U. Porto Doctoral Programme n Economcs The Economcs of Two-sded Markets 2. Platform competton! Paul Belleflamme, CORE & LSM! Unversté catholque de Louvan! Aprl 10-13, 2012
Learnng objectves At the end of ths lecture, you should be able to o Understand how two competng platforms set prces on both sdes. o Compare two-sded snglehomng settngs wth compettve bottlenecks. o Understand why competng for-proft platforms may gve hgher ncentves to nnovate to sellers than free platforms. o Examne the effects of two-part tarffs and of negatve wthn-sde effects on platform competton. Background readngs o Armstrong, M. 2006. Competton n Two-Sded Markets. RAND Journal of Economcs 37, 668-91. o Belleflamme, P. and Petz, M. 2010. Platform Competton and Seller Investment Incentves. European Economc Revew 50, 1059-1076. o Belleflamme, P. and Toulemonde, E. 2009. Negatve Intra-Group Externaltes n Two-Sded Markets. Internatonal Economc Revew 50, 245-272. 2
A model of platform competton! Model! Pla%orm 1 Mass 1 of sellers; lnear transport cost τ s 0 1 Mass 1 of buyers; lnear transport cost τ b Pla%orm 2 o 2 horzontally dfferentated platforms! o Mass 1 of buyers and mass 1 of sellers unformly dstrbuted on [0,1].! o A buyer at platform buys 1 unt from each seller on ths platform.! o Buyer & seller surplus (gross of any opportunty cost) of vstng platform :! v b = n s u M b and v s = n b π M s Membershp fees set by platform Number of sellers and of buyers actve on the platform Net gan from trade for each unt on the buyer sde Net gan from trade for each unt on the seller sde 3
Two-sded snglehomng Model (contʼd)! o Buyers and sellers are restrcted to vst only one platform Snglehomng on each sde o Partcpaton suffcently attractve! All buyers and sellers partcpate:! n 1 b + n 2 b = 1 and n 1 s + n 2 s = 1 o Tmng! Platforms smultaneously set membershp fees on both sdes.! Buyers and sellers smultaneously choose whch platform to vst.! Buyers and sellers decsons o Indfferent agents: standard Hotellng specfcaton n b = 1 2 + v b v b j 2τ b and n s = 1 2 + v s v s j 2τ s 4
Two-sded snglehomng (2) Buyers and sellers decsons (cont d) o Developng the prevous expressons yelds An addtonal seller attracts u/τ b addtonal buyers. An addtonal buyer attracts π/τ s addtonal sellers. o Assumpton n b (n s ) = 1 2 + 1 2τ b n s (n b ) = 1 2 + 1 2τ s [(2n 1)u (M s M j b b )] [(2n b 1)π (M s M j s )] Indrect network effects are not to strong: (u/τ b ) (π/τ s ) < 1 or uπ < τ b τ s Otherwse only platform would be actve (tppng) 5
Two-sded snglehomng (3) Buyers and sellers decsons (cont d) o Solvng the prevous mplct expressons: n b = 1 2 + u(m j s M s ) + τ s (M j b M b ) 2(τ b τ s uπ) n s = 1 2 + π(m b j M b ) + τ b (M s j M s ) 2(τ b τ s uπ) Number of buyers (sellers) at one platform not only wth membershp fee for buyers (sellers) on ths platform but also wth membershp fee for sellers (buyers) because of ndrect network effects 6
Two-sded snglehomng (4) Platforms prcng decsons o Platform s problem: max M b,m s (M b C b )n b o Frst-order condtons n a symmetrc equlbrum + (M s C s )n s M b 1 = M b 2 = M b = C b + τ b π τ s (u + M s C s ) Value to the pla=orm of add>onal sellers that one add>onal buyer a?racts M s 1 = M s 2 = M s = C s + τ s u τ b (π + M b C b ) Lke n Hotellng model Value to the pla=orm of add>onal buyers that one add>onal seller a?racts 7
