Either or Both Competition: A Two-sided Theory of Advertising with Overlapping Viewerships

Transcription

1 Ether or Both Competton: A Two-sded Theory of Advertsng wth Overlappng Vewershps Attla Ambrus Emlo Calvano Markus Resnger October 2015 Abstract In meda markets, consumers spread ther attenton to several outlets, ncreasngly so as consumpton mgrates onlne. The tradtonal framework for competton among meda outlets rules out ths behavor by assumpton. We propose a new model that allows consumers to choose multple outlets and use t to study the effects on advertsng levels and the mpact of entry and mergers. We dentfy novel forces whch reflect outlets ncentves to control the composton of ther customer base. We lnk consumer preferences and advertsng technologes to market outcomes. The model can explan several emprcal regulartes that are dffcult to reconcle wth exstng models. Keywords: Meda Competton, Two-Sded Markets, Endogenous Mult-Homng, Vewer Composton, Vewer Preference Correlaton JEL-Classfcaton: D43, L13, L82, M37 A prevous verson of ths paper by Ambrus and Resnger crculated under the ttle Exclusve vs. Overlappng Vewers n Meda Markets. We would lke to thank an anonymous referee, Smon Anderson, Elena Argentes, Rossella Argenzano, Mark Armstrong, Susan Athey, Alessandro Bonatt, Drew Fudenberg, Matthew Gentzkow, Doh-Shn Jeon, Bruno Jullen, Marco Ottavan, Martn Petz, Jesse Shapro, Gabor Vrag, and Helen Weeds for very helpful comments and suggestons. We would also lke to thank partcpants at the Eleventh Annual Columba/Duke/Northwestern IO Theory Conference, the Becker-Fredman Meda Conference at Chcago Booth, the CESfo conference n Munch, the Meda Workshop n Sena, the Meda Markets Conference at EUI Florence, the MaCCI and ICT conference n Mannhem, and the NUS Mult-Sded Platforms Workshop, and at the Unverstes of Toulouse, Bergen, and Bern for ther useful comments. We also thank Gna Turrn, Vvek Bhattacharya and especally Peter Landry for careful proofreadng. Department of Economcs, Duke Unversty, Durham, NC E-Mal: [email protected] Center for Studes n Economcs and Fnance, Unversty of Naples Federco II. E-Mal: [email protected] Department of Economcs, Frankfurt School of Fnance & Management, Sonnemannstr. 9-11, Frankfurt am Man, Germany. E-Mal: [email protected]

2 1 Introducton A central queston the ongong debate about the changng meda landscape s how compettve forces shape advertsng levels and revenues and hence assst n achevng a number of long-standng publc nterest goals such as enhancng entry and dversty of content. In meda markets, outlets fght for consumer attenton and for the accompanyng stream of advertsng revenues. Onlne advertsng networks, such as the Google and Yahoo ad-networks, and tradtonal broadcastng statons, such as CNN and Fox News, are among the most promnent examples. The tradtonal approach n meda economcs posts that consumers stck to the outlet they lke best (for example, Anderson and Coate, 2005). So, f anythng, consumers choose ether one outlet or some other. Compettos for exclusve consumers as all outlets are restrcted a pror to be perfect substtutes at the ndvdual level. Whle compellng, ths approach fals to account for the fact that many consumers satsfy ther content needs on multple outlets. Ths s ncreasngly so as content moves from paper and TV towards the Internet. In fact, many contend that a dstngushng feature of onlne consumptos the users ncreased tendency to spread ther attenton across a wde array of outlets. Table 1 shows the reach of the sx largest onlne advertsng networks, that s, the fracton of the U.S. Internet users who, over the course of December 2012, vsted a webste belongng to a gven network. Ths table shows that whle Google can potentally delver an advertsng message to 93.9% of all Internet users, even the smallest of the sx networks (run by Yahoo!), can delver a whoppng 83.3%. The table hghlghts a key feature of these markets: dfferent outlets provde advertsers alternate means of reachng the same users. Table 1. Top 6 Onlne Ad Networks by reach. (Source: Comscore press release: ComScore MMX Ranks Top 50 U.S. Web Propertes for December 2012, 28th January 2013) Motvated by these observatons, the paper has two goals. Frst, we propose an alternatve model of competton that replaces the assumpton of perfect substtutablty by allowng consumers to access content on multple outlets. So, wth two outlets, consumers can choose ether one outlet or both (or none). Specfcally, we work under the (extreme) assumpton that consumer demand for one outlet does not affect the demand for another outlet. Ths s what we call ether or both competton contrast wth the standard framework dscussed above. We clam that ths model of compettos an appealng alternatve to exstng ones for several reasons. It s a good approxmaton of realty n some non-trval contexts where substtutablty s lmted. For example, choosng Facebook.com for onlne socal networkng servces s arguably orthogonal to choosng Yelp.com as one s suppler of restaurant revews. 1 Moreover, and somewhat surprsngly, Gentzkow, Shapro and Snknson (2014) document 1 Accordng to the source supra cted, Facebook and Yelp are among the top 10 most-vsted U.S. webstes and n fact 1

3 lmted substtutablty even tradtonal meda markets such as that of U.S. newspapers. They show that on average 86% of an entrant s crculaton comes from households readng multple newspapers or households who prevously dd not read any newspaper. Second, we apply the model to study the market provson of advertsng opportuntes, whch has been the focus of a large lterature n meda markets. For nstance, does ncreased competton between meda outlets reduce the amount of ads? Is competton weakened f outlets supply dverse content? For example, should we expect the mpact of entry of Fox News on MSNBC s choces to be dfferent than that of Fox Sports on ESPN s choces? 2 We propose a characterzaton of the ncentves to provde advertsng opportuntes n duopoly and draw mplcatons for the equlbrum advertsng levels and for the mpacts of entry and mergers. We also lnk consumer preferences and advertsng technologes to market outcomes. In partcular, we consder competton between two ad-fnanced outlets that receve demand from consumers and advertsers. Consumers dslke ads whereas advertsers want to reach as many consumers as possble. Outlets choose the overall quantty of ads and then sell t to advertsers. In dong so, they trade off reduced consumer demand wth hgher ad-revenues per consumer. A key component of our model s that consumers who cannot be reached through the rval outlet are more valuable to an outlet than those who can. Intutvely, the rents assocated to the latter consumers are competed away. So shared or overlappng busness s worth relatvely less. Ths mples n our model that outlets do not only care about the overall consumer demand level, as n exstng models, but also about ts composton,.e., the fracton of exclusve versus overlappng consumers. 3 Indeed, t s common for ad networks to assess the extent of overlap and for advertsers to take nto account the extent of duplcaton large cross-outlet campagns. 4 Characterzng the equlbrum choces of the outlets, we fnd that accountng for mult-homng changes the nature of competton substantally. In partcular, we show that two novel forces come nto play when some consumers are shared. In duopoly, mult-homers receve advertsng messages from two dfferent sources. Wth dmnshng returns from advertsng, ths mples that ads are less valuable than they are for a monopolst. Ths duplcaton effect nduces competng outlets to supply fewer ads. Second, the fact that mult-homng consumers are of lower value mples that a reducton the advertsng level s less benefcal for a competng outlet than for a monopoly outlet. Ths occurs because such a reducton leads to the acquston of some less valuable mult-homng consumers, whereas for a monopoly outlet all consumers are exclusve. As a result, duopolsts are less wary of ncreases n advertsng level. Ths busness-sharng effect nduces competng outlets to rase advertsng levels. We provde a full belong to dfferent advertsng networks. 2 Fox News has, arguably, a conservatve bas, so t s unlkely to appeal to MSNBC s core lberal vewers. In contrast, Fox Sports, arguably, caters to the same preferences as ESPN. 3 Ths s consstent wth the well-documented fact n the televsondustry that the per-vewer fee of an advertsement on programs wth more vewers s larger. In the U.S., for nstance, Fsher, McGowan and Evans (1980) fnd ths regularty. Our model accounts for t snce reachng the same number of eyeball pars through broadcastng a commercal to a large audence mples reachng more vewers than reachng the same number of eyeball pars through a seres of commercals to smaller audences, because the latter audences mght have some vewers n common. See Ozga (1960) for an early observaton of ths fact. 4 For example, Google assesses the effect on an advertsng campagn for auto nsurance ots Dsplay Network (GDN) by emphaszng that GDN exclusvely reaches 30% of the auto-nsurance seekers that do not vst Yahoo, 36% that do not vst Youtube and so on. See Google Dsplay Network vs. Portal Takeovers for Auto Insurance seekers avalable at 2

4 characterzaton of how the novel effects nteract and shape equlbrum outcomes. To understand under what condtons ether effect prevals, we trace out the mpact of competton to two sources: a preference-drven and a technology-drven source. We frst determne how the correlaton of consumer preferences affects the equlbrum advertsng level. A key observatos that a postve correlatomples that there are relatvely many overlappng and only few exclusve consumers. In partcular, f preferences are postvely correlated, a consumer wth a hgh (low) value for outlet 1 s also lkely to have a hgh (low) value for outlet 2. Therefore, he jons ether both or no outlet wth a hgh probablty. By reducng ts advertsng level, an outlet attracts more consumers, both sngle-homers and mult-homers. Compared to ts customer base, these margnal consumers are comprsed of a larger porton of sngle-homers. Snce sngle-homers are more valuable, there s hgh ncentve to reduce the advertsng level. The duplcaton effect domnates the busness-sharng effect, leadng to low advertsng levels n equlbrum. Conversely, f the consumer preference correlatos negatve, advertsng levels ncrease wth entry. We provde a frst emprcal pass that provdes suggestve evdence for these results, usng data from the U.S. cable TV ndustry. In ths ndustry, broadcasters and advertsers meet on a seasonal bass at an upfront event to sell commercals on the networks upcomng programs. Snce at ths stage the networks supply of commercal breaks s already determned, channels compete (among other thngs) n advertsng levels. We explot the changes n competton brought about by entry of TV channels n the 1980s and 1990s. Whle we fnd n aggregate ancrease n the advertsng levels after entry, ths ncrease was smaller (or even negatve) for channels n segments such as sports or moves & seres, where vewer preference correlaton can be expected to be postve. 5 The nterplay between the duplcaton and the busness-sharng effect has also mplcatons for content choce. Increasng the extent of dfferentaton (that s, choosng a content that s more negatvely correlated wth the one of compettors) attracts more exclusve vewers. At the same tme, ths nduces the rval to compete more aggressvely by ncreasng ts supply of ads. As a consequence, choosng an ntermedate level of correlaton mght be optmal. On the technology sde, we show that dfferences n the returns from advertsng to overlappng and exclusve consumers determne f advertsng levels ncrease or decrease after entry. To buld ntuton, suppose that mult-homng consumers are relatvely more dffcult to nform through advertsng (for nstance, because they spread ther attenton thn; hence, spendng a smaller amount of t on each outlet than exclusve ones). Ths enhances the busness-sharng effect because t further lowers the opportunty cost of losng shared busness. Other thngs held constant, ths leads to ncreased ad levels n duopoly. On the other hand, the strength of the duplcaton effect ncreases as well f margnal returns from an extra ad to overlappng consumers dmnsh compared to the returns from an extra ad to exclusve consumers. Ths tends to reduce advertsng levels n duopoly. Due to these countervalng forces, the result s ambguous. However, we show that the busness-sharng effect domnates f the advertsng technology takes the wdely-used exponental form. 6 On the normatve sde, we show that the conventonal wsdom that there s aneffcently amount 5 The fndng that advertsng levels rse wth compettos also n lne wth the so-called Fox News Puzzle, whch s that the wave of channel entry durng the 1990s n the U.S. cable TV ndustry concded wth ancrease n advertsng levels on many channels. 6 If mult-homng consumers are easer to nform through advertsng, both effects are also present but wth opposng mplcatons. 3

