Non-Obviousness and Complementary Innovations

Transcription

1 Non-Obviousness and Complementary Innovations Yann Ménière To ite this version: Yann Ménière. Non-Obviousness and Complementary Innovations. European Eonomi Review, Elsevier, 008, 5 (7), pp < /j.euroeorev >. <hal > HAL Id: hal Submitted on 19 Jun 009 HAL is a multi-disiplinary open aess arhive for the deposit and dissemination of sientifi researh douments, whether they are published or not. The douments may ome from teahing and researh institutions in Frane or abroad, or from publi or private researh enters. L arhive ouverte pluridisiplinaire HAL, est destinée au dépôt et à la diffusion de douments sientifiques de niveau reherhe, publiés ou non, émanant des établissements d enseignement et de reherhe français ou étrangers, des laboratoires publis ou privés.

2 Patent Law and Complementary Innovations Yann Ménière y CERNA, Eole Nationale Supérieure des mines de Paris CORE, Université Catholique de Louvain-la-Neuve Otober 31, 007 JEL ode: O34 Keywords: Innovation, Patent, R&D, Complementarity I am grateful to John Barton, Matthieu Glahant, François Lévêque, Pierre Piard, Katharine Rokett, Suzanne Sothmer and the partiipants of the Berkeley innovation seminar for their helpful omments. Of ourse any mistakes are my own. y meniere@erna.ensmp.fr 1

3 The patent system was initially designed to provide inentives to develop stand-alone innovations in elds suh as mehanis, hemials or pharmaeutials. Its appliation is therefore problematial in more reent elds suh as biotehnology and ICT industries, where innovation patterns are di erent. A well-known problem onerns umulative innovations. Patent law must then trade o the rights granted to upstream patent owners with the inentives to develop subsequent innovations (Sothmer, 1991; O Donoghue, Sothmer and Thisse, 1998; Deniolò, 000). Another issue onerns omplementary innovations, whih are the fous of the paper. When nal produts embody several omplementary innovations, the sattering of patents between various owners jeopardizes the ommerial exploitation of the produts beause of negotiation and royalty staking issues (Merges & Nelson, 1990; Heller & Eisenberg, 1998; Shapiro, 001). In biotehnology, this is the ase of therapeuti proteins or geneti diagnosti tests that require the use of multiple patented gene fragments (Heller & Eisenberg, 1998). It is also very frequent in ICT industries suh as eletronis, omputer hardware and software, where rms have to navigate "patent thikets" (Shapiro, 001). Shapiro (001) reports, for example, that in the semi-ondutor industry rms reeive thousands of patents eah year and manufaturers an potentially infringe on hundreds of patents with a single produt". The situation is similar in the U.S. software industry, where there are potentially dozens or hundreds of patents overing individual omponents of a produt (FTC, 003). I study the problem of the prodution of omplementary innovations in a model of dynami R&D ompetition between two rms, and argue that in some ases omplementary innovations should not be patentable as suh, but bundled with other innovations prior to patenting. To do so I onsider two omplementary innovations and examine whether they should be patented separately or

4 as a bundle. This approah ehoes several papers on umulative innovations where patentability requirements are de ned as the need to develop two or more suessive innovations before obtaining a patent (Sothmer and Green, 1990; Hunt, 1995; O Donoghue, Sothmer and Thisse, 1998; Deniolò, 000). As regards omplementary innovations, the optimal patenting rule depends on a trade-o between the pro t loss due to sattered omplementary patents, and the possible bene t of patent dislosure. The sattering of omplementary patents between di erent owners reates a double marginalization issue. Sine eah patentee behaves as a monopolist, the Cournot (1838) theorem predits that pries do not maximize the rms pro ts (Shapiro, 001; Lerner & Tirole, 005) 1. The requirement that omplementary innovations be bundled prior to patenting an be a way to prevent this pro t loss. However, small innovations are not dislosed when innovations have to be bundled prior to patenting (Sothmer and Green, 1990). As a result, rms lose the possibility to quit the rae after a rst innovation has been patented, whih leads to R&D ost dupliations. I show that patent dislosure has a positive soial e et, although it does not permit a fully e ient oordination between rms. In this ontext, bundling innovations prior to patenting an be more e ient if innovations an be developed quikly. As I argue in the Conlusion, this ondition is onsistent with the legal de nition of the "inventive step" patentability requirement. The paper is strutured in six setions. First, the model is introdued in Setion. Setion 3 then onsiders the ase in whih innovations an be patented separately, while Setion 4 fouses on the ase in whih they must be bundled prior to patenting. Setion 5 ompares the soial outomes of the two requirements. Finally, Setion 6 onludes and disusses the poliy impliations of the model. 1 To overome this problem, patent holders an ooperate to lower their royalties by designing an appropriate ross-liensing agreement. Still, suh agreements are not however systemati and their negotiation and monitoring also generate substantial transation osts. 3

