Strategic Differentiation by Business Models: Free-to-Air and Pay-TV s

Transcription

1 Strategic Differentiation by Business Models: Free-to-Air and Pay-TV s Emilio Calvano CSEF - University of Naples Michele Polo Bocconi University, IEFE and IGIER October 2014 Preliminary and incomplete, please do not quote or circulate Abstract Free-to-air and Pay-tv business models usually cohabit in Media markets. We study a model in which two identical broadcasting stations compete for heterogeneous viewers and advertisers. We find that differentiation by business model can endogenously arise in equilibrium.when the advertising technology is very effective and the value of an informed viewer is large. The free-to-air platform offers high quality (exclusive) eyeballs to advertisers whereas the pay-tv platform offers high-quality (free of commercials) content to viewers. Symmetric free-to-air equilibria may exist, if the advertising technology is not very effective while the value of informed viewers for advertisers is high. A merger between a free-to-air and a pay-tv platform maintains different business models of the two channels, with an increase in the advertising space and the subscription fee. This result casts some doubts on defining different relevant markets for the free-to-air and the pay-tv segments. 1 Introduction A common empirical observation in media markets is the coexistence of platforms (TV channels, newspapers) that adopt very different business models: free-to-air channels raise advertising revenues distributing contents for free, while pay-tv (premium) channels collect subscriptions from viewers offering content free of commercials. Similarly, We thank Bruno Jullien, Augusto Preta, Marcus Reisinger, Patrick Rey, John Sutton, and seminar participants at the 2014 Media Conference at the Florence School of Regulation and the 2014 Earie Conference in Milan. 1

2 the free press gains on advertising revenues only, whereas traditional newspapers add to advertising revenues the readers price of the copy. 1 This facts pose both positive and normative questions. On the positive side, why do these opposite funding regimes, with advertisers and consumers respectively footing the bill, emerge and cohabit in media markets? Can these striking differences in business models be a result of strategic interaction? On the normative side, should we classify these apparently different classes of operators in different relevant markets or not? Existing theories of price skewness in media markets (and other platform industries) have so far focussed on the reasons why all platforms in a market may tilt their pricing structure mostly on one, or the other side. Today there is a well established understanding of symmetric business models equilibria characterized by asymmetric price structures, with all platforms adopting a similar, unbalanced, price structure and cross subsidising one side at the expense of the other. Which side is favoured, then, depends on the asymmetry in the willingness to pay for interactions across sides, a well established result in two sided markets. For a given total price, the profit maximizing structure favors the side whose relative demand elasticity weighted by the relative size of the externalities is higher. In other words, those who are more reluctant to join the platform (e.g. watch tv) and at the same time relatively more valuable to the opposite side (e.g. advertisers expected value of informing is high) are subsidized. This way, a fundamental issue in two sided markets, the unbalancedness of price structures, is well explained, but another key features, the coexistence of opposite price structures across operators, is left aside. In this paper we investigate whether a principle of differentiation driven by strategic considerations can be an appropriate explanation of two ex-ante identical platforms opting for opposite price structures and business models. We set up a simple model of duopoly competition with (potentially) multi-homing viewers and advertisers. Viewers have a preference for variety, choose which plaforms to subscribe and the viewing time spent on each of the accessible platforms. Further, they dislike advertising breaks and are heterogeneous in their willingness to pay for free-of-ads airtime. Multi-homing viewers push the platforms to compete for advertisers, that are ready to pay a station the value of the incremental probability of informing the viewers through that given channel. The advertising technology, then, 1 Examples of asymmetric business models in platform markets can be found also in the early age of credit cards (Diners vs. American Express), online job search platforms (Careerbuilder vs. Monster), managed care plans in the US insurance health market. See Ambrus and Argenziano (2009) for details. 2

3 determines the probability of informing a viewer when the message is broadcasted. We show that there exist equilibria in which the tv stations employ opposite skewed price structures in order to soften competition and extract higher rents, each charging one and different side. The basic mechanism that sustains this result can be explained as follows. In our model viewers dislike advertising break, and therefore evaluate a platform with less commercials as a higher quality channel. Offering contents free-of-ads, then, enhances at most the viewers willingness to pay for subscription, the more so for those types that are more annoyed by commercials. This effect creates a large revenue potential for a platform to offer the contents free-of-ads at a positive subscription fee, an incentive to adopt a pay-tv business model, when the other follows a free-to-air business model. The types more annoyed by advertising breaks, then, will subscribe the pay-tv. If the pay-tv channel does not host commercials, the only way for advertisers to reach the viewers is to place their ads on the other channel. This station, in turn, can extract the full value of informing the viewers, since advertisers have no alternative to reach them. Then, when facing a pay-tv the other station has an incentive to cut the subscription fee, expanding the audience and advertising revenues, up to the point when the content is offered for free, adopting a free-to-air business model These effects, however, are not suffi cient to construct an asymmetric business model equilibrium, since the incentive to raise money from a side different from the one exploited by the other station has to be compared with the alternative of sharing with the rival the rents extracted on its same side. In other words, opposite business models arise in equilibrium when a station facing a free-to-air tv finds it more convenient to raise money from subscribers rather than competing with the other channel for the advertisers money, and vice versa. In our model the interplay of competition for advertisers and the features of advertising technology have a crucial role in this perspective. Competition for advertisers, in general, allows the stations to retain as advertising fee only the incremental value of broadcasting the message on their channel. With a very effi cient advertising technology, the probability that a commercial captures the attention of the viewer at the first exposure is very high, whereas a second exposure delivers a small incremental contribution to reach a viewer. Competition for advertisers, then, pushes up the revenues of the first channel and reduces those of the imitator. Conversely, when the technology is not effi cient, a second exposure substantially enhances the probability of informing the viewer, compared to the first, not decisive, view. Competition for advertisers, in this second case, does not squeeze the revenues of a second channel 3