Two-sded snglehomng (5) Platforms prcng decsons (cont d) o Nash equlbrum membershp fees M b * = C b + τ b π and M s * = C s + τ b u o Note: pecularty of the model market s covered A prce reducton by one platform doesn t lead to market expanson but only to an ncrease n market shares (on both sdes) o The sde of the market that exerts a strong ndrect network effect on the other tends to be subsdzed. o The sde of the market wth lttle product dfferentaton tends to pay a lower fee. o confrms qualtatve results obtaned n the monopoly platform case. 8
Two-sded snglehomng (6) Subgame-perfect equlbrum o Equlbrum partton: equal splt of buyers and products o Equlbrum net surpluses Increasng n the net gan of the other sde and, to a lesser extent, n the net gan of the own sde. o Equlbrum platforms profts: v b * = 1 2 u + π (C b + τ b ) v s * = 1 2π + u (C s + τ s ) Decrease wth the sze of ndrect network effects. Why? They make buyers and sellers more valuable to attract and thus ntensfy prce competton. True as long as both platforms are actve. Π = 1 2 (τ b + τ s u π) 9
Two-sded snglehomng (7) Generalzaton o More general formulaton for ntra- and nter-group network effects o Notaton v b = u(n b,n s ) M b and v s = π(n b,n s ) M s o Equlbrum fees: Evaluated at (½, ½) 10
Two-sded snglehomng (8) Comparson wth monopoly o Elastcty of the number of buyers and sellers w.r.t. to membershp fees are η b = M b / τ b and η s = M s / τ s o Equlbrum markups M b (C b 2n s π) M b = 1 η b and M s (C s 2n b u) M s = 1 η s -1 n monopoly formulae Compared to the monopoly platform case, membershp fee on one sde s reduced twce as strongly n the sze of the ndrect network effect exerted by the other sde. Effect of a lost seller on the platforms proft s more pronounced under competton. Ths lost seller jons the compettor s platform and thus makes t more dffcult to keep the same number of buyers. 11
Compettve bottlenecks Effects of multhomng o Suppose sellers can multhome whle buyers can only snglehome. o A seller lost to one platform s not a seller ganed by the other platform. o Intermedares have to be more concerned wth losng buyers. o Intermedares compete fercely for buyers Tends to lead to low and possbly even negatve prces for buyers accessng the platform. o Lesson: In a market wth competng ntermedares n whch sellers can set up shops at both ntermedares, the sellers surplus s gnored n the prcng decsons of the ntermedary. For any gven number of buyers, the ntermedary maxmzes the jont surplus between buyers and the ntermedary tself. 12
Compettve bottlenecks (2) Model o Indfferent agents Same as before for buyers: ndfference between the 2 platforms For sellers: ndfference between platform and no partcpaton n b = 1 2 + v j b v b and n 2τ s = v s b τ s o Developng the prevous expressons yelds 13
Compettve bottlenecks (3) Model (cont d) o Solvng for platforms prcng decsons M b * = C b + τ b π 4τ s (3u + π 2C s ) M s * = 1 2 (C s + π 2 ) u 4 On the seller sde, platforms have monopoly power. If they focused only on sellers, they would charge a monopoly prce equal to C s /2 + π/4 (assumng that each seller would have access to half of the buyers and, therefore, would have a gross wllngness to pay equal to π/4). Ths prce s adjusted downward by u/4 when the ndrect network effect that sellers exert on the buyer sde s taken nto account. On the buyer sde, platforms charge the Hotellng prce, C b + τ b, less a term that depends on the sze of the ndrect network effects. 14
Extenson 1 - Sellers nvestment ncentves Abstract model of trade on a platform (Belleflamme and Petz, EER, 2010) K sellers; each sells a mass 1/K of products; draw ther locaton from a unform dstrbuton (learn t after nvestment decson; prvate nformaton); lnear transport cost τ s 0 1 Platform 1 Platform 2 Mass 1 of buyers; draw ther locaton from a unform dstrbuton (prvate nformaton); lnear transport cost τ b 15
