Multi-homing, Product Differentiation and Competition

Transcription

1 Muli-homing, Produc Differeniaion and Compeiion Jiangli DOU and Bing YE July 7, 01 We would like o hank Simon P. Anderson, Emmanuelle Auriol, David Bardey, Jacques Crémer, Xiaojing Hu, Doh-Shin Jeon, Bruno Jullien, Yassine Lefouili, Jean-Marie Lozachmeur, Lucas Maesri, Alexander Rasch, Sander Renes, Parick Rey, David Sauer, Paul Seabrigh, Jean Tirole, Yaron Yehezkel and all of he paricipans for 011 ECORE Summer School on Marke Failure and Marke Design, 6h Annual Congress of he European Economic Associaion, 8h Annual Conference of he European Associaion for Research in Indusrial Economics and Seminar in Toulouse for helpful commens and suggesions. All errors are of our own. Toulouse School of Economics. Conac informaion: jldouwhuias@gmail.com. Deparmen of Economics, Zhejiang Universiy. Conac informaion: colinyebing@gmail.com.

2 Absrac This paper invesigaes he compeiion beween wo horizonally differeniaed firms (plaforms) whose producs have parially overlapping funcionaliies. If firms make heir producs compaible wih each oher, consumers can consume boh producs and derive uiliy from he non-overlapping funcionaliies. We show ha he equilibrium compaibiliy level chosen by firms is less han socially opimal. In addiion, less differeniaed producs would induce boh firms and social welfare maximizer o allow purchasing boh. If we exend he model o a wo-sided framework, he plaform wih a higher qualiy produc would enforce single purchase if he nework exernaliy is large enough. Keywords: Compeiion, Produc Differeniaion, Compaibiliy, Mulihoming, Two-Sided Marke JEL classificaion: D4, D60, L1, L0, L50

3 1 Inroducion In many markes, in paricular in he case for informaion goods, some consumers purchase only one of he producs ha offered, while ohers purchase wo or many of hem. For example, people who use Microsof Office o process ex someimes also insall TEX on heir compuer, while some users use only Microsof Office or TEX. One consumer may purchase wo operaing sysems, Microsof Windows and Linux, while one operaing sysem is enough for mos of us. Some people may insall Tencen QQ, Skype and MSN on he same compuer in order o cha wih differen friends, bu some users may use only one of hose programs; game lovers may play muliple games (WII, PS, XBOX) during one day, bu some oher users prefer only a specific one. Even if he funcions of hese programs overlap, purchasing an exra produc can increase he uiliy of consumers when he overlap is no perfec. However, he larger he overlap, he smaller he exra gain ha can be obained from insalling boh programs. Someimes, he consumers are resriced o buy only one produc due o he echnological barriers se by firms. For example, he barriers se beween wo anivirus sofware programs, 60 and Tencen QQ: when users insall one of hem, hey will be asked o uninsall he oher one. 1 Anoher example is in he anirus sui agains Microsof. In 004, he European Union (EU) compeiion commission cied ha Microsof wihheld needed ineroperabiliy informaion from rival sofware companies which prevened hem from making sofware compaible wih Windows; on February 008, he EU compeiion commission announced is decision o fine Microsof Corporaion 899 million euros (US $1.5 billion), approximaely 1/10 of he company s ne yearly earnings, for failing o comply wih he 004 anirus order. Similar compeiion happened beween wo online TV plaforms: PP- Sream and PPLive. They are he wo major sofware programs which provide online TV or movies based on PP echnology in China. Each of hem has more han 00 million subscribers wih an average of 0.5 million users online simulaneously. PPSream broadcass 17 ypes of programs allocaed 1 Even if wihou echnological barriers, he coexisence of wo anivirus sofware programs does no work very well because of he working principle for his kind of programs. I was announced by some expers ha insalling wo anivirus sofwares had a negaive influence on compuer funcional, or even made some funcional no work. For example, he ime o boo compuer wih 60 anivirus insalled is seconds, 8 seconds wih Kaspersky insalled, while 51 seconds wih boh sofwares insalled. Under he es of mass files copying, i akes 59 seconds for he compuer wih Kaspersky anivirus, 5 seconds wih Rising anivirus, bu i akes 78 seconds for he compuer wih boh anivirus insalled o finish he copying process. 1

4 among 50 channels wih more han 10 housand programs, and PPLive broadcass 11 ypes programs wih 457 channels bu fewer programs han PPSream. Many shows are broadcased by boh eniies, bu each of hem has some specific TV programs. For example, PPSream has more movies, especially recen movies and live broadcas han PPLive, bu PPLive has more spors channels and local TV channels from mainland China. These broadcas plaforms are boh horizonally and verically differeniaed. Their qualiy essenially depends no only on he number of TV series and films hey can play bu also on he conen of he programs. Purchasing a second service enlarges he number of TV series and films ha a consumer can wach on his compuer, so ha he specific value of buying a second TV broadcas sofware comes from he number of TV series and films which are specific o ha sofware. In 010, PPSream se echnological barriers o preven consumers from consuming boh services from he same compuer. Ineresing quesions arise: how do wo producs compee when heir conens parially overlap? Is compaibiliy where consumers can mulihome and use boh producs in he ineres of firms? Do he firms sraegies on compaibiliy enhance or harm social welfare? To answer hese quesions, we consider an indusry of wo firms ha sell producs which are boh horizonally and verically differeniaed. Each produc has is own specific par while here exis a common par (overlap) belongs o boh producs. Each firm can se is produc incompaible wih is opponen s so ha he consumers can consume only one of he producs (single-home) bu no boh (muli-home). Wihou produc overlap, allowing muli-homing should be beer for he firms because hey have more demands and less severe compeiion. Wih overlap, each firm can no charge on he common par as hey compee as a Berrand compeiion. Therefore allowing muli-homing could make firms worse-off because of overlap and horizonal differeniaion. The larger he degree of overlap, he more similar he wo producs are, he less willing are he consumers o purchase boh producs, hence he lower he profi each firm earns when he users can muli-home. Similarly, he smaller he horizonal differeniaion, he less difference he consumers evaluaion beween hese wo producs, and he less he consumers are willing o consume boh, herefore he lower he profi each firm obains. The lawsui beween PPSream and PPLive began in April of 010. Firs PPLive copied some programs from PPSream, hen PPSream se echnological barrier so ha he individual who consumed PPSream would uninsall PPLive auomaically. The consumers can no consume PPSream and PPLive a he same ime (can no insall boh on he same compuer). Laer on, in Ocober of 010 hey made a join announcemen o sop he dispue under he pressure by he Chinese Minisry of Indusry and Informaion Technology.

