Degree of innovativeness and market structure: A model

Transcription

1 CESPRI Centro d Rera su Proess d Innovazone e Internazonalzzazone Unverstà Coerale Lug Boon a R. Sarfatt, Mlano Tel /7 fax Danela Greo Degree of nnovatveness and arket struture: A odel WP n. 178 Aprl 2006 Stapato n propro da: Unverstà Coerale Lug Boon CESPRI a Sarfatt, Mlano Anno: 2006

2 Degree of nnovatveness and arket struture: A odel Danela Greo Abstrat A lted nuber of busness frs engage n dsruptve nnovatve atvty. When frs dede aong alternatve nnovatve patterns, nertal fores ay bas ther hoes n favour of eental nnovatons. Ths paper proposes a odel that opares frs value when frs an nvest n strateges plyng dfferent degrees of nnovatveness. The odel shows that eental strateges eerge as a donant strategy for olgopolsts when taton of eental nnovaton s suffently slow and frs are not too asyetr n ther aess to knowledge. If these ondtons are not respeted, the odel exhbts an addtonal syetr Nash equlbru where frs selet al nnovatons. Keywords: Radal nnovaton, Inreental Innovaton, Iperfet opetton, Patent rae JEL lassfaton: D21, D81, L20, O33 Post-Do fellow, Boon Unversty, Mlan. a S. Mansueto 4, 20136, Mlan, Italy. Tel e-al: [email protected] The author has benefted fro the helpful oents of Professors Frano Malerba, Mararosa Battaggon, Fausto Panunz and Chrstan Garavagla as well as partpants at Unverstà Boon and CESPRI senar. 1

3 1. Introduton Only a very sall proporton of busness frs atually engage n sgnfant nnovatve atvty. Epral evdene shows that no ore than fve perent of enterprses launh al nnovatons (Bauol, 2004): frs ostly pursue nnovatve strateges that follow well-known patterns and explot the adaptaton of pror nventons as a aor soure of proveent (Roberts, 1987). Ths stylzed fat s eludated here by developng a odel reprodung the ehanss behnd frs hoe aong dfferent nnovatve strateges. Whereas there exsts n lterature a huge debate onernng the effet of opetton on the nentve to nnovate, an exhaustve analyss of alternatve nnovatve strateges deternants and effets n ters of arket struture has not been arred out yet, although the thee appears to have rual platons. Ths work as at fllng suh a gap by nvestgatng expltly the value of an nvestent n nnovaton when nnovaton s pursued wthn the urrent tehnologal traetory or wthn a new one. The odel depts a stuaton of perfet opetton where frs hoose the nnovatve strategy to pleent. The dstnton between al and eental nnovatons, usually aptured n the lterature by referrng to norporated knowledge, s odelled on ultple densons: the level of the nvestent rsk they ply, the expeted preu, the extent and duraton of the pat on arket struture: thus, the deson between al and eental strateges s affeted not only by the dfferent degrees of rsk and osts nvolved, but depends rually on approprablty reges. A al nnovaton, n fat, ples suh a degree of novelty that t allows to apply for patent proteton: the fr that wns the patent rae takes the whole arket. On the other sde, an eental nnovaton s not proteted and the nnovator s rents an be eroded by tators: nnovaton peular features that ake taton dffult an ontrast the delne n the nnovator s profts but only partally. Moreover, an eental nnovaton perts oexstene between the suessful nnovator and hs rvals, whose profts derease after the eental nnovaton but ontnue to be postve. 2

4 The paper frst dsusses the way how prevous ontrbutons onernng nnovatve strateges and the nfluene of arket struture are norporated n the odel s defntons and assuptons. Then, the odel s presented: frs nentves to eental nnovaton are oputed and the equlbru s derved. Results show that the eental strategy s not a suboptal outoe, but eerges as a donant strategy when the taton of an eental nnovaton s not edate and opettors are not too asyetr n ters of nnovatve ablty. Therefore, the preferene for eental patterns that eerges fro the data s deterned by the opetton aong olgopolsts who are slar n ters of nnovatve nvestents and who operate wthn a tehnologal rege that allows for a ertan degree of approprablty also for eental nnovaton that are not proteted by patents. Fnally, a generalzaton to a strateg nteraton aong n olgopolsts allows for the analyss of the pat of the degree of opetton on the hoe of the nnovatve strategy: the larger the nuber of opetng frs, the hgher the nentve to selet an eental nnovaton also n a syetr setup.. 2. Innovatve strateges and nfluene of arket struture Innovaton strateges. Eono and anageral studes have reognzed the portane of defnng possble degrees of nnovatveness. A ontnuous nterval of feasble outoes les between dsrupton and onservaton, and dfferent labels have been alternatvely used to refer to ts extrees. An nnovaton s al f t requres frs to proess dfferent knds of nforaton nstead of pursung predtable hanges that ply a logal extenson of the exstng knowledge (Henderson, 1993). Kaluzny, eney and Gentry (1972) ephasze that al nnovatons depart fro eental ones n ters of the level of nvestent rsk. Inreental nnovatons deterne the proveent of a proess, a produt, or a serve wth respet of a spef donant desgn, produt arhteture or produton proess; al nnovatons, on the ontrary, represent a breakthrough that s often able to generate new ndustres or arket lnes (Malerba, 2000). 3