Sellers nvestment ncentves (2) Comparson between o Intermedated trade: 2 for-proft platforms o Non-ntermedated trade: 2 free platforms (benchmark) In 3 dfferent market structures o Both sdes of the market snglehome o Sellers multhome, buyers snglehome o Buyers multhome, sellers snglehome Seller nvestments o Dfferent types: Cost reducton, qualty mprovement, marketng measures that facltate prce dscrmnaton or demand expanson o Long-term decsons gvng commtment to sellers Decded before sellers know ther opportunty costs of vstng platforms and before platforms set ther prces. 16
Sellers nvestment ncentves (3) Tmng for ntermedated trade o Stage 1: Intermedares smultaneously set membershp fees on both sdes of the market (for sellers, fee s per product) + sellers and buyers learn ther locaton (ths s prvate nformaton for them) Sellers are ex ante dentcal Ths stage dsappears f trade s non-ntermedated. o Stage 2: Sellers and buyers decde whch platform(s) to vst o Stage 3: Sellers set the prce of ther goods smultaneously Assumpton: Sellers prcng decsons are ndependent. o Stage 4: Buyers make purchasng decsons Assumpton: A buyer at platform has a downward-slopng demand functon for each product traded on ths platform 17
Sellers nvestment ncentves (4) Reduced-form representaton of buyer-seller nteracton o Net gans from trade absent any nvestment! For buyer: u 0 For seller: π 0 o Net gans from trade after nvestment! For buyer: u 1 = u 0 + Δ u For seller: π 1 = π 0 + Δ π We also propose mcro-foundatons for these generc functons. 18
Sellers nvestment ncentves (5) Man results: Sellers may have stronger ncentves to nnovate f competng platforms are for-proft and charge membershp fees. Why?! o Due to for-proft ntermedaton, sellers partly nternalze ncreases n consumer surplus resultng from ther nvestment. When? It depends on o Market structure (whch sde of the market, f any, multhomes?) o Type of nvestment (how does t affect sellers profts and consumer surplus?) 19
Sellers nvestment ncentves (6)" Both sdes snglehome (e.g., specalzed magaznes)! Surplus (gross of any opportunty cost) of vstng platform! o o Suppose 0 k K sellers have nvested, so measure κ = k/k of products beneft from an nnovaton! Number of buyers and of products on the platform v s = v b Indfferent types! n bπ 1 M s n b π 0 M s = n s (κ u 1 + (1 κ)u 0 ) M b b 12 = 1 2 + (n 1 s n 2 s )(κ u 1 + (1 κ)u 0 ) + M 2 1 b M b 2τ b f seller has nvested otherwse Membershp fees set by ntermedary s 12 = 1 2 + (n 1 b n 2 b )π 0 + M 2 1 s M s and s 2τ 12 = 1 s 2 + (n 1 b n 2 b )π 1 + M 2 1 s M s 2τ s 20
Sellers nvestment ncentves (7) Nash equlbrum membershp fees (same analyss as before) M * b = C b + τ b π and M * s = C s + τ b u wth u = κ u 1 + (1 κ)u 0, π = κπ 1 + (1 κ)π 0 Equlbrum partton: equal splt of buyers and products Equlbrum net surpluses 1 v * s = 2π 1 + u (C s + τ s ) 1 2π 0 + u (C s + τ s ) v * b = 1 2 u + π (C b + τ b ) f seller has nvested otherwse o Increasng n the net gan of the other sde and, to a lesser extent, n the net gan of the own sde 21
Sellers nvestment ncentves (8) Seller nvests n none or all of hs products. Per product net surplus (supposng 0 k < K sellers nvest)! If no nvestment : If nvestment : V s (κ + V s (κ) = 1 2π 0 + u (κ) (C s + τ s ) 1 K ) = 1 2 π 1 + u (κ + 1 K ) (C s + τ s ) Incentves to nnovate under ntermedated trade! I m = V s (κ + 1 ) V (κ) = 1 (π π ) + 1 (u u ) K s 2 1 0 K 1 0 Non-ntermedated trade: each seller nteracts wth ½ of the buyers " I n = 1 (π π ) 2 1 0 Comparson:! I m I n = 1 K (u 1 u 0 ) = 1 K Δ u 22
