* Assistant Professor of Economics, at INSEAD, Boulevard de ...

"BARRIERS TO IMITATION AND THE INCENTIVE TO INNOVATE" by 0. CADOT* and S. A. LIPPMAN** 95/23/EPS

* Assistant Professor of Economics, at INSEAD, Boulevard de Constance, 77305 Fontainebleau Cede; France. ** Professor of Economics at the John E. Anderson Graduate School of Management, UCLA, Los Angeles, CA 90024-1481, USA.

A working paper in the 1NSEAD Working Paper Series is intended as a means whereby a faculty researcher's thoughts and findings may be communicated to interested readers. The paper should be considered preliminary in nature and may require revision.

Printed at INSEAD, Fontainebleau, France

Barriers to Imitation and the Incentive to Innovate Olivier Cadot and Steven A. Lippman 1

February 1995

Abstract When innovation is followed by imitator entry, the degree to which the innovator can appropriate the rents induced by its innovations influences the rate of innovative activity. Our interest focuses upon the interaction between the rate of innovative activity and the length of the delay between the innovation and imitation, in a model in which innovative activity generates a sequence of new innovations in the face of market saturation and discounting. The optimal rate of innovation depends upon four distinct economic forces: the appropriability effect stressed in the literature, fighting market saturation, a competitive motivation (to maintain the monopoly position), and a strategic motivation (to deter entry). The goal of our analysis is to elicit the circumstances in which each force dominates. Because of these countervailing forces, the optimal rate of innovation may not be monotone in the delay 1; furtermore, a more easily saturated market can benefit the innovator. JEL classification numbers: 030, 031. Keywords: Innovation, Imitation, Entry deterrence.

'Respectively INSEAD, bd de Constance, 77305 Fontainebleau, France; and Anderson School of Management, UCLA, Los Angeles, CA 90024-1481, USA. This research was supported in part by INSEAD and the John E. Olin Center, UCLA. We are grateful to Richard Rumelt and Bernard Sinclair-Desgagne for useful conversations and comments.

1 Introduction Modern growth theory (going back to the writings of the Austrian school) as well as a long list of empirical studies, discussed in Scherer (1980, Chapter 15), stress the importance of technological progress to dynamic economic performance (in contrast to the static efficiency of perfect competition). In order for innovation to be profitable, it is clear that innovators must be able to reap, at least temporarily, sufficient profits to compensate for its substantial cost, risk, and creativity. But a myriad of wellknown examples — including the introduction of diet cola by Royal Crown Cola, the personal computer by Apple, the (Beta format) VCR by Sony, and the CAT scanner by EMI — evidence the fact that imitation can follow closely on the heels of successful innovation, eroding the rents accruing to the initial innovator. Some protection, in the form of either legal rights or economic barriers to imitation, is thus necessary to ensure an adequate rate of technological progress. Statistical evidence indeed supports the conclusion (Scherer, 1980, p. 438) that "A bit of monopoly power in the form of structural concentration is conducive to invention and innovation." What is not clear is just what level of protection is needed to power the socially optimal rate of innovation; furthermore, it is not certain that more protection always increases the incentive to innovate. Levin et al (1987), for instance, note (p. 788) that "Because technological advance is often an interactive, cumulative process, strong protection of individual achievements may slow the general advance"; they cite the semiconductor industry as an example in which the rapid progress experienced in the 1950s and 1960s would have been impeded under a regime of strong protection. 1 Empirical reality and history not withstanding, it has been a commonplace in the economics literature on innovation (going back at least to Schumpeter in 1911) that more appropriability, usually in the form of a longer patent life, would increase monotonically the rate of innovative activity. The basic tradeoff relevant to patent policy was thus, in the early patent literature, 2 between the dynamic incentive effects of appropriability and the static welfare costs of monopoly power. More recent work 'In addition to a deliberate policy of the US Department of Defense of ensuring (through secondsourcing and other means) a wide dissemination of technological advances throughout the industry, Levin et al stress (p. 94) that "Indeed, but for two accidents of history - the invention of the transistor by AT&T rather than by a firm less willing to disseminate its knowledge and the simultaneous occurrence of complementary product and process innovations at TI and Fairchild in the late 1950s - the patent system might have retarded the advance of semiconductor technology." 2 See for instance Arrow (1962); Nordhaus (1969, 1972), or Scherer (1972).

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has focused on slightly different questions, such as how governments can use simultaneously patent length and compulsory licensing fees to maximize welfare (see for instance Tandon, 1983), or how patent length and 'breadth' (or scope) ought to be traded off for a given level of appropriability (Gilbert and Shapiro, 1990; Klemperer, 1990). 3 A recent paper, by Gallini (1992), also showed that a longer patent length may encourage imitators to 'invent around' the patent, thus failing to provide more appropriability. But the basic assumption, that more appropriability is conducive to more innovative effort, has by and large not been questioned. Yet Levin et al warn (p. 787) that "it should not be taken for granted that [...] better protection necessarily leads to more innovation." Mindful of this, the present paper revisits the question of the incentive effects of appropriability on innovative effort. Specifically, we focus, in a model of repeated innovation, on the interaction between the rate A of innovative activity and the exogenous delay £ between the introduction of a new product or process and its imitation. As suggested by the case of the semiconductor industry, our analysis (see Theorem 1) produces a non-monotonic relationship between A and £: intermediate levels of protection in the face of imitation engender the greatest amount of innovative activity. The reason is that, unlike one-shot innovation, repeated innovation serves not only to create a rent initially, but also, later on, to defend it against imitator entry. Ex post product-market competition 4 can thus have favorable incentive effects on the pace of innovation, because it forces innovators to fight for their position through (stochastically) more frequent product improvements.

1.1 Delays to Imitation: Patents and Isolating Mechanisms Prior to undertaking an innovative activity, the innovating firm (hereafter called the developer) must believe not only that the (expected) rents produced by the forthcoming innovation will be sufficient to cover the expense attributable to the innovative activity but also that these rents will flow to the developer and not be competed away by imitation. In theory, a patent confers perfect appropriability of a length of time £ during which the new invention is legally protected from imitation. However, the study by 3Patent scope is also considered by Matutes, Regibeau, and Rockett (1991) among others. 4 Such competition is different from the ex ante rivalry between firms racing for the patent. The latter is, of course, always favorable to more innovative effort - in fact, such rivalry can lead to socially wasteful overspending in R&D; see Reinganum (1989) for a survey of the vast literature on patent races.

