Strategic patent breadth and entry deterrence with drastic product innovations

International Journal of Industrial Organization 24 (2006) 177 – 202 www.elsevier.com/locate/econbase

Strategic patent breadth and entry deterrence with drastic product innovations Amalia Yiannaka a,*, Murray Fulton b a

Department of Agricultural Economics, University of Nebraska-Lincoln, 314D H.C. Filley Hall, Lincoln, NE 68583-0922, USA b Department of Agricultural Economics, University of Saskatchewan, 51 Campus Drive, Saskatoon, Canada SK S7N 5A8 Received 13 September 2004; received in revised form 16 February 2005; accepted 9 June 2005 Available online 22 August 2005

Abstract This paper examines the innovator’s patent breadth decision that maximizes innovation rents when the innovation is drastic, and there is potential entry by a superior quality product and a likelihood of patent challenge. Analytical results show that the innovator can use patent breadth to deter entry, and in most cases, entry deterrence can be accomplished with narrower rather than broader patent protection. When entry cannot be deterred, a narrow patent breadth can enhance product differentiation in a vertically differentiated product market. D 2005 Elsevier B.V. All rights reserved. JEL classification: L20; L13; O34 Keywords: Patent breadth; Entry deterrence; Innovation rents; Patent challenge; Patent infringement; Patent validity

1. Introduction Innovators seek patent protection as a means of safeguarding their innovations from infringement and thus of appropriating innovation rents. The degree of innovation rent appropriability enabled by a patent is primarily defined by two elements—patent length * Corresponding author. Tel.: +1 402 472 2047; fax: +1 402 472 3460. E-mail address: [email protected] (A. Yiannaka). 0167-7187/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ijindorg.2005.06.001

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and patent breadth (Merges and Nelson, 1990; Klemperer, 1990). While statutory patent length is standardized and predetermined by law and thus not affected by the innovator, patent breadth is case specific and is determined, to a large extent, by the innovator’s patenting behavior. The innovator, through the number and the nature of claims made in the patent application, specifies the technological territory over which protection is claimed—the breadth of patent protection sought for the innovation. These patent claims constitute the basis for the Patent Office’s decision on the breadth of protection granted (if any). The patent examiner can accept the claims as made, reject them or request amendments but cannot add claims; thus, it is the innovator who determines the maximum patent breadth that could be potentially granted to the innovation (Cornish, 1989). In addition, a number of procedural means allow innovators to strategically alter the breadth of protection claimed during patent prosecution and delay the issuance of their patent (DeWitt, 1998).1 The patent claims remain important after the granting of the patent as they form the foundation for rulings by the courts on patent validity and infringement issues (Merges and Nelson, 1990; Miller and Davis, 1990; Cornish, 1989). The innovator’s patent breadth choice is a strategic decision that has important tradeoffs. The greater is the breadth of patent protection, the harder it is for potential competitors to enter into the patentee’s market with non-infringing innovations and thus the longer the patentee can maintain the limited monopoly that the patent grants (Green and Scotchmer, 1995; O’Donoghue et al., 1998). However, the broader is a patent, the greater is the likelihood of both infringement and patent validity challenges by competitors and/or third parties, which if successful will reduce the effective patent life (Merges and Nelson, 1990; Lerner, 1994; Lanjouw and Schankerman, 2001).2 This possibility is especially critical in light of the increase in patent litigation during the last decades, particularly in the field of biotechnology, and the increase in the number of patents that are invalidated after being challenged (Barton, 2000; Choi, 1998; Lanjouw and Schankerman,

1 These procedural means include continuation, continuation-in-part, divisional and reissue applications, and have been the subject of numerous court cases over the years, including Miller v. Brass Co., Webster Electric Co. v. Splitdorf Electric Co. and recently Ford Motor Company v. Lemelson (DeWitt, 1998). The innovatorTs ability to broaden patent claims during the patent granting process and to influence the timing of patent issuance has been linked to the problem of submarine patents. These are patents that are kept dsubmergedT by the innovator through successive continuation applications during which claims may be altered to include unclaimed improvements; the innovator surfaces the patent when the technology embodied in the patent becomes commercially viable. Changes in the USPTO practices (the statutory patent life is (since 1995) 20 years from the date of filing rather than 17 years from issuance and patent applications are published 18 months after patent filing (since 2000)) and a 2-year limitation on broadening continuation and reissue applications have mitigated the problem of submarine patents. These changes, along with the numerous court cases that have emerged around the procedural practices described above, are a clear indication that innovators attempt to use the features of the patent system for their potential benefit. 2 Lerner (1994), in an empirical analysis of the importance of patent scope for the value of the firm, finds that broad patents are faced with more potential infringers and are thus more likely to be litigated. Lanjouw and Schankerman (2001) empirically studied the factors that expose patents to litigation risk using a data set covering all patent validity and patent infringement suits involving patents granted by the USPTO during the period 1975– 1991. They found that patents with more claims were more likely to be involved in litigation—i.e., infringement and invalidity suits.

