Intermediated vs. Direct Sales and a No-Discrimination Rule

Transcription

1 BGPE Discussion Paper No 131 Inermediaed vs Direc Sales and a No-Discriminaion Rule Sebasian Wismer January 013 ISSN Edior: Prof Regina T Riphahn, PhD Friedrich-Alexander-Universiy Erlangen-Nuremberg Sebasian Wismer

2 Inermediaed vs Direc Sales and a No-Discriminaion Rule Sebasian Wismer This version: January 013 Firs version: February 01 Absrac When sellers join a plaform o sell heir producs, he plaform operaor may resric heir sraegic decisions In fac, several plaform operaors impose mos-favored reamen or no-discriminaion rules NDRs, asking sellers no o offer beer sales condiions elsewhere In his paper, I analyze a model ha allows for an endogenous spli-up of consumers beween sales channels Compeing sellers migh se differen prices across channels, depending on he plaform ariff and presence of a NDR I find ha he plaform operaor imposes a NDR if he faces high ransacion coss, if seller compeiion is weak, and if he iniial disribuion of consumers on channels is srongly skewed Prohibiing NDRs can have boh posiive and negaive effecs on welfare Keywords: Inermediaion, Plaform pricing, No-discriminaion rule JEL classificaion numbers: D40, L4, L81 I am graeful o Norber Schulz and Peer Welzel for insighful guidance and coninuous encouragemen I also hank Florian Englmaier, Johannes Muhers, and paricipans of he 39h Annual Conference of he EARIE Rome, 01 and he 13h BGPE research workshop for helpful commens Bavarian Graduae Program in Economics, Universiy of Wuerzburg, Indusrial Economics, Sanderring, Wuerzburg, Germany, sebasianwismer@uni-wuerzburgde

3 1 Inroducion Sellers ofen simulaneously use several ways of disribuion or sales channels o reach consumers Differen channels are likely o differ in ransacion coss Furhermore, each consumer s willingness o pay for a specific produc may depend on he channel used for purchase Consequenly, sellers usually face incenives o se differen prices across channels 1 However, if a seller joins a markeplace offered by an inermediary, he inermediary may resric he seller s pricing decisions More specifically, an inermediary who has some marke power may prohibi sellers offering cusomers beer sales condiions elsewhere, in paricular selling he same produc a a lower price in oher sales channels, by imposing a mos-favored reamen or no-discriminaion clause For example, HRS, he leading German online hoel reservaion plaform, only liss hoels which agree o offer he bes room raes and mos favorable booking condiions on he HRS plaform Several oher online ravel agens eg Bookingcom and Expedia limi hoels decisions on room raes in a similar way Furhermore, in May 010, Amazon s European plaforms inroduced a price pariy rule where hey ask sellers who offer heir producs in Amazon s markeplaces no o se lower prices for hese producs elsewhere A similar rule has applied o he US markeplace Amazoncom for several years Boh Amazon s price pariy rule and he mos-favored reamen clauses imposed by HRS and oher plaforms of online ravel agens jus recenly became subjecs of liigaion In all cases described above, many sellers or hoels 3 wan o be lised on a plaform, in paricular o reach consumers who migh no search for hem ouside he respecive plaform A he same ime, hey also offer producs ouside he plaform using heir own sores/websies or acceping direc requess from poenial cusomers The plaform charges sellers considerable fees/commissions primarily based on ransacion volume, whereas direc sales ypically generae differen coss Under a no-discriminaion rule NDR, sellers prices usually canno reflec all cos differences Therefore, consumers who come o know ha a seller uses several sales channels do no inernalize differences in coss when choosing in which channel o buy as he zero price difference does no signal cos advanages This problem can become even more severe if consumers are likely o search for offers in alernaive channels of he same provider afer hey found a maching produc in one channel: if sellers are free o se differen prices across channels, hey can seer consumers o he mos profiable channel, in conras o he siuaion under a no-discriminaion rule However, compeing sellers may no perfecly inernalize consumers channel preferences and he inermediary s coss when seing heir prices 4 Therefore, i is naural o ask abou he con- 1 Wolk and Ebling 010 find ha sellers indeed pracice channel-based price differeniaion Cf Office of Fair Trading 01, Bundeskarellam 01, injuncion agains HRS s mos-favored reamen clause Higher Regional Cour Duesseldorf, file no 33 O 16/1, and appendix, p 6 3 In he following, I use he erms no-discriminaion rule NDR and sellers also as represenaives for mosfavored reamen clauses and hoels, respecively 4 Furhermore, if he plaform provides useful services eg deailed produc informaion, reviews, reducion of search coss which require invesmens by he inermediary bu also promoe direc sales, his phenomenon

4 sequences of no-discriminaion rules on seller behavior, he spli-up of consumers beween channels, and he inermediary s decision on fees charged o sellers and buyers However, o dae, here is no sudy ha explicily addresses hese consequences 5 In his paper, I analyze a framework of a dominan inermediary who offers sellers a plaform o reach consumers Sellers serve horizonally differeniaed producs and compee wih each oher Each seller can offer her respecive produc boh direcly and in he markeplace operaed by he inermediary Consumers apply a sequenial decision rule: hey compare producs based on prices in one of he wo sales channels, choose heir preferred produc, and hen decide in which channel o buy In paricular, his assumpion inroduces a cerain spillover effec beween channels: being acive in one channel can lead o addiional sales in he oher channel 6 Taken ogeher, I analyze a model ha allows for an endogenous spli-up of consumers beween channels wih compeing sellers who migh se differen prices across channels In his model, boh consumers and sellers decisions are affeced by he ariff chosen by he inermediary and his decision on imposing a no-discriminaion rule Firsly, I find ha wihou a no-discriminaion rule he division of he inermediary s fee beween sellers and buyers does no affec he spli-up of consumers beween channels: sellers fully inernalize ransacion-based fees charged o consumers when seing heir prices 7 Wihou a no-discriminaion rule, each seller s channel-dependen prices generally differ from each oher The price difference reflecs cos differences, relaive imporance of each channel for produc choice, and differences in consumers channel valuaions, resuling in a redisribuion of consumers beween channels Secondly, if he inermediary imposes a no-discriminaion rule, his ariff sysem is no longer neural Furhermore, when deciding wheher o join he plaform, sellers rade-off he coss of providing a cerain amoun of heir produc over he plaform wih he benefis of reaching addiional consumers on he plaform The inermediary imposes a nodiscriminaion rule if his coss for processing a ransacion are relaively high, if seller compeiion is weak, and if he iniial disribuion of consumers on channels is srongly skewed in paricular, if mos consumers produc choice is based on prices on he plaform If hese crieria are me, each seller s incenives o specialize on direc sales under a no-discriminaion rule are relaively weak Hence, he inermediary prefers imposing a no-discriminaion rule, charging fees ha are compaible wih all sellers being acive on his plaform, o no imposing a no-discriminaion rule Each seller s ouside opion, specializing in direc sales and refusing o join he plaform, implies less consumers being aware of her respecive offer However, which basically causes a free-riding effec can lead o an inefficienly low level of such invesmens 5 Aguzzoni e al 01 offer an up-o-dae review of he lieraure on price relaionship agreemens and heir poenial effecs, indicaing ha here is no sudy ha examines such agreemens in inermediaed markes For more deails, cf he lieraure secion below 6 This effec someimes called billboard effec seems naural and is well-known a leas in he hoel indusry, cf eg Anderson 011 Furhermore, he assumpion on sequenial consumer decisions seems plausible as consumers rarely compare all prices of several producs across channels For a relaed empirical analysis of consumer search behavior across online book sores, cf eg De Los Sanos, Horaçsu and Wildenbees 01 7 Noe ha his neuraliy propery does no necessarily hold for membership fees which consumers migh pay up fron as hese can lead o an unravelling problem, cf Gans 01 and my lieraure review 3

5 specializaion would also have a posiive effec on seller profis: besides saving relaively high plaform fees, i may relax seller compeiion Welfare implicaions depend on he difference beween he inermediary s perransacion coss and he coss sellers incur when selling direcly o buyers, he disribuion of consumers heerogeneous valuaions across channels, and he size of he iniial fracion of plaform consumers Wihou a no-discriminaion rule, boh an over- and an underuse of he plaform channel can arise Imposing a no-discriminaion rule always resuls in an underuse of he inermediary s markeplace; his is due o he basic inefficiency caused by he inermediary having marke power Consequenly, prohibiing no-discriminaion rules can have boh posiive and negaive effecs on welfare, even in a framework ha excludes boh service argumens and foreclosure effecs Relaed lieraure Considering he erminology used boh by compeiion auhoriies and in my inroducion erms like no-discriminaion rules and mos-favored cusomer clauses, a firs view my work may be seen as closely relaed o he lieraure on cerain price relaionship agreemens in which a seller guaranees cusomers no o offer beer condiions o any oher cusomer across-cusomers agreemens or mos-favored cusomer clauses or no o offer condiions worse han hose offered by compeiors across-sellers agreemens like low-price guaranees 8 However, he presen sudies focus on sellers who direcly gran heir cusomers some guaranee, excluding any form of inermediaion beween hose wo groups, while I analyze a specific form of a mos-favored reamen clause imposed by an inermediary who offers a markeplace bu does no conrol prices of he raded goods In paricular, Aguzzoni e al 01, who summarize poenial effecs of price-relaionship agreemens PRAs, poin ou ha hey have no found any economic lieraure ha specifically sudies he possible compeiion effecs of hird-pary PRAs 9 Furhermore, hey sae ha o dae h[e] lieraure [on wo-sided markes] does no sudy he compeiive effecs of across-plaforms pariy agreemens 10 In line wih he firs saemen, I am no aware of any sudy ha specifically analyzes an inermediary s decision on imposing a no-discriminaion rule or concluding an acrossplaforms pariy agreemen in a framework wih imperfecly compeing sellers who may se differen prices across channels However, across-plaforms pariy agreemens exhibi a leas some similariies wih so-called no-surcharge rules which paymen card neworks as a specific kind of plaform operaors may impose Before reviewing relaed work on card neworks and no-surcharge/no-discriminaion rules, I firsly address sudies on wo-sided 8 In paricular, boh across-cusomer and across-seller agreemens can faciliae collusion cf eg Cooper, 1986; Neilson & Winer, 1993; Schnizer, 1994; Hviid & Shaffer, 010 Furhermore, price-maching guaranees may be used o signal a low price level eg Moorhy & Winer, 006 or o deer enry eg Arbaskaya, Aguzzoni e al 01, p84 Third-pary PRAs include across-plaform pariy agreemens which are concluded beween sellers and a plaform operaor and limi sellers pricing decisions 10 Aguzzoni e al 01, p96 4