5 1 The model I onsider a tehnology whih onsists of two omplementary innovations. These two innovations are assumed to be pure omplements. Both are essential to exploit the tehnology, and they have no use when isolated from eah other. A monopolist exploiting the tehnology makes a pro t. The R&D setting is derived from Sothmer and Green (1990). The timing of eah innovation follows the same Poisson disovery proess with a hit rate per unit of time and per innovation. Thus the expeted researh time for an innovation is 1. I normalize the R&D ost per unit of time and per innovation to one monetary unit. As a result, the ost of developing an innovation is determined only by the Poisson hit rate of the R&D proess, independently of any onsiderations regarding the prie of researh inputs. Contrary to the model of Sothmer and Green (1990), the two innovations that onstitute the tehnology are not umulative: their development proesses are independent and simultaneous. Two idential rms ompete in R&D for developing the tehnology. The disount rate is denoted by r. I make the general assumption that: 1 > 0 (1) This assumption guarantees that the tehnology is worth developing. More preisely, it implies that it would be pro table for a single rm to invest in the development of one of the two innovations if that ensured it a pro t equal to one half of the tehnology s value. The rm would invest 1 at eah time period dt, and would expet a pro t with a probability. Its expeted pro t would thus be equal to 1 = (r + ). I use the model to ompare two di erent patent poliy settings. In a rst 4

6 setting, eah innovation is patentable. It is thus possible, although not neessary, that eah rm patents a di erent innovation. The dislosure of a rst patent informs the other rm that it an stop trying to develop this innovation, and that it will have to share the rent if it patents the seond innovation. In a seond setting, only the bundled tehnology is patentable. Therefore a rm must develop both innovations by its own means in order to obtain a patent. In both ases I assume that patents onfer perfet protetion against imitation. When rms are unable to inlude both innovations in a single patent, they grant separate lienses on their respetive patents, whih reates a double marginalization problem (Shapiro, 001). This issue an be aptured in a simple way in the ontext of a ompetitive industry that produes at zero ost and uses two omplementary innovations i = 1;, eah liensed at royalty R i (i = 1; ) per unit of output. If the patents are held by di erent rms, the ompetitive prie is equal to p = R 1 + R, whereas the prie is R when a single rm lienses the innovations as a bundle. Assuming a standard demand funtion for the produt, Shapiro (001) shows that in a Nash equilibrium, (pro t maximizing) unoordinated liensors set their royalties so that R 1 + R > R. As a result, total pro ts 0 are smaller than the pro t a single liensor would have made. This is the standard result of the Cournot (1838) theorem. If patents are held by di erent rms, eah liensor sets its royalty without notiing the fat that high royalties derease the other liensor s pro t. Therefore royalties are beyond the level R that maximizes total pro ts. In this paper, I denote the pro t loss due to double marginalization by = 0, whih orresponds to the di erene between monopoly and total Cournot pro ts. Sine this ost results from the dispersion of omplementary patents between di erent owners, I refer to it as Note that the e et of dislosure is not the same with umulative innovations as with omplementary innovations. In the former ase, the ahievement of one innovation is neessary to enable the development of the other one. In the latter ase, rms invest simultaneously in both innovations, and reat to the dislosure of a patent by stopping their investment in the underlying innovation. 5