5 The dstnton between al and eental nnovatons appears to be based on several levels and s onsequently dffult to odel. Industral organzaton lterature fouses on proess nnovaton and dstngushes between gual and drast nnovatons (Cabral, 2000). The latter ase refers to an nnovaton that s able to dsplae the nnovator s rvals as t akes the exstng produt obsolete. As a onsequene of a drast nnovaton, the fr s average ost of produton an be dereased untl a level that allows an equlbru pre lower than the ost before the nnovaton. However, produt nnovaton an be read as an proveent n the qualty of a fr s produt (Bonanno and Haworth, 1998) that stll redues the nnovator s pre-ost argn, but that reahes ths outoe through an ease n onsuers wllngness to pay (Cohen and Klepper, 1996). Therefore, these setups an be enopassed by nterpretng a produt nnovaton as equvalent to a drast ost redung nnovaton when we agne the new produt to be already known but to be produed only at a prohbtvely hgh ost before the nnovaton (Denolò, 2001). Our defnton of al and eental nnovatons wll ground on these varegated suggestons n the a of reprodung the oplexty of the ssue: al nnovatons are soethng ore than drast nnovatons; eental nnovaton are soethng ore than gual nnovatons. We wll aount for dfferenes n norporated knowledge (that affets the probablty of suess), osts, and pat on arket struture; our defnton wll apture both produt and proess nnovatons. Inentves to nnovaton and arket struture. There s a vast lterature on the debate about the relatonshps aong ntensty of opetton, arket struture and proftablty of nnovaton, and no agreed-upon fraework has been ndvduated yet. A ttonal lne of reasonng dentfes n arket onentraton a rual stulus to nnovaton (Shupeter, 1943): few large frs (or even a onopolst fr) are ore apable of appropratng the returns of nnovaton and rely on onsstent aounts of resoures to nvest n R&D. The epral evdene, however, shows that opetton s helpful for growth: sall frs operatng n opettve arkets have hgher nentve to ntrodue nnovatons, beause the replaeent effet - eergng when a onopolst s 4

6 post-nnovaton profts replae hs pre-nnovaton profts (Arrow, 1962) - vanshes n a perfetly opettve senaro. Subsequent refneents (e.g. Bester and Petraks, 1993; Bonanno and Haworth, 1998; Boone, 2001) provde further dsusson about the Shupeteran te-off, that has been also dsussed n the perspetve of endogenous growth (e.g. Grossan and Helpan, 1991; Aghon and Howtt, 1992; Aghon, Harrs and kers, 1997). An explt analyss of the reproal nfluene between the degree of nnovatveness and the level of opetton has not been arred out yet. What an we expet when nvestgatng ths peular relatonshp? Is hgher ntensty n ndustry opetton ore onduve to al nnovatons or to eental ones? If the analogy between the aount of nnovaton and ts degree n ters of dsruptveness holds, a Shupeteran result would predt a preferene for al nnovatons when onentraton s hgh, whereas Arrow s approah would see al nnovaton favoured by tougher opetton. Our results wll be nterpreted and dsussed n ths perspetve. 3. The odel The odel nvestgates the relatonshp between arket struture and nentves to nnovate. In ths work, however, frs hoes are not between urrent state-of-the-art and nnovaton, but onern alternatve nnovatve strateges. The odel developed here stks to the lterature onernng patent raes (Dasgupta and Stgltz, 1980; Lee and Wlde, 1980; Loury, 1979; Renganu, 1982; 1983; 1985): we follow the sple verson of eoryless or Posson patent rae odel where a fr s probablty of beng a suessful nnovator depends only on ts urrent nvestent n nnovaton and not on ts past experene. However, we depart fro ttonal patent rae odels that relate the hazard rate to the aount nvested n nnovaton: here frs sustan a ost that depends on the strategy seleted but that do not affet dretly the probablty of suess. Frs dede sultaneously to pleent or not a spef nnovatve strategy and the returns of nnovatve patterns are stohastally deterned: probabltes of suess depend on the 5