5 of advertsng holds n our settng. Ad-fnanced platforms, the argument goes, do not drectly nternalze vewer welfare but only do so to the extent that more vewers ncrease ad revenues. We add to ths debate by showng that mergers can actually mtgate the bas. The rest of the paper s organzed as follows: Secton 2 dscusses related lterature. Secton 3 ntroduces the model and Secton 4 presents some prelmnary analyss. Secton 5 analyzes outlet competton and presents the man trade-offs of our model. Secton 6 consders the effects of vewer preference correlaton and Secton 7 explores the advertsng technology. Secton 8 provdes a welfare analyss. Secton 9 concludes. All proofs can be found n the Appendx. 2 Lterature Revew Classc contrbutons n meda economcs, for example, Spence and Owen (1977) or Wldman and Owen (1985), mpose perfect substtutablty and do not allow for endogenous advertsng levels or two-sded externaltes between vewers and advertsers. More recently, the semnal contrbuton of Anderson and Coate (2005) explctly accounts for these externaltes. 7 In ther model, vewers are dstrbuted on a Hotellng lne wth platforms located at the endponts. Smlar to early works, vewers watch only one channel whle advertsers can buy commercals on both channels. 8 In ths framework, Anderson and Coate (2005) show, among several other results, that the number of enterng statons can ether be too hgh or too low compared to the socally optmal number, or that the advertsng level can be above or below the effcent level. The framework wth sngle-homng vewers has been used to tackle a wde array of questons. Gabszewcz, Laussel and Sonnac (2004) allow vewers to mx ther tme between channels, Petz and Vallett (2008) analyze optmal locatons of statons, and Resnger (2012) consders sngle-homng of advertsers. Dukes and Gal-Or (2003) explctly consder product market competton between advertsers and allow for prce negotatons between platforms and advertsers, whle Crampes, Hartchabalet and Jullen (2009) consder the effects of free entry of platforms. Fnally, Anderson and Petz (2012) allow advertsng congeston and show that t can also lead to ncreased advertsng rates after entry of new platforms. These papers do not allow vewers to watch more than one staton,.e., they assume ether/or competton, and usually consder a spatal framework for vewer demand. 9 There are a few recent studes whch also consder mult-homng vewers. 10 Anderson, Foros and Knd (2015) consder a model smlar n sprt to ours,.e., both papers share the nsght that overlappng vewers are less valuable n equlbrum. In contrast to our paper, they consder a dfferent contractng envronment (per-unt prcng) and use a dfferent equlbrum concept (ratonal nstead of adaptve expectatons). The latter mples that platforms cannot attract consumers va lower ad-levels. 11 In 7 For dfferent applcatons of two-sded market models, see e.g., Rochet and Trole (2003, 2006) and Armstrong (2006). 8 In Secton 5 of ther paper Anderson and Coate (2005) extend the model by allowng a fracton of vewers to swtch between channels, that s, to mult-home. 9 A dfferent framework to model competton meda markets s to use a representatve vewer who watches more than one program. Ths approach s developed by Knd, Nlssen and Sørgard (2007) and s used by Godes, Ofek and Savary (2009) and Knd, Nlssen and Sørgard (2009). These papers analyze the effcency of the market equlbrum wth respect to the advertsng level and allow for vewer payments. Due to the representatve vewer framework, they are not concerned wth overlappng vewers or vewer preference correlaton. 10 For a demand structure, whch allows for consumer overlappng n a bundlng model, see Armstrong (2013). 11 Anderson, Foros and Knd (2015) provde a justfcaton for dong so, based on the nablty of consumers to observe the 4

6 addton, the questons addressed n Anderson, Foros and Knd (2015) are dfferent and complementary to those nvestgated n our paper. They manly analyze publc broadcastng and genre selecton, and show e.g., that the well-known problem of content duplcatos amelorated wth mult-homng vewers. 12 By contrast, our analyss provdes mplcatons of vewer composton on market outcomes and characterzes the margnal ncentve of a meda platform to supply advertsng opportuntes. Athey, Calvano and Gans (2014) and Bergemann and Bonatt (2011, n Sectons 5 and 6) also consder mult-homng vewers but are manly concerned wth dfferent trackng/targetng technologes and do not allow for advertsements generatng (negatve) externaltes on vewers, whch s at the core of our model. Specfcally, n Athey, Calvano and Gans (2014) the effectveness of advertsng can dffer between users who swtch between platforms and those who stck to one platform because of mperfect trackng of users, whereas Bergemann and Bonatt (2011) explctly analyze the nterplay between perfect advertsng message targetng n onlne meda markets and mperfect targetng n tradtonal meda. Armstrong and Wrght (2007) also allow for mult-homng of agents. They use a Hotellng framework and analyze under whch condtons the market structure of sngle-homng agents on one sde and multhomng agents on the other sde arses endogenously. In ther model, all agents of a gven sde ether snglehome or mult-home, whle we allow agents on the same sde to dffer n ther homng behavor. Whte and Weyl (2015) also consder mult-homng agents. In contrast to our paper, they explore questons regardng equlbrum unqueness. In partcular, they show that the concept of nsulated equlbrum, developed by Weyl (2010), helps to overcome equlbrum multplcty problems n two-sded markets. On the emprcal sde, Gentzkow, Shapro and Snknson (2014) develop a structural model of the newspaper ndustry that embeds the key predcton found here that advertsng-market competton depends on the extent of overlap n readershp. They fnd that compettoncreases dversty sgnfcantly, offsettng the ncentve to cater to the tastes of majorty consumers (George and Waldfogel, 2003). 3 The Model The basc model features a unt mass of heterogeneous vewers, a unt mass of homogeneous advertsers 13 and two outlets ndexed by {1, 2}. 14 Vewer Demand Vewers are parametrzed by ther reservaton utltes (q 1, q 2 ) R 2 for outlets 1 and 2, where (q 1, q 2 ) s dstrbuted accordng to a bvarate probablty dstrbuton wth smooth jont densty denoted h(q 1, q 2 ). A vewer of (q 1, q 2 )-type jons outlet f and only f q γ 0, where s the advertsng level on outlet and γ > 0 s a nusance parameter. Gven the advertsng level on each outlet, we can back out the demand system: contractual terms offered to the advertsers. 12 For related deas, see also Anderson, Foros, Knd and Petz (2012). 13 In an Onlne Appendx, we consder a model wth heterogeneous advertsers and demonstrate that the effects dentfed wth homogeneous advertsers are also at work then. 14 We cast our model n terms of the televson context. The model also apples to nternet or rado, where the term vewers would be replaced by users or lsteners. 5

7 Mult-homers: D 12 := Prob{q 1 γn 1 0; q 2 γn 2 0}, Sngle-homers 1 : D 1 := Prob{q 1 γn 1 0; q 2 γn 2 < 0}, Sngle-homers 2 : D 2 := Prob{q 1 γn 1 < 0; q 2 γn 2 0}, Zero-homers: D 0 := 1 D 1 D 2 D 12. We make the necessary assumptons on h(q 1, q 2 ) that ensure that the demand functons D, = 1, 2, and D 12 are well-behaved, that s, there s a unque equlbrum wth nteror solutons. 15 A key property of the demand schedules s that f changes but n j s unchanged, the choce of whether to jon outlet j remans unaffected. However, the composton of vewers on outlet j changes. That s, D + D 12 does not depend on n j whle D 12 /D does. Ths property contrasts wth settngs where vewers choose one outlet over the other. 16 Tmng and Outlets Choces Outlets compete for vewers and for advertsers. They receve payments only from advertsers but not from vewers. To make the model as transparent as possble, we develop a four-stage game. In stage 1, outlets smultaneously set the total advertsng levels n 1 and n 2. In stage 2, vewers observe n 1 and n 2 and choose whch outlet(s) to jon, f any. In stage 3, outlets smultaneously offer menus of contracts to advertsers. A contract offered by outlet s a par (t, m ) R 2 +, whch specfes an advertsng ntensty m 0 n exchange for a monetary transfer t 0. Fnally, n stage 4, advertsers smultaneously decde whch contract(s), f any, to accept. 17 Although outlets can offer dfferent contracts to dfferent advertsers, below we wll show that each outlet only offers one contract n equlbrum, and ths contract s accepted by all advertsers. Ths mples that, n equlbrum, m = for the unque advertsng ntensty m offered by outlet. To ensure that the announced advertsng levels are consstent wth the realzed levels after stage 4, we assume that f total advertsng levels accepted by advertsers at outlet exceed, then outlet obtans a large negatve payoff. 18 Therefore, our game s smlar to Kreps and Schenkman (1983),.e., n the frst stage outlets choose an advertsng level that puts an upper bound on the advertsng ntenstes 15 For example, suffcent (but not necessary) assumptons to obtan a unque nteror soluton are 2 D 2 D 12 0, 0 and n 2 n 2 2 D n 2 2 D n j, = 1, 2 and j = 3. See e.g., Vves (2000) for a detaled dscusson of why these assumptons ensure concavty of the objectve functons and unqueness of the equlbrum. 16 Condtonal on the realzaton of the utlty parameters (q 1, q 2), a vewer s choce of whether to jon outlet does not depend on q j. Ths demand ndependence assumpton should not be confused wth nor does t mply statstcal ndependence between q and q j. For nstance, the model allows preferences for (say Facebook) and j (say Yelp) to be correlated to account for some underlyng common covarate factor (say nternet savvness ). In fact, the model nests those specfcatons whch add structure to preferences by postng a postve or negatve relatonshp between valuatons of dfferent outlets, such as Hotellng-type spatal models. 17 We show n the Onlne Appendx that ths game s equvalent (under some addtonal condtons on preferences) to a canoncal two-stage model of platform competton à la Armstrong (2006) n whch outlets smultaneously make offers and, upon observng the offers, all agents smultaneously make ther choces. The role of stage 1 n our model s to relax the dependence of vewers choces on advertsers choces. Indeed, vewershps are fxed before outlets sell ther advertsng slots. The assumpton that the aggregate advertsng level s fxed at the contractng stage greatly smplfes the analyss. 18 Our results would reman unchanged f we nstead assume that actual advertsng ntenstes are ratoned proportonally for partcpatng advertsers n case there s excess demand for an outlet s advertsng ntenstes. We stck to the current formulaton as t smplfes some of the arguments n the proofs. 6

8 they can sell subsequently. We use subgame perfect Nash equlbrum (SPNE) as the soluton concept. Advertsng Technology Advertsng n our model s nformatve. We normalze the return of nformng a vewer about a product to In lne wth the lterature, e.g., Anderson and Coate (2005) or Crampes, Hartchabalet and Jullen (2009), we assume that advertsers can fully extract the value of beng nformed from the consumers. The mass of nformed vewers (also known as reach ) s determned by the number of advertsng messages (m 1, m 2 ) a partcular advertser purchases on each outlet. Wthout loss of generalty, we decompose the total reach as the sum of the reach wthn the three dfferent vewers subsets. We denote the probablty wth whch a sngle-homng vewer on outlet becomes nformed of an advertser s product by φ S (m ). We assume that φ S s smooth, strctly ncreasng and strctly concave, wth φ S (0) = 0. That s, there are postve but dmnshng returns to advertsng. Smlarly, φ 12 (m 1, m 2 ) equals the probablty that a mult-homng vewer becomes nformed on some outlet. In partcular, φ 12 (m 1, m 2 ) s one mnus the probablty that the vewer s not nformed on ether outlet, that s, φ 12 (m 1, m 2 ) := 1 (1 φ M 1 (m 1))(1 φ M 2 (m 2)), where φ M (m ) s the probablty that a mult-homng vewer becomes nformed on outlet, where φ M (m ) s also smooth, strctly ncreasng and strctly concave. Payoffs An outlet s payoff s equal to the total amount of transfers t receves (for smplcty, we assume that the margnal cost of ads s zero). An advertser s payoff, n case he s actve on both outlets, s u(n 1, n 2, m 1, m 2 ) t 1 t 2, where u(n 1, n 2, m 1, m 2 ) := D 1 (n 1, n 2 )φ S 1 (m 1 ) + D 2 (n 1, n 2 )φ S 2 (m 2 ) + D 12 (n 1, n 2 )φ 12 (m 1, m 2 ) and t 1 and t 2 are the transfers to outlets 1 and 2, respectvely. If he only jons outlet, the payoff s u(, n j, m, 0) t = D (, n j )φ S (m ) + D 12 (, n j )φ M (m ) t snce the advertser reaches vewers only va outlet. Advertsers reservaton utltes are normalzed to zero. 4 Prelmnares: Contractng Stage To dentfy the compettve forces, we proceed by contrastng the market outcome of the game just descrbed, n whch two outlets compete, wth the monopoly case, n whch only one outlet s present n the market. We frst solve the contractng stage. A key observatos that after any par of frst stage announcements (n 1, n 2 ), n any contnuaton equlbrum, outlets spread ther advertsng level equally across all advertsers. Ths result follows due to dmnshng returns from advertsng. As there s a unt mass of advertsers, the number of advertsng ntenstes offered to each advertser by outlet s equal to. In turn, the equlbrum transfer s the ncremental value that advertsng ntensty on outlet generates for an advertser who already 19 In the Onlne Appendx, we allow advertsers to be dfferent wth respect to ths return. 7

9 advertses wth ntensty n j on the other outlet. 20 Clam 1: In any SPNE of a game wth competng outlets, gven any par of frst-stage choces (n 1, n 2 ), each outlet only offers one contract (t, m ). These contracts are accepted by all advertsers, and have the feature that m 1 = n 1, m 2 = n 2, t 1 = u(n 1, n 2 ) u(0, n 2 ) and t 2 = u(n 1, n 2 ) u(n 1, 0). The next clam establshes a parallel result for the sngle outlet case, whose proof we omt because t proceeds along the same lnes as the proof of Clam 1. In partcular, the monopolst offers a sngle contract that s accepted by all advertsers. Clam 2: In any SPNE of a game wth a monopolstc outlet, gven frst-stage choce monopolst offers a sngle contract (t, m ). feature that m =, and t = u(, 0)., the Ths contract s accepted by all advertsers, and has the Outlets equlbrum profts n duopoly are lower than the equlbrum proft obtaned by the monopolst. In duopoly, outlets can only demand the ncremental value from an advertser who s also actve on the other outlet, whereas a monopolst can extract the whole surplus. Specfcally denotng D (n 1, n 2 ) + D 12 (n 1, n 2 ) by d ( ), that s, d ( ) := Prob{q γ 0}, a monopolst outlet obtans a proft of d ( )φ S () because ( t only has exclusve) vewers. By contrast n duopoly outlet only obtans D ( )φ S () + D 12 (n 1, n 2 ) φ 12 (n 1, n 2 ) φ M j (n j) because t shares some vewers wth ts rval. 5 Outlet Competton In ths secton, we analyze the effect of outlet competton two ways. Frst, we consder outlet entry by comparng the optmal advertsng level of a monopolst wth the equlbrum advertsng level n duopoly. Ths allows us to brng out the fundamental trade-offs n our model. Second, we consder the effect of a merger between the two outlets on the equlbrum advertsng level, whch s partcularly relevant for polcy makers. 5.1 Outlet Entry We proceed by contrastng the equlbrum advertsng level n duopoly wth the the choce of a monopolst. 21 The latter s gven by n m := arg max d ( )φ S ( ). (1) Instead, the duopoly advertsng levels are characterzed by the fxed ponts of the best reply correspondences n d := arg max D ( )φ S ( ) + D 12 (n 1, n 2 ) ( φ 12 (n 1, n 2 ) φ M j (n j ) ) = 1, 2; j = 3. (2) It s useful to rewrte the duopolst s proft as f all vewers were exclusve plus a correcton term that accounts for the fact that outlet can only extract the ncremental value from ts shared vewers: n d := arg max d ( )φ S ( ) D 12 (n 1, n 2 ) ( φ S ( ) + φ M j (n j ) φ 12 (n 1, n 2 ) ). (3) 20 Wth a slght abuse of notaton, n what follows, we denote u(, n j,, n j) by u(, n j) and u(, n j,, 0) by u(, 0). 21 Here we adopt the conventon that denotes the monopoly outlet. 8