4 offering space for commercials. Consider then the case of an effi cient advertising technology. When the other station is free-to-air, imitation by selling additional advertising space is not an appealing strategy for the rival, since the advertisers are not willing to pay much for a second exposure. Conversely, when the rival channel is a pay-tv, the revenue potential of offering advertising space dominates the option of imitating the pay-tv business model. Indeed, by offering advertising space the channel would be the only way to reach the viewers attention, that is easily captured with an effi cient advertising technology. This latter effect, in turn, is further enhanced when the advertisers willingness to pay is boosted by high expected profits from sales to the informed viewers. We show in the paper that when sales to informed viewers are highly profitable and the advertising technology is effi cient, an asymmetric business model equilibrium exists. Conversely, if the willingness to pay to reach informed consumers is large but the advertising technology is ineffi cient, also a second exposure is valuable to the advertisers, and imitating a free-to-air rival dominates the alternative of switching to a pay-tv business model. Hence, we can establish suffi cient conditions, depending on the expected profits from informed viewers and the effi ciency of advertising technology, such that an asymmetric business model (differentiation) or a symmetric one (imitation) exist. We also show that when the two platforms merge, they have still an incentive to offer two channels and adopt opposite business models. After the merger, the new operator finances one channel with subscription fees and the other through advertising fees, and raises both of them compared with the duopoly case. Hence, differentiation in business model arises both in a duopoly and a monopoly market environment, a result that we can find also in the traditional literature on one-side product differentation. In a duopoly market, differentiation is driven by strategic consideration, to avoid burning off rents by face-to-face competition on the same side. The monopolist, instead, adopts different business model according to a discrimination purpose. A large audience (free-to-air) channel maximises the surplus of advertisers, whereas a channel free of commercials (pay-tv) maximises the surplus of viewers. Then, the fees are set, according to the two opposite business models, to extract the surplus of the targeted side. This latter result leads us also to normative issues referred to antitrust and regulatory interventions in media markets. Traditionally, pay and free-to-air tv s have been considered as belonging to different relevant markets, based on the argument that the two kinds of operators sell different services to different groups of agents without competing. Free-to-air stations are not active in the subscription market, and pay-tv 4

5 channels do not participate in the advertising market. However, this argument seems simplistic and rooted in a one-sided perspective, whereas the two-sided market approach that today prevails in the analysis of media market may help realizing that opposite business model are the result of competitive forces. Considering operators that adopt either of the two business models as belonging to the same relevant market seems a natural alternative. Contributions to the literature. Our paper contributes to the wide literature on two sided markets and their applications to media industries. To better appreciated the novelties of out approach, it is worth noting that in our model both viewers and advertizers are potentially multi-homers, while their equilibrium choices may lead some of them to patronize a single platform. In this setting, we study the endogenous emergence of different equilibrium price structures, or business models, across platforms, showing that two identical firms can opt in equilibrium for opposite and skewed price structures, each charging only one, and different, side. Regarding the single-homing versus multi-homing issue, after the seminal work by Anderson and Coate (2006), several papers have maintained their modeling options exploring various features of media markets. In this class of models, viewers have been assumed to single-home, adopting a Hotelling framework to account for their heterogeneity, while advertisers multi-home. Then, each platform becomes the gatekeeper to reach a disjoint set of exclusive viewers. Single-homing viewers, therefore, imply that platforms do not compete for advertisers, the competitive bottleneck highlighted in Armstrong (2006). Multi-homing viewers have been studied later on, in an advertising financed TV industry, for instance in Anderson, Foros and Kind (2013) and Ambrus, Calvano and Reisinger (2013). In this case, advertisers can reach (at least some) viewers through one or the other channel, and the platforms therefore compete for advertiserswhen offering non-exclusive viewers. The principle of incremental value pricing stems from this feature and applies also to our model. It implies that each channel can charge an advertising fees not higher than the incremental profits of the advertisers when this latter places its ads on that station. Skewed pricing structures have been analyzed since the beginning of the literature on two-sided markets (see Rochet and Tirole (2006) and Armstrong (2006) and, more recently, Bolt and Tienman (2008) and Schmalensee (2011). The general intuition is that a platform is more generous on the side with lower cross-side externalities, in order to increase the number of agents on that side and exploit the higher willingness to pay of the agents on the other side, increasing revenues. This intuition has then been applied in a series of papers to study the comparative 5