7 spef strategy seleted. Tehnologal unertanty takes the for of a stohast relatonshp between the rsk of nvestent and the eventual date of suessful opleton of the nnovaton. Tehnologal opetton s analysed on the bass of the profts a fr earns n equlbru untl the researh atvty has not ganed any result, plus the profts that fr earns n the equlbru followng a suessful nnovaton, when the fr tself s the suessful nnovator or when t has been defeated n the nnovatve rae by a rval Inreental and al nnovaton Consstently wth the epral evdene dsussed n the ntroduton, the deson of nnovatng and the hoe between alternatve types of nnovaton s assued to affet the evoluton of profts draatally. When no nnovatve strategy s pleented, frs equlbru profts are denoted wth the subsrbe n. Agents dede the nnovaton strategy to pleent between two optons: eental nnovaton () and al nnovaton (): a al nnovaton s ore than a drast nnovaton beause t ples a developent of totally new knowledge that goes beyond the sple reduton of produton osts. It represents the openng of a new traetory, whereas an eental nnovaton s a oveent on the old establshed traetory. Not only a al nnovaton s ore ostly, ore rsky and exhbts hgher expeted returns; t an also be proteted fro taton and has a rearkable and durable pat on arket struture. The odel does not dstngush between produt and proess nnovaton, beng eental and al nnovatons potentally related to any knd of odfatons of the state-of the-art soluton, ether onernng the way ustoers address a need or the produton ehans behnd ts onstruton (Fagerberg, Mowery and Nelson, 2004). The suess of the nvestent n a spef nnovatve path s probablstally deterned. More spefally: 6

8 Assupton 3.1. The probablty of suess n pleentng nnovaton s hgher n the ase of eental nnovaton than n the ase of al nnovaton: λ > λ The explanaton of ths assupton has been antpated above: an eental nnovaton bulds on prevously developed knowledge and takes plae nto a well-known ontext where any further proveent s grounded on prevous enhaneents. As the nnovator reans on the sae tehnologal traetory, he an beneft - on one sde - of adaptve effets, eonoes of sope, opleentartes, and tehnologal nterdependenes; on the other sde, he gans fro the takenfor-grantedness that affets the produt - or the way of asseblng t - as te passes by (Carroll and Hannan, 2000). We do not odel nnovaton s osts expltly beause frs are supposed to reason n ters of nnovatve proets net values that already aount for al nnovatons osts that are hgher than eental nnovatons osts. After the nnovaton, the nstantaneous proft of the fr rses draatally. In partular: Assupton 3.2. The edate perentage pat on profts after the pleentaton of nnovaton s assued to be lower n the ase of eental nnovatons than al ones: 0 h < h <1 < Moreover: Assupton 3.3. The expeted preu of eental nnovatons s lower than the expeted preu of al nnovatons: h λ < h λ Addtonally, after a suessful nnovaton: 7

9 Assupton 3.4. Whle a al breakthrough deternes a stable rse n the proft trend equal to a perentage ( 1+ h ) of the prevous proft level, an eental nnovaton produes an nstantaneous rse n profts of a perentage ( 1 + h ) that s followed by a gual delne, but only as far as a level that s hgher than the ntal level. Ths last assupton s the onsequene of the hgher possblty of tatng eental nnovatons that do not requre opletely new opetenes to tators, unlkely al nnovatons. Furtherore, the effet of a al nnovaton n ters of pat on arket struture s the followng: Assupton 3.5. In the ase of a al nnovaton, oexstene s not allowed: the suessful nnovator beoes onopolst and hs opettors ext the arket. Therefore, we aount for a wnner take all opetton n ase of suessful al nnovaton, whereas aheveents n eental nnovaton do not deterne rvals ext, but only ause a derease n profts. 4. Iperfet opetton Ths seton reprodues strateg nteraton between two olgopolsts, and. Proposton 4.1. Lettng δ (wth0 <δ < 1) denote the dsount rate, the present dsounted value of expeted profts over te for olgopolsts and when both do not pleent nnovaton s, q n, n = (4.1) δ 8

10 Proof. Equaton 4.1 sply derves fro, δ t n n =, e dt = 0 δ where denotes syetr Cournot profts. Fr s value s wrtten n ters of onopolst s proft ust to faltate subsequent oparsons: we defne q = (wth 0 < q < 1 ). The equaton above represents the startng pont for evaluatng the pat of al and eental nnovatons respetvely. A tehnologal breakthrough an be pleented suessfully by the olgopolst wth probablty λ and ples a persstent ease n profts. When a al nnovaton s ntrodued, n fat, for the suessful nnovator olgopoly profts rse sharply up to the onopoly level and rean stk at that level untl the end of the perod. Wth the nnovatve event, the net ash flow 1 ups of a perentage ( 1+ h ) = =. q Proposton 4.2. When opettor engages n al nnovaton and opettor does not nvest n nnovaton, s value s q, n = (4.2) δ hλ Note that represents fr s net value and already aounts for al nnovaton osts. Proof. Equaton 4.2 derves fro, n = 0 e δt e λ t λ + e ( 1 h ) t dt If the patent rae starts at nstant 0, ondtonally to the fat that fr has not yet sueeded untl nstant t (ths event ours wth probablty ( ) + h t e λ ), fr reeves a flow of dsounted profts equal to λ ( λ ) 1 wth probablty and grows at rate zero wth probablty to (4.2). that grows at a rate 1. Straghtforward oputatons leads 9

