Competition in the Pay-TV Market

Journal of the Japanese and International Economies13, 257–280 (1999)Article ID jjie.1999.0434, available online at http://www.idealibrary.com on

Competition in the Pay-TV Market∗

Mark Armstrong

Nuffield College, Oxford OX1 1NF, United Kingdom

Received February 16, 1999; revised September 13, 1999

Armstrong, Mark —Competition in the Pay-TV Market

This paper discusses competition in the emerging pay-TV market. Economic features ofthe industry are described, and the current state of the market in the UK is summarized. Twosimple formal models of the industry are analyzed: First the danger of two vertically inte-grated pay-TV networks entering into collusive agreements to exchange programming witheach other is discussed; second, the private and social incentives for signing exclusive con-tracts for premium programming are analyzed.J. Japan. Int. Econ., December 1999,13(4),pp. 257–280. Nuffield College, Oxford OX1 1NF, United Kingdom.c© 1999 Academic Press

Journal of Economic LiteratureClassification Numbers: D43, L13, L41, L82.

1. INTRODUCTION

Over the past 10 years pay-TV has played an increasingly important part inthe broadcasting industry.1 Recent advances in digital technology will mean anacceleration of this process, and consumers will shortly have a choice of watchingfrom several hundred possible channels as well as participating in various inter-active services. But as the market grows, the danger of anti-competitive conductgrows with it, and care needs to be taken that the full benefits of the revolutionare realized. The next sections provide a description of the industry and a shortaccount of the market in Britain. Then in Sections 2 and 3 I suggest theoreticalframeworks for thinking about two potentially important policy problems: (i) thedanger of pay-TV retailers acting collusively by setting high reciprocal charges for

∗ I am very grateful to Peter Culham, Benny Moldovanu, Sadao Nagaoka, and an anonymous refereefor several helpful comments and corrections. All remaining views and errors are my own.

1 Viewers always pay for TV services in some form, whether by an annual licence fee, by watchingadvertising, by monthly subscription, or by “pay-per-view.” In this paper the term “pay-TV” means thesituation in which TV services can only be viewed in return for money payment.

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0889-1583/99 $30.00Copyright c© 1999 by Academic Press

All rights of reproduction in any form reserved.

258 MARK ARMSTRONG

programming, and (ii) the likely private benefits and welfare losses of exclusivecontracts for premium programming. Brief concluding comments are contained inSection 4.

1.1. A Description of the Pay-TV Industry

Over-simplifying somewhat, there are three layers in the pay-TV industry: (i) theproduction of original programming, (ii) the retailing of programming to con-sumers (together with the possible wholesaling of programming to rival retailers),and (iii) the delivery (or distribution) of programming to consumers. For simplicity,we include within the program production sector various monopolized inputs suchas sports rights and movie rights (these scarce resources being termed “premium”programming). The retailing sector buys programming from producers, and possi-bly from rival retailers at the wholesale level, and packages these in various waysfor sale to consumers. Naturally there may be vertical integration between produc-tion and retailing, and a retailer may make some of its programs in-house (mostlikely the “basic,” or non-premium, programs). The delivery sector provides thetransmission system through which retailers supply their services to consumers.Broadband cable, encrypted satellite, and encrypted terrestrial broadcast are thethree current delivery systems.2 Naturally, there may also be vertical integrationbetween retailing and delivery.

A central ingredient of the industry is the encryption system, together withthe “set-top box” used by consumers to decode the scrambled signal. There areseveral different encryption systems currently in use throughout Europe, and itis possible that a set-top box designed for one system is not compatible withanother. It is usual to refer to the encryption/set-top box technology as “condi-tional access technology.” As well as the basic encryption software and hardware,associated functions of the conditional access provider might include subscriberbilling systems and the electronic program guide (the latter will be of increas-ing importance as the multitude of channels grows). Digital terrestrial televisionhas recently been launched in parts of Europe, and this includes many of the ba-sic free-to-air services currently broadcast using analogue technology togetherwith new subscription channels. Both types of services require a set-top box(or a new integrated digital television), but the former need not require condi-tional access technology (since viewers make no payment, at least for the timebeing).

Of most relevance for economic policy toward the industry are the areas wherethere are actual or potential bottlenecks. Obvious examples in the production sec-tor include premium program production (e.g., the football Premier League in theUK or a newly released film). If these premium programs are sold using exclusive

2 A major difference between satellite and the other delivery technologies is that, roughly speaking,satellite can only deliver a nationwide service whereas cable and terrestrial can tailor program deliveryto local areas. This fact is often used to help explain the relatively poor performance of satellite versuscable in the United States.

COMPETITION IN THE PAY-TV MARKET 259

contracts to retailers, then market power is extended into the retailing sector. How-ever, it is an open question whether exclusive contracts are really the most profitablestrategy for premium program producers (especially for pay-per-view retailing),and it may be that as competition in retailing becomes more entrenched a producerwill prefer to offer a program toall retailers at a fixed price per viewer.3 This issueis discussed later in Section 3.

In the delivery sector there are important resource constraints for each of thethree main transmission media. Economies of density mean that it is probablyunlikely, at least in the UK, for there to be more than one new cable operator inany local area (although BT may choose to upgrade its telecom network to providebroadcast services when it is permitted by the government to do so). Radio spectrumand transponder capacity on suitable satellites is limited, which puts a ceiling onthe number of channels that may be delivered by satellite. Finally, the spectrumfor terrestrial broadcasting is also limited. However, it is one of the main impactsof the new digital technology that spectrum and transponder constraints are nowmuch less of an issue than they were 10 years ago, and a country like the UK willshortly have hundreds of channels.

A more subtlepotentialbottleneck is the conditional access technology. Giventhat the decoding equipment (set-top box) will continue to be a costly item (al-though retailers may choose to subsidize these to consumers), it seems unlikelyand undesirable for a consumer to possess more than one such device. Therefore, ifa consumer’s retailer controls whether the box is also used to access other retailers’services then the retailer may—if free to do so—choose to forbid rival retailers ac-cess to its consumers. The extreme case of this would be if each consumer decidedto get all pay-TV services from a single retailer and there was no joint supply. Inthis case a retailer has a monopoly over the supply of programs to its consumers.

