Cooperative vs. non-cooperative R&D incentives under incomplete information

Transcription

1 MPRA Munh Personl RePE Arhve oopertve vs. non-oopertve R&D nentves under nomplete nformton Trun Kbr nd Srobont httopdhyy Indn Sttstl Insttute, Kolkt, Vdysgr ollege for Women, Kolkt 30 September 014 Onlne t MPRA Pper No. 55, posted 13 Otober :48 UT

2 oopertve vs. Non-oopertve R&D Inentves under Inomplete Informton* Trun Kbr Indn Sttstl Insttute, Kolkt nd Srobont httopdhyy Vdysgr ollege for Women, Kolkt Otober 014 *Aknowledgement: We would lke to thnk n nonymous referee of the ournl, who hs provded detled omments nd suggestons on the erler drft of the pper. However, ny remnng errors re ours. orrespondene to: Trun Kbr, Eonom Reserh Unt, Indn Sttstl Insttute, 03 B. T. Rod, Kolkt , Ind. E-ml Trun Kbr: trunkbr@hotml.om; Fx: E-ml Srobont httopdhyy: srobont@gml.om.

3 oopertve vs. Non-oopertve R&D Inentves under Inomplete Informton Abstrt Ths pper studes nentves for oopertve reserh vs-à-vs non-oopertve reserh n n nomplete nformton frmework. We show tht wth untty ompetton under symmetr nformton, the expeted pyoff from non-oopertve reserh goes down ompred to the se of symmetr nformton; hene RJV nentves of the frms re lrger under symmetr nformton. In ether se, however, the lrger s the sze of the ost-redung nnovton the lower s the nentve for oopertve reserh. Fnlly n our model, nomplete nformton does not ffet the onsumers welfre, but the frms beome worse off. Key words: oopertve R&D, non-oopertve R&D, RJV, nomplete nformton, onsumers welfre. JEL lssfton Index: D43, L13, O31. 1

4 1. Introduton Tehnologl progress nd eonom development go hnd n hnd. However, tehnologl progress reures well-dreted nd well-oordnted R&D efforts nd t nvolves huge nvestment nd unertnty n hevng suess. Even when the R&D sueeds, there s no gurntee tht the nnovtors wll be ble to reover the osts of R&D nvestment nd efforts beuse of the possblty of mtton, spllovers nd lekng out of knowledge. So provdng reured mount of R&D nentves to the prvte nvestors s n mportnt poly onern. To prevent or redue the thret of mtton nd lekng out of knowledge, strong nd enforeble ptent proteton my be lled for fter ll, ptent proteton mkes mtton ostly. As wy out of the problem of hgh R&D ost nd unertnty, poly mkers enourge oopertve reserh, or n prtulr, reserh ont venture RJV n whh the prvte nvestors shre the R&D ost s well s the reserh outome. 1 Free rdng problem s then lso redued. There s lredy n extensve lterture on the hoe of R&D orgnzton. Ths lterture dsusses, n prtulr, the hoe between oopertve nd non-oopertve R&D. For nstne, Mrt 11 ntrodues unertnty n R&D outome. d Aspremont nd Juemn 188 nd Suzumur 1 dsuss the hoe under spllovers. Mott 1 dsusses the hoe when produts re vertlly dfferentted. ho 1, 13 studes oopertve R&D wth morl hzrd. ombs 1 extends the model to the se when R&D ooperton mens oordntng multple reserh proets. Kbr nd Mukheree 000 dsuss the hoe between oopertve nd ndependent reserh n three-frm frmework. Mukheree nd Mrt 004 ntrodue tehnology trnsfer wth the hoe of R&D orgnzton. Slpo nd Wess 005 onsder the problem wth both spllovers nd unertnty. Kbr 006 studes the effet of mtton nd ptent proteton n the ontext of nnovtons of two produts nd Kbr 007 ntrodues synergy n R&D ooperton. On the other hnd, Mukheree nd Ry 00 onsder the 1 Followng the Ntonl oopertve Reserh At 184 lrge number of oopertve ventures hve been regstered n the US. For nstne, see Vonorts 17 nd Deoury 005. Also see Slpo 008 for dfferent forms of reserh ooperton nd the relted ssues.