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Levin et al. found (p. 810) that typical patented products in 34% of the 129 lines of business studied were imitated within 1 year of introduction (and 56% of major patented products were imitated within 3 years of introduction). 5 The study by Mansfield et al. (1981) provides further evidence of the imperfection of patent protection: 60% of patented successful innovations were imitated within 4 years of their introduction (p. 913). Both studies found that patents do not matter very much except in the chemical industries (and via the cumulative impact of cross-licensing arrangements in semiconductors). 6 Because design information embodied in a product is subject to discovery via reverse engineering and other transfer mechanisms, patents can be (necessary and) effective in protecting product innovations. When it comes to process innovations, however, patents are the least effective means of appropriation due to the direct leakage of information as well as the demonstration effect 7 : information contained in patent documents leads many firms to "refrain from patenting processes to avoid disclosing either the fact or the details of an innovation." (Levin et al., p. 795). Fortunately, however, there are a number of factors, called isolating mechanisms by Rumelt (1987) and entry barriers by economists, which inhibit imitation. In addition to patents, these isolating mechanisms come in a variety of first-mover advantages including causal ambiguity regarding the sources of efficiency (see Lippman 5Teece (1987) relates the case of the CAT scanner developed by EMI in which the embedded technology was easy to imitate and the patents were easily circumvented. The superior marketing abilities of GE and Technicare, two technologically capable imitators with strong reputations for producing high quality medical equipment, enabled them rather than EMI to capture the rents. 6 Mansfield et al. found (p. 916) that "patents are regarded as particularly important in the drug industry"; the study also reports (p. 915), "Excluding drug innovations, the lack of patent protection would have affected less than one-fourth of the patented innovations in our sample." Similarly, Levin et al. found (p. 802) that "the three industries in which product patents were viewed as most effective [were] organic chemicals, pesticides, and drugs." Taylor and Silbertson (1973) found that 64% of pharmaceutical R&D expenditures are dependent upon patent proctection. Evidently, the discrete nature of molecular structures imbues the enforcement of chemical patents against infringements with an easy to verify argument. 7The lack of protection afforded by patents is particularly strong as regards process innovations and also product innovations in electronics and machinery. As reported in Mansfield (p. 913), "The median estimated increase in [the cost of imitation] due to patent protection was ... about 7% in electronics and machinery." For many of these innovations "patents would not add a great deal to imitation cost (or time)." and (p. 914) "In the bulk of the cases, the new product could have been imitated in 2 years or less even if the imitator carried out the project at the most leisurely pace." This is a far cry from the 17 years of protection afforded, in principle, by a patent.

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and Rumelt (1982)), the ability to tie up the market in ancillary specialized assets (say via long-term contracts with suppliers), and other factors common to the industrial organization literature (e.g., economies of scale, economies of scope, customer loyalty, customer switching costs, 8 reputation embodied in brand name capita?). After patents, the most important isolating mechanism emanates from lead times or lags. These lags leading to delay in imitation can originate from the time required for competitors to recognize the market success of the new innovation, the time required to reverse engineer the new product, bottlenecks in obtaining the use of specialized marketing and distribution channels, 1 ° or delays in manufacturing (e.g., the time required to (a) learn how to manufacture a high quality product, (b) acquire and ready specialized equipment necessary for mass production, (c) line up suppliers and distributors). Tacit knowledge, causal ambiguity clothed in its less extreme form, is particularly important for retarding the imitation of entrepreneurial and process innovation. By its very nature tacit knowledge tends to be non-observable (though it could be revealed by hiring the developer's employees) and difficult to transmit. Thus, lack of employee mobility ll and secrecy (as it is in guarding the formula for Coca-Cola) are often effective in retarding imitation when tacit knowledge is involved. Whether it arises from a patent, a first-mover advantage, bottlenecks in gaining 8 Nintendo created very large customer switching costs by making their game cartridges incompatible with other game systems. 9 Teece (1987, p. 208 - 209) points out that the IBM PC was a huge success even though its architecture was ordinary and its components were standard off-the-shelf parts available from outside vendors. One key to its success was "The reputation behind the letters I, B, M." Similarly, the G.D. Searle's trade names NutraSweet and Equal for aspartame "will become essential assets when the patents on aspartame expire." 1 °Teece (1987) notes that large firms are more likely to possess the specialized assets which enable them to gain lead time. "Ziegler (1985) attests to the fact that the success of an entrepreneur facilitates the entry of other entrepreneurs and firms not only by bringing forth the new innovation which can then be imitated but also by demonstrating to these would-be entrants that profits are more than a mere possibility. Furthermore, Ziegler (1985, p. 119) notes that non-competition clauses and contingent benefits may not be effective in preventing employee defections. Thus, employees who leave to found their own firms is an important source of mobility. The most noteworthy example of entry via the appropriation of design know-how of key employees leaving the parent firm is the lineage from Bell Labs to Shockley Transistor to Fairchild Semiconductor to Intel. That part of the semiconductor industry located in the Silicon Valley is also well known for its high mobility of scientific and engineering personnel and the concomitant "free exchange of technical information." Levin (1982, p. 27)

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use of a complementary specialized asset, or tacit knowledge, the delay time £ until the developer's innovation is imitated is an important determinant of the developer's rate A of innovative activity.