10 Frst consder problem (1). Its solutos characterzed by the frst-order condton φ S d + d φ S = 0. (4) Whencreasng, outlet trades off profts onframargnal vewers due to ncreased reach wth profts on margnal vewers who swtch off. If we ntroduce the advertsng elastctes of the total demand d and of the advertsng functon φ S wth respect to, E d := d and E d φ S := φs φ S, the optmal advertsng level s characterzed by the smple and ntutve condton E φ S = E d. Consder now problem (3). In duopoly, condton (4) s augmented to account for the fact that some of the prevously exclusve vewers are now shared. Usng φ S + φm j φ 12 = φ M φ M j + φ, wth φ = φ S φm, the frst-order condton can be wrtten as φ S d + d φ S D 12 (φ M φ M j + φ ) D 12 (φ M φ M j + φ ) = 0. (5) We can now provde a condton for advertsng levels n duopoly beng larger than monopoly. Let E D12 := D 12 and E D φ M 12 φ M j + := (φm φ M j + φ ) φ φ M φ M j + φ. Proposton 1: Ancumbent monopolst s advertsng level ncreases (decreases) upon entry of a compettor f and only f where all functons are evaluated at = n m and n j = n d j. E D12 E φ M > (<) φ M j + φ, (6) E d E φ S To buld ntuton for the result, consder the smplest case n whch the two outlets are symmetrc,.e., d (n) = d j (n), φ S (n) = φs j (n), and φm (n) = φ M j (n) for all n and suppose that competng outlets behave as the monopolst does, that s, n d j = n d = n m. Can these advertsng levels consttute an equlbrum? Frst, overlappng vewers receve advertsng messages from two outlets. If each outlet chooses the same advertsng level as the monopolst, the amount of advertsng that these vewers are exposed to doubles n duopoly. Other thngs held constant, decreasng margnal returns gve ancentve to scale back advertsng on outlet, because ts margnal contrbuton to the advertsers surplus drops. Ths duplcaton effect gves an outlet the ncentve to reduce ts advertsng level. However, there s a second, arguably more subtle, effect whch goes n the opposte drecton. For a duopolst, the total varaton demand due to a small ncrease n decomposes to D / and D 12 /. The frst term s the change n the mass of exclusve vewers and the second the change n the mass of overlappng vewers. Instead, a monopolst has only exclusve vewers and s therefore wary only of the total varaton of d /. Snce exclusve vewers are more valuable than overlappng vewers, n duopoly the opportunty 9

11 cost of losng shared busness s lower than that of losng exclusve busness. Other thngs held constant, ths busness-sharng effect gves the outlet ancentve to ncrease ts advertsng levels. To see how ths ntutos represented n the formula of the proposton, frst note that the left-hand sde of (6) s the rato of the demand elastcty of overlappng vewers to the demand elastcty of vewers n monopoly. On the rght-hand sde, φ M φ M j s a measure of wasted (or duplcated) advertsng. It s the probablty that an overlappng vewer s nformed twce. Ths term s adjusted by φ to account for vewer heterogenety, that s, an overlappng vewer may become nformed wth a dfferent probablty than an exclusve one. Loosely speakng, the numerator of the rght-hand sde of (6) s a measure of the elastcty of duplcaton. It represents whch fracton of advertsng messages gets wasted due to duplcaton across outlets followng a one percentage pont ncrease n the amount of messages sent. Ths puts us n the poston to provde a clear nterpretaton of (6). If the elastcty of overlappng vewers s large relatve to the one of exclusve vewers (.e., the left-hand sde s large), the busnesssharng effect prevals and advertsng levels ncrease wth entry. By contrast, f the elastcty of wasted mpressons s large relatve to the advertsng elastcty (.e., the rght-hand sde s large), the duplcaton effect domnates and advertsng levels fall wth entry. 22 We note that the busness-sharng effect ponts n the opposte drecton than the one brought about by competton tradtonal sngle-homng setups. A key nsght there s that compettve pressure nduces competng outlets to put more emphass on lost busness than monopolsts do. (See, for example, the dscusson Armstrong (2006), Secton 4). Lost busness on one sde lowers revenues on the other sde of the market, as consumers fnd the rval more attractve because of the ndrect network effects. As a consequence, advertsng levels, whch act as a prce for vewers, fall f compettve pressure ncreases. Amportant mert of (6) s that t spells out the effect of applyng compettve pressure n terms of emprcal objects. However, ts nsght s lmted wthout a theory that suggests when the condton should be satsfed. We address ths ssue n Sectons 6 and 7. Before dong so, we analyze the effects of competton a dfferent way by consderng outlet mergers. 5.2 Outlet Mergers The polcy debate on mergers between meda platforms features two opposte stances. A frst vew mantans that the merged entty would reduce the supply of ads and ncrease prces attemptng to extract more surplus on the advertsng sde of the market. The opposte vew mantans that competton for ad-averse vewers njects downward pressure on quanttes. 23 Here we contrbute to ths debate by presentng a thrd argument that brngs n the pcture the mpact of demand composton. We contrast the duopoly outcome wth the outcome that a hypothetcal monopolst who controls both outlets would mplement. Amportant nsght n ths comparsos that f advertsng goes up on one outlet, prevously shared busness becomes exclusve on the other outlet. Ths potentally nduces dfferent ncentves to set advertsng levels because the two-platform monopolst owns the other outlet, whereas the duopolst does not. The relevant queston turns out to be: s the opportunty cost of losng 22 A smlar ntuton holds f we start from any number of ncumbent outlets, not just a monopoly outlet. See the Onlne Appendx for a formal analyss of the case wth two ncumbent outlets. 23 For example, n the merger between Facebook and WhatsApp amportant queston was f the polcy of WhatsApp to present ad-free content wll change after ts acquston by Facebook. See e.g., Facebook plans to monetze WhatsApp: Ads or moble payments? on or Updated - Facebook buyng WhatsApp - $19B n cash and stock on 10

12 shared busness smaller for a mult-outlet platform than for a sngle-outlet platform? We show that the answer to ths questos gven by a farly straghtforward condton. Proposton 2: The equlbrum advertsng level n duopoly s strctly lower than under jont ownershp (.e., n d < njo ) f and only f φ M j < φ S j. The two advertsng levels are equal f φ M j = φ S j. To buld ntuton, consder frst the case φ M = φ S. When margnally ncreasng, a monopolstc owner controllng both outlets loses some mult-homng vewers who become sngle-homng vewers on outlet j. Hs per-vewer loss s therefore φ 12 φ S j. In duopoly, when outlet ncreases, t loses some mult-homng vewers who are worth φ 12 φ S j. structures are the same. 24 advertsng levels. But ths mples that the trade-offs n both market As a consequence, we obtan that the ownershp structure has no effect on If nstead φ M < φ S, overlappng vewers can be reached wth a lower probablty by advertsers than sngle-homng vewers. Therefore, competng outlets can extract (φ 12 φ M j ) > (φ 12 φ S j ) from advertsers. Ths mples that the opportunty cost of losng an overlappng vewer s smaller for a jont owner. In other words, the busness-sharng effect for a mult-outlet monopolst s larger than for competng outlets, whch leads to lower advertsng levels n duopoly. (The opposte results occurs f φ M > φ S.) Our result s dfferent than the one obtaned n prevous work. For nstance, n Anderson and Coate (2005) competton for vewers always reduces advertsng levels relatve to monopoly. In addton, the redstrbutve mpact of a merger s very dfferent. In our model, a jont owner can fully exproprate advertsers, whereas competng outlets cannot, mplyng that advertsers are hurt by a merger. In contrast, n Anderson and Coate (2005) a merger leads to ancrease n the advertsng level and a lower advertsng prce. Hence, advertsers are better off after a merger. The result that advertsng levels do not depend on the ownershp structure for φ M j = φ S j s remnscent of common agency models (e.g., Bernhem and Whnston, 1986), that predct equvalent allocatons when frms compete and when they cooperate. However, common agency models feature a sngle agent who contracts wth multple prncpals nstead of a contnuum of agents, as n our framework. In partcular, f there s only a sngle advertser or, equvalently, f all advertsers can coordnate ther choces 25 even models featurng sngle-homng of vewers, the equlbrum advertsng levels are the same under duopoly and jont ownershp. 26 In contrast to ths, advertsers cannot coordnate ther choces n our model. Therefore, the mechansm descrbed above, whch leads to the equvalence result n our model, s 24 Note that n both cases ncreasng also mples losng some sngle-homng vewers on outlet. But the loss from these vewers s exactly the same for the monopolst and the duopolst. 25 For an analyss of consumer coordnaton outlet competton a settng wth postve network externaltes, see Ambrus and Argenzano (2009). 26 To see ths, consder the case n whch vewers jon ether outlet or j, mplyng that D 12 = 0. If there s only a sngle advertser, the transfer that outlet can charge to make the advertser accept s the ncremental value of the outlet,.e., u(n d 1, n d 2) u(0, n d j ). In the ether/or framework, u(n d 1, n d 2) = D 1(n d 1, n d 2)φ S 1 (n 1) + D 2(n d 1, n d 2)φ S 2 (n 2), whle u(0, n d j ) = D j(0, n d j )φ S j (n j). Hence, Π d = D 1(n d 1, n d 2)φ S 1 (n 1) + D 2(n d 1, n d 2)φ S 2 (n 2) D j(0, n d j )φ S j (n j). The frst two terms are equvalent to a monopolst s proft, whle the last term s ndependent of n d. Therefore, the frst-order condtons for monopoly and duopoly concde. 11

13 dstnct to the one n common agency frameworks. 6 Vewer Preference Correlaton We now analyze condton (6) n more detal to provde nsghts how entry shapes advertsng levels. The condton asks f there are any systematc dfferences between exclusve and overlappng vewers that could tlt the trade-off one way or the other. The two sdes of the nequalty stress two dfferent sources of dssmlartes between the two vewer pools, both of whch play a crucal role n duopoly. The left-hand sde focuses on relatve preferences, expressed by demand elastctes. The rght-hand sde focuses on potental dfferences n the advertsng technology, expressed by elastctes of the advertsng functon. Gven that these are two very dfferent mechansms, we tackle them separately. In ths secton, we add structure on the advertsng functons n a way that guarantees that the rght-hand sde of (6) equals one. Ths shuts down the technologcal source. Results are then purely drven by systematc dfferences n preferences across types. In the next secton, we carry out the mrror exercse. We shut down the preferences source by usng the nsghts ganed n ths secton. As we shall see, t s possble to add structure to the jont dstrbuton a way that guarantees a left-hand sde of (6) equal to one for all (n 1, n 2 ). Our fndngs n Secton 7 wll therefore hnge solely on technologcal factors. Ths break-up s mplemented for llustratve purposes only. In prncple, we could carry out the two exercses smultaneously. 27 To solate how relatve preferences shape the effect of competton, n ths secton we assume that φ M ( ) = φ S () for = 1, 2. Ths amounts to consderng the case where overlappng and exclusve vewers get nformed wth the same probablty (on a sngle outlet). Usng φ M ( ) = φ S (), one can verfy that the rght-hand sde of (6) equals 1 for all (n 1, n 2 ). 28 So condton (6) smplfes to: E D12 E d > (<)1. (7) We now seek to dentfy features of the jont dstrbuton of preferences that could lead to systematc dfferences n the relatve elastctes of demand. A strkng feature of (7) s that the effect of competton depends on the jont dstrbuton of preferences through E D12 only. So any change n the jont dstrbuton that results n a decrease of E D12 (for equal margnal dstrbutons) yelds downward compettve pressure on advertsng levels. To brng out ths effect, we add structure to the preferences. Specfcally, we assume that (q 1, q 2 ) s drawn from a bvarate normal dstrbuton wth mean (0, 0) and varance-covarance matrx Σ = [ 1 ρ ρ 1 The parameter ρ s the coeffcent of correlaton between q 1 and q 2 and therefore captures content lkeness. We can now determne how a change n the correlaton coeffcent affects vewer composton. ]. Lemma 1 D 12 s strctly ncreasng n ρ. 27 We note that analogous exercses are not necessary for the result on outlet mergers (Proposton 2). Ths result depends solely on the dfference betweenformng a sngle-homng and a mult-homng vewer. Therefore, t holds for any vewer preference dstrbuton and s ndependent of the exact shape of the advertsng technology. 28 See the proof of Proposton 3. 12