1.2. The Industry in Britain

The pay-TV industry in Britain started in 1989 when two satellite-based net-works, Sky and British Satellite Broadcasting (BSB), were licensed.4 The twocompanies used different satellites, and separate satellite dishes were needed toreceive the two signals. Sky managed to launch its initial four channels more than ayear earlier than BSB, the latter having a series of delays and not fully launching un-til mid-1990. Both companies attempted to woo subscribers by obtaining exclusivemovie rights from Hollywood studies, often for very high fees. In the event, BSBdid not manage to make up its lost ground against Sky, and Sky merged with BSBin late 1990, the combined operation being named BSkyB. As Rupert Murdoch,

3 To take an extreme example, when Hollywood studios make deals with video rental retailers, theydo not sign exclusive contracts (e.g., of the form whereby the latest Disney film will only be availablethrough the Blockbuster chain of video stores). Similarly, while some Internet service providers suchas Microsoft and America Online have offered exclusive content for their own subscribers, this is aninsignificant part of the market.

4 For a general account of the development of pay-TV in Britain, see Horsman (1998). For a morespecialized account, see MMC (1999, especially Chap. 4).

260 MARK ARMSTRONG

TABLE IDevelopment of Pay-TV in the UK

1994 1996 1998

Number of subscribers to pay TV (millions) 3.45 4.9 6.15BSkyB (satellite) market share of subscribers (%) 73 65 56Cable market share of subscribers (%) 27 35 44

the principal owner of Sky and then BSkyB, is reported to have said, “When [BSBfinally] did start, there were two kinds of technologies, offering the same programsbasically. We both had sports and movies. And the market just dried up. Everybodywas waiting to see who would win. No one wanted to buy the losing system, orhave to end up buying two systems” (quoted in Horsman, 1998, p. 55).

Cable TV companies also started in earnest around 1990, these being com-panies granted regional monopoly franchises to provide TV (and telecom) ser-vices over new, largely broadband networks. Until recently, the cable industry washighly fragmented—see Monopolies and Mergers Commission (MMC) (1995,Appendix 4.1) for details—and this may explain why it was unable to be an ef-fective player in the market for programming against BSkyB. However, there hasbeen some recent consolidation in the industry, and in 1998 three cable companies(CWC, Telewest, and NTL) served 95% of all cable subscribers—see MMC (1999,para. 4.41). Cable franchises have not been awarded across the whole country, andcompanies have not yet fully built networks to serve their franchise areas, so that50% of households do not currently have the option of obtaining services fromcable companies.

In sum, given the satellite merger, by 1991 there were just two providers of pay-TV, BSkyB and the regional cable companies. Table I gives some basic statisticsfor the UK pay-TV industry in terms of the two delivery systems.5 Thus we see thatthe number of households taking pay-TV has increased dramatically over these sixyears and that the market share of satellite TV has gradually fallen—though it isstill very substantial—as cable networks have expanded their networks. However,BSkyB reports (MMC, 1999, para. 4.69) that in cable-active areas—i.e., wherethere is a choice of pay-TV delivery systems—it obtains a share of pay-TV homesof only up to 34%.

BSkyB is the main provider of programs in the pay-TV market and sells itsprograms to cable operators as well as retailing these itself. BSkyB owns the UKnon-terrestrial rights for the output of major Hollywood studios and many keysporting events such as the football Premier League. Wholly owned BSkyB chan-nels (Sky 1, Sky News, film and sports channels, and so on) account for 43% oftotal cable and satellite viewing hours, and all independent channels have a tinymarket share.6 However, the share of viewing hours is not necessarily an accurate

5 See MMC (1999, Table 4.4).6 See NERA (1998, Table 3.4) for more detail.


measure of market power, and there is evidence that premium programming, whereBSkyB currently holds an extremely strong position, is the major driver of sub-scription. Indeed, a recent survey reported that 79% of subscribers cited premiumprogramming as their original reason for joining.7

The terms and procedures with which BSkyB obtained its all-important exclu-sive premium programming is worth discussing further, partly because they arerelevant for the theoretical models developed later in the paper. (See Horsman(1998, Chap. 5) for more detail.) In the early days of rivalry between the twosatellite systems of Sky and BSB, each company was keen to obtain exclusivemovie rights from Hollywood studios, and contracts were arranged before ser-vices were launched. Sky had won the Fox contract (Murdoch was the owner ofFox) as well as Warner and Disney, and BSB had the remaining contracts fromColumbia, MGM, Paramount, and Universal. The two firms were contracted topay Hollywood about $1.2 billion over five years, with most contracts lasting 10to 15 years. The contractual form was a mixture of lump-sum fees per film andper-subscriber charges. Typically the lump-sum element was around $750,000 perfilm, which had to be paid regardless of the number of subscribers signed up for therelevant movie channel. Although not the sole reason for the poor financial healthof the two companies, these contracts were an important factor in the enormouslosses each firm was running and which led the two firms to merge in 1990. (Themovie contracts were subsequently renegotiated with the Hollywood studios, andterms reached that were much reduced.)

Football was the second strand in BSkyB’s strategy to attract subscribers. Rightsto broadcast football had previously been “shared” between the free-to-air terres-trial broadcasters, and the football teams themselves had received very little money,despite the sport’s popularity. For instance, the annual rights fee for the top divisionmatches in the 1980s was around just£3 million—see MMC (1999, Table 4.23)for this and related data. In May 1992 the rights to screen top-level football weredue to be assigned for the subsequent five years, but now with BSkyB as one ofthe bidders. The cable companies showed no interest in bidding for these rights,perhaps because of the fragmented nature of the industry in its early years or be-cause the industry initially decided to focus on the telecom and infrastructure sidesof its business. But for whatever reason, the cable companies from an early stageseemed content to act purely as delivery companies, and to purchase virtually allpremium content at the wholesale level from BSkyB.

For the purposes of obtaining the 1992 football rights, BSkyB formed a partner-ship with the BBC, the latter planning to show match highlights in the evenings.Therefore, the battle for rights was between BSkyB/BBC and the advertising-funded free-to-air terrestrial broadcaster (ITV). In any event, BSkyB just won therights with an annualized rights fee of£38 million (MMC, 1999, Table 4.23),roughly a tenfold increase in annual income for the top football clubs comparedto the previous decade. This was a “lump-sum” contract and did not include any

7 Source, ITC, “Television, The Public’s View,” 1997. See also MMC (1999, Table 4.7).

262 MARK ARMSTRONG

per-subscriber element (as did the earlier movie rights, for instance). When therights were sold again in 1997, competition was even stiffer, with three seriousbids being considered by the Premier League (Horsman, 1998, Chap. 9). Therights were again sold on an exclusive, lump-sum basis, and again they were wonby BSkyB, this time for the sharply increased figure of£167 million per year.Although in both the 1992 and 1997 bidding rounds it was taken for granted thatrights would be exclusive, other details of the contracts were left to the bidders tochoose, with the Premier League choosing the most desirable offer on the table.For instance, in 1997 the three bidders differed greatly in their contractual specifi-cations: BSkyB’s bid was for 4 years and was on a purely lump-sum basis; a secondbid was for 5 years and included an element related to the bidder’s profitability;the third bid was for 10 years and included an element related to the number ofsubscribers—see MMC (1999, para. 4.139).

