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- University of Naples Michele Polo Bocconi University, IEFE and IGIER October 2014 Preliminary and incomplete, please do not quote or circulate Abstract Free-to-air and Pay-tv business models usually cohabit in Media markets.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

21 from exclusive viewers is increasing in the effectiveness of the advertising technology. Then, a higher ψ requires a lower value of k to sustain the choice to raise profits from advertisers rather than from subscribers. Next, consider the conditions under which a pay-tv platform finds it unprofitable to deviate when competing with a free-to-air station. If platform 2 deviates and offers a positive advertising space a 2 > 0, it reduces the gross surplus of its viewers and the revenues from subscriptions, while raising some money from advertisers. Since f 1 = 0, all viewers watch platform 1, and therefore platform 2 s viewers are multi-homers. Recall from our earlier discussion that the more effi cient the advertising technology (the larger ψ) the lower, other things held constant, the advertising surplus that platform 2 can extract by offering a second exposure. So intuitively for given k there always exists a threshold value of ψ such that for all larger values it is not convenient to offer a positive advertising space. A similar argument holds with regards to k: when k is suffi ciently low, the revenue potential of the advertising side is limited and no deviation from the pay-tv business model is profitable. In the proof of Proposition 2 (in Appendix I) we show that there exists a locus k 2 (ψ), non decreasing in ψ such that for k k 2 (ψ) and ψ > 0, a 2 = 0 < f 2 is a best-reply to f 1 = 0 < a 2 : { k2 (ψ) if k k 2 (ψ) and ψ > 0, then Π 2(a 2 = 0, f2 ) } 0 a 2 Hence, k 2 (ψ) denotes the locus that characterises the upper bound of this region, where the partial derivative is equal to zero. The locus is increasing in ψ since a more effective advertising technology (a slighlty higher ψ) reduces the ad revenues extracted from multi-homing viewers and the attractiveness of such deviation by a candidate pay-tv. Then, the choice not to offer advertising space is optimal for platform 2 even for a slightly higher value of k. Finally, as shown in the Proof of Proposition 2, the two loci k 1 (ψ) and k 2 (ψ) intersect at ψ, as shown in Figure 3. (16) Then, we can establish the following result: Proposition 2: If k1 (ψ) k k 2 (ψ) (and therefore ψ ψ), an Opposite Business Model Equilibrium exists that satisfies f 1 = 0 < a 1 < 1 2 and f 2 > 0 = a 2 With respect to the simplified example, in the full-fledged model the platforms choose also the advertising space, the channels are imperfect substitutes and the advertising technology is imperfectly informative. With substitute channels, the viewing time of multi-homing viewers depends on the amount of commercials of both stations. 21

22 k ~ k 1 ( ψ ) ~ k 2 ( ψ ) ψ Figure 3 OBME: sufficient conditions In this richer environment, the cross-platform effects work both through the change in the number of subscribers, affecting the share of single- and multi-homers, and through the viewing time spent on the accessible channels. When platform 1 increases the advertising space a 1, it reduces the viewing time of its single- and multi-homing viewers, v1 s(θ) and vm 1 (θ), and increases the time its multi-homing viewers spend on the other channel, v2 m (θ). Therefore, multi-homers obtain now a larger surplus from selecting platform 2. Then, platform 2 s incentives to raise its subscription fee f 2 are enhanced. Similarly, when platform 2 raises its subscription fee f 2, it looses some marginal consumers, that become single-homers on channel 1. From remark 2, a θ-viewer spends more time on a given channel when single-homing than when multi-homing. Hence, platform 1 s audience becomes more valuable to advertisers, allowing station 1 to raise the advertising time and revenues. Hence, endogenous advertising space and substitutability enrich the effects that sustain the asymmetric equilibrium. To sum up, under the conditions stated in Proposition 2, when platform 1 opts for a free-to-air business model, it increases the incentives of platform 2 to raise the subscription fee and to reduce the advertising space, leading to the adoption of a pay-tv business model. In turn, when platform 2 adopts a pay-tv business model, it increases the incentives of platform 1 to reduce its subscription fee and to increase its advertising space, up to a free-to air business model. 22

23 Notice that in our model the quality of airtime offered to the viewers depends on the scarcity of advertising messages. Hence, a pay-tv platform with no commercials offers a high quality airtime, entirely devoted to contents. In this perspective, although in our model platforms do not choose the quality of their programs (say, a Champions League vs. a Europa League football match, or a blockbuster vs a B-movie), a pay-tv in equilibrium is offering more valuable airtime, consistently with a widespead casual observation. Turning to advertisers, they are willing to reach the attention of the viewers, which are equally valuable as customers when they decide to purchase the advertised good. However, competition for advertisers allows these latter to pay less for reaching common viewers that can be accessed through either platform, compared to their willingness to pay to reach exclusive viewers. Moreover, in equilibrium some of the viewers that are accessed through the free-to-air channel are single-homers that spend more time watching that channel, further enhancing the advertisers willingness to pay for commercials on the free-to-air station. These different ingredients, therefore, increase the willingness to pay of advertisers to reach the viewers attention though the free-to-air station, that, with a bit of abuse, we could label as offering high quality eyeballs. In this sense, a free-to-air business model offers high quality eyeballs and low quality airtime, while a pay-tv business model delivers high quality airtime and low quality eyeballs. These affects are obtained just using prices and quantities and not, as more commonly in the literature on product differentiation, by affecting the characteristics of the products offered. 5.3 Strategic Imitation Opposite Business Model Equilibria have been obtained under additional conditions on k and ψ. This leaves open the question of what happens when these restrictions are not met. More specifically, can symmetric business model equilibria, characterized by a i = a j := a 0 and f i = f j := f 0 exist? Notice that symmetric equilibria can be of one of three different kinds. Both-free (a > 0, f = 0), Both-pay (a = 0, f > 0) and Both-mixed (a > 0, f > 0). 10 The following Proposition establishes that the latter two types do not exist in our setting. Proposition 3 If the platforms are substitutes, i.e. σ > 0, no symmetric pure strategy SPNE exist with strictly positive fees. 10 The combination (a = 0, f = 0) is trivially ruled out as an equilibrium since each platform can obtain positive profits by setting a positive fee or advertising space 23