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2001; Harhoff and Reitzig, 2004). In addition, the courts are more likely to uphold narrow patents and invalidate broad ones (Waterson, 1990). This is so because the broader is the patent scope, the harder it is to demonstrate that the invention is different from the prior art (i.e., to show novelty and nonobviousness) and that the description is enabling (Cornish, 1989; Miller and Davis, 1990; Merges and Nelson, 1990). The possibility that broad patent protection may impede a firm’s ability to safeguard and defend its technological territory raises the question as to what constitutes the optimal patent breadth for the innovator.3 The purpose of this paper is to theoretically examine the innovator’s optimal patent breadth strategy. Specifically, the paper determines the patent breadth choice that maximizes the innovator’s innovation rents. From a theoretical perspective, the analysis of a firm’s patenting behavior has primarily focused on the decision to patent the innovation or to keep it a secret (Horstmann et al., 1985; Waterson, 1990). On the empirical side, Lerner (1995) examined the innovator’s decision to patent in certain patent subclasses given competitors’ patent subclass choices and legal costs. There is no formal analysis of the innovator’s patent breadth choice once the decision to patent has been made, however. Instead, it has been traditionally assumed that the innovator has an incentive to claim das much as possibleT (Lentz, 1988; Lanjouw and Schankerman, 2001). The assumption that the innovator has an incentive to follow a dclaim as much as possibleT strategy is based on the premise of an efficiently operating Patent Office that will prune back or reject broad and/or erroneous claims during the patent granting process. If the Patent Office can efficiently prune back patent applications then the innovator is better off claiming broad patent protection since the patent breadth granted cannot be greater than the patent breadth claimed (Cornish, 1989). The assumption of an efficient patent granting process has been employed in the determination of a socially optimal patent policy (Gilbert and Shapiro, 1990; Klemperer, 1990; Gallini, 1992; Green and Scotchmer, 1995; Chang, 1995; Matutes et al., 1996; O’Donoghue, 1998). In this research, a regulator (e.g., Patent Office) determines a socially optimal patent breadth that dsufficientlyT rewards the innovator/patentee at the least social costs. Evidence shows, however, that the Patent Office typically cannot perform this role. As an example, the United States Patent and Trademark Office (USPTO) often grants patents that appear to overlap and broad patents that cannot survive a validity attack, thus leading to disputes that have to be resolved through costly litigation or settlement (Barton, 2000; Voss, 1999; Lentz, 1988; Lerner, 1994). Barton (2000) points to resource limitations in the USPTO generated by the increase in patent applications during the last decades and estimates that patent examiners spend only 25 to 30 h on average examining a patent application. These time limitations adversely affect the Patent Office’s ability to effectively conduct searches and evaluate patent claims and often lead to the examiner siding with the applicant and granting broad and/or erroneous claims. USPTO statistics on patents whose 3

The trade-off facing patentees is nicely captured in the following quote by Jerome Lemelson: bYou have to stake the four corners of your invention broadly enough so that they give you maximum protection.. . .Of course, if you write too broadly you may invalidate your claim. . .But if you write too narrowly you may miss the thing about the technology that turns out to be truly valuable.Q (as quoted in Varchaver, 2001, p. 207). A number of Lemelson’s patents, which are now controlled by a for-profit foundation, are often raised as examples of submarine patents.

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validity was directly challenged show that more than three-quarters of the re-examined patents are either revoked or amended (Barton, 2000). Choi (1998) finds that, of the patents whose validity was indirectly challenged during an infringement trial between 1966 and 1971, only 30% were found valid. Allison and Lemley (1998) point out that, since the creation of the Federal Circuit in 1982, courts litigating the validity of patents have found approximately 45% of them to be invalid. The failures present in the patent granting process suggest that the innovator cannot always rely on the Patent Office for help in refining his patent claims. This is especially true for pioneering/drastic innovations. According to the Patent Office’s policy, drastic innovations are usually granted broader protection (EPO, 2000; USPTO, 1999).4 Merges and Nelson (1990) observe that claims to drastic innovations are often allowed to cover areas beyond the area examined and disclosed by the innovator, while the narrowing of the claims of drastic innovations is usually left to the courts.5 The model developed in this paper reflects the strategic decision faced by the patentee when claiming patent breadth and the often limited role the Patent Office plays in determining patent breadth, particularly in the case of drastic innovations. Rather than determining a socially optimal patent breadth that might be chosen by the Patent Office, this paper determines the innovator’s choice of patent breadth that maximizes innovation rents. In making this decision, the innovator is aware that his efforts to safeguard his technological territory do not always conclude with the granting of the patent and that a larger patent breadth may increase the likelihood of validity challenges. To fully understand the patentee’s decision, the Patent Office is assumed to play no role in determining the nature of patent breadth. This assumption aligns with the limited role the Patent Office plays in structuring patent claims, particularly in the case of drastic innovations. Drastic innovations also have the characteristic that the innovation rents at stake are substantial, thus increasing the probability of a patent challenge (Cornish, 1989; Lanjouw and Schankerman, 2001). Specifically, the paper determines the innovator’s optimal patent breadth when faced with potential entry by a firm producing a product of superior quality and the possibility that the breadth of the patent will be legally challenged. Patent breadth is defined in terms of the area in a vertically differentiated product space that the patent protects. The theoretical model developed explicitly examines the assumption that the innovator has an incentive to claim the broadest scope of patent protection possible. The model also considers the ability of innovating firms to use patent breadth as an entry deterrent. Analytical results show that the optimal patent breadth depends in a complex way on the entrant’s R&D costs, the innovator’s monopoly profits, the trial costs for the innovator and the entrant, and the degree that patent breadth affects patent validity. More 4

According to the European Patent Office (EPO) (2000), dan invention that opens up a whole new field is entitled to more generality in the claims than an invention that is concerned with advances in a known field of technology.T 5 The more drastic is the innovation, the harder it is for an examiner to disprove enablement, that is, to find support in the prior art to object to broad claims and to demonstrate that embodiments of the claimed invention would be impossible to make without undue experimentation (Merges and Nelson, 1990).

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specifically, the results show that the innovator can use patent breadth to deter entry when the potential entrant’s R&D costs and trial costs are high. If feasible, entry deterrence is always optimal and can in most cases be accomplished with a patent breadth that is less than the maximum breadth possible. When the entry deterrence conditions do not hold, the optimal strategy for the innovator is to allow a new competitor to enter the market. When allowing entry, the innovator’s optimal strategy depends on whether the breadth of patent protection affects the entrant’s infringement decision or not. If it is never optimal for the entrant to infringe the patent, regardless of the patent breadth chosen by the innovator, the optimal strategy for the innovator is to choose the maximum patent breadth. Under this case (which generally occurs when the entrant’s R&D costs are low and the effect of patent breadth on patent validity is small), the choice of maximum patent breadth achieves maximum product differentiation. If, however, the innovator’s choice of patent breadth affects the entrant’s infringement decision (which generally occurs when the entrant has high R&D and low trial costs), then the choice of a narrower rather than a broader patent breadth can lead to greater product differentiation and thus greater profits for the innovator. The rest of the paper is organized as follows. Section 2 describes the theoretical development of the strategic patent breadth model; it describes the market conditions, defines patent breadth and models the choice of patent breadth as a sequential game of complete information. Section 3 provides the analytical solution of the model. Section 4 concludes the paper.