11 Proposton 4.3. When opettor engages n al nnovaton and opettor does not nvest n nnovaton, s value s q n, = (4.3) δ + λ Proof. Equaton 4.3 an be easly obtaned fro δt λ t e e ( + λ * )dt n, = 0 0 that s: ondtonal on the absene of nnovaton by fr before t, realzes (and onsequently earn 0) f wns the rae. f s unsuessful and ext the arket An eental nnovaton s ntrodued wth probablty λ > λ, and deternes an ease n olgopoly profts suh that h <. In Seton 3.1 we have defned the ter h λ as nnovaton h expeted preu and assued the eental nnovatve strategy to have a lower expeted preu ( h λ < h λ ). It s portant to stress the fat that the eental nnovaton s not supposed to affet arket struture persstently: t only deternes a teporary asyetry n the olgopolst opetton. We assue that, at a ertan pont n te, fr s value takes a up upward fro varable s to λ suh that ( 1+ h ) = = q. The probablty of a up n the rando (that an be alled the ean arrval rate of ths Posson proess). Nonetheless, unlke the al nnovaton ase, after the eental nnovaton there s a subsequent gual delne n profts, but only as far as a level above the status quo level: ths phase exhbt an exponental delne towards the new level that s due to rvals taton. Proposton 4.4. When opettor engages n eental nnovaton and opettor does not nvest n nnovaton, s value s ( γ ) δ + λ (1 + h ), n = q (4.4) ( δ γ )( λ + δ ) 10

12 where γ s the eental nnovaton drft that partally tgates the derease due to the dsount fator. Proof. Equaton 4.4 an be easly obtaned fro t t ( h ) e e n δ λ 1+, = + λ dt 0 δ γ whh eans that fr gets at t f has not sueeded and sees ts profts rasng up to ( 1 + h ) = (where denotes asyetr and hgher Cournot profts) and then delnng at a rate ( δ γ ) t has been suessful. n the followng perods f If s suessful n hs eental strategy, s value edately drops to (asyetr and lower Cournot profts) but slowly eases up to reah the before-nnovaton syetr Cournot profts. Hene: Proposton 4.5. When opettor engages n eental nnovaton and opettor does not nvest n nnovaton, s value s Proof. Equaton 4.5 derves fro t t n e e δ λ, = + λ δ γ 0 where = = q 1+ h ( ) 1+ h ( ) dt ( ) q + q λ ( δ γ ) n, = (4.5) ( λ + δ ) When both frs dede to nvest n nnovaton, four ases ay eerge. They an both go for a al nnovaton; they an both go for an eental nnovaton; they an hoose one a al strategy, and the other an eental one. 11

13 Proposton 4.6. The value of profts for olgopolsts and when both nnovate ally s q, = (4.6) δ + λ h λ, Proof. Equaton 4.6 an be easly obtaned fro,, t ( ) t ( h ) t e e ( e δ λ + λ λ + )dt = 0 1 followng the usual proedure: wth respet to (4.2), here the nnovatve suess of or at te t s ondtonal to the fat that both and have not been suessful untl t. If both hoose an eental nnovatve strategy, the pat of an eental nnovaton on arket struture s lower than the prevous ase s one: n fat, we stll have Cournot opetton, but frs are asyetr, obvously wth hgher profts ( > ) for the suessful nnovator and lower profts ( < ) for hs rval. If both are suessful (ths outoe s possble wth eental nnovatons, but not wth al nnovaton), for both opettors profts rse to. Proposton 4.7. The value of profts for olgopolsts and when both nnovate eentally s,, qλ = ( δ γ ) δ + λ + + λ q λ ( δ γ ) + δ + λ + λ q λ λ ( 1+ h ) (4.7) Proof. Equaton 4.7 derves fro t ( ) e e t ( ) e + δ λ λ + λ λ λ + λ δ γ + δ γ, 1, = 0 ( h ) that eans what follows: ondtonally to the fat that nether or has nnovated before t, frs get asyetr Cournot profts (hgher for the nnovator, lower for the tator) weghted for eah one s probablty of suess; f they both nnovate (event that ours wth probablty λ ), Cournot profts grow at a rate of t dt 1 +h. λ ( ) Proposton 4.8. When opettor engages n al nnovaton and opettor engages n eental nnovaton, s value s 12