24 To capture the intuition of this result, we observe that symmetric configurations make the gross utility from single-homing on either of the two channels the same. Hence, the type θ i,0 indifferent between subscribing station i or nothing is also indifferent between station j or no subscription. At the same time, imperfect substitutability implies that the gross utility from watching both channels less than doubles with respect to the gross surplus from one channel only. Since the first option requires to pay two times the fee in a symmetric configuration, the indifferent type θ i,0 strictly prefers to single-home, choosing at random one of the two stations, as observed in Remark 4. For suffi ciently higher types θ, instead, multi-homing becomes the preferred option. In other words, imperfect substitutability creates a subset of viewers that prefer to single-home, and are indifferent, in a symmetric configuration, between the two platforms. This indifference is broken when any of the two platforms slightly improves its offer, by cutting the fee, attracting all the indifferent viewers. Conversely, a both-free equilibrium in which both platforms choose a free-to-air business model exists if the revenue potential of the advertising side is suffi ciently high even when the other platform raises money from advertisers only. When f i = f j = 0, all viewers multi-home. Advertising revenues are still potentially attractive, preventing any deviation to a positive subscription fee, if the advertising technology ψ is not excessively effective, making a second exposure valuable to the advertisers, and, at the same time, the value of an informed viewer for advertisers, k, is suffi ciently high. In this case, then, it is more attractive for both firms to target the advertisers, renouncing to revenues from subscribers. This condition allows to define a region { } (k, ψ) R 2 + max Π i(f i, a > 0, f j = 0) Π i (f i = 0, a > 0, f j = 0). (17) f i c such that the opportunity cost of raising the fee, giving up advertising revenues, is larger that the benefit from collecting subscription fees. Let k(ψ) be the lower bound of this region. It is interesting to notice that the locus k(ψ) is increasing in ψ: a more effective advertising technology (a higher ψ) reduces the profits obtained from multi-homing viewers, that represents the opportunity cost of raising the subscription fee. 11 Then, to make this deviation unprofitable, we need a higher willingness to pay 11 The increasing locus k(ψ) is defined analogously to the decreasing locus k 1(ψ), and both ensure that there is no incentive to raise the subscription fee. The opposite pattern is due to the fact that k1(ψ) refers to an upraise deviation in f 1 when f 2 > 0, whereas k(ψ) is defined when f 2 = 0. In the former case, by raising its fee, platform 1 is giving up single-homing viewers, while in the latter it is losing multi-homing viewers. A higher ψ increases the ability to extract advertising revenues from single-homers whereas it reduces the rent extraction from multi-homing viewers. This opposite impact of a more effective advertising technology explains why the same opportunity cost of raising f 1, a high advertising revenue, is met with a lower k in the first case and with a higher k in the 24

25 k ~ k ( ψ ) Figure 4 Symmetric all free equilibria ψ of advertisers as captured by a higher k. Figure 4 shows the locus. The following Proposition summarises this discussion. a < 1 2 Proposition 4: If and f = 0. k k(ψ) there exist a both-free symmetric equilibrium with We cannot exclude that the existence regions defined above overlap thereby leading to multiplicity. However, we know that, for given k, an improvement in the advertising technology, as represented by an increase in ψ, initially induces symmetric all-free equilibria, and at some point moves the market equilibria to asymmetric business models. A low ψ, indeed, allows to extract suffi cient rents from advertisers when offering, in a symmetric equilibrium, the attention of multi-homing viewers. A high ψ, in turn, enhances the profits that can be obtained by offering single-homers to advertisers and, at the same time, reduces the value for advertisers of multi-homing viewers. In this case, one platform can obtain high profits from advertising whereas imitating this business model becomes unattractive. Hence, our results show that when the advertising technology is less effective, we observe in the market a larger offer of commercials, as it happens in the symmetric equilibria. A more effective technology, in turn, comes along with the concentration of advertising in a single station, while the other platform offers contents free of ads. second. 25

26 6 Mergers Consider now the case of a merger of the two stations, that creates a monopolist with two channels. Since viewers have a preference for variety, the monopolist has an incentive to offer two, rather than one channel. In this case, the advertisers might choose to place their ads on one, both or no channel. However, the monopolist has a clear incentive to restrict this choice, offering only a bundle (a 1 0, a 2 0) of advertising space on both channels, as an alternative to placing none. This way, the monopolist can avoid the Bertrand competition on common viewers that arises when an advertiser can decide to place its commercial on one rather than two stations, extracting from the advertisers the full value of all viewers, and not only of the single-homers. Consequently, the monopolist profits are Π = (f 1 c) (1 θ 1,0 ) + (f 2 c) (1 θ 12,1 ) + k ] 1 ( + 1 e ψ(a 1v1 m(θ)+a 2v m(θ))) 2 dθ. θ 12,1 [ θ12,1 θ 1,0 ( 1 e ψa 1v s 1 (θ)) dθ+(18) We can further introduce the locus { } km 1 (ψ) if k k 1 (ψ), ψ > 0 then max Π 1(f 1 ; a m 1, a m 2, f2 m ) Π 1 (f 1 = 0; a m 1, a m 2, f2 m ). f 1 c which is equivalent to the locus k 1 (ψ) defined in the duopoly case but computed at the monopoly equilibrium values. This locus delimits from below the region where the monopolist has an incentive not to set a positive subscription fee for channel 1. Further we define { km 2 (ψ) if k k 2 (ψ) and ψ > 0, then Π 2(a 2 = 0, f2 m) } 0 a 2 that, analogously to the duopoly case, sets the upper bound of the region where the monopolist has no incentive to offer positive advertising space on channel 2. Then, we can establish the following: Proposition 5: For k 1 m(ψ) k k 2 m (ψ), the monopoly equilibrium is an OBME characterized by f1 m = 0 < am 1 and f 2 m > 0 = am 2. Moreover, am 1 > a 1 and f 2 m > f 2, where a 1 and f 2 are the equilibrium advertising and subscription fee in the OBME of the duopoly case. (19) (20) Proposition 5 establishes that opposite business models would be chosen even in 26

27 case of a monopoly platform, with a higher subscription fee on the pay-tv channel and a larger advertising space on the free-to-air one, compared with the duopoly equilibria. These upward adjustments in the subscription fee and advertising space derive from the internalization of externalities across sides and platforms that the monopolist takes into account. When raising the advertising space on one channel, the vieweing time and gross surplus that is generated on the other channel raises. Equivalently, when raising the subscription fee on one channel, the fraction of singlehoming viewers on the other channel goes up. Since these latter spend more time watching the programs, they are more valuable to advertisers and advertising revenues increase. The monopolist internalizes these two effects, increasing f 2 and a 1 compared with the duopoly equilibrium. Differentiation by business models, therefore, emerges in equilibrium even when no strategic concern matters, and requires to examine more in depth the underlying effects at work. The IO literature on one sided markets may help setting the issue. If we take, for instance, the standard Hotelling model as a reference, we do observe differentiated varieties both in case of a monopolist and with two competing duopolists. 12 the two environments. The reasons why differentiation occurs are, however, very different in In case of monopoly, the firm aims at maximizing the gross surplus of the customers, being able, then, to extract it through prices. With heterogeneous consumers, their aggregate surplus is maximized by offering different varieties, in order to minimize the mismatch. We can label this case as discriminatory diff erentiation. The duopoly case is completely different. In this latter case, indeed, varieties are differentiated in order to reduce the substitutability between products, relaxing this way price competition. We have here a stance of strategic diff erentiation. In other words, in the monopoly case varieties are differentiated to maximize consumers aggregate surplus, while in duopoly differentiation is a way to retain producers surplus by relaxing price competition. Turning to our two-sided broadcasting market, we can find a similar comparison of discriminatory vs strategic differentiation. In case of a monopoly platform advertising revenues would not be dissipated if two channels were setting the same low subscription fee, with overlapping audiences, since the monopolist would be able to 12 Although we have differentiated varieties under both market structures, their value, and the associated prices are different. For instance, if we take the standard description of Hotelling preferences, where u p i (x i t) 2 is the utility from purchasing a variety x i at a price p i when the ideal variety is t and the maximal willingness to pay is u, the duopoly equilibrium when marginal costs are zero is x 1 = 0, x 2 = 1, p 1 = p 2 = 1. The corresponding monopoly equilibrium is x 1 = 1/4, x 2 = 3/4 and p 1 = p 2 = u 1/16. 27

