Patents, R&D investments, and Competition

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1 Ptents, R&D investments, nd Competition Tois Mrkepnd June 8, 2008 Astrct We nlyze the incentives of firm to crete sleeping ptents, i.e., to tke out ptents which re not exploited. We show tht sleeping ptents re discourged y incresing competition on existing product mrkets nd y other reserch firms. Also, the effects of competition in innovtion nd production re different. Moreover, we show tht sleeping ptents re not necessrily in the core products of firm. The key is tht the mrginl costs might e ffected, nd thus the competitiveness of the firm. We lso show tht mrkets for licensens my rek down, nd thus tht sleeping ptents re not the result of high trnsction costs. 1 Introduction Ptents re normlly considered n encourgement to invest nd introduce new products nd technology, nd lso to void the free-riding prolem. This is nd hs een the min justifiction of wrding firms with monopoly. It decentrlizes the innovtion process nd the risk of R&D. I.e., it is not the pulic who should finnce the reserch nd therey ssess the socil vlue of the innovtion. Insted it rests with the innovtor to ssess the vlue nd low vlue will hurt the innovtor nd not the tx pyers. This rgument hs een countercted. With sequentil nd complementry innovtions, wrding ptents cn reduce the investments in R&D. Additionl, one must tke into ccount the dedweight costs of monopoly power, the repliction of R&D costs, nd the protection costs, i.e., the costs the ptent owner hve to prevent other firms from violting their ptent. Here we rgue tht ptents my e used strtegiclly in order to prevent competitors from exploiting the invention while the ptenting firm does not use it, nd therey the firm cn influence the competitiveness of the mrkets. I.e., we stu the presence of sleeping ptents. We show tht the numer of sleeping ptents is inversely relted to the competition on oth the innovtion 1

2 mrket nd the existing product mrkets. Moreover, we nlyze the effect of competition on the numer of sleeping ptents, oth competition on the existing mrkets nd on the innovtion mrket. The point is tht investments nd ptents cn e used strtegiclly, when firms compete on n existing mrket. Innovtion nd lunching of product cn e used to lowering mrginl costs on nother mrket, nd hence used to crowd out competitors. One criticl ssumption is tht there is positive lrge scle effect of co-production within firm etween the old product nd the new product, i.e., economics-of-joint-scle. Second, on the mrket for the old product there is strtegic competition with non-zero profit. Using this result, we otin the conclusion tht more competition on the output mrkets increses the introduction of new products y reducing the numer of sleeping ptents. But on the other hnd, incresed competition decreses the innovtion, t lest when the competition is sufficiently strong. Thus, the totl effect of competition is migious. Thus, we wnt to justify the rgument y Plomers, [5] tht... firm my use ptent merely for locking purposes... ecuse it wnts to prevent competitors from strengthening their position... According to [5] IBM, Phillips nd Siemens use only 40 % of their intellectul property portfolio. She lso finds evidence tht the sleeping ptents re potentil vlule in the portfolio, nd hence tht the sleeping ptents re not unimportnt innovtions ut rther serve strtegic purpose. However, she conclude tht At the hert of these prolems is the lck of mrkets for intellectul property.. But we show tht this is not true! Even if the firms re le to trde on mrket for intellectul property rights, i.e., trde licenses, this mrket would not necessrily perform efficiently. We show tht necessry condition is tht there is nerly perfect competition. The ide of strtegic complements (nd sustitutes) is not new, nd t lest since Bulow et l., [1] the strtegic interction etween firms when they compete in severl mrkets ws introduced. As they rightly point out, competition cn e ffected when compnies compete ginst ech other on severl mrkets, nd not just within the sme mrket. They show y mens of n exmple tht susi cn hrm the receiving firm. In our exmple the opportunity of innovtion does not hurt the firms, ecuse they cn choose to invest or not. The literture on ptenting nd strtegic considertions is vst. In Ktz & Shpiro, [3], they nlyse the development incentives (nd not the reserch incentives), i.e., the improvement of existing products. The strtegy of the firm is siclly stopping prolem, nd the 2