2. The strategic patent breadth model 2.1. Model assumptions The optimal patent breadth strategy is determined in a sequential game of complete information. The agents in the game are an incumbent innovator/patentee and a potential entrant. The innovator, having invented a patentable drastic product innovation and having decided to seek patent protection, decides on the patent breadth claimed. The potential entrant decides on whether to enter the patentee’s market and, if entry occurs, where to locate in a vertically differentiated product space. Both the patentee and the entrant are risk neutral and maximize expected profits. It is assumed that the regulator (e.g., Patent Office) always grants the patent as claimed; thus, the regulator is not explicitly modeled. As discussed in the previous section, the assumption that the Patent Office plays no role in refining the patent claims is a realistic assumption for drastic innovations; this assumption also allows a clear focus on the trade-offs faced by the innovator. The patentee’s investment decision that led to the development of a new product is not examined—this decision is treated as exogenous to the game. Although the patent breadth decision is likely to affect the innovation decision, this aspect is not examined in order to focus attention on the patent breadth decision. In addition, it is assumed that the patentee and the entrant each produce at most one product and that the entrant does not patent her product since it is assumed that further entry does not occur. The production process for

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the entrant is assumed to be deterministic, so that once the entrant chooses a location she can produce the chosen product with certainty. It is also assumed that there is no time lag between making and realizing a decision. The patentee and the entrant, if she enters, operate in a vertically differentiated product market. To reflect the focus on drastic innovations and to keep the analysis tractable, it is assumed that no substitute exists for the products produced by the patentee and the entrant. Consumers differ according to some attribute k, that is uniformly distributed with unit density f(k) = 1 in the interval k a [0,1]. Each consumer buys one unit of either the patentee’s or the entrant’s product but not both. The patentee is assumed to have developed a product that provides consumers with utility U p = V + kq p
p p, where V is a base level of utility, p p is the price of the product produced by the patentee and q p is the quality of the patentee’s product. The entrant’s product is assumed to be a superior product with quality q e N q p that provides consumers with utility U e = V + kq e
p e, where p e is the price of the entrant’s product. Product i (i = p, e) is consumed as long as U i z 0 and U i N U j . It is assumed that V is large enough so that V z p i 8i = p, e and the market is always served by at least one product. The consumer who is indifferent between the two products has a k denoted by k*, where k* is determined as follows: Up ¼ Ue Z k4 ¼

pe
pp : qe
qp

ð1Þ

Since each consumer consumes one unit of the product of her choice, the demand for the products produced by the patentee and the entrant is given by y p = k* and y e = 1
k*, respectively. Without affecting the qualitative nature of the model, the quality of the patentee’s product q p is set equal to zero; thus k* = ( p e
p p)/( q e). The entrant’s quality q e is thus interpreted as the difference in quality between her product and that of the patentee, or more generally as the distance the entrant has located away from the patentee. The maximum distance between the patentee’s and the entrant’s product is normalized to equal one, i.e., q e a (0,1]. The patentee is assumed to have incurred the development costs associated with the product quality that he wishes to patent. Thus, the R&D costs for the patentee are sunk. For the entrant, market entry can only occur if she develops a higher quality product. To do so, she incurs R&D costs F e ( q e), where F e = b( q e2)/(2) and b z (4)/(9). The restriction on the parameter b ensures that the quality chosen by the entrant, q e, is bounded between zero and one. Larger values of the parameter b imply lower R&D cost effectiveness and hence larger R&D costs, all else equal. Note that with this formulation, F eV ( q e) N 0 and F eW ( q e) N 0; thus, it is increasingly costly for the entrant to locate away from the patentee in the one-dimensional product space (i.e., to produce the better quality product). In addition, since q e represents the quality difference between the patentee’s and the entrant’s product, the filing of a patent by the patentee provides the entrant with knowledge of how to produce the patentee’s product (i.e., F e (0) = 0—the assumption of perfect information disclosure by the patentee is made). The R&D costs are assumed sunk once they have been incurred; once these costs are incurred, production by both the patentee and the entrant occurs at zero marginal cost. It is also assumed that once the entrant has chosen her quality,

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q e , neither she nor the patentee is able to relocate; effectively the relocation costs are such that it is not optimal for relocation to occur. The implications of relaxing this assumption are discussed throughout the analysis. The patent breadth claimed and granted to the patentee’s product is denoted by b and defines the area in the one-dimensional product space that the patent protects, thus, b a [0, 1].6 If the entrant locates at a distance q e b b the patent is infringed. To keep the analysis simple, it is assumed that the patentee always takes the entrant to trial if infringement occurs. This assumption implies some restrictions on the parameters in our model that are discussed later. It is further assumed that the filing of an infringement lawsuit is always met with a counterclaim by the accused infringer that the patent is invalid.7 The costs incurred during the infringement trial by the patentee and the entrant are denoted by C p and C e, respectively. These costs are assumed to be independent of the breadth of protection and of the entrant’s location. The trial costs will only be incurred if q e b b and they are assumed to be sunk—once made, they cannot be recovered by either party.8 The patent system being modeled is assumed to be that of the fencepost type in which patent claims define an exact border of protection. Under the fencepost system, infringement will always be found when an entrant locates within the patentee’s claims, unless the entrant proves that the patent is invalid (Cornish, 1989).9 In the fencepost system, the probability that infringement is found does not depend on how close the entrant has located to the patentee. The implication of assuming a fencepost patent system is that the probability that infringement will be found (given that the entrant has located at q e b b) is equal to the probability that the validity of the patent will be upheld. Thus, the fencepost patent system implies that the events that the patent is found to be infringed and that the patent is found to be invalid can be treated as mutually exclusive and exhaustive.10 Patent validity is directly linked to patent breadth. In general, the broader is the patent protection, the harder it is to show novelty, nonobviousness and enablement (Cornish, 1989; Merges and Nelson, 1990; Miller and Davis, 1990). Thus, the broader is patent protection, the harder it is to establish validity. In addition, as mentioned previously, evidence from the literature shows that courts tend to uphold narrow patents and invalidate broad ones (Waterson, 1990; Merges and Nelson, 1990). To capture these observations, the probability l(b) that the patent will be found to be valid, or equivalently that infringement will be found, is assumed to be inversely related to patent breadth—i.e., lV(b) b 0. 6