6 statics of duopoly markets where both TV platforms are following a pay-tv, or alternatively a free-to-air business model. Peitz and Valletti (2008) analyze a TV market with single-homing viewers and multi-homing advertisers, studying the advertising intensity and content choice when both platforms choose either a pay-tv or a free-toair business model. Similarly, Kind, Nielssen and Sorgard (2009) show the fee and advertising equilibrium levels when the degree of substitutability or the number of firms changes, in a symmetric business model setting. Dietl, Lange and Lin (2012) analyse the equilibrium advertising level when one platform is exogenously contrained to set a subscription fee (pay) and the other is free-to-air, while Armstrong and Weed (2007) explore also the case of different business models in a single-homing viewers setting. In Spiegel (2013) a monopolist supplies software and chooses between selling the package or distributing it for free but tracking users preferences and inserting target ads (adware). Finally, Ambrus and Argenziano (2009) study in a general setting the case of asymmetric network equilibria, with some restrictive assumptions (single-homing agents) and a specific way to solve for the muliplicity of equilibria. Hence, to the best of our knowledge, so far no paper has analysed the case of symmetric and unconstrainted platforms, able to set both a subscription fee and offer advertising space, that compete in a general multi-homing two sided market, opting in equilibrium for opposite business models. The rest of the paper is organized as follows: Section 2 presents the model, Section 3 illustrates the optimal advertising fee. Section 4 analyses a simplified example useful to capture the main intuitions. Section 5 analyses the full-fledged case and asimmetric (Section 5.2) and symmetric (Section 5.3) equilibria. Section 6 addresses the case of mergers and some policy implications. Concluding remarks follow. All the proofs are in the Appendix. A second Appendix fully analyses viewers choices. 2 The model Consider a two-sided market with two competing broadcasting stations (or channels) indexed by i = 1, 2. Both stations serve two separate groups of agents, viewers and advertisers, of measure 1 and N respectively. Viewers can choose to watch, and advertisers can choose to place advertising messages, on either of the two stations, both or none. Each station i sets a subscription fee f i 0 that viewers must pay to watch the channel. In addition they set the overall quantity a i 0 of advertising messages broadcasted and advertising fees {t n i } j=1,..n advertiser n = 1,.., N must pay 6

7 to be allocated a subset a n i of these messages.2 The platforms incur an administrative marginal cost c 0 to collect the subscription fees from a viewer. The cost c is nil if the platform distributes for free its content setting the fee to zero, whereas it may be positive when the fee is positive as well. The stations profit is equal to the sum of subscription and advertising revenues minus costs. Viewers. Viewers draw utility from watching the contents broadcasted by the stations. They are heterogeneous in the utility they derive from the viewing time spent on contents, and they are indexed by θ [0, 1]. Since viewers obtain no utility from commercials, that, in turn, subtract viewing time from contents, advertising is a nuisance. Let v i 0 denote the amount of viewing time spent watching station i, a i as the fraction of total programming time devoted to commercials ( quantity of ads or advertising space on i) and b i = 1 a i the fraction 3 of programming time referred to contents on channel i. It follows that b i v i is the time a viewer spends watching contents on channel i. Following Levitan and Shubik (1980) we assume that the utility of a generic θ viewer is given by the following quadratic specification: U(v 1, v 2 ; θ) = θ (b 1 v 1 + b 2 v 2 ) 2 σ (v1 2 + v 2 2 2) σv 1 v 2. (1) For simplicity θ is assumed uniformly distributed on the unit line. The parameter σ [0, 1) measures the degree of substitutability between channels. Perfect substitutability corresponds to σ 1 and no substitutability to σ = 0. Given a vector of advertising quantities and subscription fees (a i, a j, f i, f j ), denoted ρ, viewers make their subscription choices, that are driven by the utility from optimally allocating the viewing time across accessible channels and contents. Let a viewing profile v := {v i (θ), v 2 (θ)} θ [0,1] refer to a set of viewing times, one per θ-viewer. Type θ s payoff is U(v; θ) minus all fees paid. Depending on ρ and θ, the viewer optimally subscribes to none, one (single-homer) or both (multi-homer) stations. This functional form captures three key features. First, viewers display a preference for variety. Spreading a given amount of viewing time across multiple stations raises utility. This feature naturally conveys a tendency to consume multiple sta- 2 For example, a i can be interpreted as the total number of 30 seconds advertising slots (or commercials) broadcasted while a j i ai is the amount of these slots allocated to a particular advertiser j. 3 For simplicity we assume that advertising (and therefore contents) is uniformely spread over the entire total programming time. Hence, in each fraction v i of total programming time, corresponding to the time spent watching chanel i, a viewer is exposed to an amount a iv i of advertising messages. 7