3 winner is the firm tht develops first. However, their emphses on stndlone incentives nd preemption incentives re lso t the core of this pper. Close to our pproch is Gilert & Newery, [2] who consider monopoly, where the two products re sustitutes, i.e., the cross-elsticities of the demnd function re positive. However, while formlly the gme is nmic, the monopoly chooses the time of invention, ssumptions mke it siclly sttic model. Since the model ssumes monopoly on ll mrkets, the model is unsuitle for nlysis of the impct of competition on sleeping ptents. Moreover, we do not ssume the first-mover dvntge of one firm. They show tht n incument monopoly will ttempt preemptive innovtion, nd thus, in order to retin the monopoly power, the incentives for innovtion is higher thn under oligopoly. Their innovtion model is deterministic, nd thus the firm knows tht if it lunches the R&D project then the firm will surely innovte. Also they fil to rgue why license could not solve the prolem. Lin, [4] investigtes in some sense the opposite sitution of our, where the firms initilly compete on the product mrket nd then proceed to R&D rce. The focus of the nlysis is lso on how R&D investments nd the choice of product mrket strtegy. The R&D process is different thn ours, most importntly, the firms cn choose different levels of R&D expenditures, while investment choice is indivisile. Then product mrket decisions cn influence R&D expenditures, nd vice vers. The use of monopolized products in one mrket to drive out other firms in nother mrket, is lso used in the tying literture s explined in Whinston, [7]. The monopolizing firm cn tie the sle of ptented good with product exposed to competition, nd hence win mrket shres on the oligopolistic mrket. In tht sense the monopolizing firm cn commit to lrge production on the oligopolistic mrket nd hence the Stckelserg model reemerges. However, neither of the cited ppers considers the possiility of sleeping ptents! Much of the literture hve focused on the entry deterrence effect of R&D nd ptenting, while we emphsize the potentil crowding out effect. Or more precisely, the prevention of otining economics of scle in the costs of joint-production etween to commodities. Also, we nlyze the effect of monopoly power upon incentives to engge in innovtive ctivity. In this pper, the firms re ctive on the mrket of n existing product. However, they re not symmetric - we ssume tht one firm is not production efficient in the new product. A short outline of the pper is s follows: In section 2 we introduce the model, in section 3 we stte the pyoff of the gme nd stte conditions under which we cn otin sleeping ptents s equilirium phenomenon. In section 5 we show how competition cn chnge the result of section 3, such tht sleeping ptents does not occur. Finlly, in section 6 we conclude on our results nd stte the limittions of our nlysis. 3