7 the sattering ost in the rest of the paper. I moreover assume from now on that it is exogenous. For simpliity, I fous the analysis on the rms private surplus, although the double marginalization issue also a ets onsumers through pries. In Setion 4, I use the sum of the innovators expeted pro ts as a measure of soial welfare, the most e ient organization of R&D thus being the one that maximizes total pro ts. Although biased, this approah to e ieny does not a et my key result. If onsumer surplus were taken into aount, soial e ieny would still require that trivial innovations not be patentable 3. Innovations an be patented separately Consider rst the patent rae when innovations an be patented separately. The dynami game is represented in Figure 1. As a rst step, the rms deide simultaneously whether to enter the rae or not. Sine the two innovations are symmetrial and have idential and independent Poisson hit rates, a rm will either invest in R&D for both innovations, or not invest at all. If the rms deide to invest, they have equal hanes to be the rst one to ahieve and patent an innovation. At Node n = 1;, rm n has just developed, patented and dislosed a rst innovation. In this ase both rms must deide either to ontinue investing for the seond innovation, or to give up. I denote by v n i (x 1; x ), rm i s expeted payo at those Node n = 1;, where x i f0; 1g indiates whether rm i = 1; 3 Formally, introduing onsumer surplus would not hange the analysis of investment strategies in Setions and 3. In Setion 4, it would imply three modi ations in the expression of soial surplus. First, the pro t generated by the tehnology would be replaed with a parameter w equal to the sum of and the onsumer net surplus from the onsumption of the good produed with the tehnology. Seond, the private sattering ost would be replaed with a publi sattering ost parameter s equal to the sum of and the loss of net onsumer surplus due to double marginalization. Third the private disount rate r would be replaed with a soial disount rate er. Formally, all these hanges are equivalent to a variation of the parameter in the total "private" expeted surplus. Hene they would not hange Propositions 3 and 4. 6

8 deides to give up (x i = 0) or to ontinue investing in the seond innovation (x i = 1). Figure 1: The patent rae when innovations an be patented separately The equilibrium onept is sub-game perfetion. I proeed bakwards to identify the equilibria in pure strategies. Consider rst Node 1. Firm 1 has just patented an innovation, and both rms have to deide whether to ontinue or not. Table 1 shows the expeted payo s to 1 and at this node. v1 1 (x 1 ; x ) ; v 1 (x 1 ; x ) x = 0 x = 1 ( x 1 = 0 (0; 0) ) r+ ; ( 1 x 1 = 1 r+ ; 0 ( 3 ) 1 ) 1 r+ r+ ; ( ) 1 r+ Table 1. Firms expeted payo s after 1 has patented a rst innovation If both rms deide to stay in the rae, eah rm inurs an R&D ost 1 at 7

9 eah time period dt until the seond innovation has been ahieved. There is a probability that rm 1 ahieves the seond innovation in time period dt. If this ours, the payo to rm 1 is (sine it has already patented the rst innovation), while the payo to rm is 0. But there is also a probability that rm innovates before rm 1. In this ase, the rms have to share the pro t and inur the sattering ost, leading to symmetrial individual payo s of ( ) =. Finally the expeted payo s to rms 1 and in time period dt are + ( ) = 1 and ( ) = 1 respetively. As the time of ahievement of the seond innovation has exponential distribution with parameter, the present expeted payo s to rms 1 and are respetively v1 1 (1; 1) = ( (3 ) = 1) = (r + ) and v 1 (1; 1) = ( ( ) = 1) = (r + ). If rm gives up, its ontinuation payo is v 1 (x; 0) = 0; x f0; 1g. Firm 1 still inurs an R&D ost of 1 at eah time period dt. It ahieves the seond innovation with a probability, for a payo. Sine rm 1 remains alone, the time of ahievement of the seond innovation has now an exponential distribution with parameter, leading to a ontinuation payo of v 1 1 (1; 0) = ( 1) = (r + ). Lemma 1 Assume that a rm has patented a rst innovation. Then if innovation. 1 both rms ontinue to invest in R&D to develop the seond If < 1 the rm that patented the rst innovation keeps investing in R&D to develop the seond innovation, while the other rm stops investing in R&D. Proof. See Appendix 1. Lemma 1 summarizes the outomes of the subgame at Nodes 1 and (see Figure 1). The rm that patents an innovation rst will always keep investing in R&D in order to develop the seond innovation. It is never pro table for it 8