Note that since this is a quality ladder model our definition of patent breadth is similar to the dleading breadthT notion introduced by O’Donoghue et al. (1998). 7 This is a standard defense adopted by accused infringers (Cornish, 1989; Merges and Nelson, 1990). 8 With this assumption, the possibility of the court awarding legal fees to either party is excluded. 9 In contrast, a signpost patent system implies that claims provide an indication of protection and the claims are interpreted using the doctrines of equivalents and reverse equivalents. Under a signpost system, the closer the entrant locates to the patentee, the easier it is to prove infringement using the doctrine of equivalents. In addition, infringement may be found even when the entrant locates outside the patentee’s claims using the doctrine of reverse equivalents. 10 Since further entry is not anticipated in our model, our analysis and results are not affected by whether the entire patent or only certain claims are invalidated (i.e., the patent breadth is narrowed) during the infringement trial.

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Specifically, l(b) = 1
ab.11 Thus, 1
l(b) = ab is the probability that the patent will be found to be invalid. The validity parameter a, a a (0, 1), reflects the degree that patent breadth affects patent validity. For any given patent breadth, the greater is the validity parameter a, the greater is the probability that the patent will be found invalid. Finally, the model does not consider the possibility of either ex ante or ex post licensing. Ex ante licensing (i.e., the licensing of the innovation before the entrant makes her entry and investment decisions) in the case of sequential innovations has been considered by Green and Scotchmer (1995). Modeling of ex ante licensing, were it to be undertaken, requires an understanding of the threat points of the patentee and the entrant. By examining the profits that would exist in the absence of licensing, the model developed in this paper establishes the payoffs that would be considered by the patentee and the entrant when negotiating an ex ante license; incorporating these threat points into a model of licensing is a task for future research. Ex post licensing is ruled out in the case where the entrant enters and does not infringe, since the entrant does not require a license to operate under this case. If the entrant infringes the patent and the patent is upheld during the infringement trial, the patentee has no incentive to license the product, since doing so leads to duopoly competition; it is assumed that the duopoly profits earned by the patentee and the entrant are lower than the profits earned when the patentee operates as a monopolists. Finally, if the entrant infringes the patent and the patent is not upheld, then no patent exists that can be licensed. 2.2. The game The strategic patent breadth game consists of three stages. In the first stage of the game, the patentee applies for a patent, claiming a patent breadth, b, which is granted by the Patent Office. In the second stage of the game, a potential entrant observes the patentee’s product and the breadth of protection granted to it and chooses whether to enter the market. If the entrant does not enter, she earns zero profits while the patentee operates as a monopolist in the third stage of the game and earns monopoly profits P pM . If the entrant enters, she does so by choosing the quality q e of her product, thus determining whether the patent is infringed. If the entrant chooses a quality greater than or equal to the patent breadth claimed by the patentee (i.e., q e z b), then no infringement occurs, and she and the patentee compete in prices in the third stage of the game and earn profits P eNI and P pNI, respectively. If the entrant locates inside the patent breadth claimed by the patentee (i.e., q e b b), the patent is infringed and a trial occurs in which the validity of the patent is examined. With probability l(b), the patent is found to be valid (i.e., infringement is found), the entrant is not allowed to market her product and the patentee operates as a monopolist in the third stage of the game. With probability 1
l(b), the patent is found to be invalid and the entrant and the patentee compete in prices. The payoffs for the patentee and the entrant when the entrant chooses q e b b are E(P pI) and E(P eI), respectively. Fig. 1 illustrates the extensive form of the game outlined above. 11 Patent breadth is not the only factor affecting the validity of the patent. A patent may also be invalidated because of unallowable amendments during patent examination and because the innovation is not regarded as an invention under the patent law (Cornish, 1989). By assuming that the innovator has generated a patentable innovation, the latter case is excluded. To keep the analysis simple, it is also assumed that the probability of patent invalidation due to unallowable amendments is negligible.

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Stage one

185

Patentee: Chooses patent breadth b

Stage two

Entrant

Does not enter

Enters

Entrant: Chooses product quality q e

Does not infringe - qe ≥ b

Infringes - qe < b

No trial

Trial

µ

1

V Stage three Payoffs: A

Payoffs: B

I

Payoffs: C

P: π *p = Π Mp

P: π *p = Π

NI p

P: π *p = E ( Π Ip )

E: π

E: π e* = Π

NI e

E: π e* = E ( Π eI )

* e

= 0

−µ

Fig. 1. The patent breadth game in extensive form.

The solution to this game is found by backward induction. The third stage of the game in which the patentee and the entrant – when applicable – compete in prices is examined first, followed by the second stage in which the entrant makes her entry decision. The first stage in which the patentee makes his decision regarding patent breadth is examined last.

3. Analytical solution of the game 3.1. Stage 3—the pricing decisions In the third stage of the game, two cases must be considered—the case where the entrant has entered and the case where she has not. Considering the last case first, in the absence of entry by the entrant, the patentee will charge p p = V and earn monopoly profits P pM = V. If entry occurs (i.e., either when q e z b or when q e b b and the patent is invalidated), the problem facing duopolist i is to choose price p i to maximize profit P i = p i y i
F i (i = p, e),

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where y p = k* = ( p e
p p)/(q e) and y e = 1
k*=( q e + p p
p e)/( q e) from Eq. (1). Recall that the R&D costs, F p and F e for the patentee and the entrant, respectively, are assumed to be sunk at this stage in the game. The Nash equilibrium in prices, as well as the resulting outputs and profits, are given by: qe 1 qe ð2Þ Patentee : pp4 ¼ ;yp4 ¼ ;pp4 ¼ 3 3 9 2qe 2 4qe ;y4e ¼ ;p4e ¼ : ð3Þ 3 3 9 Since the entrant has the higher quality product, she charges the higher price. Profits are increasing in the distance q e between the patentee’s and the entrant’s location. The greater is the difference in quality between the two products, the less intense is competition in the final stage of the game and the greater are the profits for both the incumbent and the entrant.12 Entrant : p4e ¼