28 charge the full value of these multi-homing viewers. However, this strategy would not be an equilibrium: charging the same subscription fee is not necessary to extract the full value from advertisers, whereas by doing so the monopoly platform would fail to extract profits from viewers through a high subscription fee. We conclude that also with two sided markets, differentiation (of business models) by a monopoly platform aims at maximising, and extracting, the surplus of both sides, a discriminatory motivation. With two competing stations, when one platform sets a positive subscription fee while not offering advertising space, it cover only a fraction of (high θ) viewers. Imitating such a strategy would still generate some profits, due to imperfect substitutability of the two platforms. However, the other station has a better alternative, since advertisers are willing to pay (the full value) to reach the viewers. This alternative is further enhanced by the other platform adopting a pay-tv business model. Since the low types do not subscribe the pay-tv channel, they would spend more time on the other channel if offered for free, further enhancing the advetisers willingness to pay. In the same vein. when one station adopts a free-to-air business model, imitating it still brings some money to the other station when the advertising technology is not perfectly effi cient, since a second exposure marginally increase the probability to capture viewers attention. But the other channel may profit even more exploiting the fact that offering the content free of ads increases the willingness to pay of high type viewers, that can be charged a high subscription fee. This discussion suggests that our strategic differentiation result is not a simple interation of the well known result derived in the one-sided product differentiation literature. Indeed, in the traditional framework consumers heterogeneity is crucial, because a low quality firm can gain only if there is a group of consumers that are not ready to pay much for a high quality product. Then, offering a lower quality allows to obtain positive profits on this low segment, whereas imitating the top product would dissipate profits with cut-throat competition. In our two sided case, instead, agents heterogeneity is not essential, since a platform prefers to make money by dealing with the agents on the other side rather than competing for a subset of the agents on the same side served by the other platform. Hence, it is the profit opportunity offered by the other side, rather than the possibility of serving a different subset of (heterogeneous) customers that leads to adopting opposite business models. 28

29 7 Welfare To complete the analysis we can consider the welfare maximising level of advertising and subscription fees that a benevolent social planner would implement. The welfare generated by the activities of the platforms comes from the two sides involved. On the advertisers front, the gross surplus corresponds to the expected profits from the sales induced by informing the consumers, that is the expected profits k from informed viewers times the full value of informing the single- and multi-homing viewers. Hence, the gross surplus on the advertising side grows with the exposure of the θ-viewers that subscribe access, and is therefore (initially) increasing in the advertising space a and decreasing in the subscription fee f. Notice that, since all advertisers are identical and participate, the advertising fee t simply splits the gross surplus between the platform and the advertisers, without affecting its size. The surplus on the viewers side, instead, corresponds to the gross utility of the viewers that subscribe access and watch the contents. It is therefore decreasing in both the subscription fee f, that reduces participation, and the advertising space a, due to the nuisance. Since viewers are heterogeneous, their decision to subscribe, and the gross surplus generated, are affected at the margin by a and f. Moreover, the gross utility from watching contents differs in case of single-homers - Ui s (θ) as from (12) - or multi-homers - U12 m (θ) as from (10). As a first step, a benevolent social planner would offer both channels, since viewers have a preference for variety and a second exposure improves their attention to commercials. Then, total welfare corresponds to: W = + θ12,1 θ 1,0 1 θ 12,1 { [ ( Ui s (θ) + k 1 e ψa 1v1 s(θ))]} dθ+ { [ ( U12(θ) m + k 1 e ψ(a 1v1 m(θ)+a 2v2 m(θ)))]} dθ. (21) Since subscription fees reduce viewers participation and the probability of informing them, welfare is maximised by setting them equal to their marginal cost, that is zero when no fee is raised. Hence, f w 1 = f w 2 = 0. Therefore, θ 1,0 = θ 12,1 = 0 and all the viewers multi-home. The optimal level of advertising, then, maximizes W (f w 1 = f w 2 = 0) = 1 0 { [ ( U12(θ) m + k 1 e ψ(a 1v1 m(θ)+a 2v2 m(θ)))]} dθ. 29

30 Since a 1 and a 2 symmetrically affect total welfare, a symmetric solution entails W a i = 1 0 { U m 12 (θ) a i + ke ψ(a 1v m 1 (θ)+a 2v m 2 (θ)) ψ(v m i + a i v m i a i v m } j + a j dθ = 0. a i Since vi m v + a m v i j i a i + a m j a i = θ(1 2aw ) 2 at a symmetric allocation a 1 = a 2 = a w and the first derivative in the integral is negative, we conclude that a w < 1 2. Then, we can state the following: Proposition 6: A benevolent social planner off ers two free-to-air channels with advertising space a w 1 = aw 2 < Policy implications on market definition A policy implication of Propositions 2 and 5 refers to market definition in antitrust or regulatory issues. The traditional approach of the European Commission and most of the national Antitrust Authorities has stated that free-to-air and pay-tv operators belong to different relevant markets. 13 This conclusion has been based on two main arguments. The first refers to the retail markets, and is based on the observation that a free-to-air operator does not deal with viewers but only with advertisers, the opposite occurring for a pay-tv. Then, a free-to-air platform does not compete on subscriptions with a pay-tv, that, in turn, does not compete for advertising revenues with a free-to-air operator. The second argiment refers to the wholesale level and the packaging of contents. It is argued that certain premium contents, as attractive movies and sport events, are sold by the content producers to the pay-tv operators whereas a free-to-air platform could not compete for them. This approach to market definition, then, has deeply affected the outcome of important antitrust cases involving mergers or abuse of dominance. Our results seem particularly relevant in this perspective. The existence of asymmetric business model equilibria, indeed, shows that two perfectly symmetric platforms may end up selecting opposite business models in the attempt to relax revenue competition on the same side. Although this outcome may be interpreted as the absence of any competition between them, Proposition 5 shows that cross side effects still remain, making a merger to monopoly quite adverse to subscribers and 13 See, for instance, for the European Commission, case IV/M.993 Bertelsmann/Kirch/Premiere in 1998, case COMP/M Newscorp/Telepiù in 2003, case COMP/M Newscorp/BSlyB In the UK, see, for instance, Competition Commission s decision on BritishSky Broadcasting Group Plc and Manchster United Plc in

31 advertisers, that pay more. Hence, we argue that in an antitrust perspective defining separate relevant markets may fail to take into account persistent interactions of the two platforms across sides. 8 Conclusions We have developed a symmetric model of media platform in which both firms have the same feasible set of instruments, i.e. subscription fees and advertising space, to raise revenues. We established that only symmetric free-to-air equilibria exists when the advertising technology is not very effective. In this case multiple exposure of viewers is valuable to advertisers, and the platforms end up offering for free their content and raise money from advertisers only. When instead the advertising technology is suffi ciently effi cient, that is when it is very likely to capture the attention of a viewer at a first exposure, then an asymmetric equilibrium exists in which the two firms opt for opposite business models. The free-to-air channel offers for free the contents, and raises revenues only on the advertisers side. Conversely, the pay-tv does not insert advertising breaks, chasing in revenues from the subscribers only. Each business model creates the incentives for the rival platform to opt for an opposite one in equilibrium. This result has possibily implications for public policies, and in particular competition policy and regulation, where traditionally the free-to-air and the pay-tv operators have been considered as belonging to different relevant markets. Our result, showing that this outcome comes out of a perfectly symmetric problem, where platforms differentiate by business model to increase equilibrium revenues, may lead to reconsider this traditional approach, including all TV operators in a two-sided relevant market. 9 Appendix I: Proofs Proof of Proposition 1: Firm i s 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 (22) i, f j ) f i < f j ( ) where Π S i (f i) = f i 1 2f 1/2 i /b are the profits from subscriptions and Π A i (f i, f j ) = ( ) 2k f 1/2 j f 1/2 i /b are those from advertising. The profits from subscription, Π S i (f i) are concave and have a maximum at f i = f S = b2 9 irrespective of f j, with Π S i ( b2 9 ) = b