5 One of he imporan propery of equilibrium wih muli-homing users is ha each firm serves as a special ype of monopoly. The overlap and each firm s own qualiy, bu no he rival s qualiy and price, shapes demand, and he prices are sraegic independen. Inuiively, we would expec ha compaible producs o allow mulihoming induces a higher social welfare. We show ha he opposie could be rue. If he prices charged by firms could no be changed, allowing consumers o muli-home obains a higher social welfare as he demand increases. While each firm responds according o he demand i faces and he rival s pricing sraegy o charge a differen price as ha when consumers can only singlehome. Moreover, he price changes are differen beween wo firms because of produc differeniaion, which induces an inefficien allocaion of consumers. Wih he asymmeric adjusmen of prices, i happens ha some consumers purchase a produc from he firm which is furher away from is locaion because he overlap makes he oher produc less aracive, which induces a social welfare loss because hey have o pay a higher ransporaion cos. Differen resul comes ou if we analyze from he compeiion policy perspecive, from which we only care abou he addiional benefi and addiional cos o consumers when hey can consume anoher varian. Compaible producs has wo effecs on he consumers: muli-homing users have more consumpions bu hey have o incur he ransporaion cos and pay prices o boh firms. When he consumers can consume boh producs, hey should deermine he addiional value from consuming a second produc. We show ha he social welfare maximizer has he same preference as he one from he compeiion policy perspecive if and only if he horizonal differeniaion is large and he overlap is no very large, or he horizonal differeniaion is medium and he overlap is very small. If eiher one of he horizonal differeniaion or he overlap is small, he social welfare maximizer has he same preference as he firms equilibrium sraegy. In realiy, many markes are characerized by plaforms ha obain profis from adverisemen, such as adverisers and end users conacing via TV channels. The adverisers care abou he number of users who are poenial consumers for he adverised produc. Users, however, someimes dislike adverising while someimes hey obain useful informaion from he adverisemen. In he economic lieraure of his wo-sided marke framework where users provide posiive exernaliy o adverisers while adverisers provide negaive exernaliy o users has been considered recenly. An imporan assumpion in hese papers (e.g., Anderson and Coae (005)) is ha he users single-home o choose only one plaform while adverisers can muli-home o pu adverisemen on serval plaforms. Therefore his is no compeiion for adverisers beween plaforms.

6 In secion 4, we analyze his wo-sided marke framework under which adverisers care abou he number of users, while he users do no care abou he adverisemen. If one plaform makes is produc incompaible wih he rival s, i only works on he users side. The adverisers do no care abou he number of imes hey conac wih one user, which implies ha singlehoming users are more valuable o he adverisers han he muli-homing users. Allowing he users o muli-home has wo effecs: on he one hand, each plaform aracs more users ha are valuable o adverisers; on he oher hand, he number of single-homing users on each plaform decreases, inducing he adverisers o be less willing o join one addiional plaform. The sandard resul in he classical wo-sided marke lieraure ha i is opimal for each plaform o subsidize he users and charge he adverisers can be obained in his framework. Imposing he consrain of nonnegaive prices o assume ha here is no price on he users side, we have differen resuls in his wo-sided marke framework. The plaform which provides a higher qualiy produc will enforce single-homing if he nework exernaliy is large and he horizonal differeniaion is small. The larger he nework exernaliy, he more adverisers care abou he number of users on he oher side of he plaform, hence he plaform wih produc qualiy advanage would like o enforce single-homing o obain a larger marke share and charge a higher price from he adverisers in order o ge a higher profi. If we use his model o analyze he compeiion beween PPSream and PPLive, neiher of hem charges a posiive price o he users as he nework exernaliy is large so ha each plaform s opimal sraegy is charging a posiive price o he adverisers and zero price o he users; PPLive copied some programs from PPSream as his makes is profi larger; PPSream se he echnology barrier o preven consumers from muli-homing as i prefers single-homing in his case. The paper is organized as follows: we firs inroduce he relaed lieraure in Secion ; hen we characerize he basic model of compeiion and compaibiliy sraegy from boh he firms and he regulaor s poin of view in Secion ; in Secion 4 we exend he basic model o a wo-sided marke framework; in Secion 5 we analyze he special case of compeiion beween wo free TV channels; finally we conclude in Secion 6. Relaed Lieraure Compeiion and Muli-homing: Gabszewicz and Wauhy (00) explore price compeiion beween wo verically differeniaed firms when consumers can muli-home by purchasing boh producs (hey call i join pur- 4