6 markes and plaform pricing Plaform markes The classical lieraure on wo-sided markes 11 eg Roche & Tirole, 006; Armsrong, 006 basically discusses a plaform s pricing behavior in reduced-form models ha capure nework effecs hrough he number of members on he oher side of he plaform Accordingly, each player s uiliy depends on everyone s joining decision However, in he canonical models, uiliy does no depend on oher decision variables of any member of he wo sides of he marke, in paricular no on seller pricing in case of a rade plaform However, here are a few recen excepions which discuss proporional fees and, herefore, endogenize seller pricing Shy & Wang, 011; Miao, 011; Wang & Wrigh, 01; Muhers & Wismer, 013 Neverheless, hese sudies do no allow for sellers bypassing he plaform direc sales or any oher form of compeiion beween plaforms In conras, Gans 01 analyzes a framework where a single seller conen provider can reach consumers users of a mobile plaform boh in an inermediaed marke and ouside he markeplace He finds ha he plaform provider canno charge membership fees o consumers up fron as he faces an unravelling problem Imposing a mos-favored cusomer clause may miigae his problem, enabling he plaform provider o charge posiive membership fees o consumers Paymen card neworks, inerchange fees, and he no-surcharge rule NSR During he las decades, a considerable amoun of sudies focussed on he analysis of paymen card neworks Alhough here are differen nework srucures, all models share some basic feaures When a consumer wans o purchase a produc from a seller and i comes o paying, he consumer usually has a leas wo opions: card or cash paymen assuming ha he seller acceps and he consumer carries boh means of paymen Boh sellers and consumers may pay differen kinds of fees o accep/carry and o use debi or credi cards As he ariff sysems of card neworks ypically comprise ransacion-based componens, sellers may have incenives o se prices based on he paymen mehod used, discriminaing beween differen means of paymens by surcharging or graning discouns However, card neworks may impose no-surcharge or no-discriminaion rules, prohibiing hose pracices 1 11 Jullien 01 offers a comprehensive up-o-dae survey on wo-sided BB plaforms, including a general inroducion o wo-sided markes 1 Legislaion on he NSR considerably differs across counries In he EU, imposing a NSR is prohibied: The paymen service provider shall no preven he payee from requesing from he payer a charge or from offering him a reducion for he use of a given paymen insrumen European Commission, 007a, aricle 53, meanwhile implemened by all Member Saes However, surcharging may be generally prohibied NSR imposed by law his is he case in 10 saes of he US and several counries in Europe eg Ausria, Ialy, Sweden faciliaed by he Paymen Services Direcive which also saes ha Member Saes may forbid or limi he righ o reques charges aking ino accoun he need o encourage compeiion and promoe he use of efficien paymen insrumens In mos saes of he US, card neworks are free o impose a NSR 5

7 My work may be seen as a conribuion o his srand of lieraure: sales channels correspond o differen means of paymen and he plaform operaor plays he role of a uniary card nework, or, in case of a four pary model, he role of an issuer who possesses marke power and can se boh buyer fees and he inerchange fee which is passed hrough by compeiive acquirers In he following, I survey several models of paymen card neworks and some empirical insighs on no-surcharge rules 13 As a precursor of he lieraure on wo-sided markes, Roche and Tirole 00 discuss he inerchange fee ie, he ransacion-based paymen beween issuing and acquiring bank in a four pary credi card nework Acquiring banks are assumed o be perfecly compeiive, seing he seller fee/discoun equal o he sum of inerchange fee and heir per-ransacion coss Issuing banks have marke power and se boh he inerchange fee and he consumer fee, playing he balancing plaform role Two sellers serve cardholders and non-cardholders, compeing à la Hoelling and seing he same price o boh cusomer groups Under he no-surcharge rule, he inerchange fee/seller discoun is se equal o or above he efficien level, possibly leading o an overprovision of card paymen services Alhough he main analysis is conduced under he NSR, Roche and Tirole argue ha lifing he NSR would imply neuraliy of he inerchange fee sellers simply pass coss hrough and price-discriminae and would lead o an underprovision of card services Consequenly, he welfare implicaion of lifing he NSR is ambiguous However, he nework s decision on imposing a NSR remains unexplored Focussing on he poenial neuraliy of inerchange fees, Gans and King 003 explain ha he inerchange fee does no affec he marke oucome under paymen separaion, ie, if sellers can perfecly price-discriminae beween cash-paying consumers and card users, or if each seller only serves one of he wo groups Langle and Uhlenbrock 011 analyze he deerminaion of he seller fee under he NSR when consumers pay no fees They assume ha here are wo disinc groups of fixed exogenous sizes: card users and cash-paying consumers In a framework of differeniaed Berrand compeiion beween wo sellers, hey analyze how he proporion of card users and demand parameers affec he opimal seller fee Bourreau and Verdier 010 demonsrae ha a paymen plaform may se a low inerchange fee o deer a seller, who compees wih anoher seller à la Hoelling, from bypassing he plaform by issuing privae cards As he issuing seller can charge a fee for using her privae card, hey implicily allow for price discriminaion beween users of he privae card and all oher cusomers cash-paying or non-privae card users However, he second seller canno price-discriminae in heir framework, and he sudy does no offer a comparison beween uniform pricing and surcharging/price discriminaion Wrigh 003 analyzes inerchange fees and he adopion of a NSR based on he framework inroduced by Roche and Tirole 00 However, Wrigh assumes ha seller pricing is 13 Verdier 011 offers a good survey of he lieraure on inerchange fees The Repor on he reail banking secor inquiry European Commission, 007b offers empirical insighs ino he European banking sysem, in paricular card paymen arrangemens and inerchange fees 6

8 eiher monopolisic or perfecly compeiive He finds ha wih a monopoly seller, he NSR is boh profiable o he card associaion and socially desirable as i diminishes oherwise excessive surcharging by he seller and also limis he inerchange fee ha he seller is willing o accep o he efficien level Wih perfec compeiion beween sellers, boh a social planner and he card nework are indifferen beween allowing sellers o price discriminae and imposing he NSR Furhermore, he level of he inerchange fee becomes irrelevan; under he NSR, sellers specialize on eiher cash-paying consumers or card users, seing heir respecive price equal o heir perceived per-ransacion coss Schwarz and Vincen 006 analyze he NSR when a paymen nework faces a single monopoly seller Unlike Wrigh 003, Schwarz and Vincen ake each consumer s paymen mode as exogenously given wo groups of consumers wih fixed sizes, bu ransacion quaniies are variable elasic demand They find ha under he NSR he paymen nework prefers a price srucure wih low consumer fees In general, he paymen nework prefers he NSR, o he derimen of cash-paying cusomers and he seller The overall effec on welfare depends on he proporion of card users relaive o cash users, he feasibiliy of graning consumers rebaes charging negaive fees, and he seller s benefi from card vs cash ransacions Economides and Henriques 011 analyze he no-surcharge rule in a classic wo-sided marke framework, offering a microeconomic foundaion of nework effecs They allow for various forms of seller compeiion/marke power by assuming ha, wihou a NSR, he price of a good equals a linear combinaion of consumers willingness o pay and seller s perceived marginal coss seller fee minus individual benefi from card paymen Alhough his assumpion seems fairly general, i may also cause some problems wihin he given framework: firsly, as heir assumpion rules ou any sraegic effecs of card accepance, sellers only accep cards if heir per-ransacion benefi exceeds he seller fee Therefore, perceived marginal coss are negaive in equilibrium and seller s surcharge for card paymens is always negaive, ie, cash prices are higher han card prices Secondly, prices may become negaive if sellers have lile marke power and he absolue value of he perceived coss is high The empirical sudies of Bol, Jonker and van Renselaar 010 and Jonker 011 examine he surcharging behavior of Duch reailers NSRs are prohibied in he Neherlands and he corresponding consumer responses They find ha abou 0% of all sellers indeed price discriminae by surcharging card ransacions Jonker poins ou ha sellers become more likely o accep card paymens wih increasing compeiion, while surcharges increase in heir marke power However, i urns ou ha he majoriy of consumers ries o avoid surcharges eiher by choosing differen means of paymen or by visiing anoher sore Alogeher, alhough some sudies on paymen card neworks provide insighs ino he effecs caused by NSRs, mos work focusses on he inerchange fee Despie some general heoreical analogies beween NSRs and oher across-plaforms pariy agreemens, he work surveyed above presumes a specific indusry srucure Furhermore, i includes several limiaions The sudies mos closely relaed o my work are Roche and Tirole 00, Wrigh 7

9 003, and Schwarz and Vincen 006 Roche and Tirole do no focus on NSRs, and, hence, do no analyze he inermediary s decision o impose a NSR Wrigh only allows for exreme forms of seller compeiion Schwarz and Vincen analyze a framework wihou seller compeiion and wih an exogenous spli-up beween card users and cash users, bu allow for elasic demand Ouline The remainder of he paper is srucured as follows: in secion, I inroduce he framework In secion 3, I solve he model backwards, comparing sellers decisions wih and wihou a no-discriminaion rule, and analyzing he inermediary s decision on imposing a nodiscriminaion rule In secion 4, I discuss welfare implicaions of no-discriminaion rules Finally, I give a discussion in secion 5 and some concluding remarks in secion 6 Framework I consider a framework wih hree sellers 14 who can become acive in wo sales channels: a plaform or markeplace 15 provided by an inermediary, and a direc sales channel Each seller offers a single produc possibly using boh channels Producs are horizonally differeniaed: hey are equidisanly locaed on he circumferences of wo Salop circles 16 Each Salop circle represens one sales channel Sellers face linear producion coss The coss no including plaform fees ha boh channels have in common are normalized o zero I assume ha sellers incur addiional perransacion coss for processing sales ouside he plaform; his cos difference parameer is denoed by c 17 The inermediary provides a plaform and can charge sellers and buyers per-ransacion fees if rade akes place in his markeplace The seller fee is denoed by f s, and he buyer fee is called f b The inermediary bears coss of k for each ransacion conduced over his plaform Consumers apply a sequenial decision rule In a firs sep, hey selec heir favorie produc based on he prices observed in one of he wo sales channel In a second sep, hey buy one uni of he seleced produc, using he channel ha yields he highes individual ne uiliy I assume ha consumers are heerogeneous in hree independen dimensions Firsly, hey can be divided ino wo disjunc groups: a mass of consumers searches for producs ouside he plaform and selecs heir favorie produc based on prices in he direc sales channel d The remaining mass, labeled M m, chooses heir respecive favorie produc 14 I choose hree sellers o allow for a racable analysis of asymmeric scenarios wih one seller specializing on a single sales channel 15 In he following, I use he erms plaform and markeplace inerchangeably 16 I use wo circles o allow asymmeric scenarios wih a differen number of sellers in each channel If all sellers are acive in boh channels, boh circles are idenical and, hence, one circle would suffice o describe horizonal produc differeniaion For he basic model of a circular marke, cf Salop Noe ha his cos difference does no accoun for he seller fee inroduced below 8

