Incentive for Innovation and the Optimal Allocation of Patents

Transcription

1 Workng Paper Seres No.1, Faculty of Economcs, Ngata Unversty Incentve for Innovaton and the Optmal llocaton of Patents Kojun Hamada Seres No.1 ddress: Faculty of Economcs, Ngata Unversty 8050 Ikarash 2-no-cho, Nsh-ku, Ngata Cty , Japan Emal address: Tel. and fax:

2 Incentve for Innovaton and the Optmal llocaton of Patents Kojun Hamada Faculty of Economcs, Ngata Unversty 8050 Ikarash 2-no-cho, Nsh-ku, Ngata Cty , Japan Emal: ugust 12, 2011 bstract Ths paper dscusses the relatonshp between the ncentve for nnovaton and the optmal allocaton of patents by applyng a property rghts approach from the theory of ncomplete contract. We explore a model n whch two research laboratores make R&D nvestments to obtan an nnovatve patent and after successfully obtanng the patent, they determne an optmal ownershp structure of the patent by consderng the effect of ownershp allocaton on ther noncontractble relaton-specfc nvestments. Frst, we show that jont ownershp between two partes s the optmal ownershp structure for the patent. If a selfsh relatonspecfc nvestment s relatvely more mportant than a cooperatve one, a jont ownershp wth no veto power s the optmal allocaton of the patent, and conversely, f the cooperatve nvestment s relatvely mportant, jont allocaton wth blateral veto power s the optmal allocaton. Second, both laboratores have hgher ncentves to make R&D nvestments when no agreement has been reached between the partes wth regard to the ownershp of a patent than when an ex ante agreement s reached wth regard to the optmal allocaton of the patent. Keywords: Innovaton; Patents; Property rghts; Jont ownershp; R&D nvestment JEL classfcaton: L1, O32, D23 Correspondng author. ddress: 8050 Ikarash 2-no-cho, Nsh-ku, Ngata Cty , Japan Tel. and fax: Emal address: khamada@econ.ngata-u.ac.jp 1

3 1 Introducton The patent system has been establshed n almost all countres wth the ntenton of ncentvzng nnovaton among nventors and protectng them from ntellectual theft, by grantng exclusve rghts for the use of the nnovaton to nventors (or ther assgnees) for a lmted perod. Smlar to other ntellectual property rghts, the law guarantees that an nventor who has been granted a patent obtans exclusve control rghts over hs/her nventon as an ntangble asset, ncludng the rght to prevent others from makng, usng, sellng, or dstrbutng the patented nventon wthout permsson. n ssue concernng patent ownershp s who should own a patent from the perspectve of economc effcency, and ths ssue has been dscussed for a long tme by economsts and patent practtoners. Notably, jont ownershp of patents s a wdely prevalng busness practce. In partcular, the economc ratonale behnd the jont ownershp of patents chosen by research authortes needs to be explaned. Ths paper attempts to answer such a queston about the ownershp structure of patents by applyng a property rghts approach from the theory of ncomplete contract. Whle there s substantal exstng lterature on patent ownershp, partcularly jont ownershp, the research contaned n the exstng artcles manly takes two drectons. One s the drecton of ex ante jont ownershp before an nnovaton s completed, and the other s ex post jont ownershp after the nnovaton s completed. 1 The former analyzes the ex ante stuaton before a patent s obtaned, and t examnes how the decson to merge or form a jont venture between research nsttutes affects the ncentve to make R&D nvestments for nnovaton. The latter analyzes the ex post stuaton after a patent s obtaned, and t examnes how patents should be properly used ex post. The papers that deal wth the ex ante stuaton emphasze that a merger or a jont venture results n cost effcency. In several semnal papers, Gandal and Scotchmer (1993) show that a jont venture can mplement the nvestment levels that maxmze jont proft by the ablty to delegate research actvtes to more effcent frms. hattacharya et al. (1990) and rocas (200) clarfy that under jont ventures, researchers can foster sharng of nformaton for productve knowledge or skll that could not have been obtaned f they were competng wth each other. Several papers show that jont ventures allow researchers to 1 Scotchmer (200) contans a bref survey on both types of research artcles n Ch.6. 2

4 share the spllover of the newly generated knowledge (Katz and Shapro, 1987; d spremont and Jacquemn, 1988; Kamen et al., 1992; Suzumura, 1992; ok and Tauman, 2001). Lerner and Trole (200) whch deals wth the ex post stuaton, explore a model that specfes the condton under whch patent pools, whch are agreements among patent owners to lcense sets of ther patents, can enhance welfare. Most of the exstng lterature on patents focuses on the analyss of ether the ex ante or the ex post stuaton, wth regard to the tmng before or after a patent s obtaned. In contrast, ths paper attempts to analyze both stuatons, by ncludng both the ex ante stage n whch researchers make R&D nvestments to obtan a patent and the ex post stage n whch researchers commercalze the obtaned patent. Our paper explores a model that examnes not only how the ownershp structure for patents whch s determned at a later stage, affects the ncentve for R&D nvestments made wth the am of obtanng a patent but also how the determned ownershp structure affects the ncentve for the commercalzaton of the patent. Therefore, unlke the exstng lterature, by ncorporatng the nvestments made both before and after the ownershp structure of a patent s determned, n our model, we attempt to analyze both the ex ante and ex post stuatons before and after the patent has been obtaned. In the model, we apply a property rghts approach from the theory of ncomplete contract n order to clarfy the relatonshp between the ncentve for nnovaton and the optmal allocaton of patents. Snce the property rghts approach has been employed n the semnal artcles of Grossman and Hart (1986) and Hart and Moore (1990), a number of contrbutors have dscussed the optmal allocaton of ownershp rghts n the world of ncomplete contracts (see Hart (1995)). 2 Whle consderable exstng lterature on patents focuses on the stuaton of complete contracts, few papers deal wth the optmal allocaton of patents n the context of ncomplete contracts. In the world of complete contracts, for example, by concludng a lcensng contract approprately, researchers can share the proft generated from ther nnovaton even before the nnovaton s completed, and they can reduce the rsk of nnovaton even when the nnovaton s not successfully completed. However, as nnovaton s unpredctable n essence, t may 2 In the recent years, however, the theoretcal foundaton of the theory of ncomplete contracts has developed rapdly. The economc explanaton of the hold-up problem and asset ownershp has been reexamned through a new theoretcal dea, for example, the dea that contracts serve as reference ponts. For new theoretcal foundatons of the theory of ncomplete contracts, see Hart and Moore (2007, 2008) and Hart (2009). 3