Sellers nvestment ncentves (9) Proposton 1. In the two-sded snglehomng model, forproft tradng platforms gve stronger nvestment ncentves for sellers f and only f the nvestment ncreases the buyer s surplus. Intuton! o If nvestment ncreases buyerʼs surplus, then platforms charge lower fees to sellers.! o Ths provdes an extra ncentve to nvest w.r.t. free platforms (where ths prce effect s absent).! o Naturally, the opposte prevals f nvestment decreases buyerʼs surplus.! 23
Sellers nvestment ncentves (10) Compettve bottlenecks? o Proposton 2. In the compettve bottleneck model n whch sellers are on the multhomng sde, for-proft tradng platforms gve stronger nvestment ncentves for sellers f and only f the change of the buyer s surplus s larger than the change of the seller s surplus. o Proposton 3. In the compettve bottleneck model n whch buyers are on the multhomng sde, for-proft tradng platforms gve stronger nvestment ncentves for sellers f the jont buyer s and seller s surplus ncreases. 24
Sellers nvestment ncentves (11) Summary: hgher ncentves under ntermedated trade f Intuton (1) buyers and sellers snglehome : Δ u > 0 (2) buyers snglehome/sellers multhome : Δ u > Δ π (3) sellers snglehome/buyers multhome : Δ u + Δ π > 0 o As the ntensty of competton for sellers ncreases, for-proft platforms are more lkely than open platforms to provde better seller nvestment ncentves. o Condton become less demandng when nature of platform competton moves From (2) to (1) From (1) to (3) 25
Sellers nvestment ncentves (12)! Mcro foundaton of buyer-seller relatonshp and of dfferent types of nvestment.! 26
Extenson 2 Two-part tarffs! Platforms often charge two-part tarffs to at least one of the sdes,.e., combnatons of! o Membershp (or subscrpton) fees, and! o Usage (or per-transacton) fees! Examples! o Software platforms developers are charged a fxed fee for gettng access to the systemʼs source code and n addton pay royaltes for the applcatons they sell to users.! o Credt card systems.! Implcatons of ths form of prce dscrmnaton on the profts of competng platforms and on the welfare of the two sdes?! 27
Extenson 2 Two-part tarffs (2)! Modfed model! o Buyer & seller surplus (gross of any opportunty cost) of vstng platform :! v b = (u m b )n s M b and v s = (π m s )n b M s o Platform ʼs proft! Usage fees set by platform Per-transacton cost Π = (M b C b )n b + (M s C s )n s + (m b + m s c)n b n s o Each platform has now 4 choce varables.! General result: there exst a contnuum of equlbra n the prce-settng game.! 28
Extenson 2 Two-part tarffs (3)! Two-sded snglehomng (Armstrong, RAND, 2006)! o Suppose c = 0 and 4τ b τ s > (u+π) 2 o A contnuum of symmetrc equlbra exst wth platforms chargng T b = M b + m b n s and T s = M s + m s n b, where! M b = C b + τ b π + 1 2 (m s m b ) M s = C s + τ s u + 1 2 (m b m s ) 0 m b 2u and 0 m s 2π Π = 1 (τ + τ u π) + 1 (m + m ) 2 b s 4 b s o Platformsʼ proft at equlbrum:! Increasng n the usage fees.! Why? Hgh usage fees reduce, and even overturn, the cross-sde network effects that make the platform market so compettve.! o Multple equlbra arse because each platform has a contnuum of best responses for a gven choce of tarff by ts rval.! Dfferent combnatons of fxed and usage fees yeld same proft.! 29
