only physical flows, balance. We provide a few preliminary insights about nonreciprocal access prices in Section 6.

We analyze the mature and transition toward competition phases of the industry. Define a network's coverage as the fraction of consumers who can be served by the network at a given point of time. The "coverage" should in general be thought of as a geographic coverage, but it may admit other interpretations such as the installment of functionalities needed by certain types of consumers or the calling capacity. The ability to serve a customer does not preclude a cost of connecting (fiber or copper wire to the home, handset for mobile telephony), billing, and servicing that customer. We will therefore allow for a fixed per-customer cost, which a network incurs when attracting a customer within its coverage. A mature industry involves competition between two full-coverage networks. The transition phase corresponds to competition between a full-coverage incumbent and an entrant with (endogenous) partial coverage.

In this and the companion article we analyze how access charges affect the competitiveness of the industry when the network can and cannot discriminate on the basis of where the call terminates. Networks often charge the same price to their customers whether their call terminates on net or off net. On the other hand, we will show that networks individually have an incentive to charge different prices for the two types of calls. Such price discrimination is made possible by standard billing technologies (such as that used by MCI, whose friends-and-family program involves discrimination against calls directed to its rivals' customers). In France, discrimination exists between the fixed-link network and the mobile phone networks, but not between the mobile networks. A key policy decision in the deregulated environment will be the legal treatment of such price discrimination. As this article (which rules out price discrimination based on call termination) and its companion piece (which studies price discrimination) demonstrate, the nature of competition is markedly different and is likely to be tougher when networks can price discriminate.

We analyze the effect of policy rules that have been discussed in the context of network competition, such as the imputation rule (or the Baumol-Willig efficient component pricing rule, according to which the difference between an operator's retail and access prices cannot be lower than the operator's marginal cost on the competitive segment) or mandated cost-based access pricing rules.

Our modelling is directly inspired by the telecommunications industry. Some of our insights may carry over to other competing-network industries, but one should be wary of hasty generalizations. While the need for cooperation among producers competing on complementary segments exists in many industries, each industry has its own specific revenue flows generated by interconnection agreements. Consider for example the apparently similar situation of banks' ATM networks. In many countries these networks are interconnected so that a bank's customer can withdraw money at any other bank's ATMs in the same way a phone customer can call customers subscribing to other networks. Yet the mutual-access contributions exhibit a different pattern: The interconnection bill paid by a bank to other banks depends on the number of its subscribers (as in telecommunications) and on the other banks' investments in ATMs (which in general need not be proportional to these banks' market shares). Perhaps closest to the telecom case is the airline industry. Suppose that two airlines operate on the same route and that passengers on that route tend to always go with the same airline, either because of fixed subscription fees as in France or because of frequent- flyer programs as in the United States. There are potential gains of "interconnection" between the airlines, in that passengers benefit from agreements enabling them to switch airlines in case reservations on one flight are closed or there is overbooking, and in


that many passengers enjoy the convenience of increased departure time variety (indeed, it is often suggested that entrants may have a hard time attracting business trav- ellers with a limited flight offering). To the extent that an airline's flight frequency and seat availability are related to its market share, the mutual-access contributions (if interconnection were mandated or agreed upon) might exhibit a pattern similar to that in the telecommunications industry.

The article proceeds as follows. Section 2 relates our work to the existing literature. Section 3 describes the model of the mature phase of the industry for linear tariffs. Section 4 sets the benchmark of the (Ramsey or contestable) outcome. Section 5 analyzes how the reciprocal access charge affects the competitiveness of the industry. Section 6 briefly discusses nonreciprocal access pricing. Section 7 extends the model to allow for a partial coverage by one network, studies whether the access charge can be used as a barrier to entry, and analyzes the entrant's optimal choice of coverage. Section 7 also derives the optimal policy facilitating the entrants' extension of coverage through the unbundling of the incumbents' network elements. Section 8 investigates how industry conduct under nonlinear pricing departs from that under linear pricing. Section 9 looks at the impact of the efficient component pricing rule (ECPR) in a deregulated environment. Section 10 summarizes the main insights.

2. Related literatures

* Our work overlaps with, but is quite distinct from, three literatures:

E Access pricing in regulated industries. Because unfettered competition between networks has remained until recently a very distant prospect, the literature on interconnection charges has naturally developed in a regulatory context, and mainly one in which a dominant operator controlling a bottleneck is required to interconnect with entrants competing on a complementary segment.8 This literature analyzes whether regulatory control over access charges and retail prices, industry contributions to the joint costs, incentive schemes, and other instruments are capable of bringing the industry into the neighborhood of a Ramsey optimum.9 One important distinction between the previous work on access and the work presented here is that in this article each company controls a bottleneck (its own customers) to which its rival must have access. The second key point of departure is that we focus on the impact of access prices on final product competition, and, in the tradition of competition policy and with the exception of a brief study of the imputation rule, we do not envision any regulation, direct or indirect, of retail prices.

? Network externalities. There is a large literature, beginning with the work of Farrell and Saloner (1985) and Katz and Shapiro (1985) (see, e.g., Economides and White (1994)), on the advantages conferred upon large networks when consumers value being in the same network as other consumers. The focus of the literature is on the multiplicity of equilibria, on the impact of small initial asymmetries, and on the private incentives for making networks compatible. Although interconnection is motivated by network externalities, the issues studied in the network-externalities literature do not arise in our work because networks are interconnected and therefore consumers attribute no direct payoff to other consumers opting for their network.

8 In Economides and Woroch (1 995b) and part of Armstrong (1996), consumers belong to a single network, but network sizes do not depend on prices. While this assumption is reasonable for the study of double marginalization by domestically protected telephone monopolies in the international phone market, a primary focus of our analysis is the study of market share competition between networks.

9 See, e.g., Laffont and Tirole (1994) for a review of the main arguments.


? Mix and match. Starting with the articles of Matutes and Regibeau (1988) and Economides (1989), economists have extensively analyzed the competition between producers of complementary goods. In this tradition, Economides and Woroch (1995a) analyze an industry in which consumers do not pick a network but rather purchase various components from different firms.10

Independently, Armstrong (1996) has studied a two-way access problem similar to the one in this article for the case of linear pricing. There is some overlap (mainly Propositions 2 and 3 of this article) between his work and ours. Three articles have recently built on the framework of ours. Doganoglu and Tauman (1996) allow the (reciprocal and negotiated) access fees to depend linearly on the retail prices. That is, access is sold at a discount relative to retail. They show that a pure-strategy equilibrium always exists and that it generates an almost competitive outcome when networks are close substitutes. Carter and Wright (1996) study the effects of brand loyalty, whereas Beaudu (1996) extends the analysis to vertically differentiated networks.

3. The model

* Cost structure. Two full-coverage networks have the same cost structure. Serving a customer involves a fixed cost f : 0, say of connecting the customer's home to the curb and of billing and servicing her. A network also incurs a marginal cost co per call at the originating and terminating ends of the call and marginal cost cl in between. For example, cl may stand for a switching cost in the case of local competition or for the marginal cost of trunk lines in the case of long-distance competition. The total marginal cost of a call is thus

c 2co + c1.

Note that we do not include any fixed network cost, that is, some joint and common cost of serving the various customers. It is straightforward to add such a cost (and indeed we will need to do so in Section 7 when we discuss entry).

? Demand structure. The networks are differentiated a la Hotelling. Consumers are uniformly located on the segment [0, 1]. The two networks are located at the two extremities of the segments, namely at xl = 0 and x2 = 1. Given income y and telephone consumption q, a consumer located at x and joining network i has utility

y + v0 - tIx - xiI + u(q),

where vo represents a fixed surplus from being connected to either network, t I x -xi denotes the cost of being connected to a network with "address" xi (i = 1, 2) different from the consumer's "address" x, and the variable gross surplus, u(q), is given by

q1 -(1/7i) u (q)= 1'

which yields a constant elasticity demand function

10 It should be noted that neither our work nor the access pricing literature covers the case of two regulated networks.


u'(q) = p =* q = p-n.

We assume that the elasticity of demand, -q, exceeds one.11 The assumption of constant elasticity of demand is made primarily for technical convenience, as it simplifies con- siderably the study of global second-order conditions and of equilibrium uniqueness.

Under uniform pricing (see Section 8 for the study of two-part tariffs), the consumer's variable net surplus is

p-(-1) v(p) = max {u(q) - pq} =

q 7-

We will assume throughout that vo is "large enough," so that all consumers choose to be connected to a network. This assumption is particularly pertinent when we study situations with small substitutability. The reader may object that in our model a small substitutability corresponds to a larger transportation cost t, which raises the possibility that customers in the middle of the Hotelling interval elect not to join any network. To preserve the validity of our analysis as a, the substitutability parameter defined below, tends to zero, one must assume that the fixed surplus of being connected, vo, increases as o- tends to zero so that the market remains "covered." By abuse of terminology, we will define the "case o- = 0" (which, properly speaking, cannot arise in our model) by taking the limit as o- -> 0.

For given prices Pi and P2 charged by the two networks, market shares are determined as in Hotelling's model. Namely, a consumer located at x = a is indifferent between the two networks if and only if

v(pl) - ta= v(p2) - t(1 - a)

or

a = a(P1, P2)- + '[v(pI) - v(p2)], (1) 2

where

1 2t

is an index of substitutability between the two networks. Note that

aa aa = -(ql and = oq2,

aPi aP2

and that the two networks' market shares are a1 = a and a2 = 1 - a, since both networks have full coverage.

11 The need for a demand elasticity larger than one (which is not supported by the data at the current price levels; see Taylor (1994)) is a consequence of our simplifying constant elasticity assumption and of our desire to be able to consider situations with low substitution effects between networks leading to quasi- monopoly pricing. With higher substitution effects the analysis applies as well to lower elasticities.


4. The- Ramsey benchmark m For future reference, we derive the social optimum under the constraint that the industry breaks even. Consumer variable welfare is

W(pI, P2) = a(p1, P2)V(Pl) + [1 - a(p1, P2)]V(P2) - T[a(p1, P2)], (2)

where T(a) denotes the average consumer's disutility from not being able to consume her preferred service.12 T(a) is minimized at a = 1/2. The industry budget constraint is

a(pl, P2)[(P1 - c)q(pl)] + [1 - a(pl, P2)][(P2 - c)q(p2)] = f- (3)

Maximizing (2) subject to (3) yields a symmetric solution, Pi = P2 = pR, where the Ramsey (or contestable) price pR is the lowest price that satisfies the budget constraint

(pR - c)q( pR) = f (4)

In the following, we will assume that the Ramsey price is strictly lower than the monopoly price (that is, that the market is viable), where the monopoly price, pM, solves

max(p - c)q(p). p

That is,

M _ _

P ~~~~C.