3.2. Stage 2—the location decision by the entrant In Stage 2, the entrant must choose one of three options—Not Enter, Enter and Not Infringe the Patent, or Enter and Infringe the Patent. For any given patent breadth, b, the entrant chooses the option that generates the greatest profit. The outcome of the Not Enter option is straightforward—the entrant earns zero profits. The outcomes of the other two options depend on a number of factors, including patent breadth, R&D costs and trial costs. The benefits and costs associated with the Enter and Not Infringe option are examined immediately below, followed by an examination of the benefits and costs associated with the Enter and Infringe option. Once the net benefits of each option are formulated, the most desirable option for the entrant is determined for any given patent breadth. 3.2.1. Entry with no infringement ( q e z b) For the entrant to enter without infringing the patent, the entrant must choose a quality location that is greater than or equal to the patent breadth—i.e., q e z b. Let q *e be the optimal quality the entrant would choose when the patent breadth is not binding, where q e* solves the following problem: 4qe q2
b e : ð4Þ max Pe ¼ pe
Fe ¼ qe 9 2 Optimization of Eq. (4) yields the optimal quality q e*: 4 : ð5Þ qe4 ¼ 9b Eq. (5) indicates that the less costly it is to produce the better quality product (i.e., the smaller is b), the further away from the incumbent the entrant locates. Note that, when the entrant’s R&D cost parameter takes its minimum value (b = (4)/(9)) the entrant never infringes the patent as q*e = 1. 12 The result that both firms benefit from an increase in product differentiation is a well-established outcome in simultaneous games when firms first choose their location in product space and then compete in prices (Lane, 1980; Motta, 1993; Shaked and Sutton, 1982).

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As long as q e* z b, the patent breadth does not affect the location chosen by the entrant, since the entrant can choose her optimal quality without fear of infringement. Thus, patent breadth will only be binding if q*e b b. Under these conditions, an increase in quality beyond q e* results in a reduction in profits, since the entrant’s profit is decreasing in q e for all q e N q e*. As a result, the entrant, when faced with a binding patent breadth and not wishing to infringe the patent, will always choose a quality equal to the patent breadth chosen by the patentee (i.e., q e = b). Thus, a profit-maximizing entrant that wishes to not infringe the patent will choose her entry location q eNI as follows: ( 4 4 if bV 9b NI qe ¼ 9b ð6Þ 4 b if bN 9b while the profits earned by the entrant are: ( 8 4 if bV 9b NI Pe ¼ 481b b 2 4 : if bN 9b 9b
2b

ð7Þ

3.2.2. Entry with infringement ( q e b b) If the entrant enters and infringes the patent held by the patentee, a trial takes place.13 If the patent is found to be valid during trial, the entrant cannot enter and the patentee has a monopoly position in the market, while if the patent is found to be invalid, the entrant is allowed to market her product and the patentee and the entrant operate as duopolists. With this background, the quality chosen by the entrant is determined by solving:14   4qe q2
b e
Ce : max E PIe ¼ ð1
lÞpe
Fe
Ce ¼ ab ð8Þ qe 9 2 The optimal quality chosen is given by: 4ab : ð9Þ qIe ¼ 9b From Eq. (9), it follows that the optimal quality under infringement satisfies the condition q eI b bZ a b (9b)/(4) 8a a (0, 1) and b N (4)/(9) (recall that when b = (4)/(9) the 13 With no trial, the patentee’s profits are ( q e)/(9); with a trial, the expected profits are lP M p + (1
l)( q e)/ (9)
C p, where l = 1
ab. Thus, the patentee will choose a trial if (1
ab)(P M p
( q e)/(9)) N C p. It is assumed that P M p and C p are such that this expression holds for all values of a a (0, 1), b a (0, 1), and q e a (0, 1]. Relaxing this assumption raises the possibility that the entrant, by the choice of location q e, can induce the patentee to not invoke a trial. Since consideration of this possibility greatly expands the analysis to be undertaken, the assumption that a trial always occurs is maintained. 14 The problem in Eq. (8) assumes that the entrant cannot relocate after choosing q e and captures the notion that relocation is sufficiently costly (e.g., due to the need to revamp marketing strategies or to reconfigure production facilities) that it is never optimal. Although the emphasis of this paper is on the case of costly relocation, the key elements of the costless case are considered; these two cases bracket the range of possibilities. As will be seen, while the particulars differ, the same basic results and trade-offs are at work in both cases. In the costless case, the entrant with zero costs of relocation has three options—Not Enter, Enter and Not Infringe, or Enter and Infringe. The profits for the first two options are the same as in the costly case. The expected profits of the last option differ somewhat, however. If the entrant enters and infringes the patent, she ultimately faces two potential outcomes— she will relocate to b if the patent validity is upheld or she will relocated to q*e if the patent is found to be not valid. Thus, the entrant’s expected profits from entering and infringing the patent when there are no relocation costs are Enrc ðPIe Þ ¼ lð 49 b
b2 b2 Þ þ ð1
lÞð 49 q*e
b2 q*e 2 Þ
Ce , where q*e = (4)/(9b) and l = 1
ab.

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patent is never infringed). Eq. (9) shows that when the entrant infringes the patent she finds it optimal to locate at a distance proportional to the breadth of the patent. Because there is uncertainty with respect to whether she will be able to continue in the market, the entrant dunderlocatesT in order to reduce the R&D costs, which are incurred with certainty. The expected profits for the entrant are given by Eq. (10):   8a2 b2 E PIe ¼
Ce : 81b