32 The profits from advertising, Π A i (f i, f j ), instead, are decreasing and convex, with a maximum at f i = 0, where the audience and the willingness to pay of advertisers are maximised. Let us consider first whether a symmetric equilbrium f i = f j exists. If k = 0 then Π i (f i, f j ) = Π S i (f i) for any f j and platform i s profit is maximised for f i = f S. Hence, a symmetric equilibrium exists and is unique with f i = f j = f S. If k > 0 consider a candidate symmetric equilibrium f i = f j = f. Then, Π A i (f, f) = 0. If f f S the profits from subscription Π S i (f i) are not maximised. If f = f S the profits are not maximised either, since, by slightly cutting the fee f i below f S, firm i has only a second order loss on the subscription profits Π S i (f i) but a first order gain in advertising profits Π A i (f i, f S ). We conclude that when k > 0 no symmetric equilibrium f i = f j exists. Let us now turn to candidate asymmetric equilibria where, without loss of generality, we set f i < f j. Since Π j(f j, f i ) = Π S j (f j), it must be f j = f S. Firm i s profits are Π i (f i, f S ) = Π S i (f i) + Π A i (f i, f S ), i.e. they are the sum of two continuous functions defined over the compact interval f i [ 0, f S]. Hence, they admit at least one maximum. One local maximum is at the corner solution f i = 0. Turning to interior maxima, it is easy to check that the first and second order conditions hold at: f(k) = ( b + 2 ) 2 b 2 12k. 6 Hence, there exists an additional interior local maximum if and only if k b 2 /12. Notice that f(k) does not depend on f j, although the level of profits Π i (f(k), f j ) increases in it. Moreover, f(k) converges to f S = b2 9 as k 0 and is decreasing in k, with f( b2 12 ) = b2 36. To find the global maximum, and therefore the best reply to f j = f S, we can observe that Π i (f(k), f j ) Π i (0, f j ) f(k) 1/2 (1 2 b f(k)1/2 ) 2k b k b2 16. Hence, for k b2 16 firm i s best reply to f j = f S is f i = f(k) whereas for k b2 16 firm i s best reply to f j = f S is f i = 0. Finally, let us consider the global best reply for firm j. If k b2 16, firm i sets optimally f i = 0. Then, it is trivially true that firm j s best reply to f i = 0 has to be f j = f S since there is no way, for firm j, to set a fee lower than f i. If, instead, k b2 16 and therefore f i = f(k), firm j has two alternatives: to set a fee higher than f i, i.e. to set f j = f S and gain Π S j (f S ) = b2 27. Alternatively, firm j could deviate 32

33 and set f j = 0 becoming the cheaper platform and getting Π j (0, f(k)) = 2k b f(k)1/2. Then, f j = f S is the best reply to f i = f(k) if, after rearranging, f(k) < ( b3 2k )2, that [ ] is verified for k. 0, b2 16 We conclude that, for k b2 16 there exists a Nash equilibrium with f i = f(k) and fj = f S and for k b2 16 there exists a Nash equilibrium with f i = 0 and fj = f S. Q.E.D Proof of Proposition 2: Let (a 1 > 0 = f 1, a 2 = 0 < f 2 ) be a candidate ABME. To prove that this equilibrium exists we need to show that (a 1 > 0 = f1 ) = arg max Π 1 (a 1, f 1 ; a 2, f2 ) a 1,f 1 (a 2 = 0 < f2 ) = arg max Π 2 (a 2, f 2 ; a 1, f1 ). a 2,f 2 Firm 1. Let us consider firm 1 first: to analyse the optimal setting of f 1 it is convenient to study the optimal fee that maximises the subscription profits Π S 1 and the one that maximises the advertising profits Π A 1, where Π 1 = Π S 1 + ΠA 1. Given a 2 = 0 < f 2 we consider the case where viewers sort by not selecting any platform (θ [0, θ 1,0 ), possibly an empty set), subscribe platform 1 (θ [θ 1,0 θ 12,1 )) and subscribe both (θ [θ 12,1, 1]. This corresponds to the optimal choices of viewers in a neighborhood of the candidate equilibrium. In Appendix II we show that this case corresponds to a subset of (a 1, f 1 ), labeled region α. The profits Π 1 in this case are not lower than the profits platform 1 obtains when viewers sort according to a different sequence of choices, what happens outside region α. Hence, considering the expressions in this case guarantee to find a global maximum for Π 1 for any a 1 0 and f 1 0. The profits from subscription: Π S 1 = { (f 1 c)(1 θ 1,0 ) for f 1 > 0 0 for f 1 = 0 (23) are continuous and concave, and admit an internal maximum f S 1 > 0. Turning to the advertising profits, given a 2 = 0 < f 2 θ12,1 ( Π A 1 = k 1 e ψa 1v s(θ)) 1 ( 1 dθ + 1 e ψ(a 1v m(θ))) 1 dθ θ 1,0 θ 12,1 since viewers in θ [θ 1,0 θ 12,1 ) single-home whereas viewers in θ [θ 12,1, 1] multi- 33

34 home. Notice that f 1 affects them only through θ 1,0, the lower bound of the singlehomers, where θ 1,0 f 1 > 0 for f 1 > 0. Then, it is equivalent to maximise advertising profits through f 1 or θ 1,0, and we choose this latter. Since v1 S(θ) = θb 1 2 σ, the first and second order conditions are: Π A 1 = k(1 e ψa b 1 θ 1,0 1 2 σ ) 0 θ 1,0 Π A2 1 θ 2 1,0 = kψ a 1b 1 a 1 b 1 2 σ e ψ 2 σ θ 1,0 0. Hence, the profits from advertising are maximised at θ 1,0 = f A 1 = 0, where ΠA 1 θ 1,0 = 0 since θ 1,0 (f 1 = 0) = 0. Moreover, they are increasing in k and ψ. Second, the total profits Π 1 = Π S 1 + ΠA 1 are the sum of two functions concave in f 1, and there exists a f 1 (k, ψ) = arg max f1 >0 Π 1 ( 0, f1 S ). Notice that, since at f1 = 0 the marginal subscription costs c become nil, there is a second maximum at f 1 = 0. Third, since an increase in k or ψ increases advertising profits, f 1 (k, ψ) is decreasing in k and ψ: when advertising has a larger revenue potential (high k) and is more effective (high ψ), advertising profits plays an increasing role in maximising total profits Π 1 = Π S 1 +ΠA 1, and the optimal fee f 1 (k, ψ) decreases. Then, for given ψ there exists a k 1 such that Π 1 (f 1 (k 1, ψ), a 1, a 2, f 2 ) = Π 1(0, a 1, a 2, f 2 ). In other words, Π 1 has two equivalent maxima at f 1 (k 1, ψ) and at 0. Hence, for k k 1 (ψ; a 1, a 2, f 2 ) the optimal fee is f 1 = 0. The locus k 1 (ψ;.) is decreasing in ψ. When ψ 0, the probability of informing the single-homing viewers vanishes, and we need a very large k to give suffi ciently high profits from advertising to induce a zero subscription fee. Hence, lim ψ 0 + k 1 (ψ;.) =. Among these loci, that depend also on a 1, the relevant one is the locus where a 1 = a 1, the optimal advertising space that we are going to find. Let us label this locus as k 1 (ψ) = k 1 (ψ; a 1, a 2, f 2 ). Moving to the choice of the advertising space a 1 and setting f 1 = 0 = a 2, f 2 > 0, we can notice that Π 1 is continuous in a 1, Π 1 (a 1 = 0) = Π 1 (a 1 = 1) = 0. Moreover, since θ 1,0(f 1 =0) a 1 = θ 1,0 b 1 = 0, vs 1 a 1 = θ 2 σ < 0, vm 1 a 1 = θ(2 σ) 4(1 σ) < 0 and vm 2 a 1 = θσ 4(1 σ) > 0, the partial derivative of Π 1 with respect to a 1 at f1 = 0 = a 2, f 2 > 0 is Π 1 (f 1 =0=a 2,f 2 >0) a 1 [ θ = k 12,1 ( a 1 e ψa 1 v1 m(θ12,1) e ψa 1v1 s(θ 12,1) ) e ψa1vm(θ) 1 ψ θ((2 σ)(1 2a 1) σ) 4(1 σ) θ 12,1 θ12,1 0 dθ e ψa 1v1 s(θ) ψ θ(1 2a 1) 2 σ dθ+ (24) 34