5. Reciprocal access pricing

* This section first analyzes price competition for an arbitrary reciprocal access charge, which may have been determined by a regulator or an arbitrator or else can have been agreed upon by the interconnecting firms. The section then investigates this choice of the access charge.

R Price competition with reciprocal access pricing. Let a denote the unit access charge to be paid for interconnection by a network to its competitor. We shall restrict attention to access charges exceeding a-co - c ? 0. (This condition will suffice to obtain our results. It, as well as the stronger condition a 2 0, can be motivated by the fact that with negative access charges, a network can make an unbounded amount of money by installing a computer that calls the other network's customers.) Network i's profit is given by

12 For an arbitrary a, this measure of the distance between preferred and actual brand choice is given by

T(a) = t[(2) ? (1 - )(1 a )]

=a2 (1 a)21


Xi= ai[(pi - c - aj(a - c))q(pi) - f] + aiaj(a -co)q(pj),

or

XTi = ai[(pi - c)q(pi) - f] + aiaj(a - c)[q(pj) - q(pi)]. (5)

Equation (5) shows that network i's profit can be decomposed into the retail profit,

ai[(pi - c)q(pi) - f] ai[R(pi) - ],

that it would make if all calls terminated on net, plus an access revenue (or deficit),

Ai = aiaj(a - co)[q(pj) - q(pi)].

If the access charge exceeds the marginal cost co of giving access, network i makes money on access if and only if it terminates more calls than it originates, that is, if and only if it is more expensive than its rival. Note further that a reciprocal access pricing arrangement that results in balanced contributions due to equal final prices (A1 = A2 = 0) is not equivalent to a "bill-and-keep" system in which networks would not pay access charges to each other; a network's incentive to raise price is affected by the existence of a positive access charge, as we shall see.

We first derive the first-order condition for a symmetric equilibrium, and then address the second-order conditions and the possibility of existence of asymmetric equilibria. Let us maximize network l's profit over p1:

max a(p1, P2)[(P1 - c)q(pl) - f] + a(pi, P2)[1 - a(p1, p2)](a - co)[q(p2) - q(pl)]. P1

At a symmetric equilibrium, Pi = P2 = p, a = 1/2, A1 = A2 = 0, and d[a(l - a)]/da = 0. The first-order condition is therefore

-[(p - c)q' + q] + a [(p - c)q(p) - f] - -(a - co)q' = 0, (6) 2 ap 1 4

which, for our discrete-choice model, can be rewritten in two equivalent ways:

1 + 2rf + I/ (a - co)

'~~p7 l+2Uf+~~~~~~2~~~~ (7) pa 7 + 2o-p*q(p*)

or

( a - '")o

*i~* ~(c o) = -[1 - 2arr(p*)], (8) p O

where

IT(p) (p - c)q(p) - f

is per-customer profit when the two networks charge identical prices.


Condition (8) admits a simple comparison with the standard monopoly pricing formula ((pM - c)/pM = 1/h). The first difference is that at a symmetric equilibrium, each network's marginal cost must account for the access premium (or discount) on off-net calls, and is equal to c + (a - c)/2 on average. The second difference with the standard monopoly formula is due to the impact of price on market share. A unit-price increase lowers market share by oa times sales per customer (3a/3p1 = oa dvldpl = o-uq); each unit loss of market share implies a profit loss of IT(p). The higher the profit, the more reluctant networks are to lose market share.

A symmetric equilibrium necessarily yields strictly positive profit to the networks as long as the access charge is high enough, namely: (a - co)/2 > -(1 - l/q)(pM - pR);

for, suppose that ri(p*) = 0. Then [p* - (c + (a - c)/2)]/p* = l/h from (8). And so, unless the access charge is much lower than the marginal cost of access, the candidate equilibrium price exceeds the Ramsey price: p* > pR. If instead the access charge is very small and if f > 0, then the candidate symmetric equilibrium Pi = P2 = P* given by (7) may generate losses.

The following proposition establishes the existence of a unique symmetric equilibrium when the access charge and/or the substitutability of the networks is not too large, and the nonexistence of a (pure-strategy) equilibrium if a and/or or are large (even if f = 0).

Proposition 1 (existence). (i) Fix a > 0 and all parameters but the access charge a. Then for a close to the marginal cost c0, there exists a unique equilibrium, which is symmetric and characterized by Pi = P2 = p*, given by

* (c+ a co)

=-[1 - 2a(p*)]. p* R

Suppose a > v(pM)12. Then, there exists ao such that for a 2 ao and for all f 2 0, there exists no equilibrium.

(ii) Fix all parameters but the substitutability o-. If the access charge a is such that

[(ai - 1)/q](f - pM) > (a - co)/2 2 [(ai - 1)/1j](pR - pM),

where j- is the largest solution to R(p) = f, then for oa small, there exists a unique equilibrium, which is symmetric and characterized by Pi = P2 = p*, as above.

If a - col :- [2(rq - 1)bj](pM - pR), for a large enough there exists no equilibrium.

Proof. See Appendix A.

Existence thus requires the access charge or the substitutability of the two networks not to be too high. The nonexistence for high access charges and high substitution is not a mere technical problem but a robust economic problem, which can be described as follows. Note first that a large access charge inflates the final price in any shared market equilibrium (in particular, in a symmetric equilibrium p* increases without bound when a increases). But when prices are very high and the two networks are close enough substitutes, each network has an incentive to undercut its rival to corner the market. (In particular, if Pi = P2 = p* such that 0 < v(p*) ? v(pM) - 1/2ou, not only P1 = P2 = p* may generate negative profits, but each network can moreover corner the market and get the full monopoly profits by charging the monopoly price.) On the other hand, a cornered-market configuration cannot be an equilibrium either,


since either one network makes a positive profit, and the other could then mimic it and obtain half this profit, or no network makes a profit, and then, if the access charge is very high, a network could obtain positive profit by raising its price and generating access revenue. Therefore, if the two networks are sufficiently substitutable, there cannot exist an equilibrium for large access charges. (However, it can be shown that if the substitutability oa is sufficiently small (below a given threshold), an equilibrium always exists, even for arbitrarily large access charges.) The same argument applies to situations with a large substitutability: The two networks either make negative profits or have an incentive to undercut each other and corner the market in a shared-market configuration; and again no cornered-market configuration can be part of an equilibrium. 13

A brief inspection of equations (7) and (8) shows how the symmetric equilibrium price changes with the parameters:

Proposition 2 (determinants of competitiveness). (i) The access charge is an instrument of tacit collusion: as long as the equilibrium Pi = P2 = p*(a) exists, p* increases with a.

(ii) The symmetric equilibrium price p* decreases with the substitutability of the two networks. It converges to the Ramsey price as oa tends to infinity. (That is, for any given a, p* goes to pR when a --> oo. But for this result to have content, one must take a to co as oa - oo in order to preserve existence.) For oa = 0, it is equal to the monopoly price for marginal cost c + (a - c)/2, and thus involves a double marginalization if there is a markup on access.

Proof. See Appendix A.

E Determination of mandated and negotiated access charges. Next, we can look for the access prices, aR and am, that would be set by a benevolent, omniscient regulator and by the two firms colluding to implement the monopoly price, respectively, assum- ing a subsequent price equilibrium exists (which is guaranteed if the assumptions in Proposition 1 are satisfied).

Proposition 3 (Ramsey and monopoly access prices). (i) The Ramsey access charge, aR, is smaller than the marginal cost of access. It grows with the fixed cost f of connecting, billing, and servicing a customer but is independent from o-.

(ii) The monopoly access charge, am, exceeds the marginal cost of access. It decreases with the fixed cost f but increases with the substitutability or.

Proof: (i) From (8), to obtain p* = pR, the access price must satisfy

R (c+ a C _ 1

pR 2 R

p

or, after some manipulations,

2 c (1 (pM_ pR) (9)

13 As usual, the nonexistence result raises the issue of what the parties ought to expect to happen when equilibrium fails to exist. A mixed-strategy solution does not seem very appealing in this particular context, as firms can revise their prices once they discover they are not on their reaction function. Also, we would expect capacity constraints to play a significant role in such circumstances.


Since the Ramsey final price increases with the fixed cost and the monopoly final price does not depend on the fixed cost, the Ramsey access price grows with the fixed cost. A higher fixed cost requires a higher degree of collusion.

(ii) Using the monopoly condition (pM - c)lpm = 1/, equation (8) yields

aM - Co 2o-pM7FM a -C0 (10)

2

where

ITM = (pm c)q(pm) -f

is the monopoly profit. We conclude that a exceeds co, and decreases with f. Intuitively, a higher fixed cost lowers the profitability of attracting a customer and thus softens the competition between the networks. The networks then agree to reduce the access charge in order to avoid double marginalization. Q.E.D.

Note that when oa becomes small, a R remains constant and am decreases to co. Hence Proposition 1 guarantees the existence of the equilibria yielding pR and pM for of small. Equilibrium profits are, moreover, strictly positive when the access charge is higher than a .

The first part of Proposition 3 states that the socially optimal access charge lies below the marginal cost of access. This result depends on the absence of joint and common cost, since such a cost would need to be covered through a markup on the access charge. The reason why the Ramsey access charge in the absence of joint and common cost lies strictly below marginal cost is that final prices are not regulated, and so the network's market power must be offset by a (reciprocal) subsidy on the access input; indeed, the Ramsey access charge converges to marginal cost when the networks become close substitutes.

That the access charge may be used by the networks as an instrument of tacit collusion will not come as a surprise to antitrust practitioners. The latter have long suspected that cross-licensing and patent-pool agreements among competitors may be anticompetitive. And indeed the result on collusion in network interconnection has the same logic as the conventional antitrust wisdom on mutual licensing agreements. There is here an interesting twist, though. In a simple-minded cross- licensing or patent-pool arrangement, a firm must pay an exogenous (that is, constant) per-unit-of-output fee to its rival or to the joint venture owning the patents. Thus a firm's perceived marginal cost is unaffected when it engages in a retail price cut. In contrast, in the telecommunications environment a firm pays an endogenous per-unit-of-output fee to its rival, since this fee increases with the rival's market share. Therefore, a retail price cut also lowers the firm's perceived marginal cost (as long as there is a markup on the access charge). This observation shows that the collusion argument is more complex in the case of telecommunications, and also provides intuition for why the view that the access charge is an instrument of tacit collusion must be qualified by a study of the stability of retail competition.

