Inter-Technology versus Intra-Technology Competition in Network Markets by Tobias Langenberg *

Transcription

1 EURAS Yarbook of Standardization, Vol 5 Homo Oconomicus XXI1(1) (ACCEDO, Munich 005) Intr-Tchnology vrsus Intra-Tchnology Comptition in Ntwork Markts by Tobias Langnbrg * Abstract: Th modl analyzs th comptition btwn two firms whn thir incompatibl tchnologis xhibit ntwork ffcts in that high xpctd sals incras th willingnss to pay for th corrsponding good An incumbnt firm facs th stratgic choic of whthr to shar its suprior tchnology (via fr licnsing) with a followr or to kp its tchnology for itslf Th first option of sponsoring intra-tchnology comptition incrass th incumbnt firm s ntwork and thus consumrs willingnss to pay On th othr hand, th lattr option involvs intr-tchnology comptition Dpnding on th rlativ cost advantag of th incumbnt firm, th ntry of th rival tchnology may b blockadd, both tchnologis can coxist in an incompatibl duopoly or th incumbnt firm may dtr th ntry of its rival Th modl invstigats th incumbnt firm s choic of whthr to sponsor intra-tchnology comptition or to insist on intr-tchnology comptition 1 Introduction A fundamntal qustion of stratgy for a firm facing horizontal comptition in a ntwork markt is whthr to shar its tchnology with othr firms and to compt within a joint ntwork or to kp its tchnology for itslf 1 With just two firms, this stratgic choic involvs thr combinations of stratgis (Bsn and Farll, 1994) In th first, both firms prfr intr-tchnology comptition to dtrmin th industry standard In th scond cas, which corrsponds to th Battl of th Sxs, both firms want to compt within a joint ntwork but thy * Institut of Public Financ, Univrsity of Hamburg, Von-Mll-Park 5, D-0146 Hamburg, -mail: langnbg@conuni-hamburgd I would lik to thank Manfrd J Hollr, Hid Conn, Jörg Gröndahl and two anonymous rfrs for hlpful commnts on an arlir draft 1 Altrnativly, firms could nsur (at last partial) compatibility by using convrtrs In this cas, thy might adopt diffrnt tchnologis without losing th ntwork advantag of a joint tchnology For this altrnativ, s Farrll and Salonr (199)

2 T Langnbrg cannot agr on th standard: Each sponsor wants th othr to join its ntwork but would b willing to join th othr s if th altrnativ is incompatibility (Bsn and Farrll, 1994, p 15) Finally, in th last cas, on sponsor may prfr to maintain its tchnology whil th comptitor may wish to join th rival s ntwork It is an mpirical qustion whthr firms actually invit potntial rivals to licns thir tchnology and to compt within a joint ntwork In th arly 1980s, Intl licnsd its microprocssor dsigns to AMD Latr on, Intl rvrsd this dcision and brok off its agrmnt with AMD (s, for xampl, Shapiro and Varian, 1999, p 15) Anothr wll-known xampl for both intrtchnology and intra-tchnology comptition is th VHS/Btamax contst to dtrmin th standard for vido casstt rcordrs Dspit an arly lad and a suprior quality, th Sony Btamax systm was finally drivn out of th markt by th VHS systm from Japan Victor Corporation (JVC) Th ultimat victory of VHS can b attributd to JVC s stratgy of licnsing its tchnology to othr manufacturrs (s, for xampl, Grindly, 1995, pp ) In this modl, w follow Economids (1996) who assums that high xpctd sals incras th willingnss to pay for th ntwork good H shows that it can b bnficial for th xclusiv holdr of a ntwork tchnology to invit comptitors into its ntwork Th rason for this sming paradox (Economids, 1996, p 31) is that th holdr of th tchnology cannot crdibly commit to a ntwork siz which xcds its rlativly low profit-maximizing monopoly output Consumrs xpctations hav to b fulfilld at th quilibrium lvl Th invitation of othr firms is a slf-binding dvic for th innovator bcaus th rational consumrs anticipat that th markt s total output riss with th numbr of comptitors Whras th modl by Economids is confind to intra-tchnology comptition, this papr also dals with intr-tchnology comptition W focus on two firms A and B, ach is th xclusiv holdr of a tchnology Th modling of intr-tchnology comptition is basd on a systm of two linar dmand functions Total dmand can b incrasd by ntwork ffcts, i th markt siz is not fixd such as in modls of th Hotlling-typ Two asymmtris occur: First, firm A is assumd to b th quantity ladr Scondly, th tchnologis may hav diffrnt marginal costs Th incumbnt firm A facs th problm whthr to shar its suprior tchnology (via fr licnsing) with th potntial comptitor B or to kp its tchnology for itslf Lik in th modl by Economids, th invitation of comptitor B into product markt A incrass th ntwork siz and thus consumrs willingnss to pay S Hollr, Knips and Niskann (1997) for an ovrviw of various modls with ntwork ffcts