35 That is positive for a 1 = 0 and negative at a 1 = 1. Since θ 12,1 a 1 = σθ 12,1 < 0 b 2 and v1 m(θ) < vs 1 (θ), the first term is negative, and therefore at the internal maximum 0 < a 1 < 1 2. In words, starting from a low level of advertising, fincreasing a 1 reduces the share of high value single homers and the advertising fee that can be required, but increases the effectiveness of commercials and the willingness to pay of advertisers. Taking the two derivatives together, a positive ψ and a k > k 1 (ψ) are suffi cient conditions for f 1 = 0 < a 1 to be global best replies to a 2 = 0 < f 2. Firm 2. Let us now consider firm 2. The profits at a 1 > 0 = f 1 are: Π 2 = (f 2 c)(1 θ 12,1 ) + k [ 1 θ 12,1 The partial derivative with respect to a 2 is : Π 2 a 2 = (f 2 c) θ 12,1 a 2 +k where ( e ψa 1 vm 1 e ψ(a 1 vm 1 +a 2v m 2 ) ) dθ [ θ ( ) ] 1 12,1 e ψ(a 1 vm 1 +a 2v2 m ) e ψa 1 vm 1 + Ω(a 2, θ)dθ a 2 θ=θ12,1 θ 12,1 ] ( Ω(a 2, θ, ψ) = ψ a v1 m 1 + v m v m ) a 2 e ψ(a 1 vm 1 (θ)+a 2v m(θ)) 2 ψa v1 m 1 e ψa 1 vm 1 (θ). a 2 a 2 a 2 Notice that Ω(a 2 = 0, θ, ψ) = ψv m 2 e ψa 1 vm 1 (θ) ψv m 2 > 0. Moreover, [( ( Ω = ψ 2 vm 2 ψ a v1 m 1 + v m v m ) ) a 2 e ψ(a 1 vm 1 (θ)+a 2v m(θ)) ( 2 + ψ a v m ) ] e ψa 1 vm 1 (θ) < 0 a 2 a 2 a 2 a 2 a 2 since vm 2 a 2 < 0. Moreover, lim ψ Ω = 0 since Ω containts expressions in the form ψe ψ that initially increase, have a maximum at, say, ψ and then asymptotically tend to zero when ψ. Since θ 12,1 a 2 = (2 σ)θ 12,1 b 2 > 0 the first term of Π 2 a 2 is negative and the second is non positive, while the third is positive at a 2 = 0 and decreases, and vanishes when ψ increases indefinitely. Now we can contruct the optimal choice a 2 = 0 in the following way. For a given 35

36 pair (k, ψ) consider the sign of Π 2 (a 2 = 0) = (f 2 c) θ 1 12,1 + k Ω(a 2 = 0, θ, ψ)dθ. a 2 a 2 θ 12,1 If Π 2(a 2 =0) a 2 0, then a 2 = 0 is the global maximum since the first negative term dominates the second positive term also for a 2 > 0, being Ω a 2 < 0. Moreover, a 2 = 0 is the optimal choice even for higher ψ, since the second positive term decreases in ψ, preserving the sign of the derivative. The same holds true if we reduce k. Notice that this case typically happens when k is very small. If, instead, Π 2(a 2 =0) a 2 > 0, it means that the second positive term of the derivative dominates the negative first term. Since the former is multiplied by k, we can reduce k, for given ψ, or we can increase ψ (reducing Ω) up to the point where Π 2(a 2 =0) a 2 0. This identifies a locus k 2 (ψ, f 2, a 1, f 1 ) along which Π 2(a 2 =0) a 2 = 0. To sum up, when k is zero or negligible the derivative is negative for any ψ since the first negative term dominates. Let us define k, such that when k = k and the second term in the derivative is maximised at ψ, then Π 2(a 2 =0) a 2 = 0. Since Ω is decreasing in ψ, Π 2(a 2 =0) a 2 < 0 for ψ > ψ. For k > k we need a ψ > ψ to reduce the value of the second term and still obtain Π 2(a 2 =0) a 2 = 0. We conclude that the locus k 2 (ψ, f 2, a 1, f 1 ) is flat at k = k for ψ ψ and then increasing in ψ. Among the loci k 2 (ψ, f 2.a 1.f 1 ), that depend on f 2 we shall select k 2 (ψ) = k 2 (ψ, f2, a 1, f 1 ), the one associated with the optimal fee f2, that we are now going to find. The partial derivative is: [ Π 2 θ 12,1 θ12,1 ( = 1 θ 12,1 f 2 +k e ψ(a 1 vm 1 (θ 12,1)+a 2 v2 m(θ 12,1)) )] e ψa 1 v1 m(θ 12,1), f 2 f 2 f 2 that at a 2 = 0 admits the closed form solution f 2 (a 1) = (2(1 σ) + σa 1 )2 18(2 σ)(1 σ). Since Π 2 is concave in f 2, f 2 (a 1 ) is the optimal fee. Then, k k 2 (ψ) is a suffi cient condition such that a 2 = 0 and f 2 (a 1 ) are a best reply to f 1 = 0 < a 1 < 1 2. Since k 2 (ψ) is initially flat at k = k and then increasing while k 1 (ψ) is decreasing with lim ψ 0 + k 1 (ψ) =, the two loci intersect at some ψ. Then, k 1 (ψ) k k2 (ψ) and ψ ψ a ABME exists. Q.E.D Proof of Proposition 3: Let us consider a candidate symmetric equilibrium ρ sim = (a i = a j = a 0, f i = f j = f > 0). Remark 4 states the sorting of viewers 36