14 The lemma shows that the vewer composton changes monotoncally wth the correlaton coeffcent,.e., a hgher correlaton coeffcent, ceters parbus, s equvalent to ancrease n the extent of vewer overlap. Recall that the total demand of outlet depends only on the margnal dstrbuton, whch s unchanged by ancrease n ρ. Therefore, only the compostos affected by ρ. At frst thought, Lemma 1 suggests a negatve relatonshp between ρ and the equlbrum advertsng level. The hgher the number of overlappng vewers, the stronger the duplcaton effect. However, a larger ρ could enhance the busness-sharng effect as well. Indeed, a larger D 12 may lead to a larger fracton of the varaton comng from overlappng vewers. Other thngs held constant, ths suggests a postve relatonshp. The resultng ndetermnacy s reflected by the fact that what matters s how the elastcty of the demand D 12 changes wth correlaton. The next lemma proves that a systematc relatonshp between E D12 and jont preferences as captured by ρ exsts. Lemma 2 E D12 decreases wth ρ for all n 1 = n 2 > 0. To mantuton behnd ths result s that the fracton of margnal consumers who are shared changes wth ρ at a dfferent rate than the fracton of the total consumers who are shared. To see ths n a smple way, consder, as an extreme example, the Hotellng model n whch vewer preferences are perfectly negatvely correlated. In ths model (focusng on anteror equlbrum), snglehomng vewers are located close to the respectve outlet whereas mult-homng vewers are n the mddle. A change n the advertsng level of outlet affects only the margn between mult-homers and snglehomers on outlet j but not the margn between mult-homers and sngle-homers on outlet. Therefore, although the nframargnal vewers consst of exclusve and overlappng vewers, all of the margnal vewers are overlappng ones. Ths mples that (n absolute terms) D 12 / s large compared to D 12 ; hence, E D12 s also large. As a consequence, the busness-sharng effect domnates the duplcaton effect. Therefore, platform entry tends to ncrease advertsng levels. Our analyss generalzes ths nsght by showng that t apples for all ρ < 0. It also demonstrates that the nsght reverses f vewer preferences are postvely correlated. In that case, the total vewer demand s comprsed of a large porton of overlappng vewers. Instead, the composton of margnal vewers conssts of a relatvely large porton of exclusve ones. Ths mples that E D12 s small because (n absolute terms) D 12 / s small relatve to D 12. As a consequence, the duplcaton effect domnates the busness-sharng effect. Ths leads to downward pressure on advertsng levels. Recall that d, and hence E d, dos not change wth ρ. So we obtan a smple characterzaton: Proposton 3 Ancumbent monopolst s advertsng level ncreases upon entry of a compettor f and only f ρ s negatve. That s, sgn(n d n m ) = sgn(e D12 E d ) = sgn(ρ), where all functons are evaluated at = n m and n j = n d j. Before movng on, we use ths result n two dfferent ways. Frst, we dscuss the mpled strategc consderatons of outlets when choosng whch knd of content to produce. Second, we dscuss how ths result can be used as a frst emprcal test of the theory. Implcatons for Content Choce Whle content has been kept exogenous so far, a natural applcaton of ths model s content choce. 13

15 In partcular, t allows us to add to the ongong debate on competton and dversty n the meda, whch s often spelled out as deologcal dversty. The analyss reles on two premses: 1) potental entrants can affect the degree of correlaton at a content-producton stage. Ths stage s akn to product postonng n standard models of product dfferentaton; 2) a decrease n ρ can be read as ancrease n the supply of more dverse content. Our am s not to provde a full-fledged model of dfferentaton, whch would be largely outsde the scope of the paper. Rather, we seek here to dentfy broad mechansms that we do not expect to be senstve to a partcular model specfcaton: 1) Would an entrant that caters to the same vewers as the ncumbent be more or less proftable than an outlet that caters to those who fnd the ncumbent unappealng? 2) In lght of Proposton 2, do strategc consderatons enhance or reduce the ncentves to dfferentate one s content from the rval s? What we have n mnd s a smple two-stage game. At stage 1, an entrant observes the content of the ncumbent and chooses the extent of dfferentaton, measured by ρ. The entrant ncurs a quadratc nvestment cost k(1 ρ) 2, where k > 0 s an arbtrary constant. Ths cost functon captures the dea that duplcaton (ρ = 1) s costless whle dfferentatos ncreasngly costly. So the entrant maxmzes π d( ρ) k(1 ρ)2, where π d s the equlbrum proft of outlet n duopoly. At stage 2, competton takes place as descrbed n Secton 3. Gven a well-behaved problem, n equlbrum ρ equates the margnal cost wth the margnal beneft of dfferentaton. The latter s gven by 29 π d ( ρ) = ( ( D 12 ρ n j (φ12 φ M j ) )) D 12 ρ n j φ S + D 12 (φ S φm + φ M j φ 12 ). j φ 12 n j Ths term shows how the ncentves to dfferentate are shaped. Its decompostos farly straghtforward n lght of our prevous results. The frst term n the large bracket on the rght-hand sde ( D 12 / ρ) s postve. 30 It captures the basc nsght that decreasng correlaton leads to a demand that s comprsed of relatvely more exclusve vewers, whch are more valuable to advertsers. Other thngs held constant, the entrant has ancentve to nvest n dverse content (or, dmnsh ρ). The second term accounts for the rval s reacton ( n j / ρ(...)). As dscussed, a lower ρ results n an equlbrum n whch the rval outlet competes more aggressvely for advertsng dollars by ncreasng ts supply of ads. Ths mechansm, whch we conventonally refer to as the strategc one, may pont n the opposte drecton as more ads from the rval reduce the extent of rent extracton from overlappng vewers. Interestngly, our drect and strategc effect can have opposte forces than standard models of dfferentaton (see, for example, d Aspremont, Gabszewcz and Thsse (1979) on horzontal dfferentaton or Shaked and Sutton (1982) on vertcal dfferentaton). In these models, the strategc effect s that frms become more dfferentated to soften competton whle the drect effect s that frms have a smaller secured demand (a smaller hnterland ). In our case, the opposte could hold, escapng competton through less dfferentaton. Anterestng follow-up questos how consumer preferences shape ρ. equvalent to the queston how changes n the prmtves shft π d / ( ρ). In our settng, ths s A frst parameter, consdered n the lterature on advertsng and product desgn, s the dsperson of consumer valuatons (e.g., Johnson and Myatt, 2006). It bascally captures the extent of preference heterogenety. A smple way to consder ths ssue n our settng s to parametrze the varance-covarance 29 We use here that D 12/ ( ρ) = D 12/ ρ and n j/ ( ρ) = n j/ ρ. 30 Note that the second bracket φ S + φ M j φ 12 s also postve. 14

16 (a) Change n dsperson (b) Change n nusance Fgure 1: π d 1 ( ρ, σ) 10 (1 ρ)2 matrx by a varance parameter σ, symmetrc across outlets: [ ] σ ρ Σ =. ρ σ A basc observatos that by movng mass towards the rght tal of the margnal dstrbutons, dsperson ncreases both d and D 12 for all postve values of (n 1, n 2 ). Havng more shared busness obvously ncreases the returns form dfferentaton. Ths gves the enterng outlet ancentve to choose a lower ρ. To confrm ths ntuton we solved numercally for the optmal value of ρ for dfferent values of σ. Fgure 1-(a) shows the second-stage profts as a functon of ρ for dfferent values of σ. For llustratve purposes, we lmt to two curves correspondng to σ = 1.5 (dashed) and σ = 1 (sold). The proft values on the left ordnate represent the proft values wth σ = 1.5 and those on the rght ordnate are the proft values wth σ = 1. Profts ncrease wth sgma. The reasos that dspersoncreases the overall demand d and therefore brngs n extra rents. It s evdent from the fgure that a larger dsperson shfts the peak to the left. Therefore, outlets choose a larger degree of dfferentaton, the more heterogeneous vewers are. The ntutos that, due to hgher profts wth ncreased dsperson, outlets gans more from a margnal ncrease n dfferentaton. Fgure 1-(b) refers to a change n the nusance cost γ. We perform the same exercse and ncrease γ from 1 to 1.5. Dong so reduces profts, and ths nduces outlets to choose a lower extent of dfferentaton. Intutvely, f vewers dslke ads to a greater extent, demand falls, mplyng that there s less surplus to be extracted. Ths, n turn, reduces outlets ncentves to nvest n costly dfferentaton. Therefore, our model predcts that the extent of dfferentatoncreases wth factors that nduce a larger vewer demand. Emprcal Analyss We provde a bref emprcal nvestgaton of the lnk between entry and correlaton on advertsng levels. The analyss explots varaton the extent of compettve pressure brought about by entry and ext of TV channels n the Basc Cable lneup n the 80s and 90s. As our data are lmted, we regard our results as suggestve evdence. The dataset s provded by Kagan-SNL, a hghly regarded propretary source for nformaton on 15

17 broadcastng markets. It conssts of an unbalanced panel data set of 68 basc cable channels from 1989 to The channels cover almost all cable ndustry advertsng revenues. We know the date for each new network launch wthn our sample perod (a total of 43 launches). In addton, for each network actve n each year we have nformaton on the average number of 30-second advertsng slots per hour of programmng (n jargon avals ). We also have a good coverage for other network varables, such as subscrbers, programmng expenses and ratngs. We study the relatonshp between the avals broadcasted by each channel and the number of ncumbents. As our model characterzes the effects of varyng competton, we consder each channel wthn ts own compettve envronment. That s, we defne a relevant market segment for each of the 68 channels. The hypothess s that channels wth content talored to the same segment compete for vewers and advertsers. For ths purpose, we dvde channels n three segments: () sports channels (henceforth Sports), () channels broadcastng manly moves and TV seres (henceforth Moves&Seres), and () all remanng channels, whch s used as a reference group. To test whether vewer preference correlaton affects the relatonshp between entry and advertsng levels, we estmate separate parameters for the Sports and the Moves&Seres segments. Our workng hypothess s that the vewers preferences wthn these segments are postvely correlated. Our model predcts that avals would fall after entry n the Sports and Moves&Seres segments relatve to the reference group. 31,32 There are manly two dffcultes wth the analyss. A frst one s the ssue of entry endogenety on ncumbent performance. In general, t s hard to nstrument for entry (see e.g., Berry and Ress, 2007) and we do not have explotable varaton for ths purpose. A second one s that we do not drectly observe consumers preferences and thus ther correlaton across dfferent outlets. Ths sad, we beleve t s reasonable to assume that those who watch ESPN are more lkely to watch ESPN2 or FoxSports. We use a panel analyss, that pools all channel-year observatons from , so t reles on wthn- and across-channel varaton. 33 We estmate the followng lnear regresson model: log(avals t ) =β Outlets t + β M Outlets t MovesSeres dummy + β S Outlets t Sports dummy + γ x t + α + δ t + ɛ t, where Avals t s the average number n year t of 30-second advertsng slots per hour of programmng by channel, Outlets t s the number of channels n channel s segment at the end of year t, Sports dummy and MovesSeres dummy are dummy varables equal to 1 when channel belongs to the Sports and to the Moves&Seres segments, respectvely, (and zero otherwse), x t s a vector of channel-tme controls, α s a channel fxed effect and δ t s a tme fxed effect. Gven that the dependent varable s transformed n logs, whle the man explanatory varable s measured n unts of channels, β has the followng nterpretaton: when a new channel enters the control segment, the ncumbents ncrease ther 30-second advertsng slots by 100β%. The coeffcents β M and β S measure the addtonal effect that the number 31 Our data does not nclude vewer prces. Ths should not be a problem because ther mpact was not partcularly mportant durng our sample perod (see for example, Strömberg, 2004). In addton, vewer prces were hghly regulated n the 1990s. 32 We note that we ntended to create a separate News segment as well, as ths segment provdes a natural counterpart to the others n that vewer preferences can be reasonably assumed to be negatvely correlated. Unfortunately, the number of channels here s too small to obtan statstcally meanngful results. The pont estmates we obtan are nevertheless consstent wth Proposton 2 (detals are avalable from the authors). 33 In Appendx B, we demonstrate that usng a model of entry epsodes leads to smlar conclusons as the panel analyss. 16