10 based on he prices which he sellers charge wihin he inermediary s markeplace m Then, he assumpion on sequenial consumer decisions creaes a spillover effec beween channels: consumers search for producs and learn abou exisence in heir respecive channel i {d,m}, bu may buy in he oher channel j {m,d}, j i This implies ha i no selling in channel i resuls in losing all poenial buyers from group i mass M i is no aware of produc/seller exisence, and ha ii i may be profiable o se a relaively low price in channel i and a higher price in channel j i, aracing consumers in channel i who may finally buy in channel j if hey like channel j much beer, or, cross-subsidizing beween channels ha differ in perceived coss Secondly, consumers differ in heir aiude owards horizonal produc characerisics: consumers choosing heir favorie produc in channel i {d, m} are uniformly disribued on he circumference of he respecive Salop circle for channel i If a consumer who is locaed a x buys from a seller who is locaed a y on he circumference of he Salop circle ha belongs o he consumer s channel, he consumer incurs quadraic ransporaion or mismach coss of dx, y, where dx, y min { x y,1 x y } equals he shores quadraic disance beween he consumer s and he seller s locaion 18 The parameer can be inerpreed as a measure of sellers marke power Thirdly, consumers obain heerogeneous benefis from using he plaform insead of he direc sales channel 19 All consumers are assumed o have he same iniial reservaion value r before ransporaion coss for buying a produc in he direc sales channel The addiional benefis from plaform usage may be posiive or negaive and are disribued according o a differeniable cumulaive disribuion funcion F v 0 Hence, he uiliy of a consumer who is locaed a x and buys from a seller who is locaed a y is given by r p d dx, y if he buys a a price of p d, using he direc sales channel, or by r + v p m dx, y if he buys a a price of p m in he markeplace Timing The iming is given as follows: 1 The inermediary decides on imposing a no-discriminaion rule and ses corresponding per-ransacion fees f s and f b 18 While a linear disance funcion would also be feasible, he quadraic one ensures exisence of pure-sraegy equilibria in he pricing game also in asymmeric scenarios where one of he sellers serves a single sales channel 19 A leas a cerain degree of household heerogeneiy seems reasonable For empirical evidence on heerogeneous channel valuaions of households, cf eg Chinaguna, Chu and Cebollada 01 0 As pars of he analysis require a concree specificaion of his disribuion, I laer will assume ha he addiional benefis follow a uniform disribuion wih k c v, v, where [v, v ] denoes he suppor 9

11 Sellers disribuion and pricing decisions: i Sellers simulaneously choose in which channels o offer heir producs 1 ii Sellers simulaneously se channel-dependen prices 3 Consumers sequenial buying decisions: i Consumers decide which produc o buy based on prices in he channel ha corresponds o heir respecive group M i, i {d,m} ii Consumers buy one uni of he chosen produc, using he bes sales channel The price ha seller k {1,,3} charges in channel i {d,m} will be denoed by p k,i If he inermediary imposes a no-discriminaion rule, sellers are no allowed o discriminae beween channels, ie, each seller charges a uniform price p k I assume ha sellers and he inermediary maximize heir expeced profis, ie, hey are risk neural Consumers maximize heir individual surplus All ouside opions are normalized o zero In order o ensure exisence of pure-sraegy equilibria in ou-of-equilibrium pricing subgames where one seller specializes on a single sales channel, I resric he raio beween he ex-ane consumer masses: M m 1 8,8 3 Analysis In he following, I solve he model inroduced in he previous secion for he case of a symmeric Nash equilibrium wihin he pricing subgame all sellers being acive in boh sales channels Wihin he analysis of sage, I examine sellers pricing decisions, firsly wihou a no-discriminaion rule, hen under a no-discriminaion rule I show ha no seller has an incenive o be acive in only one channel wihou a no-discriminaion rule under a mild regulariy condiion If he inermediary imposes a no-discriminaion rule, his ariff reflecs he sellers paricipaion consrains Finally, I analyze he inermediary s decision on imposing a no-discriminaion rule 31 Consumers sequenial buying decisions Decision on sales channel Given his individual addiional uiliy v from buying producs on he plaform, a consumer who seleced seller k s produc, k {1,,3}, prefers buying ouside he plaform ie, in he direc channel if r p k,d r + v f b p k,m, 1 During he following analysis, I focus on cases wih all sellers being acive in boh sales channels, ie, I ensure ha a unilaeral specializaion on a single sales channel is no profiable o any seller I absrac from monioring problems and sellers aemps no o comply wih an imposed NDR as plaform operaors can easily observe sellers prices in oher online channels and, moreover, can invie/incenivize consumers o repor non-conform seller behavior examples include Amazon s Tell us abou a lower price funcion and heir Price Check app, or HRS s money-back guaranee 10

12 or, equivalenly, if v f b + p k,m p k,d Hence, if a uni mass of consumers wans o buy produc k and he respecive seller is acive in boh channels, a expeced mass of Pr v f b + p k,m p k,d =F f b + p k,m p k,d buys ouside I presume full marke coverage, ie, r being sufficienly high Selecion of favorie produc Each consumer s selecion of his respecive favorie produc wihin a given channel i {d, m} follows he basic Salop model Consumers locaions x [0,1 are denoed by he lengh of he circumference beween hem and he locaion of seller 1 s produc, measured clockwise Hence, he locaion of seller 1 s produc is defined as x 1 = 0, he locaion of seller s produc is x = 1 3, and seller 3 s produc is locaed a x 3= 3 Firsly, I analyze a siuaion of all hree firms being acive in channel i A consumer belonging o mass M i, i {d,m}, who is locaed a x [ 0, 1 ] is indifferen beween seller 1 s and seller s produc if his locaion x fulfills 1 p 1,i + x = p,i + 3 x x= p,i p 1,i A consumer who is locaed a x [ 1,1 is indifferen beween seller 1 s and seller 3 s produc if his locaion x fulfills p 1,i + 1 x = p 3,i + x x= p1,i p 3,i Accordingly, given he price of seller k and he prices of he wo oher sellers l 1 and l, a fracion of chooses he produc of seller k q k,i p 1,i, p,i, p 3,i = pl 1,i + p l,i p k,i If only wo sellers, wihou loss of generaliy labeled and 3, are acive in channel i and are equidisanly locaed on he respecive circumference, i is sraighforward o show ha a fracion of chooses he produc of seller k l 3 q k,i p,i, p 3,i = 1 + pl,i p k,i 3 Sellers disribuion and pricing decisions Pricing decisions under full paricipaion wihou NDR If all sellers are acive in boh channels, he overall mass of consumers who buy from seller k equals Q k p d, p m q k,d p d + M m q k,m p m, 3 If k and l are asymmerically locaed on he circumference, he slope of q k,i changes; in paricular, if hey are locaed as in he case wih hree sellers eg a x k = 1 3 and x l = 3, i follows q k,i p k,i, p l,i = pl,i p k,i 11

13 wih p i p 1,i, p,i, p 3,i, i {d,m}, defined as price vecors As he spli-up beween channels is deermined by he sum of he buyer fee f b and he price difference p k p k,m p k,d, seller k s expeced profi can be wrien as π k p d, p m Q k p d, p m {F f b + p k p k,d c+1 Ff b + p k p k,m f s } 4 In a symmeric equilibrium wih p 1,i = p,i = p 3,i, i {d,m}, he wo firs order condiions π k p k,i = 0, i {d,m}, imply 5 M p k = f s c+ d +M m F f b + p k 1 f f b + p k This equaion implicily defines he equilibrium price difference p k Taking a closer look a he criical level of addiional plaform benefi ṽ f b + p k, I arrive a he following resul: Proposiion 1 No wo-sidedness wihou NDR As long as sellers are acive in boh channels and are free o se differen prices across channels, he allocaion of consumers beween boh channels only depends on he overall fee f b + f s, bu no on is spli-up beween sellers and buyers As he overall number of ransacions is fixed I assume ha he willingness o pay r is sufficienly high and sellers fully inernalize he impac of heir decision on he division of sales beween channels, he allocaion of fees does no maer and he inermediary s fee srucure feaures neuraliy 6 Hence, resricing he analysis by an assumpion on he disribuion F is wihou loss of generaliy regarding he ambiguous spli-up of fees beween sellers and buyers However, i resrics he pass-hrough rae, ie, how sellers reac o a change of he overall fee Neverheless, I make he following assumpion for he sake of racabiliy: Assumpion 1 Addiional plaform benefis are uniformly disribued Addiional plaform benefis follow a uniform disribuion wih suppor [v, v] The difference beween inermediary s and seller s coss, k c, is conained in his suppor 7 In he subsequen analysis, I refer o he respecive cumulaive uniform disribuion funcion by F u, and o he respecive densiy funcion by f u, indicaing use of assumpion 1 8 Given his assumpion, equaion 1 can be solved for p k : 9 p k = 1 + M m v v+ v+f s f b c 4 I assume ha he disribuion represened by F is such ha all opimizaion problems are well-behaved In paricular, his is he case under assumpion 1 5 All derivaions and proofs are relegaed o he appendix 6 Noe ha his resul is in line wih previous lieraure, also cf my lieraure review 7 The assumpion k c v, v ensures ha neiher of boh sales channels is redundan from a social poin of view Noe ha he suppor may conain negaive values Hence, k c < 0 is no ruled ou 8 Sellers pricing decisions under a no-discriminaion rule can be calculaed wihou assumpion 1; prices in absence of a no-discriminaion rule and he inermediary s ariff decisions explicily rely on his assumpion 9 During he subsequen analysis, I assume ha he difference f b + f s c is such ha he indifferen consumer defined in 3 lies wihin v, v The opimal fees indeed fulfill his condiion, cf he analysis of sage 1 1