14 , qλ = δ + ( δ γ ) λ + λ + δ + λ q + λ λ ( 1+ h ) (4.8) Proof. Equaton 4.8 s obtaned fro t ( ) ( ) e e t h t ( ( ) e δ λ + λ λ + λ δ γ + )dt 1, = 0 that an be easly nterpreted on the bass of prevous proofs. Proposton 4.9. When opettor engages n al nnovaton and opettor engages n eental nnovaton, s value s q + q λ ( δ γ ), = (4.9) δ + λ + λ Proof. Equaton 4.9 derves fro, = 0 t ( ) t e e δ λ + λ + λ ( δ γ ) dt whose nterpretaton s straghtforward. It s portant to note that equatons 4.8 and 4.9 hold f the al nnovaton takes plae before the eental nnovaton ( T < T ). If ths does not happen, we have to aount also for a lted perod where the eental nnovator experents an ease n profts nstead of earnng syetr olgopoly profts and the al nnovator (stll unsuessful) sees a reduton n hs profts. Ths stuaton lasts untl the oent al nnovaton ours. Therefore, f T < T fr s value s hgher than the level expressed by equaton 4.8, whereas fr s value s lower than the aount n equaton 4.9. We do not opute these new values beause ths effet ust renfores our results (see next seton). 13

15 5. Inentves to eental nnovaton Our oneptualzaton of frs value n ase of eental and al nnovaton ples that, n ths odel, opettors always have an nentve to nnovate, as we opute frs net value and do not onsder expltly the osts of nnovatng 1. Our fous, however, les n the hoe between alternatve nnovatve strateges whose return s stohast. If only one fr nvests n nnovaton and onsequently no strateg effet plays a role, whh s the best strategy between a al and an eental one? We reall Katz and Shapro (1987) s stand-alone nentve and defne n a slar fashon the nnovate-alone nentve to eental nnovaton for fr. Defnton 5.1. The nnovate-alone nentve to eental nnovaton for fr the expresson: a I, n, n = (5.1) where and have been desrbed n the prevous seton., n, n The nnovate-alone nentve to eental nnovaton an be oneved as a pure nentve to eental nnovaton, beause t s not affeted by strateg nteraton as fr s the only one that nnovates. Proposton 5.1. The nnovate-alone nentve to eental nnovaton unless γ < hλ. a I s postve Proof. The nnovate-alone nentve to eental nnovaton an be obtaned as the followng dfferene: a ( δ γ ) + λ (1 + h ) q I = q δ γ λ + δ δ h λ ( )( ) that equals a = {( )[ ] + ( 1 + )( I q δ γ h λ λ λ h δ h λ )} < 0 1 Ths assupton does not ean that nnovaton s free, nether that al and eental nnovatons have the sae ost: we sply onsder profts after havng subtrated the ost of the spef nvestent n nnovaton (that s obvously hgher n the ase of al nnovaton). 14

16 Therefore: λ 1 + h ( )( δ hλ ) > ( hλ + λ )( δ γ ) As ( λ h λ ) > ( + λ + h λ ) +, that expresson s postve f λ < γ. Ths proposton shows that, when a opettor works out as he were the only one who nnovates, a rual deternant of hs hoe between an eental and a al strategy s gven by the speedness of delne n profts due to the eental nnovaton. If t s hgher than a spef threshold, represented by the al nnovaton preu, the eental strategy s preferred. On the ontrary, wth returns fro eental nnovaton that drop onsderably (due to a sall value of γ ), or wth very hgh al nnovaton preu, the al strategy s preferred. The nentve to nnovate eentally assues a dfferent for when we onsder opetton between frs and. The pre-epton 2 nentve to eental nnovaton for fr an be obtaned by oparng fr 's value when nnovates to fr 's value when nnovates. As here two nnovatve strateges are avalable to and, we an defne two types of pre-epton nentve to eental nnovaton for fr by dstngushng between the pre-epton nentve to eental nnovaton when nnovates ally and pre-epton nentve to eental nnovaton when nnovates eentally. Defnton 5.2. The pre-epton nentve to eental nnovaton for fr when nnovates ally s defned as e _ I,, = (5.2) Proposton 5.2. The pre-epton nentve to eental nnovaton for fr when nnovates ally e I _ s postve unless λ λ > δ. 2 See for nstane Fudenberg, Glbert, Stgltz and Trole (1983). 15

