A Dynamic Competitive Analysis of Content Production and Link. Formation of Internet Content Developers

Transcription

1 A Dynamic Compeiive Analysis of Conen Producion and Link Formaion of Inerne Conen Developers Liye Ma Carnegie Mellon Universiy Job Marke Paper 1 Sepember 2010 PRELIMINARY VERSION PLEASE DO NOT CIRCULATE OR CITE WITHOUT AUTHOR S PERMISSION 1 I am indebed o Baohong Sun and Kannan Srinivasan for heir guidance. I benefied from discussions wih Kinshuk Jerah, David Krackhard, Yaroslav Kryukov, and Joachim Vosgerau. I also hank seminar paricipans a Carnegie Mellon Universiy for heir helpful commen. All errors are mine.

2 A Dynamic Compeiive Analysis of Conen Producion and Link Formaion of Inerne Conen Developers Absrac The emergence of hundreds of revenue sharing conen websies has grealy conribued o he proliferaion of Inerne social media. Conen a hese websies is supplied by exernal independen developers, whom he websies arac hrough revenue sharing. This leads o a compeiion among developers, as each ries o arac viewership o her own conen. A feaure recenly inroduced a many sies, namely allowing developers o link o one anoher, leads o inriguing ineracions among he conen developers, and is impac on conen producion and overall websie viewership is lile undersood. In his sudy, we develop a dynamic oligopoly model for he compeiion among conen developers a a websie. Each developer produces conen and forms links o maximize her discouned viewership ne of cos of acions, and heir sraegic ineracion is characerized as a Markov-perfec equilibrium. Applying he wo-sep esimaor of Baari, Benkard, and Levin (2007) o he daa obained from a popular Inerne produc review sie, we invesigae he following issues: (1) why and how do developers form links? (2) Will linking encourage or discourage conen producion? (3) Wha marke srucure will emerge? (4) Will linking increase or decrease he overall websie viewership? We find ha reciprocal links are naurally encouraged by a promoe-he-promoer effec. This in urn induces developers wih more conen o sraegically iniiae links o invie reciprocaion. In addiion, we find ha link formaion affecs he incenive o produce conen developers wih more conen and unfavorable nework posiions are encouraged o produce, while developers in he opposie saes are discouraged. Furhermore, he curren linking policy may impede compeiion by giving compeiive advanage o a subgroup of conen developers, and our simulaion suggess ha limiing links could increase overall viewership by 17%. Our sudy is among he firs o examine he inerdependence beween online link formaion and conenion producion in a dynamic and compeiive seing. Keywords: Inerne conen, social media, nework, producers, dynamic game, empirical IO 1

3 1. Inroducion Conen is he lifeblood of Inerne markeing. The emergence of hundreds of revenue sharing conen websies has grealy conribued o he recen proliferaion of social media. A wide range of conen vial for online business and consumer aciviies is provided a hese websies: produc reviews a Epinions.com faciliae online reailing; video clips a Youube.com generae adverising revenue; aricles a Fool.com arac subscribers, ec. Millions of viewers visi hese websies on a monhly basis, making hem a maor componen of Inerne business (Table 1). Such websies ypically generae revenue hrough adverising or sales referral. Consequenly, heir success depends crucially on he amoun of viewership raffic hey can arac. 2 A key characerisic of such revenue sharing conen sies is he democraizaion of conen: insead of hiring employees o creae conen, companies operae hese websies as plaforms where exernal, independen developers come o supply conen. Since he success of he websies depends crucially on he viewership heir conen aracs, he websies mus encourage he independen conen developers, or producers, o produce acively. 3 To encourage conen producion, websie companies ypically share revenue wih each producer based on he viewership her conen aracs. Ineresingly, his creaes an inra-websie compeiion among he independen producers, as each seeks o maximize he viewership of her own conen, and when viewers come o he websie and choose among differen producers conen, producers effecively compee agains each oher for viewership. To arac viewership, producers naurally 2 Display adverising fee can be charged on a pay-per-impression basis, wih raes quoed in cos per milli, which is he fee for every housand imes he adverisemen is viewed, or on a pay-per-click basis, where a fee is charged every ime an adverising link is clicked. Sales referral commission is ofen charged on a pay-per-acion basis, where a conen sie is paid based on he sales i helps e-commerce sies generae by direcing viewers o hose sies. The amoun of viewership raffic is he key o all hese revenue models. 3 Boh developer and producer are widely acceped erms in he indusry, and hey are used inerchangeably in his sudy. 2

4 need o acively produce conen he more conen a producer provides, he more likely a viewer will find wha she needs from ha producer, and he higher her viewership. 4 [Inser Table 1 Abou Here] Making he compeiion more inriguing is anoher feaure ha is being increasingly inroduced o such websies: iner-producer linking. As Table 1 shows, mos such sies now allow producers o creae links poining o oher producers a he sie. Links may vary by name, such as rus, favorie, follow, ec, bu all serve as a form of endorsemen of he arge by he source, and make he arge s conen easily accessible from he source s. Such links ogeher form a producer nework ha evolves over ime. Since Inerne viewers ofen navigae hrough links o view conen, and search engines also rely on he link srucure o rank search resuls, where a producer is posiioned in his nework significanly influences he viewership of her conen. In general, he more incoming links a producer has, and he beer posiions he sources of he links have, he beer is her posiion in he nework (Brin and Page 1998). This is because incoming links drive viewership raffic o a producer s conen, and a producer wih more and beer incoming links also ges preferenial placemen when search engine displays search resuls. The inroducion of iner-producer linking leads o several inriguing quesions. Markeing research on conen and linking is sill a he early sage. Exising research has shown, in a saic and analyical seing, ha linking can promoe he posiion of he arge, and meanwhile enhance he conen of he source a viewer may visi a producer even if she does no have he desired conen, if she can poin o anoher producer who does (Mayzlin and Yoganarasimhan 2008, Kaona and Sarvary 2008). 5 However, quesions relaed o link formaion in a dynamic conex 4 Oher facors also maer, such as he qualiy and diversiy of conen, and will be accouned for in his sudy. 5 This refers o he exension on reference links in Kaona and Sarvary (2008). The main model of ha paper focuses on adverising links which are price mediaed, which does no apply o he siuaions in our sudy, as he links among conen producers a hese sies are no bough and sold bu esablished by he sources on voliion. 3