8 tions. Second, viewers dislike advertising in the sense that they would rather prefer ad-free content. Third, viewers are heterogeneous in their willingness to pay for an extra unit of viewing time net of advertising breaks. As we shall see, this implies that viewers sort in equilibrium, with lower θ-viewers optimally choosing to satisfy their content needs on one station only (single-homing) and higher θ-viewers multi-homing on both stations. Advertisers. Advertisers wish to inform viewers. They are assumed all alike so their index is dropped. The value of informing a viewer does not depend on θ and is equal to k 0, that can be thought as the expected profits from a sale to an informed viewer. 4 For simplicity this value does not increase with the number of times a viewer is informed. The advertising technology in place determines the probability that a viewer exposed to a commercial pays attention to it and is informed about the product. Hence, this technology establishes the relationship between the amount of advertising messages and the probability of informing the viewer. In order to inform their customers, advertisers need to broadcast advertising messages. Consider an advertiser n who is placing (a n 1, an 2 ) advertising messages on the two channels and consider a θ-viewer characterized by viewing time (v 1 (θ), v 2 (θ)). We assume that the probability that advertiser n informs the θ-viewer through its commercials on station i is equal to: φ n i (a n i, v i (θ)) = φ n i := 1 e ψan i v i(θ). (2) We offer in Appendix a simple micro-foundation that derives (2) from natural assumptions on the primitives of a basic stochastic process that governs advertising. The parameter ψ 0, discussed below, captures how effi cient the advertising technology is in capturing the attention of a viewer that watches the channel, and inform her about the product. As the viewer can be potentially informed through either of the two stations or both, then the probability that this viewer is informed on product n at least once on some station is denoted φ n and assumed equal to (arguments omitted) φ n := 1 (1 φ n 1 )(1 φ n 2 ). That is one minus the probability that the viewer is not informed on channel 1 nor on channel 2. Rearranging yields: φ n (a n 1, v 1 (θ), a n 2, v 2 (θ)) = φ n := 1 e ψ(an 1 v 1(θ)+a n 2 v 2(θ)) (3) 4 A simple way to interpret this parameter is as follows. Suppose advertisers are monopolistic firms selling products with markup µ. A viewer can buy from a firm only if it is informed. Then k can be interpreted as µ times the probability that an informed viewer purchases. So, for example if on average one in one hundred informed consumers ends up purchasing then k = µ

9 From (3) it follows that φ n = φ n i whenever only channel i offers advertising while channel j does not, or advertiser n does not place its commercials on platform j (a n j = 0) and/or the viewer does not watch channel j and single-homes on i (v j(θ) = 0). In all these three cases, the only way for advertiser n to reach the attention of viewer θ is by placing ads on channel i, that becomes a competitive bottleneck. Given a viewing profile v, advertiser n s expected net surplus from buying (a n 1, an 2 ) ads is obtained by integrating (3) across all viewers types: k e ψ(an 1 v 1(θ)+a n 2 v 2(θ)) dθ t 1 t 2 (4) where t i is the advertising fee payed to channel i. If, instead, advertiser n places ads only on channel i, then k 1 represents advertiser n s net surplus. 0 1 e ψan i v i(θ) dθ t i (5) The expressions (2) and (3) embed a number of key hypothesis. First, the marginal return from advertising is positive but decreasing in a n i. An extra ad is always valuable but less so with the number of ads already bought. These diminishing marginal returns property reflect the informative nature of advertising. The idea is that with some probability an additional ad informs an already informed viewer and therefore does not produce surplus. Secondly, the marginal return of a n i decreases with an j. Advertising on i and j are substitute ways to inform the same viewer, provided the viewer multi-homes. Finally viewers who watch more television are easier to inform. To simplify the analysis we assume from the outset that all advertisers who accept i s offer are allocated an equal share of the total amount of ads, that is a n i = a i N = ã i for i = 1, 2. 5 Then, we can omit the superscript n of the functions φ n i and φ n : φ i = φ i (ã i, v i (θ)) and φ = φ(ã 1, ã 2, v 1 (θ), v 2 (θ)). The effi ciency parameter ψ plays an important role in our analysis. For example, it can be interpreted as the probability that the message sinks in conditional on a consumer being exposed to it. That is a higher ψ corresponds to a higher probability that a consumer pays attention to the ad. The limiting case ψ corresponds to a consumer infinitely attentive. In that case merely watching a channel for some 5 Ambrus, Calvano and Reisinger (2013) show that this assumption is harmless when advertisers are all alike. To see this notice that diminishing marginal returns mean that an increase in the time allocated to a specific advertiser brings a positive but decreasing contribution. Then, since the advertisers are homogeneous, a station can extract the maximum rents from the total time allocated to commercials, a i by maximising the number of advertisers, allocating an equal amount a n i = a i to N each of them. 9