17 Proof. Equaton (5.2) assues the for q λ q + e _ ( δ γ ) q I δ + λ + λ δ + λ h that s postve f q ( λ + δ + λ ) > 0.e. when δ > = λ λ λ Ths effet n favour of eental nnovaton s even stronger when T > T. Proposton 5.2 suggests that, when hs opettor nnovates ally, the olgopolst stll has a postve nentve to nnovate eentally f he does not dffer too uh fro h n ters of hs probablty of suess n nnovaton pleentaton: the dfferene between frs probabltes of suess should be lower than a threshold that equals the dsount rate. Defnton 5.3. The pre-epton nentve to eental nnovaton for fr when nnovates eentally s defned as e _ I,, = (5.3) Proposton 5.3. The pre-epton nentve to eental nnovaton for fr when nnovates eentally e I _ s postve. Proof. Equaton 5.3 an be wrtten as q λ qλ ( δ γ ) + e _ on δ γ I = δ + λ + λ ( ) + δ + λ + λ q λ λ ( 1 + h ) qλ δ + λ ( δ γ ) + λ δ + λ + λ q λ ( 1 + h ) Ths expresson s postve f q λ ( δ γ ) δ + λ + λ > q δ + λ + λ 1 λ λ 1 ( 1 + h ) + + ( + ) δ λ λ λ 1 h 16

18 that leads to q λ ( δ γ ) δ + λ + λ > q ( λ h λ + λ λ ( 1 + h )) q ( λ h λ ) < 0 where the rght-hand sde an be approxated to q ( h λ ) < 0 λ. Ths effet n favour of eental nnovaton s renfored when T > T. Proposton 5.3 ephaszes that an olgopolst always prefers to pursue an eental nnovatve strategy when he expets hs opettor to selet an eental nnovatve pattern. 6. The equlbru After provdng a oplete desrpton of players and s values under alternatve nnovatve strateges, we turn to the analyss of the equlbru eergng nto the sultaneous gae of and. Players are syetr and players strateges are funtons of ther own value. n Defnton 6.1. The strategy of player ι {, } s a appng Γ : R { 1,0,1 } nnovate, 0 eans nnovate ally, and 1 eans nnovate eentally. ι, where -1 eans non Gven the strateges for all players, the frst step onssts of elnatng donated strateges. Proposton 6.1. Under ondtons spefed n propostons 5.1, 5.2 and 5.3, strategy donated strategy. = 1 Γ ι s a Proof. We frst opare equatons (4.1), (4.2) and (4.4). It s easy to show that 5.1, for transtvty reasons also holds. n, n <, n Then we opare equatons (4.3), (4.6) and (4.9). straghtforward to show that 5.2, n, <,, n > n, n, > n,. Reallng proposton ; due to proposton 17

19 Fnally, we opare equatons (4.5), (4.7) and (4.8). As equatons 4.5 and 4.8 dffer ust beause 4.8 has a lower denonator, we an onlude that and, due to proposton 5.3, also the ondton, > n, s satsfed., > n, Proposton 6.2. Under ondtons spefed n propostons 5.1, 5.2 and 5.3, strategy = 0 Γ ι s a donated strategy. Proof. See propostons 5.1, 5.2 and 5.3. Therefore, a syetr Nash equlbru an be haraterzed as follows. Proposton 6.3. The syetr Nash equlbru for frs and s to adopt strateges: G N ι ( ) 1 = 0,1 f f γ γ > h < h λ λ λ λ λ λ < δ > δ Proposton 6.3 shows that a syetr Nash equlbru where both opettors pleent an eental nnovaton always eerges n the sultaneous gae analyzed. Ths equlbru s also a donant strateges equlbru when ondtons γ > hλ and λ λ < δ both hold. If only one ondton holds, t s a syetr unque Nash equlbru. If both ondton do not hold, an addtonal syetr Nash equlbru where both olgopolsts selet a al nnovaton strategy eerge. 7. Degree of opetton and degree of nnovatveness In the a of dsentanglng the spef effet of strateg nteraton and the nfluene of the nuber of frs n the arket, we brefly exane the ase of onopoly and the generalzaton of the olgopoly ase to n opettors. As oexstene after an eental nnovaton s one of the drvng fores of the odel, we expet the results to hange when a fr stands alone. Followng 18

20 the sae proedure llustrated above, t s straghtforward to opute the onopolst s value under alternatve nnovatve strateges and to show that al strateges are always preferred. Proposton 7.1. When the onopolst does not engage n nnovaton, hs value s n = (7.1) δ Proposton 7.2. When the onopolst engages n al nnovaton, hs value s = (7.2) δ h λ Proposton 7.3. When the onopolst engages n eental nnovaton, hs value s ( 1+ h ) λ 1+ δ γ = δ + λ (7.3) Proofs. Proofs of propostons 7.1, 7.2 and 7.3 are straghtforward. Agan, we opute the nentve to eental nnovaton for the onopolst. Only the nnovatealone nentve plays a role n ths ontext beause no strateg nteraton ours. In ths setup, the delne n profts onsequent to an eental nnovaton s obvously not due to taton, but s antaned to gve the flavour of eental nnovatons lghter pat not only n ters of nstant rse n profts, but also n ters of extent. Defnton 7.1. The nnovate-alone nentve to eental nnovaton for fr s defned as I a = (7.4) 19