5 and he ineracion of linking and conen producion decisions largely remain open. For example, how do producers form links over ime, how do producers adus heir producion decisions under he presence of linking, and how does one respond o ohers decisions? More imporanly, from he perspecive of he websie, would allowing producers o link encourage or discourage conen producion, and would i increase or decrease he overall viewership a he websie? The obecive of he websies inroducing he linking feaure is cerainly o encourage producion and increase raffic. Bu o find ou wheher his obecive is me, we need a deailed undersanding of how conen producers inerac wih one anoher as hey compee for viewership. Considering his, we address he following quesions in our sudy: (1) Wha drives a producer s linking decisions over ime, and when and o whom would she link o? (2) Will he abiliy o form links encourage or discourage a producer o produce conen, and how does his impac vary across producers? (3) Wha marke srucure will emerge from his compeiion hrough conen producion and link formaion under a given linking policy design a a websie? (4) Finally, wha is he overall effec of linking on he viewership a he websie level, and should he websie company regulae linking? Since hese websies rely on he producers producing conen o arac viewers, ye hey can only incenivize bu canno conrol hose producers, answers o he above quesions are crucial o help he websie companies undersand conen producers decision process, draw implicaions from i, and improve heir plaform design. In his sudy, we model he compeiion among conen producers a a websie as a dynamic game. In our model, each producer chooses her acions (produce conen and link o oher producers) over ime o maximize her payoff discouned viewership ne of coss incurred in producing conen and forming links. Producers adop Markov sraegies, and such sraegies ogeher consiue a Markov-perfec equilibrium, or MPE (Maskin and Tirole 1988, Ericson and 4

6 Pakes 1995). The equilibrium characerizes he dynamic ineracions among conen producers and he radeoffs hey face. In making her decisions, a conen producer balances he cos and benefi of her acions, boh immediae and in fuure, and accouns for he sraegic reacions from oher producers, as one s acions can change he compeiive posiions of ohers. We esimae he model using he wo-sep esimaor recenly developed by Baari, Benkard, and Levin (2007). Applying he model and esimaion approach o a daase obained from a popular Inerne produc review websie, we esimae he viewership demand and cos funcions, and analyze he driving forces of producers decisions and heir implicaions. Our sudy leads o several findings. We firs demonsrae ha link formaion is a dynamic sraegic decision. We show ha he naure of he compeiion encourages reciprociy linking o someone who already links back due o a promoe-he-promoer effec. In he dynamic conex, his endency owards reciprociy furher encourages cerain producers o sraegically iniiae non-reciprocal links in anicipaion of he reciprocaion from arges, which increases viewership in fuure hrough improved posiion brough abou by incoming links. We find ha a producer wih higher conen volume is more likely o sraegically iniiae such links o invie reciprocaion. Nex, we find he dynamic effec of linking can eiher encourage or discourage conen producion, depending on he siuaions of he producers: o obain and in anicipaion of fuure rewards hrough incoming links, a producer will produce he mos conen when she has high conen volume bu low nework posiion. Meanwhile, he prospec of linking discourages a producer wih low conen volume bu high nework posiion from producing conen, as she expecs her relaive nework posiion o diminish over ime. Furhermore, our analysis suggess ha he curren linking design overall could impede compeiion. We find ha alhough boh more conen and higher nework posiion lead o higher 5

7 viewership, only he laer leads o higher ne benefi once cos is accouned for. Thus poenial advanage from having more conen is mosly compeed away, ye significan compeiive advanage is accrued o beer nework posiion. Tha a subgroup of producers enoys susainable advanage over ohers may sofen he compeiion, and lead o inefficiency from he websie s perspecive. This is confirmed in our simulaion, which suggess ha alleviaing he imbalance hrough reducing links could lead o higher overall viewership a a websie. We conribue o he lieraure by oinly modeling conen producion and link formaion decisions, invesigaing heir iner-dependence in a dynamic seing, and evaluaing he impac of linking when boh decisions are deermined endogenously. Exising sudies have analyzed he impac of commerce nework on firm profis (Sephen and Toubia 2009) wihou explicily modeling he formaion process of such nework, and modeled he formaion of conen neworks on he web in a saic seing where conen is exogenously given (Kaona and Sarvary 2008). Our sudy exends he lieraure by analyzing how linking and conen producion decisions inerac wih each oher, and we evaluae he impac of linking on websie viewership when is effec on conen producion is accouned for. Furhermore, by sudying he decision process and compeiion in a dynamic conex, we show how iner-emporal radeoffs and he sraegic ineracions among producers drive decisions over ime, which canno be shown in a saic framework, such as he sraegic inviaion of reciprocal links and he conen producion in anicipaion of incoming links from oher producers. We also conribue o he lieraure by providing a raional economic framework for empirically analyzing he formaion of links in a dynamic sraegic seing. Our empirical findings provide much needed recommendaions o indusry managers. 6