10 to stop investing and rely on the other rm to omplete the tehnology, sine it would then have to share pro ts whih it ould appropriate entirely by ahieving the last innovation. Under these onditions the other rm will stay in the rae only if 1, and will otherwise give up. This implies that a high sattering ost is not inurred. Sine only one rm ontinues to invest in the development of the seond innovation, the sattering ost is replaed with longer innovation delays. Consider now Node 0 on Figure 1. At this node, no innovation has been developed yet and the rms have to deide whether to invest in R&D or not, in order to develop the tehnology. I assume that rms annot avoid ompetition by agreeing ex ante to oordinate their R&D investments. I also assume that a rm annot wait for its ompetitor to patent a rst innovation before investing and trying to patent the seond innovation 4. I therefore look for the onditions under whih it is pro table for both rms to invest simultaneously in both researh lines, and show that this is the ase when parameter is high enough. To identify the onditions under whih the rms an expet a positive pro t from a patent rae, I must alulate their payo s in two di erent ases, depending on what would happen after a rst innovation had been patented (Nodes 1 and ). Let V denote the expeted pro t of a rm at Node 0 when both rms keep investing after a rst innovation has been patented. Conversely, let V a denote the expeted pro t at Node 0 when a rm gives up after a rst innovation has been patented. To simplify the presentation, I alulate these payo s for rm 1. Let us rst onsider the ase where both rms ontinue investing at Nodes 1 and. If the rms invest at Node 0, there is a probability that rm 1 ahieves one of the innovations in time period dt (so that the rms arrive at 4 This assumption simpli es the analysis. It is realisti sine the other rm ould ounter this strategy e etively by relying on serey rather patenting to protet its rst innovation. 9

11 Node 1). Then the expeted payo to rm 1 is v1 1 (1; 1), as given in Table 1. There is an equal probability that rm ahieves one of the innovations in time period dt (so that the rms arrive at Node ). In this ase, the payo to rm 1 is v1 (1; 1). Sine eah rm invests in parallel in two researh lines, the time of ahievement of the rst innovation has an exponential distribution with parameter 4. The present expeted payo to rm 1 if it enters is nally V = v1 1 (1; 1) + v1 (1; 1) : () r + 4 Let us assume now that the rm that did not innovate gives up at Nodes 1 and. If the rms invest at Node 0, there is a probability that rm 1 ahieves one of the innovations in time period dt (so that the rms arrive at Node 1). The expeted payo to rm 1 is then v 1 1 (1; 0). There is an equal probability that rm ahieves one of the innovations in time period dt (so that the rms arrive at Node ). In this ase, the payo to rm 1 is v 1 (0; 1) = 0. Sine the time of ahievement of the rst innovation has an exponential distribution with parameter 4, the present expeted payo to rm 1 if it enters is nally V a = v1 1 (1; 0) : (3) r + 4 Lemma There exist () = + + r, a () = + r suh that: and f () = + - if > Max f () ; f ()g, both rms ontinue after the rst patent. - if a () < < f (), one rm gives up after the rst patent. - if < Min f () ; a ()g, the rms do not start the R&D rae. Proof. See Appendix. Lemma is illustrated in Figure for a partiular value of r, without loss of generality. Given the disount rate and sattering ost parameters r and, 10

12 the rms start an R&D rae if the expeted pro t is large enough and if the expeted time of development 1= is short enough. After the rst innovation has been patented and dislosed, both rms ontinue if the expeted market pro t is large enough. The possible sattering ost then has a negligible impat on the inentive power of. By ontrast, the sattering ost really matters when the market pro t is low. In that ase the rm that has not innovated yet prefers to quit the rae rather than ompeting in R&D for ( ) =. The innovator then develops the seond innovation alone. It avoids the sattering ost but must expet a longer delay until the omplete tehnology is developed. It is worth to noting here that the fat of one rm giving up after the rst patent has been dislosed, extends the range of parameters for whih the rms will invest in R&D, for a < when > p r=. In that respet, patent dislosure inreases the soial surplus. Figure : Equilibria when the innovations an be patented separately Proposition 3 deals with the soial impat of patent dislosure, measured 11

13 as the di erene between the rms aggregate pro ts when a rm gives up and when both rms ontinue after the rst patent. Proposition 3 Equilibria in whih a rm gives up always maximize the rms expeted surplus. Equilibria in whih both rms ontinue maximize the rms expeted surplus i g (), where g () = + r + 1. If < g (), the rms expeted surplus would be greater if one rm gave up. Figure 3 indiates the di erene between the equilibrium surplus (in bold) and the other senario for eah equilibrium. It shows rstly that the equilibrium in whih a rm gives up after the rst patent is always welfare improving. This on rms and generalizes Lemma s nding that the possibility to give up after the rst patent dislosure extends the range of parameters (to a < < ) for whih rms will invest. In other ases (e.g. < < f ()), the rms would start the R&D rae anyway, but would maximize the total expeted payo s if a single rm developed the seond innovation alone. This is beause, given the low value of, avoiding the sattering ost is more important than delaying the seond innovation. The soial e ieny of equilibria in whih both rms ontinue after the rst patent is more ambiguous. The rms deision to ontinue is e ient when pro ts are large ( > g ()). The sattering ost is then negligible and it is more e ient if the tehnology is ompleted quikly. If the market pro t is not large enough and/or the innovation takes time to develop (f () < < g ()), it would be more e ient for a rm to give up after the rst patent. However the rm that did not innovate prefers to ontinue, whih redues the payo that rms an expet at the beginning of the rae. This is equivalent to a patent rae pattern where rms invest in exess to appropriate an innovation rent. 1