Extenson 2 Two-part tarffs (4)! Compettve bottlenecks (Resnger, 2011)! o Same problem of contnuum of equlbra wth two-part tarffs.! o The proft and the welfare of the two sdes s dfferent n each of these equlbra. Model lacks predctve power.! o Proposed soluton! Allow for heterogeneous tradng behavor of agents on both sdes.! Unque equlbrum even n the lmt as the heterogenety vanshes.! o Model! Sellers can multhome; buyers can only snglehome.! On each sde: 2 types dffer wth respect to ther tradng behavor.! A mass b of buyers nteract wth each seller only wth probablty β <1.! A mass s of buyers nteract wth each buyer only wth probablty σ <1.! wth b, s > 0 but small.! Platforms are unable to prce dscrmnate across types.! 30
Extenson 2 Two-part tarffs (5)! Compettve bottlenecks (contʼd)! o Buyer & seller surplus! v b = (1 s)(u m b )n s + s(u m b )σn sσ M b (regular) (1 s)(u m b )βn s + s(u m b )βσn sσ M b (b - type) v s = (1 b)(π m s)n b + b(π m s )βn bβ M s (regular) (1 b)(π m s )σn b + b(π m s )σβn bβ M s (s - type) o Leads to a unque equlbrum, even wth b,s 0! See detals n Resnger (2001).! Note: hs model dffers slghtly from the one presented here! Notaton! Dstrbuton of sellers! 31
Extenson 2 Two-part tarffs (6)! Compettve bottlenecks (contʼd)! o Intuton! The two types react dfferently to a partcular combnaton of the membershp and the usage fee.! E.g., seller of type s trades less often to keep hs utlty constant, an ncrease n usage fee must be coupled wth a smaller reducton of the membershp fee than to keep the utlty of a seller of regular type constant.! The effect on proft of a margnal change n ʼs usage fee s no longer a constant multple of the effect of a margnal change n ʼs membershp fee.! Ths multple vares contnuously as the fees change because the rato of the two types that jon platform also vares contnuously.! Each platform has a unque optmal combnaton of the fees as a reacton to the prce quadruple of ts rval.! 32
Further ssues 1 Effects of competton! Competton on two-sded markets may be prce-ncreasng! o Böhme and Müller (2010)! Compare monopoly and duopoly model of a two-sded market.! Consumers / Advertsers! If 2 platforms, consumers snglehome whle advertsers multhome.! The two settngs are fully comparable! Homogeneous good produced at zero costs wthout capacty constrants! Identcal parameterzaton of market szes.! They determne the duopoly equlbrum and the monopoly optmum n terms of the parameters and obtan solutons wth and wthout subsdzaton (prces below margnal cost) of one market sde.! They show that there exsts a contnuum of economcally plausble parameter sets for whch duopoly equlbrum prces exceed optmal monopoly prces and one wth no observable prce effect of competton,.e. one where optmum and equlbrum prces become equal.! Effect of competton on total welfare? Ambguous n subsdzaton cases, but strctly postve f no subsdzaton takes place.! 33
Further ssues 1 Effects of competton (2)! Prce-ncreasng competton (contʼd)! o Intuton! Two conflctng effects of competton! Tradtonal effect of reducng prces.! Demand-enhancng effect on the sngle-homng market sde, whch drves prces upwards.! It s possble that the former effect does not fully compensate the latter effect, whch ether causes no observable prce effect or prce-ncreasng competton.! o Implcatons! Merger analyss mergers do not necessarly lead to hgher prces n twosded markets! 34
Further ssues 2 Wthn-sde effects! So far! o Focus on cross-sde effects.! o Competton among exstng platforms.! To be consdered! o Wthn-sde effects competton among sellers.! o Launch of a new platform! Belleflamme and Toulemonde (IER, 2009)! o Can a for-proft platform succeed n an envronment where agents have the possblty to nteract on a free (publc or open) platform?! o If yes, how?! o What are the effects of wthn-sde effects (ntra-group externaltes)?! 35