4 2 The Model Consider the following model: there re two commodities L = 2: one which is currently ville, denote it y commodity 1, nd one which is potentilly ville, denote it y commodity 2. There re two firms j =, ech with the cpility of producing commodity 1 nd potentil cpility of producing commodity 2. On the existing mrket they compete l Cournot with n inverse demnd P 1 (x,1, x,1 ) = P 1 (x,1 + x,1 ), where x j,i is the output y firm j of commodity i nd P i < 0. There re 2 periods, t = 1, 2. Further, the totl vrile cost of firm j given the output of oth commodities is c j (x j,1, x j,2 ). We ssume tht the cost function c j is convex, i.e., c2 j, c2 j 0, nd c2 j + c2 j 2 2 c j x 2 1 x 2 1 x 2 1 x 2 x 1 1 x 2 0. Further, we ssume complementrities in the production process, define y the condition 2 c j x j,1 x j,2 = 2 c j x j,2 x j,1 0, i.e., the mrginl costs of the first commodity decrese with production of the second commodity. This could e the cse where two products use the sme inputs, nd tht the firm cn otin quntity discount, nd thus lowering the vrile costs. It could lso e n improved utiliztion of cpcities, such tht the productivity of the inputs increses. Since the second commodity is not ville, it hs to e innovted. The innovtion process consists of two prts: the R&D prt nd the lunching prt. Firm j cn initite R&D project t fixed cost K j in which cse there is proility of π (0, 1) of successful project. The fixed costs of R&D could e hiring reserches, testing fcilities etc. The new commodity is suject to ptent, such tht only single firm cn uphold the right to produce nd sell the commodity, nd if oth firms innovte the commodity, the ptent right is ssigned with n equl proility 1 2. Next, the innovting firm must py n dditionlly fixed cost of F j in order to produce/lunch the new commodity. This could e costs of investing in new mchineries, promotion costs, fill out the ptent ppliction, protection costs etc. We ssume wlog. tht the only decision the firms hve to mke in period one is whether to strt project or not. These decisions re mde simultneously. Hving oserved the outcome of the innovtion project, nd ptent rights re llocted, the firms simultneously choose quntity to produce on their ccessile mrkets. We ssume through out the pper tht there exists n interior Nsh equilirium of the finl stge Cournot-gme. An interprettion of the model could e s follows: the firms could e locted in the sme country where the ptent hs expired this is mrket 1, nd interprete mrket 2 s foreign mrket where there is no ptent on the sme product. Thus, the ptent in the foreign country is on the sme product s in the domestic country, nd the R&D costs re neglectile or zero. 4

5 A second interprettion is tht the ptents re on different products ut tht s ptent is requirement for the developement of the product of firm. The conclusions of our nlysis would e unchnged if the two resulting projects were different ut they oth exclude ech other s use. An exmple of this is the developement of sthm medicin where the producer hs prevented others from developing genetic tests which cn revel which ptients the medicin will hve ny effect on. 3 Sugme Perfect Equilirium Bsiclly, there re three period 2 scenrios: one of the firms otins the ptent while the other does not or neither of the firms otins ptent. Denote (u I, u I ) the period 2 profits if is wrded the ptent, (uii, u II ) if is wrded the ptent nd (u III, u III ) if neither re wrded the ptent. The profits in ech finl outcome re then given s follows: in outcome I, when otins the license while does not, 1 u I = mx x,1,x,2 0 P 1(x,1 + x,1 )x,1 + P 2 (x,2 ),2 c (x,1, x,2 ) F χ + (x,2 ) u I = mx x,1 0 P 1(x,1 + x,1 )x,1 c (x,1, 0), in outcome II, when does not otin the ptent while does, we hve u II = mx x,1 0 P 1(x,1 + x,1 )x,1 c (x,1, 0) u II = mx x,1,x,2 0 P 1(x,1 + x,1 )x,1 + P 2 (x,2 )x,2 c (x,1, x,2 ) F χ + (x,2 ), nd, finlly, in outcome III, where neither firm otins the license, u III = mx x,1 0 P 1(x,1 + x,1 )x,1 c (x,1, 0) u III = mx x,1 0 P 1(x,1 + x,1 )x,1 c (x,1, 0). Thus, there re siclly two different ending stges on the commodity mrkets, they oth compete on the old mrket nd either there is monopoly or no production in the new mrket. The set of histories of the extended gme is then 1. none of the firms strt-up the project, then they continue the old Cournot gme, 2. oth firms strt-up project, then either oth projects re successful, either fils, or precisely one project succeeds, or 1 Where χ + is the function χ + (x) = 1 if x > 0 nd zero otherwise. 5