14 Figure 3: Dislosure and soial surplus 3 Innovations must be bundled prior to patenting Consider now the patent rae when innovations must be bundled prior to patenting. In this ase, a rm that has ahieved one innovation does not dislose it beause it is not proteted against imitation. As a result, a rm has to ahieve the tehnology entirely on its own in order to obtain a patent. There is no sattering ost and the payo to the patentee is always. In these onditions the patent rae is a two hits one, as represented in Figure 4. The rms initially invest in eah innovation simultaneously (Node 0). Thus a rm inurs the R&D ost of two researh lines until it has ahieved the rst innovation (Nodes 1 and 1 for rm 1, and Nodes and 1 for rm ), or alternatively until the other rm has patented the whole tehnology. In the rst ase, the rm ontinues to inur the R&D ost of one researh line until it or 13

15 the other rm has patented the tehnology. In the seond ase, the R&D rae ends with the patent. Figure 4: The patent rae when the innovations must be bundled prior to patenting Let us alulate the rms payo s when innovations are bundled prior to patenting. Let u n i denote the expeted payo of rm i = 1; at Node n f1; ; 1; 1g. At Node 1, the expeted payo s of the rms are equal: u 1 1 = u 1 = u 1. Eah rm has already ahieved one innovation and the rst rm that will ahieve the seond innovation will win the rae. (A similar argument an be made for Node 1.) Eah rm inurs an R&D ost 1 at eah time period dt until the omplete tehnology has been ahieved. There is a probability that rm 1 ahieves a seond innovation in time period dt. In this ase rm1 s payo is and rm s payo is 0. Symmetrially, there is a probability that rm ahieves a seond innovation. Its payo is and that of rm 1 is 0. Sine the time of ahievement of the most reent innovation has exponential 14

16 distribution with parameter, the present ontinuation payo to eah rm is u 1 = ( 1) = (r + ). I an now ompute the ontinuation payo s to rms 1 and at Node 1. At this Node, only rm 1 has already ahieved an innovation. I will thus denote by u 1 1 the expeted payo s to rm 1, and by u 1 the expeted payo to the rm that has not innovated yet, namely rm. Firm 1 inurs an R&D ost 1 at eah time period dt in order to ahieve the seond innovation, while rm inurs the R&D ost of two parallel researh lines. The probability that rm 1 ahieves its seond innovation in time period dt is. If it sueeds the rae ends, implying that its payo is and rm s payo is 0. On the other hand the probability that rm ahieves an innovation in time period dt is. The rms will then be at Node 1 and their payo s will be u 1. The time of ahievement of the next innovation has exponential distribution with parameter 3. The rms expeted payo s after one rm has ahieved a rst innovation an thus be expressed as follows: u 1 1 = + u1 1 r + 3 u 1 = u1 r + 3 The last step onsists in alulating the payo s to the rms at Node 0, if they enter the rae. At this stage no innovation has been ahieved yet, so that both rms invest in both researh lines. Therefore eah rm inurs a ost in time period dt. One rm, say rm 1, may ahieve an innovation with a probability at eah time period dt. In this ase its payo is u 1 1. There is also a probability that rm ahieves an innovation in time period dt. The payo to rm 1 is then u 1 = u 1. As there is a probability 4 that either rm 1 or rm ahieves an innovation in time period dt, the expeted entry payo to 15

17 eah rm is U = u1 1 +u1 r+4 : After some alulations this writes: U = 63 r 16 8r + r (r + ) (r + 3) (r + 4) (4) Firms enter the patent rae only if U 0, whih an be expressed as a ondition on : U 0, (r + 4) (r + 6) b () (5) 4 Optimal patentability requirement The last step onsists in omparing the soial e ets of the patent raes under the two poliy settings. I onsider as optimal the poliy that yields the greatest expeted prodution surplus. The welfare omparison thus takes into aount the expeted total osts of the R&D, the delay of ahievement of the whole tehnology, and the possible sattering ost. I show that for su iently large values of the Poisson hit rate, a strong patentability requirement is optimal. Propositions 1 and state that this result holds when the innovations an be alulated separately, irrespetive of the rms ontinuation strategies. Proposition 4 (i) The requirement that innovations be bundled prior to patenting prevents the development of innovations with a low value (e.g. suh that Min f a () ; ()g < b ()) that would be developed if they were patentable separately. (ii) Suppose > 1 so that all rms ontinue their R&D after a rst patent. In that ase, > 0 always exists so that patenting separate innovations is optimal if < and patenting bundled innovations is optimal otherwise. 16