10 time (i.e. v i > 0) suffi ces to be informed by all advertisers with ã i > 0. Timing and Equilibrium. In period 1 the stations simultaneously set the subscription fee and the quantity of ads (a i, f i ). In period 2 viewers decide which, if any, stations to patronize and the viewing time v i (θ) on the accessible channels. In period 3 the stations simultaneously post the advertising fee t i that an advertiser has to pay in order to be allocated a i N ads on station i. Observed the fees, the advertisers simultaneously decide whether to accept either of the two offers, both or none. 6 We look for pure strategy subgame perfect Nash Equilibria. 3 Preliminary analysis: the equilibrium advertising fee Moving backwards, given viewers and platforms choices we start by deriving the equilibrium advertising fees t i and t j. We do so in two steps. First, we characterize the willingness to pay of an advertiser given ã i, ã j. Then, we derive the equilibrium fees. The willingness to pay for ã i is equal to the payoff that an advertiser obtains if it accepts i s offer minus the payoff that he would get by rejecting it and placing ads ã j only on platform j. In this latter case, the advertiser obtains the net surplus: k 1 0 φ j (ã j, v j (θ))dθ t j. The net surplus of an advertiser from accepting i s and j s offers is instead: k 1 0 φ(ã 1, ã 2, v 1 (θ), v 2 (θ))dθ t i t j. Since the platforms compete for advertisers, competition drives down the advertising fees. The advertising fee t i, therefore, cannot be higher than the difference between the payoff from accepting both offers, placing its ads on both stations, and the payoff from accepting and advertising only on station j: t i k 1 0 [ φ(ã1, ã 2, v 1 (θ), v 2 (θ)) φ j (ã j, v j (θ)) ] dθ. (6) In line with the literature we refer to this expression as the incremental value of station i. It captures the idea that the willingness to pay for an allocation of ads on 6 It is implicitly assumed that unsold inventory is recycled for self-promotion purposes, advertising TV shows and so on. 10

11 i equals the surplus that these ads deliver in excess to what the allocation ã j does on the other platform. (6) covers several relevant cases. (i) if a subset Θ S i of viewers subscribe only channel i (single-homers) while a subset Θ M of viewers multi-home, then for the singlehomers φ(ã i, ã 2, v i (θ), 0) = φ i (ã i, v i (θ)) and φ j (ã j, 0) = 0 and (6) can be rewritten as follows: t i k Θ S i [ φ i (ã i, v i (θ))dθ + k φ(ã1, ã 2, v 1 (θ), v 2 (θ)) φ j (ã j, v j (θ)) ] dθ, Θ M that is, channel i collects the full value of single-homers and the incremental value of the viewers that multi-home. (ii) if there are no ads on j (a j = 0) then all channel i s viewers are exclusive, no matter if they single- or multi-home. φ(ã i, 0, v i (θ), v i (θ)) = φ i (ã i, v i (θ)) and φ j (0, v j (θ)) = 0, which implies: t i k [ Θ S i ] φ i (ã i, v i (θ))dθ + φ i (ã i, v i (θ))dθ, Θ M Then, where we distinguish single- and multi-homing viewers since the viewing time (and the associated probability to inform) of the two groups may differ. Since advertisers are all alike by assumption and the stations can post take-it-orleave offers, then the stations are able to extract the entire willingness to pay, that is, the inequalities above hold with the equal sign in equilibrium. Therefore in any equilibrium the advertising fee t i equals the incremental value of station i as defined, in general, in (6). Notice that both stations exert their market power over exclusive viewers, acting as a competitive bottleneck to reach them. Hence, they fully extract the advertising surplus originated from informing them. On multi-homing viewers, instead, competition for advertisers drives down the rents that a station can extract. This corresponds to the value of the increase in the probability of informing the viewer after a second exposure. The more effective the advertising technology is in attracting the attention of the viewers, as captured by an increase in ψ, the lower the value of a second exposure. In the limit, a second exposure brings no additional value, and we have: Remark 1: Suppose that the advertising technology is infinitely eff ective ( ψ ). Then in any SPNE no station extracts the surplus associated to informing multihoming viewers. Formally: lim ψ t i = k Θ S i φ i (ã i, v i (θ)dθ. 11

12 4 A simplified example To introduce the strategic considerations that lead to an asymmetric outcome we start from a simplified version of the model, We freeze one of the two strategic variables available to the stations, the amount of ads. In addition we consider the simplest case with no substitutability and infinite effi ciency of the advertising technology. In this particular setting we show that an asymmetric equilibrium always exists. Later (section 5) we tackle the richer model described in section 2, showing that the new effects at play there actually reinforce the baseline logic presented here. Formally for the sake of this section we assume that: A1: The quantity of advertising is exogenous and symmetric (a i = a j = a); A2: The stations are independent (σ = 0); A3: The advertising technology is infinitely effective (ψ ) To simplify the exposition assume also that c = 0. 7 θ-viewer simplifies to: The utility function of a U(v 1, v 2 ; θ) = U(v 1, 0; θ) + U(0, v 2 ; θ) = θbv 1 v θbv 2 v 2 2, where b := 1 a. A2 implies that viewer s choices are separable: the optimal viewing time v i (θ) does not depend on a j, and therefore the gross utility of either station depends only on the time spent on that channel, making the subscription choices separable as well. Indeed if a θ-viewer subscribes to i, then vi θb (θ) = 2. Type θ subscribes to i if and only if U(vi (θ), 0; θ) = ( ) θb 2 2 fi. So we have: v i (θ) := { θb 2f 1/2 i b 2 θ θ i,0 :=, i = 1, 2 (7) 0 θ θ i,0 where θ i,0 is the type indifferent between subscribing to i and nothing. We omit the dependence on ρ = (a 1, a 2, f 1, f 2 ) to streamline the notation. Note that separability together with A1 implies that if f j > f i 0 then θ j,0 > θ i,0 0. Hence, all subscribers of the more expensive station also subscribe to the cheaper one. In any continuation equilibrium, then, if f j > f i 0 viewers will sort in three groups: relatively higher types (θ > θ j,0 ) multi-home, intermediate types 7 All results in this section carry over to the case in which costs are strictly positive in a straightforward manner. Subscription costs play instead a role in section 5. 12