8 The res of he paper is organized as follows. In secion 2 we review relevan lieraure. We hen develop he dynamic game model in secion 3. Following ha, we discuss in secion 4 he approach used for esimaing his model. Secion 5 discusses he empirical applicaion, where we explain he daa used in our sudy, analyze he resul, and discuss he simulaion. Finally, we conclude in secion Relevan Lieraure Our work is relaed o he broad lieraure on Inerne conen and on economic neworks. Markeing researchers have shown grea ineres in Inerne conen, specifically on produc reviews and online word-of-mouh (WOM). Chevalier and Mayzlin (2006) invesigae he effec of online book reviews on sales, and find ha improvemen in reviews leads o higher relaive sales. Godes and Mayzlin (2004) find ha he dispersion of conversaion in online communiies has explanaory power on TV raings. Chinaguna e al. (2010) find he valence of online reviews influence he box-office sales of movies. While he effec of online produc reviews has been sudied frequenly, relaively less aenion has been paid o he supply of such reviews, especially when hey are supplied as informaion goods wih profi incenive. Supply-side srucural models have generally only recenly gained aenion in markeing (Srinivasan 2006), and our work fills in his gap in he case of Inerne conen. Our work is also relaed o he formaion of economic neworks and heir impacs. A rich lieraure exiss on he formaion of social and economic neworks. For example, Bala and Goyal (2000) develop a non-cooperaive game model o sudy linking decisions. Jackson (2004) gives an exensive survey on nework formaion lieraure wih emphasis on sabiliy and efficiency. Mos sudies use cerain general value funcions arising from nework; while given he wide variey of neworks, i is reasonable o expec ha he benefi of he nework, and is formaion in 7

9 urn, be siuaion specific. Two sudies in markeing focus on he creaion of links online. Mayzlin and Yoganarasimhan (2008) invesigaes why an auhor of an Inerne blog may link o anoher compeing blog, even hough doing so effecively promoes her rival. They show ha he abiliy o link o informaion is valuable o readers in addiion o he abiliy o produce he informaion if he blog does no have he informaion, readers will sill appreciae a link o anoher blog ha does. The borrowed conen effec in our sudy models his effec. Kaona and Sarvary (2008) sudy he formaion of links among conen sies as a non-cooperaive game, where links are creaed eiher for paid adverising or for reference effec in he exended model. In boh sudies, he conen a he websies is reaed as exogenous. In conras, Sephen and Toubia (2009) sudy he effec of online commercial neworks. They find ha allowing online reailers o link o one anoher creaes economic value, and such value comes from improved accessibiliy. The sudy focuses on he effec of he nework and does no explicily address is formaion process. Our sudy conribues o he lieraure by oinly sudying boh nework formaion and conen producion decisions and highlighing heir ineracion effec in a dynamic seing. Our work draws from he rich lieraure on empirical indusrial organizaions from he mehodology perspecive. Specifically, we adop he concep of Markov perfec equilibrium, or MPE (Maskin and Tirole 1988, Ericson and Pakes 1995, Maskin and Tirole 2001), for modeling dynamic oligopolisic compeiions. Early esimaion mehods for MPE (Pakes and McGuire 1994, Pakes and McGuire 2001) exend he nesed fixed poin approach (Rus 1987) o explicily compue equilibrium sraegies. Bu he high dimensionaliy of ypical dynamic compeiion models resrics he use of such mehods o games wih only few players. Recen advancemen leads o several wo-sep esimaors (Aguirregabiria and Mira 2007, Baari, Benkard and Levin 8

10 2007, Pakes, Osrovsky and Berry 2007) which exend he condiional choice probabiliies approach (Hoz and Miller 1993). Such wo sep esimaors bypass explici compuaion of equilibrium by calculaing coninuaion values hrough forward simulaion, and by doing so enable he esimaion of dynamic games wih many players. Ackerberg e al. (2007) provides a comprehensive survey of hese esimaion mehodologies. We implemen he esimaor developed in Baari, Benkard and Levin (2007), hereafer BBL. The BBL esimaor has been used for sudies in indusrial organizaions (e.g. Ryan 2009), and has been adoped in markeing lieraure recenly (Yao and Mela 2010). 3. Model We discuss he model in his secion. To prepare for he model, we begin wih a brief summary of he key elemens of he indusry seup. We consider a conen websie on he Inerne. Viewers come o he websie o view conen, which is produced by exernal, independen conen producers, whom he websie aracs hrough revenue sharing. Each conen producer seeks o maximize he viewership of her own conen over ime. In addiion o producing conen, a producer can creae links poining o oher producers. Since viewers can easily follow a link o navigae o he arge producer s conen from he source producer s, a link benefis he arge producer by puing her in a good posiion o receive viewership raffic. Furhermore, when viewers search for a specific opic and he conen from muliple producers maches ha search crieria, he search engine ranks he search resuls based on he linking srucure, where producers wih more incoming links and links from oher producers wih good posiions receive preferenial placemen. Links hus again help he arges hrough his posiional benefi. For he source of a link, he benefi is o enhance conen, as a 9

11 producer who links o oher producers makes i convenien for viewers o find he conen hey wan, and will be favored by viewers. This indusry seup leads o a compeiion among conen producers, since each producer cares abou her own viewership only, and viewers choose he conen from muliple producers. 6 To arac viewership effecively, each producer mus make her producion and linking decisions while aking ino accoun her own siuaion, oher producers siuaions, and he sraegic response o her acions by oher producers. She also needs o balance curren and fuure benefis. Such consideraions lead o ineresing dynamic ineracions. For example, more conen aracs higher viewership, bu producing conen also incurs a cos. Depending on a producer s posiion, his cos-benefi radeoff may or may no usify producion. However, having more conen may also arac links from oher producers, which improves her posiion laer on. This addiional benefi could make conen producion worhwhile, even if i does no arac much immediae viewership. Such dynamic ineracions among maximizing agens call for a dynamic oligopoly model, which we use in his sudy. In our model, here are J independen conen producers compeing for viewership. Time is discree and is indexed by, = 1,2,.... In each ime period, each producer decides wheher o produce conen and wheher o link o oher producers. In he following subsecions, we firs describe he viewership demand marke ha clears in each ime period given producers conen saes and he link srucure. We hen discuss producers dynamic conen producion and link formaion decisions, and how conen and link srucure evolve according o such decisions. 6 For example, a viewer may search for a opic, and read only he op wo aricles on he lis rerieved by he search engine. In his case, each producer wans her conen placed in he op wo posiions, and is compeing agains oher producers for ha. 10