From early on there have been controversies over the wholesale terms at whichBSkyB offered its premium programming to rival cable networks. (This was de-spite the fact that the cable networks could equally well have bid for premium rightsbut chose not to do so.) BSkyB offered a complex tariff scheme (the so-called “ratecard”) for its wholesale programming, which for instance involved discounts de-pending on the proportion of a cable network’s subscribers who choose to takeBSkyB’s premium programs—see Office of Fair Trading (1997) and Oftel (1997b)for more details. However, to a first approximation, wholesale fees for program-ming were on a per-subscriber basis, and not, for instance, on a lump-sum basis.In the next section, where wholesale programming markets are discussed, we willassume this per-subscriber form of contract.

In 1997 licences were awarded to provide terrestrial digital pay-TV. The mainpay-TV licence, which was for three-quarters of the available new channels, wasbid for by British Digital Broadcasting (a consortium of BSkyB and two existingterrestrial companies, Carlton and Granada) and DTN (wholly owned by the cablecompany NTL). The main worry with the former bid was the involvement ofBSkyB, and the concern was that this would mean the consortium would notcompete effectively against BSkyB for premium programming rights, for instance.In the end, the ITC preferred the bid offered by BDB over that of DTN but insistedon the removal of BSkyB from the consortium. The resulting entity has beengiven the brand name ONdigital.8 ONdigital has, from its start, been much moreinvolved in obtaining its own programming than has been the case with the cableindustry, and has its own basic programming (supplied by the terrestrial owners,Carlton and Granada) as well as exclusive rights to European UEFA football leaguematches.9

8 For more detail on the competition issues arrising from the involvement of BSkyB in terrestrialdigital, see Oftel (1997a).

9 The rights fees for this per match are apparently close to those paid by BSkyB for the PremierLeague matches—see MMC (1999, para. 5.27).


2. COMPETITION IN THE PAY-TV MARKET: VERTICAL INTEGRATION

In this section we consider a drastically simplified model of the pay-TV industry.Specifically, we suppose that TV networks each produce programs “in-house,”which they may sell to each other, and there is no outside market for programs.Thus the model is one of complete vertical integration between program supplyand production. An alternative interpretation might be where exclusive contracts topremium programming have already been secured, perhaps as currently in the UKwhere one firm has exclusive rights to one sporting event and another has rights toa second (BSkyB has the Premier League and ONdigital has the UEFA league).An analysis of the market for independent premium programming is postponed toSection 3 below.

There are two symmetrically placed broadcasters, A and B, who each producea differentiated set of programs and who deliver programs. As well as any fixedcosts involved in program production, there is a fixed per-subscriber connectioncostk comprising the cost of digital decoders, satellite dishes, cables to the home,and so on. Once programs have been produced the marginal cost of supplying themto a subscriber is zero (provided that the per-subscriber costk has been incurred).All subscribers have the same tastes for the programs, and they obtain gross utilityu1 when consuming a single set of programs (the same utility for the programs ofA or B), and gross utility ofu2 when consuming both sets of programs. Utility isquasi-linear, so ifp is the price paid for programs, net utility is justui − p (wherei = 1 or 2). Thus firms are symmetric, in the sense that connection costs are thesame and consumers derive the same utility from both separate sets of programs.It is natural to suppose that

u1≤ u2≤ 2u1. (1)

(The left-hand inequality implies that the incremental utility from consuming afurther set of programs is non-negative, and the right-hand side implies that thereare no economies of scope in joint consumption, so that programs are substitutesrather than complements.) We assume throughout thatk< u2 so that maximumconsumer utility is greater than the minimum cost of supply. In order to ensurean elastic response on the part of consumers, suppose that the outside option ofconsumers—that is, the utility they obtain if they do not purchase any pay-TVservices—varies across consumers.10 If the outside option of a consumer isθ , say,then suppose thatθ is distributed across consumers with the distribution functionF(θ ). Therefore, if the maximum net utility available in the pay-TV market isv,the fraction of consumers who buy is justF(v). (We introduce this parameter inorder to have a negative welfare impact of high prices, as seems natural.) Thefollowing simple example may help fix ideas throughout this section:

10 We could think of this outside option as the opportunity cost of the time they spend watchingpay-TV, which might otherwise be spent on other activities (including watching free-to-air broadcastservices).

264 MARK ARMSTRONG

EXAMPLE. u2 = 1, k = 12, andθ is uniformly distributed on [0, 1].

We will consider three kinds of regime, one where firms supply only theirown programs to subscribers (termedno interconnection) and two others wherenetworks are “interconnected” in some sense. The two kinds of interconnectionconsidered arewholesale interconnection, in which firms supply each other withtheir programs at the wholesale level (so that each firm retains control over retailpricing decisions to customers), andcustomer interconnection, in which firmsare granted access to each other’s customers (so that the firm which producesthe relevant programs retains retail pricing control on these programs to the rivalnetwork’s customers). In the two cases of interconnection we refer to the chargethat one firm makes to the other for (i) rights to its programs (in the case ofwholesale interconnection) or (ii) rights to its customers (in the case of customerinterconnection) as the “access charge.”

We model pricing decisions in a two-stage manner and suppose that the twofirms first negotiate over the access charge and then choose their retail tariffs non-cooperatively given this charge. Because the industry is assumed to be symmetric,it makes sense to assume that the access charge is the same in each direction.Given this, negotiations are straightforward as we will see that firms have the sameincentives when choosing the symmetric access charge.11

Before analyzing the three cases below, for reference we note that the jointprofit-maximizing outcome is obtained by (i) each customer being connected tojust one firm so that there is no duplication of fixed costs and (ii) firms each offeringboth sets of programs in a bundle for a pricep∗, where

p∗ maximizesF(u2− p)(p− k). (2)

In the above example, it is easily shown thatp∗ = 3/4, and 25% of the potentialmarket subscribes to pay-TV at the profit-maximizing price. In general, collusiveindustry profits areF(u2− p∗)(p∗ − k). Throughout this section we make thetechnical assumption that the functionF(u2− p)(p− c) is single-peaked inp (foreach value ofc) so that we may use first-order conditions.