6 3. one of the firms strts-up project, while the other does not, then the enterprising firm either succeeds or fils. Assume tht u I = mx x,1 0 P 1 (x,1 +x,1 )x,1 c (x,1, 0), i.e., tht the optiml choice of firm if it otins the ptent is not to lunch the product, nd tht this is common knowledge, then u I j = uiii j for every j =,. Oviously, when F is lrge enough this is the cse. A sufficient condition is tht ũ m mx P 1 (x 1 ) + P 2 (x 2 ) c (x 1, x 2 ) F, x 1,x 2 i.e., tht the monopoly profit of firm 1 does not exceed the lunching costs. Then the expected pyoffs in the imtrix (where firm is the row plyer nd firm is the column plyer) re given y: Π 4 = uiii, Π 4 = uiii, Strt Don t Strt Π 1, Π 1 Π 3, Π 3 Don t Π 2, Π 2 Π 4, Π 4 Π 1 = 1 2 π2 (u I + u II ) + π(1 π)(u I + u II ) + (1 π) 2 u III K Π 1 = 1 2 π2 (u I + uii ) + π(1 π)(ui + uii ) + (1 π)2 u III K Π 2 = (1 π)u III Π 2 = (1 π)u III Π 3 = (1 π)u III + πu II + πu II K + πu I K Π 3 = (1 π)u III + πu I. The outcome tht oth firms undertke the project is n equilirium if Π 1 Π 2 nd Π 1 Π 3, i.e., tht undertking the project, given tht the other firm undertkes the project, is more profitle tht not undertking the project. Inserting the expressions for Π 1, Π 1, Π 2, Π 3 into these inequlities nd rerrnging, we otin u I u II 2 K π 2 (1) u II u I K (1 1. (2) 2π)π Note tht u I u II is the gin to from steling the project from, nd hence dmpens the competition on the existing mrket, nd u II u I is the gin for y preventing for dmpening the competition. We note tht the proility of success influences on the decision in tht if π 0 then the left hnd side is unffected while the right hnd side pproches, 6

7 nd hence neither of the firms wnts to lunch the project when π is smll enough. We lso note tht when π 1 2 firm will lwys strt the project, if u II u I 0. The results in section 4 implies tht uii < u I = u III, i.e., firm s profit is decresed y firm otining the ptent. Also using the sme results, we hve tht u II u III = u I, i.e., firm in the lst stge is etter of hving the ptent thn not. The min ssumption is however tht of strtegic complements. We then otin the min result of this pper Proposition 1 Assume tht P < 0, 2 c x 1 x 2 < 0, nd ũ m F, then for K, K sufficiently smll enough it is Nsh equilirium, for oth firms to undertke the R&D project - not to lunch the product, nd to lunch the project if it otins the ptent. Informlly, the rgument goes s follows. Denote y x 1 (x 2) the set of Nsh equiliri of commodity 1 with x 2 eing the production of commodity 2 is x 2, nd let u j (x j,1, x,2, x,2) e the finl stge profit. j x. j,1 Then oviously when x u j,1 increses the profit of j decreses, i.e., Thus, in ny equilirium if the other firm increses his output, ceritus prius, the profit of the firm decreses, since, ccording to the envelope du theorem, we hve tht j dx j,2 = P 1 x dx j,1 j,1 dx j,2, the effect on the profit depends purely on the strtegic effect y the other firm. This is n ovious ppliction of strtegic complements nd sustitutes, s defined y [1]. But then ccording to the complementrities in the cost function the lunching of commodity 2 will increse the supply of the firm in mrket 1 nd thus lower the profit of the other firm. However, firm 1 cn prevent this y ptenting commodity 2 even though it is not profitle ex nte. We thus need to find conditions under which u I u II the suject of section 4. > 0, nd this is Note however tht, when π(u II u I ) > K there is single Nsh equilirium in this gme, where oth firms strts the project, nd depending upon whether firm or otins the ptent, the product is lunched onto the mrket. 4 Finl Stge Pyoffs We shll now investigte the effect of incresing the innovted product on the oligopolistic mrket. This is ctully nothing more thn comprtive sttic of the Nsh equilirium in the finl stge of our extensive form gme. We wnt sufficient conditions under which the introduction of the new product enefits the innovting firm, while it hurts the non-innovting firm. Informlly, the rgument for our result is s follows: Introducing the new product lters the mrginl costs nd thus the est response function 7

