Platform Competition in Two-Sided Markets

PLATFORMCOMPETITION IN TWO-SIDED MARKETS

Jean-CharlesRochet Jean Tirole Universite´ deToulouse, InstitutD’ EconomieIndustrielle, InstitutD’ EconomieIndustrielle Centred’ Etudes et de Recherches en AnalyseSocio-Economique

Abstract Manyif notmost markets with network externalities are two-sided. To succeed, platforms in industriessuch as software,portals and media, payment systems and the Internet, must “ get bothsides of the market on board.” Accordingly, platforms devote much attention to their businessmodel, that is, to howthey court each side while making money overall. This paper buildsa modelof platformcompetition with two-sided markets. It unveils the determinants ofprice allocation and end-user surplus for different governance structures (pro t-maximiz- ingplatforms and not-for-pro t jointundertakings), and compares the outcomes with those underan integrated monopolist and a Ramseyplanner. (JEL: L5, L82, L86, L96)

1. Introduction Buyers of video gameconsoles want games to play on; gamedevelopers pick platforms that areor will be popular among gamers. Cardholders value credit or debit cards only to the extent that these areaccepted by the merchants they patronize; afliated merchants benet froma widespread diffusion of cards among consumers. Moregenerally, many ifnot most marketswith network externalities arecharacterized by the presence of two distinct sides whose ultimate benet stems frominteracting through acommon platform. Platform owners or sponsors in these industries must address the celebrated “chicken- and-egg problem”and be carefulto “get both sides on board.”Despite much theoretical progress madein the last two decades on the economics of network externalities and widespread strategy discussions of the chicken-and-egg problem,two-sided marketshave received scant attention. The purpose of this paper is to start lling this gap. The recognition that many marketsare multisided leads to new and interesting positive and normative questions. Under multisidedness, platforms must choose aprice structure and not only aprice level fortheir service. For example, video gameplatforms such as Sony, Sega and Nintendo makemoney on game

E-mail addresses: Rochet: [email protected]; Tirole: [email protected]

©2003 by the European Economic Association Rochet and Tirole Platform Competition in Two-Sided Markets 991 developers through per-unit royalties on games and xed feesfor development kits and treatthe gamersside as aloss leader. Interestingly, operating system platforms forthe PCand handheld devices have adopted the opposite business model and aimat making money on consumers. The choice of abusiness model seemsto be key to the success of aplatformand receives much corporate attention. Table 1provides afewillustrations 1 of the two-sided marketsand shows that platforms often treatone side asapro tcenter and the other as aloss leader, or, atbest, as nancially neutral. Anumber of these illustrations are discussed in “mini case studies ” in Section 7. And Table 2lists afewimportant segments of the new economy that will be searching fora proper business model in the next fewyears. Such conventional wisdom about business models found in the trade press and summarizedin Table 1is of course subject to criticism. To reason in termsof pro tcenters, costs areoften “intuitively, ” but arbitrarily allocated to either side of the market.Yet, the conventional wisdom points at some morefundamental logic related to prices and surpluses on both sides of the market.A majorobjective of our paper is to unveil this logic and the determinants of the choice of abusiness model. Fromboth positive and normative viewpoints, two-sided marketsdiffer fromthe textbook treatmentof multiproduct oligopoly or monopoly. The interaction between the two sides gives riseto strong complementarities, but the corresponding externalities arenot internalized by end users, unlike in the multiproduct literature(the sameconsumer buys the razorand the razorblade). In this sense, our theory is across between network economics, which emphasizes such externalities, and the literatureon (monopoly or competitive) multiproduct pricing, which stresses cross-elasticities. For example, socially optimal “Ramsey” prices arenot driven solely by superelasticity formulaebut also re ecteach side ’scontribution to the other side ’s surplus. Some new questions raised by two-sided marketsare more speci c to the existence of competition between platforms. Inanumber of markets, afraction of end users on one or the two sides connect to several platforms. Using the

1. There are of course other illustrations, for example scienti cjournals, that must match readers and authors. Interestingly, the Bell Journal of Economics for anumber of years after it was launched was sent for free to anyone who requested it. There is currently much discussion of how the business model for scienti cjournals will evolve with electronic publishing. The list of social gatherings examples of cross-subsidization could be extended to include dating or marital agencies which may charge only one side of the market. Acouple of explanations regarding markets that will not be discussed in Section 7: Social gatherings: celebrities often do not pay or are paid to come to social happenings as they attract other participants (who may then be charged ahefty fee); similarly, in some conferences, star speakers are paid while others pay. Real estate:In many countries buyers are not charged for visiting real estate properties and thus marginal visits are heavily subsidized. Tobe certain, the sale price re ects the real estate agency fee, but this does not imply that the arrangement is neutral (see Section 8). Shopping malls :shoppers are subsidized. They don ’tpay for parking; in France they can also buy gasoline at asubstantial discount. Discount coupon books :These are given away to consumers. Intermediaries charge merchants for the service. Browsers:The picture given in Table 1is abit simplistic. In particular, Netscape initially made about one third of its revenue on the client side before giving the software away. But Netscape always viewed the software running on top of the operating system on the web servers as amajor source of pro t. 992 Journal of the European Economic Association June 2003 1(4):990 –1029

TABLE 1. ILLUSTRATIONSOF EXISTING BUSINESS MODELS

Loss leader/break-even Pro t-making segment/ Product segment/subsidized segment subsidizing segment Software Video games consumers (consoles) software developers Streaming media consumers servers Browsers users Web servers Operating systems (Windows; application developers (development clients Palm, Pocket PC) tools, support, functionality, ...) Text processing reader/viewer writer Portals and media Portals “eyeballs” advertisers Newspapers readers advertisers (Charge-free) TVnetworks viewers advertisers Payment systems Credit and differed debit cards cardholders merchants (Visa, MasterCard, Amex, . . . ) Online debit cards merchants cardholders Others Social gatherings celebrities in social happenings other participants Shopping malls consumers (free parking, cheap gas) shops Discount coupon books (Want consumers merchants Advertiser) (Legacy) Internet Web sites dial-up consumers Real estate buyers sellers

Internet terminology, wewill say that they “multihome.” For example, many merchants accept both AmericanExpress and Visa; furthermore,some consum- ershave both Amexand Visa cards in their pockets. Many consumers have the Internet Explorer and the Netscape browsers installed on their PC,and anumber of Web sites arecon gured optimally forboth browsers. Readers maysubscribe to multiple newspapers, B2B exchange membersmay buy or sell their wareson

TABLE 2. PROSPECTIVE APPLICATIONS Instruments of cost allocation or Platform Two sides cross-subsidization B2B buyers/sellers design of auctions, information ows Internet backbone services consumers/websites termination (settlement) charges Pools and standards relevant sides level of royalties, inclusiveness of pools Software as aservice consumers/application development tools and other efforts to create (.Net vs. Java) developers an applications development environment, backward compatibility, pricing Rochet and Tirole Platform Competition in Two-Sided Markets 993 several exchanges, and realestate sellers and buyers mayuse the services of multiple realestate agencies. Competitive prices on one marketthen depend on the extent of multihoming on the other side of the market.For example, when Visa reduces the (transaction-proportional) charge paid by the merchants, 2 merchants become moretempted to turn down the morecostly Amexcard as long as alarge fraction of Amexcustomers also owns aVisa card. More generally, multihoming on one side intensi es price competition on the other side as platforms use low prices in an attempt to “steer” end users on the latter side toward an exclusive relationship. 3 This paper studies how the price allocation between the two sides of the marketis affectedby a)platform governance (for-pro tvs. not-for-pro t), b) end users’ cost of multihoming, c)platformdifferentiation, d) platforms ’ ability to use volume-based pricing, e)the presence of same-side externalities, and f) platformcompatibility. Italso investigates how privately optimal pricing structures compare with socially optimal ones. The paper isorganized as follows. Section 2describes the simplest version of the model, in which end users incur no xed cost and platformpricing is linear on both sides of the market,and analyzes the (pro tmaximizerand Ramsey planner) monopoly benchmarks. Section 3derives equilibrium behavior when two (for-pro tor not-for-pro t)platforms compete. Section 4obtains some comparative statics in order tohelp predict the choice of business model. Section 5compares the price structures in the case of linear demands. Section 6generalizes the model and results in order to allow for xed user costs and nonlinear platformpricing. Section 7summarizesthe main results and provides seven “mini case studies ” to illustrate how our theory mayshed light on existing and future business models. Last, Section 8concludes with some general considerations about two-sided markets. As wediscussed, our work puts network economics and multiproduct pricing together. Fromthe early work of Rohlfs (1974) to the recenttheoretical advances and applications toantitrust through the pioneering work of Katzand Shapiro (1985, 1986) aswellas Farrelland Saloner (1985, 1986), alarge body of literaturehas developed on network industries. Tomakeprogress, however, this literaturehas ignored multisidedness and the price allocation question. In contrast, the competitive multiproduct pricing literature(e.g., Baumol, Panzar,

2. The mechanism through which this reduction operates is indirect and is described in section 7. 3. The occurrence of steering is easiest to visualize in those illustrations in which platforms charge per-end-user-transaction fees: The seller of ahouse or aB2Bsupplier may only list the house or the wares on the cheapest platform. In industries in which platforms do not charge per-end-user-transaction fees, steering is more subtle as it operates through effort substitution. For example, asoftware platform offering better software development kits, support, and application programming interfaces not only encourages the development of applications optimized to this platform, but is also likely to induce application developers to devote less attention to rival platforms. Aportal or TVnetwork ’scut in advertising rates induces advertisers to advertise more on their medium and to substitute away from other media. Ashopping mall ’scut in rental prices or improved layout may induce ashop to increase its size or appeal and lead the latter to neglect or abandon its outlets in rival shopping malls, and so forth. 994 Journal of the European Economic Association June 2003 1(4):990 –1029 and Willig 1982, Wilson 1993) has carefully described the interdependency of pricing decisions but it has not considered the af liation externalities that lie at the core of the network economics literature. In contrast with the buyer of a razor,who internalizes the impactof his purchase on the demand and surplus attached to razorblades, our end-users do not internalize the impact of their purchase on the other side of the market. Our paper is most closely relatedto the recenttheoretical literatureon chicken- and-egg problems. 4 This literaturehowever assumes either that there is amonopoly platform(Baye and Morgan 2001, Rochet and Tirole2002, Schmalensee 2002) or that platforms arefully interconnected (Laffont, Marcus, Rey, Tirole2003) and so end-users enjoy the samelevel of connectivity regardless of the platformthey select. Parkerand Van Alstyne (2000) study monopoly pricing inasituation in which the demand forone good depends (linearly) on its price and on the quantity of the other good sold. They characterizethe price structure as a function of the network externality coef cients. They then look atthe incentive of aproducer of agood to enter a(complementary or substitute) marketwith another incumbent producer. With complements, entry losses maybe pro table because entry puts pressure on price and boosts the pro tof the core business. Caillaud and Jullien (2003) study competition among intermediaries. In their model, platforms actas matchmakersand can use sophisticated pricing (regis- tration fees, and possibly transaction feesprovided the intermediaries observe transactions). Indeed, one of their contributions is toshow that dominant rms arebetter offcharging transactions ratherthan registrations when deterring entry. They also show that competition is moreintense when platforms cannot deter multihoming. Theircontribution iscomplementary to ours. For example, it assumes homogeneous populations on either side, and thus abstracts fromthe elasticity-related issues studied in our paper. Last, in amodel related to that of Caillaud and Jullien (2003), Jullien (2001) shows that an entrant represents a much stronger competitive threat on anincumbent platformwhen third-degree price discrimination is feasible. The ability to “divide and conquer ” forces pro t down, so much so that the incumbent may preferplatform compatibility.