5 not be approprate to lmt the analyss of patents resultng from nnovaton n the context of complete contracts, such that all future contngences are foreseeable for both partes. Moreover, as patents are essentally ntellectual property rghts even f ntangble, t s mportant for economsts and practtoners to answer the queston of who should own these rghts. Therefore, whle consderng the context of ncomplete contracts, we dscuss the relatonshp between the ncentve for nnovaton and the optmal allocaton of patents, by adoptng a property rghts approach to analyze patent ownershp. In the prevous studes dealng wth the context of complete contracts, among other papers, Faulí-Oller and Sandonís (2003) and Sandonís and Faulí-Oller (2006) compare a merger that s a jont venture wth a lcensng contract between research laboratores, by focusng on the effect of the merger on competton polcy. In ther models, when research laboratores undertake a jont venture by mergng, the structure of competton n a product dfferentated market changes from a duopoly to a monopoly (or n general, decreases the number of frms n the ndustry). Thus, n the settng of ther model, the jont venture s a mere nstrument to mtgate the compettve pressure n the fnal market. lcensng contract shares the fruts of nnovaton between research laboratores whle mantanng duopolstc competton. Therefore, f the laboratores can agree upon the lcensng contract wth no restrctons on contractble terms, the customer would always prefer ths contract to a jont venture, because consumer surplus s larger under a duopoly than under a monopoly. On the other hand, f a lcensng contract has some restrctons, t cannot completely restore the outcome of a jont venture. The abovementoned studes provde an economc ratonale for jont ventures, so that the researchng partes merge to ncrease the monopoly n the compettve market. However, f an nnovaton has not been completed, the market compettve poston of upcomng products that are a result of nnovaton wll be undetermned n the present. Therefore, n a case where the future s uncertan, the ratonale for undertakng a jont venture to decrease the compettve pressure may not be strong. ddtonally, as t s well known, n the exstng economc theores that are bult around the world of complete contracts, t s dffcult to explan the boundares of frms n a comprehensve manner. 3 y applyng a property rghts approach, we clarfy how patent ownershp affects the ncentve for nvestments and attempt to explan the boundares of frms wth regard to who 3 For a dscusson on the boundares of frms, see Hart (1995).

6 should own a patent. We show that jont ownershp between two partes can be the optmal ownershp structure of patents. n establshed concluson n the property rghts approach states that the jont ownershp of a physcal asset cannot be optmal. On the other hand, by changng the settngs of the basc model, several studes have proposed that jont ownershp can be optmal. Halonen (2002) consders an nfntely repeated game and argues that jont ownershp may be optmal because the worst ownershp structure n the one-shot game provdes the hghest punshment. De Meza and Lockwood (1998) change the presumpton about the renegotaton process by consderng dfferent outsde optons and show the possblty of an optmal jont ownershp. Rosenkranz and Schmtz (1999) show that when two partes nvest n human captal and decde on know-how dsclosure, jont ownershp wth blateral veto power can be optmal. Rosenkranz and Schmtz (2003) extend ther prevous research to a dynamc model wheren the optmal ownershp structure, ncludng jont ownershp, may change over tme. Schmtz (2008) explans the optmalty of jont ownershp on the bass of the prvate nformaton that the contractng partes have about the payoffs they can realze on ther own. In ths paper, we explan the optmalty of jont ownershp by usng a logc smlar to that of Rosenkranz and Schmtz (1999), because our paper examnes the ownershp of patents that are a result of technologcal nnovaton as well. However, the Rosenkranz and Schmtz s paper deals wth the specfc crcumstances of patent nformaton n whch two partes decde on the knowhow dsclosure of nnovaton. Moreover, the model n ther paper does not explctly nclude any nvestment behavor of the partes, despte the fact that the optmalty of jont ownershp s obtaned by the nature of know-how dsclosure as cooperatve nvestment, as n the sense of Che and Hausch (1999). Ths paper consders two types of nvestments, a selfsh one and a cooperatve one, n a more general settng and attempts to explan the optmalty of jont ownershp by consderng the relatve mportance between the two nvestments. We explore a model n whch two research laboratores make R&D nvestments to obtan an nnovatve patent, and after successfully obtanng the patent, they determne the optmal ownershp structure of the patent by consderng the effect of the ownershp allocaton on ther If we do not consder relaton-specfc nvestments n human captal, but nvestments n physcal captal, jont ownershp can be optmal. See Hart (1995, Ch.3). 5

7 noncontractble relaton-specfc nvestments. Frst, we show that jont ownershp between two partes s the optmal ownershp structure of patents. If the selfsh relaton-specfc nvestment s relatvely more mportant than the cooperatve one, jont ownershp wth no veto power s the optmal allocaton of patents, and conversely, f the cooperatve nvestment s relatvely mportant, jont ownershp wth blateral veto power s the optmal allocaton. Second, when no ownershp agreement has been reached between two partes before a patent s obtaned, both laboratores have a hgher ncentve to make R&D nvestments than when an ex ante agreement has been reached upon wth regard to the optmal allocaton of a patent. The second concluson s partcularly mportant n the context of ths paper, because unlke the exstng lterature, ths paper explans how the ex post ownershp allocaton of patents affects the ex ante ncentve for nnovaton. Ths concluson suggests that the ex post preferred ownershp allocaton, whch s jontly owned, does not necessarly ncrease the ex ante ncentve for nnovatve nvestment. The remander of the paper s organzed as follows. Secton 2 ntroduces the model n whch two research laboratores make ex ante and ex post nvestments before and after determnng the ownershp structure for a patent. Secton 3 dscusses the optmal ownershp structure for patents. Secton examnes the ncentve for the ex ante R&D nvestment for nnovaton. Secton 5 concludes the paper. 2 The model There are two rsk-neutral partes, and, whch represent two ndependent research laboratory managers. They engage n R&D actvtes ndependently and am to obtan a patent for an nnovaton at some pont n the future. The two partes recognze that at a future stage, they can generate some proft from ther nnovaton through a jont collaboraton between themselves, although the possblty of future collaboraton s not stpulated through any contract n the ntal stage. lthough t s usually thought that and own essental physcal assets that are necessary to successfully carry out ther R&D actvtes, we do not dscuss the ownershp of physcal assets n our analyss. 5 We dstngush between the two stages n the model as follows. 5 lternatvely, t s thought that on the ntal date t = 0, and each own a physcal asset necessary to carry out the R&D actvtes, and on the followng date t = 1, the partes renegotate the effcent ownershp 6