6. Nonreciprocal access pricing * So far we have assumed that the regulator sets, or else the two firms agree on, a reciprocal access charge. This section, in contrast, assumes that the firms set their access


charges noncooperatively (and therefore possibly asymmetrically). It analyzes a two- stage game in which networks first select access charges and second choose retail prices.

Such a situation might arise in a deregulated environment in which agreements between competitors on intermediate prices are frowned upon by antitrust authorities. But although we emphasize this fully noncooperative environment, we should point out that the framework of this section is of independent interest as a building block for the case of cooperatively set access charges. Indeed, suppose that the firms bargain over (symmetric or asymmetric) access charges. Then the interconnection agreement they reach depends on the noncooperative outcome that would prevail if the negotiation broke down.

As usual, we start by solving the second, price-competition stage, taking access charges as given, and then look at the setting of access charges. For given access charges (a1, a2), network i's profit is (for i, j = 1, 2, i $ j)

Ti(P1, P2; a,, a2)

- ai(Pp1 P2)[R(pi) - f] + ai(pl, P2)aj(Pl, P2)[(ai - c0)q(pj) - (aj - c.)q(pi)].

In the second stage, network i maximizes its profit with respect to pi, taking al, a2, and pj as given, yielding a price equilibrium {pe(a1, a2), pe(a1, a2)}. Then in the

first stage, each network i maximizes its profit 1T,(pe(a1, a2), pe(a1, a); al, a) with respect to its access charge ai.

E Noncompeting networks. As a benchmark, consider first the case of no substitution (v = 0). Network l's profit is then

-I[R(pl) - f] - (a - co)q(pl) + I(a, - co)q(P2)- 2 4 24

As can be seen from the expression of profits, if the two networks set their access and retail prices simultaneously, each would set an "infinite" access charges for use of its own network.'4 The second-stage equilibrium prices, pi(aj), are the monopoly prices for marginal costs c + (aj - co)12:

p,(a1)= 77 + 2 ] i,j= 1,2, i $j.

In the first stage, network i's first-order condition is

1 i- a- co 72 =

-q(pje(ai)) 1 - i ,7 = 0. 4 2pje (a2p;(a ) 7)

The equilibrium is thus unique, symmetric, and characterized by

14 Note that a rule such as ECPR may not prevent such behavior. For example, under "marginal-cost" ECPR (ai - co ' pi - c, see Section 9), network i could still gain by taking ai and pi to infinity (thereby giving up on retail profit but obtaining infinite access revenue) as long as qj > 0. The only equilibrium has infinite prices and qa = a- = 0 (the industry shuts down).


a - co= c

2 r '

n2c

- 1)2

This equilibrium features a classic "double markup." The relevant marginal cost for a network is

c + a = c M

2 q )- 1

which leads to a final price that is higher than the industry monopoly price; this final price corresponds to a monopoly price based not on the industry marginal cost but the perceived marginal cost, which is equal to the industry monopoly price:

P= (P)2

c \c

D Competition for market share. This double marginalization subsists for a small substitutability. One may wonder, though, whether it is alleviated by the substitutability. While competition for customers exerts a downward pressure on the retail price, competition may also induce networks to jack their access price up in order to force their rival to raise its retail price and lose market share. Thus, the impact of substitutability on access and retail prices is a complex issue, which we study in the case of small substitutability. In Proposition 4 (and only in this proposition) we assume for simplicity that the firms must quote a price and cannot turn down consumers. This rules out the possibility that a firm charge a high access price in order to induce its rival to exit under the prospect of negative profits.

Proposition 4 (noncooperative access charges). If 0f is small, there exists a symmetric equilibrium of the noncooperative two-stage game in access charges and retail prices. Starting from o- = 0, a small increase in 0f has an ambiguous impact on the equilibrium access charge: a decreases if vr < (,q - 1)f (where vo denotes the equilibrium profit per firm for o- = 0), but increases otherwise; in both cases, however, the equilibrium retail price p decreases.

Proof See Laffont, Rey, and Tirole (1997).

As we already noted, an increase in the substitutability of the two networks reduces the retail markup. The impact on the access markup is more ambiguous. On the one hand, an increase in the substitutability enhances the benefit of the impact of a higher access price on the rival network's retail price: Increasing one network's access charge tends to increase the other network's retail price and thus to increase one's network market share, and this all the more so as networks are more substitutable. On the other hand, an increase in the substitutability reduces this strategic effect on the other network's retail price, since the latter network is more reluctant to increase its price if the two networks are more substitutable. Starting from no substitution, introducing (a slight) substitution may give more weight to the latter effect (e.g., if per-customer profits are small even for o- = 0), in which case the access markup decreases as well as the retail markup, or to the former (e.g., when f = 0, so that per-customer profits are relatively high for o- = 0), in which case the access markup increases with the


substitutability of the two networks. Proposition 4, however, shows that the latter effect cannot dominate the decrease in the retail markup, so that overall, increasing the substitutability between the two networks alleviates the double-marginalization problem (but a high substitutability may again lead to the nonexistence of an equilibrium).

Remark. The thrust of this section is the standard point that double marginaliza- tions result from the noncooperative setting of intermediate and final good prices. The associated inefficiency arises with a vengeance with n > 2 networks. For example, it is easy to see that for oa = 0, the industry shuts down as n becomes large. When setting its access charge, a network realizes that it has only a small impact on other networks' final price. Access charges and final prices therefore tend to infinity as the number of networks grows larger and larger.

7. Entry

* Next we analyze the competition between two asymmetric networks and the entry process.'5 The entrant, network 2, initially has no coverage. To enter it must therefore either lease facilities from the incumbent, network 1, or build its own facilities. The second option involves a fixed joint and common cost of partially or fully duplicating the incumbent's local network. The incumbent starts with full coverage.

The February 1996 Telecommunications Act and the August 1996 FCC Report and Order envision three types of entry in the local market. Under resale entry the incumbent leases the services such as basic telephone services or other services (billing and collection, information services, ISDN, etc.) to entrants. Section 251 (c)(4)(A) of the act imposes on all incumbent local exchange carriers the duty to offer for resale at wholesale rates any telecommunications service that the carrier provides at retail to subscribers who are not telecommunications carriers. Under facilities-based entry the entrants build their own local network. Last, under unbundling, a hybrid arrangement, the entrants lease some (or all) elements of the incumbent's facilities (say, their transmission facilities) and may build some others themselves (say, the switches). Under facilities-based entry the only access charge is the transport-and-termination or interconnection charge a considered previously; in contrast, resale or unbundling entry involves an access charge paid by the entrants to the incumbent for elements or the whole that the incumbent and the entrants pay to each other.

We analyze in turn unbundling-based and facilities-based entry.

E Unbundling-based entry. Let us first assume that the entrant leases the local transmission facilities from the incumbent. The incumbent incurs a fixed cost f of connecting individual customers (for notational simplicity we will ignore the costs of servicing and billing these customers) whether the customer signs up with the incumbent or the entrant. The entrant leases the connection to the customer at price A per customer. We denote by C the incumbent's joint and common cost per inhabitant of building the local network (unlike f, C cannot be avoided by not connecting a customer). The total fixed cost to be recouped by customer is thus f + C (since there is a fixed-size, unit-mass population of customers). The Ramsey price pR has to be redefined accordingly: (pR - c)q( pR) = f + C. We consider the case where the entrant builds its own switches and thus incurs marginal cost c0 at the originating or terminating ends of a call (in American terminology, the entrant is then a "true unbundler").

Under unbundling-based entry, the two networks' profit functions become

15 We continue to make the assumption of balanced call pattern. It is particularly strong in the context of entry. For the entrant's coverage is not random, as it targets markets (cities, businesses) with specific calling patterns. We believe future work should relax the balancedness assumption in order to obtain a better understanding of the impact of entry.


I1 = r1T + a2(A - ) - C

and

72 = 72 - a2 (A -S f,

where ri is given by equation (5). Let us look for access charges {a, Al} (a for transport and termination, and A for

the lease of the incumbent's transmission facilitites) that implement the Ramsey optimum. In order to obtain F =72 = 0 and P1 = P2 = pR, the only possible access charges are

a = aR < cO

and

= f + C.

To understand this result, recall that in the absence of joint and common cost, some subsidy on access charges must be built in in order to offset the networks' market power and to keep the unregulated retail prices down. This downward pressure on retail prices can be obtained in two alternative ways: a low interconnection charge a or a low lease price A. Indeed, a low lease price subsidizes the entrant and encourages both the incumbent and the entrant to build market share. It is, however, optimal to create the downward pressure on retail price solely through the interconnection charge a, as this preserves the level playing field between the two operators; in contrast, a subsidy on the lease price (A < f + C) would favor the entrant to the detriment of the incumbent, since for any pair (a, A1) leading to Pi = P2 = pR, the networks' profits are respectively Hii = (A - f - C)/2 and rr2 = -(- f -C)/2.

Proposition 5 (unbundling-based entry). Under unbundling-based entry, the socially optimal transport and termination charge is set below marginal cost (a < co), and the socially optimal lease price is equal to the customer's connection cost plus the incumbent's per-customer joint and common cost (A = f + C).

E Facilities-based entry. To analyze facilities-based entry, we distinguish between two institutional frameworks. In the first, interconnection at some access price a (which is assumed to be positive, but not so high as not to allow the entrant to cover the joint and common cost of entry) is mandated by a regulator. The thrust of our analysis will be to show that the entrant may then not be handicapped by its smaller coverage even if a is large, and that it may actually even choose to keep a small coverage for strategic reasons. In the second framework, interconnection negotiations are fully unconstrained, so there is no interconnection as long as firms do not come to some mutual agreement. As we will see, the entrant's position is then quite uncomfortable unless it duplicates the incumbent's coverage.

Mandated access charge. We assume that network 1, the incumbent, has full coverage. Network 2, the entrant, chooses its coverage a E1 [0, 1] and incurs an investment cost d(y), where d(-), the joint and common cost, is increasing and convex.

In a first step, we take the entrant's coverage a and the reciprocal access charge a as given, and we look at price competition between the incumbent and the entrant. We then analyze the entrant's choice of coverage, still taking the mandated access


charge as given. A key assumption of our analysis is that the incumbent is not allowed (or does not have the information) to price discriminate according to whether the customer is within the entrant's territory.

It is now important to make a distinction between network 1's market share a1 and its market share a in the overlap, that is, the market share that network 1 commands among those consumers that can be served by both networks:

a1 = 1 -(1 - a)

and

a2 = (' - a),

where, as earlier,

1 a = a(P1, P2) = - + o-I[V(pl) - V(p2)]. 2

Our first result is that in a pure-strategy equilibrium the entrant undercuts the incumbent, at least for a close to c0. Let (P1, P2) denote equilibrium prices. For a close to c0, pR < P1 P2 <pM. As before, the profit functions are

7 = a1[R(pl) -f] + aa2(a- co)[q(P2) -q(pl)]

and

T2= a2[R(P2) f] + aja2(a co)[q(pl) q(p2)].