2. Monopoly Platform Benchmark

The two-sided marketsdescribed heretofore differin some respects, and we thereforeshould not aimat capturing all speci cities of all industries. Our strategy will be to include anumber of key ingredients common to our illustrations in abasic model, and then to generalize our analysis in order to

4. The policy implications of two-sidedness are discussed in Evans (2003). The reader will nd further illustrations of two-sided markets and an interesting analysis thereof in Armstrong (2002). Rysman (2000) is the rst empirical paper to estimate network effects in atwo-sided context, namely the market for Yellow Pages. It is also related to the earlier literature on competition between intermediaries: Stahl (1988) and Yanelle (1997). Rochet and Tirole Platform Competition in Two-Sided Markets 995 extend its relevance to various two-sided markets. For the moment, weassume that end users incur no xed usage cost and that platformpricing is linear. This basic model is agood representation of the credit card market;the readermay want to keep this in mind, although it will be clearthat the insights have much broader generality. Economic value is createdby “interactions ” or “transactions ” between pairs of end users, buyers (superscript B)and sellers (superscript S).Buyers are heterogenous in that their gross surpluses bB associated with atransaction differ. Similarly, sellers ’ gross surplus bS froma transaction differ.Such transactions aremediated by aplatform. The platform ’smarginal cost of atransaction is denoted by c $ 0. As an illustration, consider the case of payment cards. The buyer wants to purchase abundle of goods or services fromthe merchant atacertain price p. In our vocabulary, a “transaction ” takes place ifand only ifthe buyer pays by card instead of using another payment instrument (say, cash). Bene ts bB and bS correspond to differences in utility of buyers and sellers when they pay by card ratherthan cash. Under the No Surcharge Rule (very often imposed by payment card networks) 5 the merchant is not able to charge different retailprices forcard and cash payments. Thereforethe distributions of bB and bS areindependent of the prices chosen by platforms and merchants, and can be taken as exogenous. In the absence of xed usage costs and xed fees, the buyers ’ (sellers’) demand depends only on the price pB (respectively, pS)charged by the monopoly platform. Thereare network externalities in that the surplus of abuyer with gross per transaction surplus bB, (bB 2 pB) N S,depends on the number of sellers N S,but the buyers ’ “quasi-demand function ”:6

NB 5 Pr~bB $ pB! 5 DB~ pB! is independent of the number of sellers. Similarly, let

NS 5 Pr~bS $ pS! 5 DS~ pS! denote the sellers ’ quasi-demand forplatform services. Consider a(buyer, seller)pair. Without loss of generality wecan assume that each such pair corresponds to one potential transaction. In contrast with search models a`laBaye and Morgan (2001) or Caillaud and Jullien (2003), wetake as given the matching process between buyers and sellers, and focus on the proportion of such matches that effectively results in a

5. Even in the countries where the NoSurcharge Rule is not imposed, as in the UK,it turns out that merchants seldom charge different prices for card and cash payments. We discuss in Section 8the possible reasons for this fact, and more generally for the non-neutrality of the price structure in two-sided markets. 6. The word “quasi-demand function ” is used to re ect the fact that, in atwo-sided market, actual demand depends on the decisions of both types of users (buyers and sellers in our terminology). In our speci cation, this demand is simply the product of the quasi-demands of buyers and sellers. 996 Journal of the European Economic Association June 2003 1(4):990 –1029

“transaction. ”7 Assuming forsimplicity the independence between bB and bS, the proportion (orvolume) of transactions is equal to the product D B(pB) 3 DS( pS).8 We consider in turn the case of aprivate monopoly, and that of apublic monopoly maximizing social welfaresubject to budget balance.

2.1 Private Monopoly

Aprivate monopoly chooses prices so astomaximizetotal pro t: p 5 ~ pB 1 pS 2 c! DB~ pB! DS~ pS!. Assuming that D B and D S arelog concave, itis easy to see that p is also log concave (jointly in( pB, pS)).Its maximumis characterizedby the rst-order conditions: ~log p! 1 ~DB!9 5 1 5 0, pB pB 1 pS 2 c DB ~log p! 1 ~D S!9 5 1 5 0. pS pB 1 pS 2 c DS In particular: ~DB!9DS 5 DB~DS!9. This condition characterizesthe values of pB and pS that maximizevolume fora given total price p:The volume impact of asmall(absolute) variation of prices has to be the sameon both sides. Ifwe introduce the elasticities of quasi-demands: pB~DB!9 pS~D S!9 hB 5 2 and hS 5 2 , DB DS the private monopoly prices can be characterizedby atwo-sided formulathat is reminiscent of Lerner ’s formula: pB pS pB 1 pS 2 c 5 5 . (1) hB hS In fact,the total price p 5 pB 1 pS chosen by the private monopoly isgiven by the classical Lernerformula:

7. In the payment card example, a “transaction ” between acardholder and amerchant means that the payment is by card rather than by cash. 8. This multiplicative formula was rst used by Schmalensee (2002). Most of our results can be extended to the more general case where bB and bS are not independent, in which case the transaction volume Q has amore general expression Q(pB, pS) 5 Pr(bB $ pB, bS $ pS). Rochet and Tirole Platform Competition in Two-Sided Markets 997

p 2 c 1 h 5 , or p 5 c, (2) p h h 2 1 where h 5 hB 1 hS,the total volume elasticity, is assumed to exceed 1. What is new in formula(1) is the way in which this total price is allocated between the two sides of the market: hB hB pB 5 p 5 c, (3) h h 2 1 and hS hS pS 5 p 5 c. (4) h h 2 1

B S PROPOSITION 1. (i) Amonopoly platform ’stotal price , p 5 p 1 p , is given by the standard Lerner formula for elasticity equal to the sum of the two elastic - ities, h 5 hB 1 hS: p 2 c 1 5 . (2) p h (ii) The price structure is given by the ratio of elasticities (and not inverse elasticities ): pB pS 5 . (5) hB hS

2.2 Ramsey Pricing

We consider now the case of aRamsey monopolist maximizing welfaresubject to budget balance, and derive the Ramsey formulaein our context. 9 The net surpluses on each side foran average transaction aregiven by standard formulae:

1` Vk~ pk! 5 Dk~t!dt

E k p for k [ {B, S}. Under budget balance, social welfareis highest when the sum of both sides ’ net surpluses: W 5 VS~ pS! DB~ pB! 1 VB~ pB! DS~ pS!,

9. Asimilar formula is derived in Laffont et al. (2003) in amodel in which network externalities are reaped through platform interconnection. 998 Journal of the European Economic Association June 2003 1(4):990 –1029 is maximizedsubject to the constraint: pB 1 pS 5 c. The rst-order, “cost allocation ” condition is: W W 5 . pB pS This gives: VS~DB!9 2 DBDS 5 2D SD B 1 V B~D S!9. Aftersimpli cation, weobtain acharacterization of Ramsey prices:

PROPOSITION 2. Ramsey prices embodythe average surpluses created on the other side of the market and are characterized by two conditions: pB 1 pS 5 c ~budget balance !. (6) and pB VB pS VS 5 ~cost allocation !. (7) hB F DBG hS F DSG Condition (7)characterizes the price structure that maximizessocial surplus fora given total price p.Returning to the formulayielding the private monopolist’sprice structure, pB pS 5 , (19) hB hS the additional termsin Formula (7)(the bracketed terms)re ectthe average surpluses per transaction forbuyers and sellers. (Later,when wecompareprice structures across governance forms,we will compareprices fora given price level. That is, wewill say that two governance formsgenerate the sameprice structure ifthey give riseto the sameprices fora given price level target p 5 pB 1 pS.Ofcourse differentgovernance formsgenerate differentprice levels.)