8 The frst stage (the ex ante stage) precedes the tme when the success or falure of the R&D actvtes s determned and a patent s obtaned. In the second stage (the ex post stage), both partes make relaton-specfc nvestments to commercalze the patent after t has been obtaned. In the frst stage, on date t = 1, and choose R&D nvestment levels e 0 and e 0, respectvely, ndependently and noncooperatvely, whch are measured by ther costs. We assume that the nvestment levels are observable by the partes but not verfable by the courts. fter both and make R&D nvestments on date t = 2, the success or falure of the R&D actvtes of each party s determned. Wth probablty π (e ) (resp.π (e )), (resp.) becomes a successful nventor and can obtan a patent, whch s consdered ntellectual property for an ntangble asset that has the propertes of an excludable publc good. π (e ) (0, 1), π (e ) > 0, and π (e ) < 0 are assumed. Moreover, n order for the soluton to be nteror, we assume that lm e 0 π (e ) s suffcently larger than unty and for the suffcently large e = e, lm e e π (e ) = 0. Wth probablty π (e ) π (e ), both and succeed n nnovatng and can obtan a patent. In ths case, both nvestors have the rghts to freely access the patent. Wth probablty π (e ) (1 π (e )), only succeeds n nnovatng and can own the obtaned patent. Wth probablty (1 π (e )) π (e ), only succeeds n nnovatng and can own the obtaned patent. Wth probablty (1 π (e )) (1 π (e )), both and fal to nnovate and no patent can be obtaned. In each case n whch the party (or partes) succeed(s) n nnovatng, the successful nnovator(s) obtan(s) the rghts to access the patent ntally because a patent has the propertes of an excludable publc good. We assume that the probablty structure s common knowledge for the partes but not verfable by the courts. Only when a patent s obtaned on date t = 2, the ownershp structure of the patent can be dscussed on date t = 3. In the second stage, after a patent s obtaned on date t = 2, on date t = 3, the nventor(s) own(s) the patent ntally. On date t = 3, the partes agree to renegotate the ownershp structure of the patent. We consder four dfferent property rghts regmes for patent o {,, J, N}. Frst, consder two vertcal ownershp structures that gve one of the two partes veto power over the use of the asset. o = denotes the ownershp structure n whch party s the owner, and when the partes do not collaborate, t can prevent the other party from usng the asset. nalogously, o = denotes the ownershp structure n whch party s the owner. structure of two physcal assets. 7

9 Next, consder two knds of horzontal partnershps. Usually, f there s a physcal asset, jont ownershp means that each party has veto power such that t can block the other party from usng the asset. However, f the asset s a patent, jont ownershp can also mply that each party can use the asset on ts own. o = J denotes jont ownershp wth blateral veto power for both partes. On the other hand, o = N denotes jont ownershp wth no veto power for both partes. We denote the ntal ownershp structure by ô on date t = 3, when the nventor(s) own(s) the patent ntally, and denote the fnal ownershp structure after renegotatng over o. On date t =, after renegotatng the ownershp structure of the patent, and make relaton-specfc nvestments to commercalze the patent, (x, y ) and (x, y ), respectvely, whch are measured by ther costs. x 0; =, denotes the selfsh nvestment and y 0 denotes the cooperatve nvestment, n the sense that Che and Hausch (1999) frst categorzed and examned. On the fnal date t = 5, the partes can decde whether to collaborate, and when the collaboraton s realzed, the payoffs of partes are determned through barganng on ths date. The addtonal value generated under the relaton-specfc collaboraton wll be splt between both partes accordng to the Nash barganng soluton wth equal barganng powers. The tme structure s llustrated n Fgure 1. 1st (ex ante) stage 2nd (ex post) stage R&D nvestment patent s created renegotaton of ownershp relaton-specfc nvestments payoffs are realzed Fgure 1: The sequence of events We now descrbe the payoff structure. When a patent s generated on date t = 2, and am to generate a surplus of V (x, x, y, y ) = v (x, y ) + v (x, y ) through a collaboraton between the two, by commercalzng the patent. On date t =, when the ownershp s renegotated, f party s the owner (o = ), t earns w (x, y ) when the partes do not collaborate, and t can prevent the other party from usng the asset such that s default payoff s 0. If party s the owner (o = ), t earns w (x, y ), whle gets a payoff of 0 when the partes do not collaborate. If both players have blateral veto power (o = J), each party receves 8

10 a payoff of 0 f they do not collaborate, whle n the case of no veto power (o = N), s and s default payoffs are w (x, y ) and w (x, y ), respectvely. When no patent s obtaned on date t = 2, collaboraton does not generate any value. In ths case, both partes get payoffs of 0. In order to guarantee nteror solutons, we assume that v (x, y j ) 0;, j =,, j s strctly concave n (x, y j ). x denotes the selfsh nvestment by party and y 0 denotes the cooperatve nvestment by the other party j n the sense of Che and Hausch (1999). Throughout, all functons are assumed to be twce contnuously dfferentable. In order for the soluton to satsfy the frst-order and second-order condtons, we assume that v x > 0, v y > 0, v xx < 0, v yy < 0, and v xxv yy (v xy) 2 > 0. 6 Lkewse, we assume that w x > 0, w y > 0, w xx < 0, w yy < 0, and w xxw yy (w xy) 2 > 0. To presume that the nvestment s relatonally specfc, we make the usual assumpton that the total surplus as well as margnal surplus are always larger f the partes collaborate: V (x, x, y, y ) = v (x, y ) + v (x, y ) > w (x, y ) + w (x, y ), v x > w x > 0, and v y > w y > 0. efore concludng the model descrpton, we present the frst-best outcome of the relatonspecfc nvestment levels n order to compare them wth those n the ncomplete contracts examned n the followng secton. Gven the above assumptons, the frst-best nvestment levels are unquely defned: x F = arg max v (x, yj F ) x and y F frst-order condtons for party are v x (x F frst-order condtons for party are v y (x F, yf, yf ) = 1 and v x (x F = arg max v j (x F j, y ) y. The ) = 1 and v y (x F, yf ) = 1., yf ) = 1. Lkewse, the 3 Optmal ownershp of patents We examne the optmal ownershp allocaton of patents on date t = n the 2nd stage by usng backward nducton. fter the partes agree upon the fnal decson on the optmal ownershp allocaton, o {,, J, N}, on date t = 3, they choose the nvestment levels (x, y ) on date t =. Provded the partes antcpate that the surplus from barganng on date t = 5 wll be 6 Subscrpts denote partal dervatves wth respect to correspondng varables. 9