Profit maximization requires that a network does not gain by mimicking its rival's price (in which case it gets half of the market in the overlap and has no access deficit or revenue). So

1 2 [(1 -a) + 2I[R(P2) -f]

and

?T2 -[R(p1) f]- 2

Adding up these two inequalities and using the expressions for rT1 and IT2, we obtain

[1 - + aja - -[R(p1) - R(P2)] 0.

Suppose now that P2 > Pi* Then a > 1/2, and (given P2 < pM) R(P2) > R(p1), a contradiction.


Next, suppose that Pi = P2 = p < pM. A simple inspection of the first-order conditions for the two firms shows that they cannot be satisfied simultaneously.'6 In- tuitively, network 1 has more incentive to raise price, as it can exploit a captive market. This incentive would not exist if the incumbent could charge different prices in the territory covered by the entrant and in the complementary territory. In that case, it would charge the symmetric equilibrium price p* derived in Section 5 in the overlap and would charge pM in its monopoly territory.

The economics of undercutting are illustrated in Figure 1. For a close to c0, we know from Section 5 that when the entrant has full coverage (,a = 1), profit functions are symmetric and strictly quasi-concave, and that an equilibrium exists and is stable. Let Pi = rA(p2) and P2 = rg(p,) denote the two reaction curves. For a close to c0,

network 2's reaction curve is quasi-independent of the network's coverage, since the postinvestment profit function, v29, is almost proportional to a. In contrast, by revealed preference'7 rA shifts eastward as a decreases; that is, an expanding captive market transforms the incumbent into a pacifistic fat cat.

A corollary of the fact that the entrant undercuts the incumbent is that the entrant incurs an access deficit.

Next, we demonstrate our second and related result of interest, namely that the entrant underinvests strategically in order to transform the incumbent into a fat cat and induce it to charge a high price.'8 Let {p1*(A), p* (,)} denote the equilibrium prices,

2g(Pl, P2' A) denote network 2's second-stage profit, and

v= 9(p*(p_), p2*(I), ,t) - d(Z)

denote network 2's equilibrium profit, net of investment. One has

n - + a1 p9 (11)

The term in brackets in (11) is the direct effect, taking network l's price as given. The second term in the right-hand side of (11) is the strategic effect. A wider coverage lowers network l's price (dp/*ldp < 0) and thus indirectly reduces network 2's profit (as avg2/ap, > 0). 19

16 The first-order condition for network i is

aOa. [R(p) - f] + aiR'(p) - a12(a - co)q'(p) = 0,

ap,

where

i = -,guaq(p) is independent of i api

and

a, > a2-

17 This is demonstrated by showing that a27TI1/ap Jag is negative for a close to c0. 18 This behavior by the entrant is related to but differs slightly from the puppy-dog ploy, in which the

entrant remains small in order not to be aggressive. In both situations, the entrant remains small in order to tame the incumbent. Our analysis is similar to that of the strategic investment in goodwill (see, e.g., Fuden- berg and Tirole (1984)).

19 The welfare impact of this strategic underinvestment in coverage may be more ambiguous. On the one hand, it softens competition. On the other hand, the strategic undercoverage may well have a positive welfare effect by decreasing an excess coverage induced by imperfect competition.


FIGURE 1

p2 r 1 r4 ro

Partial coverag

Full coverage

S ~~~~~~~~~~r ' 2

PTM

Again, our conclusions rely on the incumbent's not being able to price discriminate between its monopoly territory and the overlap territory; under such price discrimination, there would be no strategic effect (dp*ldu = 0) and the entrant would choose full coverage if and only if -iT9 (1) 2 d'(1).

Proposition 6 (entry behavior). Assume that the full-coverage incumbent cannot price discriminate between its monopoly territory and the competitive territory. Provided that the access charge is close to the marginal cost of access,

(i) the entrant undercuts the incumbent and therefore generates more outflow per customer than its rival and incurs an access deficit; and

(ii) the entrant underinvests in coverage in order to soften price competition.

Bilateral interconnect negotiations. The picture is quite different when interconnection is to be freely negotiated without any external intervention and in particular in the absence of any default access charge that a party could invoke to impose interconnection on the other party. Suppose that the parties negotiate an interconnection agreement (a,, a2) in a Rubinstein-Stahl alternative-offer bargaining game and that they enjoy their noninterconnected profit as long as no agreement is signed. From our balanced calling pattern assumption, a consumer who can call a fraction ,t of the population at price p has variable net surplus ,tv(p). (We are a bit casual with equilibrium selection in the situation of noninterconnected networks in what follows, but we hope the thrust of the argument is clear.)

Assume in a first step that the entrant's coverage is small. As long as no agreement is reached the incumbent can corner the market at price pM if ,A is very small or at price pi C pM for a larger coverage, where Pi is the limit price for network 1: v(pl) = ,uv(pR) + 112o-. That is, given that network 2 cannot charge less than pR

without losing money and therefore cannot offer surplus in excess of AV(pR) to consumers, network 1 corners the market by charging pi (provided consumers co- ordinate on the Pareto-dominating equilibrium). Thus with ,A small, the incumbent enjoys a sizable profit and the entrant no profit at all before an agreement is reached. This puts the entrant in a difficult bargaining position. Presumably, it will have to agree on a high al and a small as.

LAFFONT, REY, AND TIROLE / 19 20 / THE RAND JOURNAL OF ECONOMICS

Indeed, if ,u is small enough so that v(pM) 2 uv(pR) + 1/2-, the incumbent delays indefinitely the interconnection agreement, as any such agreement would introduce competition, lowering industry profit and therefore the incumbent's own profit.

In contrast with the situation in which interconnection is mandated at some access price, the entrant now has an incentive to overinvest in coverage. That is, the entrant ought to choose a coverage that exceeds the level it would choose were the equilibrium interconnect agreement exogenously imposed. The point is that by choosing a higher ,u, the entrant reduces the incumbent's preagreement profit (and possibly makes a preagreement profit of its own). The entrant thereby puts more pressure on the incumbent and reaches a better deal. We thus observe that a top-dog strategy of overinvesting in coverage may prove beneficial for the entrant in an unconstrained-negotiation situation. On the other hand, the entrant might not need to overinvest if it could force interconnection even at a very high price, as this default rule would by itself put pressure on the incumbent.

8. Competition in two-part tariffs * This section returns to the full-coverage network and studies competition in two- part tariffs. It shows that some of the insights derived for uniform pricing generalize to nonlinear pricing, but it also unveils new insights that are specific to competition in nonlinear prices.

Because the customers' demand function is known and the same for all consumers that subscribe to a given network, networks cannot do better than offering two-part tariffs:

Ti(q) = Fi + piq, i = 1, 2,

where the fixed fee Fi can be interpreted as a subscriber line charge and pi will be called the marginal price or usage fee. For future reference, it is useful to define the Hotelling per-firm profit when consumers have unit demands:20

H IT 4o-

As we will see, when two-part tariffs are available, network competition with multiunit demands strongly resembles competition with unit demands.

After subtracting the fixed fee Fi, the net surplus offered to network i's consumers becomes

Wi = v(p1) - Fi.

It will be convenient to view the network competition as one in which the networks pick usage fees and net surpluses rather than usage fees and fixed fees, for market shares are determined directly by the net surpluses. Network i's market share is

ai = a(wi, wj) = + 0r(wi - w). (12)

Network i thus solves

20 For its computation see, e.g., Tirole (1988). With unit demands, equilibrium prices are equal to c + t and so TH = t/2 = 1/4o-.

LAFFONT, REY, AND TIROLE I 21

-ri = max{a(wi, w)[[pi - c - (1 - a(wi, wj))(a - co)]q(pi) + [v(pi) - wi- f]] {PjJVty}

+ a(wi, w,)(1 - a(wi, wj))(a - co)q(pj)}.

Using the fact that v'(pi) = -q(pi), the first-order condition with respect to pi yields (whenever ai > 0)

Pi = C + aj(a-co). (13)

As usual, two-part tariffs yield pricing at marginal cost. Marginal cost, however, is not the industry marginal cost, c, but rather the marginal cost, c + aj(a - c0), faced by network i. Note also that the network with the larger market share faces a lower marginal cost and thus charges a lower usage fee and incurs an access deficit.21

The next proposition further characterizes the outcome of competition in nonlinear tariffs.

Proposition 7 (competition in nonlinear tariffs). (i) When the degree of substitutability (u) or the access markup (a - co) are not too high, there exists an equilibrium in nonlinear tariffs, which is, moreover, unique and symmetric. In contrast, there is no (symmetric or asymmetric) equilibrium for a > co and o- high or for ar > l/v(c) and a high. Also, there is never a cornered-market equilibrium.

(ii) A network's optimal usage fee is its perceived marginal cost, c + aj(a - co), and not the industry marginal cost, c. And thus, at a symmetric equilibrium, p = c + (a-co)12.

(iii) The symmetric equilibrium subscriber fee, F*, is equal to the net marginal cost of adding a subscriber to the network, f - (a - co)q(p*)12, plus the Hotelling

markup 1/2o-. The symmetric equilibrium profit is independent of the access charge and is equal

to the profit that would obtain under unit demands:

* = ,H 1 4o-

Proof: See Appendix B.

Even though the tension between excessive marginal prices implied by high access charges and the temptation of undercutting remains in competition with two-part tariffs, creating an economically meaningful nonexistence problem, the welfare implications appear quite different.22

In contrast with the case of linear prices, the symmetric-equilibrium profit is independent of the access charge and is the same as under unit demands (as long as consumers remain connected, of course, which they do if v0 is high and a is not too large)! This result in turn implies that the equilibrium profit is independent of the access charge, a key difference with the uniform pricing case. To obtain some intuition for this result, suppose that the access charge a is raised by 8a. Each network's marginal cost increases by 8a12, and so do usage fees. To keep net surplus and market share constant, a network must reduce its fixed fee by -5F = q~al2. This lowers the gain from attracting a new customer by q~al2. On the other hand, the increase in the access

21 A further noteworthy property is that equilibrium prices always satisfy the marginal-cost ECPR; see Section 9 for a discussion of alternative ECPRs.

22 Note that the Ramsey benchmark with two-part tariffs differs from that defined by (9). Indeed, at the Ramsey optimum the marginal price is equal to c and the fixed fee is equal to f.


charge provides an additional incentive to attract a customer, as this saves an extra amount in access charges equal to q~al2. The two effects cancel, and thus the intensity of competition does not vary with the access charge.