5 problem when the R&D outome s ertn but there s unertnty n ptent pprovls. Suh n unertnty, t s shown, my ndue the frms to do oopertve reserh. Surprsngly, no work so fr hs studed the effet of nomplete nformton n the hoe between oopertve nd non-oopertve R&D. One we norporte symmetr nformton nto the problem, the mportnt uestons tht one my rse re the followng: Wht s the nentve for non-oopertve R&D under nomplete nformton? Does t go up or down ompred to the se of omplete nformton? Does ths lter the hoe of R&D orgnzton? How does ths omprson depend on the sze of the nnovton nd probblty of suess? Wht ould be the possble welfre effet of nomplete nformton for the onsumers nd produers? And so on. Hene the purpose of the present pper s to extend the nlyss of Mrt 11 to the se of symmetr nformton bout the R&D outome nd then dsuss the hoe between oopertve nd non-oopertve reserh. We ssume tht under nonoopertve R&D eh frm n observe only whether t tself s suessful, nd gven the nformton bout ts own suess or flure, t knows only the ondtonl probbltes of suess or flure of ts rvl frm. The mount of ost reduton resultng from suessful R&D effort, however, s eul for both the frms. Thus, two possble unt osts re relevnt for onsderton, the ost when R&D sueeds nd tht when R&D fls. When the gme rehes the stge of ompetton n the produt mrket, eh frm hs prvte nformton bout ts own unt ost, nd only probblst noton bout ts rvl frm s unt ost. Thus, bsed on the levels of unt osts, eh frm n hve two dsrete types: low, when R&D hs been suessful, nd hgh, when R&D hs fled. 3 On the other hnd, sne under RJV frms ondut ther reserh n sngle lb nd ontrbute to R&D efforts, ll the prtners hve eul knowledge of nd ess to the R&D outomes. 3 In dfferent ontext though, Ds Vrm 003 lso trets ost reduton due to dopton of proess nnovton s prvte nformton whh onsttutes types of frms whh ompete n n mperfetly ompettve mrket nd bd for obtnng the proess nnovton. He heks for the exstene of Byesn- Nsh eulbrum of the uton whh ensures n effent lloton of the onerned proess nnovton. The dfferene n tretment wth our pper s tht we onsder ost reduton due to own R&D efforts rther thn n dopton of proess nnovton through uton nd we onsder dsrete types. Also n our ontext the mount of ost reduton s ommon knowledge, but when the gme proeeds to the stge of 3

6 Then the frms re to dede ex nte whether they wll ooperte n R&D nd shre R&D osts nd outomes. They wll ooperte n reserh f nd only f the ex-nte the expeted pyoff from ooperton s strtly lrger. We derve the followng results. Frst, the presene of nomplete nformton redues the expeted pyoff of non-oopertve reserh; hene nentves for oopertve reserh vs--vs non-oopertve reserh re lrger under nomplete nformton. Seond, f the R&D ost s not lrge, oopertve reserh ours f nd only f the probblty of suess n R&D s ether low or hgh. On the other hnd, the lrger the sze of the nnovton, the lower s the nentve for oopertve R&D. Note tht symmetr nformton hs two opposng effets. It benefts the frm to the extent t holds prvte nformton. It hurts the frm beuse t does not extly know the rvl s type. Fnlly, the exstene of nomplete nformton hurts the frms, not the onsumers; hene the overll welfre of the eonomy my fll. 4 The pper s orgnzed s follows. In seton we set up the model nd dsuss the problem. Seton 3 derves welfre mpltons of nomplete nformton. Seton 4 onludes the pper.. Model We onsder n nterton of two symmetr frms both n R&D nd produton. ll them frm 1 nd frm. In the frst stge the frms ondut R&D nd n the seond stge they ompete n the produt mrket non-oopertvely. R&D, however, n be ether oopertve or non-oopertve. In ether se, the R&D outome s stohst. We ssume tht f n mount R > 0 s nvested n R&D nd the R&D s suessful, the unt ost of produton flls from the present unt ost > 0 to. Here > 0 represents the mount of ost reduton due to the suessful nnovton. Let 0,1 be the produt mrket ompetton, eh frm s unertn bout the type of ts ontender, nd thus eh frm hs prvte nformton bout ts tul unt ost. 4 See, n ths ontext, Mukheree nd Ry 007 whh dsusses the effets of proess ptents on nnovton nd welfre. 4