12 Finally, we explain he dynamic compeiion and he equilibrium concep, and discuss he radeoffs faced by producers which shape heir sraegies. 3.1 Viewership Demand There are M consumers, or viewers, in each period. 7 Each viewer chooses o view he conen of one conen producer among he J producers a he websie, or chooses o go o an exernal websie, i.e. he ouside opion. This viewership consiues he demand for producers conen. We adop a logi demand model, which has been widely used in modeling oligopolisic compeiions (e.g. Berry 1994, Berry e al 1995, Dube e al 2009), o characerize viewership demand in his per-period marke. 8 The discree-choice framework of he logi demand model reflecs he compeiive naure of he viewership demand, i.e. viewership of one producer s conen may come he cos of anoher s. A viewer i s laen uiliy from reading he conen of producer in period is: (1) u i,, ui,, + ε i, = 0 + ε i,0,, = f ( C,, P,, C b, ; β ) + g( Q, Q i b, ; γ ) + ε i,, = 1.. J = 0 b b In equaion (1), u = f C, P, C ; β ) + g( Q, Q ; ) is he deerminisic componen of he i,, (,,, i, γ uiliy. C, is he conen quaniy of producer a ime, P, is a numeric measure of her nework posiion, and Q is a vecor of qualiy variables of he producer ha remains consan 7 The erms viewer and reader are used inerchangeably in his sudy. 8 The logi demand model is based on a discree-choice framework, ye i is possible ha a reader may read muliple aricles of a producer in a period, e.g., reading he produc reviews of differen producs, or he conen of several producers. An in-deph modeling of such behavior requires deailed clicksream daa of readers which we unforunaely do no have. Insead, we rea each pageview as one single viewer in our model (ha is, if a viewer reads hree produc review aricles in he period, i is couned as hree viewers in he model). This reduced-form reamen of readership demand can be improved by explicily modeling a viewer s navigaion behavior, which we leave for fuure research as richer daa become available. 11

13 over ime. 9 Furhermore, C, measures he oal quaniy of borrowed conen, i.e. conen b derived from linking o oher producers. Similarly, Q b, measures he average qualiy of he producers being linked o. These measures are explained in deail laer when we discuss producer acions and he nework srucure. The funcion f (.; β i) specifies how conen, nework posiion, and borrowed conen ener ino he uiliy funcion, wih β i as he parameer. Since viewer navigaion behavior is no explicily modeled, we esimae muliple specificaions of funcional forms for f (.; β i), wih he bes specificaion chosen hrough model selecion. The funcion g (.;γ ) capures he qualiy differeniaion among producers. Qualiy is used mainly for conrol purpose in our sudy, so we adop a linear specificaion wih γ as he parameer: b b g ( Q, Q ; γ ) = ( Q, Q ) γ. The relaive araciveness of a producer is deermined by he amoun of conen she has, i.e. he conen quaniy, he locaion of he producer in he nework, i.e. he nework posiion, and he qualiy of he producer. Furhermore, he araciveness of a producer is also influenced by he conen of he oher producers she links o. Inuiively, he more conen a producer has, he more viewership she would receive, as viewers are more likely o find he conen hey wan. Similarly, he more prominen a producer s posiion in he nework, he higher viewership demand she would receive, as her conen will receive more preferenial placemen by he search engine, and more viewers may be direced o her conen when hey navigae hrough he links. Borrowed conen should furher enhance a producer s araciveness due o he convenience benefi i affords he viewers. We expec hese o be refleced from he parameer vecor β i in 9 In our model, we rea qualiy as a characerisic of he producers insead of conen. This assumes away poenial variaion of qualiy across differen conen produced by he same producer. This is a reasonable assumpion in he conex of our sudy, since he qualiy of individual conen is no observed before a viewer decides o view he conen. 12

14 accordance wih he specific funcional form. For example, we expec all coefficiens o be posiive if facors ener he uiliy funcion linearly. Finally ε is an i.i.d random componen which follows he ype I Exreme Value i,, disribuion, resuling in he familiar logi probabiliy of viewer i choosing producer a ime : (2) Pr i,, = J 1+ exp{ u ' = 1 i,, exp{ u } i, ', } Noe ha his viewership model is a reduced form one, and assumes away any explici sae-dependence on viewer s side. In realiy, a viewer s behavior in one period may be influenced by her pas behaviors, e.g. she becomes a rouine follower of a conen producer. In our model, his dependence can come indirecly hrough he persisence of a producer s sae: a produc review of an obsolee produc produced earlier may be of no value now, bu i araced viewers a ha ime, some of whom hen coninues o visi he producer s page, and his is refleced in he uiliy funcion where a cumulaive measure of conen is used. 10 Viewers may have differen navigaion paerns and conen requiremens, which resuls in differen relaive emphasis placed on differen componens in he uiliy funcion. 11 This heerogeneiy is capured using a laen class approach (Kamakura and Russell 1989). Tha is, we assume here are N segmens of viewers, each characerized by is own se of coefficiens, β { n } n= 1.. N, and porion of each ype is denoed as λ n, so ha λ n = 1. N n= 1 10 Since he emphasis of our sudy is on producer s producion and linking behavior, srucurally modeling viewer s persisence over ime adds grea complexiy o he model bu migh no provide much added value. I also requires deailed viewer navigaion daa. We leave he oin srucural modeling of producer and consumer behavior for fuure research. 11 In he case of a sequence of page views, cerain page views may be relaed more o he page conen (e.g. following a opic search) while ohers may be relaed more o nework posiions (e.g., navigaing hrough links or using a search engine ha accouns for nework posiions). The heerogeneiy also capures his effec, since a viewer in he model acually corresponds o a viewer-page view pair in he real world, as discussed earlier. 13