8 of the innovting firm. By the ssumption of complementrities in the cost function the mrginl costs decreses, nd thus the innovting firm cn increse the output of commodity 1 in order to mximize profit. Geometriclly, the response function shifts outwrd, nd thus for given quntity of the non-innovting firm the est response of the innovtion firm is to increse its own production. This more ggressive ehvior y the innovting firm on the oligopolistic mrket forces the non-innovting firm to reduce its own quntity, nd therey reducing its profits. Proposition 2 If P 1 (x) < 0 for every x > 0 nd 2 c j x 1 x 2 < 0, then dx j,1 dx j,2 < 0 dx j,1 dx j,2 > 0. To see tht the response function 2 R j (x j1, x j2 ) of the innovting firm in mrket 1 shifts outwrd note tht ccording to the implicit function theorem we hve tht dr j (x j1, x j2 ) dx j2 = dx j1 dx j2 = 2 c j x j1 x j2 P 1 x j1 + 2P 2 c j x 2 j1 > 0. Note tht if P 1 > 0 ut sufficiently smll, the conclusion of Proposition 2 still holds. However, with P 1 sufficiently lrge nd positive the response function shifts inwrd nd thus the innovting firm retrcts output from mrket 1. Note, tht in this cse, the non-innovting firm is ctully etter of, nd oviously the innovting firm is lso etter of: Lemm 1 We hve tht for ny j mx x j1,x j2 P 1 (x j1 + R j1 (x j1 ))x j1 + P 2 (x j2 )x j2 c j (x j1, x j2 ) χ(x j2 )F j mx x j1 P 1 (x j1 + R j1 (x j1 ))x j1 c j (x j1, 0). There re cses where this might not e the cse. There might exists multiple equiliri, such s the cse in digrm 4. The point is tht moving from one equilirium to nother when the quntity of commodity 2 chnges is not locl nlysis - rther it clls for glol nlysis. Note tht moving from B to A implies tht the quntity of decreses, while moving from C to D implies n increse of the quntity of. Note lso, tht moving from C to A would imply tht ny pth s: [0, 1] R 2 such tht s(0) = C nd s(1) = A nd (u, u )(s(r)) = (π (r), π (r)) should e discontinuous. 2 I.e., R j solves the eqution P 1(R j (x j1, x j2 ) + x j1 )R j (x j1, x j2 ) + P (R j (x j1 ) + x j1 ) c j(x j1,x j2) x j1 = 0 8

9 x 1 R 1 A B D C E R 1 x 1 Figure 1: Multiple Nsh equiliri Geometriclly, we hve tht when the slope of the response function of R is numericlly lrger thn the slope of R 1 then x 1 increses when x j2 increses while x 1 decreses. When 2 c j = P = 0 there exists n unique x 2 j1 Nsh equilirium such tht R j = 1 2. We sy tht NE (x 1, x 1 ) is regulr in x 2 if 1 > dr(x 1,x 2 ) dr (x 1,x 2 ) dx 1 dx 3 1. Assuming n unique equilirium in ech finl stge gme gives us the required result. Proposition 3 If P 1 (x) < 0 for every x > 0, 2 c j (x 1,x 2 ) x 1 x 2 < 0 for every x 1, x 2 R +, nd for every x 2 there exists n unique, regulr equilirium (x 1 (x 2), x u I. 1 (x 2), x 2 ), then there exists NE such tht u I > u II nd u II > Proof. Se the Appendix A. Consider the following simple exmple, where we otin prmeter vlues of prticulr model where SPE s descried in Proposition 1: Exmple 1 liner inverse demnd function P i (X) = i i X nd cost functions c j (x 1, x 2 ) = 1 2 cj 1 x2 1 cj 12 x 1x cj 2 x2 2. Assume tht cj 1 cj 2 (cj 12 )2 such tht the cost function is convex. We ssume in order to otin n interior solution 1 ( c 1 + 2c 1) + c 1c 1 > 2 1 c c (c 12). 2 3 Note tht this implies tht ny gme with liner (inverse) demnd functions nd constnt returns to scle is regulr, nd moreover dr dr dx dx =