On the other hand, given that programs have already been produced, the first-best welfare outcome involves all consumers being offered both sets of programsat marginal cost, i.e.,p= k. However, this will not cover the fixed costs of pro-gramming (and other overheads), so the second-best welfare outcome is the lowestprice that covers these overheads—given that the collusive pricep∗ in (2) allowspositive profits, the second-best price is lower thanp∗.

No interconnection. Here each firmi sets its pricepi for watching only itsown programs—see Fig. 1. There are then two cases to consider:

11 If firms also choose access charges non-cooperatively, it is intuitve that they will generally settoo high a charge, both in terms of joint profits and in terms of overall welfare—see the analysis inArmstrong (1998) and Laffontet al. (1998) for more details in the telecommunications context.


FIG. 1. No interconnection.

Case 1: k> u2 − u1. Here firms do not find it profitable to serve the secondunit of demand (i.e., if the rival firm supplies programs to a consumer, a firm cannotprofitably serve that consumer as well). Therefore consumers go to either one firmor the other (but not both). Since consumers gain the same utility from the programsof each firm, price is bid down to marginal cost, so thatp= k. In the above example,since it is required thatu1> u2/2, the parameter values automatically ensure thatthis case is the relevant one.

Case 2: k< u2−u1. Suppose firm B sets the pricepB> u2− u1. Then, sinceits price is above marginal utility, no one buys its product if they have alreadybought A’s. Since A’s best response must involve attracting subscribers, B will notobtain any subscribers with this high a price, so it cannot be part of an equilibriumstrategy for a firm to set its price aboveu2− u1. Suppose next thatpB≤ u2− u1.Then any consumer who buys from A will also buy from B, so A will choosepA

to maximizeF(u2− pA − pB)(pA − k) subject topA ≤ u2− u1 (otherwise no onewill buy from A). The equilibrium therefore involves both firms choosing the pricek< p≤ u2− u1 defined recursively by

p = arg maxp≤ u2−u1

: F(u2− p− p)(p− k).

Here, because firms have market power—they have positive consumer demand ifthey charge a price up to (u2−u1)—firms now make strictly positive profits, whichin total are equal toπ = 2F(u2− 2p)( p−k). (Of course these profits are less thanthe collusive profits above.)

266 MARK ARMSTRONG

FIG. 2. Wholesale interconnection.

Wholesale interconnection.Suppose now that the two firms agree to supplyeach other with their own programs. Specifically, suppose that for an “accesscharge” ofa per subscriber a firm may purchase the other firm’s programs. (Notethat we assume that the interconnection contract takes the form of a per-subscribercharge, rather than, say, a lump-sum payment for the rights to programs. Thiscorresponds roughly to how wholesale rates are set in the UK, as discussed above.)Given the symmetry of the industry, it makes sense to suppose that firms agreethat the access charge is the same in each direction, i.e., the charge is “reciprocal.”Figure 2 illustrates this case.

Given a particular choice of access charge we assume that prices in the retailsector are chosen non-cooperatively.

The following simple result shows that firms will buy each other’s programs ifand only if the access charge is no greater than consumers’ willingness-to-pay forthe extra set of programs:

LEMMA 1. (a)Suppose that the reciprocal access charge satisfies a> u2− u1.

Then in equilibrium neither firm buys the rival’s programs, and equilibrium is justas in above the “no interconnection” case.

(b) If a≤ u2− u1 then any firm active in the retail market buys its rival’s pro-grams.

Proof. Each firm has three options: (i) sell both sets of programs directly toconsumers, (ii) sell only its own programs directly to consumers, or (iii) sell itsown programs only to the rival firm. Suppose a firm is active in the retail sector, i.e.,it follows strategy (i) or (ii), and that it wishes to offer net utilityu (for instance,to attract consumers from its rival’s service). What is the most profitable way to


generate this level of utility? If it follows strategy (i), it can make profits equal to

u2− u− k− a,

whereas if it follows strategy (ii) it makes profits of

u1− u− k.

The latter is strictly greater than the former if and only ifa > u2−u1. This proves(b).

We have also proved that strategy (iii) cannot be profitable ifa > u2− u1 sincethere is no demand at the wholesale level. Therefore, equilibrium whena > u2−u1

is as described in the “no interconnection” section above.

The next result shows how the access charge feeds through into equilibriumretail prices for moderate levels ofa:

LEMMA 2. Suppose that the reciprocal access charge satisfies

a≤min

{u2− u1,

1

2(p∗ − k)

}(3)

(where p∗ is the collusive retail charge in(2), above). Then equilibrium in theretail sector is given by each firm offering both sets of programs for a charge ofp= 2a+ k. Each firm makes profit equal to

π (a) = F(u2− 2a− k)a. (4)

Proof. Suppose firm B offers its subscribers both sets of programs for thechargep= 2a+ k. If A offers the same tariff, then all participating consumerswill go to one or the other firm and each firm makes profita from each of theseconsumers, either by serving the consumer directly, chargingp= 2a+ k and in-curring the cost (k+a), or by supplying programs to the rival for a charge ofa.Then firm A can certainly guarantee itself a total profit equal toF(u2− 2a− k)a.

However, there is no way the firm can make strictly greater profits. To see thisconsider three possibilities: (i) subscribers buy both sets of programs from B,(ii) subscribers buy both sets of programs from A, or (iii) subscribers only buy A’sprograms (from A). Clearly A’s profit in case (i) is justF(u2− 2a− k)a, since nocosts are incurred and A makesa per subscriber from selling its programs to B.With case (ii) A must offer a pricep no greater than B’s pricep= 2a+ k in orderto attract subscribers from B, in which case it makes profitF(u2− p)( p−a− k).But the functionF(u2− p)( p−a− k) is maximized at some price greater thanp∗, and from the assumption that the function is single-peaked inp we deduce thatit is increasing over the rangep≤ 2a+ k≤ p∗. (The second of these inequalitiesfollows from the assumption ona.) Therefore A makes strictly lower profits bystrictly undercutting B. Finally, strategy (iii) is never optimal givena≤ u2 − u1

from Lemma 1 above. In sum, A cannot do better in response to B’s strategy than

268 MARK ARMSTRONG

to offer both sets of programs for a price ofp= 2a+ k, which establishes theresult.

The market shares of the two firms are indeterminate since they both offer thesame price for services that are perfect substitutes, but the profits obtained by thetwo firms do not depend upon the market shares.