15 3.2 Conen Producer In any ime period, a conen producer is characerized by a collecion of variables: b b { C,, P,, C,, Q, Q, }. Conen, nework posiion, and borrowed conen all evolve over ime according o he acions of boh producer and oher producers. A producer can ake wo ypes of acions, conen producion and link formaion. We discuss hese acions below and how he variables evolve according o hese acions Conen Producion A producer s conen quaniy, C,, is deermined solely by her own producion decisions over ime. In each period, a producer decides wheher o produce addiional conen o add o her webpage wrie anoher produc review, break anoher news sory, creae anoher analyical repor, ec and if yes, he amoun of conen o produce. We denoe his acion by producer a ime as a,, where he superscrip p indicae i is he producion decision. Specifically, p (3) a p, 0 = k do no produce conen produce k unis of conen, k {1,2...} In he equaion, k represens he number of unis of conen produced. Each uni of conen may correspond o an aricle in he real world, hus he acion is discree. Producing conen increases he conen quaniy a a producer s webpage, C,. Meanwhile, here is an opposie, depreciaion, force a work: a produc review will become less needed as he reviewed produc becomes obsolee; a news sory will become non-news afer a few days; an analyical repor will become less relevan as he siuaion expires, ec. Similar o exising lieraure modeling capaciy depreciaion (e.g. Besanko and Doraszelski 2004), we assume ha 14

16 he producer s conen a a websie depreciaes wih a cerain raio over ime. Combining he effecs of producion and depreciaion, he conen quaniy a a producer s webpage evolves as: (4) δ p C, = C, 1 + a, In equaion (4), δ (0,1) is he depreciaion rae of he conen. The smaller he value of δ is, he faser is he depreciaion. Producing conen is a cosly aciviy. We denoe he cos of producing k unis of conen prod prod by producer as c ( k, X ; φ), wih c ( 0, X ; φ) = 0, i.e. he producer incurs no cos if she does no produce conen. X is a vecor of characerisics of producer ha may affec cos, and φ is a vecor of parameers for he producion cos funcion. The producion cos is expeced o be an increasing funcion of k, he unis of conen produced. The exac funcional form of prod c (.) used in his sudy is specified in secion 5 where we discuss he empirical applicaion Link Formaion In each ime period, a producer may also creae a link poining o anoher producer, assuming one o ha producer does no already exis. 12 We denoe his acion by producer a ime as a,, where he superscrip l indicae i is he linking decision. Specifically: 13 l (5) a l, 0 = ' do no creae link creae a link o producer ', ' {1.. J}, ' 12 Links are a producer level insead of conen level, e.g. from producer A o B insead of a specific aricle of producer A o ha of producer B. 13 In our model, we consider he case where only creaion bu no removal of links is allowed. This is consisen wih he daase used in he empirical applicaion. In real-world seings, cerain websies allow link removal, while ohers do no. I is sraighforward o exend our model o allow link removal. Also, we assume ha a producer can creae only one link in a period. This assumpion is also made based on he daase used in his sudy, and i is also sraighforward o change i o allow a producer o creae muliple links in a period. 15

17 Link formaion may also be a cosly aciviy. To form a link, a producer needs o spend ime specifying so a he websie. We denoe he cos of creaing a link by producer as c link ( ', X ; ψ ). The cos may vary according o he arge of he link. For example, if reciprociy has inrinsic value, he producer will incur higher cos creaing a non-reciprocal link, i.e. links o a producer ' when ' already links back a her, han creaing a non-reciprocal one. Similar o producion cos, ψ is he vecor of parameers for he linking cos funcion. The exac funcional link form of c (.) used in his sudy is specified in secion Producer Nework and Nework Posiion The links creaed by all producers ogeher form a producer nework, which is formally represened as a direced graph. Each node in he graph corresponds o a producer, and an edge exiss if he producer corresponding o he source node has a link poining o he producer corresponding o he desinaion node. The nework evolves as producers creae links over ime. The nework a ime period is denoed as G. posiion, From he opology of he nework, a numerical measure of each producer s nework P,, can be derived. As discussed earlier, he posiion of a producer in he nework grealy influences he amoun of viewership raffic direced o her conen he more incoming links a producer s has, and from he more prominen posiions hose incoming links come, he more raffic will be direced o he producer. Thus, boh he number of incoming links and he posiions of he sources maer. The PageRank measure (Brin and Page 1998), iniially adoped by Google, eleganly capures boh effecs. Saisically, PageRank represens he probabiliy of reaching each web page in a nework when viewers follow a random walk along he links. 16