13 Π i Π A i ( i j f, f ) S Π i ( f i ) f j S f fi Figure 1 Profits from advertising and subscriptions θ [θ i,0, θ j,0 ] single-home on i and low types (θ < θ i,0 ), if any, subscribe no station. With equal fees, instead, all active viewers multi-home. Given viewers demand, station i s profits from subscriptions only are: Π S i (f i ) := f i (1 θ i,0 ) = f i ( 1 ) 1/2 2fi. b For future reference let f S denote the global maximizer of Π S (f i ). Consider now the advertising side of the market. Recall from Remark 1 in the previous section that ψ implies that advertising profits are equal to the value of informing single-homers only: if f i f j and zero otherwise. 8 Π A i (f i, f j ) := t i = k(θ j,0 θ i,0 ) = 2k b ( ) f 1/2 j f 1/2 i, Figure 1 represents separately the profits from subscription Π S i (f i) and, for given f j, the profits from advertising Π A i (f i, f j ). Concerning these latter, notice that platform i, by cutting the fee f i below f j, gains some singlehoming viewers and therefore some advertising revenues. Hence, despite assuming an exogenous and symmetric level of advertising quantities a, advertising revenues still depend on the platforms strategies even in this simplified set-up. 8 Since Π A i (f i, f j) 0 for f i f j from below, Π i(f i, f j) is continuous in f i. 13

14 So station i s total profits are: { Π i (f i, f j ) = Π S i (f i) f i f j Π S i (f i) + Π A i (f i, f j ) f i < f j. (8) Proposition 1: Under A1 A3 an equilibrium exists and is unique (up to permutation of the indexes). Furthermore: (i.) If k = 0 the equilibrium is symmetric with f i = f j = f S := b2 9. ( b+ 2 b 2 12k 6 (ii.) If 0 < k b2 16 the equilibrium is asymmetric with f i = f S and the wedge fj f i is increasing in k with lim k 0 fi = f S. (iii.) For k b2 16 the equilibrium is asymmetric with f i = 0 < f j = f S. ) 2 < f j = If k = 0 there is no advertising surplus. Due to the no substitutability assumption (σ = 0), the stations choice problem essentially reduces to a textbook monopoly problem in subscription prices. To see this, recall that viewing choices are separable. Absent cross-price effects it is as if the stations operate in distinct markets. So in equilibrium each platform charges the monopoly price f S. It follows that two sidedness (i.e. k > 0) is necessary for an asymmetric equilibrium outcome. The thrust of the proposition is that, under A1-A3, k > 0 is also suffi cient for an asymmetric outcome. That is to say, the mere possibility of extracting ad revenues (no matter how small they are) implies that no equilibrium can have firms choosing the same fee. To build intuition consider the simplest case where one station is free (case (iii.) in the Proposition) and consider firm j s (i.e. the pay-tv) incentives. As i is free, all types θ [0, 1] watch it while only types θ [θ j,0, 1] have access to channel j and multi-home. Since competition for advertisers eliminates the rents from multihomers, platform j cannot obtain any advertising profits, i.e. t j = 0, and rips off only subscription profits in equilibrium for all f j. By definition then f S is the unique best reply to f i = 0. Consider now i s incentives given f j = f S. Facing a rival platform that charges a positive fee viewers θ [0, θ j.0 ] do not watch the pay-tv channel, and are potentially single-homers. So by choosing a fee f i below f S, firm i trades-off subscription profits, that fall due to the reduced fee, for advertising profits. As it stands out from the shape of the profit function in figure 2, charging the same subscription fee f S as the rival cannot be optimal for firm i. Undercutting slightly f S has a first order positive impact on advertising profits (the acquired viewers would be valuable single-homers), whereas it only has a second order impact on subscription profits by the definition of f S. So, charging f S can t be optimal as long as k > 0. 14

15 f j Firm i best reply Firm j best reply Asymmeric equilibria Figure 2 : Best replies f i The larger k the stronger the incentives to sacrifice profits from subscription to gain profits from advertisers. Indeed, the degree of asymmetry increases in the revenue potential k of the advertising side, up to the point where one station becomes free. Figure 2 offers an alternative viewpoint. It depicts the shape of the best reply correspondence, highlighting the two features of the game driving the asymmetric outcome. The first one is a fundamental property of the game which is strategic substitutability. Intuitively the larger the rival s fee, the larger the temptation to undercut to cater some (or all) of the viewers remained unserved as single-homers, valuable on the advertising side. And the lower the rival subscription fee, the lower the fraction of unserved low type viewers and the associated advertising profits, making a high fee and subscription profits more attractive. Strategic substitutability by itself, however, is not enough to generate an asymmetric equilibrium. The second key feature is the discrete jump along the 45 degrees line. It reflects the fact that no equilibrium with k > 0 can involve the two firms choosing the same fee. Proposition 1 provides a first pass at our motivating questions. On the positive side, we obtain a first illustration of a symmetric strategic set-up with firms imple- 15