Since the profit function is single-peaked, each firm’s profitπ (a) in (4) is in-creasing over the range 2a+ k≤ p∗, and if 2a+ k= p∗ then the collusive outcomeis attained. Therefore, if parameters in the industry are such that the right-handside of (3) binds first, i.e., if

u2− u1 ≥ 1

2(p∗ − k), (5)

then firms can induce the collusive outcome by choosing the highest possibleaccess charge in (3). We summarize this in the following result:

PROPOSITION1. Suppose industry parameters satisfy(5) above. Then firmswill agree to set the reciprocal access charge

a∗ = 1

2(p∗ − k),

which induces the collusive price p∗ as the equilibrium in the retail market.

Condition (5) is required to ensure that a firm has no incentive to “bypass”the other firm’s programs at the optimal access charge by supplying only its ownprograms to subscribers. To see this, we can rewrite the condition as

p∗ − 1

2(p∗ − k)− k ≥ [ p∗ − (u2− u1)] − k.

The left-hand side of this is the profit per subscriber it makes from selling bothprograms at the pricep∗, and the right-hand side is the profit it could make bybypassing the other’s programs. (Here, the term in [ ] is themaximum price the firmcould charge if it were to supply only one set of programs.) In the above example(5) holds provided thatu1< 7/8, which holds unless the two sets of programs arevery close substitutes, and the profit-maximizing access charge isa∗ = 1/8.

Note that it is important for the access charge to be levied on a per-subscriberbasis, since the charge then affects the marginal cost of serving subscribers—iffirms just levied a lump-sum charge for the rights to screen each other’s programthen marginal costs would not be affected and collusion could not be sustained.12

12 If firms did offer programs on a lump-sum fee basis, we would face the technical difficulty thatno equilibrium would exist (that covers the lump-sum cost): since firms offer perfect substitutes andtheir marginal cost is justk, they must set prices equal tok, which does not cover the lump-sum chargemade for programs.


The insight that firms have an incentive to set a high mutual access chargein order to sustain collusion in the retail sector is similar to that obtained in thetelecommunications setting by Armstrong (1998) and Laffontet al. (1998). Bycharging a high (but not too high) access charge, each firm is willing to buy therival firm’s programs, which increases its cost of supply fromk to k+a. Thissustains high prices in the retail sector at the collusive level. The analysis in theearlier papers demonstrated that it was necessary for the rival products to not betoo closely substitutable if collusion was to be sustained, and the same conditionis required in this context. Condition (5) requires thatu1 not be too close tou2,which would be violated if the two sets of programs were close substitutes (i.e., ifu2≈ u1).

On the other hand, if (5) is violated then the best that the firms can do is to seta∗ = u2 − u1, which yields retail prices below the collusive level. (If they set ahigher access charge than this, then Lemma 1 shows that neither firm buys eachother’s programs, and the profits are as in the “no interconnection” case, whichare certainly lower than those with this choice of access charge.) Thus even if (5)does not hold then firms can still manipulate the access charge to increase profitsabove the no-interconnection level.

Customer interconnection.Finally, suppose that the two firms agree to granteach other access to their own customers. Specifically, suppose that for an accesscharge ofa per customer one firm may use the other firm’s delivery system todeliver its own programs to the rival’s customers. Again, given the symmetry itmakes sense to suppose that this charge is the same in each direction. Now, firmA, say, chooses two retail prices,pA

1 , which is the price for watching A’s programsif the customer connects to A’s network, andpA

2 , which is the charge for watchingA’s programs if a customer is connected to B’s network. See Fig. 3.

The following result shows how the access charge affects the balance betweenthese two prices but not the overall profits obtained (at least for levels ofa whichare not too great). Definep to be the price that satisfies the first-order condition

2F(u2− p)− F ′(u2− p)( p− k)= 0.

Note thatp is the price satisfying the recursive relation:

p= arg maxp

: F(u2− p)(2p− p− k).

Most importantly for this analysis, the first-order condition implies thatp> p∗,so that the pricep is above the collusive price.

PROPOSITION2. Suppose that

a≤ [u2− u1] − 1

2[ p− k] . (6)

270 MARK ARMSTRONG

FIG. 3. Customer interconnection.

Then equilibrium in the retail sector is given by each firm offering the price

p∗1=1

2( p+ k− 2a),

for watching its own programs and being connected to its network, and the price

p∗2=1

2( p+ 2a− k)≤ u2− u1,

for watching its own programs if connected to the rival network. Customers watchboth sets of programs at the combined price

p∗1+ p∗2= p,

which is above the collusive price.

Proof. Suppose firm B offers this pair of prices.Suppose first that firm A also offers this pair of prices. Since the bound (6)

implies thatp∗2≤ u2 − u1, if a customer buys at all she will buy both programs.Firm A then makes a profit of (p− k)/2 from each active consumer and makes atotal profit of F(u2 − p)( p− k)/2. (As in the wholesale interconnection case, itis indeterminate which customers choose to connect to A, but the firm makes thesame profit whether a customer connects to it or whether the customer connectsto B and buys A’s programs indirectly.)

We next show that the firm cannot get higher profits by offering a different pairof retail prices, sayp1 andp2. It has two possible strategies: (i) it serves all active


customers itself and sells both sets of programs, or (ii) B serves all active customersand A sells these customers its own programs.

With (i) we must havep1+ p∗2≤ p∗1+ p2, in which case it makes total profit of

F(u2− p1− p∗2)(p1+a− k)= 1

2F(u2− p)(2p− p− k),

where we have writtenp= p1+ p∗2. From the definition ofp, the right-handside of the above is maximized by settingp= p, i.e., settingp1= p∗1. Thus it isnot profitable for A to deviate if it follows strategy (i). With (ii) we must havep∗1+ p2≤ p1+ p∗2, in which case it makes a profit of

F(u2− p∗1 − p2)(p2− a)= 1

2F(u2− p)(2p− p− k),

wherep= p∗1+ p2. Thus, as above, it is optimal to setp= p, i.e., to setp2= p∗2,and no deviation is superior.

Provided that the right-hand side of (6) is positive—which, sincep> p∗, is astronger condition than (5) above—we see in particular that an access charge ofzero (which is the marginal cost of providing access in this model) causes prices tobe above the collusive level. This is bad both for profits and for consumer welfare.The access charge affects the balance of prices for directly and indirectly suppliedprograms, but this has no impact on profits since thesumof the prices is all thatmatters. In the above example it is easily shown thatp= 5/6, so an access chargeof zero will result in this inefficient price provided thatu1< 5/6.

Discussion. The model has ignored the crucial issue of how programs areproduced or otherwise obtained by firms. For instance, one could extend the modelby introducing an initial stage of production in which firms can choose the qualityof programs, as measured by the gross utility parameterui , at some cost, sayrepresented by an increasing functionc(ui ). Once programs are produced, this costwould then be sunk and the subsequent interactions could be modeled as above, andfirms would choose their respective qualitiesuA anduB, taking the resulting returnsinto account. A more ambitious extension would be to introduce an outside marketfor premium programming, where the suppliers of premium programs would signcontracts—exclusive or otherwise—with the networks, again taking into accountthe subsequent interactions between the two firms. (A step in this direction is takenin the next section.)