18 PageRank is equivalen o he eigenvecor cenraliy of a damped adacency-graph of he nework. Ineresingly, a rich lieraure in sociology has well esablished he imporance of eigenvecor cenraliy in social neworks (e.g. Bonacich 1987, Faus and Wasserman 1992, Wasserman and Faus 1994, Bonacich and Lloyd 2001), where higher cenraliy i is associaed wih higher presige. Recen markeing lieraure (Kaona & Sarvary 2008) has also adoped PageRank in characerizing he nework posiion of players. Following hese, we use he PageRank of each producer in he nework as he measure of her nework posiion: (6) PageRank P, =, The compuaion of PageRank is explained in he Appendix. The higher he PageRank, he more prominen a producer s posiion is in he nework. This is he nework posiion measure ha eners ino he demand funcion as specified in equaion (1). Tha incoming links increase a producer s posiion also means a producer s own posiion will reduce when she creaes a link poining o anoher producer an ougoing link increases he arge s posiion, and since posiion is relaive, i would also reduce ha of he source. This consiues a sraegic cos of link formaion, which mus be balanced wih he benefi of borrowed conen Borrowed Conen When a producer has a link o anoher producer ', he conen of producer ' can be easily accessed when a reader is viewing producer s conen. This augmens he source s conen, making he producer s webpage more appealing (Kaona and Sarvary 2008). This effec is capured in our model using borrowed conen, C,, which is simply he sum of he conen of b all oher producers being linked o a he ime: 17

19 b (7) C = C J, ', I{ ', ' } ' = 1 In he equaion, I {.} is he indicaor funcion which equals 1 if he link exiss and 0 oherwise. Similarly, he borrowed qualiy Q b, is he average of qualiy measures of he producers being linked o: J J,, ' } ' = 1 ' = 1 b (8) Q = Q ' I{ ', '}/ I{ ' 3.3 Dynamic Compeiion The compeiion among conen producers over ime is naurally modeled as a dynamic game. The key characerisic of he compeiion is ha acions aken by producers no only deermine he curren payoff, bu also affec fuure sraegic ineracions. Consequenly, when a producer makes conen producion and link formaion decisions, she needs o accoun for no only he curren benefi, bu also he fuure benefi according o he sraegic response o her acions by oher producers. In each ime period, he sae of he compeiion is fully described by a se of commonly observed sae variables. Producers ake acions o maximize heir respecive discouned payoffs. Such acions are aken based on he curren sae of compeiion and in anicipaion of he sraegic response. The soluion concep for producer s opimizing behavior is ha of Markovperfec equilibrium, or MPE (Ericson and Pakes 1995). In an MPE, he sraegy played by each producer is a Markov sraegy, where acions are fully deermined by he curren sae, and he sraegy of each producer consiues he bes response o oher producers sraegies. 18

20 3.3.1 Sae The sae a ime period, denoed as s, is he collecion of he individual conen saes of all producers and he sae of he producer nework: s = s,..., s, G ), where s = C, Q, X } ( 1, J,, {, characerizes he quaniy of producer s conen in period and he characerisics of he producer relaed o qualiy and cos, and G conains he opology of he producer nework. Noe ha s, does no include P,, as he posiion of each producer in he nework is fully deermined by he opology of he nework, which is encoded in G ; nor does i include C, or b Q,, as he b borrowed conen is deermined oinly by he opology of he nework and he conen of all producers. In anoher word, P,, C, and b Q, are derived from he sae insead of he b primiives of he sae Acion p l In each ime period, producer s acion a = a, a ) is is conen producion and link, (,, formaion decision. Le a denoe he vecor of acions aken by all producers a ime, i.e. a = a,..., a ). ( 1, J, Consisen wih exan lieraure (e.g. Rus 1987, BBL 2007), we assume ha before choosing her acion a ime, each producer receives an acion-specific privae shock ν a ) ha is independen among producers and over ime. Since in our seing he acions are, (, discree, his privae shock is a vecor where each elemen corresponds o a specific acion ha can be aken a he ime. Also consisen wih exan lieraure, we assume he privae shock follows an exreme value disribuion. This privae shock is needed in dynamic game models o 19

21 accoun for he variabiliy in acions ha goes beyond he observed saes. The collecion of acion-specific privae shocks across all producers is denoed as ν = ν,..., ν ) Payoff ( 1, J, In each ime period, according o he viewership marke demand and producer acions, producer s curren-period payoff is: N prod p link l (9) π ( a, s, ν, ) = mr Mλn Prn, ( s ) c ( a,, X ; φ) c ( a,, X ; ψ ) + ν, ( a, ) n= 1 In equaion (9), mr is he marginal benefi associaed wih each viewer visi, and Mλ n is he number of viewers in segmen n. In each period, he payoff of producer is he benefi of viewership demand ne of any cos associaed wih he acion aken by he producer. Each producer is concerned no us wih he payoff of he curren period, bu also he overall payoff over ime. The oal discouned payoff o producer a ime, which he producer seeks o maximize, is: (10) E[ τ β π ( aτ, sτ, ν, τ ) s ] = τ In equaion (10), β [0,1) is he discoun facor. The expecaion is over he privae shock, producers acions in he curren period, as well as fuure saes, acions, and privae shocks. As is shown clearly in he equaion, he payoff o a producer depends on no only her own acions, bu also he acions of oher producers. This leads o sraegic ineracions which are characerized using an MPE. 20