7 chase opion in heir paper), in Gabszewicz and Wauhy (00), hey do no analyze firms sraegy on permiing muli-homing. Anderson and Coae (005) sudy how firms (TV channels) compee for adverisers when consumers (viewers) can only single-home. Ambrus and Reisinger (006) exend heir model by allowing consumers o muli-home, and compare he equilibrium level of adverisemen o he case when consumers can only single-home. In heir model, wo producs are horizonally differen and heir basic values fully subsiue for each oher. Anderson, Foros and Kind (010) analyze he Hoelling price compeiion where consumers can eiher single-purchase or muli-purchase. They show ha higher preference heerogeneiy increases equilibrium prices and profis wih single-purchase, bu decreases hem wih muli-purchase. Reisinger (011) analyzes he wo-sided marke framework where plaforms are differeniaed from he users perspecive bu are homogenous for adverisers. In his framework, alhough here is Berand compeiion for adverisers, plaforms obain posiive margins in he adverising marke. In addiion, plaforms profis can increase in he users nuisance coss of adverising. Compeiion and Compaibiliy: Wih Hoelling model, Doganoglu and Wrigh (006) sudy wo firms compeing sraegies on compaibiliy and is efficiency when consumers can (or can no) muli-home by purchasing boh horizonally differeniaed producs. In heir paper, he fundamenal values of producs fully overlap. Consumers can ge he same uiliy from he fundamenal value no maer wheher hey buy boh producs or jus one. While consumers can enjoy he nework exernaliy of boh producs no maer which produc hey buy if firms choose compaibiliy for heir producs. Kaz and Shapiro (1985) sudy firms decisions on compaibiliy for heir producs where consumers can only single-home in an oligopoly model. Casadesus-Masanell and Ruiz-Aliseda (009) exend he idea of Kaz and Shapiro (1985) ino seings wih wo-sided plaforms and indirec nework effecs, and find ha incompaibiliy gives rise o asymmeric equilibria wih a dominan plaform ha earns more han i earns under compaibiliy. Two-Sided Markes and Muli-homing: When here is no produc differeniaion on eiher side of he marke, Armsrong and Wrigh (007) showed ha compeiive equilibria can be undermined when plaforms can offer exclusive conracs o one side of he marke. Exclusive conracs work by making i easier for a plaform o unsele equilibrium wih muli-homing on one side. Armsrong (006) shows ha if he firs group pus more weigh on he nework benefis of being in conac wih he wides populaion of he 5

8 second group consumers han i does on he coss of dealing wih more han one plaform, hen he firs group agens do no make an eiher-or decision o join a plaform. Farhi and Hagiu (007) show ha he possibiliy of subsidizaion of one side in a wo-sided marke can lead o fundamenally new sraegic configuraions in oligopoly. Gabszewicz and Wauhy (004) analyze compeiion beween wo plaforms where he agens are heerogenous, hey show ha in equilibrium, muli-homing akes place on one side of he marke only. Moreover, he only equilibrium exhibiing posiive profis for boh plaforms replicaes he collusive oucome. Golafainy and Kovac (007) provide a formal heory of compaibiliy choice beween sub-sequen generaions of echnology in wo-sided markes. They classify he compaibiliy regimes ha can occur in wo-sided markes. Poolsomba and Vernasca (006) explore he possibiliy of parial muli-homing in wo-sided marke where on he each side here are wo ypes of agens. They show ha in order for an equilibrium wih parial muli-homing on boh sides o exis, he nework benefis of high ype agens mus be sufficienly higher han ransporaion coss. The Basic Model: Compeiion beween Two Firms.1 Se Up Consider a model wih wo firms, i = A, B, which sell wo horizonally differeniaed producs. The firms are locaed a he wo end poins of he Hoelling line of lengh equals o 1. Firm A locaes a he far lef (poin 0) and firm B locaes a he far righ (poin 1). Each firm provides produc wih qualiy i = A, B respecively. Therefore he producs are verically differeniaed if A B. These wo producs parially overlap and hey have some common pars. The consumers can choose only one of he producs if eiher one of he firms se some echnological barriers so ha he producs are incompaible wih each oher. Oherwise, if he producs are compaible, he consumers have he opion o consume boh. To ease our exploraion, we assume ha boh he fixed cos and he marginal producion cos are zero. We model he iming of compeiion beween hese firms in he following way: 1. Firms decide he compaibiliy of heir producs.. Firms se heir prices. 6

9 . Consumers make heir consumpion decisions. There is a mass 1 of individuals, uniformly disribued on he Hoelling line. For each produc, each consumer buys eiher one uni of he produc or none. When firms se he prices P A and P B for he wo producs, he uiliy of he consumer locaed a x [0, 1] is A x P A if he only consumes produc A, B (1 x) P B if he only consumes produc B, u = (1) A + B C P A P B if he consumes boh producs, 0 if he consumes neiher produc. Here C denoes he common pars or he degree of overlap beween hese wo producs. When he consumer buys one addiional produc when he has already bough he produc from he oher firm, he can obain more uiliy from he specific par of he produc (A C or B C). The parameer characerize he horizonal differeniaion beween hese wo producs, which denoes he disance disuiliy from no geing he mos preferred produc. Following he convenion in he previous lieraure, we use he erminology ransporaion cos as below. 4 Before going furher wih our analysis, we make he following wo assumpions. Assumpion 1. 0 C B A B + C. The region of parameers saisfying assumpion 1 is represened by figure 1. Assumpion 1 expresses he facs ha a) firm A has a qualiy advanage and b) consuming anoher produc will always bring a non-negaive marginal benefi. The las inequaliy A B + C ensures ha he qualiy advanage of produc A is no oo large so ha here exiss an equilibrium ha each firm faces a demand less han 1 eiher he producs are compaible or incompaible. This inequaliy ogeher wih assumpion ensure ha all consumers are served and here is effecive compeiion beween he wo firms. For simpliciy we use his linear formula o denoe he fixed amoun C of overlap. Here we can say ha A and B are bundles of producs, each of hem conains some differen programs, hence he overlap C no only refer o he number of he common programs bu also he conens of programs conained in boh bundles of producs, for example: If produc A conains program a, b, c, d, e and produc B conains program d, e, f. In his case we have A = 5, B = and heir common program C =. 4 We use his horizonal differeniaion as he consumers preferences are heerogeneous, for example, o TV channels, someone prefers spors while someone prefers movies. Here we can also explain as he uni cos for consuming one produc, such as spending ime o purchase or consume he produc. The lineariy of ransporaion cos gives he resul ha everyone obains he same uiliy when hey consume boh producs. 7