14 This implies ha he indifferen consumer beween boh channels is characerized by he criical level of addiional plaform benefi ṽf b + f s = 1 + M m v v+ v+ f b + f s c, 3 which reconfirms he neuraliy of he fee srucure Furhermore, as he criical level of addiional uiliy from plaform use is increasing in boh fees, and, in paricular, in he seller s perceived difference of ransacion coss, f b + f s c, less consumers use he plaform if fees are increased or sellers face lower coss c Moreover, he ex-ane disribuion of consumers beween channels affecs he equilibrium spli-up: he more consumers search for heir favorie producs on he plaform, he larger he mass of plaform buyers for a given fee level The laer fac reflecs ha sellers incenives o se lower prices o arac consumers in a channel become sronger if he relaive mass of consumers in his channel who can be allured increases I will come back o his channel imporance effec wihin he following discussion of sellers pricing decisions Lemma 1 Pricing wihou NDR under uniformly disribued plaform benefis Wihou a no-discriminaion rule, if all sellers are acive in boh channels, prices are given by p k,m = f s+ 9 + F uṽf b + f s f b+f s c v v v, 4 + M m v v and p k,d = c+ 9 { 1 F u ṽf b + f s } f b+f s c v + M m v v v v 5 Noe ha hese prices reflec boh compeiion beween sellers wihin each channel and compeiion across channels The firs wo summands of each price equal he respecive price ha would arise in an independen marke wih hree sellers, offering differeniaed producs and compeing à la Salop The hird summand of each price capures how sellers inernalize ha he disribuion of consumers beween channels is affeced by he price difference If he M ex-ane fracion of consumers in he direc sales channel, d, does no coincide wih he +M m relaive spli-up ha would resul jus from he difference beween he overall plaform fee f b + f s and ouside coss c, prices differ from he basic prices c+ 9 and f s+ 9, respecively: Corollary 1 Benchmark: independen-markes pricing The prices defined by equaions 4 and 5 coincide wih he respecive prices ha would resul M in wo independen markes wih compeiion à la Salop if d +M m = f b+ f s c v v v Corollary Benchmark: uniform pricing Sellers volunarily se uniform prices if f s c = fb + f s c v v v +M m v v However, noe ha he level of p k,m is somewha arbirary as for any given overall fee f b + f s, every disribuion of his overall fee on sellers and buyers resuls in he same payoffs for all agens Furhermore, aking a closer look a prices, I find ha he deviaion from independen-markes pricing in fac consiues a cross-subsidizaion beween channels wih no effec on he seller s overall profis: 13

15 Proposiion Cross-subsidizaion and seller s expeced profis If all sellers are acive in boh channels, each seller s profi equals he sum of he basic Salop profis, + M m 7 Hence, he loss from deviaing from independen-markes pricing in one channel is compensaed by he gains from he higher price in he oher channel If he mass of consumers who choose heir preferred produc in he direc sales channel is relaively large, his amplifies he effec of a change in p d relaive o he effec of a change in p m Hence, if he direc sales channel is relaively imporan for produc choice, compeiion becomes relaively fiercer in his channel, bu more relaxed in he plaform channel, and vice versa The combinaion of horizonal produc differeniaion wih uni demand and uniformly disribued consumers implies ha he wo effecs lower prices in one channel, bu higher prices in he oher one cancel ou and overall profi equals he basic Salop profi Before urning o sellers pricing decisions under a no-discriminaion rule, I make he following mild assumpion o ensure ha specializaion on a single sales channel is never profiable o a seller wihou a no-discriminaion rule: Assumpion Differeniaion parameers and ex-ane disribuion of consumers The raio beween he range of addiional plaform uiliies, v v which measures heerogeneiy of consumers ases regarding sales channels, and he ransporaion cos parameer which capures differences in consumers ases regarding producs is relaively small, given he ex-ane disribuion of consumers beween channels represened by γ M m : v v v v 3+γ 15+8γ 1+γ 15+13γ 15γ+8 +3γ 18γ, 6 1+γ γ 15γ Proposiion 3 Specializaion on a single sales channel is no profiable wihou NDR Wihou a no-discriminaion rule, a unilaeral specializaion on a single sales channel is no profiable o a seller, given assumpions 1 and Noe ha assumpion consiss of wo sufficien condiions which ensure ha specializaion is no profiable o a seller, 30 even under exreme fee levels ha would maximize specializaion incenives If a seller specialized on channel i {d,m}, his would relax compeiion in channel j {m,d}, j i, and, hence, he remaining sellers would increase prices in his channel, indirecly increasing he overall price level and, in paricular, prices in channel i Specializaion is mos aracive if produc differeniaion is small, ie, compeiion wihin channels is fierce, 30 The upper bound for he raio v v in condiion 6 akes is minimum value a γ=1507, and he upper bound in condiion 7 akes he same minimum value a γ=

16 given differeniaion beween channels as measured by v v and consumers relaive exane disribuion on channels, capured by γ The effecs of seller specializaion under a no-discriminaion rule are discussed below Pricing decisions under full paricipaion and NDR In his paragraph, I consider sellers pricing decisions under a no-discriminaion rule wih all sellers being acive in boh channels Seller k s profi, given he vecor p = p 1, p, p 3 of uniform prices, equals π k p Q k p {p k F f b c 1 Ff b f s }, where he overall mass of consumers who buy from seller k under uniform pricing equals 1 Q k p + M m pl 1 + p l p k Accordingly, under uniform pricing, he spli-up of consumers beween channels only depends on he buyer fee f b and is no affeced by sellers pricing decisions as p k = 0 Proposiion 4 Pricing decisions and expeced profis under NDR Under a no-discriminaion rule, each seller ses a price of 9 + F f b c + 1 F f b f s if all sellers are acive in boh channels The corresponding profi is given by + M m 7 Sellers prices reflec heir average coss Due o he mode of compeiion, he assumpion on inelasic demand, and he linear srucure addiive addiional benefis from plaform use in combinaion wih sequenial consumer decision, sellers profis under a nodiscriminaion rule wih full paricipaion equal he profis wihou no-discriminaion rule, alhough sellers canno price-discriminae Pricing under NDR when one seller does no serve plaform consumers In order o check when serving only he direc sales channel is profiable o a seller, I calculae he profi of a seller who specializes on his channel when he oher sellers are acive in boh channels and a no-discriminaion rule is imposed 31 Aferwards, I compare his profi wih he equilibrium profi repored in proposiion 4, deriving a seller paricipaion consrain Suppose seller 1 does no offer her produc in he markeplace Then, her profi from serving only consumers in he direc sales channel is given by 1 π 1 p= p+ p 3 p 1 p 1 c 31 A specializaion on plaform sales would only be profiable if f s was below a hreshold smaller han c cf he condiion derived in appendix, p 34 Such a small fee would never be opimal for he inermediary as he would gain from higher fees due o higher per-ransacion revenues and a larger mass of poenial cusomers in case he seller does no specialize on plaform sales 15

17 The profi of seller who faces wo compeiors in he direc sales channel and only one compeior in he markeplace reads 3 1 π p= p1+ p 3 p 1 + M m + p3 p Defining {p F f b c 1 Ff b f s } {p F f b c 1 Ff b f s } γ M m 8 as he raio beween he masses of consumers in he markeplace and he direc sales channel, calculaing sellers bes responses, and insering hem ino each oher leads o p1 dev = 1+ 5γ 15+8γ 9 + c γ 1 Ff b f s c, γ and p dev = p3 dev = 1+ 10γ 15+8γ 9 + c γ 1 Ff b f s c 10 These prices consis of a markup erm and a weighed average of he respecive seller s own average coss and he compeiors average coss The markups can be undersood as follows: when seller 1 specializes on one channel, his relaxes compeiion beween sellers and 3 in he oher channel Therefore, sellers and 3 face incenives o se higher markups in he markeplace compared o a siuaion where all hree sellers are acive in boh channels As hey can only se uniform prices, his implies ha sellers and 3 se higher markups in boh channels In response, seller 1 also increases her markup, bu o a lesser exen Comparing he profi of he specialized seller and he profi of a seller if all sellers are acive in boh channels, I arrive a he following resul: 33 Proposiion 5 Non-profiabiliy of unilaeral specializaion on direc sales channel When a no-discriminaion rule is imposed and all oher sellers are acive in boh channels, specializaion on he direc sales channel is no profiable o a seller if 15+8γ 1 Ff b f s c 9 1+γ 15+13γ 11 3+γ Noe ha he righ-hand side of condiion 11 is sricly posiive for γ>0and sricly increasing in γ There are hree effecs ha arise if he seller specializes on ouside sales: i Reduced mass of poenial cusomers: he seller loses all poenial cusomers who selec heir favorie produc on he plaform ii Less compeiive pressure: due o relaxed compeiion wihin he plaform, all prices include higher markups under specializaion 3 This profi is calculaed under he assumpion ha he disance beween sellers and 3 on he Salop circle ha represens he plaform equals 1 The derivaion for locaions corresponding o he scenario wih hree sellers can be found in he appendix; my resuls are robus agains changes in he locaions of he remaining wo sellers 33 Again, his resul remains qualiaively unchanged when locaions of sellers and 3 in he plaform channel correspond o heir locaions in he oher channel, cf p 34 16

18 iii Cos savings: all consumers who choose he specialized seller s produc buy direcly from he seller This reduces he seller s coss: wihou specializaion, a fracion of 1 F f b would buy using he plaform, creaing addiional coss for he seller of f s c per ransacion 34 Accordingly, specializaion is only aracive if relaively few consumers selec heir favorie produc on he plaform γ is small, if he ransporaion cos parameer is relaively small fierce seller compeiion/weak produc differeniaion, or if he seller fee f s drasically exceeds he coss c of a direc ransacion 33 Inermediary s decision on fees and NDR In he following, I firsly derive he inermediary s profi-maximizing fee and he corresponding profi if he does no impose a no-discriminaion rule Secondly, I calculae he maximum profi he can achieve when imposing a no-discriminaion rule, aking ino accoun consrain 11 which ensures paricipaion of all sellers in boh channels Finally, I analyze his decision on imposing a no-discriminaion rule by comparing boh profi levels boh calculaed for he case of uniformly disribued addiional plaform benefis Profi-maximizing fee level wihou NDR Given assumpions 1 and, wihou imposing a no-discriminaion rule, all sellers are acive in boh channels, regardless of he fees se by he inermediary The number of ransacions conduced over he inermediary s plaform equals +M m {1 F u ṽf b + f s }, wih ṽf b + f s as defined in 3 under he uniform disribuion assumpion His profi comprises his ransacion volume and his margin f b + f s k, and i is given by Π 0 f b, f s = + M m {1 F u ṽf b + f s } f b + f s k Bearing in mind proposiion 1, ie, he spli-up of f b + f s beween buyers and sellers being arbirary wihou a no-discriminaion rule, I arrive a he following resul: Lemma Profi-maximizing fee level wihou NDR Wihou imposing a no-discriminaion rule, he inermediary achieves a maximum profi of v v Π 0 = 1+γ by seing a fee level of f b + f s = c+ v+ k c v + v v γ { 1 1 F u k c+ 1 } 1 1+γ The opimal fee level is increasing in average ransacion coss, in boh he level and he spread of addiional uiliy from plaform usage, and in he raio γ defined in 8 which can be inerpreed as imporance of he plaform for produc choice 34 In his verbal discussion, I implicily assume ha f s > c The opimal plaform fee indeed exceeds c if addiional plaform uiliies are likely o be posiive; oherwise f s c can be negaive, bu relaively large compared o he level of negaive addiional plaform uiliies, cf he subsequen analysis 17