22 3.3.4 Sraegy and Equilibrium We assume all producers follow Markov sraegies. A Markov sraegy profile σ of he dynamic game is he collecion of he sraegies of all producers: σ = ( σ1, σ 2,..., σ J ) where σ is he sraegy played by producer which depends on he sae and he privae shock, σ S ν A : a, where S is he se of all saes, ν is he se of privae shocks and A is he se of all acions producer can ake. Given a sraegy profile, a producer s value funcion is he expeced discouned payoff given he sae, inegraed over privae shocks. I can be wrien recursively as follows: (11) V ( s; σ ) = Eν [ π ( σ ( s, ν ), s, ν ) + β V ( s'; σ ) dp( s' σ ( s, ν ), s) s] When choosing a sraegy, a producer needs o ake ino accoun no only he curren sae, bu also oher producers sraegies. Following convenion in lieraure, we use σ o denoe he sraegies played by all producers oher han producer. A producer s opimizaion problem is: (12) V ( s; σ ) = max{ E [ π (( σ ( s, ν ), σ ( s, ν )), s, ν ) + β V ( s'; σ ) dp( s' ( σ ( s, ν ), σ ( s, ν )), s) s]} σ ( s, ν ) ν The sraegy which is he soluion o equaion (12) for producer is he bes response of * * * * he producer o ohers sraegies. An MPE is a sraegy profile σ = ( σ, σ,..., ) where each producer s sraegy is he bes response o oher producers sraegies. Tha is, in an MPE, when holding he sraegies of oher producers unchanged, no producer can increase is own expeced payoff by unilaerally deviaing o anoher sraegy: 1 2 σ J * * * (13) V ( s; σ, σ ) V ( s; σ, σ ), s, σ 21

23 Wih observaions of viewership demand and producer acions according o he saes over ime, we can esimae he parameers for he viewership demand model and he dynamic srucural parameers, i.e. cos parameers, using he opimaliy condiion implied by he equilibrium, which we discuss in deail in secion Iner-emporal Tradeoffs We now qualiaively discuss he radeoffs conen producers face in heir producion and linking decisions which are incorporaed in he model. When deciding wheher o produce conen, producers obviously face a radeoff beween he cos incurred in producing conen and he viewership such conen aracs over ime. Furhermore, here are several radeoffs induced by linking, which lead o ineresing ineracions among producers. To begin wih, when linking o anoher producer, a producer faces he radeoff beween borrowing he conen of anoher producer and lower nework posiion arising from promoing her compeior. Depending on how much he borrowed conen will help and how severely he link will reduce her own nework posiion, he producer may or may no find i worhwhile o form a link. Ineresingly, when we ake his radeoff a sep furher, o consider no only wheher o form a link bu also whom o link o, we can see his radeoff provides a simple explanaion o a well known phenomenon in neworks: he endency o form reciprocal links. Reciprociy can be explained by social norm in sociology lieraure (Gouldner 1960), and hrough reward and punishmen schemes in repeaed games (Axelrod and Hamilon 1981). In he seing of our sudy, however, reciprociy may arise naurally from he consideraion of nework posiion. To see his, recall ha he source s nework posiion posiively influences he arge s. Suppose producer A wans o creae a link, and producer B already has a link o producer A while producer C does no. Then if A links o B, hereby improving B s posiion, he enhanced posiion of B will be parially carried over o A. 22

24 Whereas if A links o C, who is no A s source, hen A will no ge his indirec benefi. Oher hings equal, his promoe-he-promoer effec would favor reciprocal links over non-reciprocal ones. 14 Tha is, i is beer o promoe one s own promoer insead of anoher producer. More radeoffs come ino play when we consider he ineracions among producers over ime. When making linking decisions, since a reciprocal links are naurally encouraged, a forward-looking producer may inenionally creae a non-reciprocal link, if she expecs ha he producer she links o would reciprocae in he near fuure. Tha is, a producer may sraegically creae a link o invie reciprocaion. The radeoff she faces in his decision is beween lower nework posiion now and higher nework posiion laer on, if and when he arge reciprocaes. Furhermore, he prospec of linking may also encourage or discourage conen producion. A producer may be encouraged o produce more conen han she oherwise would, if she expecs ha by producing more conen, she can arac incoming links from oher producers laer on. The radeoff she faces in his decision is beween he cos of producing conen now and beer nework posiion laer on when she receives incoming links. A he same ime, if a producer expecs her compeiors o receive incoming links, which diminishes her relaive nework posiion over ime, she may produce less han she oherwise would. All hese radeoffs play a cenral role in deermining conen producion and link formaion decisions, and lead o he equilibrium sraegy adoped by conen producers. 4. Esimaion Our esimaion requires ha he conen producion and link formaion decisions of all producers over a number of ime periods are observed, so is he per-period viewership of each producer s 14 A Mone-Carlo simulaion using random graphs will easily show ha, on average, he reducion in nework posiion hrough creaing a reciprocal link is less han ha hrough creaing a non-reciprocal link. 23

25 conen in muliple ime periods. The parameers o be esimaed are he segmen-specific viewership demand coefficiens and he sizes of he segmens, he qualiy coefficiens, he conen depreciaion rae, he marginal benefi o he producer per reader visi, and he cos parameers of conen producion and link formaion, as summarized below: Param = ({ βn, λn} n= 1.. N, γ, δ, mr, φ, ψ ) The marginal benefi and he cos parameers are no oinly idenified. Considering his, we normalize mr = for idenificaion, which implies ha he uni of accoun for cos is he marginal benefi per housand views. 15 The firs half of he parameers, βn, λn} n= N, γ, ), are ({ 1.. δ he parameers governing he viewership marke in each period. The idenificaion ress on he cross-secional and iner-emporal variaion of he conen and nework of producers, ogeher wih he corresponding variaion of viewership. The second half of he parameers, ( φ, ψ ), are he dynamic srucural parameers ha ogeher wih he viewership demand parameers govern he dynamic compeiion, he idenificaion and esimaion of which res on he opimaliy condiion of he equilibrium. Esimaing dynamic games is challenging due o curse of dimensionaliy he sae space has high dimensionaliy as i incorporaes he saes of all players. Early esimaion mehods (e.g. Pakes and Mcguire 1994) rely on explicily solving for equilibrium hrough value-funcion ieraion, and have limied scalabiliy. Recenly developed wo-sep esimaors call for esimaing as many srucural parameers offline as possible, and bypassing he compuaion of equilibrium when esimaing he dynamic srucural parameers. Our esimaion is implemened using one such wo-sep esimaor as specified in BBL (2007). BBL approaches he esimaion ask in wo sages. In he firs sage, we recover he equilibrium sraegy of producers in reduced form, based 15 This follows he indusry sandard on display adverising, where fees are quoed as cos-per-mille, or CPM, which represens he amoun an adveriser needs o pay for every housand imes an adverisemen is displayed o viewers. 24