11 splt accordng to the Nash barganng soluton wth equal barganng powers, the payoffs of party and on date t = 5 gven an ownershp structure o are U (x, x, y, y o) and U (x, x, y, y o), where U (x, x, y, y o) = 1 2 [V (x, x, y, y ) + w (x, y )] x y f o = 1 2 [V (x, x, y, y ) w (x, y )] x y f o = 1 2 V (x, x, y, y ) x y f o = J 1 2 [V (x, x, y, y ) + w (x, y ) w (x, y )] x y f o = N (1) and lkewse U (x, x, y, y o) = 1 2 [V (x, x, y, y ) w (x, y )] x y f o = 1 2 [V (x, x, y, y ) + w (x, y )] x y f o = 1 2 V (x, x, y, y ) x y f o = J 1 2 [V (x, x, y, y ) + w (x, y ) w (x, y )] x y. f o = N (2) Gven an ownershp structure o, the partes optmal nvestment levels (x, y ) are unquely determned by the followng frst-order condtons: U (x, x, y, y o) = 0, U (x, x, y, y o) = 0, x y (3) U (x, x, y, y o) = 0, U (x, x, y, y o) = 0. x y () Let the nvestment levels (x, y ) be mplctly defned as follows: (a) Under o =, (x o= v x (x o= v y (x o=, yo=, yo= (b) Under o =, (x o= v x (x o=, yo=, yo= ) + w x (x o= ) and (xo=, yo= ) = 2, and v y (x o=, yo= ) = 2, v x (x o=, yo= ) = 2, v x (x o=, yo= ) and (xo=, yo= ) satsfy the followng equatons:, yo= ) w y (x o= ) = 2,, yo= ) = 2., yo= ) satsfy the followng equatons: ) + w x (x o=, yo= ) = 2, 10

12 v y (x o=, yo= (c) Under o = J, (x o=j v x (x o=j v y (x o=j, yo=j, yo=j (d) Under o = N, (x o=n v x (x o=n v y (x o=n, yo=n, yo=n ) w y (x o=, yo=j, yo= ) and (xo=j ) = 2, and v y (x o=, yo= ) = 2. ) = 2, v x (x o=j, yo=j ) = 2, ) = 2, and v y (x o=j, yo=j ) = 2., yo=n ) + w x (x o=n ) w y (x o=n ) and (x o=n, yo=n, yo=n, yo=j ) satsfy the followng equatons:, yo=n ) satsfy the followng equatons: ) = 2, v x (x o=n, yo=n ) = 2, and v y (x o=n ) + wx (x o=n, yo=n ) = 2,, yo=n y comparng these equatons, we can obtan the followng lemma. ) w y (x o=n, yo=n ) = 2. Lemma 1. The followng equatons are satsfed: (x o= (x o=, yo=, yo= ) = (xo=j ) = (xo=n, yo=j, yo=n ), (xo=, yo= ), and (xo= ) = (xo=j, yo=j ),, yo= ) = (xo=n, yo=n ). Proof. See ppendx. Ths lemma has the followng mplcatons: The level of selfsh nvestment s the same when a party does not own a patent and when jont ownershp wth blateral veto power s establshed (x o=j = x o=j ). 7 The level of cooperatve nvestment s the same when a party owns a patent and when jont ownershp wth blateral veto power s establshed (y o= = y o=j ). The level of selfsh nvestment s the same when a party owns a patent and when jont ownershp wth no veto power s establshed (x o= = x o=n ). The level of cooperatve nvestment s the same when a party does not own a patent and when jont ownershp wth no veto power s establshed (y o=j = y o=n ). These results are explaned by the fact that the dfference n the ownershp structure of property makes a dfference n the threat ponts when partes fal to negotate proft sharng accordng to the property rghts approach. Other relatonshps depend on the functonal characterstcs of v (x, y j ) and w (x, y j ). For analytcal smplfcaton, we assume the followng. 7 x o=j denotes the level of selfsh nvestment of party when party j owns a patent. Other notatons are appled n the same manner. 11

13 ssumpton 1. w (x, y ) = k v (x, y ), k [0, 1), j =,, j, and v (, ) s dentcal for both partes. 8 Under ssumpton 1, the nvestment levels under each ownershp allocaton of patent satsfy the followng condtons: (a) Under o =, (x o= (1 + k )v x (x o= v y (x o=, yo=, yo=, yo= (b) Under o =, (x o= v x (x o=, yo= (1 k )v y (x o= (c) Under o = J, (x o=j v x (x o=j v y (x o=j, yo=j, yo=j ) and (xo= ) = 2, v x (x o=, yo=, yo= ) = 2, and (1 k )v y (x o=, yo= ) and (xo= ) satsfy the followng equatons: ) = 2,, yo= ) = 2. ) = 2, (1 + k )vx (x o=, yo= ) = 2,, yo= (d) Under o = N, (x o=n (1 + k )v x (x o=n (1 k )v y (x o=n, yo=j, yo= ) satsfy the followng equatons: ) = 2, and v y (x o=, yo= ) = 2. ) and (xo=j ) = 2, v x (x o=j, yo=j ) = 2, ) = 2, and v y (x o=j, yo=j ) = 2., yo=n, yo=n, yo=n ) and (x o=n, yo=j ) satsfy the followng equatons:, yo=n ) satsfy the followng equatons: ) = 2, (1 + k )vx (x o=n, yo=n ) = 2, ) = 2, and (1 k )vy (x o=n, yo=n ) = 2. Under ssumpton 1, by comparng the above equatons wth those of the frst-best nvestment, we can obtan the followng lemma wth regard to nvestment levels. Lemma 2. Under ssumpton 1, the followng nequaltes are satsfed: () x F > xo, yf > yo, xf () If v xy s suffcently small, x o= Proof. See ppendx. > xo, and yf > yo o {,, J, N}. > x o=j, yo= < y o=j, xo= > x o=j, and yo= < y o=j. Part () of ths lemma mples that the frst-best nvestments are larger than the second-best ones, rrespectve of whether the nvestment s selfsh or cooperatve. Ths result s a typcal 8 lthough we consder ssumpton 1 for smplcty, t s mpled that there s no qualtatve dfference n results even wthout ths assumpton. 12