19 Corollary 3 Channel allocaion wihou NDR When he inermediary does no impose a no-discriminaion rule, he indifferen consumer beween channels is given by A fracion of F u ṽ 0 = { 1 ṽ 0 = v γ } v v+ k c v γ k c v of all consumers buys in he direc sales channel v v The fracion 1 F u ṽ 0 of consumers who buy in he markeplace is decreasing in he relaive cos difference capured by F u k c= k c v and increasing in γ The laer fac can v v be explained as follows: he larger γ, he lower sellers plaform prices compared o prices in he direc sales channel, and, hence, he higher he fracion of consumers buying over he plaform Profi-maximizing fees under NDR If he inermediary imposes a no-discriminaion rule, buyers channel choices are no affeced by he prices ha sellers charge assuming full marke coverage Consequenly, he inermediary s profi wih uniform prices and full seller paricipaion reads Π 1 f s, f b = + M m 1 F u f b f b + f s k 14 Lemma 3 Profi-maximizing fees under NDR and full seller paricipaion When imposing a no-discriminaion rule, he inermediary can achieve a profi of v v Π 1 = 1+γ { v v } 15+8γ 1+γ 15+13γ F uk c 9 3+γ 15 by seing a buyer fee of and a seller fee of f b = k c + v γ fs = c+ 1+γ 15+13γ 9 3+γ 1 Ff b 17 The inermediary ses his seller fee f s such ha consrain 11 binds, 35 while he buyer fee f b is se o achieve he profi-maximizing spli-up of buyers beween channels Corollary 4 Channel allocaion under NDR When he inermediary imposes a no-discriminaion rule, he indifferen consumer beween channels is given by ṽ 1 = f b as defined in 16 Consequenly, a fracion of F uṽ 1 = k c v v v of all consumers buys in he direc sales channel If he inermediary imposes a no-discriminaion rule, he fracion 1 F u ṽ 1 of consumers who buy in he markeplace only depends on he disribuion of addiional plaform benefis 35 Noe ha he inermediary s profi is increasing in f s as long as all sellers remain acive on he plaform, cf equaion 14 I focus on symmeric oucomes wih all sellers being acive on he plaform 18

20 and he cos difference k c Again, i is decreasing in he relaive cos difference F u k c= k c v v v ie, in paricular, decreasing in he inermediary s coss k and increasing in sellers coss c However, he spli-up does no depend on γ as he effec of he ex-ane consumer disribuion is absorbed by he seller fee f s bu does no ener f b Inermediary s decision on imposing a NDR Comparing profis 1 and 15, I can sae he following resul: Proposiion 6 Profiabiliy of imposing a NDR The inermediary decides o impose a no-discriminaion rule if 15+8γ 1+γ 15+13γ v v 9 3+γ { > 1 1 F u k c+ 1 } 1 1+γ 1 F uk c 18 Condiion 18 comprises hree facors ha influence he profiabiliy of imposing a nodiscriminaion rule: i he raio beween produc differeniaion parameer as an inverse measure of seller compeiion and spread of addiional plaform benefis v v as a measure of channel differeniaion, ii he relaive cos difference F u k c difference in per-ransacion coss relaive o consumers addiional plaform benefis, iii he iniial spli-up of consumers on sales channels γ as a measure of imporance of he plaform for produc choice An increase in he firs facor,, makes imposing a no-discriminaion rule relaively more v v profiable: if sellers face weaker compeiion ie, a higher level of, he equilibrium spliup of consumers on sales channels, and, moreover, he inermediary s profi wihou a nodiscriminaion rule remain unchanged However, an increase in diminishes sellers specializaion incenives, relaxing heir paricipaion consrain, and, hereby, increasing he inermediary s profi under a no-discriminaion rule 36 An increase in he second facor, F u k c, always resuls in lower plaform profis However, he profi under a no-discriminaion rule and he profi wihou a no-discriminaion rule are affeced o differen exens, changing he difference beween hem, and, hence, araciveness of imposing a no-discriminaion rule More specifically, he inermediary s margin in equilibrium responds in he same way, regardless of his decision on a no-discriminaion rule, bu he channel spli-up characerized by he indifferen consumer is less sensiive o a change in coss in absence of a no-discriminaion rule as he price difference p k implies a lower pass-hrough rae Since sellers prices are also driven by he channel imporance effec wihou a no-discriminaion rule, he overall effec of a change in F u k c depends on γ: if γ and F u k c are small, an increase in F u k c makes imposing a no-discriminaion 36 Noe ha I consider a change in his facor solely due o a change in A change in v v affecs F u k c, oo 19

21 rule less aracive, while for high levels of F u k c and/or γ, an increase in he relaive cos difference makes imposing a no-discriminaion rule more aracive 37 The effec of he hird facor, he raio beween he iniial mass of plaform consumers and consumers in he direc sales channel, is driven by wo forces: under a no-discriminaion rule, γ limis he seller fee, while wihou a no-discriminaion rule, γ disors he price difference since i deermines relaive compeiive pressure wihin each channel While he lef-hand side of condiion 18 is only slighly concave ie, close o linear in γ, he righ-hand side has a more concave shape Depending on he firs wo facors, wo scenarios can be disinguished: a Imposing a no-discriminaion rule is profiable regardless of he level of γ his is he case if is relaively large weak seller compeiion and/or F u k c akes an exreme level in paricular, if he inermediary faces relaively high coss b Imposing a no-discriminaion rule is profiable only for exreme ie, low or high levels of γ his is he case if is relaively small and F u k c does no ake exreme levels in paricular, F u k c no close o 1 38 Taking a closer look a he inermediary s profis, he impac of he parameer γ can be undersood as follows: on he one hand, wihou a no-discriminaion rule, sellers prices in he direc sales channel are relaively low compared o prices in he markeplace for small levels of γ as in hese cases he direc sales channel is relaively more imporan for consumers produc choice Therefore, only few consumers buy using he plaform channel because of he large price difference p k = p k,m p k,d ha arises if γ is small Accordingly, he inermediary s profi wihou a no-discriminaion rule is increasing in γ, and an increase in γ makes imposing a no-discriminaion rule less aracive On he oher hand, an increase in γ diminishes sellers specializaion incenives, relaxing he paricipaion consrain ha limis he inermediary s seller fee when he imposes a no-discriminaion rule Therefore, an increase in γ also leads o an increase in he inermediary s profi under a no-discriminaion rule, and imposing a no-discriminaion rule becomes more aracive For very small levels of γ ie, M m, imposing a no-discriminaion rule, balancing he equilibrium channel spli-up despie a very skewed iniial spli-up of consumers on sales channels, is very aracive When increasing γ saring from a small level, he firs effec increase in profi wihou no-discriminaion rule dominaes, and, hence, imposing a no-discriminaion rule becomes less aracive for inermediae values of γ ie, M m However, for larger values of γ ie, M m, he second effec increase in profi under nodiscriminaion rule due o relaxed paricipaion consrain dominaes, and imposing a nodiscriminaion rule becomes more aracive again In paricular, scenario b demonsraes ha boh forces can be decisive 37 Formally, he righ-hand side of condiion 18 is increasing in F u k c if F u k c< 1+γ 1, and decreasing in F u k c oherwise 38 For example, for he parameer consellaion v v = 1, = 1, F u k c=05, imposing a no-discriminaion rule is profiable if γ<05067 or γ>3614, also cf figure 1 0

22 F u k c NDR Γ v v = 085 F u k c NDR Γ v v = 1 F u k c NDR Γ v v = 115 Figure 1: Profiabiliy of imposing a no-discriminaion rule for differen raios of v v Focussing on scenario b, figure 1 illusraes under which combinaions of he second facor F u k c and he hird facor γ he inermediary imposes a no-discriminaion rule for differen levels of he differeniaion raio : for all parameer consellaions wihin he v v shaded regions ie, ouside he convex whie regions, he inermediary prefers o impose a no-discriminaion rule 4 Welfare implicaions I now urn o he welfare implicaions of imposing a no-discriminaion rule I illusrae ha under cerain parameer consellaions, he inermediary imposes a no-discriminaion rule, maching he socially desirable oucome regarding he no-discriminaion rule However, under differen parameer consellaions, a ban on no-discriminaion rules would increase welfare Social welfare comprises he inermediary s profi, sellers profis, and consumer surplus Firsly, he inermediary imposes a no-discriminaion rule only if his is profiable o him Secondly, wih all sellers remaining acive on he plaform under a no-discriminaion rule, sellers profis are consan, irrespecive of he inermediary s acual decision on imposing a no-discriminaion rule Therefore, wihin he given analysis, indusry profis never decrease if he inermediary decides o impose a no-discriminaion rule If he spli-up of consumers beween channels did no change when imposing a nodiscriminaion rule, he inermediary would gain solely o he derimen of consumers As all consumers gross uiliies would remain unchanged, social welfare would remain consan However, he indifferen consumer beween he wo channels is deermined endogenously and usually differs beween boh scenarios no-discriminaion rule imposed/no imposed Hence, given he assumpion of markes being fully covered, he allocaion of consumers on channels deermines he overall effec on welfare Lemma 4 Firs-bes oucome The welfare-maximizing oucome is characerized by he indifferen consumer ṽ = k c 1

23 From a social poin of view, consumers should buy using he plaform channel if and only if heir addiional benefi from plaform use covers he cos difference k c Comparing he channel allocaion in he firs-bes oucome wih he allocaion under a no-discriminaion rule given by corollary 4, I can sae he following resul: Corollary 5 Underuse of plaform channel under NDR Under a no-discriminaion rule, he plaform channel is underused, ie, 1 F u ṽ >1 F u ṽ 1 This resul follows direcly from he assumpion ha k c v, v and is due o he monopoly inefficiency which is refleced in he profi-maximizing buyer fee f given in 16 b Wihou a no-discriminaion rule, here may be an overuse or an underuse of he plaform channel: Corollary 6 Plaform use wihou NDR In absence of a no-discriminaion rule, he plaform channel is underused if and only if F u ṽ < M m Conversely speaking, wihou a no-discriminaion rule, he plaform is overused in case of a very high cos difference k c which equals ṽ and a large iniial fracion of plaform consumers capured by γ= M m In his exreme case, he channel imporance effec ie, sellers disoring plaform prices downwards due o a high γ overcompensaes he effec caused by he plaform s monopoly markup which only parially inernalizes he former effec Under all oher less exreme parameer consellaions, he mass of consumers who buy in he direc sales channel given by corollary 3 is excessive and he plaform is underused also in absence of a no-discriminaion rule Focussing on he laer cases, I find ha his underuse problem may be more severe han under a no-discriminaion rule, depending on he cos difference k c and he iniial spli-up of consumers on heir naive sales channels: Proposiion 7 Imposing a NDR increases social welfare Imposing a no-discriminaion rule resuls in more consumers buying in he plaform channel, and, hence, in an increase in social welfare if F u ṽ < +M m In absence of a no-discriminaion rule, he inermediary s opimal fee level only parially offses he channel imporance effec on final prices Consequenly, sellers discriminaing prices reflec his effec and he equilibrium spli-up of consumers on channels depends on he iniial channel disribuion In consras, under a no-discriminaion rule, he equilibrium spli-up of consumers on channels is solely deermined by he buyer fee se by he inermediary and reflecs his monopoly power, bu i does no depend on he iniial channel spli-up of consumers For large iniial fracions of consumers in he direc sales channels, plaform prices subsanially exceed prices in he direc sales channel in absence of a no-discriminaion rule, leading o lile plaform usage Imposing a no-discriminaion rule eliminaes his inefficien