10 C A A A 5 A 5 A A B Figure 1: The region of parameer values saisfying assumpion 1. Assumpion. A + B. We borrow erminology from he wo-sided marke lieraure and say ha a consumer single-homes when he purchases only one of he wo goods and ha he muli-homes when he purchases boh producs. Noe however ha before secion 4, here are no nework effecs whasoever in our model.. Compeiion Equilibrium In subsecion..1, we characerize he equilibrium in he case when consumers mus single-home, and.. he equilibrium when consumers can muli-home...1 Compeiion wih Muli-homing no Allowed If he consumers are resriced o consume only one varian, here exis wo differen ypes of equilibria according o differen values of he ransporaion cos. For inermediae value of, he marke is fully covered and shared by wo firms; for small value of, firm A wih qualiy advanage produc becomes a monopolis o cover he whole marke and firm B has no sale. We 8

11 have he following equilibrium resul in he second period: 5 Lemma 1. The equilibrium oucome when users can only single-home is: 1. If A B < A+B, hen P s A = + A B P s B = A B, D s A = 1 +A B 6, D s B = 1 A B 6. If A B, firm A covers he whole marke, and, πa s = +A B +, πb s = A B + P s A = A B, D s A = 1, π s A = A B. (A B) ; 18 (A B). 18 Here we use Pi s and πi s o denoe he equilibria price and profi where he consumers are enforced o single-home. In he equilibrium wih marke sharing, each firm s price and profi increases wih he horizonal differeniaion (dpi s /d > 0, dπi s /d > 0). The inuiion is ha higher horizonal difference induces sronger preference, which enails more inelasic demand, more marke power, and higher profi. Differen from he sandard resuls in symmeric Hoelling model, where prices and profis are independen of he produc qualiy, he firm wih higher qualiy produc earns he higher demand, price and profi. Wih he qualiy difference A B increases, firm A s price and profi increases while firm B s decreases. As A B is he qualiy advanage of firm A (disadvanage of firm B). The larger A B, he more he inelasic consumers (or firm A s original consumers) are willing o pay, herefore i could charge a higher price o obain a higher profi. Similarly for firm B, he larger he qualiy disadvanage, he less he inelasic consumers are willing o pay, hence firm B has o charge a lower price... Compeiion wih Muli-homing Allowed If he consumers can muli-home, hey have o deermine he addiional value of buying a second produc. Each of hem prefers he produc closer o his own locaion, herefore he buys ha firs. The addiional value could be obained from buying he oher produc depends on he degree of overlap. The wo firms do no compee for he marginal consumer who is indifferen beween consuming eiher produc, heir pricing sraegy only affecs heir own demand. There exis pure sraegy equilibria where here exis posiive 5 The deailed analysis could be found in Appendix A. 9

12 buyers for boh producs only if A+B C. If (A + B C)/ < (A + B)/, here is no pure sraegy equilibrium under which muli-homing users exis. 6 For large value of, some consumers muli-home on hese wo producs and each firm faces a demand less han 1. For inermediae value of, all of he consumers buy produc A and some of hem also buy produc B. For small value of, every consumer buys boh producs. We have he following equilibrium resul: 7 Lemma. If he consumers can muli-home, we have he following equilibria: A C 1. If is large, i.e. < A+B C, hen a sricly posiive mass 1 of consumers buy boh producs. A C + B C P m A P m B = A C = B C, DA m = A C, πa m =, DB m = B C, πb m = (A C) ; 4 (B C). 4 B C. If is inermediae size, i.e. < A C, hen a mass B C consumers buy boh producs. No consumers buy only produc B. of P m A = A C, D m A = 1, π m A = A C ; P m B = B C, DB m = B C, πb m = (B C). 4. If is small, i.e. B C, all he consumers buy boh producs, and P m A = A C, D m A = 1, π m A = A C ; P m B = B C, D m B = 1, π m B = B C. Here we use P m i and π m i o denoe he equilibria price and profi when muli-homing users exis. In he equilibrium where each firm faces a demand less han 1, each firm s price and profi depends only on is own produc qualiy and he degree of overlap bu no he opponen s qualiy. Indeed, here is no direc compeiion beween he wo firms if he users are no resriced o buy only one varian, and he firms compee as Berrand compeiion on he common par C hence each of hem could only charge on is own specific 6 The proof for non-exisence of pure sraegy equilibrium appears in Appendix B. Bu he equilibrium under which all users single-home is sill an equilibrium in his case. 7 Deailed analysis could be found in Appendix A. 10

13 par A C or B C. Furhermore, each of hem has monopoly power on is own specific par and earns monopoly profi, which is increasing wih is own produc qualiy and decreasing wih (dπ m i /d < 0). The overlap C measures he addiional value from buying a second varian. The larger C reduces he addiional value being obained from purchasing a second varian, herefore each firm earns a lower profi (dπ m i /dc < 0)... Single-homing vs. Muli-homing If he users have o single-home, he users become more heerogenous when increases, hen each firm s marke power on is own consumers increases, inducing higher prices and higher profis. Under muli-homing, when he users become more heerogenous, each firm covers a smaller marke segmenaion and earns a lower profi. The inuiion is ha each firm has monopoly power on is own specific par bu could no charge on he common par C, herefore each of hem charges a monopoly price on is own specific par A C or B C, which is independen on he ransporaion cos. Higher degree of heerogeneiy will reduce he mass of populaion which is willing o buy boh producs. If we compare he wo equilibria where each firm faces a demand less han 1, ha is, case 1 in boh lemmas, we noe ha boh firms charge a higher price under single-homing (PA s > P A m, P B s > P B m A C since > ). The wo producs parially overlap. Given he compaibiliy sraegy in he firs sage, in order o arac users o consume is produc in addiion of is opponen s, each firm has o charge a lower price (he price only charged on he special par of each produc). Firm A faces a larger demand when he consumers can muli-home bu firm B has a smaller demand if C > A+B. The inuiion is ha larger C makes purchasing boh less aracive o consumers, inducing more inelasic consumers o produc A due o is qualiy advanage. Furhermore, firm A s price decreases more and demand increases more han ha of firm B. 8. Compaibiliy Sraegy A firm will prohibi muli-homing if and only if is profi is greaer under single-homing, and he consumers will be allowed o muli-home only if boh firms have greaer profis under muli-homing. For simpliciy, we only consider he case where A+B C which ensures ha here exis pure sraegy 8 We have + A B from lemma 1 and. A C > A B B C and A C [ 1 + A B 6 ] > B C [ 1 A B 6 ] 11