16 menting opposite business models, thereby extracting surplus from different sides. On the normative side, the result casts a grain of doubt on the traditional antitrust view of different relevant markets for the free-to-air and pay Tv s. Indeed, these two business models are the equilibrium outcome of two ex-ante identical platform, that choose to raise profits on opposite sides. We ll come back on this point in Section 6. 5 The full-fledged case We move now to the full-fledged model, removing the restrictions of the introductory example. This way we can first of all check the robustness of the asymmetric equilibria etablished in Proposition 1. Moreover, we introduce additional effects that enrich the equilibrium analysis. The strategy space of the platforms is expanded by allowing them to choose the amount of advertising a i they offer, affecting the viewing time, the gross utility of watching a channel and therefore the subscription choices of the viewers. Moreover, with substitute channels (σ > 0) the viewers decisions on subscription and viewing time on a given channel depend on the subscription fees and advertising time of both platforms, making the strategic interaction richer. A platform moving to a profit structure biased on the viewers subscriptions may now reduce advertising to increase the viewers gross surplus and willingness to pay. Finally, when the advertising technology is imperfectly effi cient (ψ finite) a second exposure retains some incremental value for advertisers, increasing the profits of a platform that offers advertising space and competes with a free to air station. All these effects affect the relative profitability of imitating the rival platform s price structure and business model, or alternatively the incentive to opt for an opposite business model, making the analysis richer. As we illustrate below, we can establish suffi cient conditions for both asymmetric and symmetric equilibria to exist also in the full-fledged model, confirming and enhancing the findings of the introductory example. We start by characterizing viewers choices. In move then to finding suffi cient conditions under which strategic differentiation by business model arises, focussing on the extreme case whereby profits derive from one side of the market only, with different stations extracting revenues from opposite sides. Finally we show that, under a wider set of conditions than in the simplified example, symmetric equilibria exist. 16

17 5.1 Viewers Choices In stage 2 the viewers choose which station(s) to subscribe and the optimal viewing time on the stations they have access to. With substitute stations (σ > 0), the optimal viewing time depends on whether the viewer has access also to the other station (multi-homes) or not (single-homes). In what follows we focus on two particular cases which reflect choices at the candidate symmetric and asymmetric equilibria described below. A full characterization of viewers behavior is provided in Appendix II. Consider first the optimal viewing time conditional on the subscription choices. Multi-homing: If a θ-viewer has access to both channels, she chooses her optimal viewing time v1 m, vm 2 maximizing U(v 1, v 2 ; b 1, b 2, θ). The optimal viewing time is then v m i (θ) = θb i 4(1 σ) (9) i = 1, 2, where b i = 1 a i is the fraction of the programming time devoted to contents and b i = (2 σ)b i σb j. 9 Plugging into the utility function we have the gross surplus from watching both channels. After rearranging: U m 12(θ) = θ b 1v m 1 + b 2v m 2 2 = θ 2 [ (2 σ)(b 2 8(1 σ) 1 + b 2 ] 2) 2σb 1 b 2. (10) Single-homing: Conditional on single-homing on channel i, the optimal viewing time maximizes U(v 1, v 2 ; b 1, b 2, θ) under the constraint v j = 0. That leads to: The associated gross surplus is v s i (θ) = θb i 2 σ. (11) U s i (θ) = (θb i) 2 2(2 σ). (12) Remark 2: When the two channels are substitute ( σ > 0), if a θ-viewer has access to only one out of the two channels, she spends more time on it than when having access to both, for given amount of ads: v s i = v m i + σ 2 σ vm j > v m i. 9 Notice that we implicitly assume here that b i > 0 and b j > 0 for 2 σ σ bj > bi > bj, a condition σ 2 σ that guarantees that the viewing time is positive on both channels. 17

18 Consider now the optimal subscription profile. Given ρ =(a i, a j, f i, f j ), a θ-viewer solves: max {0, U s 1 (θ) f 1, U s 2 (θ) f 2, U m 12(θ) f 1 f 2 }. Since we are interested in an asymmetric equilibrium in which one firm charges only the advertisers (we shall conventionally label this firm as firm 1) and the other (firm 2) raises revenues only from subscribers, we focus here on a subset of all the possible combinations of subscription choices across the viewers types θ [0, 1]. Let us analyse the subscription choices in a neighborhood (region A, properly defined in Lemma 4 of Appendix II) of the configuration 0 = f 1 < f 2 and a 1 > a 2 = 0. The pattern of subscriptions for increasing θ entails very low types not subscribing either channel (if f 1 > 0), then a subset of viewers that pay for access to the cheaper platform 1, and finally a set of high types that pay both subscription fees. The first group of viewers gets the reservation utility 0, the single-homers that subscribe only platform 1 have a gross utility U1 s (θ) from the content they watch, and finally the multi-homers obtain U12 m(θ). The gross utilities U s 1 (θ) and U m 12 (θ), are increasing and convex in θ, with U s 1 (θ) flatter in θ than U12 m (θ). Hence, they single-cross. Let us define the following thresholds: θ 1,0 = [2(2 σ)f 1] 1/2 θ 12,1 = [8(2 σ)(1 σ)f 2] 1/2 b 1 U s 1 (θ 10 ) f 1 = 0, b 2 U m 12(θ 12,1 ) f 1 f 2 = U s 1 (θ 10 ) f 1 These thresholds identify the θ-viewer s type that is indifferent between the two subscription choices that are shown in the subscript, separated by a comma. Remark 3: When 0 = f 1 < f 2 and a 1 > a 2 = 0 and in a neightborhood of it (region A), properly defined in Lemma 4 of Appendix II, the viewers that subscribe no channel ( Θ, empty if f 1 = 0), only platform 1 ( Θ 1 ) or both ( Θ 12 ) are defined as follows: Θ = [0, θ 1,0 ), (13) Θ 1 = [θ 1,0, θ 12,1 ) Θ 12 = [θ 12,1, 1] 18