24 price disorion If he ex-ane fracion of consumers in he direc sales channel exceeds he firs-bes fracion F u ṽ, his posiive effec dominaes he addiional monopoly inefficiency, resuling in a more efficien channel spli-up and higher welfare Connecing his resul and he discussion of proposiion 18, i is easy o consruc boh cases in which he inermediary profiably imposes a non-desirable no-discriminaion rule, and cases in which he inermediary imposes a no-discriminaion rule wih a posiive effec on social welfare In paricular, imposing a no-discriminaion rule is boh profiable o he inermediary and desirable from a social poin of view if seller compeiion is very weak ie, v v while he inermediary s relaive cos advanage is relaively large ie, F u k c is small Similarly, a no-discriminaion rule can be profiable and lead o more plaform use for inermediae levels of F u k c if only few consumers selec heir favorie produc on he plaform cf scenario b from profiabiliy discussion in previous secion In conras, a ban on no-discriminaion rules would be desirable if he plaform is very imporan for produc choice high level of γ while he inermediary faces a mild relaive cos disadvanage eg F u k c = In his case, he inermediary imposes a nodiscriminaion rule and ses a relaively high buyer fee, resuling in poor plaform usage If 3 he inermediary could no resric pricing, he would se a relaively high fee level, bu he srong channel imporance effec would drive sellers plaform prices down, reducing he price difference p k and leading o more plaform usage han under a no-discriminaion rule 5 Discussion As poined ou in he inroducion, several prominen inermediaries impose nodiscriminaion rules, resricing sellers pricing decisions However, before idenifying condiions under which an inermediary profis from imposing a no-discriminaion rule, and before discussing possible implicaions on welfare, i is necessary o undersand why sellers may wan o se differen prices across sales channels in he firs place Given he framework inroduced above, wihou a no-discriminaion rule, sellers prices firsly reflec he difference beween plaform fees and per-ransacion coss in he direc sales channel Secondly, he relaive imporance of channels for consumers produc choice, deermined by he ex-ane disribuion of consumers on sales channels, leads o pricing disorions whose exen depends on he degree of channel differeniaion For very skewed iniial consumer disribuions, prices in he channel in which mos consumers decide which produc o buy are lower han he respecive independen markes price, while consumers in he oher channel face a higher price level Thirdly, prices would be affeced if seller specializaion on sales channels arose However, under assumpion, specializaion on a single sales channel is never profiable wihou a no-discriminaion rule as produc differeniaion measured by is relaively large compared o channel differeniaion measured by v v Accordingly, if he inermediary does no resric sellers pricing decisions, he equilibrium spli-up of consumers on sales channels is deermined by he difference beween he 3

25 overall fee level and per-ransacion coss, channel differeniaion, and he iniial disribuion of consumers on channels In paricular, he inermediary has no direc conrol over he allocaion of consumers on channels In conras, if he inermediary imposes a no-discriminaion rule, he channel spli-up no longer depends on he price difference beween channels which would reflec he overall fee, bu only on he buyer fee Therefore, imposing a no-discriminaion rule resuls in he inermediary having more conrol However, as sellers now canno se relaively higher prices in he plaform channel in response o a high seller fee, consumers do no inernalize he differences in sellers channel-dependen per-ransacion expendiures when deciding in which channel o buy heir preferred produc Consequenly, sellers face sronger specializaion incenives, which limi he fee he inermediary can charge Taken ogeher, he inermediary prefers o conrol he spli-up of consumers on sales channels direcly by imposing a no-discriminaion rule if i he marke is characerized by a parameer consellaion ha resuls in an unfavorable equilibrium spli-up of consumers on sales channels from he inermediary s poin of view, and ii he coss due o he seller paricipaion consrain do no exceed he benefi from he improvemen of he spli-up on channels 39 In paricular, imposing a no-discriminaion rule is mos aracive if he iniial disribuion of consumers is srongly skewed: wih a very small iniial fracion of plaform consumers, only few consumers buy in he plaform channel due o he subsanial price difference p k, and imposing a no-discriminaion rule resuls in more plaform usage In conras, if mos consumers selec heir preferred produc on he plaform, sellers specializaion incenives are weak and he inermediary can charge high seller fees under a no-discriminaion rule while reducing he number of plaform ransacions direcly by charging a high buyer fee If he inermediary faces a relaively srong cos disadvanage ie, his per-ransacion coss are high compared o he coss ha a seller bears when selling in he direc sales channel, again, imposing a no-discriminaion rule is more profiable: less ransacions are conduced over he plaform, bu he inermediary gains due o a higher fee level In he laer case, a ban on no-discriminaion rules is likely o be welfare-enhancing as i resuls in more plaform usage, which improves he allocaion of consumers on sales channels excep for very exreme cases in which non-resriced pricing resuls in a relaively srong overuse of he plaform channel However, alhough no-discriminaion rules always lead o an underuse of he plaform channel compared o he firs-bes usage level, plaform usage can sill be lower wihou a no-discriminaion rule, and imposing a no-discriminaion rule is welfare-enhancing under cerain condiions 39 Noe ha he coss due o he limied seller fee can also become negaive if produc differeniaion measured by and/or plaform imporance, ie, γ, is large, meaning ha he inermediary can exrac a larger par of he sellers profis under a no-discriminaion rule 4

26 6 Concluding remarks and oulook By analyzing a framework in which compeing sellers can reach consumers hrough differen channels, his sudy yields insighs ino sellers pricing behavior and he division of sales beween channels Furhermore, i allows he examinaion of he ariff decision of a plaform provider and is impac on marke oucomes In paricular, boh profiabiliy and efficiency of no-discriminaion rules are discussed Depending on several facors imporance of he plaform for produc choice, sellers marke power, channel differeniaion, and cos differences, he plaform operaor decides in favor of or agains imposing a no-discriminaion rule As he effec of a no-discriminaion rule on efficiency desirable spli-up of consumers beween channels may be posiive or negaive, boh parameer consellaions under which he plaform operaor s decision o impose a no-discriminaion rule maches he socially desirable oucome and consellaions where i fails o mach he welfare-maximizing oucome can be idenified As Aguzzoni e al 01 indicae, so far here has no been any sudy explicily analyzing no-discriminaion rules or, more generally, hird-pary price relaionship agreemens in inermediaed markes Alhough pars of he subsanial work on paymen card neworks exhibi cerain heoreical analogies wih he framework inroduced in his sudy, ha lieraure focusses on a differen indusry srucure Even when absracing from he addiional bank level inermediaion, he sudies on no-surcharge rules show cerain limiaions ha resric applicabiliy on he cases menioned in he inroducion In conras o he sudies of Wrigh 003 and Schwarz and Vincen 006, my framework allows for imperfec merchan compeiion and accouns for he spillover effec whose presence seems reasonable in a muli-channel sales framework 40 and impacs boh specializaion incenives and price levels Alhough his sudy may also be seen as an exension o he lieraure on no-surcharge rules imposed by paymen card neworks, he main conribuion is he provision of a framework ha fosers he ongoing debae abou he effecs of across-plaforms pariy agreemens also called mos-favored reamen clauses or no-discriminaion rules on he use of differen rade opporuniies In paricular, i sheds ligh on he resricions which several prominen plaform operaors eg HRS, Bookingcom, Amazon use and which recenly became subjecs of liigaion However, his sudy only consiues a firs sep owards a beer undersanding of such pracices and absracs from several aspecs which may also affec oucomes in inermediaed markes Firsly, in his sudy, exisence of a direc sales channel inroduces compeiion beween channels, bu excludes sraegic ineracions beween muliple plaform operaors Fuure research could inroduce a second inermediary, analyzing he effecs on poenial 40 The spillover or billboard effec, ie, being acive in one channel affecs sales in he oher channel due o consumers endogenous decision where o buy heir preferred produc, has been documened a leas for he hoel indusry cf fn 6 Furhermore, i has also been used as an argumen wihin he opinion of he Higher Regional Cour Duesseldorf file no 33 O 16/1 on HRS s pracices 5

27 compeiion foreclosure effec of across-plaforms pariy agreemens or on acual compeiion beween wo esablished plaform operaors Secondly, if plaform operaors face invesmen coss o esablish heir plaforms or incur fixed coss o mainain or improve heir plaform services, imposing a no-discriminaion rule may also be seen as a means o miigae free-riding: wihou a resricion on sellers pricing decisions, consumers uilize plaform services o find heir preferred produc, bu may buy in anoher cheaper channel which does no offer any service This problem may lead o an underprovision of desirable services or, more generally, a lack of invesmen incenives If he inermediary gains from a cerain desirable invesmen under a no-discriminaion rule, bu canno recover his invesmen coss wihou imposing a pricing resricion, prohibiing such resricive pracices may resul in an inefficienly low invesmen level Thirdly, fuure research could exen his framework by allowing for differen ypes of plaform fees On he one hand, charging membership fees o consumers seems o be a heoreical opion, in paricular, as hese may miigae poenial free-riding problems However, none of he plaform operaors menioned in he discussion so far charges consumers non-zero membership fees, and charging membership fees may no be feasible due o several reasons eg consumers being uncerain abou he individual benefis of plaform services or commimen issues On he oher hand, fuure work could include proporional fees ie, royalies based on revenues as hese may induce addiional effecs of no-discriminaion rules on plaform profis In paricular, wih per-ransacion fees, he plaform operaor usually gains from cross-subsidizaion beween channels as his leads o more ransacions on his plaform However, if sellers cross-subsidizing leads o lower prices on he plaform, he effec on plaform profis may be less clear under proporional fees 7 Appendix Background: HRS s mos-favored reamen clause HRS s bes-price guaranee/mos-favored reamen clause HRScom, 01: In principle, HRS expecs is parner hoels o offer i he lowes room raes available The Hoel guaranees ha he HRS price is a pariy wih or lower han he lowes rae available for he Hoel on oher reservaion and ravel plaforms on he Inerne or on offer on he Hoel s own Web pages As reacions on HRS s aemp o exend his mos-favored reamen clause on prices a he recepion desk and warning non-complying hoels, he German Carel Office sared an invesigaion cf Bundeskarellam, 01, and he Higher Regional Cour Duesseldorf issued an injuncion agains warning leers ha base on he exended version file no 33 O 16/1 Background: Amazon s price pariy rule In he EU, Amazon inroduced a price pariy rule in May 010 Amazoncouk, 011: 6