1.2 Model and Results We consider the interaction between a single innovator whose innovative activity generates a sequence of new inventions and a single imitator whose ability to appropriate the rents generated by the new inventions is restricted by his inability to enter the market for a period t after the introduction of each new invention. This paper explores the tension between the innovator's rate A of innovative activity and its ability to appropriate the value bestowed by the new inventions. This ability is measured by the delay £ until the imitator enters the market for each new invention. Henceforth, to facilitate communication we refer to the delay £ as the patent length. Of course, the delay t can, as discussed at length above, emanate from other sources. We begin with a brief consideration of a 'one-shot' model of innovation and imitation in which the force of appropriability acts (as anticipated) to accelerate innovation: A increases in £. After this, the R&D activity is modeled as generating a sequence of innovations beginning first with a model in which the imitator is committed followed in section 3 by a model in which it is possible to deter entry. We demonstrate that the optimal rate of innovation depends upon four distinct economic forces: the appropriability effect stressed in the literature, the fight against obsolescence (or market saturation), the competitive motivation (to maintain the monopoly position), and the strategic motivation (to deter entry by an imitator). Theorem 1, our main result, establishes the (surprising) result that a decrease in appropriability can in fact induce more innovative activity. The driving force behind this result is the dynamics introduced by the foreseeable sequence of innovations in which the developer is induced to increase his rate of innovation in order to maintain his (monopolistic) position as the only firm with the right to market the currently dominant product. Whereas appropriability increases with the delay £, the competitive pressure dwindles. Theorem 1 also shows that the net effect of these two opposing forces first increases and then decreases in t: the optimal rate of innovative activity is not monotone. Theorems 2 and 3 describe the set of Nash equilibria when entry deterrence is possible; moreover, it is shown in Theorem 3 that entry deterrence can entice the developer to overinvest in R&D. As our analysis progresses, the four forces are often seen to work in opposition; 5

consequently, non-monotonicities in of the developer's optimal rate A of innovation, as exhibited in Theorems 1-3, are to be expected. In the same vein, Theorem 4 verifies the existence of circumstances in which more obsolescence actually benefits the innovator. The paper concludes with a discussion of policy implications.

2 Patent Length and the Incentive to Innovate 2.1 The Basic Appropriability Effect The `appropriability effect' of patent length on innovation stressed in the literature can be captured in a simple one-shot model of innovation and imitation. 12 At time t = 0, the innovating (or developing) firm, labelled firm D, chooses an intensity level \ of its R&D effort: A is a surrogate for the size of firm D's R&D department. The (random) arrival time r of the innovation is distributed exponentially with rate A. 13 In order to have an R&D department of size A, firm D incurs a flow cost of c(A) per unit time until time r when the discovery takes place. 14 We assume that the function c is convex, continuously differentiable, and c(0) 0. Upon discovery, the new product is costlessly brought to market; from then on, the instantaneous profit rate decreases exponentially at rate (> 0) as the market saturates. 15 Firm D's new 12The one-shot models of Gilbert and Shapiro (1990), Klemperer (1990), and Gallini (1992) analyze the trade-off between patent width and patent breadth. Gilbert and Shapiro (1990, p. 106) "simply identify the breadth of a patent with the flow rate of profit available to the patentee while the patent is in force." They provide simple conditions under which (socially) optimal patent policy sets = oo. Klemperer's (1990, p. 116) definition of patent breadth "is the region of (differentiated) product space covered" so that (p. 115) "Wider patents reduce consumers' freedom to substitute competitively provided, unpatented varieties of the product." As the importance of the welfare loss when a less-preferred variety is purchased increases relative to the welfare loss when no variety within the product class is purchased, the optimal patent becomes wider and shorter. Unlike our paper, neither of these two papers is concerned with the supply of inventive activity. In Gallini's (1992) model patent breadth is the cost of imitation. In her model with competitive imitation, an increase in imparts a greater incentive to imitators to invent around the patent; consequently, an increase in I can induce the developer to curtail his inventive activities. 13A constant hazard rate is not necessarily the best formulation because it amounts to assuming that past effort has no bearing on the instantaneous probability of success, but it simplifies the analysis considerably. 14In effect, the firm's R&D department is fired at t, but one could equivalently suppose that the firm must employ its R&D department forever without affecting the result. 15This assumption is not needed at this stage but is introduced here to ensure uniform treatment of the problem between this subsection and the rest of the paper.

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product is protected from imitation by a patent of length £. During the protection period (7 < t < T + £), firm D collects a rent (net of all production costs, but not of R&D costs) at a flow rate of rm e-13t . At time t = T + t, the patent lapses and the imitator introduces a substitute for firm D's product, reducing firm D's rent to r e- pt , with rc < rm . All costs and rents are discounted at rate a. Taking account of market saturation and discounting, the value v(s) of the prize awarded to innovation is given by

y

i

00

v(t) = f r„,,e-("+'5)s ds + i rce -('+43)s ds = [r, — (r,, — rc)e-(a+0)e] I (a+ o I

l

e).

(1)

Both intuition and (1) reveal that v'(t) > 0 : imitation washes away the developer's prize, but patent protection lessens this erosion. Because the prize v(1) is received at time 7, firm D's net expected discounted profits 71- over an infinite horizon is given by (recall that Ec al" = Aga + A))

D

7r

D = E [e - "v(t) — for c(A)C" ds] = [A v (€) — c(a)]/(a + A).

(2)

The first-order condition for profit maximization (by choice of A) is tav(t) + c(A)]/(a + A) = ci(A),

(3)

where the left-hand and right-hand side of the equation are, respectively, the marginal benefit and marginal cost of R&D effort. Let A*(t) be the solution to (3). Under the second-order condition (which is easily shown to hold), the sign of the comparativestatics effect of a change in patent length £ on optimal effort A* is given by the sign of the cross-partial derivative 02 7r D /49Aat, where

82

1D iaAat = at/(t)/(a + A) 2 = a(rm — rc)e-(a+'3)4/(a + A) 2 > 0.

Thus, dA*(t)/dt > 0. Firm D's R&D effort unambiguously rises in response to a longer patent. When innovative activity is a one-shot affair, it cannot be used by the developer to fend off imitation. We turn now to a slightly different setting where repeated innovation serves not only to create a rent but also to defend it.

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2.2 Repeated Innovation with a Precommitted Imitator We modify here the setting of subsection 2.1 only in allowing firm D to sequentially introduce new generations of the product. Each new generation renders the previous one obsolete: sales of the old generation fall to zero as soon as the new generation is introduced. 16 Each generation is protected by a patent of duration 1; as soon as the patent expires, imitation begins and, as per section 2.1, the developer's revenue flow falls by a factor of rc/rm . The imitator is committed to staying in the market without regard to the size of A. (We consider imitator exit in the next section.) Firm D chooses the size A of its R&D department at time t = 0; its choice cannot be revised thereafter.' As before, the flow cost associated with a department of size A is c(A). The random additional times required to produce each successive generation are independent and have the same distribution as r; as in section 2.1 r is exponentially distributed with parameter A. We say that the ith 'cycle' begins with the introduction of the ith generation and ends with the introduction of the i + 1 st generation. The expected discounted cycle length -y satisfies -y -.-:- Ec cer = A/(a + A). Let r be firm D's expected discounted revenue during a cycle and let R be its expected discounted revenue over the infinite horizon so that max-er,t}

r = E [Imill{.7.'1} rni e –(a+43)s ds]+ ELI o i = {rn, — (r,, — Tc)e—(12+.8+1 /(a + 0 + A),

rye-(a+°3)* c/s1

R = rsy + r•y 2 + • • • = r-/(1 — -y) = .1r/a, and rD , firm D's net expected discounted profits over an infinite horizon, satisfies irD -=[

co

+A,8 + A) ] frn, _ (rm _ rc)e-(a+o+A)/ _ c, .