37 between the two platforms. A subset of viewers θ [0, θ i,0 ) subscribes no channel. A subset θ [θ i,0, θ ij,i ) single-homes and is indifferent between subscribing channel i or j, choosing with some probability (say 1/2) one of the two stations. The higher types θ (θ ij,i, 1] multi-home. Notice that the set of indifferent viewers disappears when σ = 0, since in this case U m 12 (θ) = 2U s i (θ) at ρsim and, with symmetric offers, all those viewers that subscribe choose to multi-home. Given ρ sim, when σ > 0 each channel has an incentive to slightly reduce the subscription fee, capturing the whole group of indifferent viewers and increasing profits. More precisely, the increase in profits if platform i slightly undercuts the other platform s fee is Π i = 1 2 [ f i (θ ij,i θ i,0 ) + k θij,i θ i,0 ] ( 1 e ψa ivi s(θ)) dθ > 0. This means that, when the channels are imperfect substitutes, a positive subset of viewers exists that moves to the cheaper platform when indifference is broken through undercutting. These arguments hold true for k 0 and a i = a j 0. that is, no matter if the advertising side produces a profit or not. Hence, no symmetric configuration with positive subscription fee can be an equilibrium since it is more profitable for either platform to slightly undercut each other. If σ = 0, as in the introductory example, no subset of indifferent viewers exists, and the profit function is continuous. Then, as shown in Proposition 1, when a i = a j 0 and k = 0, a symmetric equilibrium with positive fees exists. Q.E.D. Proof of Proposition 4: Consider the case a i = a j > 0 and f i = f j = 0. Since with zero fees all the viewers multi-home, the profits of platform i are Π i = k 1 0 ( e ψa jv m j (θ) e ψ(a iv m i (θ)+a jv m j (θ))) dθ. The first order conditions for a symmetric equilibrium are then Π i a i = kψ 1 0 [( v m i + a i v m i a i v m ) j + a j e ψ(a ivi m a i (θ)+a jvj m(θ)) v m ] j a j e ψa jvj m(θ) dθ a i Since in a symmetric advertising configuration a i = a j = a we have vi m = θb 2, vm i θ(2 σ) 4(1 σ) and v j a i = θσ 4(1 σ), the first order conditions above can be rewritten as Π i a i = kψ 1 0 [ θ(1 2a) e ψa(1 a)θ dθ θaσ ] 2 4(1 σ) e ψa(1 a)θ/2 dθ. 37 a i =

38 < 0. Hence, in the candidate symmetric equilib- Then, Π i(a=0) a i > 0 and Π i(a=1/2) a i rium a (0, 1/2). We have now to check that setting a zero fee is optimal given a i = a j = a when the other platform is offering the content for free. If f j = 0 and platform i deviates and raises its fee, its profits are 1 ( Π i = (f i c) (1 θ ij,j ) + k e ψa jvj m(θ) e ψ(a ivi m θ ij,j (θ)+a jv m j (θ))) dθ, that can be read as the sum of the profits from subscription and from advertising. Then, Π i f i = 1 θ ij,j (f i c) θ ij,j f i [ k e ψa jvj m(θij,j) e ψ(a ivi m (θ ij,j)+a j v m j (θ ij,j)) ] θ ij,j f i, where θ ij,j f i > 0. The first term gives the impact of a positive subscription fee f i on subscription profits and the second on the profits from advertising. The former are maximised at f i = fi S > 0 whereas the latter at f i = 0. Hence, when firm 1 deviates setting a positive fee, the internal maximum is at f(k) ( 0, fi S ) decreasing in k, to be compared with the corner solution f i = 0, where the platform saves on the marginal administrative costs c of collecting subscriptions. Then, for given a i = a j = a > 0 and ψ there exists a k(ψ) such that the two maxima are equivalent, i.e. Π i (f i = f(k)) = Π i (f i = 0) when k = k(ψ). For any k larger than that, it is optimal to set f 1 = 0, giving up subscription revenues but gaining a valuable subset of viewers. Among these loci, we define k(ψ) the one associated with a i = a j = a. This locus is increasing in ψ since a higher ψ reduces the value of a second exposure. Then, in order to prevent a firm from deviating by setting a positive subscription fee, we need a higher k to preserve the revenue potential on the advertising side. The last symmetric configuration to consider is a i = a j = f i = f j = 0, where firms get no profits. Since any firm can obtain positive profits by raising its fee and/or its advertising space, this cannot be an equilibrium. Q.E.D. 38

39 Proof of Proposition 5: Notice that the profits of the monopolist, Π = (f 1 c) (1 θ 1,0 ) + (f 2 c) (1 θ 12,1 ) + k ] 1 ( + 1 e ψ(a 1v1 m(θ)+a 2v m(θ))) 2 dθ. θ 12,1 Π, can be written as: 1 Π = Π 1 + f 2 (1 θ 12,1 ) + k where = Π 2 + f 1 (1 θ 1,0 ) + k Π 1 = (f 1 c)(1 θ 1,0 )+k [ θ12,1 θ 1,0 θ 12,1 [ θ12,1 θ 1,0 are firm 1 s profits in the duopoly case and [ θ12,1 θ 1,0 ( 1 e ψa 1v s 1 (θ)) dθ+ ( 1 e ψa 2v m 2 (θ)) dθ = (25) ( 1 e ψa 1v1 s(θ)) ] 1 ( dθ + 1 e ψa 1v m(θ)) 1 dθ. θ 12,1 ( 1 e ψa 1v1 s(θ)) ] 1 ( dθ + e ψa 2v2 m(θ) e ψ(a 1v1 m(θ)+a 2v m(θ))) 2 dθ θ 12,1 1 ( Π 2 = (f 2 c)(1 θ 12,1 ) + k e ψa 1v1 m(θ) e ψ(a 1v1 m(θ)+a 2v m(θ))) 2 dθ θ 12,1 are the duopoly profits of firm 2. Then, f 1 only affects Π 1 and Π f 1 = Π 1 f 1 < 0 for k suffi ciently large, identifying the same suffi cient condition on k of the duopoly equilibrium. Π = Π 1 θ 12,1 f 2 k θ ( ) 1 12,1 1 e ψa 2v2 m(θ 12,1 +k e ψa2vm(θ) 2 v2 m ψa 2 dθ > Π 1 a 1 a 1 a 1 a 1 θ 12,1 a 1 a 1 since θ 12,1 a 1 < 0. Then, we have a m 1 > a 1 where a 1 advertising in the duopoly case. Turning to the second platform, is platform 1 s equilibrium [ Π = Π 2 θ ( ) ] 1 12,1 +k e ψa 1v1 m(θ12,1) e ψa 1v1 s(θ 12,1) + e ψa1vm(θ) 1 v1 m ψa 1 dθ. a 2 a 2 a 2 θ 12,1 a 21 39

40 Π Then, lim ψ a 2 = Π 2 a 2 case. Finally, Since v1 m(θ) < vs 1 (θ), Π f 2 f2 m > f 2. Q.E.D. < 0, implying the same suffi cient conditions of the duopoly Π = Π [ 2 θ12,1 ( )] + k e ψa 1v1 m(θ12,1) e ψa 1v1 s(θ 12,1). f 2 f 2 f 2 > 0 at the duopoly equilibrium fee f2, implying that 10 Appendix II: viewers choices In this Appendix we completely characterize the choices of the viewers of different type θ for all the possibile configurations of subscription fees and advertising space of the two platforms. In Section 5.1 we have already established the optimal viewing time of singlehoming ( v i s(θ) = θb i 2 σ ) and multi-homing ( vm i (θ) = θb i 4(1 σ) ) viewers. The associated gross surplus is then for multi-homers and for single-homers. U m 12(θ) = θ b 1 v 1 + b 2 v 2 2 = θ 2 [ (2 σ)(b 2 8(1 σ) 1 + b 2 ] 2) 2σb 1 b 2. U s i (θ) = (θb i) 2 2(2 σ) Given ρ := ((a i, f i ), (a j, f j )) a θ-viewer selects the channels to subscribe choosing: max {0, U s 1 (θ) f 1, U s 2 (θ) f 2, U m 12(θ) f 1 f 2 }. We now proceed by identifying the optimal subscription choice of a θ-viewer and then identifying the subscription patterns across types. In the following Lemmas we establish the main features of viewers choice. Lemma 1: Given ρ := (a i, f i, a j, f j ) and θ (0, 1], we have and U s i (θ) U s j (θ) and U s i θ U s j θ U m 12(θ) > max {U s 1 (θ), U s 2 (θ)} and U m 12 θ 40 if b i b j. { U s > max i θ, U j s } θ (26)