Second, the model is symmetric, which may be appropriate for analyzing themarket in the “long run,” but it ignores important asymmetries in the early stages.For instance, if one firm is able to enter the market before other firms then it mayhave an incentive to refuse to serve firms considering entry with its programs inorder to attract subscribers to its own service (who are then “locked in” to someextent due to the sunk cost nature of the delivery technology).

272 MARK ARMSTRONG

These major limitations aside, however, I hope this simple formal model servesto illustrate the potential dangers of pay-TV firms signing mutually advantageousreciprocal contracts to (i) supply each other with programs or (ii) to give eachother access to customers. Provided that the two firms’ programs are not too closesubstitutes, the joint profit-maximizing outcome can be sustained by negotiationover thewholesaleprice for programs. By contrast, if firms were required to offeraccess to each other’s customers at marginal cost (i.e., to seta= 0 with customerinterconnection) then equilibrium retail charges will often beabovethe collusivelevel.

3. COMPETITION IN THE PAY-TV MARKET: THE MARKETFOR PREMIUM PROGRAMMING

The previous section analyzed a model of full vertical integration, and therewas no outside market for programming. Here we investigate the incentives for asupplier of programming to deal exclusively, or otherwise, with downstream pay-TV retailers. The basic model here differs from the previous section in a number ofother ways: (i) retailers do not resell any exclusive rights they may obtain to theirrival (although we will see that this is an innocuous assumption); (ii) we allowretailers to be asymmetric, as this seems an important part of the motivation forexclusive contracts, and (iii) we suppose that retailers offer differentiated productsa la Hotelling. (The reason for (iii) is that given the firms are asymmetric, we needto assume product differentiation in order for both firms to be active in the market.)

There are two television retailers, A and B, which supply programs to a popu-lation of consumers. Consumers view the programs supplied by the two retailersas differentiated, and ifvi is the utility (net of any charges levied) of programssupplied by firmi then the consumer located at 0≤ x≤ 1 obtains net utility ofvA − tx if she buys from A andvB− t(1− x) if she buys fromB.13 Consumers areuniformly distributed on the unit interval. Suppose that firmi has marginal cost ofsupplying a consumer with its programs ofci .

The marginal consumer is given by

x= 1

2+ vA − vB

2t. (7)

It can be calculated that total consumer surplus is given by

V = 1

2(vA + vB)+ 1

4t(vA − vB)2− 1

4t. (8)

13 This differentiation (as captured by the “transport cost” parametert) might stem from the differentprograms offered by the two firms, or it might have to do with preferences over different modes ofdelivery (cable vs satellite, and so on).


For firm i =A,B suppose that gross utility (i.e., not including the retailing charge)is exogenously given byui and the retailing charge ispi , so thatvi = ui − pi .Therefore, the marginal profit per subscriber of firmi is pi − ci ≡ si − vi , wheresi = ui − ci is the gross surplus per subscriber available to firmi . Without loss ofgenerality, suppose that firm A is the firm with the competitive advantage, i.e., thatsA ≥ sB. The total profits of firmi (excluding any fixed costs) are just its marginalprofit per subscriber multiplied by the number of subscribers, i.e., are given by

πi (vi , v j )= (si − vi )

(1

2+ vi − v j

2t

).

It can easily be shown that equilibrium in this market is given by

v∗i =2si + sj

3− t (9)

and firmi makes equilibrium profit of

π∗i =1

2t

(t + si − sj

3

)2

. (10)

From (7) firm A’s equilibrium market share is

x∗ = 1

2+ sA − sB

6t. (11)

If we wish to focus on the case where firm A does not corner the market, parametersmust be such thatx∗ < 1 in (11). In addition the market is covered (which is neededfor this analysis to be valid) provided that

t ≤ sA + sB

3.

Total industry profits equilibrium are

5∗ = t + (sA − sB)2

9t.

Finally, from (8) and (9) equilibrium consumer surplus is given by

V∗ = 1

2(sA + sB)+ (sA − sB)2

36t− 5

4t, (12)

and hence total welfare (as measured by the sum of consumer surplus and profits)

274 MARK ARMSTRONG

is given by

W∗ = 1

2(sA + sB)+ 5(sA − sB)2

36t− 1

4t. (13)

The fact that industry profits are increasing in the degree of asymmetry in themarket (as measured by (sA − sB)2) is important for the incentives to offer exclu-sive contracts. Note that welfare in (13) may be decreasing insB in asymmetricmarkets—from (11) this, perhaps “perverse,” effect can only happen if the equi-librium market share of firm A is at least 80%.

Now suppose there is a firm (not A or B) that holds rights to some premiumprogramming (e.g., a sporting fixture or a film), and this firm is considering sellingthese rights to A or B (or both). Suppose that all consumers are prepared to payup toα >0 to watch this content, i.e., if networki makes this program availablethen its gross utility increases fromui to ui +α. For simplicity, we suppose thatthe cost of supplying the program on either firm’s network is zero. (This makes nodifference to the analysis.) We suppose thatα is sufficiently small so that firm Aobtaining exclusive rights does not cause it to corner the market, i.e., that

t ≥ α+ sA − sB

3. (14)

We examine various ways in which the program supplier can sell rights to the twodownstream rivals.14

Lump-sum fee for rights to the premium program.Suppose firmi is grantedexclusive rights to the program. In this case, since it incurs no extra marginal costfor supplying the program, the effect is to increasesi to si +α, so from (10) itbenefits by

bi = 1

2t

(2α

3

[t + si − sj

3

]+ α

2

9

)> 0 (15)

14 The following section is closely related to the analysis in Jehielet al.(1996), which builds in part onthe earlier papers by Kamien and Tauman (1986) and Katz and Shapiro (1986). The two earlier papersconsider how the inventor of a cost-reducing innovation could best make the innovation available to anoligopoly. Since a cost-reducing innovation is formally similar to a quality-enhancing innovation, theproblem of how to allocate programming rights to a downstream oligopolistic TV industry is virtuallyidentical to this earlier problem. However, these earlier papers assumesymmetryin the oligopoly, which(i) greatly simplifies the analysis and (ii) makes certain simple, butad hoc, selling formats (for instance,to auction the rights to the highest bidder) seem much more natural. In the present asymmetric context,it is too restrictive to consider these simple symmetric selling procedures, so we must use more generalprocedures (as is also done in Jehielet al.).


compared to the status quo. Similarly, if firmj wins the exclusive contract firmiloses profits of

l i = 1

2t

(2α

3

[t + si − sj

3

]− α

2

9

)> 0 (16)

compared to the status quo. (Note that the lossl i is positive from the assumption(14).) The firm with the initial competitive advantage, i.e., firm A, has both greaterbenefit from winning the exclusive contract and more to lose from losing thecontract. On the other hand, if the seller grants the rights to both firms, the neteffect on their profits is zero sincesi − sj is then unchanged.