3. Competing Platforms

3.1 Modeling

We now assume that two platforms compete forthe markets(we will also look atthe case inwhich both platforms arejointly owned, in order to comparethe outcome under platformcompetition with those obtained in Section 2in the private monopoly and Ramsey cases). Rochet and Tirole Platform Competition in Two-Sided Markets 999

3.1.1 End users’bene ts. As earlier,buyers and sellers areheterogenous: Their bene ts fromtransacting vary across the two populations and areprivate B information. These bene ts aredenoted bi forthe buyer (when the transaction takes place on platform i) and bS forthe seller, and aredrawn fromcontinuous 10 B distributions. The proportional feescharged by platform i are pi for buyers S B and pi forsellers. Abuyer with gross surplus bi fromtransacting on platform B B i is willing to use that platformprovided that bi $ pi .However, the buyer B B B B prefersto transact on platform j if bj 2 pj . bi 2 pi .Similarly, asellerwith S S S type b is willing to trade on platform i provided that b $ pi ,and prefersto S S trade on platform j if pj , pi . Notice that atransaction can occur only ifthe two sides have at least one platformin common; that is, there exists atleast one platformon which both are willing to trade. Ifboth multihome (areaf liated with both platforms), the choice of platformis apriori indeterminate. Inaccordance with our illustrations, weassume that, whenever aselleris af liated with the two platforms, the buyer chooses the one on which the transaction takes place. 11

3.1.2 Transaction Volumes. The buyers’ behavior generates “quasi-demand functions”:

B B B B B Di 5 Di ~ pi ! 5 Pr~bi 2 pi . 0!, (8) and

B B B B B B B di ~ p1 , p2 ! 5 Pr@bi 2 pi . max~0, bj 2 pj !#. (9) B Di is the proportion of buyers who arewilling to use platform i when the seller B is af liated only with platform i.Similarly, di is the proportion of buyers who arewilling to trade on platform i when the sellermultihomes. Byconstruction, these functions satisfy the following properties:

B B B B di # Di # d1 1 d2 . (10) B B We assume that the distribution of ( b1, b2)is symmetric,which implies that B B B B ˆ B B B B demand functions arealso symmetric: D1( p ) 5 D2( p ) [ D ( p ) and d1( p1, B B B B B B B p2) [ d2( p2, p1).When prices areequal p1 5 p2 5 p ,wewill use the simpli ednotation:

10. For simplicity, we assume that the seller ’sgross surplus does not depend on the platform where the transaction takes place. Furthermore, when performing the welfare analysis, weequate these bene ts with the social values of the service brought about by the platforms. However, sellers may exert externalities on each other. For example, aseller ’sacceptation of apayment card may affect rival sellers. The welfare analysis (but not the positive one) must be amended correspond- ingly. For more on this, see Rochet and Tirole (2002). 11. This assumption is satis ed by most of our illustrations: acardholder selects the card when the merchant accepts multiple cards, the reader or viewer selects the newspaper, portal or TV network, the videogame user selects the platform if the game is written for several consoles, etc. Notice that this assumption introduces aslight asymmetry between the two sides of the market. 1000 Journal of the European Economic Association June 2003 1(4):990 –1029

B B B B B d ~ p ! ; di ~ p , p !. B B B S We focus forthe moment on symmetricprices: p1 5 p2 5 p and p1 5 S S S S S p2 5 p .Asellerof type b af liates with both platforms when b $ p and none otherwise. The transaction volumes on each platformare thus equal to Q 5 dB~ pB! DS~ pS!. (11) The sellers’ net surplus is, as earlier,

1` VS~ pS! 5 E DS~t!dt, pS while the buyers ’ net surplus is

1` 1` B B B B B B V ~ p1 , p2 ! 5 d1 ~t1, p2 !dt1 1 D2~t2!dt 2 E B E B p1 p2

1` 1` B B B 5 d2 ~ p1 , t2!dt2 1 D1~t1!dt 1. E B E B p2 p1

3.1.3 Joint Ownership Benchmarks: The private monopoly and Ramsey bench- marksstudied in Section 2correspond to the situation in which both platforms areunder joint ownership and charge identical prices. For instance, DB~ pB! 5 2dB~ pB! where

B B B B B B B B d ~ p ! 5 d1~ p , p ! 5 d2 ~ p , p !.

3.1.4 Governance: We assume that the two platforms arecontrolled by competing entities, either pro t-maximizing rms(Section 3.3) or not-for-pro t associations (Section 3.4). Important examples of such associations can be found in the payment card industry (Visaand MasterCard).In such associations, prices forbuyers and sellers aredetermined by competition (both intra and inter platforms)on downstream markets(issuing banks on the buyers ’ side, and acquire on the sellers ’ side).

3.2 Transaction Volumes for AsymmetricPrices

In order to analyze competition, weneed to determine transaction volumes on each platformfor arbitrary prices, thus extending formula(11) to nonsymmetric S S prices. Suppose that Platform1 is cheaper forsellers: p1 , p2.Asellerof type Rochet and Tirole Platform Competition in Two-Sided Markets 1001 bS has three possibilities: 12 no trade, af liation with Platform1 only, af liation S S with both platforms. The rst possibility is optimal whenever b # p1. The choice between the other two possibilities involves atrade-offbetween alower volume (when af liated with Platform1 only) and anobligation totrade on the most expensive platform(when af liated with both platforms). The corresponding expected net surpluses of asellerof type bS arerespectively ( bS 2 S B B S S B B B S S B B B p1) D1( p1) and (b 2 p1)d1( p1, p2) 1 (b 2 p2)d2( p1, p2).The sellerchooses to multihome when bS is large enough, moreprecisely when pSdB 2 pS~DB 2 dB! S ˆ 2 2 1 1 1 b . b12 ; B B B . (12) d2 2 ~D1 2 d1 ! We can now summarizesellers ’ optimal decisions:

S S sellers with low types ( b # p1)do not trade, S ˆ sellers with high types ( b $ b12)trade on both platforms, S S ˆ sellers with intermediate types ( p1 , b , b12)trade only on the less expensive platform(here, Platform 1).

By undercutting the rival platform, each platformthus induces some sellers (those with intermediate types) to stop multihoming, astrategy known as S S “steering.” The formulaefor p1 . p2 areobtained by permutation of indices. S S S ˆ ˆ When p1 and p2 converge to the sameprice p , b12 and b21 both converge also S ˆ ˆ to p ,which establishes continuity of the formulaegiving b12 and b21. Letus denote by si(i 5 1, 2) the following indices: B B B d1 1 d2 2 Dj si 5 B i, j 5 1, 2; i Þ j. di

Given property (10), si belongs to the interval [0, 1]. Itmeasures the “loyalty” of consumers of platform i,i.e. the proportion of them who stop trading when platform i ceases to be available. We call si the “singlehoming ” index of Platform i.Itis equal to 0when buyer demand facedby the selleris independent of whether B B B the selleris af liated with Platform i (d 1 1 d 2 5 Dj ).It is equal to 1when all B Platform i buyers arelost when the sellerstops af liating with that platform( Dj 5 B B B ˆ B dj ).For asymmetricprice con guration (with D1 5 D2 5 D ), we have Dˆ B s 5 s 5 s 5 2 2 . 1 2 dB S Starting froma symmetricprice structure, suppose platform1 decreases p1 by asmallamount «.This increases demand forPlatform 1 in two ways: The platform S S S attractsnew merchants ( p1 2 « # b1 , p1) and “steers” formermultihoming S S ˆ ˆ S merchants (p1 , b1 , b12).Given that ( b12/p1) 5 1 2 (1/s2),the effectiveness of steering depends on s2:it is nil when s2 5 1 and in nite when s2 5 0.

12. Af liation with Platform 2only is clearly dominated. 1002 Journal of the European Economic Association June 2003 1(4):990 –1029

We arenow in aposition to determine the volume of transactions on each B S S platformas afunction of prices pi and pi .We restrictourselves to the case p1 S S S S # p2 (the case p2 , p1 is obtained by symmetry).Let us denote by D the sellers’ “quasi-demand function ”: DS~ pS! 5 Pr~bS . pS!. S ˆ From the af liation decisions derived previously, aproportion D (b12) of S S S ˆ sellers multihome, while aproportion D ( p1) 2 D (b12) are af liated only with Platform1. Assuming that the probability of ameeting between abuyer and a selleris independent of their types, the total expected volumes of transactions on the platforms are: B B B S ˆ B B S S S ˆ Q1 5 d1 ~ p1 , p2 ! D ~b12! 1 D1 ~ p1 !$D ~ p1! 2 D ~b12!%, (13) forPlatform 1, and: B B B S ˆ Q2 5 d2 ~ p1 , p2! D ~b12!, (14) ˆ forPlatform 2, where b12 is given by formula(12). As already noticed, these S S formulaeare continuous across the “diagonal” p1 5 p2: B B B S S lim Qi 5 d i ~ p1, p2! D ~ p !. S S p1®p S S p2®p

3.3 Competition between Proprietary Platforms

Proprietary platforms choose prices so as to maximizepro t. Consider, for example, Platform1 ’s pro t:

B S p1 5 ~ p1 1 p1 2 c!Q1. (15) As in the case of amonopolist, this maximization can be decomposed into B S the choice of aprice level, p1 5 p1 1 p1,and that of aprice structure given a price level. The rst-order conditions are:

B S Q1 B S Q1 Q1 1 ~ p1 1 p1 2 c! B 5 Q1 1 ~ p1 1 p1 2 c! S 5 0, p1 p1 or

Q1 Q1 Q1 S 5 B 5 2 B S . (16) p1 p1 p1 1 p1 2 c The following analysis is complex, as it must handle apotential lack of smoothness of the objective function. Itcan be skipped in a rst reading. The end result (Proposition 3) is remarkably simple, though. S S Recall the expressions of volumes on both systems, when, say, p1 # p2: Rochet and Tirole Platform Competition in Two-Sided Markets 1003

B B B S ˆ B B S S S ˆ Q1 5 d1 ~ p1 , p2 ! D ~b12! 1 D1 ~ p1 !$D ~ p1! 2 D ~b12!%, (13) B B B S ˆ Q2 5 d2 ~ p1 , p2! D ~b12!, (14) where pSdB 2 pS~DB 2 dB! ˆ 2 2 1 1 1 b12 5 B B B . (12) d2 2 ~D1 2 d1 ! S S B B We focus on symmetricequilibria ( pi [ p , pi [ p ),forwhich volumes have simpler expressions:

B B B S S Qi 5 di ~ p , p ! D ~ p !. While Q dB 1 1 B B S S B 5 B ~ p , p ! D ~ p !, (17) p1 p1 the rst derivative in formula(17) is not necessarily well de ned since volumes S S S S have adifferent expression according to whether p1 , p2 or p1 . p2: B B S ˆ ˆ B B S S S ˆ Q1 5 d ~ p ! D ~b12! 1 D ~ p !$D ~ p1! 2 D ~b12!% S S when p1 , p2, and

B B S Q1 5 d ~ p ! D ~bˆ 21! S S 13 S S when p1 . p2.Interestingly, Q1 turns out tobe differentiable even at p1 5 p2. Indeed, atsymmetricprices:

S S S S ˆ ˆ 13. The left- and right-derivatives of Q1 with respect to p1 at p1 5 p2 5 p (implying b12 5 b21 5 pS) are: Q bˆ 1 S 12 B B S B S 5 ~D !9 S @d 2 Dˆ # 1 ~D !9Dˆ , S p1 D p1 L and Q bˆ 1 S 21 B S 5 ~D !9 S d . S p1 D p1 R Moreover ˆ B B ˆ B b12 Dˆ 2 d b21 d S 5 2 B B , and S 5 B B . p1 2d 2 Dˆ p1 2d 2 Dˆ And so Q ~Dˆ B 2 dB!2 ~dB!2 1 S ˆ B S S 5 ~D !9 B B 1 D 5 ~D !9 B B S p1 D F 2d 2 Dˆ G 2d 2 Dˆ L Q dB 2 1 S ~ ! S 5 ~D !9 B B . S p1 D 2d 2 Dˆ R S Thus Q1 is differentiable with respect to p1. 1004 Journal of the European Economic Association June 2003 1(4):990 –1029

Q dB 2 1 S ~ ! S 5 ~D !9 B B . (18) p1 2d 2 Dˆ Using (16), (17), and (18) weobtain asimple formfor the rst-order condition fora symmetricequilibrium: dB dB 2 i S S ~ ! B D 5 ~D !9 B B , pi 2d 2 Dˆ or:

B B B B S 2d 2 Dˆ d i /pi ~D !9 2 5 2 . S dB DS dB D DS The rst termon the left-hand side of this latterformula is the singlehoming index s de ned earlier,which measures the proportion of “unique customers. ” The second termis the ratio of the own-brand elasticity of demand forbuyers

B B B p d i /pi hB 5 2 o dB over the buyers ’ price pB.Finally, the last termis the ratio of the elasticity of sellers’ demand over sellers ’ price. Thus wecan state:

PROPOSITION 3. Asymmetric equilibrium of the competition between proprietary platforms is characterized by: pB pS B S p 1 p 2 c 5 B 5 S . ho ~h /s! The formulaeare thus the sameas in the monopoly platformcase, except that a)on the buyer side, the demand elasticity hB is replaced by the (higher) B S own-brand elasticity ho,and b) on the sellerside, the demand elasticity h is replaced by the equivalent of an own-brand elasticity hS/s.When all buyers singlehome ( s 5 1), the own-brand elasticity and the demand elasticity coincide. But as multihoming becomes morewidespread ( s decreases), the possibility of steering increases the own-brand elasticity hS/s.

3.4 Competition between Associations

When platforms arerun by not-for-pro tcooperatives owned by members (operators on the buyer and sellersides), prices paid by the end users areset by the membersand not by the platforms. Platformshowever have animportant say in the price structure, especially ifcompetition among membersis intense on both sides of the market.In our model, an association ’sonly strategic decision Rochet and Tirole Platform Competition in Two-Sided Markets 1005 is the choice of access charges between members.Neglecting platformcosts, the zero-pro tcondition implies that these access “charges” exactly offset each other as one side receives the charge paid by the other side. For example in the payment card industry the access charge is called the interchange feeand is paid by acquirers (the sellers ’ banks) to issuers (the buyers ’ banks).14 This section studies the access charge chosen by competing associations and compares the corresponding prices for nal users (buyers and sellers)with those resulting fromcompetition between pro t-maximizing systems. While the section is currently most relevant to the payment card industry, its potential applicability is much broader. For example, re ecting recentconcerns about unequal access to B2B exchanges, some have suggested that these exchanges be run as nonpro tassociations. Furthermore, and as will be observed in Section 7.2, networks of interconnected networks (e.g., communication networks) areeco- nomically similarto nonpro tplatforms. The memberscompete on two downstream markets, the buyer and the seller downstream markets. Given access charge ai on platform i,the net marginal costs fora memberof platform i of serving abuyer and aseller, respectively, are B S B S c 2 ai and c 1 ai, where c and c represent the gross marginal costs incurred by the memberson each side of the market.We makethe simplifying assumption that intraplatform competition results in constant equilibrium margins charged by memberson downstream markets: mB on the buyers ’ side and mS on the sellers’ side. Equilibrium prices arethus given by:

B B B S S S pi 5 c 2 ai 1 m , pi 5 c 1 ai 1 m . This assumption is forexample satis ed if (a)membersbelong to asingle association and aredifferentiated in adirection orthogonal to that of platform differentiation; 15 and (b)memberson agiven platformare little differentiated. Intense intraplatform competition then results in Hotelling competition between memberstaking as given (asa rst-orderapproximation) the number of end users on the platform(which is basically determined by the platforms ’ access charges given that the members ’ markups aresmall). 16 Under this simplifying assumption, the pro ts of all membersof an association areproportional to the volume of transactions on the association ’s

14. The determination of access charges within associations has so far only been studied in the context of the payment card industry and under the assumption of amonopoly platform [Rochet and Tirole (2002), Schmalensee (2002)]. 15. Mathematically, in ageneralized Hotelling framework, the “transportation cost ” for an end-user when selecting a(platform, member) pair is the sum of the transportation cost to the platform and that to the member. 16. If members have dual membership instead (e.g., they are both af liated with Visa and MasterCard, or they provide support or write applications for two cooperatively designed operating systems or videogame platforms), then requirement ( b)is unnecessary in that margins are constant even if member differentiation is not small relative to platform differentiation: See Hausman, Leonard, and Tirole (2003). But one must then inquire into the associations ’ governance structure. Our treatment carries over as long as governance leads each association to maximize its volume. 1006 Journal of the European Economic Association June 2003 1(4):990 –1029 platform. The interests of all membersare thus completely aligned. Regardless of its exact structure the association selects the access charge so as to maximize its volume. Furthermore the total price on each system is constant:

B S pi 1 pi 5 c 1 m, (19) where m 5 mB 1 mS is the total margin on downstream marketsand c 5 cB 1 cS. Last, in order to be able to comparethe association with the cases of a monopolist and of competing proprietary platforms, wemust assume that the quasi-demand functions arethe same.That is, the membersare only selling the varieties of each platformthat the proprietary platforms wereselling. Because wekept quasi-demand functions quite general, there is no dif culty in assuming this isindeed the case. The outcome of the competition between the two associations is character- B S B S ized by two price vectors ( pi , pi ), i 5 1, 2, such that: forall i, ( pi , pi ) maximizesthe volume Qi on system i subject to (19), taking asgiven the price B S vector ( pj , pj )on the other system. The rst-order conditions fora symmetricequilibrium aregiven by pB 1 pS 5 c 1 m, (20) (condition on total price)and the equivalent of condition (5):

Qi Qi B 5 S , (21) pi pi (sameimpact on volume of amarginal price increase on each side of the market). The analysis of the price structure is thereforeidentical to that forproprietary platforms. The price level is lower forassociations with healthy competition among their membersbut mayexceed the proprietary platforms price level ifdouble marginalization is strong.

PROPOSITION 4. Asymmetric equilibrium of the competition between associations is characterized by pB 1 pS 5 c 1 m and pB pS B 5 S . (22) sho h Comparing now Propositions 2and 4, wesee that even when downstream marketsare perfectly competitive (the margin m converges to zero)and so the price level is socially optimal, competition between not-for-pro tassociations need not generate an ef cient outcome. Indeed, the condition foran ef cient price structure (given in Proposition 2) is: Rochet and Tirole Platform Competition in Two-Sided Markets 1007

pB VB pS VS 5 , (7) hB F DBG hS F dSG while the condition characterizing competition between associations is different:

pB pS B 5 S . (22) sho h This is natural, as ( a)the associations do not internalize the end-users ’ surpluses, and ( b)the associations aimat steering sellers (which isre ected by B the presence of s)and stealing buyers (asindicated by the presence of ho) away fromthe rival association, while marketshare considerations play no role in a Ramsey program. Itis thereforeperhaps remarkablethat the two conditions coincide in the special case of linear demands, which weexplore in detail in Section 5.

4. Determinants of Business Model

Let u be aparameterthat affectsthe volume of transactions on the platforms. In this section, weconsider the impactof asmallvariation in u on user prices pB and pS,depending on industry structure (monopoly or duopoly) and on the platforms’ governance structure (for-pro ts or associations). We concentrate on three important determinants of industry conduct and performance:

Marquee buyers: In the rst application, u represents a(small)uniform shift in sellers’ surpluses, due to the presence of marquee buyers on the other side of the market.As aresult, the sellers ’ demand function becomes:

DS~ pS, u ! 5 DS~ pS 2 u !.

Installed Bases/Captive Buyers: In the second application, u represents the (small)mass of buyers who areloyal to their platform, independently of prices. Such buyers, say, aretied by long-term contracts. As aresult, the buyers ’ demand functions become:

B B B B B B di ~ p1 , p2 , u ! 5 di ~ p1 , p2 ! 1 u, DB~ pB, u ! 5 DB~ pB! 1 u, Dˆ B~ pB, u ! 5 Dˆ B~ pB! 1 u.

Multihoming: Inthe third application, u represents an exogenous increase in the singlehoming index of buyers. Assume forexample that d B does not depend on 1008 Journal of the European Economic Association June 2003 1(4):990 –1029 u, while D B decreases in u. Then s( pB, u) 5 2 2 [DB( pB, u)/d B( pB)] is B 17 increasing in u, while ho does not depend on u. Proposition 5analyzes the impact of smallvariations of u on the prices pB and pS.

PROPOSITION 5.

(1)In the case of amonopoly platform (for-pro tor association) and with log concave demand functions, the seller price increases when there are marquee buyers and decreases when there are captive buyers. The buyer price moves in the opposite direction. (2)The same result holds under competition between associations, except that the comparative statics with respect to captive buyers requires a regularity condition. (3)In the case of competing associations, an increase in the multihoming index of buyers (keeping demand elasticities constant) leads to an increase in the buyer price and adecrease in the seller price.

Intuitively, marqueebuyers makethe platformmore attractive forthe sellers. The platformthen raises its price pS to sellers, which reduces the de facto marginal cost, c 2 pS,of provision of the service to the buyers. The buyer price thereforefalls. The intuition is similarin the case of captive buyers. Captive buyers allow the platformto raisethe price pB to buyers, thus reducing the de facto marginal cost c 2 pB of serving sellers. Aregularity condition however is required here inthe case of platformcompetition, which createsa countervailing steering effect:Each platform ’sbuyer membership is then “more unique” to the platform, and so it is morecostly fora sellerto forgo the platform. Last, an increase in multihoming makes steering moreattractive and puts adownward pressure on the sellerprice.