41 Proof of lemma 1: From direct inspection we can observe that U12 m(θ) and U i s(θ) are increasing and convex in θ. When single-homing, moreover, In other words, when having access to just one channel, a θ-viewer gets a higher gross surplus from the channel with less advertising breaks (a higher quality of the airtime). Notice that U s i θ = θb2 i 2 σ > 0, that is, the gross surplus when single-homing is increasing in θ and steeper the higher the quality of the airtime. Hence, if a platform has more ads than the other, its gross surplus when single-homing is flatter than the rival s. Moreover, U m 12 = U s i + 2(1 σ) 2 σ ( vm j ) 2, (27) implying that the gross surplus when multi-homing is larger than when single-homing, and that it is increasing and steeper in θ than the gross surplus when multi-homing. Q.E.D. Lemma 1 establishes single crossing relationships between the gross surplus of multi- and single-homing viewers that are helpful when we consider their choice according to their type θ. Let us label platform 1 such that 0 f 1 f 2 and σ 2 σ b 2 < b 1 b 2, that is, platform 1 is cheaper but offers a lower quality of the airtime, having more advertising breaks. This is the interesting case, that includes also perfectly symmetric platforms. Then, define the following thresholds: θ i,0 = [2(2 σ)f i] 1/2 Ui s (θ i,0 ) f i = 0, i = 1, 2 b i [ ] 2(2 σ)(f2 f 1 ) 1/2 θ 1,2 = b 2 2 U b2 1 s (θ 1,2 ) f 1 = U2 s (θ 1,2 ) f 2 1 θ 12,i = [8(2 σ)(1 σ)f j] 1/2 U12(θ m 12,i ) f 1 f 2 = Ui s (θ 12,i ) f i θ 12,0 = [ b j 8(2 σ)(1 σ)(f 1 + f 2 ) [(2 σ)(b 1 + b 2 )] 2 2(2 σ)(1 σ)b 1 b 2 ] 1/2 U m 12(θ 12,0 ) f 1 f 2 = 0. 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. Notice that, since U12 m(θ), U 1 s(θ) and U 2 s (θ) are increasing and convex in θ, with U12 m steeper than U 2 s(θ), the platform with a higher quality b 2 of the airtime, that, in 41

42 turn, is steeper than U1 s (θ), all the types above a threshold strictly rank in the same way the two alternatives that are indifferent at the threshold, while the types below make the opposite ranking. Hence, for instance, U s i (θ) f i >(<)0 for θ >(<)θ i,0 etc. The following lemma establishes the rankings among thresholds. Lemma 2: Suppose that 0 f 1 f 2 and σ 2 σ b 2 < b 1 b 2 Then if θ 12,j θ 12,i then θ 12,i θ 1,2. if θ 12,j = θ 12,i = θ 1,2 then θ i,0 < θ j,0 Proof of Lemma 2: The first inequality implies that U m 12(θ 12,i ) f 1 f 2 = U s i (θ 12,i ) f i U s j (θ 12,i ) f j. But since U s j (θ) is steeper than U s i (θ), θ 12,i θ 1,2. Moving to the second expression, the first equality implies that U m 12(θ 12,i ) f 1 f 2 = U s i (θ 12,i ) f i = U s j (θ 12,i ) f j. But since U s j (θ) is steeper than U s i (θ), then U s j (θ) f j < U s i (θ) f i for θ < θ 1,2. Then, U s j (θ i,0) f j < U s i (θ i,0) f i = 0 and therefore θ i,0 < θ j,0. Q.E.D. We can now analyze the subscription choices of a θ-viewer for given b i, b j, f i and f j. The following Lemma identifies the subsets of viewers (possibly empty) that choose no channel, single-home on platform 1 or 2 or multi-home. Lemma 3: The subsets of viewers choosing no channel ( Θ ), channel 1 ( Θ 1 ), channel 2 ( Θ 2 )or both ( Θ 12 ) are identified by the following intervals: Θ = [0, min {θ 1,0, θ 2,0, θ 12,0, 1}), Θ 1 = [θ 1,0, min {θ 1,2, θ 12,1, 1}) Θ 2 = [max {θ 2,0, θ 1,2 }, min {, θ 12,2, 1}) Θ 12 = [max {θ 12,0, θ 12,1, θ 12,2 }, 1] Proof of Lemma 3: The viewer subscribes no channel iff U s i (θ) f i < 0, i = 1, 2 42

43 and U m 12 (θ) f 1 f 2 < 0. From the definition of the different thresholds the expression follows. This set is empty if min {θ 1,0, θ 2,0, θ 12,0 } = 0. The θ-viewers that single-home on channel 1, the cheaper but low quality channel, are identified by the following inequalities: U s 1 (θ) f 1 0, U s 1 (θ) f 1 U s 2 (θ) f 2 and U s 1 (θ) f 1 U m 12 (θ) f 1 f 2. From the definition of the different thresholds the expression follows.notice that no viewer single-homes on platform 1 if θ 1,0 > min {θ 1,2, θ 12,1, 1}. Conversely, the channel 2 single-homers are characterized by U s 2 (θ) f 2 0, U s 2 (θ) f 2 U s 1 (θ) f 1 and U s 2 (θ) f 2 U m 12 (θ) f 1 f 2. The corresponding region obtains given the definition of the thresholds. This region is empty, implying that there is no single-homer on platform 2, if max {θ 2,0, θ 1,2 } > min {, θ 12,2, 1}. Finally, a θ-viewer multihomes if U m 12 (θ) f 1 f 2 0, U m 12 (θ) f 1 f 2 U s i (θ) f i for i = 1, 2. The expression directly follows from the definition of the thresholds. No viewer opts for multi-homing if max {θ 12,0, θ 12,1, θ 12,2 } > 1. Q.E.D. Our final step is to identify the admissible sequences of choices for θ [0, 1] for given b 1 b 2 and f 1 f 2. The following Lemma identifies, for given b 1 b 2 and f 1 f 2 three different regions corresponding, for increasing θ, to different sequences of choices by viewers. Lemma 4: for θ [0, 1] for given b 1 b 2 and f 1 f 2 let us define the following regions: A = B = C = { [ ] [ σ (b 1, f 1 ) b 1 2 σ b b 2 ]} 1 2, b 2, f 1 0, f 2 b 2 2 { [ ] ( σ (b 1, f 1 ) b 1 2 σ b b 2 ]} 1 b 2 1 2, b 2, f 1 f 2 b 2, f 2 b { [ ] ( (b 1, f 1 ) σ b 1 2 σ b b 2 ]} 1 2, b 2, f 1 f 2 b 2, f 2 2 Then, in region A for θ [0, 1] viewers choices are characterized by the following sequence: {, 1, 12}. In region B, instead, the sequence of choices for increasing θ is {, 1, 2, 12}. Finally, in region C we have {, 2, 12}. 43