14 example of the hold-up problem, whch leads to undernvestment n relaton-specfcty. Part () of the lemma mples the followng: Consder a case n whch there are few substtutable or complementary relatonshps between the selfsh nvestment and the cooperatve one. In other words, the change n y j has a lmted effect on the margnal ncrease n v accordng to the ncrease n x. In ths case, the selfsh nvestment when a party owns a patent s greater than when jont ownershp wth blateral veto power s establshed (x o= > x o=j ). On the other hand, the cooperatve nvestment when a party does not own a patent s smaller than when jont ownershp wth blateral veto power s establshed (y o=j < y o=j ). The result of part () n Lemma 2 states that f a party can have exclusve rghts for the use of a patent property, the party has a large ncentve for the relaton-specfc selfsh nvestment compared to the jont ownershp wth blateral veto power. The reason for ths s that when a party obtans a patent, the party can ncrease ts own threat pont, and ths leads to the mprovement of the ncentve for selfsh nvestment. Moreover, t s stated that f a party possesses exclusve rghts for the use of the patent, the other party has a small ncentve for the relaton-specfc cooperatve nvestment compared to the jont ownershp wth blateral veto power. The reason for ths s that when the other party obtans a patent, a party can obtan no gan even f the other s threat pont s better by makng a cooperatve nvestment. 9 From Lemma 1 and Lemma 2, we can summarze the relatonshp among nvestment szes under the frst-best nvestment and four dfferent ownershp structures for the second-best nvestment as follows: Summary of relaton-specfc nvestments () x F () x F () y F (v) y F > xo= > xo= > yo= > yo= = x o=n = x o=n = y o=j = y o=j > x o= > x o= > y o= > y o= = x o=j = x o=j = y o=n = y o=n 9 However, t should be noted that f we extend the analyss to the more general case when substtutablty (v xy < 0) or complementarty (x xy > 0) between two nvestments s possble, we may obtan dfferent nequaltes from those of Lemma 2. Whether the same result as Lemma 2 can be obtaned when v xy < 0 or v xy > 0 depends on the functonal characterstcs of v (x, y j ), and a detaled calculaton s rather complcated. Throughout the paper, we assume that v xy s suffcently close to zero. 13

15 On the bass of the dscusson on the relatonshp concernng the sze of relaton-specfc nvestments summarzed above, we present the followng proposton. Proposton 1. If the selfsh nvestment s relatvely mportant, jont ownershp wth no veto power s the optmal allocaton of a patent. On the other hand, f the cooperatve nvestment s relatvely mportant, jont ownershp wth blateral veto power s the optmal allocaton of a patent. Proposton 1 mples that jont ownershp s always the optmal allocaton of a patent, rrespectve of whether the selfsh nvestment s relatvely mportant. In the context of the property rghts approach, t s well known that f partes engage n actvtes of relaton-specfc nvestments n human captal that cannot be specfed n the ex ante contract, jont ownershp of a physcal asset cannot be optmal. In contrast, Proposton 1 clarfes that when we consder the ownershp of a patent as an ntangble nonexcludable asset, jont ownershp between two partes can be optmal. Ths proposton explans why jont ownershp of patents s wdespread. The ratonale for the establshment of a jont venture for R&D actvtes as an actual form of jont ownershp s presented whle consderng the ncentves for relaton-specfc nvestments. Rosenkranz and Schmtz (1999) present a concluson that s smlar to Proposton 1. They show that when two partes nvest n human captal and decde on know-how dsclosure, jont ownershp wth blateral veto power can be optmal. However, Rosenkranz and Schmtz (1999) deals wth the specfc crcumstances of patent nformaton n whch two partes decde on knowhow dsclosure of nnovaton, and they do not analyze the know-how dsclosure as an nvestment behavor by partes explctly n ther model, despte the fact that the optmalty of jont ownershp s obtaned by the nature of know-how dsclosure as a cooperatve nvestment n the sense of Che and Hausch (1999). We explore a model n whch two types of nvestment, selfsh nvestment and cooperatve nvestment, are explctly dealt wth and explan the optmalty of jont ownershp on the bass of the relatve mportance between the two nvestments. s stated n Proposton 1, the ncentve for nvestment s dfferent between selfsh nvestment and cooperatve nvestment. Whle the party to whch patent ownershp s allocated has a hgher ncentve for selfsh nvestment than otherwse, the other party that does not own a patent has 1

16 the smaller ncentve for selfsh nvestment than otherwse. If both partes do not have veto power under jont ownershp, nether one of the partes s allowed to use the patent. Therefore, under jont ownershp wth no veto power, both partes can have large ncentves for selfsh nvestment. On the other hand, whle a party has a hgher ncentve for cooperatve nvestment when the opponent owns a patent than otherwse, the other party has the smaller ncentve for cooperatve nvestment, because the opponent does not own a patent. If both partes have blateral veto power under jont ownershp, they can ensure that the opponent has the rght to use the patent. Therefore, under jont ownershp wth blateral veto power, both partes can have large ncentves for cooperatve nvestment. s a result, on the bass of the relatve mportance between the two nvestments, jont ownershp wth or wthout veto power s chosen as the optmal ownershp structure by both partes. Now, we present an example that specfes the functonal form of v (x, y j ) n order to provde a more concrete result for Proposton 1. Specfy the functon as v (x, y j ) = x + a yj (= x a y 1 2 j ), a > 0. (5) a s a parameter that represents whether the selfsh nvestment x or the cooperatve nvestment y j has a more sgnfcant nfluence on the surplus v. 10 If a < 1, the selfsh nvestment s relatvely more mportant than the cooperatve nvestment, and vce versa f a > 1. The equlbrum nvestment levels n the frst-best and the second-best cases are as follows: The frst-best nvestment: x F = 1, xf = 1, yf The second-best nvestment: = a2, and y F = a2. x o= = (1+k ) 2, x o= = 1, yo= = (1 k ) 2 a 2, and y o= = a2. x o= = 1, xo= = (1+k ) 2, y o= = a2, and y o= = (1 k ) 2 a 2. x o=j = 1, xo=j = 1, yo=j = a2, and y o=j = a2. x o=n = (1+k ) 2, x o=n = (1+k ) 2, y o=n = (1 k ) 2 a 2, and y o=n = (1 k ) 2 a 2. In ths example, we can confrm that Lemma 1 and Lemma 2 hold. That s, the followng equatons are satsfed: 10 v x > 0, v y > 0, v xx < 0, v yy < 0, v xy = 0, and v xxv yy (v xy) 2 > 0 are satsfed. 15