10 Consider the prmeter vlues ( 1, 2, 1, 2, c 1, c 2, c 12, c 1, c 2, c 12, π) = (3, 5, 1, 1, 1, 1, 0.05, 1, 1, 0.05, 1). When F > firm will not use the ptent. The gross gins re u I u II = nd u II ui + F = Thus, the required lunching costs of firm is F = if there is no potentil for trding license from to. But then for F K (0.0458, ) nd K we hve SPE of this gme where the ptent is otined y firm with proility 1 2 nd put to sleep. Also, will not sell the ptent to t price which is willing to py, nd the mrket for licenses reks down. Let us introduce the possiility of choosing level of R&D investment. This investment level ffects the proility of the succes of the project. One could lso ssume tht it influenced the qulity of the resulting invention, however, we hve chosen to discrd this effect, since it does not ring ny new insights. Denote y y j 0 the level of investment in the project y firm j, nd K j (y j ) the totl costs of inititing the project t the level y j. We ssume tht K j (y j ) is differentile whenever y j > 0. Given tht firm j chooses the investment level y j, j =,, the proility of succes y the firm is π j (y, y ). Oviously, the proility of success increses with the mount of investment, π j y j > 0. The pyoff given the strtegies re then Π (y, y ) = 1 2 π (y, y )π (y, y )(u I + u II ) + π (y, y )(1 π (y, y ))(u I + u II ) + (1 π (y, y ))(1 π (y, y ))u III K (y ) Π (y, y ) = 1 2 π (y, y )π (y, y )(u I + uii ) + π (y, y )(1 π (y, y ))(u I + uii ) + (1 π (y, y ))(1 π (y, y ))u III K (y ). Then the equilirium of the gme solves yj = rg mx y 0 Π j (y, y j ) for ll j =,. A necessry condition for optimlity in n interior solution is tht Π j (y ) y j = 0, while if y j = 0 then Πj (y ) y j 0. We next compute the prtil derivtive of, which is (ssuming tht π = π, i.e., symmetric proility functions) Π y = π y ((1 + π)u II (1 2π)u I ) K. But then if (1 + π)u II > (1 2π)u I then y > 0 nd firm will invest positive mount for some K ( ) nd we re ck the nlysis prllel to ove. 10

11 5 Competition Suppose tht we dd n 2 1 extr firms into the model. We wnt to decompose the effect of competition into two seprte effects: the effect on the proility of the project eing success nd the effect from decresing mrkup on the existing mrket. This decomposition we otin s follows: in the first cse we dd only firms tht cn initite project ut cnnot compete in the existing mrket. In the second cse we dd only firms tht cn produce on the existing mrket. The first implies tht π 0 while the second implies tht u I u II Innovtion competition Assume tht we dd n 2 1 new identicl firms with cost chrcteristics (C, K, F ), which stisfies tht mx P 2 (q) C(q) F > 0 q mx q P 2 (q) C(q) mx P 1 (x 1j )x 1j + P 2 (q)q c j (x 1j, q) j x 1j, q K K j, nd F F j. Thus, it is profitle for every new firm to lunch the project given tht they hve otined the ptent, the surplus of the new firms is greter thn the old firms, nd the R&D costs nd lunching costs re smller in the new firms thn the old. These conditions re unnecessrily strong, ut gurntees tht ech new firm undertkes the project whenever the old firms does so. They re oviously not necessry, only sufficient. If k n firms initite the project, then the proility tht firm otins the ptent is π k = (k, j) π j (1 π) k j j 1 j k where (k, j) is the inomil formul. This formul is derived s follows: π j (1 π) k j is the proility tht j firms out of k possile innovte nd there re (k, j) wys of j firms innovting while k j does not, nd when this hppens there is proility of 1 j tht the firm otins the ptent given tht j 1 other firms innovte. It cn e shown tht lim n π n = 0. Denote y G1 n the gme with n 2 dditionl innovtion firms. Then our min result is tht: Proposition 4 There exists K, K > 0, N 1, N 2 0, N 2 > N 1 such tht for every N 2 n N 1 we hve tht there is single Nsh equilirium of G n 1 where does not strt R&D project while strts the project nd lunches it. 11