Another way to look at this result is to compare it to the uniform pricing case: In both cases, the increase in the access fee leads to an increase in the usage fee and makes it more desirable for networks to build market share. In the uniform pricing case, building market share magnifies the access deficit. There is no such countervailing incentive with two-part tariffs, as a decrease in the fixed fee enables networks to build market share without generating an access deficit. So, while equilibrium profits need not be lower than under uniform pricing because of the enhanced ability to capture consumer surplus through the fixed fee, the industry is more competitive than under uniform pricing. Hence, the operators do not gain any more from high access charges, and the policy of pricing access at marginal cost, which would be socially desirable, is not necessarily resisted by the operators if they can jointly determinate the access charges. This, however, still requires a cooperation between the operators, since although they are indifferent between all symmetric access charges, they are not indifferent with respect to unilateral increases in their own access charges. In particular, starting from a, = a2 = c0, it can be shown that a small unilateral increase in one network's charge does increase this network's equilibrium profit. Hence, although in principle they would jointly agree on the efficient access pricing (a, = a2 = c0), each has an incentive to depart from that and increase its own access charge, and a noncooperative determination of access charges still fails to yield the socially preferable outcome.

However, all the traditional reasons that make nonlinear prices difficult (incomplete information on consumers' tastes, negative redistributional effects of fixed fees), to the extent that they cannot be overcome by menus of tariffs, are likely to restore partially the tacit collusion effect of high access charges. To model precisely these phenomena is beyond the scope of this article.23

9. The efficient component pricing rule

* The previous analysis has focused on reciprocity as the sole relationship to be satisfied by access prices. An oft-advocated constraint on access pricing is the Baumol- Willig or efficient component pricing rule (ECPR), according to which the access price charged by a network to its competitors should not exceed the network's price on the competitive segment minus the network's cost on that segment. In other words, the access charge should not exceed the opportunity cost for the network of losing a call on the retail segment. An alternative approach to ECPR is the "imputation methodol- ogy," according to which a bottleneck owner should be required to provide monopoly service elements at (at most) the price it imputes into its own competing services (subject to a budget constraint on the competitive segment), that is, the difference between retail price and marginal cost on the retail segment (Hausman, 1994). Although there is no difference between the opportunity cost and the imputation methodologies in the standard context in which they are applied (a single bottleneck giving access to a potentially competitive segment), we will argue that their philosophies and implications differ slightly when applied to network competition.

The New Zealand final appellate court (privy council) decision of October 1994 is particularly relevant for our analysis. In its dispute with Clear Communications, New Zealand Telecom, the dominant operator, argued that it was entitled to recover its opportunity cost when setting its interconnection charge. While the high court had ruled

23 Note that the recognition of consumer heterogeneity could create some scope for specialized networks.


in favor of Telecom and the court of appeal in Clear's favor, the privy council finally decided that the use of ECPR by Telecom was lawful under section 36 of the Commerce Act. This endorsement of ECPR by the privy council has been controversial, if only because the rule was designed to apply to a regulated environment (as William Baumol pointed out in testimony). Little is known about the impact of ECPR in an industry where retail prices are not regulated.24 The purpose of this section is to provide some insights about the likely functioning of ECPR in a deregulated environment.

E Interpretations of ECPR in the context of network competition. ECPR has been designed and applied in regulatory and antitrust contexts in which a dominant firm controls a bottleneck segment (the essential facility) and competes with other firms in a second, complementary segment. It is unclear how ECPR should be interpreted in the context of network competition.25 Ex post, that is, after consumers have joined a network, both the originating and terminating ends are bottlenecks; each is monopolized by a network and is essential to the completion of a call. Ex ante, that is, before consumers have joined a network, the complementary segments are (imperfectly) competitive. We first formulate some educated guesses about how ECPR is likely to be interpreted by regulators and courts in the context of network competition, and then we investigate its impact on competition.

Consider first an ex post point of view and suppose that consumers have allocated themselves to networks. At this ex post stage, one can adopt an imputation approach and compare the access price charged by the terminating network to the originating network to the price the former charges to itself for its on-net calls, which cannot exceed its retail price pi minus the cost, co + cl, that it incurs outside the bottleneck terminating segment (a higher transfer price would generate losses for originating the call). Hence, the access price ai charged by network i for terminating calls originating on the other network should satisfy ai ' pi - (cO + cl), or

ai- co Pi-c. (14)

We will refer to (14) as the marginal-cost ECPR, since it is based on the marginal cost of calls and does not include any fixed cost of connecting and servicing a customer.

An ex post opportunity-cost approach to ECPR could translate into

ai-co - Pi-(co + cl + a) i, j = 1, 2, i 7 j.

The left-hand side represents the revenue network i collects from a call originating on network j, whereas the right-hand side represents the revenue that would be collected if network i insisted on providing the call (this would require getting origination access to network j). This approach would lead to

a, - co ', -c-(a2- cO) (15)

ta2- CO P2-c -(a I- co)-

This approach has the drawback that the constraint faced by one network depends upon the access charge set by the other network (in contrast with the standard application of ECPR to single bottleneck situations), which may make it difficult to implement in practice.

24 See Laffont and Tirole (1994, 1996) for an assessment of the optimality of ECPR under retail price regulation, and Baumol, Ordover, and Willig (1996) for a further discussion.

25 See, e.g., Kahn and Taylor (1994).


Alternatively, we can adopt an ex ante viewpoint. Since at this stage networks compete for customers, it seems reasonable to interpret the opportunity cost of losing market share as the loss of a customer rather than of call completion. When, for example, network 1 loses a customer to network 2, network 1 incurs a revenue loss equal to

[PE - c - a2(a2 -co )]q(p 1)-

where a2 is the access charge levied by network 2. Network 1's added access revenue relative to this forgone customer is equal to

tl(al - co)q(p2)-

So one can interpret the opportunity-cost rule as the requirement that

al(al - co)q(p2) [PI - c - a2(a2 - co)]q(pl) - f. (16)

An obvious drawback of (16) is that its compliance by network 1 now depends on both the access and retail prices chosen by network 2 (again in contrast with the marginal-cost ECPR defined in (14), or even with the ex post opportunity-cost approach, where only the other network's access charge matters). This property is likely to make it unacceptable as a constraint on conduct and suggests again that it is not straightforward to build an opportunity-cost approach to ECPR in the context of network competition. Let us finesse this difficulty and make a substantial leap in the interpretation by considering that in a symmetric situation, network 2 will charge the same access and retail prices as network 1 (a2 = a,, P2 = PI). This strong identifying restriction resolves the dependence of the constraint to be satisfied by a network on the strategy followed by its competitor and leads to an interesting interpretation of ECPR. At a symmetric equilibrium, the ex ante opportunity-cost rule becomes

al -cO < PI - + (p)] (17)

This is simply the average-cost ECPR. From an ex ante viewpoint, the average cost of serving a customer in a symmetric equilibrium is equal to c + flq(pl) and so the opportunity cost is Pi - [c + flq(pl)]. The average-cost ECPR is the single-product version of "average incremental cost," which is what Baumol and Willig have intended ECPR to mean.26

Lastly, we can develop an ex ante imputation approach to ECPR. From an ex ante perspective, the maximal price a-, that network 1 could charge to itself is such that

[pI - c - aI(1 - co)- a2(a2 - co)]q(p1) - f = 0,

yielding

~l(al - c0)q(pl) ? [P -c - a2(a2 - cO)]q(pl)-- (18)

In contrast with the opportunity-cost approach, the imputation rule generates a constraint that does not depend on the final price of the competing network; however, this

26 We are grateful to William Baumol for helpful reactions to this discussion of ECPR.


constraint still depends upon the access price charged by the other network. Note finally that both approaches boil down to the average-cost ECPR in symmetric configurations.

a Does the Ramsey access charge satisfy ECPR? The popularity of ECPR is grounded in its optimality as a subrule27 in specific circumstances. Willig (1979) sup- plied a key insight by deriving ECPR in the context of a contestable market. As is well known, however, the assumption of contestability is strong. In particular, it presumes perfect substitutability between goods, identical cost structures, and hit-and-run entry. Beside being restrictive, these assumptions have the drawback of predicting an absence of competition in the retail market. Building on the work of Baumol and Willig, Laffont and Tirole (1994) consider a more general framework and show that ECPR emerges as part of an optimal regulatory scheme in "symmetric contexts" in which (i) retail goods are differentiated but face symmetric demands, (ii) cost structures on the retail segment are identical, (iii) the cost of giving access does not vary across competitors, and (iv) no market power is exercised on the retail segment by the competitors of the regulated bottleneck owner. While departing from it is often desirable,28 ECPR remains a useful benchmark as long as it is employed in the context in which it was designed and some adjustments are made to reflect the various asymmetries between the vertically integrated firm and its competitors.

An interesting question is whether the Ramsey access charge we have obtained in the context of network competition satisfies ECPR. Comparing (9) and marginal-cost ECPR (as defined by (14)) shows that the Ramsey allocation formally satisfies marginal-cost ECPR if the latter is interpreted as an inequality constraint (that is, aR - co is lower than pR - c) but does not satisfy marginal-cost ECPR if it is interpreted, as is often the case, as a binding constraint (that is, the access charge given by a - = pR - C is too high and would thus generate high retail prices in excess of their Ramsey level). Furthermore, marginal-cost ECPR cannot be the correct benchmark for access pricing for two reasons: market power and fixed costs.

Market power. As we noted, the optimality of ECPR has been derived in some regulatory contexts or in the context of a perfectly contestable market. In a deregulated environment, firms with market power add a markup on retail over marginal cost. To insulate the market-power effect, let us assume that there is no fixed cost, f = 0. Then pR = c and marginal-cost ECPR yields a = co. But market power implies that for a = co, p > pR.

As is well known, this markup is optimally offset by a subsidy. In the context of access pricing, this subsidy can take the form of a discount on access.29 Note that in contrast with the classic case of an output subsidy to a monopolist, the discount on access does not generate further rents for the networks, as the subsidy received by a network on its off-net calls is offset by the subsidy it pays for terminating its competitor's off-net calls. The Ramsey access charge satisfies a "sub-ECPR," as

aR - co < 0 < pR - C.

Fixed cost. Networks' prices determine not only the volume of calls, but also the allocation of customers between networks. To the extent that connecting and servicing

27 ECPR only provides a link between access and retail prices and is therefore a partial rule. Indeed, even in the circumstances in which it is consistent with optimality, its actual optimality depends on the retail prices being set at their right level.