(4)

16We ignore time-consistency and intertemporal pricing issues [see Bulow (1982), Stokey (1981), Waldman (1993)]. 17This assumption is tantamount to assuming that adjustment costs associated with changes in A are very large, or, in the words of Robert Reich (quoted in Cohen and Levinthal (1994)), "once off the technologicalescalator it's difficult to get back on". That R&D is necessarily a continuous activity is supported by Cohen and Levinthal's statement (p. 237), "to integrate complex technological knowledge successfully into the firm's activities, the firm requires an internal staff of technologists and scientists who are both competent in their fields and familiar with the firm's idiosyncratic needs and capabilities."

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The first-order condition is 1 (a + )3)r„, a + 13 + ( At (r, — r,)e + )5 -FA [a±fi+A a -I- )3 + A

= e(A),

(5)

and the second-order condition holds. Let Ain (t) denote the (unique) solution of (5). Again, under the second-order condition, the effect of a change in patent length on optimal R&D effort ) in (t) is given by the sign of the cross-partial derivative. Straightforward calculations produce 5 2 7r D /OAN = (1 — tA)(r m — rc)e-(Q4-'3+A)t/a. Thus, Ain (.e) satisfies ch in /d.€ > 0 if and only if tA in (t) < 1.

(6)

A useful benchmark is the optimal level G out of firm D's R&D effort when there is no imitator. Define Rout by A out Ain (t). FIGURE 1 HERE

THEOREM 1

With repeated innovation, there exist two critical values 4 < 4 such that (i) Ain (t) > Acrut whenever £ > 4 and (ii) )in (t) is increasing for £ < 4 and decreasing for t >

PROOF See appendix.

Theorem 1 shows that the appropriability effect identified in section 2.1 and stressed by the literature -- namely, the value v(t) of the patent increases with the patent length £ -- is just one part of the story. When each new innovation is protected by a patent of finite duration, it behooves the innovator to continue R&D because each new product introduction "refreshes" the market and forces the imitator to incur yet another delay £. 18 Thus, innovation is based on a tactical motivation (fight market saturation) and a competitive motivation (temporarily throw the innovator out of the market and become a monopolist). Even if there is no market saturation (,3 = 0), in which case innovation is exclusively driven by the developer's 18This result is not due to the deterministic nature of the delay Suppose that the imitation delay is due not to patent protection but rather to the inherent difficulties in "reverse-engineering" a new product, so that the arrival time of the imitation is stochastic. Provided that the instantaneous probability of success is increasing in past effort spent on that particular product (which is not true for the exponential distribution), the reasoning goes through. 9

competitive motivation, the reasoning is unchanged. When the duration of patent protection increases, two forces work against each other in the determination of Ain (t)On the one hand, the size v(s) of the prize (appropriability) increases so it pays to increase R&D; on the other hand, the competitive pressure from imitation is reduced so the need to defend that rent with new product introductions diminishes. Theorem 1 reveals that the second effect dominates beyond 4. This result, intermediate levels of protection (I) in the face of imitation engender the greatest amount of innovative activity (A), comports with the vast empirical literature studying the relationship between concentration and technological progress. Scherer (1980, p. 438) concludes that "the most favorable climate for rapid technological change ... is a subtle blend of competition and monopoly." When £ < to, the imitator's ease of entry hampers the developer's ability to defend his monopoly rents severely enough to overwhelm the competitive force. In this case the force of appropriability dominates, and the developer innovates at a rate below ) out • This basic non-monotonicity result was established in a context where the imitator's behavior is entirely passive. We turn now to the strategic interaction between the innovator's R&D effort and the imitator's entry decision.

3 Innovation and Entry Deterrence The cost of "reverse-engineering" is k per product imitated, and the imitator now faces an entry decision at time t = 0. Clearly the imitator's decision will be affected by the remaining length T - l of the product cycle over which the imitation cost k can be recouped. The innovator understands this channel of influence on the imitator's entry decision. The obvious question is whether the possibility of deterring the imitator from entering can induce the developer to overinvest in R&D. Theorem 3 demonstrates that overinvestment can occur. However, the imitator's lack of commitment can also spur a reduced level of innovative activity for large (and some other) values of We consider two games where the innovator chooses A while the imitator chooses in or out. If the imitator selects the strategy q from his strategy space [0, 1], he has selected the action in with probability q and out with probability 1 — q. When q = 1 [q = 0], we shall say that he has selected in [out]. Using the same reasoning as in section 2,

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the imitator's expected discounted profit 7r 1 over one cycle 19 is given by ri ( A ; t)

max{

E i

rie -(a+o).

ds _

1{.7.>1} &e —cre]

'M

r i e --(.+0-FA)t / (a #

ke-(c'e+A)t,

(7)

where r1 is the imitator's rate of profit while selling in the market. Define A c (t) by A c (t) = (r1/k)e-131 — a — # (see figure 2). By construction, ri(Ac(1),€) -a:- 0: A c is the imitator's zero-profit curve. When the developer's rate A of innovative activity exceeds Mt), the imitator's expected profit is strictly negative and he chooses not to enter. When the inequality is reversed, he enters. The first game has simultaneous decisions; the second is a Stackelberg game with the developer moving first. 3.1 Simultaneous Game

Let A(q; £) and Q(A; 1) denote, respectively, the developer's and the imitator's best response correspondences, and let A*(t) and Q*(j) denote the (set of) Nash equilibrium rate of innovation and entry status (they need not be unique). Theorem 2 tells us that for each I 'the' equilibrium rate A*(t) of innovative activity is restricted to A in (i), A out , or (when Mt) lies between A in (t) and A 0,,t ) Ac(e), a convex combination of these two numbers. Let q(i) satisfy equation (8) in the appendix. THEOREM