12 Proof. This follows esily from eqution (1) nd (2), nd the fct tht lim n π n = 0 with π = π n. Also, note tht 2K K πn 2 (1 1 2 π)π = 2K π(k + K ) π 2 (1 1 2 π) when π n 0, nd thus tht the difference etween the right-hnd side of equtions 1 nd 2 pproches infinity s π n 0. Of course, if π n 0, in the limit, oth firms will ondon the project. However, for some intermedite levels of innovtion competition, firm is squeezed out of the innovtion mrket while firm remins. 5.2 Production competition Next, introduce n 2 new firms which do not hve the cpility of doing R&D in the new product. However, they re le to produce the old commodity. Using the Cournot-pricing formul, we hve tht for firm P 1 (X n 1 ) C (x n j,1, 0) P 1 (X n 1 ) = sn ɛ n, where s n j x j,1 X n 1 = xn j,1 n j xn j,1 is the mrket shre of firm j, x n j is the equilirium vlue of the gme G2 n of firm j = 1,..., n, nd ɛn P 1(X1 n) is the P 1 (Xn 1 )Xn 1 price-elsticity of commodity 1. Rememer tht we re considering the Nsh equilirium where firm is grnted the ptent, ut does not use it. Then s s n 0 we must hve tht if X n 1 P 1 (X n 1 ) C (xn,1,0) P 1 (X n 1 ) is ounded wy from zero, then 0, i.e., lim n P 1 (X1 n) C (x n,1, 0) = 0. This however = 0. The condition tht lim n s n j = 0, must implies tht lim n u I u II necessrily imply tht the intruding firms do not crowd-out other firms, otherwise the ctive firms on the mrket is finite nd ounded. For more thorough investigtion in generl equilirium frmework see [6]. Also, since y ssumption P 2 (x 2 )x 2 c (x 1, x 2 ) K > 0 nd thus u II P 1 (x 1 + X )x 1 + P 2 (x 2 )x 2 c (x 1, x 2 ) K > P 1 (x 1 + X )x 1 c (x 1, 0), we lwys hve tht u II > u I. Denote y G2 n the gme with n 2 dditionl competitors on the product mrket. Proposition 5 For some K, K > 0, there exists N 0 such tht for every n N we hve tht there is single Nsh equilirium of G2 n where does not strt R&D project while strts the project nd lunches it. 12