21 Proposton 7.4. The nnovate-alone nentve to eental nnovaton negatve. Proof. Equaton 7.4 an be wrtten as a ( δ h )[ ( )] λ λ 1+ h I = δ hλ + δ λ δ γ that leads to a I = δ γ h λ λ + δ h λ λ 1+ h {( )( ) ( )[ ( )]} Let us suppose that I a h λ < γ. Therefore we an wrte {( δ h λ )( [ h λ λ ) ε + λ + λ h ]} < 0 = Ths result an only be renfored wth an hgher al nnovaton preu h λ > γ. a I for the onopolst s As we expeted, whereas eental nnovaton always eerged as an equlbru for the olgopolsts, the onopolst has an hgher nentve to selet al strateges. Followng the sae lne of reasonng, we expet an ease n the nuber of opetng frs to favour the hoe of eental nnovatve strateges. The generalzaton of the results shown n Seton 4 s straghtforward: when aountng for rvals nnovaton, we ust have to reeber than t ours wth a probablty Λ ( n) that s defned as the su of the ( n 1) opettors probabltes of beng suessful nnovators, where olgopolsts n the ndustry: n represents the nuber of Defnton 7.2. The probablty that olgopolst experenes rvals suessful nnovaton s equal to n ( ) = s Λ n λ (7.5) s Obvously, the generalzaton to n frs does not affet the nnovate-alone nentve to eental nnovaton nor the pre-epton nentve to eental nnovaton when opettors nnovate eentally, whh s always postve and does not depend on probabltes. What turns to be 20

22 ore nterestng s the pre-epton nentve to eental nnovaton when opettors nnovate ally. Proposton 7.5. The pre-epton nentve to eental nnovaton for fr when ts rvals e _ nnovate ally eases as n eases. I n Proof. After the generalzaton to n frs, equaton (5.2) assues the for q λ q + e _ ( δ γ ) q I n = n n s s δ + λ + + λ δ λ h λ s s that s postve f n s q λ + δ + λ > 0 s.e. when s δ > λ λ n s Thus, f n rses, the nequalty s easer to satsfy. If n λ s s n, Λ = 1and the nequalty s always verfed. Therefore, tougher opetton due to a larger nuber of rvals n the ndustry plays n favour of the hoe of eental nnovatve strateges. 8. Dsusson Ths paper starts fro the analyss of a stylzed fat ephaszng that a vast perentage of the nnovatve atvtes frs arry out an be lassfed as eental, whereas al nnovatons are rarely launhed. We ntrodue an orgnal and exhaustve way of deptng eental and al nnovatons and develop a odel that reprodues the way frs hoose aong dfferent nnovatve strateges. The dstnton between al and eental nnovatons s odelled on several densons: the level of the nvestent rsk, the expeted preu, the ntensty and length 21

23 of the pat on arket struture. Drast nnovatons studed n ndustral organzaton an be therefore nterpreted as a partular ourrene nluded nto the al nnovatons wder set. The odel espeally seeks for arket and opettors ondtons under whh eental nnovatons eerge as an equlbru outoe, reprodung the epral evdene. Inreental strateges do not appear to be a suboptal outoe as lterature on nerta, path dependene and lok-n (e.g. Davd, 1985; 2000) ght suggest. On the ontrary, the hoe of reanng on the urrent tehnology eerges as a donant strategy when opettors at strategally and tehnology exhbts spef features. The odel proves that olgopolsts atng as ratonal desonakers exhbt a postve nentve to nnovate eentally unless returns to eental nnovaton do not exhaust too qukly n te or unless a sgnfant asyetry n opetenes haraterzes opettors. Therefore, a rual role n favourng the pleentaton of ore or less dsruptve nnovatve strateges s played by the spef attrbutes of the tehnologal rege: the degree of approprablty (Malerba and Orsengo, 1993; Bresh, Malerba and Orsengo, 2000), n fat, deeply affets the rapdty n taton of eental nnovatons and onsequently the reduton of profts that the eental nnovator experenes n te. When approprablty s low, due to an eono envronent haraterzed by large knowledge spllovers, nvestng n an eental strategy ay be not worthy. As Sherer (1980) las, f tators an swar n to opy the nventon as soon as t has been ntrodued, post-nnovaton pres wll fall rapdly to the level of produton osts, wpng out our supernoral profts. Sne tehnologal progress s nterpreted as one of the ost portant densons of ndustry perforane, the haratersts of the property rght syste provdes frs nentves to engage n nnovaton (Katz and Shapro, 1985a; 1985b). Aordng to ths work s results, we an argue that fors of proteton lke seretness and dffulty n tatng ould be ore favourable to eental nnovaton, whereas a proteton based on patents s ore benefal for al nnovatons. Another sgnfant deternant n shapng the nentve to eental nnovaton s represented by frs dosynrat haratersts. Frs level of knowledge and opetenes 22