17 x F = 1 > xo= = x o=n = (1+k ) 2 > x o= = x o=j = 1 x F = 1 > xo= = x o=n = (1+k ) 2 > x o= = x o=j = 1 y F = a2 > y o= = y o=j = a2 > y o= = y o=n = (1 k ) 2 a 2 y F = a2 > y o= = y o=j = a2 > y o= = y o=n = (1 k ) 2 a 2 We can calculate the value of v (x, y j ) n the frst-best and the second-best cases as follows: The frst-best value: v,f = 1+a2 2 and v,f = 1+a2 2 The second-best value: v,o= = 1+k +a 2 and v,o= = 1+(1 k )a 2 v,o= = 1+(1 k )a 2 and v,o= = 1+k +a 2 v,o=j = 1+a2 and v,o=j = 1+a2 v,o=n = 1+k +(1 k )a 2 and v,o=n = 1+k +(1 k )a 2 We can obtan the total surplus from collaboraton, V = v + v. The frst-best total surplus: V F = 2+a2 +a2 2 The second-best total surplus: V o= = 2+k +a 2 +(1 k )a 2 V o= = 2+k +a 2 +(1 k )a 2 V o=j = 2+a2 +a2 V o=n = 2+k +k +(1 k )a 2 +(1 k )a 2 y smple calculaton, t s confrmed that V F > V o o {,, J, N}. y comparng V under dfferent ownershp structures n the second-best case, we can obtan the followng corollary for Proposton 1. Corollary 1. Gven v (x, y j ) = x +a yj, suppose that both partes are dentcal wth regard to ther payoff functon. That s, assume that a = a a and k = k k. () If a < 1, V o=n > V o= = V o= > V o=j. () If a > 1, V o=j > V o= = V o= > V o=n. Proof. See ppendx C.

18 Corollary 1 has the followng mplcatons: When a functon s specfed as v (x, y j ) = x + a y j, a < 1 (resp. a > 1) means that selfsh nvestment s relatvely more (resp. less) mportant than cooperatve nvestment. s shown n Proposton 1, n Corollary 1, f selfsh nvestment s relatvely mportant (a < 1), jont ownershp wth no veto power can realze the hghest surplus n all possble ownershp allocatons. On the other hand, f cooperatve nvestment s relatvely mportant (a > 1), jont ownershp wth blateral veto power can realze the hghest surplus. In Corollary 1, t s confrmed that when the value functon v (x, y j ) s denoted by (5), jont ownershp ether wth or wthout veto power s always optmal, rrespectve of whch, the selfsh or cooperatve nvestment, s relatvely mportant. It should be noted that Proposton 1 and Corollary 1 hold under the assumpton that both partes are dentcal. If we extend the analyss to the stuaton where both partes are not dentcal, the ownershp allocaton of patents, whch s dfferent from jont ownershp, can be possble. In the above example, n whch v (x, y j ) satsfes (5), we consder the general case n whch a a and k k hold. That s, both partes dffer n the relatve mportance between two nvestments and the sze of an outsde opton as the threat pont. When partes are not dentcal n ths example, we can put forth the followng proposton, whch generalzes Corollary 1. Proposton 2. Gven v (x, y j ) = x + a yj, suppose that both partes are not dentcal, that s, a a and k k. The total surpluses under four dfferent ownershp allocatons of patents satsfy the followng nequaltes: () If a < 1 and a < 1, V o=n > max{v o=, V o= } > mn{v o=, V o= } > V o=j. V o= V o= f and only f k (1 a 2 ) k (1 a 2 ). () If a < 1 and a > 1, V o= > max{v o=j, V o=n } > mn{v o=j, V o=n } > V o=. V o=j V o=n f and only f k (1 a 2 ) k (1 a 2 ). () If a > 1 and a < 1, V o= > max{v o=j, V o=n } > mn{v o=j, V o=n } > V o=. V o=j V o=n f and only f k (1 a 2 ) k (1 a 2 ). (v) If a > 1 and a > 1, V o=j > max{v o=, V o= } > mn{v o=, V o= } > V o=n. V o= V o= f and only f k (1 a 2 ) k (1 a 2 ). Proof. See ppendx D. 17

19 Proposton 2 has the followng mplcatons: () If the selfsh nvestment s relatvely more mportant for both partes than the cooperatve nvestment, jont ownershp wthout veto power s the optmal allocaton of patent rghts. Ths result corresponds to part () of Corollary 1. On the other hand, (v) f cooperatve nvestment s relatvely more mportant for both partes than selfsh nvestment, jont ownershp wth blateral veto power s the optmal allocaton of patent rghts. Ths result corresponds to part () of Corollary 1. Under the assumpton that the partes are dentcal, only these two results are presented. However, f we extend the analyss to treat both partes dfferently wth respect to the relatve mportance between two nvestments, another ownershp allocaton besdes jont ownershp can be optmal. s shown n parts () and (), f two partes dffer n the relatve mportance between selfsh and cooperatve nvestments, the optmal ownershp allocaton of patent rghts s the exclusve ownershp by a party such that the other s cooperatve nvestment has a more sgnfcant mpact on ts surplus than ts own selfsh nvestment. It s shown that when both partes are not dentcal n the mpact of two nvestments, exclusve ownershp by a party can be optmal. Exclusve ownershp s optmal because, when the party that beleves that cooperatve nvestment s more mportant than selfsh nvestment owns a patent, the other party that does not own the patent has the largest ncentve for cooperatve nvestment n all possble ownershp structures. s the mpact of cooperatve nvestment exceeds that of selfsh nvestment, the largest surplus s realzed under ths exclusve ownershp. Incentve for nnovaton In ths secton, we examne the ncentve for the ex ante R&D nvestment n the frst stage when both partes make R&D nvestments for nnovaton and the outcome of R&D actvtes s determned. If a patent was obtaned on date t = 2, the nventor(s) who succeed(s) n nnovaton own(s) the patent for the nnovaton (or more precsely, has the rght to freely access the patent) ntally on date t = 3. On date t = 3, the partes agree to renegotate the optmal ownershp structure o {,, J, N} for the patent. 18