13 Thus in oth cses of the pure strtegy equiliri, we otin n inferior result on the welfre spect, since the efficient lloction would e to let lunch the project, nd not - since he will not strt the production. Also, n increse in the production of the existing product will increse the welfre. We note tht firm is willing to sell the ptent to the firm t price p s u I u II while firm is willing to uy the ptent t price p u II u I. Thus, whenever p p s mrket for licenses would wke up the sleeping ptent. However, whenever p < p s the opposite is true, nd there is no potentil for ny trde of license etween the two firms. 6 Concluding remrks We hve seen tht competition on existing mrkets ffects the numer of sleeping ptents, i.e., ffects the numer of ville commodities. We show tht this is oth true, when it comes to the competition in commodities nd in reserch. There is however essentil difference etween the two types of competition. While competition on the product mrket is eventully positive in reducing the numer of sleeping ptents, competition in the innovtion mrket will eventully mke the innovtion unprofitle for the firms y reducing the expected gin from innovtion. A nturl question is why the legisltors cn not just specify in the ptent legisltion tht the firms is required to use the ptent. There re severl difficulties with such requirement nd reltes oth to the prcticl implementtion nd the theoreticl model. First of ll, ssume tht the firm winning the ptent is required to produce t lest ɛ > 0 mount of the commodity. Then y the continuity of model implies tht for ɛ sufficiently smll the conclusions holds. Prcticlly, how should the competition uthorities know how lrge ɛ should e. Also, our nlysis clls for the competitive uthorities to tke roder view with regrd to the multi-mrket effects on the ptent rules thn just nrrow nlysis of prtil effects in single mrket. Also, it mkes the concept of socil vlue much more complex since the mrket institution, e.g., the competition, influences the socil vlue. Could the efficient firm orrow nd uy up the inefficient firm? or how out licensing? The first question is oviously dependent on the efficiency of the finncil mrkets nd the orrowers ility to orrow. Here one cn point to orrowing constrints imposed y informtion symmetries s is well-known in the economic litterture. Second, it is not esy to see tht if the vlue of the ptent to firm is higher thn the vlue to firm, then there is no potentil for trde, i.e., if the loss in the profit of firm when otins the ptent is lrger thn the gin in the profit of firm when otins the 13

14 ptent. We note tht this could mke up n empiricl testle proposition: nmely tht firm which would otherwise hve sleeping ptent will license the ptent to competitor if the new mrket hs n insignificnt effect on the profit of firm. There re of course numerous extensions of these results: e.x. sttionry versus stnd-on-the-shoulders environment, symmetric informtion on the vlue of ptent etc. The resulting equilirium here considered is highly inefficent: there is the dupliction of R&D costs nd the dedweight costs re mximized. This model s results shows tht sleeping ptents should not only e expected in core res of the firms product (in our model the demnd for the products re totlly independent), ut re lso sed upon the expected exploittion of complementrities of the competitors. A Appendix In generl gme with i = 2 plyers nd responsfunctions (R j ) j=1,2 the Nsh equilirium conditions re x = R (x, y) x = R (x, y), for some prmeter y. Solving for smll, infinite smll chnge in y then yields ( ) ( ) ( ) dx dr 1 1 dr dx = dx 1 dr dr dr dr dx dx dx 1. But then tking dr = 0 nd dr ) ( dx dx = > 0, this reduces to 1 1 dr dx dr dx ( dr dr Thus, we hve tht dx dr dr > 0 iff. 1 > dx dx or dr 1 dx > dr. dx Thus, when we consider the effect on the profit, ccording to the envelope dπ j dx j,1 theorem we get dx j,2 = P x j,1 dx j,2 < 0 from the first order condition, nd hence the profit decreses strictly. Note tht ccording to the fundmentl theorem of clculus we hve tht π j (x j2 ) π j (0) = x j2 0 ds, nd thus if dπ j(s) dx j2 dr dx ). dπ j (s) dx j2 < 0 for every s > 0 we hve tht π j (x j2 ) < π j(0). 14

15 References [1] Jeremy I. Bulow, John D. Genkoplos, nd Pul D. Klemperer, Multimrket oligopoly: Strtegic Sustitutes nd Complements, Journl of politicl Economics 93 (1985), [2] Richrd J. Gilert nd Dvid M. G. Newery, Preemptive ptenting nd the persistence of monopoly, The Americn Economic Review 72 (1982), [3] Michel L. Ktz nd Crl Shpiro, R&d rivlry with licensing or imittion, The Americn Economic Review 77 (1987), [4] Ping Lin, Product mrket competition nd r&d rivlry, Economic Letters 58 (1998), [5] Neus Plomers, Sleeping ptents: ny reson to wke up?, preprint (2003), ville t DI-0506-E.pdf. [6] Kevin Roerts, The limit points of monopolistic competition, Journl of Economic Theory 22 (1980), [7] Michel D. Whinston, Tying, foreclosure, nd exclusion, The Americn Economic Review 80 (1990),