ð10Þ

When patent breadth is negligible (i.e., b approaches zero), the expected profits from infringement approach
C e, since the probability of the patent being found valid approaches one. As patent breadth increases, expected profits from infringement also rise, a reflection of the increased probability that the patent will be found invalid. 3.2.3. The entry/infringement decision The decision made by the entrant whether to enter, and if entry occurs, whether to infringe the patent, depends on the patent breadth, b, and three variables that are treated as exogenous in this study—the R&D cost parameter b, the trial costs C e and the validity parameter a. As shown in Eq. (7), when patent breadth is such that b V q *, e the entrant always finds it profitable to enter the market locating at her most preferred location ( q*) e without triggering the trial outcome. For patent breadth values such that b N q*, e the behavior of the entrant is captured in the following Proposition. Proposition 1. When b N q e*, three possibilities exist for the entrant: (a) Entry Deterrence—If there exists a patent breadth bˆ a (q e*, 1] where bˆ solves P eNI (bˆ) V 0 and E(P eI (bˆ)) V 0, then entry by the entrant can be deterred if the patentee chooses bˆ. (b) Entry and Inducement of Infringement/Non-Infringement—If there exists a patent breadth b˜ where b˜ solves P eN (b˜) = E(P eI (b˜)) N 0, then entry by the entrant cannot be deterred regardless of the patent breadth chosen. The entrant will not infringe the patent if b V b˜ and will infringe the patent if b N b˜. (c) Entry and No Infringement—If the conditions specified in (a) and (b) do not exist (i.e., bˆ, b˜ a (q e*, 1] do not exist), then the entrant will always find it optimal to enter without infringing the patent, regardless of the patent breadth that has been chosen. These three cases are examined in more detail below (the proofs of each part of Proposition 1 are included in the discussion) and are illustrated in Fig. 2. Notice that the different cases in Fig. 2 are drawn for specific combinations of the values of the critical parameters, b, a and C e. 3.2.3.1. Case I—entry deterrence. The entrant can be deterred from entering the market when there exists a patent breadth, bˆ , where bˆ satisfies the following conditions: P eNI(bˆ ) V 0, E(P eI(bˆ )) V 0 and bˆ a ( q*, e 1] (i.e., the expressions in Eqs. (7) and (10), respectively, are less than or equal to zero). In fact, there might be a range of patent breadth values that deter entry. Define b¯I as the patent breadth that makes the entrant indifferent

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189

Fig. 2. The entrant’s profits under infringement and no infringement when entry can be deterred – panels (i) and (ii) – and when entry cannot be deterred—panels (iii) and (iv).

between entering the market and infringing the patent and not entering the market. Thus, b¯ I solves: E(P eI(b¯ I )) = 0 where b¯ I a ( q e*, 1].15 Also, define b¯ NI as the patent breadth that makes the entrant indifferent between entering the market without infringing the patent and not entering the market—i.e., b¯NI ffi satisfies P eNI(b¯ NI) = 0, where b¯ NI a ( q *, e 1]. It is qffiffiffiffiffiffiffiffiffi ¯ 81bC straightforward to show that bI ¼ 8a2 e and b¯ NI = (8)/(9b); since b¯ NI a ( q e*, 1], b¯ NI exists only for b values such that b z (8)/(9). Given the above, any b a ( q e*, 1] such that b V b¯ I makes entry under infringement unprofitable for the entrant, while any b a ( q e*, 1] such that b z b¯ NI makes entry under no infringement unprofitable for the entrant. Thus, the entrant will not find it profitable to enter the market if there exists a bˆ a ( q e*, 1] such that b¯ NI V bˆ V b¯ I . Case I is illustrated in Fig. 2, panels (i) and (ii). 15

The assumption is made that the entrant will not enter when she is indifferent between entering and infringing the patent and not entering.

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3.2.3.2. Case II—entry and inducement of infringement/non-infringement. Let b˜ be the patent breadth that makes the entrant indifferent between infringing and not infringing the patent, while still generating positive profits for the entrant—i.e., b˜ solves P eNI(b˜ ) = E(P eI(b˜ )) N 0 where b˜ a ( q e*, 1]. Note from Eq. (5) that q e* = 1 when b = (4)/ (9); thus b˜ is defined only for b N (4)/(9). The entrant will enter and not infringe when b a (0, b˜ ], while the entrant will enter and infringe when b a (b˜ , 1] (the assumption is made that when the entrant is indifferent she will choose to not infringe the patent). Note that the entrant will not infringe the patent when b˜ = 1. The expression for b˜ is derived in the Appendix. Patent breadth b˜ is a function of the R&D effectiveness parameter, b, the validity parameter, a, and the trial costs C e. The greater are the costs of producing the higher quality product, the greater is the validity parameter and the smaller are the entrant’s trial costs, the smaller is the patent breadth, b˜ (i.e., (Bb˜ )/(Bb) V 0, (Bb˜ )/(Ba) b 0 and (Bb˜ )/(BC e) N 0). While a formal proof of these results is provided in the Appendix, the intuition behind them is easily seen. The more costly it is to produce the better quality product (i.e., the larger is b), the smaller are the entrant’s (expected) profits under both non-infringement and infringement; however, non-infringement becomes relatively less profitable than infringement for the entrant (the P eNI curve shifts inwards more than the E(P eI) curve shifts downwards). Thus, as b increases, the patent breadth that makes the entrant indifferent between infringing and not infringing the patent declines. In addition, the greater is the value of the validity parameter, a, the greater are the expected profits under infringement (the E(P eI) curve shifts upwards) while the entrant’s profits under no infringement are unaffected and thus the smaller is the patent breadth that makes the entrant indifferent between infringing and not infringing the patent. Finally, the greater are the trial costs, C e, the less profitable is infringement for the entrant (the E(P eI) curve shifts downwards) while the entrant’s profits under non-infringement are not affected and thus the greater is the patent breadth that makes the entrant indifferent between infringing and not infringing the patent. Case II is illustrated in Fig. 2, panel (iv) for b values such that b z (8)/(9). 3.2.3.3. Case III—entry and no infringement. While Case II examines the case of entry where the innovator’s choice of patent breadth determines whether the entrant infringes or not, Case III looks at entry where the entrant will never infringe the patent, regardless of the patent breadth chosen. This outcome occurs when the validity parameter and the NI I entrant’s trial costs and R&D effectiveness are such that, 8b a ( q*, e 1], P e N E(P e) and NI P e N 0. This occurs only for b values such that (4)/(9) V b b (8)/(9). To see that Case III occurs under the conditions where Cases I and II do not, note that at the entrant’s most preferred location q e* non-infringement is always more than  profitable NI I 4 8 128a2 infringement for the entrant. That is, for b ¼ q*e ¼ 9b ;Pe
E Pe ¼ 81b
6561b3 þ NI e P e = (8)/(81b) N 08b z (4)/(9). The CE N08bz 49 1aað0;1Þ1Ce z0. In addition, at q*, above conditions imply that if a b˜ a ( q*e , 1] does not exist (i.e., there is no patent breadth for I which E(P e) = P eNI N 0), then P eNI N E(P eI) 8b a (0, 1]. Since there is no b˜ a ( q e*, 1] or bˆ a ( q e*, 1], these is also no b¯ NI such that P eNI(b¯ NI) = 0 which, in turn, implies that P eNI N 08b a (0, 1]. As a consequence, entry with non-infringement is the most profitable action for the entrant. Case III is illustrated in Fig. 2, panel (iii).