5. Linear Demands

We illustrate the results obtained so farin avariant of the Hotelling model, wherea buyer ’spreferencesfor platforms arerepresented by his location x on aline. Buyers areuniformly distributed on aline of length ( D 1 2d).Platforms 1and 2aresymmetrically located atadistance D/2of the origin of the line ( x 5 2(D/2) forPlatform 1 and x 5 D/2forPlatform 2). The number D parametrizes the degree of substitutability between platforms. Buyers have also access to

17. This is, for example, the case in the Hotelling speci cation presented in Section 5, when the marginal transportation cost of buyers increases only for distances in the noncompetitive hinterland B B of the rival platform, so that d i is unaffected while D decreases. Rochet and Tirole Platform Competition in Two-Sided Markets 1009 outside options, represented conventionally by two other symmetricplatforms (denoted 19 and 29),located further away fromthe origin ( x 5 2(D/2) 2 d and x 5 (D/2) 1 d)and charging the same,exogenous, price p0. The number d will serve us as ameasureof the weight of “unique consumers. ” When using a 2 platformlocated atdistance d,buyers incur aquadratic transportation cost 12 d , (the transportation cost parameteris normalized to 1without loss of generality). Proposition 6(proved in the Appendix) exhibits three main implications of the linear case. First, the price structure is the sameregardless of whether the industry is served by aprivate monopoly, competing proprietary platforms or competing associations. Second, ifdemand is linear on the sellerside as well, then this common price structure is Ramsey optimal. Taken together, these results show that without detailed information about the demand structure, one should not expect clearcomparisons of price structures across governance mechanisms. Nor arepolicy interventions to alterthe price structure (asopposed to the price level) likely to be solidly grounded. Third, Proposition 6provides suf cient conditions forthe second-order conditions to be satis ed in the linear demand case.

PROPOSITION 6. Suppose that the buyers ’ quasi-demand is described by an Hotelling model , with uniform distribution and outside options with distance D between the two platforms and distance d between each platform and its nearest outside option , and that the market is not covered (not all potential buyers buy).

(1) The buyer singlehoming index is equal to:

s 5 D/~D 1 d!, and decreases when the platforms become more substitutable .

The platforms ’ ability to steer (undercut in order todiscourage sellers from multihoming) decreases with the buyer singlehoming index. On the buyer side, total elasticity is equal to own-brand elasticity times the singlehoming index:

B B h 5 ho s.

(2)The price structure is the same under amonopoly platform, competing proprietary platforms and competing associations. Itsatis es

pB pS 5 . hB hS

(3)If furthermore seller demand is linear, then the price structure in the three environments is Ramsey optimal. 1010 Journal of the European Economic Association June 2003 1(4):990 –1029

(4)The price vectors given informulae (31) and (32) satisfy the second- order conditions for an equilibrium if and only if d/D issmaller than (1 1 =5)/2.

6. Generalization to Fixed User Feesand Usage Costs

In many of the examples presented in the Introduction, xed costs, either xed feescharged by the platforms or xed usage costs, play an important role. In order to demonstrate the robustness of our results to the introduction of xed costs, wenow adapt our model accordingly. Tosimplify the analysis, weassume that buyers singlehome (forexample, consumers read asingle newspaper or connect to asingle portal). Second, wefocus on the symmetricequilibrium. Thereis asizeable literatureon tipping in the presence of user xed costs and wehave little to add to this literature. Last, we rst look atthe case in which there is no direct exchange of money between the two sides of the market,as is the case foradvertising in newspapers, TVs, and portals; wewill latershow how to extend the analysis to cases, such asvideogames, exhibiting direct monetary transactions between end-users. Platformsincur xed costs C B and C S per buyer and seller, as well as marginal cost c per transaction between them (presumably c 5 0foradvertis- B S B S ing). Letplatform i charge xed fees Ai and Ai and variable charges ai Ni and S B B S ai Ni to buyers and sellers, where Ni and Ni arethe numbers of buyers (eyeballs) and sellers (advertisers) connected to platform i.Abuyer with B (possibly negative) average bene t bi of receiving anad and with xed usage B cost g i (also possibly negative) has net utility

B B B S B B Ui 5 ~bi 2 ai ! Ni 2 Ai 2 gi . Similarly, asellerwith average bene t bS of reaching aconsumer and with xed cost g S of designing anad forthis newspaper has net utility:

S S S B S S Ui 5 ~b 2 ai ! Ni 2 Ai 2 g . B B The buyers areheterogenous over parameters( bi , g i )and sellers are heterogenous over parameters( bS, g S). The strategic choices forthe platforms arethe per “transaction ” (eyeball viewing anad) markups: ~ AB 2 CB! ~ AS 2 C S! B B i S S i pi ; ai 1 S and pi ; ai 1 B . Ni Ni Assuming that readersbuy asingle newspaper, the number of copies sold by newspaper i is given by

B B B Ni 5 Pr~Ui . max~0, U j !!, Rochet and Tirole Platform Competition in Two-Sided Markets 1011

B B B S which is equal to some function d i of prices ( p1, p2)and numbers of ads ( N 1, S N 2)of the two newspapers B B B S B S B B S B B Ni 5 di ~ p1, N1; p2, N2! ; Pr~~bi 2 pi ! N i 2 C 2 g i B B S B B (23) $ max@0, ~bj 2 pj ! Nj 2 C 2 g j #!. S S B N i is itself afunction of pi and N i : S S S B S S B S Ni 5 D ~ pi , Ni ! 5 Pr~~b 2 p i ! N i . g !. (24) These formulas arevalid provided xed costs forbuyers arehigh enough so that no buyer buys the two newspapers (no multihoming forbuyers). Substituting (24) B B into (23), and solving for( N1, N2),one obtains demand functions forthe buyers: B B B S B S Ni 5 ni ~ p1 , p1; p2 , p2!. Let us de ne the own- and cross-elasticities forbuyer demand: nB pB nB pS B i i B i i ho ; 2 B B and hS ; 2 S B . pi ni pi ni On the sellerside, wede ne the own-price elasticity and the network elasticity: DS pS D S NB hS ; 2 and hS ; . pS DS N N B D S With this notation, the formulaefor transaction volumes and platformpro t look remarkably similarto the ones obtained earlier.Platform i maximizes:

B S B S pi 5 ~ pi 1 pi 2 c! Ni Ni . Simple computations yield:

B S PROPOSITION 7. Asymmetric equilibrium is characterized by prices ( p , p ) satisfying: pB pS B S p 1 p 2 c 5 B S 5 S B S . ho ~1 1 hN! h 1 hS ~1 1 hN! While wesimpli ed the model by assuming singlehoming ( s 5 1), the presence of xed costs implies that network externalities impact not only end-user surpluses, but also demands. For example, on the buyer side, the own B price elasticity ho is multiplied by afactorgreater than 1to account forthe fact that when aplatformreduces its buyer price, morebuyers connect to the platform, inducing moresellers to connect and further increasing buyer demand. And similarly on the sellerside. In morestructured applications, the formulaein Proposition 7maysimplify. For example, in the advertising example, it is reasonable to assume that sellers 1012 Journal of the European Economic Association June 2003 1(4):990 –1029 incur no xed usage cost ( g S [ 0), since the advertising campaign has already been prepared forother media. In this case formula(24) shows that D S does not B S depend on N , so that hN 5 0, and pB pS B S p 1 p 2 c 5 B 5 S B . ho h 1 hS Last, let us turn to the (videogame or operating system) case in which the transaction between the sellerand buyer involves aprice charged by the seller to the buyer. Additional complications arisebecause of this monetary transaction between buyers and sellers. The equilibrium price of this transaction is then determined by competitive forces in the marketfor videogames or software applications and depends on the pricing policies of platforms. To illustrate how to extend the model to re ectthis, weassume that sellers have marketpower and no marginal cost and that buyers differonly in the xed cost of learning how to install and use an operating system or aconsole (and in the identity of their preferredapplications). They receivegross surplus v fora fraction a of the applications (wherethe corresponding applications aredrawn in i.i.d. fashion among consumers) and v . v fora fraction (1 2 a). When a is large (so that (1 2 a)v , v), it is ef cient forthe platforms to induce developers to charge the low price p 5 v,so that buyers buy all games and receivea net marginal surplus bB 5 (1 2 a)(v 2 v).Then wecan assume w.l.o.g. that aS 5 0, so that bS 5 v.Using the samenotation as above, the net utilities of atypical buyer and a typical sellerare

B B S B B Ui 5 b Ni 2 Ai 2 gi ,

S S B S S Ui 5 b Ni 2 Ai 2 g . B S Denoting again by pi and pi the per transaction mark-ups: AB 2 CB AS 2 C S B i S i pi 5 S and pi 5 B , Ni N i B S and d i , D the associated demand functions, weobtain the sameformulae as in Proposition 7.

7. Summary and Mini Case Studies

Letus now summarizethe paper ’skey insights. The main contribution has been to derive simple formulaegoverning the price structure in two-sided markets, and this fora wide arrayof governance structures (private monopoly, Ramsey planner, competition between for-pro t or nonpro tplatforms). But wealso obtained morespeci cinsights. Onthe public policy side: Rochet and Tirole Platform Competition in Two-Sided Markets 1013

1) The Ramsey price structure does not correspond to a “fair cost allocation. ” Rather, like private business models, itaimsat getting both sides on board. 2) The main conceptual differencebetween private and Ramsey price structures is that the lattertakes into account the average net surplus createdon the other side of the marketwhen attracting an end user on one side. Yet, private business models do not exhibit any obvious price structure bias (indeed, in the special case of linear demands, all private price structures areRamsey optimal price structures).

On the business model front, weobtained:

3) Monopoly and competitive platforms design their price structure so as to get both sides on board. 4) An increase in multihoming on the buyer side facilitatessteering on the sellerside and results in aprice structure morefavorable to sellers. 5) The presence of marquee buyers (buyers generating ahigh surplus on the sellerside) raises the sellerprice and (in the absence of price discrimination on the buyer side) lowers the buyer price. 6) Captive buyers tilt the price structure to the bene tof sellers.

We now develop seven “mini case studies ” meantto emphasize the attention paid by platforms to the pricing structure. Arigorous validation of testable implications 3) through 6) lies beyond the scope of this paper, and wehope that future researchwill performthe econometric studies needed to con rm or in rm these hypotheses inspeci cindustries. We only offersome casual empiricism; this preliminary evidence seemsquite encouraging of the theory.