24 deternes ther probabltes of suess n nnovaton. What eerges as rual n our odel s the level of syetry n opetenes dstrbuton between opettors: the one that departs onsstently fro the other ght have a postve nentve to pursue a al nnovaton. Ths result reflets the dea that the exstene of a perforane gap ay onsttute an portant stulus to overoe nerta when explotatve strateges are exhausted (Hage, 1980). The odel also sheds lght on al nnovatons, that ay eerge as an addtonal equlbru outoe when the ondtons prevously entoned are not respeted,.e. when taton s rapd and asyetry s sgnfant. Ths result s onsstent wth the stylzed fat that frs (rare) dsruptve atvty takes plae when newoers (norporatng a dfferent knd of knowledge) ake ther appearane, espeally n a ontext where approprablty s low. The onopoly ase provdes a few nsghts about the effets of the absene of strateg nteraton. Unlke olgopolsts, the onopolst always exhbts a postve nentve to pleent al nnovatons. The generalzaton of the odel to a strateg nteraton aong n frs shows that an ease n opetton does not produe an ease n the nnovatveness degree, supportng the Shupeteran sde of the debate: the larger the nuber of frs, the hgher the onservatveness n nnovatve strateges. Olgopolsts see to hnder eah others dsruptveness and selet a strategy that allows the to oexst n the arket: rvals eental nnovatons generate a lower negatve externalty than al nnovatons beause they deterne an saller reduton n opettors profts. If al nnovatons are udged as preferable fro a welfare pont of vew - as they open up new, superor traetores - a way of prootng the that we learn fro our results s to nternalze ths negatve externaltes, for nstane by prootng fors of ooperatve R&D suh as researh ont ventures. 9. Conlusons A well-known stylzed fat n the eonos of nnovaton las that nnovatve patterns exhbt a hgh degree of nerta and path dependene. Ths work attepts to understand the ondtons that 23

25 ake eental nnovatons beng extreely ore frequent than al nnovaton. Frs hoes between alternatve nnovatve strateges are reprodued wthn a patent rae odel where eental nnovatons are assued to be less rsky, to have a lower expeted value and to affet arket struture n a shorter and less sgnfant extent wth respet to al nnovatons. Nondsruptve proveents, however, let oexstene of opettors possble. The odel shows that olgopolsts eental hoe eerges as a donant strategy equlbru when profts delne n te after an eental nnovaton s not too rapd and when olgopolsts exhbt a low degree of asyetry. If one of these ondtons s not respeted, an addtonal equlbru where olgopolsts both nnovate ally eerge. Interestngly, the odel llustrates that a onopolst has always an hgher nentve to selet a al strategy and that, n ontrast wth oon belefs, arket opetton sees to affet the degree of nnovatveness negatvely. 24

26 Referenes Aghon, P., Harrs, C. and kers, J., Copetton and growth wth step-by-step nnovaton: An exaple. European Eono Revew 41, Aghon, P. and Howtt, P., A odel of growth through reatve destruton. Eonoetra 60, Arrow, K., Eono welfare and the alloaton of resoures for nventons. In: R. Nelson (Ed.), The Rate and Dreton of Innovatve Atvty, Prneton Unversty Press, Prneton. Bauol, W.J., Eduaton for Innovaton: Entrepreneural Breakthrough vs. Corporate Inreental Iproveents, NBER, 30 th Aprl. Bester, H. and Petraks, E., The nentve for ost reduton n a dfferentated ndustry. Internatonal Journal of Industral Organzaton 11, Bonanno, G. and Haworth, B., Intensty of opetton and the hoe between produt and proess nnovaton. Internatonal Journal of Industral Organzaton 16(4), Boone, J., Intensty of opetton and the nentve to nnovate. Internatonal Journal of Industral Organzaton 19, Bresh, S., Malerba, F., and Orsengo, L., Tehnologal reges and Shupeteran patterns of nnovaton. Eono Journal 110(436), Cabral, L., Eonoa Industrale, Caro, Roa. Carroll, G.R. and Hannan, M.T., The Deography of Corporatons and Industres, Prneton Unversty Press, New York. Cohen, W.M. and Klepper, S., Fr sze and the nature of nnovaton wthn ndustres: The ase of proess and produt R&D. The Revew of Eono and Statsts 78 (2), Dasgupta, P. and Stgltz, J., Unertanty, ndustral struture, and the speed of R&D. Bell Journal of Eonos 11,

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