7 probblty of suess; therefore, flure ours wth probblty 1. 5 Throughout the nlyss we ssume tht the nnovton s mnor or non-drst n the sense tht even f only one frm sueeds n the nnovton effort, t stll nnot emerge s monopolst. Hene produt mrket ompetton s lwys duopoly n our model. Further, oopertve reserh s n the form of reserh ont venture RJV by whh the frms shre the R&D osts s well s R&D outomes, but under non-oopertve reserh eh frm nvests n ts own lb. Under RJV, sne both the frms ondut reserh ontly, they hve symmetr nformton bout the outome of the reserh. But under non-oopertve reserh, the reserh outome s perfetly observed by respetve frms lone nd not by ther ontenders. Hene, t the produton stge, there s symmetry of nformton bout the R&D outome. Eh frm knows whether t s tself suessful or not, but t knows only pror probblty dstrbuton over the outomes of the other frm s reserh, nd ths probblty dstrbuton long wth ts domn s ommon knowledge. Hene, wth nonoopertve reserh, the frms n the produt mrket wll ply Byesn gme. Therefore the frms wll hve to dede ex nte whether they wll ooperte n R&D or not. We ssume tht both the frms re rsk neutrl. We onsder the followng seuentl move gme. In the begnnng.e., t the R&D stge the frms dede whether they wll go for oopertve or non-oopertve R&D bsed on ther expeted pyoff estmton. Then t the produton stge they wll hoose unttes smultneously. If t s non-oopertve R&D n the frst stge, then they ply the Byesn Nsh gme n the seond stge, nd f t s oopertve R&D n the frst stge, t s smple Nsh gme n the seond stge. In the followng nlyss we onsder untty ompetton n the produt mrket wth perfet substtute goods. Let the mrket demnd for the produts be gven by p mx{ 0, 1 }; > 1 5 We dsuss the se of ontnuous dstrbuton of the R&D outome n dfferent pper. 5

8 where p s the pre of the produt nd s the supply of frm. We now estmte the expeted pyoffs of the frms from the hoe of eh of oopertve nd non-oopertve R&D..1 Benhmrk se: omplete Informton Ths s borrowed from Mrt 11. The expeted pyoff of eh frm under nonoopertve R&D s, π, 1 [ π, π, ] 1 π, R nd tht under oopertve reserh, π, 1 π, R / 3 Then the frms wll go for oopertve reserh f nd only f >, tht s, R / > [ π, π, π, π, ] 1 4 Gven the demnd funton 1, f nd be the unt osts of frms nd respetvely, the pyoff expresson of frm s gven by Hene the neulty 4 n be redued to obtn π,. 4 R / > 1 5 Sne the RHS of 5 s strtly onve n wth unue mxmum t 1/ nd RHS s 0 t both 0 nd 1, then f R s not very lrge, the bove neulty holds for both smll nd lrge, tht s, f the probblty of suess s ether hgh or low, oopertve reserh s preferred over non-oopertve reserh. We n now see the effet of nomplete nformton on the hoe of R&D orgnzton.. Inomplete nformton Non-oopertve R&D 6

9 At the end of the R&D stge eh frm knows whether t s suessful n R&D or not flure, but the other frm does not know, tht s, eh frm knows whether t hs hgh or low unt ost of produton, but ts rvl knows only the probblty dstrbuton; hene there s symmetr nformton. We need to fnd out the Byesn Nsh eulbrum n unttes. Here eh plyer s of two types, vz., suessful S or fled F, hene the S F Byesn Nsh eulbrum strtegy of plyer s,. Sne the plyers re otherwse symmetr, the symmetr strtegy hoe wll be S S 1 nd S F F 1 where see Appendx 1 S F F [ 3 ] 6 [ ] 6 The orrespondng pyoff of eh plyer n ses of suess nd flure re respetvely, S F π S nd π F. Now under non-oopertve reserh when frm nvests > 0 6 R, S F t gets gross pyoff of π wth probblty nd π wth probblty 1. Hene ex nte the expeted pyoff of frm from non-oopertve reserh s ~ S F π 1 π R 7 On substtuton, the expresson n be redued to obtn, ~ 5 R oopertve R&D Here eh frm nvests R / n the RJV nd whether the RJV sueeds or fls, the frms re lwys symmetr wth respet to R&D outome. Sne suess ours wth probblty nd flure wth probblty 1, ex nte the expeted pyoff of eh frm from R&D ooperton s, ~ [ ] R / 7