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191

Fig. 3. Combinations of b and C e (a given) that generate entry deterrence (Case I), entry and infringement/noninfringement (Case II) and entry and no infringement (Case III).

Fig. 3 illustrates the combinations of b and C e values, for a given a value, that give rise to each of the three cases. Entry deterrence (Case I), where there exists a patent breadth bˆ such that b¯ NI V bˆ V b¯ I , is represented by the dotted area on Fig. 3 and is more likely to occur for combinations of relatively high b (low R&D effectiveness) and high trial cost, C e, values. Entry and inducement of infringement/no infringement (Case II), where there exists a patent breadth b˜ such that b¯ I b b˜ b b¯ NI, is represented by the vertically hatched area in Fig. 3 and is more likely to occur for combinations of relatively high b (low R&D effectiveness) and low trial cost values, C e. Finally, entry with no infringement (Case III), where there is no patent breadth bˆ that can deter entry and no patent breadth b˜ that can induce non-infringement, is represented by the horizontally hatched area in Fig. 3 and occurs for low b (high R&D effectiveness) values.16

16

When relocation is costless, the entrant faces the same three possibilities that were considered in the main text. The combination of parameters that give rise to these three choices is similar (although not identical) to the combinations shown in Fig. 3. Note that the first two terms of E nrc(P eI) in Footnote 14 are a weighted average of the profits earned when q *e is chosen and the profits under no infringement, PNI e (when b N (4)/(9b)). Since 0 b PNI when b N (4)/(9b) and (4)/(9) V bb(8)/(9), the expected profits associated with entry and e b P( q *) e infringement are always positive and greater than those associated with entry and no infringement if the entrant’s trial costs are sufficiently low. However, as trial costs rise, Entry and No Infringement will be the optimal choice for the entrant. Thus, under costless relocation Case III occurs when b is small (roughly when (4)/(9) V b b (8)/(9)) and C e is sufficiently large. Note, however, that unlike what is shown in Fig. 3, Case III requires positive values of C e for all values of b. The Entry Deterrence case (Case I) arises when b is large (roughly when b N (8)/(9)) and C e is sufficiently large; once again, the combination is similar to that shown in Fig. 3. The reasoning is as follows. nrc With b N (8)/(9), PNI (P eI) will also be negative when b takes on larger e b 0 for larger values of b. As a result, E values, providing C e is sufficiently large. Finally, and again similar to that shown in Fig. 3, Case II (Entry and Inducement of Infringement/Non Infringement) occurs when C e is sufficiently small.

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α = 0.75 α = 0.50 α = 0.25

Ce

bI = bNI ~ b =1 4 9

8 9

β

Fig. 4. Combinations of b and Ce values that give rise to Cases I, II and II, for a = 0.75, a = 0.50 and a = 0.25.

The validity parameter a affects the combination of b and C e values that give rise to Cases I, II and III. As shown in Fig. 4, the larger is a, the smaller is the parameter area in which the entrant will enter and not infringe the patent (the area above the locus b˜ = 1 and for b a [(4)/(9), (8)/(9))), and the smaller is the parameter area that can deter entry (the area above the locus b¯ I = b¯ NI and for b z (8)/(9)). These results follow directly from the impact that the validity parameter a has on the probability that the validity of the patent will be upheld during trial, l. As a becomes larger, the greater is the probability that the patent will be found invalid, for any given patent breadth, b. As a consequence, entry is harder to deter (Case I) and when entry does occur, the entrant is less likely to find it optimal to enter without infringing the patent (Case III) for any b a ( q*, e 1]. 3.3. Stage 1—the patent breadth decision In stage 1 of the game, the patentee chooses the patent breadth b that maximizes profits, given his knowledge of the entrant’s behavior in the second stage of the game. Since the entrant’s behavior depends on the values of C e, a and b, the patent breadth chosen by the patentee also depends on these parameters. Specifically, three situations are possible, each one corresponding to one of the cases outlined above.17 These situations are presented in Fig. 5 and are analyzed below.

17 The same three scenarios are possible when relocation is assumed to be costless. If entry can be deterred, it is always optimal for the patentee to do so. If the parameter values are such that the entrant will always enter and not infringe the patent regardless of patent breadth, then the patentee always chooses the maximum patent breadth. The decision by the patentee in the third scenario differs slightly from the outcome derived below and is considered in more detail when this scenario is examined.

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193

Fig. 5. The patentee’s strategic patent breadth decision.

3.3.1. Scenario A—choose patent breadth to deter entry Proposition 2. If there are values of b, a and C e such that entry can be deterred – i.e., if there exists a bˆ a (q e*, 1] such that b¯ NI bˆ V b¯ I (Case I) – then the patentee should always choose to deter entry. When entry can be deterred, it can in most cases be accomplished by a patent breadth that is less than the maximum breadth possible. Proof. By deterring entry, the patentee earns monopoly profits P pM . Since these profits are higher than what can be earned under a duopoly, the patentee always finds it optimal to deter entry. Entry deterrence can often be achieved without choosing the maximum patent breadth. If b¯ a ( q e*, 1] such that b¯ NI V bˆ V b¯ I exists, then bˆ = 1 when b¯ NI = b¯ I = 1, which occurs only when b = (8)/(9) (recall that b¯ NI = (8)/(9b)) qffiffiffiffiffiffiffiffiffi and for combinations of C e and a values such ). Thus, as long as a bˆ a ( q e*, 1] exists, any that C e = (a 2)/(9) (recall that b¯I ¼ 81bC 2 8a