18 of channels has on the avals n the Sports and Moves&Seres segments respectvely. Table 2: Number of Incumbents and Avals - Effect by Segment (1) (2) (3) (4) (5) (6) Outlets *** ** ** *** * ( ) ( ) ( ) ( ) ( ) ( ) Outlets Moves&Seres * ** ** ** *** ( ) ( ) ( ) ( ) ( ) ( ) Outlets Sports ** *** *** ( ) ( ) ( ) ( ) ( ) ( ) Real GDP * ( ) ( ) MovesSeres dummy 0.191*** 0.257*** (0.0595) (0.0766) Sports dummy (0.0690) (0.0866) Rev Mkt Share (0.398) Ratng (0.0542) Constant 2.908*** 2.685*** 2.760*** 3.242*** 3.226*** 3.273*** (0.0351) (0.190) (0.0469) (0.0372) (0.0621) (0.0258) Observatons R Channel FE NO NO YES YES YES YES Tme FE NO NO NO YES YES YES No. of Outlets Robust standard errors n parentheses *** p<0.01, ** p<0.05, * p<0.1 Table 2 reports the estmaton results. Startng from the sngle varable model n column (1), we progressvely add controls and fxed effects: column (2) controls for the real GDP to capture the busness cycle s effect on the advertsng market. Startng from column (3), we report estmates for a fxed-effect model where the unts of observatons are the sngle channels. From column (4), we ntroduce tme dummes, whle n columns (5) and (6) we add channel-tme controls: the channel s share of revenues n ts segment and ts ratng. Snce we only have US data, the real GDP control s dropped whenever tme controls are ncluded. All regressons are estmated wth robust standard errors, whch are clustered at the segment level. Table 2 provdes evdence that entry s assocated wth ancrease n the advertsng levels on ncumbent channels. The coeffcent s postve and sgnfcant across almost all specfcatons. Ths result s n lne wth the anecdotal evdence on the postve mpact of entry of FOX News on the advertsng levels 17

19 suppled by MSNBC or CNN, whch s often referred to as the Fox News Puzzle. We are partcularly nterested n the coeffcents β S and β M whch we expect to be negatve, gven our theory. That s, we expect the effect of entry wthn the Sports and Moves&Seres segment to be dmnshed compared to the average ndustry effect (and possbly negatve overall). Indeed, the coeffcents have the expected sgn all regressons: the effect of the number of channels on advertsng levels n these two segments s sgnfcantly lower than the reference group. Ths addtonal negatve effect s partcularly strong for Moves&Seres where β M > β n almost all specfcatons. 7 Advertsng Technology Competton comes hand-n-hand wth duplcaton: n duopoly mult-homers receve the same ads from two dfferent sources. We now explore f ths fact together wth dmnshng margnal returns njects downward pressure on advertsng levels. To focus on the advertsng technology, we shut down the preference channel and assume throughout ths secton that E D12 = E d. As shown the last secton, ths assumpton holds, for example, f the valuatons for the two outlets are standard normally dstrbuted and ndependent of each other (.e., ρ = 0). Condton (6) tells us that n ths partcular case competton reduces advertsng levels f and only f 1 < E φ M φ M j + φ E φ S. The next proposton shows that compettos shaped by the outlet s relatve elastctes of nformng dfferent knds of vewers. Proposton 4 Ancumbent monopolst s advertsng level ncreases upon entry of a compettor f and only f the elastcty to nform an overlappng vewer on a sngle outlet s hgher than the elastcty to nform an exclusve vewer, that s, E φ M E φ S > 0, (8) where all functons are evaluated at = n m and n j = n d j. If advertsng levels ncrease or decrease wth entry depends on the returns from advertsng to overlappng vewers beng hgher or lower than those to exclusve vewers. Ths dfference n the effectveness of advertsng s measured by the dfference n elastctes (.e., E φ M E φ S). The ntuton behnd the result n Proposton 3 can agan be traced back to the relatve strength of the duplcaton and busness-sharng effect. Suppose that overlappng vewers are harder to nform than exclusve vewers (.e., φ M / < φ S /). Ths ncreases the strength of the duplcaton effect because platforms n duopoly can extract only a small amount for ther overlappng vewers. At the same tme, the busnesssharng effect s also more pronounced f overlappng vewers are harder to nform. Because φ M s smaller than φ S, the demand reducton followng ancrease n the advertsng level reduces profts of a duopoly platform only by a small amount compared to a monopoly platform. Ths mples that advertsng levels tend to ncrease wth entry. Therefore, f advertsng to overlappng vewers s less effectve, both effects are more pronounced, and the overall result s ambguous. Smlarly, f advertsng to overlappng vewers s more effectve, both effects get weaker n strength, leadng agan to an ambguous result. To gan further nsghts, consder the technology of the exponental form, that s, φ S (n) = 1 e bs n 18

20 and φ M (n) = 1 e bm n. 34 We allow for b M beng larger or smaller than b S, that s, overlappng vewers can become nformed wth a hgher or lower probablty than exclusves. If mult-homers spend a reduced amount of attenton on a partcular outlet, t s natural that φ M (n) < φ S (n), whch equals bm < b S. However, t s also concevable that mult-homers react more to ads because they are exposed to more content, mplyng b M > b S. In general, vewers may dffer along dmensons other than (q 1, q 2 ), whch leads to nherent dfferences between overlappng and exclusve vewers that justfes ether assumpton. Wth the exponental technology, t s easy to show that the left-hand sde of (8), E φ M E φ S, can be wrtten as (b S b M )e (bs +b M )n m + b M e bm n m b S e bs n m. (9) It s readly verfed that (9) s strctly postve for 0 < b M < b S, strctly negatve for b M > b S, and zero for b M = 0 and b M = b S. Interestngly, ths shows that n the perhaps more natural case, n whch exclusve vewers are more receptve to ads, advertsng levels n duopoly are larger than monopoly. Therefore, the busness-sharng effect domnates the duplcaton effect. Conversely, f overlappng vewers are more receptve to ads, advertsng levels n duopoly are lower. There are two cases (.e., b M = 0 and b M = b S ), n whch advertsng levels n monopoly and duopoly are the same. In the latter case, b M = b S, reachng exclusve and overlappng vewers (on a sngle outlet) s equally effectve, leadng to the same tradeoff n monopoly and duopoly. In the other extreme case, b M = 0, overlappng vewers are of zero value. Therefore, an outlet n duopoly only cares about ts exclusve vewers when choosng the advertsng level. Snce a monopolstc outlet has only exclusve vewers, the trade-off and the equlbrum advertsng level n both scenaros are agan equvalent. 8 Welfare Analyss In ths secton, we analyze how the equlbrum advertsng level relates to the socally optmal one. A common percepton meda markets s that the market leads to an excessvely hgh level of advertsng. 35 Ths usually occurs because of the lack of prces on the consumer sde, mplyng that platforms fal to nternalze the ds-utlty of nusance borne by vewers. However, the lterature on meda markets obtans a more ambguous result. Snce competton for vewers takes place n advertsng levels, ferce competton leads to very low advertsng levels, whch can result n under-provson of advertsng opportuntes. To characterze how ths tenson plays out n our model, we determne socal welfare. As mentoned, q γ s the utlty of a sngle-homng vewer of outlet and q 1 γn 1 + q 2 γn 2 s the utlty of a mult-homng vewer. Socal welfare s gven by W = γn2 γn 1 0 γn1 (q 1 γn 1 ) h(q 1, q 2 )dq 2 dq 1 + (q 2 γn 2 ) h(q 1, q 2 )dq 2 dq 1 0 γn 2 + (q 1 γn 1 + q 2 γn 2 ) h(q 1, q 2 )dq 2 dq 1 + D 1 φ S 1 + D 2 φ S 2 + D 12 φ 12. γn 1 γn 2 34 Ths functonal form was frstly ntroduced n a semnal paper by Butters (1977) and has been wdely used snce then n appled work on advertsng. It can be derved from natural prmtve assumptons on the stochastc process that governs the allocaton of messages to consumers. 35 Ths percepton trggered nterventon by regulators n several countres. For examples, lmtng the number of advertsng mnutes per hour on TV s common many European countres. 19

21 Comparng the equlbrum advertsng level wth the socally effcent advertsng level we obtan the followng result: Proposton 5: Equlbrum advertsng levels are neffcently hgh f φ M φ S. To provde ntuton we buld on Proposton 4 and consder the ncentves of a jont platform owner. Under jont ownershp, the merged entty fully nternalzes the advertsng surplus whle t does not nternalze vewer s welfare. More precsely, t only cares about vewers utltes nasmuch as they contrbute to advertsng revenue, whle the nusance costs from advertsng are not takento account. From Proposton 4, we know that competng outlets mplement the same advertsng levels as long as φ M = φ S and even hgher levels for φ M > φ S. Therefore, f φm φ S, the over-provson result follows. The result mples that φ M < φ S s necessary for competton to mprove welfare. However, even f φ M s smaller than φ S, advertsng levels n duopoly can be neffcently hgh. Frst, by contnuty, f φ M s close to φ S, over-provson occurs. In addton, evef φm s much lower than φ S, the result also holds as long as vewer ds-utlty from ads s suffcently hgh. The reasos agan that outlets do not take vewers utltes drectly nto account n ther advertsng choce. The result can only be reversed f the ds-utlty from ads s small and φ M << φ S because then advertsng levels n duopoly are much lower than wth jont ownershp. As a consequence, the condton Proposton 5 s suffcent, but not necessary. We therefore obtan the result that competton may even lead to hgher advertsng levels (and to lower welfare) than jont monopoly. Ths result contrasts wth the one of the standard compettve bottleneck model, where competton always lowers advertsng (and mproves welfare, as long as advertsng levels are not excessvely small). Ths demonstrates that the mportance of demand composton brought about by ether or both competton predcts an outcome that s closer to the common percepton of excessve advertsng n meda markets. We fnally note that Proposton 5 should be nterpreted wth cauton. The over-provson result hnges on the assumpton that advertsers are homogeneous. If advertsers are heterogeneous wth respect to ther product valuatons, an extensve margn comes nto play n addton to the ntensve margn consdered so far. Ths extensve margn arses because, as n prevous lterature, a outlet owner trades off the margnal proft from an addtonal advertser wth the profts from nfra-margnal advertsers. Ths effect would couple wth ours, potentally dmnshng ts extent. 9 Concluson Ths paper presented a model of outlet competton wth overlappng vewershps, allowng for farly general vewer demand and advertsng technologes. We emphasze the role that vewer composton plays for market outcomes, and dentfy novel compettve effects, such as the duplcaton and the busnesssharng effect. The generalty of the framework allows the model to serve as a useful buldng block to tackle a varety of questons. For example, we took the qualty of outlets to be exogenous n our analyss. Yet, competton meda markets (and n many other ndustres) often works through qualty. Our model can be used to nvestgate whether markets n whch users can be actve on multple outlets lead to hgher or lower qualty than those n whch users are prmarly actve on a sngle outlet. Another nterestng queston pertans to prcng tools. We consdered the case n whch outlets offer contracts consstng 20

22 of an advertsng level and a transfer, but n some ndustres frms prmarly charge lnear prces. How then do our results depend on the contractng envronment? Also, do lnear prces lead to a more or less compettve outcome? We leave these questons for future research. Our model s also not restrcted to the meda markets context. In partcular, a characterzng feature of our model s that consumers are mult-stop shoppers,.e., can patronze multple frms, but that a frm s revenue s lower for a consumer who buys from several other frms. Hence our model contrbutes to understandng competton settngs where frms care not only about the overall demand but also about ts composton. Such settngs arse naturally when servng dfferent types of customers yeld dfferent revenues (as n our model), as well as when there are consumpton externaltes among customers. 21

23 10 Appendx Appendx A: Proof of Propostons Proof of Clam 1: Frst suppose that there s a non-sngleton menu of contracts (t k, mk )K k=1 offered by outlet such that each of these contracts s accepted by some advertsers. Then advertsers have to be ndfferent between these contracts. Let F (k) denote the cumulatve densty of advertsers acceptng some contract (t k, mk ) for some k k. Then, by strct concavty of φ and φ 12, f outlet nstead offered a sngle contract (F (K)E(t k ), F (K)E(mk )), where the expectatons are taken wth respect to F, each advertser would strctly prefer to accept the contract, resultng n the same total advertsng level and proft for the outlet. But then outlet could ncrease profts by offerng a sngle contract (F (K)E(t k ) + ε, F (K)E(mk )), for a small enough ε > 0, snce such a contract would stll guarantee acceptance from all advertsers. The same logc can be used to establsh that t cannot be n equlbrum that a sngle contract (t, m ) s offered but only a fracton of advertsers F (1) < 1 accept t, snce offerng (F (1) t + ε, F (1) m ) for small enough ε > 0 would guarantee acceptance by all advertsers and generate a hgher proft for outlet. The above arguments establsh that the total realzed advertsng level on outlet s m, the ntensty specfed n the sngle contract offered by. It cannot be that m >, snce then by assumpton the outlet s payoff would be negatve. Moreover, snce φ S and φ 12 are strctly ncreasng, t cannot be that m <, snce then the outlet could swtch to offerng a contract (t +ε, ), whch for small enough ε > 0 would guarantee acceptance by all advertsers and generate a hgher proft for outlet. Thus m =. Fnally, note that t 1 < u(n 1, n 2 ) u(0, n 2 ) mples that outlet 1 could charge a hgher transfer and stll guarantee the acceptance of all advertsers, whle t 1 > u(n 1, n 2 ) u(0, n 2 ) would contradct that all advertsers accept both outlets contracts. Hence, t 1 = u(n 1, n 2 ) u(0, n 2 ). A symmetrc argument establshes that t 2 = u(n 1, n 2 ) u(n 1, 0). The proof of Clam 2 proceeds exactly along the same lnes and s therefore omtted. Proof of Proposton 1: We know that the equlbrum advertsng level n case of duopoly s gven by (5), whle the equlbrum advertsng level of a sngle outlet monopolst s gven by (4). To check f advertsng levels rse wth entry, let us evaluate (5) at n m n d > nm f and only f and n d j. Snce the frst terms n equatons (4) and (5) are the same, we have D 12 (φ M φ M j + φ ) D 12 (φ M φ M j + φ ) > 0. Due to the fact that the objectve functons are sngle-peaked, t follows that the ncumbent s equlbrum advertsng level n duopoly s larger than the equlbrum advertsng level n monopoly f the margnal proft evaluated at the pre-entry advertsng level s postve, gven that outlet j sets n d j. Rearrangng ths nequalty gves D 12 D 12 > ( ) (φ M φ M j + φ ) 22 φ M φ M j + φ.