14 equilibrium. Furhermore, o ease our explanaion, we assume B C From comparing he profis in lemmas 1 and, we have he following: A B. 9 Proposiion 1. In equilibrium, boh firms choose a compaibiliy sraegy if A B + B C. For a given degree of overlap C, compaibiliy is he equilibrium sraegy chosen by boh firms if he degree of produc differeniaion is small enough. The inuiion is ha he smaller is, he more similar hese wo producs are, he more server Hoelling compeiion induces a lower price each firm has o charge, herefore he lower he profi could be obained. In he limi case when = 0, he Hoelling compeiion is very close o Berrand compeiion which induces a 0 profi for firm B and very low profi for firm A. The hreshold of preference for allowing muli-homing decreases wih he producs overlap C. Indeed, allowing muli-homing has wo effecs on firms: each of hem aracs more consumers bu charges a lower price. The larger he overlap C, he less willing are he consumers o purchase boh, he lese he increase in demand bu he more he decrease in price compared wih he case when each consumer single-homes, hence he lower he profi each firm obains. In he Appendix we prove ha when > A B, for all circumsances under which firm B permis muli-homing so does firm A, hence firm A has a sronger preference for muli-homing han firm B. Boh firms allow mulihoming when A B. Therefore he equilibrium compaibiliy sraegy is deermined by firm B s sraegy. Wha is more, from he comparaive saics of, we find ha a decrease in he ransporaion cos will lead boh firms o value muli-homing more. Proposiion. Whenever firm B acceps muli-homing, so does firm A. An increase in produc qualiies A and B will never lead o more prohibiion of muli-homing. A decrease in he ransporaion cos makes boh firms o value muli-homing more. The prices charged by boh firms and he demands are increasing wih he produc qualiy when consumers can muli-home. Firm A has a qualiy advanage, hence i charges a higher price and aracs more consumers han firm B under muli-homing. As a resul for all he parameer values under which firm B allows muli-homing, so does firm A. The smaller he ransporaion cos, he more severe he compeiion beween wo firms if he 9 The value of B C and A B only change he hreshold for differen inervals we analyze, he resuls are he same eiher we assume B C A B or vice versa. 1

15 consumers could purchase only one produc, he lower he price each firm has o charge, hence boh firms value muli-homing more..4 Social Welfare Maximizaion In his subsecion we compare he single-homing and muli-homing oucomes from he perspecive of he social planner who aims o maximize social welfare. The social welfare maximizer can pu pressure on firms o enforce muli-homing bu canno se prices for he producs. Each firm se price for is own produc. From comparison of social welfare which is denoed by he un-weighed sum of consumer surplus and firms profis, we have he following resul which is proved in he Appendix: 10 Proposiion. Muli-homing is socially opimal if eiher is small or is large bu C is small. If he ransporaion cos is very large, he social welfare maximizer prefers he users o muli-home when he degree of overlap C is no very large. Allowing muli-homing has wo effecs from he social welfare maximizer s perspecive: more consumpion of consumers and larger ransporaion cos. The larger is C, he more similar he wo producs are, herefore mulihoming induces a larger social welfare loss due o he ransporaion cos. If he ransporaion cos is no very large, he social welfare maximizer prefers he users o muli-home because prohibiion of muli-homing induces a social welfare loss due o under consumpion..5 Consumer Surplus Maximizaion The consumer surplus is he difference beween social welfare and firms profis. If we consider from he compeiion policy perspecive ha here exiss a regulaor who aims o maximize consumer surplus, we have he differen resul from he firms and social welfare maximizer: 11 Proposiion 4. Muli-homing is opimal from he compeiion policy perspecive if eiher is large or is medium and C is small. 10 In he { Appendix, we prove } ha muli-homing { is socially opimal } if eiher 7 A C 7 A C max 1 (A B), or max 1 (A B), and C 1 (A+B) (A B) The proof could be found in he Appendix, which shows ha muli-homing is opimal from he compeiion policy perspecive if eiher A C < A+B C or A B < A C and C B 4 ( + A B) 16(A B) 9. 1

16 A C If he ransporaion cos is large enough (i.e, < A+B C ), he consumer surplus under muli-homing is larger han ha under singlehoming. There are wo effecs when he consumers could muli-home: more consumpion and paying wice for prices and ransporaion cos. If is large, he number of muli-homing users is small and each consumer faces a lower price if hey could muli-home. In his case, allowing muli-homing increases consumer surplus because he increase due o more consumpion A B is larger han he decrease due o cos. If is medium (i.e, < A C ), muli-homing is beer for he consumers if he degree of overlap is no very large. If is small (i.e, A B ), allowing muli-homing is worse for consumers. Because for his value of, all users consume boh producs if hey could muli-home. Bu hey have o pay o boh firms and wice for he ransporaion cos, which dominaes he effec of more consumpion..6 Comparison If we compare he hresholds of compaibiliy sraegy for he social welfare maximizer and firms, we ge: 1) for he parameer values when boh firms allow muli-homing on he consumers side, he social welfare maximizer also prefers muli-homing; ) here exis some circumsances such ha he equilibrium sraegy chosen by firms is single-homing while he social welfare maximizer prefers muli-homing, for insance, when A B < max{ 7 1 A C (A B), } and C > B [ 1 (A B)]. Proposiion 5. Whenever he equilibrium compaibiliy sraegy chosen by firms is muli-homing, muli-homing is socially opimal. Figure C. in Appendix C.4 could be helpful o figure he inuiion for proposiion 5. For given value of A, B and, he social welfare difference beween single-homing and muli-homing is always smaller han he profi difference of he wo firms. The social welfare loss due o prevening mulihoming is always larger han he profi loss. Because he social welfare maximizer cares also abou he consumer surplus in addiion o he firms profis. The loss in consumer surplus due o prevening muli-homing is larger han he increase of profis, which induces a welfare loss. Therefore he equilibrium compaibiliy sraegy chosen by firms is less han socially opimal. Figure C. describes each firm s preference for allowing muli-homing. For a given degree of overlap C, boh firms prefer he users o single-home if he differeniaion is large; when is medium, for all circumsances when 14