44 Proof of Lemma 4: Let us introduce the following loci: θ 1,0 = θ 2,0 f 1 = f 2 b 2 1 b 2 2 θ 12,1 = θ 12,2 = θ 1,2 f 1 = f 2 b 2 1 b 2 2 b 2 1 < f 2 b 2. 2 b Notice that f 1 = f b 2 2 Since we label platform 1 such that 0 f 1 f 2 and is defined for b 1 0, implying v m i 0. σ 2 σ b 2 < b 1 b 2, we have to consider the sequence of choices by the different viewers types in this region. If f 1 = f 2 = 0, then, clearly all the viewers watch both channels, due to (??) i.e. Θ 12 = [0, 1]. To analyze the other cases, it is useful to use the following facts: θ 1,0 < θ 2,0 if f 1 < f 2 b 2 1 b 2 2 θ 12,2 < θ 1,2 and θ 12,1 < θ 1,2 if f 1 < f 2 b 2 1 b 2 2 f 2 b 2 1 b 2 2 for b 1 [0, b 2 ]. In region A, as defined in the statement of Lemma 4, we have θ 1,0 < θ 2,0, θ 12,1 < θ 1,2 and θ 12,2 < θ 1,2. Then, Θ A = [0, θ 1,0), Θ A 1 = [θ 1,0, min {θ 12,1, 1}] and Θ A 12 = [min {θ 12,1, 1}, 1]. There is no viewer that opts for single-homing on platform 2 in this case, since max {θ 2,0, θ 1,2 } = θ 1,2 > min {θ 12,2, 1} = θ 12,2 since U s 1 (θ 2,0) f 1 > 0 = U s 2 (θ 2,0) f 2 and therefore θ 2,0 < θ 1,2. In other words, for increasing θ, the sequence of choices by θ-viewers is to subscribe no channel (if f 1 > 0), to subscribe the cheaper channel 1 and, for higher types, to multi-home. In region B we have θ 1,0 < θ 2,0, θ 12,1 > θ 1,2 and θ 12,2 > θ 1,2. Then, Θ B = [0, θ 1,0 ), Θ B 1 = [θ 1,0, min {θ 1,2, 1}], Θ B 2 = [min {θ 1,2, 1}, min {θ 12,2, 1}] and Θ B 12 = [min {θ 12,2, 1}, 1]. Hence, in region B the lowest types do not subscribe, if f 1 > 0, then viewers single-home on the cheaper platform 1, higher types single-home on the more expensive, high quality platform and finally highest types multihome. Region C is characterized by θ 1,0 > θ 2,0, θ 12,1 > θ 1,2 and θ 12,2 > θ 1,2. Therefore, Θ C = [0, θ 2,0), Θ C 2 = [θ 2,0, min {θ 12,2, 1}], and Θ C 12 = [min {θ 12,2, 1}, 1]. In this case, no viewer chooses to single-home on platform 1 since θ 1,0 > min {θ 1,2, θ 12,1, 1} = θ 1,2. Indeed, U2 s(θ 1,0) f 2 > 0 = U1 s(θ 1,0) f 1 and therefore θ 1,2 < θ 1,0, being U1 s (θ) flatter than U2 s (θ). Hence, now the sequence of no subscribers, single-homers on channel 2, then multi-homers characterizes the viewers choices. Q.E.D. 44

45 Given the viewers subscription choices, corresponding to a set of thresholds in Θ, we can derive the number (share) of viewers subscribing each channel. Let s r i (a i, a j, f i, f j ) be the share of viewers that subscribe for firm i when we are in region r = A, B, C. Then, we have: s A 1 = 1 θ 1,0 and s A 2 = 1 θ 12,1 s B 1 = (θ 2,1 θ 1,0 ) + (1 θ 12,2 ) and s B 2 = 1 θ 2,1 s C 1 = 1 θ 12,2 and s C 2 = 1 θ 2,0 We can notice that s A 1 > sb 1 > sc 1 and sa 2 < sb 2 < sc 2, that is, platform 1 s subscribers fall moving from region A to B to C, while platform 2 subscribers follow an opposite pattern. 11 Appendix III: Advertising technology We describe here a basic process that gives rise to a simple and intuitive expression of the probability of informing viewers by placing ads on the platforms. A station (say i) continuously broadcasts over a finite horizon [0, T ]. For simplicity let T = 1 (say, a week ). The week is partitioned into n segments of 1/n length. A broadcaster selects each segment with probability a i for advertising, and a viewer selects each segment with probability v i for viewing. (Note that the total viewing time as well as the total advertising time are random variables, with mean v i and a i respectively.). Assuming that all these selections are done independently, then the probability that an advertising break is watched by a viewer, is v i a i. Suppose that the length 1/n of each advertising break is spread equally accross all advertisers. That is suppose that each advertising break is divided in N slots of 1/(n N) length. If the platform serves less then N advertisers, assume that the residual slots are filled with info-mercials, self promotions and tune-ins. Finally suppose that the probability that a consumer is informed, conditional on watching an ad, is ψ/(n N), with 1/(n N) being the lenght of the commercial, and 0 ψ nn. ψ = nn denote infinitely attentive viewers who are informed with probability one conditional on watching an ad. It follows that the probability that a given advertiser informs (and sells to) a given consumer during a given break is equal to v i a i ψ/(n n). That is the probability that the viewer is watching the segment and there is an advertising break on channel i times the probability that the viewer pays attention to the commercial. Note that the longer the commercials (i.e. n lower), the larger the probability of paying attention to it. 45

46 Given that there are n advertising breaks, the probability of being informed in at least one of these segments is then: ( ) ψ n 1 1 v i a i, nn whose limit as n goes to infinity, that is, as the length of the reference period goes to zero, is: ψ [0, ) parametrizes the effectiveness of advertising. 1 e v ia i ψ. (28) Or, in other words, the probability that a viewer watching a channel notices the advertising message when broadcasted. ψ + coincides with the case in which the viewer notices with probability one the ads inserted in a program he is watching, whereas in the opposite case ψ = 0, no matter what a i is, the consumer never pays attention to the ad. Then, when ψ increases ads become more effective, and the probability that a message is noticed goes up. 12 References References [1] Ambrus A., Argenziano R. (2009), Asymmetric networks in two-sided markets, American Economic Journal: Microeconomics, 1, [2] Ambrus A., Calvano E., Reisinger M. (2013), Either or Both: a "Two-sided" Theory of Advertising with Overlapping Viewerships", mimeo. [3] Anderson S., Coate S. (2005), Market Provision of Broadcasting: a Welfare Analysis, Review of Economic Studies, 72, [4] Anderson S., Foros O., Kind H., (2013), Competition for Advertizers and for Viewers in Media Markets, mimeo [5] Anderson S., Foros O., Kind H., Peitz M. (2011), Media Market Concentration, Advertising Levels and Ad Prices, mimeo [6] Armstrong M. (2006), Competition in Two-Sided Markets, Rand Journal of Economics, 37, [7] Armstrong M., Weeds H., (2007), Programme Quality in Subscription and Advertising Financed Television, mimeo 46

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