3 Intr-Tchnology vrsus Intra-Tchnology Comptition 3 If th incumbnt kps its tchnology for itslf, thr diffrnt quilibria may occur Dpnding on th rlativ cost advantag of tchnology A, th ntry of tchnology B can b blockadd, 3 both tchnologis may coxist in an incompatibl and htrognous duopoly or th incumbnt can dtr th ntry of tchnology B W will show that th incumbnt can raliz a highr profit in th cas of ntry dtrrnc than in th situation whr th comptitor s ntry is blockadd 4 Convrsly, th txtbook rsult (s, for xampl, Pfählr and Wis, 1998, p 116) is that th incumbnt s ntry dtrrnc stratgy is lss profitabl By supplying th dtrrnc output, th incumbnt not only prvnts th comptitor s ntry, it also crdibly commits to a quantity which xcds th profitmaximizing monopoly output As a consqunc, consumrs hav an incrasd willingnss to pay Furthrmor, it is shown that th dtrrnc profit can ris with dcrasing marginal costs of th compting tchnology Th rason for this prvrs ffct is that th positiv ntwork ffct of xpanding th quantity may xcd th dtrrnc costs Thr alrady xist modls daling with ntwork ffcts and ntry dtrrnc Gnrally, ths modls xamin how an incumbnt xploits th ntwork ffct in ordr to prvnt th ntry of a compting tchnology For xampl, Church and Gandal (1996) assum that th incumbnt can commit arlir to an installd bas of complmntary goods than its comptitor By ovr-invsting in th installd bas, th incumbnt strngthns th indirct ntwork ffcts for its tchnology so that th markt ntry of th compting systm is prvntd In an arlir modl, Farrll and Salonr (1986) dmonstrat that th incumbnt can prvnt th ntry of a compting ntwork tchnology by using prdatory pricing In this papr, it will b dmonstratd that ntry dtrrnc can only b a fulfilld xpctations quilibrium if th incumbnt s cost advantag is not too strong In th cas of a strong cost advantag, th ntry of th compting tchnology is blockadd and th incumbnt cannot crdibly commit to a ntwork siz that xcds its profit-maximizing monopoly quantity On th othr hand, if on tchnology only has a wak cost advantag, both tchnologis coxist in an incompatibl and htrognous duopoly Th rquirmnt, that xpctations hav to b fulfilld in th quilibrium, maks it ncssary to dtrmin th quilibrium in a two-stp approach: In th 3 In sction 3, w will omit th assumption that tchnology A is suprior As a consqunc, th ntry of A can b blockadd if tchnology B has a considrabl cost advantag 4 In this papr, th usual trminology is usd which distinguishs btwn dtrrd and blockadd ntry Blockadd ntry occurs whn th incumbnt just chooss th profit-maximizing stratgy and, givn this dcision, it is not worthwhil for th comptitor to ntr th markt Entry dtrrnc rfrs to situations whr th incumbnt has to modify its stratgy in ordr to prvnt ntry bcaus th comptitor is not as wak in trms of costs or quality as in th formr cas

4 4 T Langnbrg first stp, w will comput th profit-maximizing quantitis that fulfill xpctations for a givn path Th scond stp dals with th fact that firms could lav th path Stability conditions will b drivd for ach path and it will b shown that ths conditions nsur th uniqunss of th fulfilld xpctations quilibrium Th structur of th papr is as follows: Sction prsnts th modl assumptions Sction 3 is confind to intr-tchnology comptition Sction 4 xtnds th analysis to th incumbnt s stratgic problm whthr to shar its tchnology with th comptitor or to kp its tchnology for itslf In ordr to focus on th comparison of ntry dtrrnc with th invitation stratgy, w will assum that tchnology A has a modrat cost advantag It will b dmonstratd that ntry dtrrnc can b mor profitabl for th incumbnt than inviting ntry Concluding rmarks follow in sction 5 Modl structur Suppos that thr ar two incompatibl ntwork tchnologis i = A, B xclusivly hld by two firms Th dmand for th ntwork goods A and B is givn by th following systm of linar invrs dmand functions: i i i i j i (1) p = α β y γ y + n y, i, j = A, B, i j Th paramtr γ dnots th dgr of substitutability 5 For simplicity, suppos that βa = βb = 1 holds Morovr, lt us assum 0< γ < 1, thus th markts for A and B ar intrdpndnt Ntwork ffcts for good i dpnd on th lvl of xpctd sals y i and on th ntwork ffct paramtr 0 n 1 6 Thus, ntwork ffcts push th dmand curvs (for givn xpctations) up without changing thir slops 7 For ach unit sold, th ntwork bnfit is th sam For simplicity, suppos that th tchnologis hav constant marginal costs with 0 ci < αi Hnc, at last on firm will supply a positiv quantity Th modl has thr stags In th first stag, consumrs form xpctations by backward induction, i thy anticipat th quilibrium lvls of sals In th 5 This linar dmand systm - xcpt th ntwork ffct - gos back to Spnc (1976), Dixit (1979), and Singh and Vivs (1984) 6 For a discussion of th functional form of ntwork ffcts, s Swann (00) 7 S Wis (1997) who distinguishs btwn th dmand curvs for a givn lvl of sals xpctations and th fulfilld xpctations dmand curv which is dfind by quating xpctd sals with actual dmand