Further ssues 2 Wthn-sde effects (2)! Man ntuton! o New platform faces a chcken-and-egg problem.! o Way to solve t dvde-and-conquer prcng strategy! Subsdze the partcpaton of one sde (dvde) and recover the loss on the other sde (conquer)! o Wthn-sde effects (rvalry) blur the pcture! Wllngness to pay of rval agents f only a few move! Good news: rval agentsʼ care less about other group's partcpaton.! Bad news: other group less wllng to jon f only a few rval agents jon! Man results! o Benchmark (no rvalry): always proftable to launch the new platform wth approprate dvde-and-conquer strategy! o Rvalry n one group: wthn-sde effects may undermne all attempts to launch the new platform.! 36
Further ssues 2 Wthn-sde effects (3)! Model! o 2 groups of homogeneous agents, 1 and 2: N 1 3 and N 2 3 agents! o At t = 0, the 2 groups nteract on a free platform! o At t = 1, ntermedary consders launchng a competng platform! o Both sdes sngle-home! ο π (n, n j ) gross beneft for an agent of type from nteractng on a platform wth n agents of ts own type and n j agents of the other type! o Propertes of beneft functons:! Postve cross - sde effects π (n,n j +1) π (n,n j ) Negatve wthn - sde effects (possbly) π (n +1,n j ) π (n,n j ) 37
Further ssues 2 Wthn-sde effects (4)! Benchmark: no rvalry! o Notaton! Beneft functons: π 1 (n 2 ), π 2 (n 1 ) Intal benefts: π 1 (N 2 ), π 2 (N 1 ) Outsde opton (endogenous!)! If N π (N j ) > N j π j (N ), then group s ʻhgh-value groupʼ! o Tmng! Intermedary sets membershp fee A 1 for agents of group 1.! Agents of group 1 choose whether to swtch to the new platform or not.! Intermedary sets membershp fee A 2 for agents of group 2.! Agents of group 2 choose whether to swtch to the new platform or not.! o Equlbrum concept: subgame perfecton wth unque mplementaton! Intermedary must set fees so that a unque NE ensues (wth partcpaton of both groups)! 38
Further ssues 2 Wthn-sde effects (5)! Benchmark: no rvalry (contʼd)! o Lemma 1. Suppose group j s non rval and does not move before group k. Then all agents of group j make the same swtchng decson.! Why? Homogeneous agents and no effect on other groupʼs moves.! o Stage 4. 2 potental NE! No agent swtches ff A 2 > π 2 (n 1 ) - π 2 (N 1 - n 1 ) All N 2 agents swtch ff A 2 π 2 (n 1 ) - π 2 (N 1 - n 1 ) o Stage 3. Hghest fee compatble wth N 2 agents movng! A 2 = π 2 (n 1 ) π 2 (N 1 n 1 ) 0 n 1 N 1 /2 n * 2 (n 1 ) = N 2 f n 1 N 1 /2 0 otherwse o Stage 2. No NE wth 0 < n 1 < N 1 agents of group 1 swtchng.! (More complcated argument than for stage 4!)! 39
Further ssues 2 Wthn-sde effects (6)! Benchmark: no rvalry (contʼd)! o Stage 2. 2 potental equlbra! n * 1 = N 1 f A 1 π 1 (N 2 ) 0 f A 1 > π 1 (N 2 ) coexstence of equlbra for all π 1 (N 2 ) < A 1 π 1 (N 2 ) o Stage 1. Unque mplementaton: select fee such that n 1 = N 1 s the unque equlbrum n stage 2! A 1 = - π 1 (N 2 )! Intermedaryʼs profts: -N 1 π 1 (N 2 ) + N 2 π 2 (N 1 ) Postve f group 2 s hgh-value group! Otherwse, start wth group 2! o Optmal conduct: (1) subsdze low-value group, (2) tax hgh-value group! o All agents move (same result wth smultaneous swtchng)! 40
Further ssues 2 Wthn-sde effects (7)! Effects of rvalry! o Notaton! Rval group: π r (n, n r ) Independent group: π (n r ) o Example: lnear specfcaton! π (n r ) = α n r π r (n,n r ) = α n µn r r f n > 0 0 f n = 0 wth µn r < α r 41
Further ssues 2 Wthn-sde effects (8)! Effects of rvalry lnear specfcaton! µ N (α r -α ) 1 2N (α r -α ) N r +4 2 3 N (α r -α ) N r 4 o Area 1. Subsdze rval agents! o Area 2. Subsdze rval agents (sequental) / No proft (smultaneous).! o Area 3. No proft.! o Area 4. Subsdze ndependent agents! α r -α 42