10 oopertve vs Non-oopertve R&D We re now n poston to stte the results n terms of the followng propostons. Proposton 1: Inomplete nformton bout the R&D outome redues the expeted pyoff under non-oopertve R&D. oopertve R&D nentves vs-à-vs nonoopertve R&D nentves re, therefore, lrger under nomplete nformton. Proof: The expeted pyoff from non-oopertve R&D under omplete nformton s gven by En. whh n be redued to get see Appendx Then we n esly hek tht Fnlly, we hve ~ ~ 5 4 R 10 > ~ <. therefore, oopertve R&D nentves vs-à-vs non-oopertve R&D nentves re lrger under nomplete nformton. Note tht the expeted pyoff under oopertve R&D remns unffeted wth the ntroduton of symmetry of nformton. Proposton : If R s not very lrge, then oopertve R&D s preferred to nonoopertve R&D f the probblty of suess s ether low or hgh. Non-oopertve R&D s preferred f the probblty of suess s of the ntermedte level. Proof: The result holds beuse ~ 5 / > 1 36 ~ > f nd only f, R 11 nd the RHS of 11 s nverted U-shped over 0,1. 8

11 Note tht neulty 11 s ute smlr to neulty 5. Hene the result underlyng Proposton 3 holds rrespetve of whether nformton s symmetr or symmetr. If R s lrge enough, oopertve R&D s lwys preferred. Now to see the effet of symmetry of nformton on the hoe of R&D orgnzton, we ompre neultes 5 nd 11. The RHS of eh of 5 nd 11 s strtly onve over 0,1 wth unue mxmum t 1/, but the RHS of 5 s lrger thn the RHS of 11 0,1. Thus nomplete nformton enhnes the sope for oopertve reserh. Ths result follows from the ft tht symmetr nformton extends the probblty ntervl for whh the expeted pyoff under oopertve reserh s lrger. In tht sense lso nomplete nformton nreses nentves for oopertve reserh. In Fgure 1, ondton 5 s stsfed for ll 0, U,1, nd ondton 11 holds for 0, U,1 ; < < <. Thus for, U,, oopertve R&D ours under nomplete nformton but not under omplete nformton. Sne symmetr nformton genertes unertnty for the plyers bout the extent of effeny of the rvls, they redue rsk by mens of oopertng n R&D. ondtons 5 nd 11 together suggest tht the lrger the sze of the nnovton, the lower s the nentve for oopertve reserh; however, nentves for oopertve reserh fll t slower rte under nomplete nformton. 3. Welfre Implton Gven the nlyss of the prevous seton, onsder the followng ses, dependng on the vlues of,.e., the probblty of suess n redung the unt ost by n mount. se 1: 0, U,1 Here under both omplete nd nomplete nformton the optml hoe of R&D orgnzton s oopertve reserh. Hene the expeted pyoff of eh frm under

12 omplete nd nomplete nformton re eul.e., ~ nd gven by. The orrespondng ndustry output n ether stuton s gven by [, 1, ]. Hene when the probblty of suess n R&D s too low or too hgh, nomplete nformton hs no effet on onsumer s welfre nd produers profts. se :, In ths se under both omplete nd nomplete nformton the frms wll hoose nonoopertve R&D. Then the pyoffs of eh frm under omplete nd nomplete nformton re respetvely gven by nd 7 or lterntvely, by 10 nd 8. We hve lredy shown n Proposton 1 tht ~ nformton redues eh frm s expeted proft. <. Therefore nomplete Now to see the effet on onsumers welfre, onsder the expeted ndustry output under these stutons. The ggregte output under omplete nformton s, Q [, 1,, 1, ] - [ ] 3 3 nd tht under nomplete nformton ~ Q Hene, nformton. 1 [ S 1 S F 1 F ] - [ ] 3 3 ~ Q Q, tht s, onsumers welfre s not ffeted by nomplete se 3:, U, Ths s the most nterestng se n the sense tht for these vlues of the frms wll hoose non-oopertve R&D under omplete nformton but oopertve R&D under nomplete nformton, tht s, nomplete nformton hnges the hoe of R&D orgnzton. Then the expeted pyoffs of eh frm under these regmes re gven by 10

13 nd ~. These re gven by the expressons 10 nd, respetvely. Sne for these vlues of we hve nd we hve ~ < >,.e., R < 1 / 4, then omprng ~, tht s, nomplete nformton not only hnges the hoe of R&D orgnzton but t lso redues eh frm s expeted pyoff. To see the effet on ggregte output, we hve Q gven by euton 1, but Q ~ s gven by - Q ~ [, 1, ] [ ] ~ Hene, Q Q, tht s, gn nomplete nformton hs no effet on output. The welfre results re summrzed n the followng proposton. Proposton 3: Gven the probblty of suess n R&D, s we move from omplete nformton to nomplete nformton regme, onsumers welfre remns unffeted; b The frms beome strtly worse off exept for very low or hgh probbltes of suess; nd The overll welfre of the eonomy goes down exept when the probblty of suess s ether too smll or too lrge. Note tht n Mukheree nd Ry 00, unertnty n ptent pprovls my ndue oopertve reserh, nd ompred to non-oopertve R&D regme, under oopertve reserh both onsumers nd produers strtly gn. On the ontrry, n our pper nomplete nformton my lso ndue oopertve reserh se 3 bove, but under ths stuton frms re strtly worse off lthough the onsumers welfre remns unhnged. Hene nomplete nformton tht ndues oopertve reserh my led to lower level of sol welfre. 6 6 In dfferent ontext, wth symmetr R&D osts, Mukheree nd Ry 014 hve shown tht entry redues the profts of the numbents nd hene t n redue welfre. 11