24 Usng our defntons and E D12 := D 12 D 12 E φ M φ M j + φ := (φm φ M j + φ ) φ M φ M j + φ, we can rewrte (10) as E D12 > E φ M φ M j + φ. Dvdng ths expresson by E d > 0, we obtan E D12 /E d > E φ M φ M j + φ /E d. Fnally, note that from (4) we have E d = E φ S, whch yelds E D12 E φ M > φ M j + φ. E d E φ S Proof of Proposton 2: Consder frst the case of competng outlets. From (2), we know that outlet s proft maxmzaton problem s max Π d = [ D (, n j )φ S ( ) + D 12 (, n j )(φ 12 (, n j ) φ M j (n j )) ]. The equlbrum advertsng levels are therefore characterzed by the followng system of frst-order condtons (arguments omtted): D φ S + D φ S + D 12 (φ 12 φ M j ) + D 12 φ 12 = 0,, j = 1, 2; j = 3. (10) Consder now the case of jont ownershp. The jont monopolst s problem s max Π jo = D 1 φ S,n 1 + D 2 φ S 2 + D 12 φ 12,, j = 1, 2; j = 3. (11) j Takng the frst-order condton of (11) wth respect to we obtan D φ S + D φ S + D j φ S j + D 12 φ 12 + D 12 φ 12 = 0,, j = 1, 2; j = 3. (12) We know that the total demand of outlet j, d j (n j ) = D j (n 1, n 2 ) + D 12 (n 1, n 2 ), s ndependent of. Ths mples D j / + D 12 / = 0 or D j / = D 12 /. Usng ths, we can rewrte (12) as D φ S φ S + D + D 12 ( φ12 φ S ) φ 12 j + D12 = 0,, j = 1, 2; j = 3. (13) Comparng (13) wth (10), t s evdent that at = n d, (13) s postve f and only f φs j > φm j. Ths mples that n jo > n d f and only f φs j > φm j and n jo < n d f and only f φs j < φm j. If φs j = φm j, the two advertsng levels are equvalent (.e., n jo = n d ). Proof of Lemma 1: Our goal s to show that D 12 s strctly ncreasng n ρ. D 12 s defned as Prob{q 1 γn 1 ; q 2 γn 2 }. 23

25 To smplfy the exposton, we set γ = 1. (We also do so n the proofs of Lemma 2 and Proposton 2). Ths mples D 12 := Prob{q 1 n 1 ; q 2 n 2 }. If (q 1, q 2 ) are drawn from a bvarate normal dstrbuton wth mean (0,0) and varance Σ = ((1, ρ), (ρ, 1)), we can wrte D 12 = 1 2π 1 ρ 2 n 2 n 1 e q 1 2 2ρq 1 q 2 +q2 2 2(1 ρ 2 ) dq 1 dq 2. (14) To determne the sgn of D 12 / ρ, we frst perform ntegraton wth respect to q 1 and then dfferentate wth respect to ρ. Whentegratng wth respect to q 1, we use the error functon defned as erf(n 1 ) = (2/ π) n 1 0 e q2 1 dq1 and explot the facts that lm n1 erf(n 1 ) 1 and 36 n 1 1 e q2 1 dq1 = 1 2 π 2 After takng the dervatve wth respect to ρ we obtan D 12 ρ = 1 2π(1 ρ 2 ) 3/2 0 n 2 [ 1 erf We cantegrate the rght-hand sde of (15) drectly to obtan ( n1 )]. 2 n2 1 2ρn 1 q 2 +q2 2 e 2(1 ρ 2 ) (q 2 ρn 1 )dq 2. (15) n D 12 ρ = 1 2 2π 1 2ρn 1 n 2 +n2 2 1 ρ 2 e 2(1 ρ 2 ) > 0. (16) Because the ntegrand of the expresson (14) s well-behaved, we can also reverse the order of ntegraton and dfferentaton to obtan the same result. As a consequence, we have D 12 / ρ > 0 for all (n 1, n 2 ). Proof of Lemma 2: The elastcty E D12 s gven by ( D 12 / )( /D 12 ). Takng the dervatve wth respect to ρ yelds E D12 ρ ( ) D12 = + D 12 ρ D 12 D 2 12 D 12 ρ = n ( 2 D 12 D 12 ρ D ) 12 1 D 12. (17) D 12 ρ Rearrangng (17) and usng D 12 / ρ > 0 yelds that E D12 / ρ < 0 f and only f D 12 D 12 < 2 D 12 ρ D 12. (18) ρ We can wrte D 12 as D 12 = n 2 n 1 h(q 1, q 2 )dq 2 dq 1, where h(q 1, q 2 ) s the probablty densty functon of the reservaton values (q 1, q 2 ). It s gven by q 1 2π 1 2 2ρq 1 q 2 +q2 2 1 ρ 2 e 2(1 ρ 2 ). 36 See, for example, Greene (2007). 24

26 Takng the dervatve of D 12 = n 2 n 1 h(q 1, q 2 )dq 2 dq 1 wth respect to n 1 and n 2 and usng the Lebnz rule yelds 2 D 12 n 1 n 2 = n 1 2 2π 1 2ρn 1 n 2 +n2 2 1 ρ 2 e 2(1 ρ 2 ). The rght-hand sde of the last equatos h(n 1, n 2 ). We therefore obtan that for the bvarate normal dstrbuton, D 12 / ρ whch s gven by (16) equals the dervatve of D 12 wth respect to n 1 and n 2. Hence, We can therefore rewrte (18) as n j D 12 ρ = h(n 1, n 2 ). h(, q j )dq j < n 2 n 1 h(q 1, q 2 )dq 2 dq 1 In the followng, we show that the nequalty s ndeed fulflled for = n j. We start wth the rght-hand sde. Usng h(n 1, n 2 ) = 1/(2π 1 ρ 2 )e n h(n 1,n 2 ) h(n 1, n 2 ). (19) 2 1 2ρn 1 n 2 +n2 2 2(1 ρ 2 ), we obtan h(n 1, n 2 ) 1 = 2π 1 ρ 2 e n 2 1 2ρn 1 n 2 +n2 2 2(1 ρ 2 ) ρn j 1 ρ 2. We can therefore wrte the rght hand-sde of (19) as For = n j, we obtan ρn j 1 ρ 2. n j 1 ρ 1 ρ 2. Now we turn to the left-hand sde of (19). The numerator s n j h(, q j )dq j = n 1 2 n j 2π 2ρ q j +q2 j 1 ρ 2 e 2(1 ρ 2 ) dq j. Because lm x e x = 0, the rght-hand sde of the last expresson can be wrtten as n j 1 2π 1 ρ 2 e q 2 2ρq q j +q2 j 2(1 ρ 2 ) q = dq j. To make the numerator and the denomnator of the left-hand sde comparable wth each other, we modfy the last expresson to a double ntegral form. Ths gves q = n n j q2 2ρq q j +q2 j 1 2π e 2(1 ρ 2 ) dq dq j. 1 ρ 2 q 25

27 Takng the dervate of the ntegrand yelds = n Fnally, we apply b a xdx = a b ( x)dx to get The denomnator s gven by n j n j q 1 2π ρq j q 2 2ρq q j +q2 j 1 ρ 2 1 ρ 2 e 2(1 ρ 2 ) dq dq j. q q ρq j 2π 2 2ρq q j +q2 j 1 ρ 2 (1 ρ 2 ) e 2(1 ρ 2 ) dq dq j. (20) n j h(q 1, q 2 )dq 2 dq 1 = n j 1 2π 1 ρ 2 e Dvdng (20) by (21), we can wrte the left-hand sde of (19) as q 2 2ρq q j +q2 j 2(1 ρ 2 ) dq 2 dq 1. (21) n j (q ρq j )e q2 2ρq q j +q2 j 2(1 ρ 2 ) n j e q2 2ρq q j +q2 j 2(1 ρ 2 ) dq j dq dq dq j 1 1 ρ 2. For = n j, the two ntegrals have the same length, mplyng that the left-hand sde of (19) s gven by n j n j q j e q2 2ρq q j +q2 j 2(1 ρ 2 ) n j n j e q2 2ρq q j +q2 j 2(1 ρ 2 ) dq dq j dq j dq 1 ρ 1 ρ 2 = E(q j q j n j, q n j ) 1 ρ 1 ρ 2. We are now n a poston to compare the two sdes of (19) wth each other. Snce E(q j q j n j, q n j ) < n j, we have E(q j q j n j, q n j ) 1 ρ 1 ρ 2 < n 1 ρ j 1 ρ 2. Therefore, the nequalty n (19) s always fulflled, mplyng that E D12 / ρ < 0. Proof of Proposton 3: From the last Lemma, we know that E D12 s strctly decreasng wth ρ at = n j. Because ρ only affects the composton of vewers but not the total demand, E d s unaffected by ρ. Hence, the left-hand sde of (6) s strctly decreasng n ρ. Now let us look at the case ρ = 0. The left-hand sde of (6) s gven by E D12 /E d. The denomnator can be wrtten as E d = e n2 2 e q2 2 dq, (22) whle the numerator s E D12 = n j e n2 +q2 j 2 dq j n. n j e q2 +q2 j 2 dq dq j 26

28 For n j =, the last equaton can be wrtten as n 2 E D12 = e 2 e q2 2 dq ( ) 2 = e q2 2 dq e n2 2 e q2 2 dq. (23) Dvdng (23) by (22), t s easy to see that ths equals 1, whch mples that E D12 /E d = 1 at ρ = 0. We now turn to the rght-hand sde of (6). Snce we are consderng the case φ M φ = 0. The numerator of the rght-hand sde of (6) can therefore be wrtten as = φ S, we have E φ S φ S j = φs φs j φ S φs j. Usng that φ S j s ndependent of (that s, φ S j / = 0), we can wrte the numerator of the rght-hand sde of the last expresson as φ S φ S j φ S = φs φs j φ S. The denomnator s E φ S = φs φ S. It follows that E φ S φ S = E j φ S, mplyng that the rght-hand sde of (6) s equal to 1, ndependent of ρ. Ths result coupled wth the fact that the left-hand sde equals 1 at ρ = 0 and that t s strctly decreasng n ρ yelds the result. Proof of Proposton 4: We know that n d > nm f and only f 1 > E φ M φ M j + E φ φ M = φ M j +φs φm. E φ S E φ S or E φ S > E φ M φ M j +φs φm. Wrtng out the respectve expressons for the elastctes gves φ S φ S > ( φ M φ M j + φ S φm ) φ M φ M j + φ S φm. (24) Snce φ M j / = 0, we have (φ M φ M j )/ = φ M j ( φm )/. Insertng ths nto (24) and rearrangng yelds φ S ( φ S φ M φ M j + φ S φm ) > (1 φ M j ) φm φ M φ M j + φ S φm. (25) 27

29 Smplfyng and dvdng (25) by φ M (φ M j 1) < 0 yelds φ S φ S < φm φ M or E φ S < E φ M. Proof of Proposton 5: We frst look at the last three terms n W,.e., D 1 φ S 1 + D 2φ S 2 + D 12φ 12. Takng the dervatve of these terms gves D φ S + D φ S + D j φ S j + D 12 φ 12 + D 12 φ 12. (26) We can now substtute D j / = D 12 / nto (26) to obtan D φ S + D φ S + D 12 (φ 12 φ S j ) + D 12 φ 12. It s evdent that ths expressos equvalent to (13). Therefore, at = n jo, ths expresson equals zero. Snce n d = njo for φ S j = φm j, the last three terms of W are maxmzed at = n d. However, the frst terms n W are the utltes of the vewers whch are strctly decreasng n. As a consequence, the frst-order condton of W wth respect to evaluated at = n d s strctly negatve, whch mples that there s too much advertsng n duopoly at φ S j = φm j. Because nd s even larger than n jo for φ S j < φm j, there s also too much advertsng n ths range. Appendx B: Emprcal Analyss wth Entry Epsodes Model The panel analyss has the advantage of poolng data on dfferent channels wthout takng a stance on the tme t takes for entry to mpact the ncumbent choces. However, ths strategy does not allow for accountng for wthn-channel omtted varables that vary over tme. These varables may also operate at the segment level. To account for ths, and as an alternatve way to address the same ssues as n the panel analyss, we also estmate a model for entry epsodes, where our sample s now reduced to the perods when a gven segment experences the entry of a new channel. We estmate the followng model: log(avals t ) =β + β M MovesSeres dummy + β S Sports dummy + γ x t + δ t + ɛ t Ths model can be obtaned by frst dfferencng the prevous model around the years when entry occurs. In fact, log(avals t ) = log(avals t+1 ) log(avals t 1 ) and the effect of entry (changed number of ncumbents) s captured by the constant terms. Channel fxed effects are now excluded (as they cancel out n takng frst dfferences), but we keep tme fxed effects and also add some channel controls. The constant β measures the effect of entry on the reference group, whle β S and β M measure the addtonal effect for the Sports and Moves&Seres segments, respectvely. The estmates reported n Table 3 confrm our 28