2 In the simultaneous entry game with k > 0, the following is an ex-

haustive description of all Nash equilibria: (i) if Ac (i) < A in (t) < A out , then (A out , out) is the unique equilibrium; (ii) if Ac (i) < A out < Ain, (t), then (A out , out) is the unique equilibrium; (iii) if A c (t) > max fa in (t), G out }, then (Ain (i), in) is the unique equilibrium; (iv) if Ain (i) > A c (t) > A out , then (Mt), q(t)) is the unique equilibrium. (v) if A out > Ac (t) > then the game has three equilibria: (Ain (i), (Aout, out), and (Mt), q(t))• PROOF See appendix. FIGURES 2A AND 2B HERE 19 The imitator's discounted profit over the infinite horizon is simply Airilcr. Thus, it suffices to examine 21 in order to determine the imitator's action.

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Note that there is no overinvestment in the simultaneous game: there is no such that A*(t) exceeds both A in (t) and Acid . Theorem 2 states that when the imitator faces a positive imitation cost, the possibility of keeping the imitator permanently out of the market (rather than for only one product cycle) constitutes a fourth force, distinct from the three forces identified in section 2, affecting firm D's incentive to innovate. This fourth force affects the market outcome in three ways. First, in the first region listed in Theorem 2, where A c (i) < Ain (i) < Aout , in order to keep the imitator out the developer chooses a higher rate of innovation than he would if the imitator were committed to being in the market (see figure 2a). Strategic entry deterrence also happens in one of the three equilibria in the fifth region listed in Theorem 2. Second, an increase in patent duration can cause A* to decrease in a region of I where Ain is increasing (in figure 2b this is the region where £2 < L < Li). Third, with patent duration fixed at a sufficiently high level (the second region in Theorem 2: t > 4 in figure 2a and > 4 in figure 2b), the non-committed imitator chooses to stay out, relieving firm D from the competitive pressure of imitation; as a result, the rate of innovation is lower than in the committed-imitator case. The reason

is simple: as discussed in section 2, when patent duration is longer than a certain critical value (namely to), the presence of a committed-imitator provides a positive incentive to innovate. Therefore, when the non-committed imitator chooses to stay out, firm D reduces its innovative effort compared to the committed-imitator case. In sum, strategic interaction between the developer and a non-committed imitator in a simultaneous game affects the incentive to innovate, but it does so in a non-monotone way. 3.2 Sequential Game

In the sequential game the developer moves first: he chooses a rate A of innovation. After observing A, the imitator, cognizant of the reverse-engineering cost k per product as well as the developer's choice of A, 20 decides whether or not to enter. In order to avoid non-existence of equilibrium, we assume that the imitator elects not to enter when his expected profit is zero. With this assumption, there is a unique "In regard to the entrant's knowledge of A, Cohen and Levinthal (1994, p. 228) remark that "the incumbent's endogenous expectations of future technical advances diffuse to the entrant." This diffusion of the incumbent's expectations provides some (albeit small) support for the sequential model vis-a-vis the simultaneous model.

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subgame-perfect equilibrium. 21 If MO) > Aout, we obtain, for some values of a new equilibrium which was absent from the simultaneous game, namely (Mt), out). Theorem 3 states that there exist critical regions of in which (Mt), out) is the unique equilibrium — and it entails `overinvestment'. Just as is true for a great many models in the patent race literature that "competition may lead to greater levels of investment as the incumbent makes strategic investments to dampen the entrant's investment incentives" (Cohen and Levinthal (1994, p. 228), it is also true that imitation can lead to overinvestment by the developer. 3 Consider the sequential entry game with k > 0. If MO) < A out , the unique equilibrium of the game is (Rout , out) for any £. If A c (0) > )g out , then the unique equilibrium of the game varies as follows (see figure 3):

THEOREM

(i) (Rout, out) when Ac(t) < )out, (k(t), out) when A in (.e) < Mt) < Rout, (Ain (t), in) when < Ac(t) < Aout < Ain(e), (iv) either (Ain (t), in) or Pc(t), out) when .bout < Ain(t) < Mt). Moreover, there exists at least one interval (a, b) such that A*(t) > max { Ain (i), A0,4 for a < t < b. PROOF

See appendix. FIGURE

3

HERE

Thus, in a sequential game, strategic entry deterrence can induce the developer to choose a rate of innovation that is higher than the maximum he would ever choose with a committed imitator. The reason can be made clear by using an analogy with investment in plant capacity: consider A, the rate of innovative intensity chosen by the innovator at time t = 0, as an investment in 'innovative capacity'. (Such an interpretation is consistent with the idea that A is a surrogate for the size of firm D's R&D department.) Following Tirole (1988), let us define `overinvestment' in the sequential game as a level of investment in excess of that chosen by the innovator in the equilibrium of the simultaneous game. 22 (In ranges of .e where the simultaneous game has multiple equilibria, we take the maximum value of A*(1) as the benchmark.) We 21 1n a continuous time version of this game in which the rate A is selected at each moment in time, the equilibrium we obtain in the game in which the decision is made once and for all remains an equilibrium in the more complicated game. 22See Tirole (1988), p. 325, footnote 40.

13

now ask, is there overinvestment (thus defined) in the sequential game? The answer is yes (for a 7D[A*(fl),Q*(4),S]• PROOF See appendix.

The intuition of Theorem 4 is closely related to that of Theorem 2. When is small enough, the unique equilibrium is (A in (0), in). As /3 increases to a first critical point 0_, two additional equilibria appear: (a °,40), out) and a mixed-strategy equilibrium similar to the one we constructed in Theorem 2 (see appendix). As increases further past a second critical point /3+ (> 0....), the only equilibrium that remains is (A out , out). Therefore, as /3 increases, at some point between /3_ and 0+ , the equilibrium level of innovation has to jump from Ain to Aoiit . This upward jump in A, associated with the imitator's change of status (from in to out), increases the developer's equilibrium profit. Thus, although faster obsolescence (equivalently, a smaller market) always reduces the developer's profit given the status of the imitator (in or out), in a simultaneous game obsolescence can act as a barrier to imitation. When this barrier is sufficient to preclude the imitator's entry, increased obsolescence plays to the advantage of the developer by enabling him to operate as a monopoly.