17 (0, A B ] ( A B, A C ] ( A C, ] [0, C 1 ] M,M,S M,M,M M,M,M [C 1, C ] M,M,S M,M,S M,M,M [C, C ] M,M,S S,M,S S,M,M [C, B] M,M,S S,M,S S,S,M Table 1: We summarize he equilibrium level of firms compaibiliy sraegy, social welfare maximizer s preference for muli-homing and consumer surplus maximizer s preference. The iems in he firs horizonal line denoe he value of ransporaion cos, and he iems in he firs column denoe he overlap C. We use M o denoe muli-homing and S o denoe single-homing. C 1 = B 4 1 wih 1 = (+A B) 16(A B), C 9 = B [ A B ], C = (A+B) 4 4 wih 6 = 1 7(A B), = min{ A+B, A+B C } firm B prefers muli-homing, so does firm A, herefore firm A has a sronger preference for muli-homing; boh firms prefer single-homing if is small. Figure C.4 describes he comparaive saics wih he produc qualiy A, B and he ransporaion cos. Wih he increase of produc qualiy A or B, boh firms prefer muli-homing more. 1 The inuiion is ha, wih he increase of A, he more server is firm B s qualiy disadvanage, and he lower profi i obains if he consumers could purchase only one produc, herefore firm B has sronger preference for muli-homing. For firm A, he larger qualiy i provides, he higher price i could charge and higher demand i faces when he consumers could muli-home, herefore he higher profi i obains. When he ransporaion cos decreases, boh firms value mulihoming more. The smaller he ransporaion cos, he less difference he consumers evaluaion beween hese wo producs; as a resul, he less he inelasic consumers are willing o pay; hence he compeiion beween hese wo firms are more severe, herefore each of hem earns a less profi when hey compee under single-homing. We use able 1 o describe he firms equilibrium behavior, he social welfare maximizer s and he consumer surplus maximizer s preference. From able 1, single-homing is socially opimal if and only if boh he degree of overlap C and he ransporaion cos are large enough ( A C 1 Anoher descripion for his sronger preference for muli-homing is ha, here exis an increasing funcion of A, C A (A), such ha firm A prefers muli-homing if and only if C < C A (A). Similarly, firm B prefers muli-homing if and only if C < C B (A), where C B is increasing wih A. Therefore, he hreshold C o allow muli-homing is increasing wih A. The same condiion holds for he produc qualiy B. 15

18 and C C B). The social welfare maximizer has he same preference as he one from he compeiion policy perspecive if and only if is large and C is no very large, or is medium and C is very small ( A C and 0 C C or A B A C and 0 C C 1 ). If eiher or C is small, he social welfare maximizer has he same preference as he firms equilibrium sraegy. Noe ha when A B < A C and C C B, boh he firms equilibrium behavior and consumer surplus maximizer s are singlehoming while he social welfare maximizer would enforce muli-homing, i is because he firms equilibrium behavior is deermined by firm B s sraegy, muli-homing is profiable for firm A in his case. Proposiion 6. The social welfare maximizer has he same preference as he one from he compeiion policy perspecive if and only if is large and C is no very large, or is medium and C is very small. If eiher one of or C is small, he social welfare maximizer has he same preference as he firms equilibrium sraegy. The inuiion behind proposiion 6 is ha allowing muli-homing has differen effecs on he firms profis and consumer surplus. I depends on which one dominaes from he social welfare maximizer s poin of view. Now le us compare he resuls wih hree special cases. If A = B = C, he wo firms sell he same producs and nobody buys boh. We have he classical symmeric Hoelling model if he consumers could purchase only one varian, and each firm covers half of he marke. Boh firms and he social welfare maximizer would enforce single-homing. If A > B = C, produc A is an upgrade of produc B. Nobody purchases boh producs as i is dominaed by purchasing only produc A. Therefore muli-homing equilibrium does no exis in his case. If A > B and C = 0, here is no overlap beween hese wo producs. The firms prefer muli-homing as each of hem earns a monopoly profi if he consumers could purchase boh, which is larger han he profi under Hoelling compeiion. From he social welfare maximizer s poin of view, offering anoher produc is more valuable, herefore muli-homing is socially opimal..7 An Example We use a numerical example o explain he relaionship beween he equilibrium compaibiliy sraegy of he firms, social welfare maximizer and he value of he ransporaion cos and he degree of overlap C, respecively. Assume A = 10, B = 8, and = 5. In his case, neiher firm covers he whole 16

19 marke eiher under single-homing or muli-homing. We have π s A π m A = (10 C), 0 πb s πb m = 5 + (8 C) So firm A prefers muli-homing if and only if C 10 (5 + ).07, and firm B prefers muli-homing if and only if C 8 (5 ) 1.9. Whenever firm B prefers muli-homing, so does firm A. The social welfare under single-homing and muli-homing are respecively: SW s = , SW m = C C Muli-homing is socially desirable if and only if C From comparison, whenever he equilibrium sraegy chosen by firms is mulihoming, muli-homing is socially opimal. This illusraes he resul in proposiion 5. Now le us consider anoher case for a given value of overlap C = 6, π s A π m A = , π s B π m B = Firm A permis muli-homing if.16 and firm B permis muli-homing if.08. The social welfare under hese wo cases are respecively: SW s = , and SW m = The social welfare under muli-homing is larger han ha under singlehoming for all values of. 17