26 on observed saes and acions. Esimaion of he equilibrium sraegy, also ermed he policy funcion, should srike he righ balance beween flexibiliy and daa availabiliy. A flexible funcional form is desired for accurae represenaion of he equilibrium sraegy, bu i also requires more daa. The second ask for he firs sage is o esimae he ransiion of saes over ime according o producer acions. The viewership demand will also be esimaed in he firs sage. In he second sage, using he knowledge of policy funcion, sae ransiion, and viewership demand esimaion in he firs sage, we perform forward-simulaion of he observed policy versus perurbed policies. As he observed policy consiues an equilibrium, he opimaliy condiion dicaes ha a producer s payoff when she plays he equilibrium sraegy is no less han her payoff under an alernaive perurbed sraegy, while oher producers sill follow he equilibrium sraegy. This opimaliy consrain forms he basis for consrucing he obecive funcion of a GMM esimaor. As is common in research on empirical dynamic games, we focus on symmeric pure sraegy equilibrium. Such resricion allows us o pool daa across all producers, which reduces daa requiremen and improves esimaion efficiency. 4.1 Firs Sage In he firs-sage of he esimaion, we recover he policy funcion, he sae ransiion process, and he viewership marke demand sysem Policy Funcion In equilibrium, each producer chooses her acion based on her own sae as well as he saes of oher producers and he producer nework. In he firs sage of esimaion, we recover his policy funcion, * σ, which maps saes o acions, in reduced form. BBL recommends using flexible 25

27 funcional forms o approximae he equilibrium policy wih precision, which needs o be balanced wih daa availabiliy. Facing his radeoff, we firs ransform he sae space by deriving he vecors of nework posiions and borrowed conen of all producers from he conen sae of each individual producer and he nework srucure hese are he variables ha ener he uiliy funcions direcly. We hen pariion he ransformed sae space of an individual producer ino quiniles along boh he conen dimension and he nework posiion dimension. For each cell in his pariioned sae space, we run a separae se of regressions wih producer acions as dependen variables. The independen variables include he qualiy and cos relaed characerisics of he producer, he borrowed conen and qualiy of he producer, he number of oher producers in each cell of he pariioned sae space, and he average qualiy of oher producers. 16 Since linking acions differ by desinaion, we disinguish he arge on he following four dimensions: reciprociy, conen, nework posiion, and qualiy. We separae a reciprocal link from a non-reciprocal one, and for each of he oher dimensions, we perform a median-spli on he arge: separae a high conen producer (whose conen quaniy is above median) from a low conen one (below median); separae a high nework posiion producer from a low nework posiion one; separae a high qualiy producer from a low qualiy one. 17 There are hus sixeen differen ypes of linking arges, which combined wih an acion of no-link resuls in seveneen possible linking acions. We esimae each regression funcion using generalized linear models, wih log link funcion for conen producion and logi link funcion for link formaion. 16 Essenially we are esimaing he policy funcion nonparamerically on a producer s own sae bu paramerically on oher producers saes. Ideally, he policy funcion should be esimaed nonparamerically over he enire sae space, bu he high dimensionaliy of he sae space makes his impracical, as o do so requires enormous amoun of daa. BBL suggess using local linear regression, which is similar o wha we do here. 17 Since qualiy aribues are consan over ime in our model, he muli-dimensional qualiy measure of a producer can be reduced o a single dimensional number once he viewership demand is esimaed, by weighing based on he esimaed coefficiens. 26

28 The se of regression funcions hrough his esimaion fully describes he sraegy played by each producer in equilibrium. These policy funcions form he basis for forward-simulaion ha is used in he second sage of he esimaion o recover dynamic srucural parameers Sae Transiion Sae ransiion probabiliies are needed for performing forward-simulaions in he second sage of esimaion. In our model, he ransiion of saes given he acions of all producers is deerminisic linking acions deerminisically change he nework srucure, while producion acions ogeher wih depreciaion deerminisically change conen sae. Consequenly, sae ransiion does no need o be esimaed once he policy funcion is recovered. In he second sage forward simulaion, we simply simulae producer acions based on he esimaed policy funcion, and sae ransiion can be calculaed deerminisically once he acions are simulaed Viewership Demand The viewership marke demand in each period can be esimaed raher sraighforwardly wih MLE. Denoe s N m N, ( s;{ n, βn} n= 1, γ ) = λn Prn, ( s; βn, γ ) n= 1 λ as he heoreical marke share of producer a ime given he sae and he parameers, and he acual marke share observed from daa as s ˆ m,. 19 m m Assuming ha he difference η, = log s ˆ, log s, follows an i.i.d. normal N disribuion (Holmes 2009), he parameers {{ λn, βn} n= 1, γ} can be esimaed using maximum likelihood. 20 The marke size, i.e. he oal number of viewers, M, is needed for calculaing 18 Conen producion is similar o invesmen in empirical IO, where sudies also use probabilisic sae ransiion models (e.g. Besanko and Doraszelski 2004). The difference is minor, as a radeoff beween he precision of saes and he precision of sae ransiion. Our model allows for deerminisic sae ransiion because he exac conen sae and he sae of he producer nework are used. 19 The superscrip m represens marke. This is o avoid confusion wih he same symbol s ha represens producer sae. 20 For he case of one viewer segmen only, his is he same as he inversion suggesed in Berry (1994). 27