18 (iii) Suppose now that < 1 so that one rm abandons R&D after a rst patent. If r, then a > 0 exists so that patenting separate innovations is optimal if < a and patenting bundled innovations is optimal if > a. If r <, patenting separate innovations is optimal. Proof. See Appendix 3. Proposition 4 rstly states that requiring that innovations be bundled prior to patenting may prevent the ahievement of some innovations that would be developed if they were patentable separately. This result onerns innovations whih take a long time to develop. It is due to the ine ient R&D ost dupliations that ould be prevented by means of patent dislosure. Conversely, the other parts of the Proposition show that bundling innovations prior to patenting may be more e ient when innovations an be developed rapidly. Consider rstly the ase in whih the seond rm stays in the rae after a rst innovation has been patented. Proposition 4 establishes the existene of a threshold value of the R&D Poisson hit rate above whih only the omplete tehnology should be patentable. Sine a low means that the expeted time to ahieve the innovation is long, it follows that eah innovation should be patentable separately if it takes a long time to ahieve. In ontrast innovations that an be developed quikly should be ombined with omplementary innovations prior to patenting. Bundling innovations prior to patenting an be welfare-improving beause it makes it possible to avoid the sattering ost. This bene t must however be balaned with additional R&D osts. If there is no dislosure, the rm that did not innovate ontinues to invest in both innovations, whih is soially wasteful. When developing an innovation takes a long time (low ), it is worth taking the risk of inurring a sattering ost if it an save R&D osts. Innovations should thus be patentable separately. When innovations an be developed rapidly (high 17

19 ), R&D ost dupliations are negligible and there is no need to inur the sattering ost. Innovations should thus be bundled prior to patenting. Consider now the ase in whih the value of the tehnology is low while the sattering ost is high, so that a seond rm gives up after the rst patent. In that ase the sattering ost is never inurred and the e ient poliy depends on a trade-o between R&D dupliations and short delay on the one hand, and R&D limitation (sine a rm gives up) and longer delay, on the other. Sine the ow of R&D is normalized to 1, the outome of this trade-o depends on the disount rate r. Proposition 4 states that if r > = there is a threshold value of the R&D Poisson hit rate above whih only the omplete tehnology should be patentable. In that ase the opportunity ost of postponing the development of the omplete tehnology is high. It is thus worthwhile allowing R&D dupliations in order to aelerate this development when the ost of these dupliations is aeptable, that is, when the R&D proess is rapid (high ). If r < =, delays matter less and separate patenting should prevail to avoid ost dupliations. 5 Conlusion and poliy impliations This paper ompares two R&D rae settings in whih two rms invest to develop two omplementary innovations. In the rst setting, eah innovation is patentable separately, while in the seond setting they must be bundled prior to patenting. Both poliies have some advantages. When innovations are patentable separately, the dislosure of interim patents extends the range of pro table innovations and improves the e ieny of R&D investments. A rm abandons the rae after the rst patent if the expeted market pro t is low, whih limits R&D ost dupliations and avoids the ost generated by sattered patents. When innovations must be bundled prior to patenting, the sattering 18

20 ost is always avoided but the absene of patent dislosure generates useless R&D dupliations. Compared with separate patents, this poliy generally improves the e ieny of R&D when the expeted development delay is short, although it may also slow down the development of the lowest value innovations. From a poliy perspetive, disrimination between trivial innovations and innovations that take a long time to develop is possible, by enforing a severe "inventive step" requirement. In Europe, an innovation an be patented only if (i) it is new, (ii) it has an industrial appliation and (iii) it onstitutes an inventive step, meaning that it must solve an objetive tehnial problem. In U.S. patent law, an innovation must be new, useful and non-obvious to be patentable. The latter requirement means that the innovation should not be viewed as obvious by someone skilled in the tehnology of the partiular eld, and is pratially equivalent to the European "inventive step" test. The idea that a lenient enforement of these requirements an lead to the ine ient patenting of elementary piees of tehnology has been expressed by several authors in the legal literature. Barton (003) takes the surprising example of o ee up holders to argue that a weak appliation of the non-obviousness standard in the U.S. has led to the granting of too many omplementary patents on one objet. In a paper on the intelletual property protetion of software, Lemley (1995) develops a omparable argument in the ase of software where he states that patents ould protet "either the idea of a program or [eah] of its subroutines". The present paper upholds poliy arguments that emphasize the importane of a severe appliation of this patentability requirement as a means to limit the size of "patent thikets" and to promote innovation in setors where omplementary innovations are frequent (Ja e, 000; Barton, 003; FTC, 003). It applies 19