30 prevous results: entry epsodes are assocated wth ancrease n the quantty of avals n the reference group, whle the effect s lower n the Sports and Moves&Seres segments. Snce there are half as many observatons n ths setup, the pont estmates are less precsely estmated than Table 2. Furthermore, because here we are lookng at the effect one year after entry (t+1), the magntude of the parameters s notably bgger. The pont estmate of the percent varaton avals due to an addtonal channel s on the order of 5% n column (3). Notably, the nteracton term that captures the dfferental mpact of entry n sports s around 11% less than the ndustry average. The dfference s statstcally and economcally sgnfcant. Table 3: Entry Epsodes - Average Effect and Effect by Segment (1) (2) (3) (4) MovesSeres dummy *** ** ( ) ( ) (0.0124) Sports dummy *** *** ( ) ( ) (0.0222) GDP[t-1,t+1] * ( ) ( ) Ratng *** ( ) Rev Mkt Share (0.0987) Constant ** 0.263*** (0.0213) ( ) ( ) ( ) Observatons R Tme FE NO NO YES YES Robust standard errors n parentheses *** p<0.01, ** p<0.05, * p<0.1 29

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34 Onlne Appendx for Ether or Both Competton: A Two-sded Theory of Advertsng wth Overlappng Vewershps Attla Ambrus Emlo Calvano Markus Resnger October 2015 Ths Onlne Appendx provdes supplemental materal for the paper Ether or Both Competton: A Two-sded Theory of Advertsng wth Overlappng Vewershps. Specfcally, t presents an analyss of a two-stage game n whch outlets smultaneously make offers and afterwards all agents smultaneously make ther choces, and provdes the condtons for outcome-equvalence to the four-stage game consdered n the paper. It also demonstrates that the effects dentfed n the paper are also at work n a game wth two ncumbent outlets and one entrant. Fnally, the Onlne Appendx presents an analyss of heterogeneous advertsers and relates t to the analyss of homogeneous advertsers presented n the paper. Department of Economcs, Duke Unversty, Durham, NC E-Mal: [email protected] Center for Studes n Economcs and Fnance, Unversty of Naples Federco II. E-Mal: [email protected] Department of Economcs, Frankfurt School of Fnance & Management, Sonnemannstr. 9-11, Frankfurt am Man, Germany. E-Mal: [email protected]

35 1 Two-stage game Consder the followng two-stage game: In stage 1, outlets smultaneously offer menus of contracts to advertsers of the form (t, m ) R 2 +. After observng these contracts, vewers and advertsers smultaneously choose whch outlet(s) to jon and whch contract(s) to accept, respectvely. In addton, consder the followng assumptons: A1 A2 Outlets are symmetrc. For any α [0, 1], the followng nequalty holds { } t (1 α) > α d (αñ )ϕ S (ñ ) d ((1 α)n )ϕ S (n ), (1) where d ( ) := D ( ) + D 12 ( ), ñ = arg max n d (α )ϕ S (), ( n s mplctly defned by equaton (3) of the paper and t s gven by D (n, n j )ϕs (n ) + D 12(n, n j ) ϕ 12 (n, n j ) ϕm j (n j ). ) We provde a dscusson of these assumptons after the proof of the followng proposton. There we explan that A1 can be weakened whle A2 s a relatvely natural assumpton our framework. Proposton Suppose that A1 and A2 hold. Then, there s an equlbrum n the two-stage game game wth posted contracts, that s outcome-equvalent to the equlbrum of the game defned n Secton 3 of the paper. Proof: Suppose that n the two-stage game wth posted contracts each outlet offers a contract wth = n, where n s mplctly defned by equaton (3) of the paper, and a transfer t = D (n, n j)ϕ S (n ) + D 12 (n, n j) ( ϕ 12 (n, n j) ϕ M j (n j) ). By the same argument as we used for the orgnal model, these contracts wll be accepted by all advertsers. As ths s antcpated by vewers, vewershps are D (n, n j ) and D 12(n, n j ). Snce advertsng levels are the same as n the equlbrum of the orgnal model, vewershps are also the same. Therefore, ths canddate equlbrum s outcome-equvalent to the equlbrum of the orgnal model. Let us now consder f there exsts a proftable devaton from ths canddate equlbrum. We frst show that there can be no proftable devaton contract of outlet that stll nduces full advertser partcpaton on outlet j but a smaller partcpaton on outlet. Let x denote the fracton of advertsers who accept the offer of outlet. Consder a canddate contract (, t ). Suppose that outlet s equlbrum proft from ths contract s t x. Now consder the followng alternatve contract: (x, x t ). Note that total advertsng on outlet s stll equal to x. So outlet s at least as attractve as wth the canddate equlbrum contract. Note moreover that because ϕ S and ϕ 12 are strctly concave n, the ncremental value of acceptng offer (x, x t ) must exceed x t for all levels of advertser partcpaton. So all advertsers would accept (x, x t ) regardless. It follows that outlet can margnally ncrease x t whle stll gettng full partcpaton. Therefore, profts would strctly ncrease. It follows that no offer nducng a level of partcpaton x < 1 can be part of a best reply. Now suppose outlet devates from the canddate equlbrum n such a way that t nduces a fracton α of the advertsers to sngle-home ots outlet whle the remanng fracton 1 α sngle-homes on outlet j. Usng the defnton d ( ) := D ( ) + D 12 ( ), the largest possble transfer that outlet can ask s then 1

36 bounded above by t d = d (αñ )ϕ S (ñ ) u shj, where ñ denotes the optmal devaton advertsng level and u shj denotes the payoff of an advertser who chooses to reject the contract of outlet and nstead sngle-homes on outlet j. To determne u shj we determne the advertser s payoff when acceptng only outlet j s contract, whch s the outlet s equlbrum contract after outlet has devated to nduce a fracton α of advertsers to sngle-home on outlet. We obtan u shj = d j ((1 α)n j, αñ )ϕ S j (n j) t j = d j ((1 α)n j, αñ )ϕ S j (n j) D j (n j, n )ϕ S j (n j) D 12 (n, n j) ( ϕ 12 (n, n j) ϕ M (n ) ). Outlet s proft s then α t. Hence, devatng s not proftable f α {d (αñ )ϕ S (ñ ) d j ((1 α)n j)ϕ S j (n j) + D j (n j, n )ϕ j (n j) + D 12 (n, n j) ( ϕ 12 (n, n j) ϕ M (n ) )} < D (n, n j)ϕ S (n ) + D 12 (n, n j) ( ϕ 12 (n, n j) ϕ M j (n j) ). Now suppose that the two outlets are symmetrc. Then the above condton reduces to { } α d (αñ)ϕ S (ñ) d ((1 α)n )ϕ(n ) (1 α) ( D (n, n )ϕ(n ) + D 12 (n, n ) ( ϕ 12 (n, n )ϕ M (n ) )) < 0, where n = n j = n, ñ = ñ d, ϕ M ( ) = ϕ M j ( ) = ϕm ( ), and ϕ S ( ) = ϕs j ( ) = ϕs ( ). Ths can be rewrtten as { } t (1 α) > α d (αñ )ϕ S (ñ ) d ((1 α)n )ϕ S (n ). whch s fulflled by A2. As a consequence, a devatos not proftable. We now shortly explan why the assumptons A1 and A2 are not very restrctve n our framework. Frst, consder A1. Snce the game s contnuous, A1 can be relaxed to some extent wthout affectng the result, mplyng that the proposton stll holds f outlets are not too asymmetrc. Now consder A2. It s evdent from (1), that the assumptos fulflled for α low enough. In ths case the rght-hand sde s close to 0, whle the left-hand sde s strctly postve. Now consder the opposte case,.e., α 1. In that case the left-hand sde goes to zero, whle the rght-hand sde goes to d (ñ )ϕ S (ñ ) d (0)ϕ S (n ). Evdently, d (0) > d (ñ ). Hence, the rght-hand sde s negatve f ϕ S (ñ ) s not much larger than ϕ S (n ). In general, n can be larger or smaller than ñ, mplyng that the dfference can be ether postve or negatve. However, even case ñ > n, f the slope of the advertsng functons ϕs and ϕ 12 s relatvely small, the dfference between n and ñ wll be small, mplyng that the rght-hand sde s negatve. Fnally, consder ntermedate values of α. Agan, f the dfference between n and ñ s relatvely small, the term n the bracket on the rght-hand sde of (1) s close to zero. Snce the left-hand sde s strctly postve, A2 s then fulflled as well. 2 Entry n case of two ncumbent outlets Consder the case of two ncumbents and entry of a thrd outlet. After entry, the proft of outlet s Π (n 1, n 2, n 3 ) = D (n 1, n 2, n 3 )ϕ S ( ) + D j (n 1, n 2, n 3 ) ( ϕ j (, n j ) ϕ M j (n j ) ) 2

37 +D k (n 1, n 2, n 3 ) ( ϕ k (, n k ) ϕ M k (n k) ) + D 123 (n 1, n 2, n 3 ) (ϕ jk (, n j, n k ) ϕ jk (n j, n k )) As n the case of entry of a second outlet, we can rewrte ths proft functon as the proft wthout entry plus a negatve correcton term. Ths leads to (droppng arguments) Π = (D + D k )ϕ + (D j + D jk )(ϕ j ϕ M j ) D k (ϕ S + ϕ M k ϕ k) D jk ( ϕj ϕ M j (ϕ jk ϕ jk ) ). The frst two terms are the proft n duopoly. Note that wthout entry D k dd not exst snce there was no outlet k and so outlet could get ϕ for these vewers due to the fact that they were sngle-homng on outlet. Smlarly, D jk dd not exst and these vewers were mult-homng n outlets and j. The last two terms are the negatve correcton terms. Takng the dervatve wth respect to yelds Π = Πd + D k (ϕ S + ϕ M k [ ] ϕ k) E Dk E ϕ S +ϕ M k ϕ k ( +D jk ϕj ϕ M j (ϕ jk ϕ jk ) ) [ ] E Djk E ϕj ϕ M j (ϕ jk ϕ jk ) = 0, where Π d / s the dervatve wth respect to of an outlet s proft n case of duopolstc competton. So we obtan that for E Dk > E ϕ S +ϕ M k ϕ and E k D jk > E ϕj ϕ M j (ϕ jk ϕ jk ), the busness-sharng effect domnates the duplcaton effect. The formula now conssts of two addtonal terms snce entry of a thrd outlet leads to changes n two vewer groups, namely, the exclusve ones and the overlappng ones before entry. Each term s multpled by the absolute profts of the respectve vewer group. In a smlar van, the analyss can be extended to any number of ncumbent outlets. 3 Heterogeneous Advertsers We dscuss how the trade-off characterzed n Proposton 1 extends to advertsers wth heterogeneous product values, as n Anderson and Coate (2005). As we wll show, the key nsghts obtaned n the analyss wth homogeneous advertsers carres through to heterogeneous advertsers. In partcular, outlet compettos also characterzed by the tenson between the duplcaton and busness-sharng effect. Ths holds although the analyss s more nvolved compared to homogeneous advertsers, as we need to characterze an entre contract schedule (.e., the optmal screenng contracts) offered by outlets, nstead of only a sngle transfer-quantty par. 1 Consder the followng extenson of our baselne model. The value of nformng a vewer, ω, s dstrbuted accordng to a smooth c.d.f. F wth support [ω, ω], 0 < ω ω, that satsfes the monotone hazard rate property. The value ω s prvate nformaton to each advertser. The tmng of the game s the same as before. In the frst stage, each outlet announces ts total advertsng level. Afterwards, consumers decde whch outlet to jon. Gven these decsons, each outlet offers a menu of contracts 1 Our results also hold when outlets can perfectly dscrmnate between advertsers. In that case, the results for each type are the same as the ones n case of homogeneous advertsers. 3