How much is firmi prepared to pay for the exclusive rights,giventhat j will begranted the exclusive rights ifi does not buy them? It gainsbi if it accepts the offerand losesl i if it rejects, so the net gain to accepting isbi + l i . Thusi is preparedto pay up to

bi + l i = 2α

3

(1+ si − sj

3t

)for the exclusive contract. Therefore, the most revenue that the seller can obtainby selling exclusive contracts is to sell to the firm with the initial competitiveadvantage (firm A), in which case its revenue is

Rex= 2α

3

(1+ sA − sB

3t

). (17)

Note that the seller may actually gain revenue greater thanα, which is the socialbenefit of the premium programs. From (11) and (17) this happens only if theex antemarket share of A (i.e., the market share of A before it obtains the exclusiverights) is greater than 75%.

The net effect on the firms’ profits by the availability of the rights (compared tothe status quo) in this case is given by

δπi = − l i

so that, perhaps counter-intuitively,both firms lose from the availability of theextra programming. The net effect on consumer surplus, however, from (12) is

δV = 1

2α+ α

2+ 2α(sA − sB)

36t,

and the effect on total welfare (taking into account the revenue gained by the sellerof the premium programming) is

δW= 1

2α+ 5

α2+ 2α(sA − sB)

36t. (18)

276 MARK ARMSTRONG

Note that the welfare gain from selling the rights exclusively to A may actuallyexceedα, the true social benefit of the program. From the assumption (14), anecessary condition for this to happen is that theex antemarket share of A be atleast 60%: ifα is small, then it is necessary that A’s market share be at least 80%.

So far the analysis has assumed that A does not resell the rights toB (for instance,because it is forbidden to under the terms of its contract with the seller). Would Awish to do so? If A sells the rights non-exclusively to B (i.e., retaining the rights foritself as well), then B would be prepared to paylB for these rights. A’s profits, onthe other hand, go down bybA compared to the case where it has exclusive rights.Therefore, sincelB < bA firm A is better off retaining its rights.15 The assumptionthat retailers do not resell their programs is therefore perfectly valid.

It is important that the seller is able tocommitto grant the exclusive rights to Bin the event that A rejects the seller’s offer, since it may not be in the interests of theseller to do so. (For instance, how much can the seller charge B for the exclusiverights? It can clearly chargeB at leastbB, but it might be able to get more bythreatening to give the exclusive rights to A again, and so on, in circles.) A simplescheme that appears to avoid some of these commitment issues is to auction offthe exclusive rights to the highest bidder (say, in an ascending bid auction).16 Inthis case the bidding will stop when firm B drops out at the pricebB+ lB, and thewinning bid will be

Rauct= 2α

3

(1− sA − sB

3t

). (19)

Again, though, the exclusive rights will go to firm A.17 The welfare effects are justas the above, except that the firms now have profit changes given by

δπA = bA − (bB+ lB); δπB=−lB,

i.e., firm A gains a little at the expense of the seller. Naturally, the auction mecha-nism and the full-commitment mechanism coincide in the symmetric case (sA = sB).

The revenue in (17) is strictly greater than any revenue it can obtain by sellingto both firms on a non-exclusive basis.18 Suppose that the seller offers to sell the

15 Similarly, if A grants its rival exclusive rights (so that A gives up its rights at the same time), thenit is clear that A is made worse off.

16 This is the approach taken in the symmetric model of Katz and Shapiro (1986).17 However, given that B knows that A will win the auction, if there is a cost involved in bidding

then B may not bother competing, in which case A will win the auction for much less.18 On the other hand, if the seller allocates the exclusive rights by auction then it is ambiguous

whether this yields more revenue than non-exclusive selling: revenue from the auction is greater thanthat from selling to both firms whenever

α ≥ 2(sA − sB)

so that the auction is better provided the premium programming is sufficiently valuable (or the marketis reasonably symmetric).


rights to firmi for a chargeRi , say, and that both firms accept. Then in order fori toagree to pay this charge (given thatj has also agreed) we must haveRi no greaterthan the profit loss from not having the rights when firmj does, which is justl iin (16) above. Therefore, the most the seller can get from selling non-exclusiverights is justlA + lB, i.e.,

Rnon= 2α

3

(1− α

6t

)< Rex. (20)

In this the effects on the various parties are given by

δπi = − l i ; δV = δW=α. (21)

Thus we deduce that when rights are sold on a lump-sum fee basis—and theseller can commit to its strategy—the seller should sell the rights exclusively to thefirm with the initial competitive advantage (firm A).19 However, unless the marketis rather asymmetric then social welfare is higher if the rights are allocated to bothfirms. (Consumers arealwaysbetter off with non-exclusive rights.) Therefore, ex-cept in asymmetric situations, private and social incentives to grant exclusive rightsgo in opposite directions, and welfare would be enhanced if exclusive contractswere (somehow) prohibited.

Per-subscriber fee for rights to premium program.Suppose next that the sellersells its rights on a per-subscriber basis, charging firmi a pricepi per subscriber.Then, unlike the case of lump-sum fees, this has a direct effect on a firm’s marginalcost, andsi changes tosi +α− pi . Suppose first that the seller sells these rightsnon-exclusively. Then, whatever firmj decides to do, from (10) firmi will acceptprovided that

1

2t

(t + si + [α − pi ] − s j

3

)2

≥ 1

2t

(t + si − s j

3

)2

,

i.e., if pi ≤α. (In the above,sj = sj if j rejects the seller’s offer, andsj = sj + [α−pj ] if it accepts.) Thus it is a dominant strategy fori to accept if the price it isoffered is no greater thanα. In particular, if the seller offers its program for a priceno greater than the consumers’ willingness-to-pay, both firms will in equilibriumchoose to buy. Clearly the seller will choose the highest price, and setpi =α, in

19 There is another possibility for the seller: it could offernot to supply the program toi ’s rival inreturn for a charge levied oni of Ri , say. (If i refuses to pay this fee then rights are given toj .) It iseasy to see that it is an equilibrium for each firm to pay the seller not to supply its rival provided thatRi ≤ l i ( just as in the case of non-exclusive contracts). Therefore, the seller can obtain revenue equalto lA + lB simply by offering not to supply! Naturally, there is no effect on consumer surplus or overallwelfare compared to the status quo, so this scheme is greatly inferior to the allocation of non-exclusiverights. In addition, it would in practice fall foul of any reasonable anti-trust policy.