21 in partiular to the urrent European debate on the patentability of omputer driven inventions. Software innovations have generally been patentable in the U.S. sine 1995, and obtaining software patents has been an easy task sine then (Lemley, 001; Barton, 003; FTC, 003). In ontrast, the European Patent Of- e has been more severe in applying patentability requirements (Graham et alii, 00) 5. A European Diretive aimed at updating and larifying the rules for software patentability should therefore ensure that the urrent severity of the EPO regarding patent appliations is maintained. The analysis arried out in this paper has several limitations that ould be addressed by extending the model. Suh limits primarily onern the strategies that innovators an develop to redue the osts resulting from patent sattering. In some ases, rms an irumvent dislosed patents to avoid buying a liense. Ex ante agreements suh as ross-liensing and patent pools are another possible strategy to mitigate sattering osts, and warrant further analysis. Finally, it may be espeially interesting to study grant bak lauses designed ex ante to prevent sattering osts after omplementary innovations have been developed and patented. Referenes [1] Barton, J.H., 003, inventive step, 43 IDEA 471. [] Cournot, A., 1838, Reherhes sur les Prinipes Mathématiques de la Théorie des Rihesses (Calmann-Lévy, 1974, Paris). [3] Deniolò, V., 000, Two-Stage Patent Raes and Patent Poliy, RAND Journal of Eonomis, 31, Artile 5 of the European Patent Convention states that omputer programs are not patentable "as suh". Although the EPO has already granted software patents, it has generally required that software be embodied in omplementary hardware in order to be patentable. This paper suggests that the EPO approah to software patents is eonomially relevant. 0

22 [4] Deniolò, V. and P. Zanhettin, P., 00, How Should Forward Patent Protetion be Provided?, International Journal of Industrial Organization, 0, [5] Federal Trade Commission, 003, To Promote Innovation: A Proper Balane of Competition and Patent Law and Poliy, available at [6] Graham, S., Hall, B., Harho, D. and D. Mowery (00) Post-Issue Patent "Quality Control": A Comparative Study of US Patent Re-examinations and European Patent Oppositions NBER Working Papers 8807 [7] Heller, M.A. and R.S. Eisenberg, 1998, Can Patents Deter Innovation? The Antiommons in Biomedial Researh, Siene, 80:5364, [8] Hunt, R., 1995, Nonobviousness and the Inentive to Innovate: An Eonomi Analysis of Intelleual Property Reform, Federal Reserve Bank of Philadelphia Working Paper 99(3). [9] Ja e, A.B., 000, "The US Patent System in Transition: Poliy Innovation and the Innovation Proess", Researh Poliy, 9, [10] Lemley, M.A., 1995, Convergene in the Law of Software Copyright, High Tehnology Law Journal, 10, [11] Lemley, M.A.,001,Rational Ignorane at the Patent O e, Northeastern University Law Review, 95, [1] Merges, R.P. and R.R Nelson, 1990, On the Complex Eonomis of Patent Sope, Columbia Law Review, 90, [13] O Donoghue, T., 1998, A Patentability Requirement for Sequential Innovations, RAND Journal of Eonomis, 9,