5 Intr-Tchnology vrsus Intra-Tchnology Comptition 5 AD, 0 scond stag, firm A (which is assumd to b th quantity ladr) slcts th profit-maximizing quantity of A Firm B rsponds in th third stag with th profitmaximizing quantity of B Four quilibrium paths may occur: 1 Both tchnologis can coxist in a htrognous and incompatibl duopoly, i firm B rsponds with y BI, * > 0 to th ladr quantity y AI, * > 0 Th markt ntry of firm B can b blockadd if firm A has a strong cost advantag Thn, firm A is abl to slct th profit-maximizing quantity y AM, * > 0 without paying attntion to firm B 3 In th cas of a strong cost advantag of tchnology B, th markt ntry of tchnology A may b blockadd so that followr B slcts th profit-maximizing quantity y B, M * > 0 in th third priod 4 If firm A has a modrat cost advantag, it can xploit its first movr advantag in ordr to dtr th ntry of th compting tchnology 8 Th dtrrnc quantity y * > is drivd from firm B s raction function It corrsponds to th quantity of good A which maks firm B rspond with an output qual to zro Figur 1 summarizs th timing structur and th possibl quilibrium paths which must fulfill consumrs xpctations Figur 1 Modl structur and possibl quilibrium paths 8 W do not distinguish btwn quantity and capacity in this modl Howvr, Dixit (1980) dmonstrats in a two-stag gam that th incumbnt cannot dtr ntry by invsting in a larg capacity, i th dtrrnc stratgy would not b subgam-prfct

6 6 3 Fulfilld xpctations quilibrium T Langnbrg Th fulfilld xpctations quilibrium is computd in a two-stp approach In th first stp, th profit-maximizing quantitis ar drivd for a givn path, i th quantitis must b qual to th path xpctations For xampl, considr th cas whr firm A has a monopoly and th ntry of tchnology B is blockadd As usual, w apply th backward-induction principl Starting in th scond stag, th profit-maximizing monopoly output is computd as a function of th xpctd ntwork siz Finally, in th first stag th xpctations ar ndognizd: At th quilibrium lvl, actual quantitis hav to b qual to th xpctd ons Th scond stp dals with th fact that firms could lav th path, givn th path xpctations Considr th xampl of firm A s monopoly with blockadd ntry of B In th third stag, firm B slcts th optimal quantity of good B, givn th path xpctations and firm A s optimal quantity If it wr bnficial for firm B to supply a positiv quantity of good B, i to lav th path, th path would not b consistnt any longr and consumrs would anticipat firm B to dviat Thus, rational xpctations xclud this path For th othr paths, w can dfin similar stability conditions 31 Profit-maximizing quantitis with fulfilld path xpctations This sction dals with th first stp of computing a fulfilld xpctations quilibrium For a givn path, w will driv th profit-maximizing quantitis which ar qual to th xpctd ons 311 Monopoly with blockadd ntry of th comptitor Assum that firm i has a considrabl cost advantag so that th ntry of tchnology j is blockadd Th profit function of monopolist i is givn by () im, yim, ( αi yim, n yi ci) Π = + Maximizing th profit function with rspct to y im, rsults in th monopoly quantity for givn xpctations: α (3), *( ) i ci + n y y i im yi = Th maximum monopoly profit for givn xpctations is qual to

7 Intr-Tchnology vrsus Intra-Tchnology Comptition 7 (4) im, *( yi ) ( α ) i c i + ny i = 4 Th xpctd quantity y i must b st qual to th actual quantity y im, * This dfins th lvl of fulfilld xpctations as th solution of α c n (5) yim, * = yim, *( yim, *) yim, * = i i, whr yim, *( y i) was substitutd from Equation (3) Th maximum monopoly profit with fulfilld xpctations is thn givn by (6) ( α ), * i c im i Π = ( n ) 31 Incompatibl duopoly In th scond stag, firm A slcts y A, I as th quantity of good A Firm B rsponds in th third stag with quantity y B, I of product B Th profit functions of th duopolists ar givn by i i i i j i i (7) Π = y ( α y γ y + n y c ) Maximizing th followr s profit function with rspct to y B, I rsults in th followr s optimal quantity for givn xpctations y B and for th givn ladr quantity y A, I : (8) BI, B AI, y *( y, y ) B cb γ ya, I + n yb α = Substituting Equation (8) in th profit function of firm A and maximizing with rspct to y A, I yilds th optimal ladr quantity for givn xpctations y A and y : B ( α ) ( ) ( ) (9), *(, ) A ca γ αb cb n γ yb y y A AI ya yb = ( γ )