4 Concluding Remarks Scotchmer (1991) stresses the importance of the cumulative nature of innovations: "almost all technical progress builds on a foundation provided by earlier innovators." 24 A major shortcoming of the theoretical economics literature on patents and R&D is its failure to embrace this cumulative aspect of the innovation process: this failure strips the dynamism (and life) out of the process. 25 As a consequence, any modelling effort which fails to account for more than one generation of an invention must be viewed with some suspicion, especially as regards the supply of innovations. Our paper begins to address this defect by positing an innovator whose innovative 24She proceeds by examining instruments to protect the incentives for cumulative R&D and focuses upon the problem of 'double marginalisation'. Proper "incentives to find fundamental technologies may require that the first patent holder earn profit from the second generation products that follow." (p. 30.) However, in order to "give the second innovator an incentive to invest whenever social benefits exceed R&D costs, the second innovator must earn the entire social surplus of his innovation." (p. 34.) 25 There are exceptions (e.g. Balcer and Lippman, 1984, Cauley and Lippman, 1994, Reinganum, 1985, and Vickers, 1984), but most of the literature uses a one-shot model.

activities generate a sequence of innovations, but our effort falls short in that each innovation does not build upon its predecessor: neither the incremental value nor the interarrival time of the i 1" innovation depends upon any aspect of the ith innovation. Whereas the importance of patents is arguable and varies across industries (see Levin et al.), imitation presents a serious impediment to perfect appropriability in every industry. Various isolating mechanisms, or entry barriers, facilitate the appropriation of rents generated by innovation; we summarize them by a nonnegative scalar variable £, the prototypical barrier being a patent. We show how the introduction of successive generations of a new product can be used by an innovating firm to pursue several distinct objectives simultaneously (creating a rent and subsequently defending it against the combined effects of market saturation and imitator entry); our results on the incentive effects of imitation delays derive from the interplay of these motivations. When imitation delays are sufficiently long (€ > 4), the presence of an imitator increases the incentive to innovate, i.e. an innovator faced with entry will choose a level of innovative effort higher than a monopolist would. However, the intensity of innovative effort is non-monotone in the length of the entry delay: increasing that delay beyond a threshold 4 (> £) reduces the incentive to innovate. 26 The reason is that for values of t beyond ti , the longer delay relieves the innovator of the competitive pressure of imitation which, alongside with market saturation, drives his incentive to introduce new generations of the product. In sum, the incentive effect of imitation on innovation is negative only for sufficiently small values of the entry delay t and, once positive, is largest for intermediate values of t. The policy implications of these results depend on whether imitation is socially optimal or not. If imitator entry is efficient, i.e. if the increase in social welfare stemming from competition between the innovator and the imitator outweighs the cost of imitation, 27 then for values of € greater than 4 both the incentive effect and the direct effect of longer patent duration on welfare are negative, so that optimal patent length is finite (as in Gallini, 1992 – albeit for different reasons) and is less than If, on the other hand, imitator entry 26 This result vanishes under certainty; if r (the interarrival time of new generations) is deterministic, the optimal innovative effort rises monotonically in the entry delay up to = r and remains constant afterwards. "This needs not be true. If the demand curve is very inelastic, monopoly entails little deadweight loss, so that imitator entry redistributes rents without creating much surplus; entry can then be privately optimal (if the rent redistribution is greater than the imitation cost) without being socially optimal.

16

is inefficient, optimal patent length is clearly infinite. The paper also shows how the innovator's capacity to produce sequentially new generations of a product with (stochastically) short interarrival times, by acting as a commitment, can result in strategic entry deterrence. If the imitator's entry decision is simultaneous with the innovator's intensity decision, a sufficiently long imitation delay results in what Bain (1956) called 'blockaded entry': in that case the innovator's effort is at its monopoly level and is strictly less than what it would be with a committed imitator. The level of innovative effort in the simultaneous game provides a benchmark against which we define `overinvestment' in a sequential game where the imitator decides whether or not to enter only after having observed the innovator's decision. We show that the perfect equilibrium of the sequential game can entail overinvestment; the attractiveness of such a strategy derives from the fact that more innovative capacity, by reducing the average length of time over which the imitator can recoup his fixed costs, depresses the expected profitability of entry. If more innovation is socially beneficial, imitation is thus welfare-enhancing even in ranges of £ where it does not take place in equilibrium (i.e. where the equilibrium outcome is entry deterrence rather than accommodation). 28 Our results were derived from an extremely simple model, which needs to be refined along several lines. For instance, 'market saturation' should be derived from a full model of intertemporal pricing and consumer behaviour; barriers to imitation should be variable not only in terms of delays (patent length) but also in terms of product positioning (patent scope), and so forth. Nevertheless, as they stand, these results do suggest that the consequences of moving from a one-shot to a repeated model of innovation are nontrivial for the analysis of patent protection.

281n general, the welfare effects of overinvestment in capacity depend on whether the excess capacity built as entry deterrence is used or not. Dixit (1980) showed that in a perfect equilibrium the incumbent never wants to build idle capacity. Here, the situation is simpler: if one interprets A as the innovator's 'capacity' to innovate, the variable cost of innovation is zero up to A and infinite afterwards; so the innovator will clearly always want to use all his capacity, which implies that society will benefit from it.