23 [14] O Donoghue, T., Sothmer, S., and J.-F. Thisse, 1998, Patent Breadth, Patent Life, and the Pae of Tehnologial Progress, Journal of Eonomis and Management Strategy, 7, 1-3. [15] Sothmer, S. and J.R. Green, 1990, Novelty and Dislosure in Patent Law, RAND Journal of Eonomis, 1, [16] Shapiro, C., 001, Navigating the Patent Thiket: Cross-Lienses, Patent- Pools, and Standard-Setting, Innovation Poliy and the Eonomy, 1, Appendix 6.1 Appendix 1: Proof of Lemma 1 Let rm 1 be the rm that patented the rst innovation. The Proof is derived diretly from Table 1. (i) I show rst that ontinuing is always a dominant strategy for rm 1. ( If rm ontinues, then rm 1 will ontinue if 3 ) 1 r+ > ( ) r+ or r ( 1) > 0, whih is always true when inequality (1) holds. If rm gives up, then rm 1 will ontinue if 1 r+ under inequality (1). > 0. This is always true (ii) I show afterwards that the best response of rm to rm 1 s ontinuation strategy depends on the sign of 1. If rm 1 ontinues, then rm will also ontinue if ( true if 1 ) 1 r+ :Hene if inequality (1) holds, rm will give up. > 0, whih is

24 6. Appendix : Proof of Lemma Putting the expressions of v1 1 (1; 1) and v1 (1; 1) into equation () gives V = r 4, and V > 0 if > (r + ) (r + 4) + + r. From equation (3) and the expression of v1 1 (1; 0) in Table 1; I have V a = r (r + ) (r + 4) = (r + ) 1 (r + 4) 1 r, and V a > 0 if > + r a. I now study a a = + + r This is positive i > p r a r = r We moreover know that a rm gives up after the rst innovation is patented i < + f (). I now study the sign of a f (). I have a f () = r. This expression is positive i < a. Hene a > f () if < a. I study nally the sign of f (). I have f () = r. This expression is positive i < a : Hene > f () if < a. 6.3 Appendix 3: Proof of Proposition 3 It is more e ient that both rms ontinue after the rst patent i V V a > 0. V V a = r r r (r + ) (r + ) (r + 4) is positive if ( ) r r > 0 or, whih is equivalent, if > + r + 1 g (). The funtion g () is rstly dereasing on ]0; a ] and then inreasing on [ a ; 1) 3

25 6.4 Appendix 4: Proof of Proposition 4 We prove suessively points (ii), (iii) and (i). (ii) When > 1, bundling innovations prior to patenting is optimal i U > V. I have U V = ( ) (r + 3) 1 (r + ) 1 (r + 4) 1 r r r 3. This expression is positive i r+4+r r 3 < 0 or, put di erently, i < + 3 r 4 r 1 e 1 (), where e 1 () is a ontinuous and inreasing funtion of from ]0; +1) to ( 1; +1). One an hek that e 1 ( a ) f ( a ) = 3 p r 4 3 p r r r = 4 r < 0. Hene e 1 ( a ) < f ( a ). Sine on [ a ; 1), e 1 () is inreasing towards +1 while f () is dereasing towards, it follows that there always exists a threshold value e > a suh that e 1 () < f () if a < < e 1 and e 1 () > f () if e 1 <. When > 1, we an thus de ne e 1 () so that for eah set (; r) bundling innovations prior to patenting is optimal if >. (iii) When, U > V a. < 1 bundling innovations prior to patenting is optimal i I have U V a = 4 (r + ) 1 (r + ) 1 (r + 3) 1 (r + 4) 1 r r 4r. This expression is positive i r r 4r > 0 or, put di erently, i > r + + 4r r = r r e (). e () is a ontinuous and dereasing funtion of from ]0; +1) to r ; +1. Moreover one an hek that e () f () = + r + r and e ( a ) > f ( a ). Sine on [ a ; 1), e () is dereasing towards r while f () is dereasing towards, it follows that there exists a threshold value e > a suh that e 1 () < f () i > 1 r. In that ase, there exists a threshold e () above whih bundling innovations prior to patenting is optimal for all 1 r, whih is always the ase sine > and > 1 r. Otherwise, independent patenting always prevails. 4

26 (i) We need to prove that b () > () when > 1, while b () > a () when 1, or put di erently that b () > Min f a () ; ()g (6) Proving that b () > a () when have b () a () = 4 6+r > 0. 1 The proof that b () > () when > 1 is straightforward. Indeed we an be derived from the Proof of point (ii). We know that U < V when > e 1 (), where e 1 () is a ontinuous and inreasing funtion of from ]0; +1) to ( 1; +1). We also know that e 1 ( a ) < f ( a ) = ( a ). Sine () is dereasing while e 1 () is inreasing it follows that () > e 1 () when < a. Thus = () implies that V = 0 while U < 0 when < a. It follows that b () > () when < a. Oberving that < a, b () > () when > 1. > 1 we have thus proved that 5