8 8 T Langnbrg Substituting Equation (9) back in Equation (8) yilds th followr s bst rply (10) ybi, *( ya, y B) = (4 γ )( αb cb) γ ( αa ca) n( γ yb 4 yb + γ ya) 4( γ ) Aftr having drivd th optimal quantitis of A and B as functions of th xpctd ntwork sizs, th xpctations hav to b ndognizd in th first stag W mak us of Equations (9) and (10) to dfin th fixd point conditions yii, * = yii, *( yii, *, yji, *), i, j = A, B, i j Solving ths conditions for y A, I * and y B, I * rsults in th optimal quantitis of A and B which fulfill xpctations: γ ( α ) (4 )( ) (11), * B cb n αa c y A AI =, (4 n) γ ( n 4n+ 4) (1) y γ α, * A ca + γ + n αb cb BI = ( ) ( 4 )( ) (4 n) γ ( n 4n+ 4) Th maximum profits of firm A and B ar givn by: (13) (14) [ ] γ γ αb B αa A, * ( ) ( c ) ( n)( c ) Π AI = ( n 4n+ 4) γ (4 n) γ( αa ca) + ( γ + n 4)( αb cb) Π BI, * = ( n 4n+ 4) γ (4 n), Figur shows th profit-maximizing quantitis (as dashd lins) and th maximum profits with fulfilld xpctations Quantitis and profits ar functions of altrnativ marginal costs c B Th lowr and th uppr bounds of th incompatibl duopoly ar dnotd by c B,1 and c B,, rspctivly At th quilibrium lvl, th quantitis hav to b positiv, i y AI, * > 0 and y BI, * > 0 must hold

9 Intr-Tchnology vrsus Intra-Tchnology Comptition 9 Figur Profit-maximizing quantitis and maximum profits with fulfilld xpctations for αa = αb = 1, n = γ = 08 and CA = 05 Aftr rarranging Equations (11) and (1), w s that an incompatibl duopoly with fulfilld xpctations xists if ( n)( α c ) γ ( α c ) γ 4 n γ (15) c A A A A B,1 = αb < cb < cb, = αb In Figur, th quantitis and profits of firm A ris with c B On th othr hand, th quantitis and profits of firm B dcras with c B Gnrally, quantitis and profits show normal ractions to cost variations if yii, * γ = > c j ( n 4n+ 4) (4 n) γ 0 with i, j = A, B, i j, y * BI, γ + n 4 = < c B ( n 4n+ 4) (4 n) γ y AI, * n 4 = < c A ( n 4n+ 4) (4 n) γ 0 0 and holds Sinc γ > 0, γ + n 4< 0 and n 4< 0, th dnominators must b positiv Making us of this condition, w hav

10 30 (16) T Langnbrg y * * ii, yii, γ + γ γ + 16 > 0 and < 0 n< nid = cj ci 4 In th following analysis, w will assum that n< nid holds With incrasing ntwork paramtr n and rising dgr of substitutability γ, th xistnc ara cb,1, cb, shrinks and th functions y A, I * and y B, I * bcom stpr Th cas of cb,1 = cb, corrsponds to th situation of n = nid : Th incompatibl duopoly dos not xist any longr and y * and y * ar vrtical lins A, I Proposition 1 Th incompatibl duopoly occurs as a fulfilld xpctations quilibrium if cb,1 < cb < cb, holds B, I 313 Entry dtrrnc In th scond stag, quantity ladr A can supply an xcssiv quantity of good A in ordr to prvnt th ntry of tchnology B in th following stag Th optimal rspons of firm B, givn by Equation (8), must b st qual to zro Substituting rational xpctations y B = 0 and solving for y A rsults in th dtr- rnc output which fulfills xpctations: (17)! αb c B γ y A, D α y, * 0, * B c B BI = = yad = γ A D Substitution of y, * and y B = 0 in th profit function of firm A, givn by Equation (7), yilds th dtrrnc profit with fulfilld xpctations: (18) [ γ α ] ( αb cb) ( A ca) (1 n)( b cb) Π AD, * = γ Figur 3 dpicts dtrrnc quantitis and profits as functions of altrnativ marginal costs c B In th intrval x' c B 1, firm A s dtrrnc profit, Π A, D *, riss with dcrasing marginal costs, c B, of its rival To idntify th rason for this prvrs cost ffct, it is ncssary to scrutiniz firm A s profit function Th dtrrnc profit is composd of th dtrrnc rvnu, r A, D *, and total costs ca y AD, * As shown in Figur 3, firm A has to supply a largr dtrrnc quantity, y A, D *, with dcrasing c B Th largr ntwork siz rsults

11 Intr-Tchnology vrsus Intra-Tchnology Comptition 31 in an incrasd willingnss to pay for good A 9 Th dtrrnc rvnu is hyprbolic, it is maximal at x and gos back to zro bcaus th positiv ntwork ffct of th quantity xpansion is finally offst by a ngativ pric ffct Figur 3 Entry dtrrnc output and profit for αa = αb = 1, n = γ = c A = 05 Th dtrrnc profit is positiv if (19) γ ( α ) A, D* 0 B A c Π > α A < cb < αb 1 n holds Figur 4 illustrats how th dtrrnc profit racts to variations of th dgr of substitutability If th dgr of substitutability, γ, is low, firm A nds a largr quantity in ordr to prvnt th ntry of tchnology B Thus, starting with max c B = 1, th maximum dtrrnc profit Π AD, *( c B ) and th zro point ar rachd fastr 9 Th ntry dtrrnc stratgy is not ncssarily a crdibl commitmnt Latr on, w will driv th conditions for crdibility