7.1 Credit and Debit Cards

The payment industry offersa nice illustration of implications 3) through 6). Historically, the business model forcredit and differeddebit cards has been to attractcardholders and induce them to use their cards. Visa and MasterCard are not-for-pro tassociations owned by over 6,000 bank (and nonbank) members. The associations centrally set interchange feesto be paid by acquirers (the merchants’ banks) to issuers (the cardholders ’ banks). These interchange fees areproportional to transaction volume. Ahigher interchange feeis, via the competition among issuers, partly or fully passed through to consumers in the formof lower card feesand higher card bene ts, which encourages card ownership and usage; and via competition among acquirers, partly or fully passed through to merchants, who pay ahigher merchant discount (the percent- age of the sale price that the merchant must pay the acquirer), which discourages merchant acceptance. The associations ’ choice of interchange feeshave typi- 1014 Journal of the European Economic Association June 2003 1(4):990 –1029 cally favored cardholders over merchants who kept accepting the card despite the high level of the merchant discounts (implication 3). 18 AmericanExpress, afor-pro tclosed system, works on the samebusiness model, with an even higher degree of cross-subsidization. Traditionally, it has charged amuch higher merchant discount. 19 Itcould afford to do so because the Amexclientele —in particular the corporate card clientele —was perceived as very attractive by merchants (implication 5). The gap between Amex ’s and the associations ’ merchant discounts has narrowed in the 1990s as moreand more Amexcustomers got also aVisa card or MasterCard. Such “multihoming ” by a fraction of cardholders madeit less costly formerchants to turn down Amex cards (implication 4). The online debit card marketin the United States has adopted an entirely differentbusiness model. Rather than courting consumers, it has wooed merchants through alow interchange fee.One key differencewith credit and differeddebit cards is that consumers indeed do not need to be courted (they already have intheir pocket an ATMcard, that they can use asan online debit card; so in asense they are “captive”),while merchants, to performonline debit, must install costly pinpads (which most of them have not yet done). 20 This emphasizes the relevance of implications 3and 6).

7.2 Internet

In the Internet, the instrument of cross-subsidization is the termination or settlement charge (orlack thereof)between backbones. The termination charge foroff-Net traf cbetween two backbones is, as its nameindicates, the price paid by the originating backbone to the terminating backbone forterminating the traf chanded over. Itcan be shown 21 that it is optimal to charge the “off-Net cost” to end users formarginal incoming and outgoing traf c. That is, backbones should charge asifthe traf cwereoff-Net, even though afraction of the traf cis actually on-Net. The charge forincoming (outgoing) traf c decreases (increases)one-for-one with the termination charge. This implies that ahigh termination charge isindirectly borne by end users, like websites, whose volume of outgoing traf cfarexceeds the volume of incoming traf c, and bene ts end users, such as dial-up customers, who mostly receivetraf c(downloads).

18. Looking forward, it is likely that merchant card acceptance will become more elastic with the (ongoing) advent of online debit and the (future) introduction of Web platforms. 19. And thus implicitly amuch higher “interchange fee. ” For Amex, the interchange fee is only implicit, since the company is vertically integrated and performs the three roles of issuer, system and acquirer. 20. The online offerings were rst made by regional ATMnetworks. Anumber of these networks have now been consolidated and converted into afor-pro tplatform (Concord ESF). 21. See Laffont et al. (2003) and Jeon, Laffont, and Tirole (2003) for derivations of this result in different environments. Rochet and Tirole Platform Competition in Two-Sided Markets 1015

An Internet in which backbones exchange traf cata uniform volume-proportional termination charge is similarto the case of asingle not-for-pro t platform. This analogy can be best depicted by envisioning backbones exchanging traf c at public peering points. 22 An “association ” running these public peering points and keeping track of bilateral termination charges would be similarto acredit-card association recording traf cbetween acquirers and issuers, with the termination charge the counterpart of the interchange fee.A network of interconnected networks thereforeresembles asingle not-for pro t platform. The Internet is still mostly run by pre-deregulation legacy arrangements, according to which the backbones charge nothing toeach other forterminating traf c. This business model is currently being reexamined and it is quite possible that, asis the case forregular telephony, positive termination charges will be levied in the future. The legacy arrangements may well have madesense in an epoch in which the posting of content on the Web had to be encouraged. Akey question now is whether achange in industry conditions motivates a move toward paying settlements.

7.3 Portals and Media

The business model of (nonpay) TV,and to alarge extent, newspapers has been to use viewers and readersas aloss leader, who attractadvertizers. This business model has been adopted with avengeance by Internet portals, which have supplied cheap or freeInternet access as wellas freecontent (sharequotes, news, e-mail,etc.) to consumers. The pro tcenterhas been advertising revenue, including both xed charges forbanner placement and proportional referralfees. 23 Interestingly the portal industry is considering whether to stick to this business model or move to for-feecontent. For example, Yahoo! isnow starting to charge feesfor services such as real-timeshare-quote services or auction services. Anumber of content sites have appeared that charge substantial fees foron-line content. 24

7.4 Video Games

Our last four case studies aredrawn fromthe software industry. The video game marketis atypical two-sided one. Aplatformcannot sell the console without games to play on and cannot attractgame developers without the prospect of an installed base of consumers. In its thirty years of existence, the video game

22. Even though, in practice, they mainly exchange their traf cat bilateral peering points. 23. See Elfenbein and Lerner (2001) for athorough analysis of contracts in recent Internet Portal Alliances. 24. See, e.g., the Economist (April 14, 2001, p. 65) for more details. 1016 Journal of the European Economic Association June 2003 1(4):990 –1029 industry has had four leading platforms, Atari,Nintendo and Sega, and nally Sony. The business model that has emerged uses consoles asthe loss leaderand draws platformpro tfromapplications development. Tobe certain, history has repeatedly shown that technically impressive platforms (e.g., Mattelin 1981, Panasonic in 1993, and Sega in 1985 and after1995) failwhen fewquality games arewritten forthem. But attracting gamedevelopers is only anecessary condition. In fact,the business model currently employed by Nintendo, Sega and Sony is to charge software developers a xed feetogether with aper-unit royalty on the games they produce. 25 Microsoft released in the fallof 2001 the Xbox in competition with Sony ’sdominant PlayStation 2. Interestingly, Mi- crosoft manufactures the Xbox console and uses it as aloss leader. While courting the developers 26 by using the familiarX86 chip and Windows platform and by not charging forthe Xbox Prototype kit, Microsoft has stated that it intends to draw revenue fromroyalties. Although the industry ’sbusiness model involves drawing revenue from developers, platforms can only go so farin taxing the latter.A key factorin Sony’sPlayStation ’svictory over the Sega Saturn and Nintendo 64 was that Sony offereda development platformand software application that was much cheaper (about $10,000 per seat)and much easierto use (asit was PCbased) that its two rivals ’.27

7.5 Streaming-Media Technology

Streaming-mediaplatforms incorporate encoding, compression, scripting and delivery technologies to allow the delivery of streaming content, facilitate content creation and permitinteractivity; forexample, it is central to confer- encing and Webcast. The current competition is among the RealNetworks, Microsoft, and Apple platforms. The streaming-media industry is still in its infancy and it is probably too early to point at “the” business model. The current business mostly, but not exclusively, subsidizes the client side. RealNetworks and Apple offertwo clients: abasic, freeclient and abetter, nonfree one. RealNetworks, the current leadercharges signi cant amounts on the server side forRealServer Plus and its upgrades (seeCowell 2001 fordetails). Apple incontrast is currently freeon the serverside, but has the disadvantage on running only on Macs. Microsoft ’s Windows Media is free(bundled with the operating systems).

25. Initially, Nintendo placed achip in its console. The console would not work unless an authenticating chip was present in the game cartridge. Encryption techniques allow platform manufacturers to meter game sales. 26. In September 2000, 157 developers were working on Xbox games. The Xbox is launched with 26 games. Interestingly, Electronic Arts (the maker of Fifa, SimCity, and James Bond) was able to impose special conditions on Microsoft. 27. See Cringely (2001) for more detail. Sony sold its console below cost and made the money back on game royalties. Rochet and Tirole Platform Competition in Two-Sided Markets 1017

7.6 Operating Systems

Both sides in the Microsoft browser case agreed that akey competitive advan- tage of Windows over competing operating systems isits large installed base of applications. Windows ’ business model is basically the opposite of that of videogame platforms. Windows makes money on users and as a rst approxi- mation does not makeor lose money on applications developers. 28 It xes the Applications Programming Interfacesthree or four years in advance (acostly strategy) and invests heavily in developer support. This strategy proved pro t- able in its contest with Apple and IBM ’sOS/2. Apple has no integrated developers system tools allowing developers to test their programs; the latter had to buy anIBMworkstation and acompiler. IBMviewed developer kits as a pro t center.29 While other factors undoubtedly played arole inthe competition among the three platforms, observers usually agreethat Microsoft ’s choice of business model helped Windows establish dominance.