28 See Laffont and Tirole (1994, 1996) for a list of corrections, and Armstrong, Doyle, and Vickers (1996) for a further analysis.

29 See Laffont and Tirole (1994, 1996), Masmoudi and Prothais (1994), and Armstrong, Doyle, and Vickers (1996).


a customer involves a fixed cost, Ramsey pricing of calls includes a contribution to the fixed cost:

pR

q (PR)

To insulate the fixed-cost effect, let us assume that there is no market power (O- -> co). Then aR = co yields p = pR = c + f /q( pR), which satisfies average-cost ECPR with equality. We thus see that the proper version of ECPR in the absence of market power is average-cost ECPR, that is, the version of ECPR favored by Baumol and Willig.

E Implications of ECPR. We consider the impact of ECPR when the networks contract on a reciprocal access price and then compete in retail prices subject to ECPR. The tenet of our analysis is that ECPR softens price competition, as a high access charge under ECPR is a commitment to charge a high retail price. So, suppose first that the networks agree on an access price and then pick their linear retail prices subject to ECPR:

Pi - c a - co for i = 1, 2, for marginal-cost ECPR,

Pi- + (p ) ? a - c for i = 1, 2, for average-cost ECPR.

Proposition 8 (free interconnect negotiations and ECPR yield perfect collusion). Pro- vided their retail services are sufficiently substitutable, the networks can under ECPR obtain the monopoly profit by setting access charge a such that

a - = pM - c for marginal-cost ECPR,

a - Co = pM - [c + (EM] for average-cost ECPR.

Proof: Suppose that the networks agree on this access charge. Then both versions of ECPR constrain the two networks to charge at least pM: this is clear under marginal-cost ECPR. This also holds under average-cost ECPR, as the function h(p) = p - c - flq(p) is strictly increasing for pR C p < pM.30

Would network 1, say, want to charge above pM given that network 2 charges pM? By doing so, network 1 would lose market share but would gain on access revenue. Given the hefty premium (pM - c) collected on access, this gain in access revenue might offset the loss in market share. But, with sufficient substitutability, a network cannot raise its price much without losing all its customers and thus has no incentive to do so. More formally, when network 2 charges pM, network l's profit is

Xi(Pl, pM) = al[R(pl) - f] + a1(l - al)(pM - c)[q(pM) -q(pl)],

where

30 h'(p) - 1 -IfI/pq 2 1-(p -c)/p] 2 0, where the first inequality uses the fact that p 2 pR

and so h(p) 2 0.


a1 = a(pl, pM) and da= -oq(pj).

So

= aR'(pl) - a1(l - al)(pM - c)q'(p1)

- oq(pj)[R(pj) - f + (1 - 2a,)(pM - c)[q(pM) - q(pl)]]

Next, note that network 1 attracts no customer for pi - jp where

v(pM) -v() 2o

So for oa large, the relevant price range, pi E [pM, j-], is a small interval. And the term -aq(p1)[R(pj) - f] o -aq(pM)[R(pM) - f] dominates in the derivative of IT

with respect to Pi, which is therefore negative. Q.E.D.

Proposition 8 focuses on the strongly substitutable case. This is the interesting case with regard to the question of whether ECPR promotes collusion, for we know that ECPR is not needed to obtain the monopoly price under unconstrained interconnect negotiations for oa small, while the monopoly price cannot be obtained by simply setting a high access charge if oa is high, as the temptation to undercut a bit and corner the market is strong. (Note that ECPR guarantees the existence of a collusive equilibrium as well, even if the two services are highly substitutable and required access charges are thus also very large.)

Remark. Nonlinear pricing and ECPR. Nonlinear pricing raises an additional question about the interpretation of ECPR: Is the relevant price on the competitive segment a marginal or an average price? Accordingly, with two-part tariffs and following the imputation approach of condition (14), we can contrast a marginal-price ECPR,

pi - c a-co,

and an average-price ECPR,

F. + --c ':? ai - Co. qi

It can be shown that a marginal-price ECPR constraint does not allow firms to collude, as it leaves the profit unchanged at the Hotelling level but still aggravates the marginal price distortion when the access charge exceeds marginal cost of access. Indeed, given a reciprocal access charge a, a marginal-price ECPR constraint pi - c ' a - co is binding for both networks, as each would want to set a price pi equal to its marginal cost, c + aj(a - co). So both networks charge

p = c + (a-co) and iT= ai[(p-c)q(p) + Fi ],

leading again in equilibrium to iT = IT2 = TH. In other words, ECPR reduces fixed fees and increases marginal prices away from social marginal cost c, leaving profits unchanged but reducing consumers' utility and social welfare.


In contrast, for a fixed reciprocal access charge a, and from Proposition 7, an average-price ECPR is binding if and only if (a - c)q(c + (a - c)/2) > 1/2o- + f; that is, ECPR is not binding if a is close to c0, but it is binding for larger access charges and large substitutability.3' It can, moreover, be shown that this ECPR is an instrument of tacit collusion when it is binding. In particular, the equilibrium profit is then

1 v

4o 2oq

where v ? 0 is the shadow price of the average-price ECPR constraint (hence, if this constraint is binding, v > 0 and i > 1/4o-).

10. Conclusion

* The article has developed a discrete-choice model of membership to study network competition. Let us first recap the main results, starting with the case of linear pricing.

First, we derived an existence result for retail price competition. We also showed that equilibrium fails to exist when the access charge and/or the degree of substitution between networks are high. Intuitively, high access charges lead to high prices as networks try to reduce their outflows and to collect (or avoid paying) access charges. With sufficient substitutability, each network then has an incentive to undercut a bit to build up market share and avoid paying access charges.

Second, in the region where equilibrium exists, an increase in the access charge raises final prices and profits (unless the access charge is so high that the retail price exceeds the monopoly price). When the access charge differs from marginal cost, each network must consider the impact of its price changes on the net traffic outflow. Low- ering the price of calls has two potential effects in this respect. One, it attracts additional subscribers in competition with the other network. This does not affect the net outflow at a symmetric equilibrium. Two, it induces the network's subscribers to make a greater number of outbound calls. Hence, the balance of traffic is affected at the margin. Because lowering the price triggers an access deficit at the margin, the incentive to lower the retail price is reduced and competition is weakened.

Third, under unbundling-based entry and fully depreciated joint and common cost of the incumbent's network, the socially optimal transport and termination charge is set below marginal cost, and the socially optimal lease price is equal to marginal cost. Provided the incumbent cannot price discriminate between its customers, a facilities- based entrant with less than full coverage undercuts the incumbent and incurs an access deficit. Entry with full coverage is not a necessity for the entrant, who may actually want to "underinvest" in coverage in order to transform the incumbent into a pacifistic fat cat.

31 One could also consider the "average-cost average-price ECPR":

[Pi + [ q(p)] c.

It would be binding when

(a - co)q + a - co)

Thus it is always binding for a > c0 and 2 sufficiently large.


Fourth, nonlinear price competition leads to analogous results, with a key difference: the firms can separate the two roles of pricing. An increase in the access charge has no impact on profit. While this increase boosts the final prices and results in a lower social welfare than in the case of linear prices, networks can under two-part tariffs reduce the fixed fee and build market share without incurring an access deficit. (In contrast, in the case of competition in linear tariffs, market share can be built only by lowering the usage fee and increasing the outflow.) In this sense, competition is more subdued under linear prices than under two-part tariffs. This result foreshadows the analysis in our companion article in this issue, which considers another form of price discrimination. There, networks can charge different prices for on- and off-net calls. Again, they can build market share without raising their access deficit. And indeed, an increase in the access charge may then result in a decrease in profit.

Fifth and finally, we discussed various imputation and opportunity-cost interpretations of ECPR in the context of network competition: marginal-cost and average-cost ECPR as well as some competing options. We showed that the standard notions of marginal-cost and average-cost ECPR (which, recall, were designed for other purposes than the one studied here) enable the networks to achieve perfect collusion.

Our model could be used as a backbone for a number of extensions such as nonbalanced call patterns or vertical network differentiation. One prominent extension of our work would figure broader marketing strategies. For example, it can be conjec- tured that an increase in the access charge would lead to a reallocation of marketing resources from the stimulation of call demand (which generates an outflow) toward marketing efforts geared to enlisting new customers (introductory offers, advertising targeted to nonsubscribers). Similarly, one would expect that an increase in the access charge would lead to the targeting of low-volume customers to the detriment of high- volume customers.

Appendix A

* Proof of Propositions I and 2. We prove successively the existence and uniqueness of an equilibrium for a and/or o- small, the monotonicity of p* with respect to a, and then the inexistence of equilibria for a

and/or o- large. A few preliminary lemmas will be useful.

Lemma AI. If (pe, pe) is an asymmetric equilibrium with pe < pe, then pe > pM.

Proof. Equilibrium profits are given by

are = ajieR(pfe) - f ] + Ai i = 1, 2,

with Al + A2 = 0. Mimicking network j would yield network i profit [R(pj) - f]/2; incentive compatibility thus requires that

nie -?[R(pe) - f] i, j = 1, 2, i 7 j. 2

Adding these last two conditions yields

(1 - a2) [R(pe) - R(pe)] 0.

But pe < pe implies ac < 1/2 and, since R(-) is strictly quasi-concave (strictly increasing below pM, strictly decreasing above pM), pe > pM. Q.E.D.

Lemma A2. There exists no "cornered-market" equilibrium.

Proof. Consider for example an equilibrium such that ae = 1 and thus pe < pes, and 7ie = 0. First, pe < pR

would imply ie = R(pe) - f K 0, and thus network 1 would have an incentive to increase its price. (The

only potential problem would arise if this increase in P1 would generate an access deficit. But then network


2 would have an incentive to decrease its own price (down to pR + E, say) to get positive profits.) Second, Pe > pM is impossible, since network 1 could get the entire monopoly profit by reducing its price down to pM. Hence ple < pM. But then, by charging a price slightly above pe , network 2 could get a positive market share and a positive revenue, both from its customers and from access trade. Q.E.D.

The only candidate equilibria are thus such that 0 < ael, ac < 1 and (ve, v) =(v(pe), v(pe)) satisfy

v= r(vie) argmax. *i(vi, vje) for i, j = 1, 2, i 7 j, where

*r(vj, vj) = 5i(vi, vj)[R(vi) -f] - i(vi, vj)6j(vj, vj)(a - co)[4(vi) - 4(vj)]

6i(v , vj) + J(Vi - vj) 2 J

P(v) = [(7- 1)v](n-1), 4(v) q[p(v)] [(,q - 1)v]n/(n-1), R(v) R[p(v)].