12 3 T Langnbrg Figur 4 Impact of γ on th dtrrnc profit for αa = αb = 1, n = c A = 05 Figur 4 also dmonstrats that th maximum dtrrnc profit is indpndnt of th dgr of substitutability: (0) max (1 n) αb γ ( αa c A ) max ; ( α ), *( ) A c c A B = Π A D cb = (1 n) 4(1 n) Th impact of th ntwork paramtr n on th dtrrnc profit is unambiguous, i th dtrrnc profit always riss in n : (1) d Π * AD, ( αb cb) = > 0 dn γ Figur 5 dpicts this rsult If n approachs its uppr limit n = 1, th dtrrnc profit is illustratd by a straight lin Figur 5 Impact of n on th dtrrnc profit for αa = αb = 1, γ = c A = 05

13 Intr-Tchnology vrsus Intra-Tchnology Comptition 33 3 Consistncy of quilibrium paths So far, w hav drivd th profit-maximizing quantitis which fulfill xpctations on a givn path For xampl, in th cas of blockadd ntry, it was assumd that it is not bnficial for th wakr firm to ntr th markt Th scond stp of th quilibrium analysis dals with th fact that firms may dviat from th path 31 Blockadd ntry of tchnology B Suppos that th ntry of tchnology B is blockadd Th possibl quilibrium path with fulfilld xpctations is givn by: First stag: Consumrs form th xpctations ya = yam, * and y B = 0 Scond stag: Firm A slcts th monopoly quantity y A, M * Third stag: Firm B dos not ntr th markt, i y * = BI, 0 Starting with th third stag, w xamin whthr it is bnficial for firm B to choos y BI, * = 0 Substituting path xpctations y B = 0 and th ladr quantity y = y * in firm B s bst rply, givn by Equation (8), yilds: A AM, ( n)( B cb) ( A ca) B B B A A, M ( n) () y = y ( y = 0, y = y *) = γ( α ) (3) 0 A c y A B cb cb,3 = α B n α γ α Proposition Th markt ntry of tchnology B is blockadd if cb cb,3 holds Not that th uppr bound of th incompatibl duopoly, c B,, is always smallr than th lowr bound, c B,3, of tchnology B s blockadd ntry: c γ ( α c ) γ ( α c ) 4 n γ n A A A A B, = αb < c B,3 = αb Rarranging th inquation yilds

14 34 γ α T Langnbrg γ α ( A ca) ( A c ) < A 4 n 4 n γ, which is always fulfilld Hnc, th blockadd ntry of tchnology B xcluds th incompatibl duopoly 3 Blockadd ntry of tchnology A Th nxt stp is to analyz undr which circumstancs th ntry of tchnology A is blockadd Th possibl quilibrium path is givn by: First stag: Consumrs form th xpctations y A = 0 and yb = ybm, * Scond stag: Firm A dos not ntr th markt, i y A* = 0 Third stag: Firm B supplis th monopoly quantity y * B, M In ordr to xamin whthr it is bnficial for firm A to choos y A* = 0, w hav to driv firm B s optimal rply to th ladr quantity for givn path xpctations y = y * : B BM, (4) yb( ya) = ( αb cb) ( n) γ ya ( n) Substituting Equation (4) and y A = 0 in firm A s profit function and maximizing with rspct to y A rsults in firm A s optimal quantity in th cas whr firm A supplis a positiv quantity - i it lavs th path - in th scond stag: (5) ya = γ α α ( B cb) ( n)( A ca) ( n)( ) γ ( n)( α ) (6) 0 A c y A A cb cb,1 = α B γ Proposition 3 Th markt ntry of tchnology A is blockadd if cb cb,1 is givn Not that th uppr bound of tchnology A s blockadd ntry is qual to th lowr bound of th incompatibl duopoly Hnc, th incompatibl duopoly

15 Intr-Tchnology vrsus Intra-Tchnology Comptition 35 cannot occur as a fulfilld xpctations quilibrium if th ntry of tchnology A is blockadd 33 Entry dtrrnc Firm A can xploit its first-movr advantag in ordr to prvnt th ntry of tchnology B But th dtrrnc path is only consistnt if it is worthwhil for firm A to slct th dtrrnc output y A, D * in th scond stag, givn th path xpctations Th possibl quilibrium path is givn by: First stag: Consumrs form th xpctations ya = yad, * and y B = 0 Scond stag: Firm A supplis th dtrrnc quantity y A, D * Third stag: Firm B dos not ntr th markt, i y B = 0 Suppos that firm A slcts a lowr quantity ya < yad, * in th scond stag In this cas, it is bnficial for firm B to ntr th markt in th third stag Its bst rply for givn xpctations y = 0 is qual to: α (7) *( ) B cb γ y y A B ya = > 0 B Substituting yb *( y A) and ya = yad, * in firm A s profit function yilds: (8) Π AI, ( ya) = ya(γ αa+ nαb γ αb) γ ca+ γ cb ncb ( ya) ( γ ) γ Maximizing Equation (8) with rspct to quantity y * rsults in: A, D y A and substituting th dtrrnc (9) d Π AI, γ ( αa ca) + ( γ + n 4)( αb cb) = dya γ Entry dtrrnc is not consistnt if it is worthwhil for th ladr to rduc its quantity y A and to accpt firm B s markt ntry In this cas, th first drivativ of firm A s profit function must b ngativ:

16 36 (30) d Π AI, dya T Langnbrg < 0 cb < cb, Not that c B, is th uppr bound of th incompatibl duopoly Givn th dtrrnc output y A, D * and th dtrrnc xpctations ya = yad, * and y B = 0, firm A could incras its profit by rducing its output Thus, ntry dtrrnc is not consistnt in this cas Rational consumrs would anticipat th dviation from th dtrrnc path for valus lowr than c B, Howvr, if cb > cb, holds, firm A would always lowr its profit by rducing th output This is a ncssary, but not sufficint, condition for th consistncy of ntry dtrrnc Th nxt stp is to analyz undr which circumstancs firm A would dviat from th dtrrnc path by incrasing its output Suppos that firm A chooss ya > yad, * in th scond stag In this cas, firm B would not ntr th markt in th third stag Firm A s monopoly profit for givn xpctations ya = ya, D * and yb = 0 and for th actual quantity y = 0 is qual to B (31) [ γ( α ) + ( α )] ya A ca n B cb A, M ( ya) ( ya) Π = γ Maximizing Equation (31) with rspct to quantity y = y * rsults in: A AD, y A and substituting th dtrrnc (3) d Π AM, ( n)( αb cb ) = α A c A dy γ A Suppos that th first drivativ of firm A s profit function is positiv: (33) Π d AM, dya > 0 cb > cb,3 In this cas, firm A would slct a quantity which xcds th dtrrnc output Hnc, th first-stag xpctations ya = yad, * ar not consistnt with firm A s bhavior in th scond stag Thus, if tchnology B s ntry is blockadd, y = y * is th only quilibrium with fulfilld xpctations A AM, Proposition 4 Entry dtrrnc is a fulfilld xpctations quilibrium if and only if cb, < cb < cb,3 holds, i th incompatibl duopoly and th monopoly with blockadd ntry of th compting tchnology ar not fasibl

17 Intr-Tchnology vrsus Intra-Tchnology Comptition 37 Proposition 5 Lt c B,3 b infinitsimally smallr than c B,3 If th ntwork ffct is positiv, n > 0, w hav: Π A, D *( cb,3) >Π A, D *( cb,3 ) =Π A, M * For a sufficintly strong ntwork ffct n> ned, Π A, D * xcds Π A, M * throughout th rlvant intrval cb, < cb < cb,3 Proof AD, B,3 AM, W hav that Π *( c ) = Π * is always fulfilld A D Th first drivativ of Π, * is ngativ at c B,3 : (34) Π AD, *( c B,3) n( α A c A ) = < 0 cb γ ( n) Th limit n ED follows from Π A, D *( cb, ) >Π A, M *: (35) ( γ ) n> n ED = 1 A D Sinc Π, *( c ) is concav with B Π AD, * (1 n) = < 0 cb γ and continuous, Π A, D *( cb) >Π A, M * throughout th intrval cb, < cb < cb,3 QED 33 Numrical xampl Figur 6 dpicts th diffrnt fulfilld xpctations quilibria for a numrical xampl Th dtrrnc profit, Π A, D *, riss with dcrasing marginal costs of tchnology B bcaus th incumbnt firm can crdibly commit to a largr ntwork Sinc th ntwork ffcts ar sufficintly strong, th dtrrnc profit is always highr than firm A s monopoly profit with blockadd ntry of tchnology B

18 38 T Langnbrg Figur 6 Fulfilld xpctations quilibria for αa = αb = 1, n = γ = 08 and c A = 05 Figur 7 shows th quilibrium aras, whr th marginal costs of both tchnologis ar variabl Not that Figur 6 is a cross-sction of Figur 7 at c A = 05 Th figur illustrats that th dtrrnc stratgy is only fasibl if firm A has a modrat cost advantag Figur 7 Two-dimnsional rprsntation of fulfilld xpctations quilibria for αa = αb = 1, n = γ = 08

19 Intr-Tchnology vrsus Intra-Tchnology Comptition 39 4 Entry dtrrnc vs intra-tchnology comptition In this sction, w will analyz th incumbnt s stratgic choic of whthr to shar its tchnology with th rival or to kp its tchnology for itslf Lt us rstrict th analysis to th dtrrnc rgion c B, < c B < c B,3 Rcall that tchnology A is suprior to B in this ara In ordr to xclud multipl quilibria, it is also assumd that standardization on th suprior tchnology A (by dtrrnc or invitation) is focal 10 Th timing structur is as follows: In th first stag, firm A dcids whthr to invit its comptitor into ntwork A or not This dcision affcts consumrs xpctations in th scond stag Aftr having invitd its comptitor, firm A slcts its ladr quantity in th third stag Finally, firm B chooss th optimal followr quantity of good A in th fourth stag It is assumd that firm B can ithr join ntwork A or ntr th markt with its own tchnology B but not us both stratgis at th sam tim Morovr, suppos that both firms hav th sam marginal costs c A if thy produc good A Th quilibrium analysis is similar to th prcding on First, th profitmaximizing quantitis that fulfill xpctations on a givn path ar drivd Thn, w will analyz undr which circumstancs th invitation stratgy is slf-nforcing, i it must b bnficial for firm B to join voluntarily ntwork A instad of slcting its own tchnology B Th last stp of th quilibrium analysis dals with firm A s first-stag dcision, i whthr to invit its comptitor to ngag in intra-tchnology comptition or not 41 Profit-maximizing quantitis with fulfilld xpctations Suppos that firm A has invitd its comptitor In th cas of intra-tchnology comptition, th profit function of firm A is givn by: (36) A, L ya, L( α A ya, L ya, F n ya ca) Π = +, whr th ladr output is dnotd by y A, L and th followr quantity by y A, F Th profit function of firm B is qual to (37) A, F yaf, ( α A yal, yaf, n ya ca) Π = + 10 Thrfor, it is not ncssary to analyz th invitation of firm A into ntwork B Suppos that both firms invit ach othr into thir ntworks This coordination gam, which corrsponds to th Battl of th Sxs, has multipl xpctations and quilibria rspctivly