14 4. onluson In ths pper we hve extended the model of Mrt 11 to the se of symmetr nformton bout the R&D outome n the ontext of the hoe of R&D orgnzton. We hve derved two key results. Frst, f the frms do not know eh other s osts post R&D, then they hve n dded nentve to ooperte nd enter nto n RJV greement. Seond, the frms my beome worse off under ths senro whle onsumers my not get better off. As result, totl sol welfre, onsstng of both onsumers nd produers surplus my fll. Ths leds to poly dlemm n the ontext of the hoe of R&D orgnzton. Whle poles re dreted gnst produt mrket ooperton, R&D ooperton s generlly enourged. But, followng our results, f the frms pereve symmetr nformton t the stge of fnl goods produton wth respet to the R&D outomes of the rvl, oopertve reserh my be welfre redung. 1

15 13 Appendx Appendx 1 Let e be the expeted output of frm s pereved by frm. If t the end of R&D stge frm omes up wth unt ost, ts problem s : e ] [ mx. Ths leds to ts reton funton, e. Then 1 E e e. Under symmetry ssumpton e e e, hene 3 e. Ths gves ] 3 [ 6 1 ] 3 [ 1 S Smlrly, ] [ 6 1 F. Appendx Under untty ompetton,, π. Hene, R R R , 1 ],, [ 1, π π π π

16 Referenes ho, J.P. 1, oopertve R&D wth morl hzrd, Eonoms Letters 3, ho, J.P. 13, oopertve R&D wth produt mrket ompetton, Interntonl Journl of Industrl Orgnzton 11, ombs, K.L. 1, ost shrng vs. multple reserh proets n oopertve R&D, Eonoms Letters 3, D Aspremont,. nd A. Juemn 188, oopertve nd non-oopertve R&D n duopoly wth spllovers, Amern Eonom Revew 5, Ds Vrm, G. 003 Bddng for Proess Innovton Under Alterntve Modes of ompetton, Interntonl Journl of Industrl Orgnzton, 1, Deoury, J. 005, orporte R&D nd strteg trde poly, ndn Journl of Eonoms 38, Kbr, T. 007, On the nentves for oopertve reserh, Reserh n Eonoms 61, Kbr, T. 006, On the nentves for oopertve nd non-oopertve R&D n duopoly, Arthnt New Seres 5, Kbr, T. nd A. Mukheree 000, ooperton n R&D nd produton --- A threefrm nlyss, Journl of Eonoms 71, Mrt, S. 11, Inentves for oopertve nd non-oopertve R nd D n duopoly, Eonoms Letters 37,

17 Mott, M. 1, oopertve R&D nd vertl produt dfferentton, Interntonl Journl of Industrl Orgnzton 10, Mukheree, A nd S. Mrt 004, R&D orgnzton nd tehnology trnsfer, Group Deson nd Negotton 13, Mukheree, A. nd A. Ry 007, Ptents, mtton nd welfre, Eonoms of Innovton nd New Tehnology 16, Mukheree, A. nd A. Ry 00, Unsuessful ptent pplton nd oopertve R&D, Journl of Eonoms 7, Mukheree, A. nd A. Ry 014, Entry, proft nd welfre under symmetr R&D osts, the Mnhester Shool 8, Slpo, D.B. 008, Inentves nd forms of ooperton n reserh nd development, Reserh n Eonoms 6, Slpo, D.B. nd A. Wess 005, ooperton nd ompetton n n R&D mrket wth spllovers, Reserh n Eonoms 5, Suzumur, K. 1, oopertve nd non-oopertve R&D n n olgopoly wth spllovers, Amern Eonom Revew 8, Vonorts, N 17, Reserh ont ventures n the U.S., Reserh Poly 6,

18 LHS & RHS of 5 nd 11 RHS of 5 R / RHS of 11 0 ½ 1 Fgure 1: hoe of oopertve nd Non-oopertve R&D 16