7.7 Text Processing

Akey issue confronting purchasers of text processing softwareis whether they will be able to “communicate ” with people who don ’tmakethe samechoice. Commercialsoftware vendors have in this respect converged on the following business model: They offera downgraded version of the paying softwareas “freeware.” This freeversion allows “nonusers” toopen, view, and print, but not edit documents prepared with the paying software, and copy information from those documents toother applications. Examples of such freeviewers areWord Viewer,PDF Viewer,and Scienti c Viewer.30

8. Final Thoughts about Two-Sided Markets

Our premiseis that many (probably most) marketswith network externalities aretwo- (ormultiple-) sided markets. Amarketwith network externalities is a two-sided marketit platforms can effectively cross-subsidize between different

28. Weare unaware of “hard data” on this and just report the industry ’sconventional wisdom. Nor do we have any hard data for handheld computer operating systems. Handheld computers operating systems, dominated by Palm ’splatform (75 percent market share in the United States) and Microsoft ’sPocket PCsoftware, have adopted abusiness model that is similar to Windows for PCoperating systems. Palm and Microsoft apparently charge about 10 percent of the hardware ’s wholesale price ($5 to $15) to hardware manufacturers. Both provide standard user interfaces and central support and development tools for developers of third-party software. For more detail, see ^http://www5.zdnet.com/zdnn/stories/news/0,4586,2714210,00.html?chkpt-zdhpnews01 &. 29. Software developer kits were sold at about $600. 30. For Scienti cWord, amathematics software program adding auser interface and various A other functions on to L TEX. 1018 Journal of the European Economic Association June 2003 1(4):990 –1029 categories of end users that areparties to atransaction. That is, the volume of transactions on and the pro tof aplatformdepend not only on the total price charged to the parties to the transaction, but also on its decomposition. Thereare two reasons why platforms maybe unable to performsuch cross-subsidization: a) Both sides of the market coordinate their purchases. A debit card platformnegotiating with agovernment forthe handling of interagency nancial transactions, anInternet operator offering anIntranet solution to acompany, or astreaming-media platformoffering streaming audio and video to a rmprimarily forinternal use all deal with asingle party. A subsidization of the client side by the serverside forexample does not affectthe total price of the software service and, ceterisparibus, does not affectthe demand forthe platform. 31 b) Pass-through and neutrality. Even when end users on the two sides of the marketact independently, monetary transfers between them may undo the redistributive impact and prevent any cross-subsidization. The value-added tax is an epitome of the possibility of neutrality. First-yeareconomic students aretaught that it really does not matterwhether the selleror the buyer pays the tax. In the end, prices adjust so that any tax paid by the selleris passed through to the consumer. Ifsuch neutrality holds, then the marketsdiscussed above should be treated as one-sided markets, that is marketsin which only the total per transaction price charged by the platformmatters and not its decomposition between end users. 32

Yetthinking of the marketsdiscussed inthis paper asone-sided marketsjust runs counter to evidence. First, the platformowners in all these industries devote much attention to their price-allocation business model: Isit moreimportant to woo one side or the other? The quest for “getting both sides on board ” makes no sense in aworld in which only the total price forthe end user interaction, and not its decomposition, matters.And the trade press would not contain so many descriptions of “chicken-and-egg ” problems. Second, the end users themselves arealso very sensitive to the allocation of cost between them, indicating that

31. Mobile and xed telephone services, for which most users are both callers and receivers, cannot be treated as one-sided markets. Ahigh termination charge raises the marginal cost of calls and lowers the marginal cost of call receptions. In other words, the termination charge is an instrument of cross-subsidization similar to the interchange fee in credit card markets. Telephone users are on both sides of the market for different communications only. For agiven communication, end users are on asingle side and (unless they are engaged in arepeated relationship) their consumption behaviors depend on their own price (calling price for the caller, receiving price for the receiver). As aconsequence, the choice of termination charge is not neutral. See Jeon et al. (2003) for more detail. 32. “Neutrality” refers to the pass-through property and apriori bears no connotation with respect to the well-being of end users and platforms and to social welfare. While neutrality reduces the number of instruments at the disposal of agiven platform, it is not clear whether it helps or hurts the platforms in their rivalry. Similarly, neutrality apriori may be good or bad for end users and social welfare. Rochet and Tirole Platform Competition in Two-Sided Markets 1019 some actual redistribution istaking place. Merchants vocally object to increases in interchange fees, and website operators will do so ifsettlement charges are introduced in the Internet. End users would not reactin this way ifcharges were passed through. Thereare three broad reasons why neutrality does not hold in practice: a) Transaction costs. “Transaction costs ” referto abroad range of frictions that makeit costly forone side of the marketto pass through a redistribution of charges to the other side. Often, these transaction costs areassociated with smallstakes forindividual transactions (which can become substantial when applied toalarge number of transactions). The cost of thinking about including the pass-through, writing it into a contract, advertizing it to the other side and enforcing the covenant may then be prohibitive. For example, contractural relationships between a supplier, abuyer and their banks may not specify on which payment system the settlement of the transaction will occur. Asecond type of transaction cost has to do with the absence of alow- cost billing system. Suppose that anacademicdownloads aPDF le of another academic ’spaper. The micropayments that would be required for pass-through would probably require acostly third-party billing system to be developed cooperatively by Internet backbones and service providers. 33 Athird transaction cost is the impossibility of monitoring and recording the actual transaction or interaction. In the portal and mediaexample, neutrality would imply that when the platform(portal, TVnetwork, newspaper) raises the price of advertizing, this price increase translates into asmalleramount of money given by the advertizer tothe consumer for “listening to the ad. ” But “listening” isnot easily measurable (except forthe monitoring of clicks in the Internet, and even then it is impossible tomeasurewhether the consumer pays genuine attention 34).In practice therefore, the viewer/readerreceives no compensation fromthe advertizer and neutrality does not obtain. b) Volume-insensitive costs. Neutrality also fails when atleast one side of the marketincurs costs that a)are in uenced by the platformand b) are not proportional to the number of transactions on the platform. For example, while software developers incur some costs, such as the per- gameroyalties paid by gamedevelopers, that areproportional to sales, many costs areinsensitive and affectedby the platform: The xed

33. See Laffont et al. (2003) for ademonstration that termination charges are neutral in the Internet in the absence of the frictions considered in this section. 34. Such ways of charging consumers have been considered. For example, astartup called CyberGold devised away to pay viewers of ads on the Web provided they peruse the Web ad to its last page. Advertisers were concerned about both moral hazard (clicking through ads without being really interested) and adverse selection (clickers would not be the high-demand consumers): See B.Ziegler ’s “Are Advertisers Ready to Pay Viewers, ” Wall Street Journal, 11/14/1996. 1020 Journal of the European Economic Association June 2003 1(4):990 –1029

development cost isin uenced by platformthrough software design, and so is the xed charge forthe development kit. Onthe user side, getting familiarwith the platform ’suser interfacemay also involve some xed costs.35 End user transaction-insensitive prices and non-price attributes of aplatformaffect the number of end users or applications, but not directly the termsof the transactions between the end users. The portal-and-media and realestate example offersanother illustration of this phenomenon. The advertising cost of locating apotential buyer ought to be treated by the selleras asunk cost when choosing the price to offerto the potentially interested buyer. c) Platform-determined constraints on pass-through. The platformmay also take steps that limitthe extent of pass-through. Acase inpoint isthe no- discrimination-rule adopted by credit card associations (Visa, MasterCard) and for-pro ts (Amex).36 Merchants do not pass the merchant discount through only tocardholders. So there isonly apartial pass-through between the two sides.

These reasons, which have been embodied in our model, explain why marketswith network externalities arepredominantly two-sided markets.

Appendix

PROOF OF PROPOSITION 5

(i)Monopoly. Total volume is given by Q 5 DB~ pB, u ! DS~ pS, u !. We assume that D B and D S are(strictly) log concave with respect to prices, so that the rst-order conditions aresuf cient forthe maximization of volume under aconstant margin (caseof an association) and forthe maximization of pro t(caseof afor-pro tmonopoly).

(i1)Monopoly Association. The buyer price pB induced by an association is characterizedby w~ pB, u ! 5 lB~ pB, u ! 2 lS~c 1 m 2 pB, u ! 5 0,

35. Similarly, end users seem to be averse to being “nickelled and dimed ” by Internet portals (perhaps because they have ahard time thinking through the total amounts at stake) and at fees are still quite popular in that industry. 36. In the United States, the associations ’ no-discrimination-rule takes aweaker form. Namely, merchants are not allowed to impose surcharges on card payments; but they can offer discounts for cash purchases! That very few do is an interesting fact, that is probably related to the transaction costs category. In Rochet and Tirole (2002), weabstract from such transaction costs and show that the level of the interchange fee is irrelevant if the no-discrimination rule is lifted. Rochet and Tirole Platform Competition in Two-Sided Markets 1021 where lB( pB, u) 5 2(DB(pB, u))9/(DB( pB, u)) and lS( pS, u) 5 2(DS(pS, u))9/(DS(pS, u))denote the “sensitivities ” of demands and c 1 m is the ( xed) total price. We can apply the implicit function theorem to w, given that w/pB . 0. This is because the strict log concavity of demands implies that sensitivities areincreasing. Thus pB is differentiable in u and dpB/du has the same sign as 2(w/u). We just have to compute w/u in our two examples: Marquee buyers: w~ pB, u ! 5 lB~ pB! 2 lS~c 1 m 2 u 2 pB! w 5 ~lS!9 . 0 ~since DS is log concave !. u Thus dpB/du is negative. Captive buyers: 2~DB!9 w~ pB, u ! 5 2 lS~c 1 m 2 pB! DB 1 u w ~DB!9 5 , 0. u ~DB 1 u !2 And so dpB/du is positive.

(i2)For-Pro t Monopoly. The maximumof the (log) pro tis characterizedby two conditions: 1 lB~ pB, u ! 2 5 0 pB 1 pS 2 c 1 lS~ pS, u ! 2 5 0. 5 pB 1 pS 2 c Denoting by w( p, u)the (vector)function on the left-hand side, wecan apply the implicit function theorem (this timein R 2)given that the Jacobian Dw/Dp is nonsingular (by the strict concavity of log p the determinant of Dw/Dp is positive). Thus weobtain: dp Dw 21 w 5 2 , du S DpD u where lS 1 1 1 2 Dw 21 1 pS ~ p 2 c!2 ~ p 2 c!2 5 B S DpD Dw 1 l 1 det 2 2 B 1 2 Dp 3 ~p 2 c! p ~ p 2 c! 4 1022 Journal of the European Economic Association June 2003 1(4):990 –1029 and lB w u 5 S . u l 1 u 2

Marquee Buyers: lB/u 5 0, lS/u , 0

dpB lS 1 2 2 du u ~ p 2 c!2 S 5 B . dp Dw l 1 det B 1 . 1 du 2 Dp 3 p ~ p 2 c!2 4 Thus dpB/du , 0 and dpS/du . 0.

Captive Buyers: lB/u . 0, lS/u 5 0, and so:

dpB lB lS 1 2 1 du u pS ~p 2 c!2 S 5 dp Dw 1 det 2 2 . 1 du 2 Dp 3 ~p 2 c! 4 Thus dpB/du . 0 and dpS/du , 0.