28 since 1s May, we are asking sellers who choose o sell heir producs on Amazoncouk no o charge cusomers higher prices on Amazon han hey charge cusomers elsewhere Accordingly, sellers selling under he Amazoncouk markeplace Paricipaion Agreemen need o comply wih price pariy requiremens as se forh below Price pariy for hese sellers generally means ha he iem price and oal price oal amoun payable, including delivery charges bu excluding axes of each produc offered on Amazoncouk mus no be higher han he corresponding prices a which he seller or is affiliaes offers he produc on oher non-physical sales channels This general requiremen already applies o cerain produc caegories in he Amazoncouk, Amazonfr, and Amazonde markeplaces, and has applied o he US markeplace for several years As a direc reacion, many sellers announced ha hey would no longer sell on Amazon under a price pariy rule Furhermore, afer an injucion agains Amazon s price pariy, issued by he Disric Cour of Munich file no 37 O 7636/10, used books have been exemped from he price pariy rule in Germany According o several repors in he business press, here has also been a general invesigaion by he German Carel Office Bundeskarellam In response o a parliamenary quesion on concerns abou Amazon s price pariy rule, he European Commission saed Wills, 010: The Commission wishes o inform he Honourable Member ha he Commission follows very closely he developmens in he marke for he online sales of books and is aware of Amazon s price policy As regards compliance wih compeiion rules, Aricle 101 TFEU prohibis anicompeiive agreemens beween wo or more companies In his case, i concerns a unilaeral decision aken by Amazon Therefore, i appears ha Aricle 101 is no applicable Aricle 10 TFEU prohibis companies wih a dominan marke posiion from abusing heir posiion However, he Commission has no assessed wheher Amazon has a dominan posiion The Commission is hence no in a posiion a his sage o ake a view on wheher or no Amazon s price policy is in line wih EU compeiion rules Derivaions & Proofs Pricing decisions under full paricipaion wihou NDR, proof of proposiion 1 The derivaives of seller k s profi wih respec o p k,d and p k,m read Q k p d,p m {F f b + p k p k,d c+1 Ff b + p k p k,m f s } π k ={F f b + p k + f f b + p k p k f s + c} p k,d { 1 M m p l 1,m+ p l,m p k,m p } l 1,d + p l,d p k,d 3 {F f b + p k p k,d c+1 Ff b + p k p k,m f s } 7

29 and π k ={1 Ff b + p k f f b + p k p k f s + c} p k,m { 1 M m p l 1,m+ p l,m p k,m p } l 1,d + p l,d p k,d 3M m {F f b + p k p k,d c+1 Ff b + p k p k,m f s } In a symmeric equilibrium wih p k,i = p l,i, he firs order condiions become and {F f b + p k + f f b + p k p k f s + c} {M m + } = 9 {F f b + p k p k,d c+1 Ff b + p k p k,m f s } 19 {1 Ff b + p k f f b + p k p k f s + c} {M m + } = 9 M m {F f b + p k p k,d c+1 Ff b + p k p k,m f s } 0 and he second equa- Seing equal he equaions which resul afer dividing he firs equaion by ion by M m yields which is equivalen o {F f b + p k + f f b + p k p k f s + c} M m+ = {1 Ff b + p k f f b + p k p k f s + c} M m+ M m, F f b + p k + f f b + p k { p k f s + c}= Applicaion of he implici funcion heorem proves proposiion 1: p f s = p f b = + M m p = f f b+ p+ f f b + p{ p+ c f s } f s = f f b + p f b = f f b + p+ f f b + p{ p+ c f s } f s p f b p = 1 f f b + p{ p+ c f s } {f f b + p+ f f b + p{ p+ c f s }} = 1 f f b + p{ p+ c f s } {f f b + p+ f f b + p{ p+ c f s }} As he indifferen consumer beween channels is given by ṽ = f b + p, i follows ha ṽ f b = ṽ f s Hence, if f b + f s = cons, a marginal shif beween f b and f s does no change ṽ, and he spli-up of consumers beween markeplace and direc sales channel remains unchanged 8

30 Prices under uniformly disribued plaform benefis full paricipaion, no NDR Bringing ogeher equaion 1 and assumpion 1, i follows ha p k = f s c+ +M m f b+ p k v v v 1 v v p k = 1 + M m v v+ v+f s f b c, which confirms equaion Plugging p k ino he firs order condiion wr p k,d, ie, equaion 19, leads o This is equivalen o 1 { f b + + M m v v+ v+f s f b c = p k,m f s v v { f b + 1 v v+ v+f s f b c + M m 1 v v+ v+f s f b c + M m 4 + M m v v x + M m v v+ x v+ c f s } M m+ 9 } v +c f s = p k,m f s v v, 9 wih x = v f s f b +c Solving for p k,m, aking ino accoun ha F u ṽf b + f s = ṽf b+f s v, wih ṽf v v b + f s as defined in equaion 3, yields 4; 5 follows from p k,d = p k,m p k Proof of proposiion In he symmeric equilibrium derived above, each seller s profi equals π = M m {F u ṽf b + f s p k,d c+1 F u ṽf b + f s p k,m f s } Insering equilibrium prices 4 and 5 leads o π 3 = F u ṽf b + f s + M m 9 { 1 F u ṽf b + f s } f b+f s c v + M m v v + 1 F u ṽf b + f s 9 + F uṽf b + f s f b+f s c v + M m v v This simplifies o 3 π +M m = 9 Hence, equilibrium profi equals 7 + M m v v v v Proof of proposiion 3 Firsly, I show ha specializaion on he direc sales channel is no profiable wihou a NDR, given condiion 6 in assumpion If seller 1 specializes on he direc sales channel while sellers and 3 are acive in boh channels, wihou a NDR, profis read and 1 π 1 = p,d + p 3,d p 1 p 1 c, { 1 π = p 1+ p 3,d p,d 1 + M m + p } 3,m p,m {F f b + pp,d c+1 Ff b + pp,m f s } 9

31 As before, p k p k,m p k,d, and γ M m The bes response of seller 1 can be calculaed as and The parial derivaives of π are π = 3 p,d p 1 p,d, p 3,d = 18 + c + p,d + p 3,d 4 {p,m f s Ff b + p p f s + c} { p 1+ p 3,d p,d 1 + M m + p } 3,m p,m F f b + p+ f f b + p p f s + c, π = M m {p,m f s Ff b + p p f s + c} p,m { p 1+ p 3,d p,d 1 + M m + p } 3,m p,m 1 Ff b + p f f b + p p f s + c Seing equal he las wo derivaives firs order condiions yields 1 F fb + p+ f f b + p p f s + c = 1 1 Ffb + p f f b + p p f s + c, 3 M m which is equivalen o 3 3+γ = F f b+ p+ f f b + p p f s + c Wih uniformly disribued plaform benefis, his leads o p = γ v v+ v+f s f b c From π p = 0 and symmery p,d,d = p 3,d, by insering seller 1 s bes response, i follows 3 { p+ p,d f s F u f b + p p f s + c} 1 = { c + p },d p,d + M m F u f b + p+ f u f b + p p f s + c This is equivalen o or 3 { p+ p,d f s F u f b + p p f s + c} { 5 = c 4 p,d + M } m F u f b + p+ f u f b + p p f s + c, p,d F u f b + p+ f u f b + p p f s + c { 5 = 36 + c 4 + γ } 6 F u f b + p+ f u f b + p p f s + c + 1 F u f b + p f s c p+c 30

32 This can be simplified as follows: c+ { } F u f b + p f u f b + pf s c p 56 +γ c + 1 F u f b + p f s c p p,d = 1+ 1 F 4 u f b + p f u f b + pf s c p fb + p v c+ f } s c p { 56 +γ 6 v v v v + c f b+ p v f v v s c p = fb + p v f s c p v v v v 4c v v + { p+f b + c f s v 56 +γ }+ 3 + c 4 v v f b + p v f s c p = 4v v+ p+f b + c f s v p+fb + c f s v 56 +γ v v f b + p v f s c p = c+ 4v v+ p+f b + c f s v 5+6γ = c+ 15+8γ 3 6+4γ 15+8γ γ v v v+f b+f s c 3 v v 3+γ v v +v f s f b + c Insering his price which equals p 3,d in equilibrium ino he bes response funcion, he price of seller 1 urns ou o be p 1 =c+ 5+6γ γ γ 15+8γ 1 1 Observing ha 5+6γ p,d p 1 = γ 15+8γ 6 } {{ } = 10γ 15+8γ γ 15+8γ γ v v v+f b+f s c 3 v v 3+γ v v v+f b+f s c v v he profi of seller 1 specializing on direc sales is given by π dev 1 = γ 15+8γ γ 15+8γ γ v v v+f b+f s c v v γ 15+8γ γ 15+8γ γ v v v+f b+f s c v v = γ 15+8γ γ 15+8γ 3 3+γ v v+ v f s f b + c γ v v v+f b+f s c v v 3 3+γ v v+ v f s f b + c, f b + f s c v 3 3+γ v v f b + f s c v 3 3+γ v v f b + f s c v 3 3+γ v v Specializaion on direc sales is no profiable if π dev 1 1+γ 7, which is equivalen o 15+13γ+9 3+γ γ v v + f b+f s c v f b+f s c v 3 3+γ v v v v 15+8γ 1+γ As p 1 c has o be posiive for π dev 1 being posiive his is an implici assumpion made above, specializaion is no profiable if 9 3+γ γ v v+ f b+f s c v fb + f s c v 3 3+γ v v v v 15+8γ 1+γ 15+13γ 31