20 4 Two-Sided Markes In he las secion we analyzed he basic model beween wo firms. In many cases here exis differen groups of paricipans conacing wih each oher in one marke, for insance he end users and adverisers conacing wih each oher hrough TV channel, which is wha we called wo-sided markes. In his secion we exend he basic model o he wo-sided markes case. For simpliciy, we consider he case where end users and adverisers conac hrough TV channels Se Up The users ac as in he basic model. The adverisers join he plaform in order o make more persons know abou heir produc. The number of users has a posiive nework exernaliy on he adveriser s uiliy. The more individuals who know he adverisemen, he larger probabiliy hey have more sales. If he plaform decides o exclude is opponen, i works only on he end users side. We denoe A and B as he wo plaforms, hey locae a he wo end poins of he Hoelling line, side 1 he end users and side he adverisers. Boh he end users and adverisers are uniformly disribued on [0, 1]. When plaforms charge prices P A and P B from he users side, he uiliy of an user locaed a x [0, 1] is denoed by (1), which is he same as in he basic model. When plaforms charge prices Q A and Q B o he adverisers, he uiliy of an adveriser locaed a y [0, 1] is 14 βn A y Q A if i only joins plaform A, u = βn B (1 y) Q B if i only joins plaform B, () β(n A + n B n AB ) Q A Q B if i joins boh plaforms. We denoe β as he iner-group exernaliy, n A, n B and n AB he number of users who join plaform A, plaform B and boh plaforms respecively, n AB equals o 0 if no users muli-home on boh plaforms. The adverisers care 1 In realiy, he users join he plaform in order o consume he programs. They care abou he number of conens, and here exiss anoher side of he marke: he conen provider. Since he plaform s profi comes from he adverisers, i cares he number of adverisers, while he adverisers care abou he number of users. For simpliciy, we only consider he users and adverisers in his model. 14 Here we use fixed adverising fee in sead of access fee per user so ha i is easier o denoe he nework exernaliy. If we use access fee per user, he adverisers do no care abou he number of users, hey will join he plaform if he benefi is larger han he access fee. 18

21 only abou he oal number of users who see he adverisemen, bu no he number of imes hey see i. If here is no muli-homing user, he adveriser s uiliy from joining boh plaforms is he sum of uiliy from joining he wo plaforms, and here is no direc compeiion on he adverisers side. If muli-homing users exis, he plaforms compee also on he adverisers side as he larger number of users on he oher plaform, he less willingness he adverisers o join one more plaform. For simpliciy, here is no basic value from joining he plaform for he adverisers; hey care only abou he number of users on he oher side. 15 The inequaliy A B C in assumpion 1 also holds in he wo-sided case. In order o ensure ha he marke on he adverisers side is fully covered and he wo plaforms do compee on he adverisers side, we make he following assumpion Assumpion. β max{, (A + B C)}. We consider a similar hree-sage game as in he one-sided marke case. In he firs sage, he wo plaforms decide on he compaibiliy of heir producs. In he second sage, he plaforms se heir prices on he users side and on he adverisers side simulaneously. In he las sage, he users and adverisers make heir decisions: adverisers decide on which plaform hey wan o adverise, and users decide o join he plaform or no, hey can join a mos one plaform when he plaforms are no compaible wih each oher. We use his seup for he wo-sided marke framework by adding one more side o he basic one-sided marke model. The users behavior is similar as in he basic model. We ge he basic model if β = 0. For simpliciy, we assume he horizonal differeniaion is he same o he users and o he adverisers. We have similar resul if hey are differen on wo sides of he marke bu are correlaed wih each oher (for insance, if = α 1 ). 4. Compeiion wih Muli-homing no Allowed The adverisers acion has no effec on he users side, as a resul he marke segmenaion on he users side is similar as in..1 wihou adverisers for given prices charged by plaforms in he second sage: The wo plaforms compee on he users side if he ransporaion cos lies on he middle; one of he plaforms covers he whole marke if he ransporaion cos is small enough. 15 There maybe some nuisance cos for adverisemen when he user is waching TV. Bu on he oher hand, some adverisemen on he TV channel provides informaion abou producs, which is useful for he users. The above wo effecs counerac o each oher, we assume he users ge zero uiliy from he adverisemen. 19

22 The adverisers can always join boh plaforms if hey which. If one adveriser joins one more plaform, he increasing number of users who see is adverisemen is all of he users on he addiional plaform. There is no compeiion beween plaforms on he adverisers side. The price charged by each plaform on he adverisers side affecs only is own demand. We use m i o denoe he number of adverisers on plaform i. I is easy o show ha he number of adverisers joining he wo plaforms are respecively: { } { } βna Q A βnb Q B m A = min, 1, m B = min, 1. In he second sage, for differen values of he ransporaion cos, we have differen equilibria which are described by lemma D.1 in page 47. If he ransporaion cos is large enough, he oal number of adverisers is β, which is larger han 1, herefore here exis some adverisers whose ype is close o one half pu adverisemen on boh plaforms. The number of users on each plaform is less han 1; for he adverisers wih he middle ype, he increasing number of users seeing heir adverisemens by joining one addiional plaform is larger han he ransporaion cos and adverisemen fee. We can show P A < P B and Q A > Q B if < β < 6, while P A > P B and Q A < Q B if β > 6. No he same as in he one-sided marke, where firm A which provides a higher qualiy produc charges a higher price (P A > P B ), he plaforms which charges higher price o users will charge lower price o he adverisers, and vice versa. From lemma D.1, i is easy o check ha P A < 0, P B < 0, his is a normal resul for he classical wo-sided marke models, if he adverisers care abou he number of users very much, he plaform s bes sraegy is o subsidize he users and charge he adverisers. 4. Compeiion wih Muli-homing Allowed If he wo plaforms are compaible wih each oher, he end users can join boh of hem. If one adveriser joins plaform B in addiion o plaform A, he increasing number of users seeing is adverisemen is he users who do no join plaform A, which equals 1 n A when he marke is fully covered on he users side. Hence he larger is n A, he smaller is he willingness he adverisers o join plaform B in addiion o plaform A. The users acions are similar as ha in he basic model. Each plaform faces a demand less han 1 and here exis muli-homing users if is large; all users join plaform A and some of hem also join plaform B if is medium; all users join boh plaforms if is small. 0