20 40 T Langnbrg Optimal quantitis for givn xpctations ar qual to (38) yal, *( ya) (39) yaf, *( ya) A A A α c + n y =, A A A α c + n y = 4 Summing up yilds th total output for givn xpctations: (40) y *( y ) A A A A A 3( α c + n y ) = 4 Maximum profits for givn xpctations ar qual to: (41) (4) ( α ), *( ) A ca+ n y Π A AL ya =, ( α ), *( ) A ca+ n y Π A AF ya = 8 16 Th fixd point condition is drivd from Equation (40): 3( α ) (43) * *( *) * A c ya = ya ya ya = A 4 3n Optimal quantitis and profits with fulfilld xpctations ar givn by Equations (44)-(47): (44) y * ( α ), 4 3 A ca AL, = n α (45) y * = A ca AF, 4 3n, (46) ( α ), * A c Π A AL = n (3 4),

21 Intr-Tchnology vrsus Intra-Tchnology Comptition 41 (47) ( α ), * A c Π A AF = n (3 4) Not that th ladr profit is twic as high as th followr profit This rsult rflcts th first movr advantag of th Stacklbrg ladr Figur 8 illustrats th impact of firm B s ntry on th xpctd ntwork siz of good A Suppos that th ntry of tchnology B is blockadd In th monopoly cas, A 1 rprsnts th optimal quantity of good A which fulfills xpctations This quantity is givn by th intrsction point of y* A, M ( y A) with th 45 -lin By th ntry of firm B into ntwork A, th curv y* A ( y A) is shiftd outward Th optimal quantity, which fulfills xpctations, incrass to A Th invitation is th only way to commit crdibly to a ntwork siz which xcds firm A s profit-maximizing monopoly output If firm A promisd to produc th output A by itslf, it would not b crdibl bcaus, as a monopolist, firm A has an incntiv to rduc output for any givn lvl of xpctations xcding A 1 Figur 8 Impact of th invitation on th xpctd ntwork siz At y A = 0, th curv ya *( y A) is abov th 45 -lin bcaus of α A > ca If its slop is smallr than on, th function has an intrsction with th 45 -lin: (48) dya*( ya) 4 < 1 n <, dy 3 A

22 4 T Langnbrg which is always fulfilld bcaus of th assumption n < 1 If firm A is a monopolist, th xistnc condition is rlaxd From Equation (3) follows that n < must hold in this cas 4 Consistncy of th invitation stratgy So far, w hav drivd th profit-maximizing quantitis which fulfill xpctations on a givn path Thus, in th cas of intra-tchnology comptition, it was assumd that it is worthwhil for firm B to join ntwork A Now, it must b takn into account that firm B could dviat from this path Th duopoly within markt A is givn by th following path: First stag: Firm A invits its comptitor into ntwork A Scond stag: Consumrs form th xpctations ya = yal, * + yaf, * and y B = 0 Third stag: Firm A slcts th ladr quantity y A, L * of good A Fourth stag: Firm B racts with th followr quantity y * of good A Starting with th last stag, w analyz whthr it is rally bnficial for firm B to accpt th invitation into ntwork A First, th profit-maximizing quantity of good B must b drivd, givn th ladr output y A, L * and th xpctations y B = 0 Substituting y A, L * and y B = 0 in firm B s bst rply, givn by Equation (8), yilds: A, F (4 3 )( α ) γ( α ) (49) yˆ = y ( y = 0, y = y *) = n B cb A ca B B B A A, L (4 3 n) Firm B s maximum profit for dviating from th invitation path is givn by: (50) [ γ( α c ) (4 3 n)( α c )] ˆ A A B B, if yˆ 0 B > Π B = 4(3n 4) 0, othrwis Firm B voluntarily joins ntwork A if th followr profit within ntwork A xcds th dviation profit Π ˆ B : (51) ( )(1 ), * ˆ α ˆ A c AF B cb cb B A + γ Π >Π > = α 4 3n