19 Then, the subscribers for channel 1 and 2 are: s 1 = 1 θ 1,0 and s 2 = 1 θ 12,1. (14) The number (share) of subscribers varies smoothly in (a 1, a 2, f 1, f 2 ) whenever θ 1,0 < θ 2,0. Consider next a symmetric configuration ρ sim = (a i = a j = a 0, f i = f j = f > 0). Notice that U1 s(θ) = U 2 s(θ) = θ2 (1 a) 2 2(2 σ) and U12 m(θ) = θ2 (1 a) 2 2 < 2Ui s(θ) = θ2 (1 a) 2 2 σ when σ > 0 and θ > 0, at ρ sim. Then, the gross surplus from either platform is the same whereas the gross utility from multi-homing less than doubles. Then, viewer θ 1,0 strictly prefers to single-home since U s 1 (θ 1,0 ) f = U s 2 (θ 1,0 ) f = 0 > U m 12(θ 1,0 ) 2f. Given the continuity of gross utilities, the following remark shows the pattern of subscription. Remark 4: At ρ sim, viewers θ < θ 1,0 do not subscribe any channel, θ [θ 1,0, θ 12,1 ) subscribe either platform 1 or 2 with equal probability, and θ θ 12,1 multi-home. Then, when platform 1, say, slightly cuts f 1, all the viewers θ [θ 1,0, θ 12,1 ) that, being indifferent, were previously shared between the two stations, now strictly prefer platform 1, whose demand for subscription jumps up discretely. Interestingly, when indifference is broken by a slight undercut, we obtain a discontinuous pattern in the demand for subscription that reminds the Bertrand behavior. However, our demand for subscription is derived in a setting where the two channels are imperfect substitutes rather than homogeneous products. This feature of viewers behavior has an important impact when symmetric allocations are analyzed, as we shall do later on. 5.2 Strategic Differentiation In this section we focus our attention on asymmetric equilibria in which the stations extract revenues from opposite sides of the market. Let us define an Opposite Business Model Equilibrium (OBME) as any SPNE of our game that satisfies for i, j = 1, 2, i j: 19

20 (a) Firm i chooses f i = 0 < a i (a free-to-air business model); (b) Firm j sets: a j = 0 < f j (a pay-tv business model). Hence, in the class of asymmetric business model equilibria we focus on the case when each platform raises revenues on just one side, each exploiting a different group of agents. It is important to stress that we are not restricting the strategy space of either platform in order to obtain a particular business model in equilibrium. In other words, we are not assuming, for instance, that platforms make an initial choice between a free-to-air and a pay-tv business model, and then choose the optimal advertising space or subscription fee according to the initial selection of their business model, as, for instance, in Spiegel (2013). Instead, in an OBME the two platforms select their price structures, implicitly adopting opposite business models, by optimally setting their advertising space and subscription fees given the rival s strategies with no ex-ante restriction on the action space available. We prove in what follows that an OBME exists in a particular region in the space (k, ψ), that is for particular combinations of the expected margin k from selling the advertised product to an informed viewer and the effi ciency ψ of the advertising technology in informing the viewers through commercials. The following discussion aims at providing an intuition. Consider a candidate equilibrium in which one platform, say platform 1, is choosing a free-to-air business model f1 = 0 < a 1 and the rival a pay-tv business model a 2 = 0 < f 2. Let us first analyse the conditions under which firm 1 does not gain by deviating from a free-to-air strategy when firm 2 adopts a pay-tv strategy. If platform 1 deviates and sets a positive subscription fee f 1 > 0, it looses viewers and advertising revenues while generating some money from subscribers. Then, if the revenue potential of the advertising side is suffi ciently large, firm 1 will prefer not to reduce its audience by raising f 1.. Recall that (i) the larger is the value of informing the viewers (high k), and/or (ii.) the more effi cient the advertising technology is (high ψ), the larger is the revenue potential from the advertising side of the market. In the proof of Proposition 2 (in Appendix I) we prove that there exists a locus k 1 (ψ) decreasing in ψ such that if k k 1 (ψ), ψ > 0 then f1 = 0 < a 1 are a best-reply to a 2 = 0 < f 2 : { } k1 (ψ) if k k 1 (ψ), ψ > 0 then max Π 1(f 1 ; a 1, a 2, f2 ) Π 1 (f 1 = 0; a 1, a 2, f2 ). f 1 c Hence, k 1 (ψ) is the lower bound of the region, where the above relation holds with equality. (15) This locus is negatively sloped since the advertising revenues extracted 20