20 On date t = 2, the followng four dfferent scenaros emerge as a result of the partes R&D actvtes: Case I: Wth probablty π (e ) π (e ), both partes and succeed n nnovaton and a patent s obtaned. oth nvestors have the rght to freely access the patent. Case II: Wth probablty π (e ) (1 π (e )), only party succeeds n makng an R&D nvestment and t owns a patent. Case III: Wth probablty (1 π (e )) π (e ), only succeeds n makng an R&D nvestment and t owns a patent. Case IV: Wth probablty (1 π (e )) (1 π (e )), both R&D nvestments fal to create an nnovaton and no patent s obtaned. Provded that the surplus from ownershp renegotaton on date t = 3 s splt accordng to the Nash barganng soluton, the prvate payoffs of and on date t = 3 are gven as follows: U,bo = U ( ô) [U ( o ) + U ( o ) U ( ô) U ( ô)], (6) U,bo = U ( ô) [U ( o ) + U ( o ) U ( ô) U ( ô)], (7) where ô denotes the ntal ownershp structure before the optmal ownershp allocaton s renegotated, and o s the optmal ownershp allocaton after renegotaton. s stated n Secton 3, the optmal ownershp allocaton o depends on the relatve mportance between selfsh and cooperatve nvestments. In the followng subsectons, we lmt the dscusson to the stuaton n whch both partes are dentcal. s shown n Proposton 1, f the selfsh nvestment s relatvely more mportant than the cooperatve nvestment, jont ownershp wth no veto power s the optmal allocaton of the patent (o = N), and f the cooperatve nvestment s relatvely more mportant, jont ownershp wth blateral veto power s the optmal allocaton of the patent (o = J). We frst examne the prvate payoff of each party that s obtaned by renegotatng the optmal ownershp allocaton on t = 3 n the former case n whch selfsh nvestment s relatvely mportant. Then, we subsequently examne the prvate payoff n the latter case n whch cooperatve nvestment s relatvely mportant. 19

21 .1 Case wheren selfsh nvestment s relatvely mportant In ths case, the optmal ownershp allocaton s o = N. In Case I, when both partes succeed n nnovaton, the ntal ownershp structure s ô = N. Thus, as ô = o = N, U,bo=N = U ( N). Renegotaton over ownershp allocaton does not take place. In other words, renegotaton does not rase the prvate payoff. The nventors have the rght to freely access the patent, rrespectve of whether they renegotate the ownershp of the patent. The same logc s appled to. In sum, n Case I, the prvate payoff of party remans U,bo=N = U ( N). In Case II, when only succeeds, the ntal ownershp structure s ô =. Thus, the prvate payoff of s U,bo= = U ( ) [U ( N) + U ( N) U ( ) U ( )]. Ownershp allocaton s renegotated, and nventor agrees to gve non-nventor the rght to freely access the patent by obtanng some transfer. On the other hand, as fals to nnovate, t owns nothng ntally. However, n the next stage, stands n need of collaboraton wth n order to accomplsh the commercalzaton of the patented nnovaton. Thus, the threat pont (the standng pont) of s U ( ). Thus, the prvate payoff of n Case II s U,bo= = U ( ) [U ( N) + U ( N) U ( ) U ( )]. Case III s the mrror mage of Case II. Therefore, the prvate payoffs of and are U,bo= = U ( ) [U ( N) + U ( N) U ( ) U ( )] and U,bo= = U ( ) [U ( N) + U ( N) U ( ) U ( )], respectvely. Fnally, n Case IV, both partes do not obtan patents. Thus, of course, no ownershp allocaton agreement s made. The prvate payoff of party s U,bo=? = Case wheren cooperatve nvestment s relatvely mportant In the second case, the optmal ownershp allocaton s o = J. In Case I, when both partes succeed n nnovatng, the ntal ownershp structure s ô = N. Thus, the prvate payoff of s U,bo=N = U ( N) [U ( J) + U ( J) U ( N) U ( N)]. Ownershp allocaton s renegotated. The nventors that have the rght to freely access the patent agree to jont ownershp wth blateral veto power. The same logc s appled to. In Case II, when only succeeds, the ntal ownershp structure s ô =. Thus, the prvate payoff of party s U,bo= = U ( ) [U ( J) + U ( J) U ( ) U ( )]. Ownershp 11 bo =? mples that there s no patent to be allocated by both partes. 20

22 allocaton s renegotated, and nventor, who has the rght to freely access the patent, agrees to jontly own the patent wth blateral veto power by obtanng some transfer. On the other hand, as fals to nnovate, t owns nothng ntally. y a logc smlar to that n subsecton.1, the prvate payoff of n Case II s U,bo= = U ( ) [U ( J) + U ( J) U ( ) U ( )]. Case III s the mrror mage of Case II. Therefore, the prvate payoffs of and are U,bo= = U ( ) [U ( J) + U ( J) U ( ) U ( )] and U,bo= = U ( ) [U ( J) + U ( J) U ( ) U ( )], respectvely. Fnally, as both partes fal to obtan patents n Case IV, the prvate payoff of party s U,bo=? = 0..3 Comparson of R&D nvestment levels Frst, as an deal benchmark, we derve the frst-best R&D nvestment levels. The frst-best total surplus net of the costs of relaton-specfc nvestments s V F (x F x F xf yf, xf, yf, yf ) yf. If both partes choose ther R&D nvestment levels by consderng the frst-best net total surplus and wthout consderng how the total surplus s dstrbuted between partes, they must maxmze the followng expected total surplus. [π (e ) + π (e ) π (e )π (e )](V F x F x F y F y F ) e e. (8) The frst-best R&D nvestment levels (e F, ef ) satsfy the followng frst-order condtons. π (e F π (e F )(1 π (e F ))(V F x F x F y F y F ) = 1. (9) )(1 π (e F ))(V F x F x F y F y F ) = 1. (10) However, n the real world of ncomplete contracts, the frst-best R&D nvestment levels are far from feasble. Next, we consder a more realstc benchmark case for comparson. In ths benchmark case, we presume that rrespectve of whether each party succeeds or fals to nnovate. In other words, rrespectve of who owns a patent ntally, both partes can carry out the ex post optmal ownershp allocaton at no addtonal cost n advance. That s, on date t = 1, both partes can agree the contract that specfes the ex post optmal allocaton of the patent 21

23 as a jont ownershp before the success or falure of the partes nnovatons s determned. Such an ex ante agreement on optmal ownershp allocaton can be mplemented at no addtonal cost and wthout any ncome transfer. We name ths benchmark the commtment case. s shown n Proposton 1, f selfsh nvestment s relatvely more (resp. less) mportant than cooperatve nvestment, jont ownershp wth no (resp. full) veto power s the optmal ownershp allocaton. In the commtment case, the prvate payoff of party s U ( N) f selfsh nvestment s more mportant, and U ( J) f cooperatve nvestment s more mportant. In the commtment case, party maxmzes the followng net expected prvate payoff wth regard to R&D nvestment. [π (e ) + π (e ) π (e )π (e )]U ( N) e, (11) f selfsh nvestment s more mportant, and [π (e ) + π (e ) π (e )π (e )]U ( J) e, (12) f cooperatve nvestment s more mportant. The net expected prvate payoff of party s descrbed n a smlar manner. The R&D nvestment levels n the commtment case (e, e ) satsfy the followng frst-order condtons: π (e )(1 π (e ))U ( N) = 1, (13) π (e )(1 π (e ))U ( N) = 1, (1) f selfsh nvestment s more mportant, and π (e )(1 π (e ))U ( J) = 1, (15) π (e )(1 π (e ))U ( J) = 1, () f cooperatve nvestment s more mportant. Now, we examne the R&D nvestment levels chosen by both partes on the frst date. On date t = 1, and choose R&D nvestment levels e and e, respectvely, ndependently and 22