278 MARK ARMSTRONG

which casesi remains unchanged. The total revenue for the seller with this systemis just

Rper=α.The effect on the distribution of surplus is now quite different from that withlump-sum fees:

δπi = 0; δV = 0; δW=α.Thus consumers no longer benefit at all from the new program, retailers are indif-ferent, and the seller extracts all the social benefit (equal toα).

Suppose the seller tries to sell exclusive rights. Then the most thati is preparedto pay per subscriber depends on the terms offered toj in the event it rejects theoffer. (This is in contrast to the previous case of lump-sum fees.) Suppose we makethe extreme assumption that the seller can threaten togivethe programs toj in theeventi turns it down. In this case from (10)i is prepared to paypi provided that

1

2t

(t + si + [α − pi ] − sj

3

)2

≥ 1

2t

(t + si − sj − α

3

)2

,

i.e., if pi ≤ 2α. It is clear that the seller will get more revenue from firm A, thefirm with the competitive advantage, so suppose it offers A the exclusive rights fora per-subscriber chargep≤ 2α. From (11) the number of subscribers of A is

x(p)= 1

2+ sA +α − p− sB

6t,

and the seller’s revenue is thereforepx(p). Unlessα is large,20 the constraintp≤ 2α binds, and the seller gets revenue

α

(1+ sA − sB − α

3t

).

This revenue is greater thanα, the revenue the seller obtains with non-exclusiverights, wheneverα < sA − sB.

However, the seller’s threat togive the rights to B in the event that A rejectsthe offer is surely incredible. To think about the maximum revenue the seller canobtain from a credible procedure, consider the following plan. The seller has threepolicies: (i) give the rights exclusively to A, (ii) give the rights exclusively to B,or (iii) give the rights to both firms. Suppose negotiations are such that the sellercan try each of these policies in turn (in any order) but then must give up if noagreement is reached. For instance, if the order is first (i) then (ii) and then (iii),

20 The constraint binds provided thatα≤ t + 1/3(sA − sB).


consider B’s incentives when it is offered exclusive rights under offer (ii). If theper-subscriber charge ispB, it knows that if it rejects the offer, policy (iii) will befollowed, which will be played as described above. In that final stage B obtainsa zero change in profits compared to the status quo (i.e., it is not “punished” forrejecting the offer). Therefore, B will only accept the contract under policy (ii)provided that

1

2t

(t + sB+ [α − pB] − sA

3

)2

≥ 1

2t

(t + sB − sA

3

)2

so that pB≤α. (This compares with the higher prices,pB≤ 2α, that could becharged if the seller threatens to give the rights away to A if B rejects the offer.)But if the seller offers such a price it gains a lower revenue than it would if itwaited until the last stage (when it can obtainα). Therefore it is worth bypassingthe second stage altogether. But if A foresees this in the first stage, it too will onlyaccept a pricepA ≤α in the first stage, and again the seller is better off waitinguntil the final stage. By working through the various permutations of the orderingof these policies, we can see that the best that the seller can do when using athree-stage negotiating procedure of this form is to offer non-exclusive contractsat a per-subscriber charge ofα.

Discussion. When the seller allocates rights on a lump-sum basis, which mightbe necessitated because of technological limitations that cannot verify the sub-scriber numbers of each firm, then exclusive contracts turn out to be revenue-maximizing. To do this, however, the seller needs a good deal of commitmentpower, and firm A must believe that the seller will allocate the rights exclusively toB in the event it rejects the offer. However, except in very asymmetric situations,welfare is maximized by non-exclusive contracts, in which caseall consumers ob-tain the benefits of the new programming. Also, again except in very asymmetricsituations, the seller can not achieve revenue as great asα, which is the socialvalue of its product. Thus, if lump-sum contracts for rights are used, we mightexpect that exclusive contracts are (i) optimal from the seller’s point of view and(ii) sub-optimal in terms of overall welfare.

With per-subscriber charges, which might only be possible with new technology,the seller can obtain revenueα in a simple way, without recourse to incrediblethreats. Moreover, firms follow dominant strategies to generate this revenue. Ineffect the firms simply pass on the charge for the premium programming to theirsubscribers, who thereby gain no benefit from the new service. Retailers too gainno benefit, and all the gains from trade are held by the seller. In aggregate welfareterms this is no problem, and there is nothing to choose between this system and thatin which rights are sold non-exclusively with lump-sum fees (although consumerscertainly prefer the latter system).

This analysis can be applied to the selling of broadcasting rights by the footballPremier League in the UK. Until now these rights have been offered on a lump-sum

280 MARK ARMSTRONG

fee basis, and the above analysis has argued thatexclusivityis then likely to be themost profitable way to allocate rights (as turned out to be the case with the rights inpractice). However, the analysis also argued that if a per-subscriber charge couldbe levied then (i) profits for the seller would increase and (ii) exclusivity wouldno longer be optimal for the seller, with the result that overall welfare would mostlikely increase. Three natural ways for the Premier League to receive revenues ona per-subscriber basis are to (a) make that the basis of the wholesale contract toretailers, (b) require matches to be shown on a pay-per-view basis, or (c) set upits own TV channel and retail this directly to viewers (while paying each deliveryplatform a suitable amount for transmission). The Premier League could thereforebe advised to follow one of these strategies when its rights are next sold in 2001.

4. CONCLUSIONS

This paper has presented two formal models of competitive interaction betweenpay-TV operators. The analysis has been purely static, and perhaps the most im-portant limitation of the models has been that any analysis of predatory behavioror foreclosure has not been possible. Thus, for instance, one firm could attempt tobuy up all premium programming (or satellite transponder space, or any other es-sential input) in order to forestall further entry. More detailed models are requiredfor such questions, and this is left to further work.

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Kamien, M., and Tauman, Y. (1986). Fees versus royalties and the private value of a patent,Quart. J.Econ.101, 471–491.

Katz, M., and Shapiro, C. (1986). How to license intangible property,Quart. J. Econ.101, 567–589.

Laffont, J.-J., Rey, P., and Tirole, J. (1998). Network competition I: Overview and nondiscriminatorypricing,Rand J. Econ.29, 1–37.

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Competition in the Pay-TV Market