17

References [1] Balcer, Yves, and Steven A. Lippman, (1984) "Technological Expectations and Adoption of Improved Technology," Journal of Economic Theory 34, 292-318. [2] Bain, Joseph (1956), Barriers to New Competition, Cambridge, MA: Harvard University Press. [3] Baumol, William B., John Panzar, and Robert Willig (1982), Contestable Markets and the Theory of Market Structure, Harcourt Brace Jovanovitch. [4] Bulow, Jeremy I. (1982), "Durable-Goods Monopolists," Journal of Political Economy 90, 314-332. [5] Cauley, Fattaneh G., and Steven A. Lippman (1994), "Myopia and R&D/Production Complimentarities," Economic Theory 4, 437-451. [6] Cohen, Wesley M., and Daniel A. Levinthal (1994), "Fortune Favors the Prepared Firm," Management Science 40, 227-251. [7] D'Aveni, Richard A. (1994), Hypercompetition, The Free Press, New York. [8] Dixit, Avinash (1980), "The Role of Investment in Entry-deterrence"; Economic Journal 90, 95-106. [9] Fudenberg, Drew and Jean Tirole (1984), "The Fat Cat Effect, the Puppy Dog Ploy and the Lean and Hungry Look", American Economic Review Papers and Proceedings 74, 361-368. [10] Gallini, Nancy T. (1992), "Patent Policy and Costly Imitation," RAND Journal of Economics 23, 52 - 63. [11] Gilbert, Richard, and Carl Shapiro (1990), "Optimal Patent Length and Breadth," RAND Journal of Economics 21, 106-112. [12] Hirschman, Albert 0. (1977), The Passions and the Interests, Princeton University Press. [13] Kaufer, Erich (1989), The Economics of the Patent System, Harwood, Chur, Switzerland.

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[14] Klemperer, Paul (1990), "How Broad Should the Scope of Patent Protection Be?," RAND Journal of Economics 21, 113-130. [15] Levin, Richard C. (1982), "The Semiconductor Industry," in Richard R. Nelson (ed.), Government and Technical Progress: A Cross-Industry Analysis, Pergamon Press, 9-100. [16] Levin, Richard C., Alvin K. Klevorick, Richard R. Nelson, and Sidney G. Winter (1987), "Appropriating the Returns from Industrial Research and Development," Brookings Papers on Economic Activity 3, 783-820. [17] Lippman, S. A., and R. P. Rumelt (1982), "Uncertain Imitability: an Analysis of Interfirm Differences in Efficiency under Competition," The Bell Journal of Economics 13, 418 - 438. [18] Mansfield, Edwin, Mark Schwartz, and Samuel Wagner (1981), "Imitation Costs and Patents: An Empirical Study," Economic Journal 91, 907-918. [19] Nordhaus, William D. (1969), Invention, Growth, and Welfare: A Theoretical Treatment of Technological Change, Cambridge, MA: MIT press. [20] Nordhaus, William D. (1972), "The optimum Life of a Patent: Reply", American Economic Review 62, 428-431. [21] Reinganum, Jennifer (1989), "The Timing of Innovation: Research, Development and Diffusion", in R. Schmalensee and R. Willig (eds.), Handbook of Industrial Organization, Vol. 1, Elsevier, pp 849-908. [22] Reinganum, Jennifer F. (1985), "Innovation and Industry Evolution," Quarterly Journal of Economics 100 81-99. [23] Ross, Sheldon (1983), Stochastic Processes, Academic Press. [24] Rumelt, Richard P. (1987), "Theory, Strategy, and Entrepreneurship," in David J. Teece (ed.), The Competitive Challenge, Ballinger, 137-158. [25] Scherer, F.M. (1965), "Invention and Innovation in the Watt-Boulton Steam Engine Venture," Technology and Culture 6, 165-187. [26] Scherer, F. M. (1972), "Nordhaus' Theory of Optimal Patent Life: A Geometric Reinterpretation," American Economic Review 62, 422 - 427. 19

[27] Scherer, F. M. (1980), Industrial Market Structure and Economic Performance, second edition, Rand McNally. [28] Scherer, F. M. (1983), "Concentration, ern Economic Journal 50, 221 - 225.

R&D,

and Productivity Change," South-

[29] Schumpeter, Joseph A. (1934), The Theory of Economic Development Cambridge, Harvard University Press (orig. German land. ed., 1911). [30] Scotchmer, Suzanne (1991), "Standing on the Shoulders of Giants,: Cumulative Research and the Patent Law," Journal of Economic Perspectives 5, 29-41. [31] Shapiro, Carl (1989), "The theory of Business Strategy," RAND Journal of Economics 20, 125-137. [32] Spence, A. Michael (1977), "Entry, Capacity, Investment and Oligopolistic Pricing," Bell Journal of Economics 8, 355-374. [33] Stokey, N.L. (1981), "Rational Expectations and Durable Goods Pricing," Bell Journal of Economics 12, 112-128. [34] Taylor, C.T., and Z.A. Silberton (1973), The Economic Impact of the Patent System: A Study of British Experience, Cambridge University Press. [35] Teece, David J. (1987), "Profiting from Technological Innovation: Implications for Integration, Collaboration, Licensing and Public Policy," in David J. Teece (ed.), The Competitive Challenge, Ballinger, 185-219. [36] Tirole, Jean (1989), The Theory of Industrial Organization, MIT Press, Cambridge. [37] Vickers, J. (1984), "Notes on the evolution of market structure when there is a sequence of innovations," mimeo. [38] Waldman, Michael (1993), "A New Perspective on Planned Obsolescence," Quarterly Journal of Economics 108, 273-283. [39] Winter, Sidney G. (1987), "Knowledge and Competence as Strategic Assets," in David J. Teece (ed.), The Competitive Challenge, Ballinger, 159-184.

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[40] Ziegler, Charles A. (1985), "Innovation and the Imitative Entrepreneur," Journal of Economic Behavior and Organization 6, 103-121. [41] von Hippel, E. (1988) The Sources of Innovation, New York, NY: Oxford University Press.

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Appendix Proof of Theorem 1 To begin, observe from (5) that Ain is a continuously dif-

ferentiable function, whence g(t) tAin is continuously differentiable. Furthermore, g(0) = 0 and g(t) --+ oo as £ oo, as lime.. Ain(t) = Aout > 0. Thus, there is at least one solution to g(t) = 1. Let 4 be a solution to g(t) = 1. To establish that 4 is the unique solution to g(t) 1, define h by h(t) Ain(t) 111, so that h 1 (1) = clAin (1)1d1 + 1/1 2 , h(ti ) = 0, and h' is continuous on (0, oo). Suppose that h(s) = 0; then (6) implies clAin (s)1 = 0, whence h' (s) = 1/s2 > 0. Because h' is continuous, h(t) > 0 for some neighborhood of s: h crosses 0 from below only. Therefore, h(t) = 0 has a unique solution. By (6) and the definition of 4, Ain(1) is strictly increasing on [0, 4) and strictly decreasing on (4, co]. As per (5), Ain (0) and Aout solve (a+,8)7. ,= (a-1-13+))2c'()) and (cr-143)r,„ = A)2c'(A), respectively. By assumption, c' is nondecreasing so that these equations admit but one solution each; in addition rc < rm implies that A in(0) < A.A . Thus, lime.. Ain(t) = Aout > A in (0) and A in is decreasing on [4, oo}: Ain(ii) > Aout . Because Ain is increasing on [0,4), it follows also that there is an to < 4 such that Ain (t) > A out whenever 1 > 4. 29