33 This can also be wrien as [ v v fb + f s c+ v 9 3+γ v v 15+8γ 1+γ 15+13γ 3 3+γ 1 { }] fb + f s c+ v 9 v v 3+γ The lef-hand side of his inequaliy akes is maximum a f b + f s = c+ v+v v his fee level maximizes specializaion incenives Hence, he condiion is fulfilled whenever [ v v 9 γ 3+γ + 9 ] γ 1+γ 15+13γ, 3+γ which is equivalen o condiion 6 Along he same lines, i can be shown ha specializaion on plaform sales is no profiable o a seller, given condiion 7 in assumpion If seller 1 specializes on plaform sales, profis are as follows: 1 π 1 = M m p,m+ p 3,m p 1 p 1 f s, { 1 π = M m p 1+ p 3,m p,m p } 3,d p,d {F f b + pp,d c+1 Ff b + pp,m f s } Wih uniformly disribued addiional plaform benefis, he relevan prices under specializaion can be calculaed as p,m = f s + 5γ+6 15γ v v +3γ 8+15γ and p 1 = f s { 5γ+6 15γ v v +3γ 8+15γ +3γ v v+ f b+f s c v +3γ v v+ f b + f s c v +3γ v v f s f b + c+ v +3γ v v f s f b + c+ v Specializaion is no profiable o seller 1 if v v 9 +3γ +3γ fb + f s c+ v 1+γ 15γ+8 v v γ 15γ+13 The lef-hand side akes is maximum for f b + f s = c+v Hence, specializaion is never profiable under condiion 7, } Derivaion of prices under NDR when one seller specializes on direc sales Given he profi of seller 1, 1 π 1 p= p+ p 3 p 1 p 1 c, her bes response on prices p and p 3 can be calculaed as p1 dev p, p 3 = 18 + p + p 3 + c 4 Afer deriving he profi of seller, 1 π p= p1+p 3 p 1 + M m + p3 p {p F f b c 1 Ff b f s } {p F f b c 1 Ff b f s }, 3

34 i follows ha he respecive firs order condiion in an equilibrium ha feaures symmery beween sellers and 3, ie, p = p 3, is equivalen o = M m {F f b c+ 1 Ff b f s }+ + 3 M m + 9 p1 dev M m p dev Insering he bes response of seller 1 leads o p1 dev = 1+ 5γ 15+8γ 9 + c γ 1 Ff b f s c, 15+8γ and p dev = p3 dev = 1+ 10γ 15+8γ 9 + c γ 1 Ff b f s c, where γ= M m These prices indeed consiue an equilibrium if a unilaeral discree deviaion, in paricular undercuing he oher sellers o serve all consumers, is no profiable Wih quadraic ransporaion coss, a deviaion is no profiable if he calculaed prices imply posiive marke shares for all sellers, ie, As p dev > p dev p dev p1 dev < 4 1 = 36 9 p dev p1 dev = 5γ 15+8γ 6+4γ Ff b f s c, γ his condiion is equivalen o 1 Ff b f s c< 5γ 15+8γ 30+11γ 15+8γ 6+4γ 9 = 3+γ 9 This condiion is always fulfilled if boh specializaion on direc sales is no profiable condiion 11 and γ<8, cf he subsequen analysis Proof of proposiion 5 Insering he price difference given in equaion 1 and p dev 1 defined in 9 ino he profi funcion of seller 1, her profi can be rewrien as 15+13γ γ 1 6+4γ Ff b fs c 15+8γ If all sellers are acive in boh channels, each seller earns a profi of 1+γ 7 Consequenly, a unilaeral specializaion on direc sales is no profiable if 15+13γ γ 1 6+4γ Ff b fs c 1+γ 15+8γ 7 This condiion holds if condiion 11 is fulfilled As p dev 1 0, he second alernaive, is irrelevan 15+13γ 15+8γ 1 6+4γ Ff b fs c 1+γ, 15+8γ 9 Taking a closer look on he upper bound righ-hand side of condiion 11, i can be shown ha i does no exceed he upper bound given jus above in condiion if γ 8 Hence, condiion 11 ensures exisence of he asymmeric specializaion equilibrium as a non-profiable ouside opion 33

35 Condiion: Non-profiabiliy of unilaeral specializaion on plaform sales under a NDR Along he lines of he derivaion of he prices under NDR when one seller specializes on direc sales, he bes response of seller 1 can be calculaed as p1 dev p, p 3 = 18 + p + p 3 + f s 4 In an equilibrium ha feaures symmery beween seller and 3 ie, p = p 3, he firs order condiion which follows from he maximizaion of he profi of a non-specializing seller is equivalen o and { Md F f b c+ 1 Ff b f s + + 3M m + M m 3 + 3M } m p 1 = + 9 M m p + 3M m Insering he bes response of seller 1 leads o he prices p1 dev = γ f s+ 1 9γ+4 F f b c f s, 15γ+8 p dev = p3 dev = γ f s+ 1 3γ F f b c f s 15γ+8 The profi of seller 1 under specializaion equals 1 π dev 1 = M m γ+8 + F f b 6γ+4 15γ+8 c f s Consequenly, specializaion on plaform sales is no profiable under a NDR if F f b f s c 15γ γ 15γ+13, 3γ+ where he righ-hand side is sricly posiive for γ>0 if The calculaed prices under specializaion indeed consiue an equilibrium in he pricing game F f b f s c γ 4+6γ This condiion is implied by he non-profiabiliy condiion if γ 1 8 Quaniaive effec of a change in locaions of non-specialized sellers All profis in he main body are calculaed under he assumpion ha sellers are always locaed such ha he disance o heir nex compeior in clockwise order is he same as he disance o heir nex compeior in couner-clockwise order In paricular, if seller 1 specializes on channel j, he posiions of he non-specialized sellers and 3 fulfill x 3 x = 1 in channel i j, while he disance beween any wo sellers in channel j equals 1 3 If he non-specialized sellers and 3 are locaed as in he case wih hree sellers ie, a x = 1 3 and x 3 = 3, demand for produc k l in channel i equals q k,i p,i, p 3,i = pl,i p k,i Therefore, he relaxed compeiion effec is weaker han wih perfecly symmeric posiions where he facor ha is muliplied by he relaive price difference equals < 9 4, and he price increase due o specializaion is less pronounced Therefore, he condiion for specializaion on direc sales no being profiable is less demanding han before, making he no-discriminaion rule slighly 34

36 more aracive o he inermediary More specifically, if he locaions of he non-specialized sellers are he same in boh channels, regardless of he hird seller being presen, he upper bound on 1 Ff b f s c in condiion 11 becomes 10+6γ 1+γ 10+9γ 9 4+3γ However, all rade-offs remain qualiaively unchanged and, herefore, he resuls are robus agains changes in he locaions of he non-specialized sellers in he ouside opion scenario Proof of lemma Wihou a NDR, he inermediary s profi equals 1+γ {1 Fṽf b + f s } f b + f s k Wihou loss of generaliy, I se f b = 0 o calculae he opimal fee wihou a NDR he fee srucure feaures neuraliy Then, he firs order condiion wr f s is given by 1 F p k = f p k p k f s f s k Consequenly, wihou a no-discriminaion rule, given assumpion 1 and using definiion 8, he plaform operaor s profi is maximized by seing k c v f b + f s = c+ v+ + v v γ Given his fee level, he indifferen consumer beween channels, defined in 3, urns ou o be ṽf b + f s = v+ 1 1 k c v v v + 1+γ v v γ Hence, he maximal profi equals Π 0 = 1+γ {1 F u ṽf b + f s } f b + f s k { } k c v = 1+γ 1 4 v v γ = 1+γ 1 { k c v 1 v v 1 v v = 1+γ Proof of lemma 3 { 1 1 k c v c+ v+ } v v 1+γ F u k c+ 1 1+γ } + v v k c v v v γ γ k In order o maximize he profi given in 14, he inermediary ses he maximal seller fee ha is compaible wih paricipaion consrain 11, ie, 15+8γ fs = c+ 1+γ 15+13γ 9 3+γ 1 Ff b Insering his fee ino he inermediary s profi 14 yields 15+8γ Π 1 f b = + M m 1 Ff b c+ 1+γ 15+13γ 9 + f b k 3+γ 1 Ff b { } 15+8γ 1+γ 15+13γ = + M m Ff b f b k c 3+γ Under assumpion 1, his expression akes is maximum a f b level equals { Π 1 = M 15+8γ 1+γ 15+13γ v v d + M m γ 4 = k c + v The corresponding profi 1 F u k c } 35

37 Proof of proposiion 7 Imposing a no-discriminaion rule always resuls in an underuse of he plaform channel, cf corollary 5 However, imposing a no-discriminaion rule improves he allocaion of consumers on channels if 1 F u ṽ 1 >1 F u ṽ 0 ṽ 1 < ṽ 0 Comparing expressions 16 and 13, his is he case if k c + v { 1 < v γ } v v+ k c v, 4 or, equivalenly, if k c 4 < v γ v v F u k c< 1 1+γ = + M m from ØØÔ»»ÛÛÛºÓ Øº ÓÚºÙ» Ö Ó Ø»Ö Ö» References Aguzzoni, Ô» ÐÔ»Ù ØÓÑ Ö» ÔРݺ ØÑÐ ÍÌ ²ÒÓ Á ¾¼¼ ½¼ Ç Ì½ ºÔ from ØØÔ»»ÛÛÛº Ñ ÞÓÒºÓºÙ» L, Buccirossi, P, Ciari, L, Cors, K, Tognoni, M, Spagnolo, G & Viale, C, Zampa, G L, di Giò, A 01, Sepember Can fair prices be unfair? A review of price relaionship agreemens Rerieved Amazoncouk 011, Ocober Price pariy Rerieved Anderson, C K 011 Search, OTAs, and online booking: An expanded analysis of he billboard effec Cornell Hospialiy Repor, 118 Arbaskaya, M 001 Can low-price guaranees deer enry? Inernaional Journal of Indusrial Organizaion, 199, Armsrong, M 006 Compeiion in wo-sided markes The RAND Journal of Economics, 373, Bol, W, Jonker, N & van Renselaar, C 010 Incenives a he couner: An empirical analysis of surcharging card paymens and paymen behaviour in he neherlands Journal of Ô»ÈÖ»¾¼½¾»¾¼½¾¹¼¾¹½¼ ÈÊ ÀÊË ºÔ from ØØÔ»»ÛÛÛº ÙÒ ÖØ ÐÐ Ñغ»Û Ò Ð» ÓÛÒÐÓ» Banking & Finance, 348, Bourreau, M & Verdier, M 010 Privae cards and he bypass of paymen sysems by merchans Journal of Banking & Finance, 348, Bundeskarellam 01, February Bundeskarellam examines HRS bes price clause Rerieved Chinaguna, P K, Chu, J & Cebollada, J 01 Quanifying ransacion coss in online/offline grocery channel choice Markeing Science, 311, Cooper, T E 1986 Mos-favored-cusomer pricing and aci collusion The RAND Journal of Economics, 173,

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