Existence of a unique, symmetric equilibrium for a close to co and/or small o-. Assume first a = co. Then

vi = r(vj) X &dR'(vi) + u[R(vi)- f] = 0,

and thus

oR'(vi) u2[[R(v ) -f] ( 2uR'(vj) + &jR"(vj) 2u-2[R(vi)

- f] -&R"(vi)

But R(-) is strictly concave:

)PM - 1 (v)] _ (i - l )p M<0 ["(v) -(,q 1 (v) ] I ['(v)]24(V)

Thus, in the relevant range (R() -f ? 0), 0 ' r'(-) < 1/2, i.e., Ir'( )I < K < 1. This implies that the candidate equilibrium is

(i) symmetric: if ve = r(ve) > ve = r(ve), then

Ve - ve = r(ve) - r(ve) = f r'(v) dv < K(v e - Ve), '2

a contradiction.

(ii) unique: if (Ve, Ve) and (ve, ve) are two symmetric equilibria with 1ve > Ve, then

-e Ve = r(ve) - r(ve) = f r'(v) dv E K(fe - Ve),

another contradiction. The only candidate equilibrium is thus ve = ve = v(p*), solution to

- 1)P = 2o-[R(p*) - f] = 2o- x(p*).

There exists a unique solution to this equation. It satisfies pR < p* < pM and ile = T= T(p*) > 0.

Moreover, in the range (7ri > 0, pR < i(Vi) < pM, i = 1, 2), the profit function *rj is strictly concave in vi:

a2V= &jR"(vi) + 2ouR'(vi) < 0,

and the reaction function satisfies 0 < r'(.) < ?/.

By continuity, for la-co| small enough, candidate equilibria also lie in the range


(T1 > 0, pR <13(vi) < pM, i = 1, 2),

in which the profit function remains strictly concave and the reaction function still satisfies 0 < r'(.) < 1/2.

Therefore, the equilibrium is still unique and symmetric. It is now characterized by

M p p* a- c

O_ 1)P -+ 2* = 2of7(p*)

or

*_(+ a - co)

= -[1 - 2o-7T(p*)]. p 17

Assume next that o = 0. Prices then have no impact on market shares, and

1 A 1 *ri(vi, vj) = -[R(vi) - f] - -(a - co)[4(vi) -(vj)] 2 4

Hence *i(vi, vj) is strictly concave in vi (fri can be rewritten as

[(p(vi) - (c + (a - co)12))4(vi) - f + [(a -co)12]4(vj)]2

and is thus strictly concave in vi as long as c + (a - c)/2 > 0, which is satisfied if

(a - co)/2 2 [(aq - l)/17](pR - pM) = [(a - 1)/17](pR - C),

and moreover r'(.) = 0. Thus again the equilibrium is unique and symmetric. Moreover,

[(71 1)- 1 -]( pTm) > (a - co)/2 2 [(a - l)/17](pR -

pM) = [(a -

l)/rf]pR - C

implies that both operators obtain nonnegative profits. By continuity, for a given access charge a in the above interval, o- small enough, and vi in the range

ensuring nonnegative profits for the chosen access charge, the profit function 7rj remains strictly concave in

vi and there exists K such that I r'(-) I < K < 1. Hence the equilibrium still exists and is symmetric and

unique by the same argument as for a close to co. By continuity also, both operators obtain nonnegative profits at the equilibrium. Q.E.D.

Uniqueness and monotonicity of p* with respect to a. The candidate symmetric equilibrium Pi = P2 P* must in particular satisfy

(i) the first-order condition:

PlP2l =

- [7T (p*) - C0q(p*)] _

uq(p*)Tx(p*)

l q(p*)[ a -co

-2 p*[(I7 1)(pM P*) + 1 2 -P*7T(p*)| =

or p(p*) = -7(a - co)/2, where p(p) (r} - l)(p - pM) + 2op7-(p);

(ii) the local second-order condition:

c32 7Ti 1 [ a- c 2- 2 ?q"(p*)- ouq'(p*)ir(p*)

- 2o-q(p*)7,'(p*)

= 1~(P*)[ 1)((17+ 1)P + + a 2o q7T(p*) + 4c*o ) +

which, using 17(a -c2)/2 = (p*), is equivalent to 2(p*) 2 0, where


+(p)-q - 1 + 2or-i(p) + 4opir'(p); and

(iii) the nonnegativity condition ir(p*) 2 0.

But p'(p) = -q- 1 + 2o-r(p) + 2o-pir'(p) = q/(p) - 2o-pi'(p) is clearly positive if either ir(p) 2 0

and ir'(p) 2 0 (i.e., p C pM), or /1(p) ? 0 and ir'(p) < 0. Hence, on the relevant price domain defined by

?r(p) : 0 and ip(p) ? 0, there is a unique solution p* to p(p*) = 77(a - co)/2, and moreover ap*l/ca > 0.

Nonexistence of equilibria for a or u large. Let us first consider the symmetric candidate equilibrium. It has

already been shown that p* increases with a. Moreover,

ap* 2

da r1 - 1 + 2o-(ir(p*) + p*i'(p*))

is bounded away from zero,32 implying that p* goes to infinity and thus the profit ir(p*) goes to-f when

a tends to infinity. But then, for a and thus p* large enough, each network could instead corner the market

and get a positive profit by charging a reasonable price. More precisely, denote by p* (a) the candidate

equilibrium price for a given fixed cost f and a given access charge. Since o- > v(pM)12, and ap*/da is

positive and bounded away from zero, there exists ao such that v(p* (a0)) = v(pM) - 1/2o-. But then, since p* increases with both a and f, for any f 2 0 and a > ao, v(p* (a)) < v(pM) - 1/2u, implying that each network could corner the market and get the entire monopoly profit by charging pM instead of p* (a).

Let us now take o- to infinity keeping a constant. Note that p* decreases with o- and converges toward pR when o- becomes very large. Moreover, the first-order condition characterizing p* can be rewritten as

a - c 1 +77q + 2o-f +72*- _

P c + 2P*q(p R(p*) = (p* -c)q(p*) f f + + a -

_ o f

p* r + 2o-p*q(p*) 2o- 2p* p *q(p*)'

and by a linear expansion of R(p*) around pR:

R' (pR)(p* - pR) - 77 (PR R c]

A network can instead corner the market by charging a price PI such that v(p,) = v(p*) + 1/20, that is, equal to (up to the first-order in i/o-)

* - 2o-qR

By so doing, it gains

R(p,) - f--[R(p*) - f] = R(p,) - R(PR) -2-[R(p*) -R(pR)] R' (PR)[Pa -pR --(p* -PR)]

= R'(pR) [(p* - pR) - (p* - -[a- - (c 1 - c)]

This deviation is profitable if

a - co > (pM pR).

2 77

From the first-order condition,

32 Because ir(p*) and p*iT'(p*) are bounded above. Indeed, ir(p*) is bounded by IT(pM) and

p*,x'(p*) = (aq

- l)p*(pM - p*). Thus either p* c pM and p*ix'(p*) is bounded above, or p* > pM and it

is negative.


R(p*) - f -1 __ n 2 )]

From a 2 a, c + (a - c)/2 > 0; then for p* > pR,

R(p*) f <+ j [a 2 77 1(PR pM)] < 0 i a - CO-1(R M)

We have covered all possible symmetric equilibria. Let us now consider asymmetric equilibria, and assume pe < pe. Then, from Lemma A1, pe > pM.

From the previous analysis, the equilibrium prices satisfy (using v, = r(vje), i, j = 1, 2, i # j):

Iae[77(c + (1 -a)(a - co)) - (71 - l)pl] = crpe[Ir(pe) + (2a e - 1)(a - co)(ql - qe)]

(1 - ae)[77(c + ae(a - co)) - (71 - l)pe] = rpe[I r(pe) + (2a e - l)(a - co)(qe - qe)].

If p1 goes to infinity with a, then (since P2 ? p2 by assumption) P2 also goes to infinity and both

networks' profits become arbitrarily small (for f = 0) or negative (for f > 0) for a sufficiently large. But

then, as for the symmetric equilibrium p*, each network could corner the market and get the monopoly profit

by charging the monopoly price pM. If p, remains bounded whereas P2 goes to infinity with a, the first-order condition imposes (dropping

terms that remain finite when a goes to infinity)

ae77(l - a )(a - co) = o-pe(2a e - 1)qe(a - co),

which is impossible since ael goes to one and pe remains above pR (otherwise network 1, bearing an access deficit since pe < p2, would get a negative profit). We thus now assume that pe and p2 remain bounded as a

goes to infinity. Adding up the above two conditions yields

71[c + 2a (1 - ae)(a - co)] = u(pe + pe)(2ae - l)(a - co)(qe - qe) + pW[4a (7- 1) + uIT e]

+ p2[(l - '4)(77 - 1) + O-Te].

The last two terms of the right-hand side remain bounded when a goes to infinity. As a goes to infinity, one must therefore have

27 c(4 (1 - ae') o (J(pe + pe)(2ac - 1)(q e - qe).

Either aef (or a subsequence) converges to 1/2, and then pe p~e. The right-hand side then necessarily

converges to zero, yielding a contradiction, unless qe - qe tends to infinity. But, given ple pe , qe -q e

can tend to infinity only if pe and pe tend to zero, which would yield strictly negative industry profits, and

thus each firm would be better off charging a price (slightly above) the Ramsey price. Or a e remains

bounded away from (and above) 1/2. Then qe - qe also remains bounded away from zero, since prices are

bounded above and must remain away from each other. Hence the first term of the right-hand side nec-

essarily goes to infinity with a, which implies that the left-hand side must also go to infinity, contradicting (since qe - qe is bounded away from zero) He IT(pe) - a1(l - al)(a - co)(q e - qe) ? 0 for a large enough.

Now fix a and consider a large o-, and define pa < pM by

1 V(pa) = v(pM) +

1

2ur

Since network 1 could corner the market by charging pa (since p2 > pM), necessarily pe > pa. Moreover, incentive compatibility requires

? R(pa) - f

Together with

1= ae4[R(p') - f] - A1 ? aj[R(pe) - f] ' a[R(pM) - f

this implies


R(p p) - f

R(pM) - f

Thus ae = 1 - ae2 is close to one when o- is large, and thus the profit of the high-price network is close to zero. However, this network could corner the market by charging po' such that v(fr) = v(po) + 1/20u, which itself is close to pM for o- large. Q.E.D.

Appendix B

* Competition in two-part tariffs.