0 Proof of Theorem 2 Let Lout = {t : Aout > Ac(t)}, L in = {t : Ain (t) < Mtn,

£2 = min L out , so Ac(4) = Aout , and 4 = min ft : Ain (t) > A c (t)}. Finally, let go(A,i) and g 1 (Are) stand for (A, q, t) = arD (A, q, .1)1 OA evaluated at q = 0 and q = 1 respectively. Fix £ E Li n so that Ain (l) < Mt). Clearly, (A io (t), 1) is an equilibrium. We claim it is unique in L iu \Lout . To see this, consider any A > Mt). Then Q(A; 1) = 0 so A(0; 1) = Aout < Ac(t), a contradiction. If E Lout , Aout > A c (1) so by the argument of the previous paragraph, (A out , 0) is an equilibrium and it is unique in Lout\Lin. If E Lout n L in , the game has three equilibria: (Ain (i), 1); (A*(co), 0), and a mixed-strategy equilibrium (Mt), q(t)). In order to construct the mixed-strategy equilibrium, let q(t) satisfy q(t) gi [Ac (t), I)] + [1 — q(1)] go[A,(t),11 = 0.

(8)

If such a q(t) exists, A(q, t) = Ac(t) and Q[Ac(i); ti = q(t), as 71 [Ao(t), 1,1} = i[Mt), 0,11 = 0 implies that q(t) is a weak best response to A c (t).) We need to 29 In general, tAin(i) is maximized at a value £2 > 11• 22

show that q(t) exists and is in [0, 1]. If Lout n Lin 00, £2 < 4, so t E Lost n L in 4#* £2 < < £3 . Suppose that £ = £3 , then Mt) = Ain (t) by continuity of these functions. As gi [Ain (t), 1] 0, it follows that g i [Ac(t), = 0; so, setting q(t3 ) = 1 satisfies (8). Suppose now that £ = £2 , Ao (t) = Aout so by a similar argument, setting q(t2 ) = 0 satisfies (8). Next, fix any £ E (t2, 4). By monotonicity of k(t), A in(t) < k(e) < Aout. The last inequality implies that, under the second-order condition, 9 1 [Ac(t),t] > 0. The first inequality similarly implies that go[A c(t), < 0. So q(t) gi[Ac(t), + [1 q(t) E (0, 1). Finally, if £ E out U Lin); then (Mt), q(t)) q (t)] go[Ac(t), £] = 0 is the unique equilibrium of the game. To see this, take any convex subinterval L C R+\(Lout U Lin), and denote by 1_ and 4 its min and max respectively. By construction of Lout and Lin, £ E L implies that A crut < Mt) < Ain (1). Monotonicity of Ac (t) implies that A*(t_) = Ac (L) and A*(4) = A c (t+ ). Then q(L) = 1 and q(4) = 0 satisfy (8). Next, fix any £ E (t_, 4). By the second-order condition, g1[Ac( 1),1] > 0 and go[Ac(t), < 0; so q(1) gi [Ac (1),t] + [1 - q(t)] go[Ao (t),t] = 0 implies that q(t) E (0,1). For uniqueness, consider any A > Mt). Then Q(A, £) = 0, but A(0, £) = Aout < Mt), a contradiction; a similar argument holds for any A < Ac(t). 0

Let 1 min {t 2 , t3 } and (5 = 7rp [A c( 1),Q[A c(1),i], 7rD [Ain (1), Q[Ain(i),1],1]. We claim that S > 0. To see this, note that Q[Ain (1),1] = 1 whereas Q [A c (1) , 1] = 0. Thus ir D[ A in(i) Q[Ain(i), = 7r D[Ain(i), 1 , 1] < lrD[Ain (e), o, .e] < 7rD [Aoist , 0, = 7rDPtc(i) , = 7rD [Ac Q [Ac(i), . Next, note that 7rD(A, q,i) is continuous in A and £, while Ain (.e) and Mt) are both continuous in £; so 1- D (Ain (i), 1, £) and 7D (Ao (t), 0, £) are both continuous in £. Therefore there exists an e > 0 such that for £ > - E, 7r D [Ac(i) , Q[Ac (i), 1] , 1] > 7rD [ A in (e), Q[Ain,(1) , 1] , 1] By continuity, one can find an interval [a, 1)] where A*(t) > max {A in (t), A"t } for a < t < b. Proof of Theorem 3

0 Proof of Theorem 4 Let o_ and '3+ satisfy respectively Aout(0-) = A( ii..) and Ain (4) = Ac (3+ ). Consider j3 such that ( A* (g ), Q* (0)) = (Ain (3), in) and (A*(/3 + Q*(0 + e)) = (A0, (,3 + e), out) for any e > 0. As (A in (,3), in) is the unique equilibrium to the left of [0_, 0+ ] and (A 0,43+ e), out) is the unique equilibrium to the right of [0_„ 8+] 0 exists and is in [0-, 04 Now, notice that lrD[A(in; 0), Q[ A in(0), fib = 7rD [A(out; 0), out, Irn[A(in, 0), in, 0] < rD[A(in; 0), out, 9] = 7rD[A( out ; 15), 23

Next, observe that 7r D is continuous in A and p, and that Ain(0) and A.ut(s) are continuous in j3, so 7D[A in(0), in, )3] and rip [Aout(P), out, 0] are continuous in Q. Therefore there exists an e > 0 such that 7rD[A*(,8 + 6), Q*(/3 + e), 0 + el > Q [Ao ut(p),8], 8].

7 r D[Ain(0),

Q* (P), Pl. 0

24

Figure 1

A

■

Aout

ft. Ow

£1

4.

MI.

-__

- At= 1

Figure 2a

A

£1

/ t3 \ £2

to

Figure 2b

flout

£0 £2

Q3

£1

Figure 3

to

/ a\

b

£1

Figure 4

a+0