23 There exis some adverisers who are willing o pu adverisemen on boh plaforms if and only if he number of single-homing users on each plaform is large enough. If he number of users on one plaform is close o 1, for example if n A is close o 1, joining plaform B in addiion o plaform A is no profiable for he adverisers, as he exra uiliy derived from he users no joining plaform A is small, bu hey have o pay wice he ransporaion cos and adverisemen fee. Hence here is muli-homing adverisers in his case. If eiher one plaform covers he whole marke on he users side, here is no need for he adverisers o join boh plaforms. This is denoed as he boleneck effec in he wo-sided marke lieraure. In he second sage, The equilibrium pricing sraegy depends on he value of he parameers. If he ransporaion cos is large enough so ha he number of users on each plaform is much smaller han 1, here exis wo ypes of pure sraegy equilibria: one wih some muli-homing adverisers and one wihou muli-homing adverisers. If he ransporaion cos is no very large, here exiss only one pure sraegy equilibrium wih all adverisers single-homing. The descripion of equilibria and deailed proof can be found in Appendix D. From lemma D.1 and lemma D., here exis some adverisers ha mulihome on boh plaforms only if boh he exernaliy β and he ransporaion cos are large enough. If he ransporaion cos is large, he number of users on each plaform is much smaller han 1, so ha joining an addiional plaform gives more uiliy o he adverisers. The larger he exernaliy β, he more uiliy he adverisers obain by conacing more users. From lemma D.1 and lemma D., he plaforms se negaive prices on he users side if he nework exernaliy is large enough. 5 Compeiion beween Two Free Plaforms In secion 4 we proved ha he plaforms opimal sraegy is o subsidize he end users and charge o he adverisers since he adverisers care abou he number of users very much bu no vice versa. Even if i is because we have he assumpion of 0 marginal cos and ge he resul of price being below 0, we could also ge negaive price if we have marginal cos low enough, which is very hard o implemen in realiy. In his secion, we impose he consrain of non-negaive prices and analyze he case when he plaforms charge a 0 price o he users. We use he same se up as in secion 4 excep ha he 1

24 users pay a 0 price. A user locaed a x [0, 1] ges uiliy: A x if he only joins plaform A, u = B (1 x) if he only joins plaform B, A + B C if he joins boh plaforms. () When plaforms charge prices Q A and Q B o he adverisers, he uiliy of an adveriser locaed a y [0, 1] is given by (). 5.1 Compeiion wih Muli-homing no Allowed As in secion 4, he marke coverage and marke sharing condiion on he users side is saisfied if A B < A + B, and he number of users on he wo plaforms are respecively: n A = 1 + A B, n B = 1 A B. If A B, plaform A covers he whole marke of he end users side and plaform B has no sale. The adveriser joins he plaform if i obains a posiive uiliy on his plaform. The numbers of adverisers on he wo plaforms are respecively: { } { } βna Q A βnb Q B m A = min, 1, m B = min, 1. The plaforms are exclusive on he users side so ha here is no compeiion beween hese wo plaforms on he adverisers side. In he second sage, plaform A which provides a higher qualiy produc has an advanage on he adverisers side; i charges a higher price and obains more demand han plaform B. 16 Lemma. The equilibria oucomes wih prevenion of muli-homing on he users side are as follows: 1. If is large, i.e, if β+ β +16β(A B) < A + B, boh plaforms have 8 marke share beween 0 and 1, and Q A = β (A B + ), 4 m Q B = β (B A + ), 4 m A = β (A B + ), 4 π B = β (B A + ), 4 π 16 The deailed analysis can be found in Appendix E. A = β 16 (A B + ) ; B = β 16 (B A + ).

25 . If is medium, i.e, if A B < β+ β +16β(A B) 8, all adverisers join plaform A and some of hem also join plaform B, and Q A = β (A B + ), m A = 1, π A = β (A B + ) ; Q B = β (B A + ), 4 m B = β (B A + ), 4 π B = β 16 (B A + ).. If is small, i.e, if A B, all adverisers join plaform A and plaform B has no marke share, and Q A = β, m A = 1, π A = β. As in he basic model, wih an increase of qualiy difference A B, firm A s price and profi increases while firm B s decreases. The inuiion is ha, he larger he qualiy advanage of firm A, he larger he marke share i has on he users side, hence he more valuable is his plaform from he adverisers poin of view. Therefore i can charge a higher price and obain a higher profi. In he equilibrium wih marke sharing, each plaform s price and profi decreases wih he degree of horizonal differeniaion (dq i /d < 0, dπ i /d < 0). There is no compeiion on he adverisers side hence each plaform has monopoly power on he access o is own subscribers. Boh he monopoly price and monopoly profis are decreasing wih. The similar resul could be obained if we have differen differeniaion coss for he end users and adverisers (i.e, if 1 ). Each plaform s price decreases wih 1 and is profi decreases wih 1 and. Indeed, he monopoly price does no depend on he differeniaion cos on he adverisers side bu he number of subscribers is decreasing wih 1 ; he monopoly profi is decreasing wih he differeniaion cos on he adverisers side. 5. Compeiion wih Muli-homing Allowed Once prices have been se in he second sage, he users will join boh plaforms if hey obain posiive uiliy on each of hem. We only consider he case < A + B C so ha here exiss a pure sraegy equilibrium on he users side. If > A C, he numbers of users on he wo plaforms are respecively: n A = A C and n B = B C. If B C < A C, all users join plaform A and some of hem also join plaform B. If B C, all users join boh plaforms. The adverisers care only abou he oal number of users who see he adverisemen. Therefore he single-homing users are more valuable o he