38 consstng of a transfer schedule t := [0, m] R defned over a compact set of advertsng levels. t (m) s the transfer an advertser has to pay to get an advertsng ntensty m from outlet. In the fnal stage, as before, advertsers decde whch outlet to jon. In what follows, we defne n = (n 1, n 2 ). Let us start wth the monopoly case. Wth an abuse of notaton we stll use ωu(m, ) to denote the surplus of advertser type ω from advertsng ntensty m. The overall utlty of an advertser depends on the transfer schedule n addton to the surplus. If m (ω) denotes the optmal ntensty chosen by type ω, then outlets s problem n case of monopoly s Π = max t ( ) ω t (m (ω))df (ω). (2) By choosng the optmal menu of contracts, the monopolst determnes whch advertser types to exclude, that s, m (ω) = 0 for these types, and whch advertser types wll buy a postve ntensty. We denote the margnal advertser by ω0 m. Problem (2) can be expressed as a standard screenng problem: Π = max ω0 m,m (ω) ω0 m t (m (ω))df (ω) subject to m (ω) = arg max m v m (m, ω, ) t (m ), v m (m (ω), ω, ) t (m (ω)) 0 for all ω ω m 0, ω m 0 m (ω)df (ω), where v m (m, ω, ) := ωd ( )ϕ S (m ) denotes the net value of advertsng ntensty m to type ω n the monopoly case. the partcpaton constrant. The frst constrant s the ncentve-compatblty constrant and the second one The thrd one s the capacty constrant specfyng that the aggregate advertsng level cannot exceed the one specfed by the outlet n the frst stage. Provded that the functon v m (m, ω, ) satsfes the standard regularty condtons n the screenng lterature, we can apply the canoncal screenng methodology Our assumptons on the vewer demand d ( ) and on the advertsng technology ϕ S (m ) ensure that v m s contnuous and ncreasng n ω. It also has strctly ncreasng dfferences n (m, ω). Evdently, the capacty constrant wll be bndng at the optmal soluton snce t can never be optmal for the monopolst to announce a strctly larger advertsng level than the one t uses. Applyng the above-mentoned methodology, we can transform the maxmzaton problem to get Π = max ω0 m,m (ω) ω0 m ( ω 1 F (ω) ) d ( )ϕ S (m (ω))df (ω) f(ω) subject to = ω m 0 m (ω)df (ω). We show at the end of ths secton that the optmal advertsng level can be characterzed by the followng equaton: ω m 0 ( ω 1 F (ω) ) ( ϕ d S + d ) ϕ S df (ω) = 0, (3) f(ω) m wth d := (1 F (ω m 0 ))d. We can compare ths characterzaton wth the one for homogeneous advertsers gven by equaton (4) of the paper. Due to the nformaton rent that s requred for ncentve compatblty, the outlet can no longer extract the full rent from advertsers but only a fracton of t. Ths s expressed 4

39 by the frst bracket n the ntegral. Inspectng the second bracket, the expressos analogous to the one wth homogeneous advertsers. Note that n the latter case m = mples that the dervatve was taken wth respect to n both terms. The above expressonstead accounts for the fact that the optmal allocaton m (ω) s heterogeneous across types. A second dfference comes from the frst term n the second bracket where we have d nstead of d. When changng m, only those advertsers who partcpate are affected. Ths s only a mass of 1 F (ω0 m ). By contrast, wth homogeneous advertsers all of them are actve n equlbrum. Therefore, wth heterogeneous advertsers the equaton characterzng trades off the cost and benefts of ncreasng over the whole mass of partcpatng advertsers, mplyng that the average costs and benefts are mportant. However, the basc trade-off for homogeneous advertsers and heterogeneous advertsers s the same. In partcular, the frst term n the second bracket represents the average margnal proft from ncreased reach onfra-margnal consumers, whereas the second term represents the average loss from margnal consumers who swtch off. Let us now turn to the optmal advertsng levels n duopoly. The goal s to characterze the bestreply tarff t (m ) gven outlet j s choce t j (m j ). As n the monopoly case, t s possble to rewrte ths problem as a standard screenng problem. To ths end, denote by ωu(m 1, m 2, n) the surplus of type ω from advertsng ntenstes (m 1, m 2 ). outlets s optmzaton problem s Π = If m (ω) denotes the optmal quantty chosen by type ω, then max t (m (ω))df (ω) (4) ω0,m (ω) ω0 subject to m (ω) = arg max m v d (m, ω, n) t (m ), v d(m (ω), ω, n) t (m (ω)) 0 for all ω ω0, ω ω m 0 (ω)df (ω), where v d (m, ω, n) := max y ωu(m, y, n) t j (y) max y (ωu(0, y, n) t j (y )), wth u(m, y, n) := D (n 1, n 2 )ϕ S (m ) + D j (n 1, n 2 )ϕ S j (y) + D 12(n 1, n 2 )ϕ 12 (m, y). Note that the sole dfference wth respect to the monopoly case s that each advertser s outsde opton accounts for the possblty of acceptng the rval s offer. Hence, v d (m, ω, n) s larger than v m (m, ω, ). Agan, our assumptons about the vewer demands D (n 1, n 2 ) and D 12 (n 1, n 2 ) and about the advertsng technology ϕ S (m ) and ϕ 12 (m 1, m 2 ) ensure that v d s contnuous and ncreasng n ω. It also has strct ncreasng dfferences n (m, ω). In the dervaton at the end of ths secton, we show by followng the methodology of Martmort and Stole (2009) that t s possble to characterze the best-reply allocaton as the soluton to ω 0 ( ω 1 F (ω) ) ( ϕ S d + d ϕ S + f(ω) m n D (ϕ 12 ϕ S ϕm j ) ) 12 + D 12 (ϕ 12 ϕ S ϕ M j ) df (ω)+κ = 0, m (5) wth d := (1 F (ω o))d, D12 := (1 F (ω o))d 12, and κ defned n the dervaton at the end of the secton. Ignorng κ for the moment, t s evdent that ths optmal duopoly soluton (5) s the analog of condton (5) of the paper accountng for the busness sharng and duplcaton effect wth heterogeneous advertsers. Let us fnally turn to κ. When changng the advertsng ntensty of type ω, outlet has to take 5

40 nto account that such a dfferent ntensty also affects the advertsers demand from the rval outlet, m j, gven the posted schedule t j ( ). Intutvely, the hgher the number of advertsng messages on outlet, the lower the utlty from one addtonal ad on outlet j. Ths channel brngs n new compettve forces that are absent wth homogeneous advertsers. These forces are specfc to the contractng envronment consdered and n addton to the ones dscussed so far. To stress ths, we note that f the rval outlet were to offer a sngle quantty-transfer par (or, n other words, were to mplement ancentve compatble allocaton flat across all actve types) then κ = 0. Dervaton of (3) and (5) We frst determne the soluton to the more complcated duopoly problem. (Solvng the monopoly problem proceeds along very smlar lnes and we wll descrbe t very brefly towards the end.) The problem of a duopolst s to maxmze ts profts ω t (m (ω))df (ω) wth respect to the transfer schedule, gvets rval s choce t j (m j ). From the man text, ths problem can be rewrtten as n (4). Denote by m j (m, ω) the advertsng ntensty that type ω optmally buys from outlet j when buyng ntensty m from outlet. Then, the net contractng surplus for type ω s v d [ (m, ω, n) = max [ωu(m, y, n) t j (y)] (max ωu(0, y, n) t j (y ) ] ) y y = ωu(m, m j(m, ω), n) t j (m j(m, ω)) ωu(0, m j(0, ω), n) + t j (m j(0, ω)) Incentve compatblty requres m (ω) = arg max m v d (m, ω, n) t (m), whch mples v d { (m (ω), ω, n) t (m (ω)) = max ωu(m, y, n) tj (y) (ωu(0, y, n) t j (y )) t (m) } y,y,m By the envelope theorem the dervatve of the above wth respect to ω s u(m, m j( (ω), ω), n) u(0, m j(0, ω), n) Snce ths pns down the growth rate of the advertser s payoff, we fnd that max ω 0,m ( ) ω t 0 (m (ω)) subject to the frst two constrants of (2) equals max ω 0,m ( ) ω 0 { ωu(m (ω), m j(m (ω), ω), n) ωu(0, m j(0, ω), n) t j (m j(m (ω), ω)) + t j (m j(0, ω)) [ ωu(m, m j (m (z), z), n) ωu(0, m j(0, z), n) ] dz} df (ω) ω0 = max ω 0,m ( ) ω 0 { v d (m, ω, n) Integratng the double ntegral by parts gves max m ( ),ω 0 ω 0 ω 0 [ ωu(m, m j (m (z), z), n) ωu(0, m j(0, z), n) ] } dz df (ω), } {{ } nformaton rent ωu(m (ω), m j(m (ω), ω), n) ωu(0, m j(0, ω), n) t j (m j(m (ω), ω)) + t j (m j(0, ω))+ 1 F (ω) (u(m, m f(ω) j(m (ω), ω), n) u(0, m j(0, ω), n)) df (ω) 6

41 The duopolst s best-reply allocaton of advertsng ntenstes m d (ω) then solves ( max ω 1 F (ω) ) (u(m (ω), m m ( ),ω0 ω0 f(ω) j(m (ω), ω), n) u(0, m j(0, ω), n)) ( t j (m j(m (ω), ω)) t j (m j(0, ω)) ) df (ω), subject to m (ω )df (ω ). ω0 From now on we wll denote the ntegrand functon by Λ d (m (ω), ω, n). Recall that solvng a canoncal screenng problem usually nvolves maxmzng the ntegral over all served types, where the ntegrand s the utlty of type ω mnus hs nformaton rent, expressed as a functon of the allocaton. The utlty here s the ncremental value u(m (ω), m j (m (ω), ω), n) u(0, m j (0, ω), n), mnus the dfference n transfers. The maxmzaton problem n the frst stage wth respect to can be wrtten as max ( max m ( ),ω 0 ω 0 Λ d (m (ω), ω, n)df (ω) s.t. = ω 0 m (ω)df (ω) ). (6) Let us frst determne u(m (ω), m j (m (ω), ω), n) u(0, m j (0, ω), n). Abbrevatng m j (m (ω), ω) by m j and m j (0, ω) by (m j ) we can wrte u(m (ω), m j, n) u(0, (m j) ), n) = D (n 1, n 2 )ϕ S (m (ω)) + D j (n 1, n 2 )ϕ S j (m j) + D 12 (n 1, n 2 )ϕ 12 (m (ω), m j) D j (n 1, n 2 )ϕ S j ((m j) ) D 12 (n 1, n 2 )ϕ S j ((m j) ) = d ( )ϕ S (m (ω))+d 12 (n 1, n 2 ) ( ϕ 12 (m (ω), m j) ϕ S (m (ω)) ϕ M j ((m j) ) ) +D j (n 1, n 2 ) ( ϕ S j (m j) ϕ M j ((m j) ) ), where ϕ 12 (m (ω), m j ) = ϕm (m (ω)) + ϕ M j (m j ) ϕm (m (ω))ϕ M j ((m j ) ). Adaptng results from Martmort and Stole (2009), we know that at the optmal soluton m (ω) = 0 for all ω < ω 0 and that m (ω) = arg max m Λ d (m (ω), ω, n). By our assumptons about the demand and advertsng functon, the optmal solutonvolves a schedule m (ω) that s non-decreasng. From (6), we can wrte the maxmzaton problem wth respect to the optmal allocaton of advertsng ntenstes, gven, as max m ( ),λ ω 0 Λ d (m (ω), ω, n)df (ω) + λ Pontwse maxmzaton wth respect to m ( ) yelds ( ω 0 m (ω)df (ω) ( ω 1 F (ω) ) [ ( ) d ( ) ϕs + D 12 (n 1, n 2 ) ϕ 12 ((m, m j )) ϕs (m ) f(ω) m m + [D j (n 1, n 2 ) D 12 (n 1, n 2 )] ϕs j m j m j m ] ). t j m j m = λ. (7) j m 7

42 Denotng the left-hand sde of (7) by ψ, and ntegratng both sdes from ω0 to ω, we obtan ω ψdf (ω) 0 1 F (ω0 ) = λ. The maxmzaton problem of the frst stage wth respect to s max m ( ),λ ω 0 Λ d (ω, m (ω), )df (ω) + λ ( Dfferentatng wth respect to and usng the Envelope Theorem yelds ω 0 ω 0 m (ω) df (ω) ( ω 1 F (ω) ) [ d ϕ S + D 12 ( ϕ12 ((m, m f(ω) n j)) ϕ S (m ) ϕ M j ((m j) ) ) [ ϕ 12 m j +D 12 m ϕm j (m j ) ]] [ ϕ S j m j j (m + D j j ) m ϕm j (m j ) ]] j (m df (ω) (8) j ) ). t j m j m + t j (m j ) j (m j ) = λ. Combnng (7) and (8) to get rd of λ yelds expresson (5) of the man text, where κ s defned as κ ω 0 ( ω 1 F (ω) ) { [ ] 1 f(ω) 1 F (ω) (D j D 12 ) ϕs j m j ϕ 12 m j m + D 12 j m m ϕm j (m j ) j (m j ) [ ] ϕ S j m j +D j m ϕs j (m j ) j (m + D j ( ϕ S j ) n j (m j) ϕ S j ((m j) ) ) } t j m j m df (ω) j t j m j m + t j (m j ) j (m. j ) It s evdent that f outlet j offers a sngle transfer-ntensty par, then m j equals (m j ) and both are nvarant to changes n m ( ) and. Ths mples that κ = 0. Proceedng n the same way for the monopoly outlet, we obtan that ts proft functos gven by max ( max m ( ),ω m 0 The solutos then characterzed by (3). ω m 0 ( ω 1 F (ω) ) d ( )ϕ S (m (ω))df (ω) s.t. = f(ω) ω0 m m (ω)df (ω) ). References [1] Anderson, S.P. and S. Coate (2005): Market Provson of Broadcastng: A Welfare Analyss, Revew of Economc Studes, 72, [2] Martmort, D. and L. Stole (2009): Market Partcpaton Delegated and Intrnsc Common- Agency Games, RAND Journal of Economcs, 40,