(ii)Competing Associations. In the case of associations, the equilibrium buyer price is characterizedby:

B B B S B l0 ~ p , u !s~ p , u ! 2 l ~c 1 m 2 p , u ! 5 0, where

B d 1 2 pB B B 1 B B l0 ~ p , u ! 5 B ~ p , p , u! d 1 is the “own-price sensitivity ” of buyer demand and

Dˆ B~ pB, u ! s~ pB, u ! 5 2 2 . dB~ pB, u ! In order to determine the monotonicity properties of pB with respect to u, we apply the implicit function theorem tothe left-hand side of the above equation:

B B B B S B c~ p , u ! 5 l0 ~ p , u !s~ p , u ! 2 l ~c 1 m 2 p , u !. Rochet and Tirole Platform Competition in Two-Sided Markets 1023

However weneed additional assumptions to ensure that c/pB . 0, so that pB(u)is indeed (locally) unique and differentiable, fortwo reasons:

Possible nonexistence of equilibrium, due to the factthat the volume on B S system i is not necessarily quasiconcave with respect to ( pi , pi ). The proof of Proposition 6will observe that the candidate forequilibrium (i.e., the solution of c 5 0) may sometimes be destabilized by “double deviations ” of the form ( pB 1 «, pS 2 «). The possible presence of strategic complementarities that may generate a multiplicity of equilibria.

We will assume away these dif culties and postulate that c/pB . 0 (regularity condition). 37 In this case, pB(u)is (locally) unique, differentiable, and dpB/du has the samesign as 2(c/u).We then just have to determine the sign of c/u.

Marquee Buyers:

B B B B S B c~ p , u ! 5 l0 ~ p !s~ p ! 2 l ~c 1 m 2 u 2 p ! c 5 ~lS!9 . 0. u

Captive Buyers:

B d 1 2 pB DB 1 u B 1 S B c~ p , u ! 5 B 2 2 B 2 l ~c 1 m 2 p ! 1 d 1 1 u2S d 1 uD B B B B B B c l0s d 2 D 2l0 d 2 D 5 2 2 lB 5 s 1 , 0. u d B 1 s ~d B 1 u!2 0 d B 1 u F d B 1 u G An increase in the number of captive buyers has two opposite effects.First, and as in the monopoly case, the captive customers reduce the elasticity of buyer demand, calling fora higher buyer price. Second, captive customers make steering moreattractive, which pushes toward ahigher sellerprice. The rst effectdominates the second.

(iii)Increase in Singlehoming. Again, wefocus on competing associations. The buyer price atequilibrium is determined by:

B B B B B S B c~ p , u ! 5 l0 ~ p !s ~ p , u ! 2 l ~c 1 m 2 p ! 5 0.

B B B 37. This regularity condition is satis ed when lo/p and s/p are positive. 1024 Journal of the European Economic Association June 2003 1(4):990 –1029

By the samereasoning as above, sB/u . 0 implies c/u . 0 and dpB/du . 0.

PROOF OF PROPOSITION 6

(a)Price Structure. Letting T 5 p0 1 d(D 1 d)/2, the quasi-demands aregiven by:38

B B B p2 2 p1 T 2 p1 dB~ pB, pB! 5 1 , (25) 1 1 2 D d and 1 1 DB~ pB! 5 ~T 2 pB! 1 . (26) 1 1 1 S d D 1 dD B B The expressions of d 2 and D2 areobtained by symmetry. Due to the linearity of these expressions, several simpli cations appear. For example, the singlehoming index is price independent:

B B D1 ~ p ! D s 5 2 2 B B B 5 . d1 ~ p , p ! D 1 d Similarlythe expression of the marginal seller(who is indifferent between multihoming and singlehoming with the cheapest platform),does not depend on S S buyers’ prices. For example, when p1 # p2,formula(12) gives: dB dB 2 DB ˆ S 2 S 1 1 b12 5 p2 B B B 1 p1 B B B . d1 1 d2 2 D1 d1 1 d2 2 D1 B B B Hence (for p1 5 p2 5 p ): d bˆ 5 pS 1 ~ pS 2 pS!. 12 2 D 2 1

38. The expressions of quasi-demands are easily deduced from the locations of marginal buyers:

B 1 2 1 2 x1 is indifferent between 1and 1 9: p1 1 2(x1 1 (D/2)) 5 p0 1 2(x1 1 (D/2) 1 d) , which gives: B p1 2 p0 D 1 d x 5 2 ; 1 d 2

B 1 2 B 1 2 x2 is indifferent between 1and 2: p1 1 2(x2 1 (D/2)) 5 p2 1 2(x2 2 (D/2)) ,which gives: B B p2 2 p1 x 5 ; 2 D

B 1 2 1 2 x3 is indifferent between 1and 2 9: p1 1 2(x3 1 (D/2)) 5 p0 1 2(x3 2 (D/2) 2 d) , which gives: B p0 2 p1 x 5 1 d/ 2. 3 D 1 d Rochet and Tirole Platform Competition in Two-Sided Markets 1025

ˆ B and so b12 does not depend on p .Furthermore, steering is particularly powerful (in that undercutting induces many sellers to stop multihoming) when most consumers multihome, that is when s is low. Another simpli cation that appears when buyers ’ quasi-demand is linear is that the ratio of total elasticity to own-brand elasticity is equal to the single homing index s : B B d1 d1 1 B B 1 B h p1 p2 d D B 5 B 5 5 5 s. ho d1 1 1 D 1 d B 1 p1 D d This property implies that the price structure under platformcompetition (between for-pro ts or between associations) is the sameas under amonopoly platform: pB pS 5 . hB hS Consider forexample adecrease in D.Asthe platforms become moresub- stitutable, buyer multihoming increases ( s falls);this induces platforms tosteer, resulting in low prices on the sellerside. However, competition also becomes moreintense on the buyer side, resulting in lower buyer prices ( pB falls) and thereby in ahigher opportunity cost ( c 2 pB)of servicing sellers. For linear demand on the buyer side, these two effectsoffset. Last, let us comparethe common price structure with that of the Ramsey optimum. Auseful property of linear demands is that the revenue (pricetimes quantity) is equal to twicethe product of the net surplus and the elasticity of demand. This property implies that ifseller ’squasi-demand is linear as well, (7) is equivalent to (5), and so the common price structure is Ramsey optimal.

(b)Second-Order Conditions. Inthe Hotelling model:

B S pi 5 ~ pi 1 pi 2 c!Qi;

pi B S Qi B 5 Qi 1 ~ pi 1 pi 2 c! B ; pi pi p Q i B S i S 5 Qi 1 ~ pi 1 pi 2 c! S ; pi pi

2 2 pi Qi pi Qi B 2 5 2 B ; S 2 5 2 S ; ~pi ! pi ~pi ! pi

2 2 pi Qi Qi B S Qi B S 5 B 1 S 1 ~ pi 1 pi 2 c! B S . pi pi pi pi pi pi 1026 Journal of the European Economic Association June 2003 1(4):990 –1029

At asymmetricequilibrium of the gamebetween competing proprietary platforms, wehave

2 Qi Qi ~D 1 d! B 5 S 5 2~ p 2 c! 2 ; a , 0. pi pi D d Thereforethe second-order condition is satis ed whenever the Hessian determinant of pi is nonnegative:

2 2 2 2 pi pi pi H 5 B 2 z S 2 2 B S ~pi ! ~pi ! S pi pi D H 5 4a2 2 ~2a 1 b!2 5 2b~4a 1 b!, where

2 B S Qi b ; ~ pi 1 pi 2 c! B S pi pi has adifferent expression in the two regions:

~D2 1 dD 2 d2! b 5 ~ p 2 c! when pS , pS, and 1 D2d 1 2

~D 1 d!2 b 5 ~ p 2 c! when pS . pS. 2 D2d 1 2 The second-order condition is always satis ed in the second region, since 2 b2 5 2a . 0 so that H 5 3a . 0. In the rst region, it is easy to see that b1 1 4a is always negative. Thus the second-order condition is satis ed ifand only if b1 $ 0, which is equivalent to

d2 2 dD 2 D2 # 0 or

d 1 1 Î5 # . D 2 When this condition is not satis ed, there is no symmetricequilibrium in pure strategies. The only candidate equilibrium ( pB, pS)can be destabilized by B a “double-deviation, ” whereone of the platforms (say Platform1) increases p1 S by « and simultaneously decreases p1 by the sameamount. The rst order increase in pro tis zero (asguaranteed by the rst-orderconditions) but the second-order increase ispositive: Rochet and Tirole Platform Competition in Two-Sided Markets 1027

2p 2p 2p 1 1 1 2 2 Dp1 , B 2 1 S 2 2 2 B S « 5 22b1« . 0. F ~p1 ! ~p1! p1 p1G Finally, equilibrium prices can be obtained explicitly ifwe assume that the sellers’ quasi-demand isalso linear:

DS~ pS! 5 A 2 pS. (27)

S S The volume on Platform1 when p1 # p2 is:

B B B p2 2 p1 T 2 p1 d Q 5 1 A 2 pS 2 ~ pS 2 pS! 1 S D d DF 2 D 2 1 G (28) 1 1 d 1 1 ~T 2 pB!~ pB 2 pS! 1 1 . S d D 1 dD 1 2 1 S DD S S When p1 . p2,the expression issimpler:

B B B d p2 2 p1 T 2 p1 Q 5 A 2 pS 2 ~ pS 2 pS! 1 . (29) 1 F 1 D 1 2 GF D d G In Proposition 2wehave shown that asymmetricequilibrium between competing associations must satisfy condition (22):

pB pS B 5 S . (22) sho h Using formulae(25), (26), and (27) and aftersimpli cations, this condition becomes:

pB 2 pS 5 T 2 A. (30) Recall that this condition isnecessarily satis edinasymmetricequilibrium between competing platforms, independently of their governance structure. However the value of the total price is different:

pB 1 pS 5 c 1 m forassociations, and

D D pB 1 pS 2 c 5 ~T 2 pB! 5 ~ A 2 pS!. D 1 d D 1 d forproprietary platforms. The resulting equilibrium prices are:

B 1 S 1 pA 5 2~c 1 m 1 T 2 A!, pA 5 2~c 1 m 2 T 1 A!, (31) 1028 Journal of the European Economic Association June 2003 1(4):990 –1029 forassociations, and

D D c 2 A 1 T 1 1 c 2 T 1 A 1 1 S D 1 dD S D 1 dD pB 5 , pS 5 (32) P D P D 2 1 2 1 D 1 d D 1 d forproprietary systems.

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