23 Intr-Tchnology vrsus Intra-Tchnology Comptition 43 Proposition 6 Firm B accpts th invitation into ntwork A if cb > cˆ B holds Othrwis, th invitation path cannot b a fulfilld xpctations quilibrium bcaus firm B would run its own tchnology B Figur 9 illustrats th consistncy condition for th invitation path For cb < cˆ B, firm B s dviation profit ˆ Π B xcds its followr profit Π A, F * within markt A Thus, th invitation stratgy is not fasibl If cb > cˆ B is givn, th invitation stratgy is slf-nforcing Figur 9 Consistncy of th invitation stratgy for αa = αb = 1, n = γ = c A = Th invitation dcision It rmains to b analyzd undr which circumstancs firm A will invit its comptitor instad of slcting th dtrrnc output of good A If th invitation stratgy is fasibl, firm A has to compar its invitation payoff with its dtrrnc payoff Proposition 7 Suppos that ntry dtrrnc is fasibl, i cb, < cb < cb,3 Ntwork A is closd and ntry dtrrnc occurs as a fulfilld xpctations quilibrium if Π A, D * > Π A, L * holds Convrsly, if Π A, D * < Π A, L * is givn, th invitation of firm B is a fulfilld xpctations quilibrium Sinc ˆB c B, dtrrnc intrval c B, < c B < c B, 3 c < always holds, th invitation into ntwork A is slf-nforcing throughout th

24 44 T Langnbrg Figur 10 compars th dtrrnc profits with th profits in th cas of intratchnology comptition If c B < c B holds, firm A invits its comptitor For cb, < cb < c B, firm A slcts th dtrrnc stratgy Thus, in this situation dtrrnc is a mor succssful commitmnt dvic than th invitation stratgy Figur 10 Invitation into ntwork A vs ntry dtrrnc for αa = αb = 1, n = γ = 08 and c A = 0 5 Concluding rmarks In this papr, w hav modld th problm of whthr an incumbnt firm has an incntiv to shar its tchnology with a rival firm or to kp its tchnology for itslf By sharing its tchnology, th incumbnt crdibly commits to a futur ntwork siz which xcds th profit-maximizing monopoly quantity As a consqunc, th incumbnt raps th bnfits of th consumrs incrasd willingnss to pay for th ntwork good What drivs th modl is th assumption that consumrs form rational xpctations about th ntwork siz bfor th firms ar abl to choos thir output lvls 1 This timing structur (including th Stacklbrg assumption) is th sam as in th modl by Econonomids (1996) Whras Economids modl is confind to intra-tchnology comptition, w hav prsntd a framwork daling both with intr-tchnology and intra-tchnology comptition 1 Th modl dals with rational xpctations in that consumrs xpctations involv all information availabl Of cours, in ral markt situations, thr can b uncrtainty (prhaps with rspct to th pac of tchnological progrss) S Farrll and Katz (1998) for an analysis covring othr typs of xpctations, most notably stubborn xpctations

25 Intr-Tchnology vrsus Intra-Tchnology Comptition 45 W hav analyzd th problm in two stps Th first stp was rstrictd to intr-tchnology comptition, i th incumbnt was assumd to kp th own tchnology for itslf W hav sn that th fulfilld xpctations quilibria dpnd on th rlativ marginal costs of both tchnologis Th ntry of th followr may b blockadd if th incumbnt firm has strong cost advantags But if th followr has a considrabl cost advantag, th incumbnt s ntry can b blockadd as wll On th othr hand, in th cas of wak cost diffrncs, both tchnologis coxist in an incompatibl and htrognous duopoly Entry dtrrnc is fasibl only if th incumbnt has a modrat cost advantag Each of th four possibl fulfilld xpctations quilibria has to mt consistncy conditions which nsur th uniqunss of th quilibrium Th abov rsults rflct th ida that markts ar tippy, i th coxistnc of incompatibl products may b unstabl if firms ar dissimilar in trms of costs Morovr, th rgion of th incompatibl duopoly shrinks with strong ntwork ffcts and with a rising dgr of substitutability Th cntral argumnt of th papr is that th incumbnt may raliz a highr profit in th cas of ntry dtrrnc than in th situation whr th comptitor s ntry is blockadd Th dtrrnc quantity not only prvnts th comptitor s ntry, it also incrass th incumbnt s ntwork and thus consumrs willingnss to pay Furthrmor, w hav drivd th prvrs ffct that th dtrrnc profit can ris with dcrasing marginal costs of th followr bcaus th incumbnt has to supply a largr dtrrnc quantity with incrasing strngth of its rival In th scond part of th modl, w hav analyzd th incumbnt s choic of whthr to shar its tchnology or to insist on intr-tchnology comptition W hav sn that th dtrrnc stratgy can b mor profitabl for th incumbnt (if th incumbnt s cost advantag is not too strong) than th stratgy of sharing its tchnology Sinc th incumbnt dos not intrnaliz th positiv xtrnalitis of th invitation stratgy, which xists in trms of th followr profit and in an incrasd consumrs surplus, on can xpct th dtrrnc stratgy to b wlfar infrior Consquntly, a policy rcommndation should b to oblig th incumbnt firm to licns its tchnology to th rival Rfrncs Bsn, SM and J Farrll (1994), Choosing how to compt: stratgis and tactics in standardization, Journal of Economic Prspctivs, 8, Church, J and N Gandal (1996), Stratgic ntry dtrrnc: complmntary products as installd bas, MJ Hollr and J-F Thiss (ds), Th Economics of Standardization, Spcial Issu of th Europan Journal of Political Economy, 1, Dixit, A (1979), A modl of duopoly suggsting a thory of ntry barrirs, Bll Journal of Economics, 10, 0-3

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