Proof of Proposition 7. Let us first show that no cornered-market equilibrium exists. Suppose that network 1, say, corners the market. Then, Pi = c, 7r, = F1 - f 2 0, and 7r2 = 0. But network 2 could charge P2 = C

and F2 = F1 + E. For E small enough, its profit would then be ft 2 (F2 - f)/2 2 e/2 > 0, a contradiction. We now look for a shared-market equilibrium. In such an equilibrium, condition (13) holds for both

networks and defines functions i(wi, wj). The first-order condition with respect to wi is

- [(pi - c)q(pi) + v(pi) - wi- f] - ai(wi, wj) + [1 - 2ai(wi, wj)]o-[(a - co)[q(pj) - q(pi)]] = 0. awi

(B 1)

Combined with marginal-cost pricing j3i(wi, wj) = c + aj(wi, wj)(a - co) for both networks, (B 1) defines a "pseudo reaction function" wi = w?'(wj). The slope of this reaction function is given by

+ (a - co)o-

( a' a2) dwj aWiaV +aWiap, awiap1

dw~~~ ~ + (a - CO) _ ___

The denominator of the right-hand side is

D = o[(majq'

+ qi- qi)(m-) - 1] - [1 +

2oum(qi -

qj)](o-) + (1 -

2ai)(rm)[q'(-mo) -qj(mo-)]

= m2u2[(aj + 1 -2ai)q' + (1 - 2ai)qj] -2u[1 + mou(qi -qj)],

while the numerator is

N= (-majq')(mo)-

[1 + 2oum(qi -qj)](-o-)

+ (1 - 2ai)(mo-)[q'(mo-)

- q(-mou)]

= m2o02[(aj + 1 -2ai)ql + (1 - 2ai)qj] + o[l + 2oum(qi -qj)].

Hence dwI/dwj = (D + o-)ID is positive and smaller than one if D < -o-, in which case the equilibrium is unique and symmetric. This is in particular the case when a is close to co or o- close to zero, since then D - -2ou < -cr.

Let us now study the second-order conditions. Given network j's strategy (pj, wj- v(p) - Fj), network i's best response entails pi = (wi, wj)- c + (1/2 - o-(wi - wj))(a - co), and so, keeping wj and pj fixed, network i's profit if it chooses to offer wi is

11i(w) = I+ 0-(Wi - Wj))V c + - o- (W - wi))(a - co) wi - f + (I - '(wi - wi))(a - c~~j (2 [( (2 ) 2 ]

First- and second-order derivatives of this function are

= jv + ( (2 - E(w -

wj))(a co)) - wi - f + ( -ur(wi -

wj))(a -

co)q(pj)]

+ (2 + o-(wi - wj))[q(c + 2- (wi - wj))(a - co)) o(a - c0) - 1 - u(a - co)q(p)


d 2o q c (+ - O-(Wi - - co)(a - co) -1- (a - co)q(pj)]

+ (+ wJ(Wi w)) q(c + (-O(Wi-)w) (a- co))(02(a - Co)2)

= -2o- + 2o-2(a- co)[q(pi) - q(pj)] - o-2(a - cO)2aiq'(pi).

Thus for a close to co or o- close to zero, network i's profit function is strictly concave (d2Hli/dw? -2ou). So the candidate equilibrium, which must be symmetric (w =W2 = w) and must satisfy (B1) and (13), that is,

2 ( 2 )+( 2 20) 1

is indeed an equilibrium, yielding a symmetric profit given by

7T1 = 7T2 = c + a c) - w - f + a cq(c + a ?)] = 4

We now show that when a > co and o- high or when o > l/v(c) and a high, no equilibrium exists for a or o high. Since we have already shown that no cornered-market equilibrium exists, we focus on a candidate shared-market equilibrium. It must satisfy p, = fi(w1, w2) and P2 = fi(W2, w1). Then

d 21 d 2112 d +2 = -4o- - u2(a - Co)2(alq'(p1) + a2q'(P2)) dwl dw22

2-4ua + o2(a - CO)2 min (-q'(p)), c5pcc+a-cO

since Pi and P2 lie between c (for ai = 1) and c + a - co (for ai = 0). Hence, for a > co and o- large enough, d2fli/dw? is positive for at least one of the networks, implying that this network would better deviate from the candidate shared-market equilibrium. Therefore, no equilibrium exists for a > co and o- high enough.

Consider now the case o > l/v(c) and a > co. The first-order conditions yield pi = c + (a- c)aj and

vi- wi-f + (a. - ai)(a - co)q, + ai(a - co)qj - i,

and thus

a2 Hi = ai(vi - wi- f + aj(a- c)qj) = (1 - o-(a - c)(qi-qj)).

0'

Assume a, 2 a2. Then q, = q(c + (a - co)a2) q2 = q(c + (a- c)aj) and Ift 2 0 implies

0 ? (a -co)(qI - q2) ? -. 0'

But since q2(<q(c + (a - c)/2)) goes to zero when a tends to infinity, this in turn implies that (a -co)q is bounded above by i/o- when a tends to infinity.

Consider now the following derivation for network i, which consists in cornering the market:

- ~~~1 j3=c and Fj = Fi such that - + o-(v(c)-F -wj) = 1, 2

or using network j's first-order condition for Wj,

Fi = v(c) -2- (Vj -f + (a - c)((ai - aj)qi + afjqj)- )-

Denoting by Gi = Fi - f - i the net gain for network i generated by such a deviation, we have


G1 + G2 = 2v(c) -v - V2- (a - c)[(al - a2)(q1 - q2) + a1q, + a2q2] - a+ 0'

+ (a -co)(a 2- a2)(q1 - q2)

a 2 + a2 = 2v(c) -v 1 -V2 _ - (a - c)(alql + a2q2).

But as noted above, when a goes to infinity, both q1 and q2 (and thus v, and v2) are necessarily close to zero and (ac + a22)/o- is moreover bounded above by i/o-. Hence, for a large enough,

G1 + G2 ? 2(v(c)-

Thus, if o- > 1/v(c), at least one of the two networks has an incentive to deviate from any candidate

equilibrium for a large enough. Q.E.D.

References

ANDERSON, S., DE PALMA, A., AND NESTEROV, Y "Oligopolistic Competition and the Optimal Provision of Products." Econometrica, Vol. 63 (1995), pp. 1281-1302.

ARMSTRONG, M. "Network Interconnection." Mimeo, 1996. - DOYLE, C., AND VICKERS, J. "The Access Pricing Problem: A Synthesis." Journal of Industrial

Economics, Vol. 44 (1996), pp. 131-150. BAUMOL, W., ORDOVER, J., AND WILLIG, R. "Parity Pricing and Its Critics: A Necessary Condition for Effi-

ciency in the Provision of Bottleneck Services to Competitors." Yale Journal of Regulation, Vol. 14 (1996), pp. 145-163.

BEAUDU, A. "Etude de la d6r6glementation du secteur des tel6communications." Mimeo, CREST, Paris. 1996.

CARTER, M. AND WRIGHT, J. "Interconnection in Network Industries." Discussion Paper no. 9607, University of Canterbury, Christchurch, New Zealand, 1996.

Congressional Quarterly. "Special Report. The Fine Print: A Side-by-Side Comparison of the House and Senate Telecommunications Bills." Washington, D.C., September 23, 1995.

DOGANOGLU, T. AND TAUMAN, Y. "Network Competition with Reciprocal Proportional Access Charge Rules." Mimeo, SUNY at Stony Brook and Tel-Aviv University, 1996.

ECONOMIDES, N. "Desirability of Compatibility in the Absence of Network Externalities." American Eco- nomic Review, Vol. 79 (1989), pp. 1165-1181.

AND WHITE, L. "Networks and Compatibility: Implications for Antitrust." European Economic Re- view, Vol. 38 (1994), pp. 651-667.

AND WOROCH, G. "Interconnection and Foreclosure of Competing Networks." Mimeo, 1995a. AND . "Strategic Commitments in the Principle of Reciprocity in Interconnection Pricing."

Mimeo, 1995b. FARRELL, J. AND SALONER, G. "Standardization, Compatibility, and Innovation." RAND Journal of Economics,

Vol. 16 (1985), pp. 70-83. FUDENBERG, D. AND TIROLE, J. "The Fat-Cat Effect, The Puppy-Dog Ploy, and the Lean and Hungry Look."

American Economic Review, Papers and Proceedings, Vol. 74 (1984), pp. 361-368. HAUSMAN, J. "Proliferation of Networks in Telecommunications." Mimeo, MIT, 1994. KAHN, A. AND TAYLOR, W. "The Pricing of Inputs Sold to Competitors: A Comment." Yale Journal of

Regulation, Vol. 11 (1994), pp. 225-240. KATZ, M. AND SHAPIRO, C. "Network Externalities, Competition, and Compatibility." American Economic

Review, Vol. 75 (1985), pp. 424-440. LAFFONT, J.-J. AND TIROLE, J. "Access Pricing and Competition." European Economic Review, Vol. 38

(1994), pp. 1673-1710. AND . "Creating Competition Through Interconnection: Theory and Practice." Journal of

Regulatory Economics, Vol. 10 (1996), pp. 227-256. , REY, P., AND TIROLE, J. "Network Competition: II. Price Discrimination." RAND Journal of Eco-

nomics, Vol. 29 (1998), pp. 38-56. , AND . "Network Competition." IDEI Working Paper no. 65, 1997.

MASMOUDI, H. AND PROTHAIS, F "Access Charges: An Example of Application of the Fully Efficient Rule to Mobile Access to the Fixed Network." Mimeo, Ecole Polytechnique and France Telecom, 1994.

MATUTES, C. AND REGIBEAU, P. "'Mix and Match': Product Compatibility Without Network Externalities." RAND Journal of Economics, Vol. 19 (1988), pp. 221-234.


NEW ZEALAND MINISTRY OF COMMERCE AND TREASURY. "Regulation of Access to Vertically-Integrated Natural Monopolies." Discussion Paper, mimeo, 1995.

OFTEL. "Pricing of Telecommunications Services from 1997 (Consultative Document Issued by the Director

General of Telecommunications)." London, 1995. SCHWARTZ, M. "Telecommunications Reform in the United States: Promises and Pitfalls." In P Welfens and

G. Yarrow, eds., Telecommunications and Energy in Systemic Transformation. Berlin: Springer, 1997. TAYLOR, L.D. Telecommunications Demand in Theory and Practice. Boston: Kluwer Academic Publishers,

1994.

TIROLE,- J. The Theory of Industrial Organization, Cambridge, Mass.: MIT Press, 1988. WILLIG, R. "The Theory of Network Access Pricing." In H.M. Trebing, ed., Issues in Public Utility Regu-

lation. Lansing, Mich.: Michigan State University, 1979.

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