24 noncooperatvely. The expected prvate payoff of net of the cost of R&D nvestment s as follows: π (e )π (e )U,bo=N + π (e )(1 π (e ))U,bo= +(1 π (e ))π (e )U,bo= + (1 π (e ))(1 π (e )) 0 e. (17) The net expected prvate payoff of s descrbed n a smlar manner. The R&D nvestment levels wth no commtment wth regard to patent allocaton (ê, ê ) satsfy the followng frstorder condtons. π (ê )[π (ê )U,bo=N + (1 π (ê ))U,bo= π (ê )U,bo= ] = 1. (18) π (ê )[π (ê )U,bo=N + (1 π (ê ))U,bo= π (ê )U,bo= ] = 1. (19) We compare three dfferent R&D nvestment levels the frst-best one (e F, ef ), the one n the commtment case (e, e ), and the one n a no commtment case (ê, ê ). ssume that not only the payoff functons but also the probablty functons are dentcal between both partes, that s, π( ) π ( ) = π ( ). s the R&D nvestment levels of both partes are always equal, that s, e e = e, we compare three nvestment levels, e F, e, and ê. Under dentcal condtons, the frst-best nvestment level e F satsfes the followng equaton. π (e F )(1 π(e F ))(V F x F x F y F y F ) = 1. (20) The nvestment level n the commtment case e s rearranged as follows: π (e )(1 π(e ))U ( N) = 1, (21) f selfsh nvestment s more mportant, and π (e )(1 π(e ))U ( J) = 1, (22) f cooperatve nvestment s more mportant, where U ( N) U ( N) = U ( N) and U ( J) 23

25 U ( J) = U ( J). Fnally, the equlbrum nvestment level ê wth no commtment s rearranged as follows: π (ê)[π(ê)u,bo=n + (1 π(ê))u,bo= π(ê)u,bo=j ] = 1, (23) where U,bo=N U,bo=N = U,bo=N, U,bo= U,bo= = U,bo=, and U,bo=j U,bo= = U,bo=. y comparng (20) wth (21) or (22), we present the followng lemma for a comparson between e F and e. Lemma 3. Suppose that both partes are dentcal. The frst-best R&D nvestment level s larger than when partes can commt ex ante to the ex post optmal ownershp allocaton. That s, e F > e. Proof. See ppendx E. The result of Lemma 3 s obvous. The ex post net total surplus n the frst-best case s always larger than the net prvate payoff that s gven to a party through ex post Nash barganng n the second-best case. When the expected return from R&D nvestment s large, the ncentve for nvestment s hgh. Therefore, Lemma 3 mples that the ncentve for nnovaton s larger when nnovators can properly acqure all the expected proft from nnovaton than n the commtment case of patent allocaton n the context of ncomplete contracts. Next, by comparng (23) wth (21) or (22), we can obtan the followng proposton regardng the comparson between e and ê. Proposton 3. Suppose that both partes are dentcal and w (x, y j ) s relatvely large. The equlbrum R&D nvestment level s larger when partes cannot commt ex ante to the ex post optmal patent ownershp than when they can commt to t. That s, ê > e. Proof. See ppendx F. Proposton 3, whch s the man result of ths paper, states that both partes have a hgh ncentve to make R&D nvestments to obtan a patent when no agreement on the ownershp of the patent has been reached between two partes before a patent s obtaned, compared to when 2

26 an ex ante agreement on the optmal allocaton of the patent has been reached. oth partes recognze n advance that jont ownershp wth or wthout veto power s the ex post optmal ownershp allocaton, whch s determned dependng on the relatve mportance between selfsh and cooperatve nvestments. However, f they can commt ex ante to establsh jont ownershp as the optmal ownershp allocaton of the patent before the nnovaton, the ncentve for the R&D nvestment to obtan a patent for nnovaton dmnshes. If the research laboratores pay more attenton to the ncentve for ex ante R&D nvestment, t s not necessarly desrable for them to determne the ownershp allocaton of the patent at the ex ante stage, even f ts allocaton s optmal from the ex post vewpont. Proposton 3 suggests that t s possble that the partes wll not determne an ownershp allocaton ex ante f t s desrable that t be determned ex post. 12 esdes, we cannot obtan any explct results for the comparson between e F and ê. Thus, t may be possble that e F < ê. Ths s because t may be possble that the net prvate payoff of a party after the optmal ownershp allocaton has been renegotated exceeds the ex post net total surplus. Fnally, let us provde a numercal example n order to llustrate the result of Proposton 3 n a specfed functonal form. Under the assumpton that both partes are dentcal, consder the above analyzed surplus functon, v (x, y ) = x + a y. If a < 1 (resp. a > 1), selfsh (resp. cooperatve) nvestment s relatvely more mportant. 13 Specfy an dentcal probablty functon as π(e ) = he (2 e ) = h[ (e 1) 2 +1], where h > 1 s a parameter that represents the degree of the mpact on probablty of R&D nvestment. 1 Under ths functonal specfcaton, the R&D nvestment levels satsfy the followng equatons. 12 The result of Proposton 3 may be affected by the rsk atttude of partes that make R&D nvestments. If the partes are rsk averse, they prefer obtanng a fxed amount of prvate payoff that s expected on a later date f they succeed n nnovatng, U ( N or J), to gan a fluctuatng prvate payoff, dependng on whether they succeed n nnovatng, U,bo. However, research nsttutes are more lkely to seek rsks when faced wth uncertanty. There may be no need to consder a stuaton wheren they behave as rsk averters. 13 The prvate payoffs of party are calculated n ppendx G. 1 In order to guarantee that π (e ) = 2h(1 e ) > 0, e must be n the range of [0, 1). π (e ) = 2h < 0 s always satsfed. In order to guarantee that π(e ) les n (0, 1), the doman of e must le n the nterval of [0, e], h(h 1) e 1 h π (0) = 2h > 1. (< 1). The assumpton that lm e 0 π (e ) s suffcently larger than unty s satsfed because 25