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combination of b, a and C e values other than (b = (8)/(9), C e = (a 2)/(9)) that satisfies the condition b¯ NI V bˆ V b¯ I will lead to entry deterrence being accomplished by claiming a patent breadth less than the maximum breadth possible, i.e., bˆ b 1. 5 3.3.2. Scenario B—choose maximum patent breadth Proposition 3. When the values of b, a and C e are such that the entrant will always enter and not infringe the patent, regardless of the patent breadth (i.e., Case III), the patentee always chooses the maximum patent breadth. Proof. The reasoning is straightforward. With both firms operating in the market, the profits of the patentee are increasing in the quality chosen by the entrant—i.e., p p* = ( q e)/(9) (see Eq. (2)). As Eq. (6) indicates, the entrant will choose q e = b for b N q e* = (4)/(9b). Thus, the patentee can earn maximum profits by choosing the largest possible patent breadth, which in turn causes the entrant to chose the largest possible value of q e. 5 3.3.3. Scenario C—allow entry and induce either infringement or non-infringement If the values of b, a and C e are such that the entrant will enter and either infringe or not infringe depending on patent breadth—i.e., if there exists a b˜ a ( q e*, 1] such that b¯ I b b˜ b b¯ NI (Case II), the patentee must decide whether to induce infringement or not. Consider first the profits the patentee earns if he induces the entrant to not infringe. Recall from Eq. (2) that the patentee’s profits equal p p* = ( q e)/(9) when the entrant enters without infringing. Recall also (see Eq. (6)) that the entrant will always choose q eNI = (4)/ (9b) if b V (4)/(9b), while the entrant chooses q eNI = b when b N (4)/(9b). Thus, if the patentee induces non-infringement, his profits are given by:

PNI p

8 4 > > < 81b ¼ > > b : 9

4 9b

if

bV

if

: 4 bbVb˜ 9b

ð11Þ

Since the patentee’s profits can always be increased by choosing b z (4)/(9b), the patentee can earn maximum profits and not induce infringement by choosing b NI = b˜ . The patentee’s profits are thus:18 PNI p ¼

b˜ 9

ð12Þ

The profits earned from inducing non-infringement have to be compared to the expected profits earned by inducing infringement. Recall that the entrant chooses q eI = (4ab)/(9b) when she enters and infringes the patent, and that the probability of the

18

The profit expression in Eq. (12) also holds in the case where relocation is costless.

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195

patent being found valid is l = 1
ab. The patentee’s expected profits are given by E(P pI) = lP pM + (1
l)p p
C p. Also recall that infringement cannot be induced when b˜ = 1 since in this case the entrant will never infringe the patent (see Case II). The problem facing the patentee is thus:19

 4a2 b2 max E PIp ¼ ð1
abÞPM
Cp þ p b 81b : s:t: b˜ þ eVbV1 where eY0 and b˜ p 1 ð13Þ The patent breadth that solves Eq. (13), b˘ I = (81bP pM )/(8a), does not result in maximum profits for the patentee, since the second-order conditions do not hold—i.e., B2 E ðPIp Þ 8a2 ¼ 81b N0. Thus, the optimal patent breadth that induces infringement, denoted Bb2I I I I I by b , is one of the corner values—i.e., b = b˜ + e or b = 1. If b˘ V b˜, then b = 1, while if M I I I b˘ z 1, then b = b˜ + e. Since b˘ is increasing in P p , the larger are the patentee’s monopoly profits, the more likely it is that the patentee will choose b˜ + e as the patent breadth with which to induce infringement. If b˜ b b˘ I b 1, then the choice of the optimal patent breadth that induces infringement depends on where the patentee’s expected profits are greater. With b I = 1, the patentee’s expected profits are:

 4a2
Cp E PIp I ¼ ð1
aÞPM ð14Þ p þ b ¼1 81b while with b I = b˜ + e, the expected profits are:

   4a2 ˜ 2 lim E PIp I ˜ ¼ 1
ab˜ PM ð15Þ b
Cp : p þ eY0 b ¼b þe 81b Assuming the patentee induces infringement, the patentee chooses b I = 1 when E(P pI )bI = 1 N E(P pI)bI = b¯ + e . This condition is satisfied when (4a)/(81b) (1 + b˜ ) N P pM . Thus, the patentee is more likely to induce infringement by choosing the maximum patent breadth (i.e., b I = 1) when the entrant’s trial costs C e are large and the R&D effectiveness b is small (recall that (Bb˜ )/(BC e ) N 0 and (Bb˜ )/(Bb) V 0) and when the monopoly profits P pM are small. To understand the economic incentives at play in the patentee’s decision, consider the impact of monopoly profits on the patentee’s incentive to induce infringement by claiming the maximum breadth of protection. Under infringement, the entrant’s location is proportional to the breadth of the patent (i.e., q eI = (4ab)/(9b)); thus, the greater is patent breadth, the further away from the patentee the entrant locates and the greater are the profits at the last stage of the game for both players. When monopoly profits are small, the larger profits brought about by the increased level of differentiation between the two products more than offsets the potential loss of monopoly profits that occurs because of the greater probability of the patent being found invalid, and the inducement of patent infringement by choosing maximum patent breadth becomes the optimal strategy. When 19

If relocation is costless, the problem facing the patentee is to choose patent breadth to maximize E nrc(P Ip) = l(b)/(9) + (1
l)(4)/(81b)
C p. This expression is maximized at b I = (1)/(2a)+(2)/(9b). Thus, if a and/ or b are large, the patentee will choose a patent breadth less than one to induce infringement. Note that this result differs from that considered in the text where the patentee either chooses b I = b˜ + e or b I = 1.

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monopoly profits are large, however, the patentee chooses to induce infringement by choosing a patent breadth that is less than the maximum, since doing so reduces the likelihood of patent invalidation that would prevent him from realizing these profits. Proposition 4. When entry cannot be deterred and the patentee can use patent breadth to induce the entrant to infringe or not infringe the patent (i.e., there exists a b˜ a (q e*, 1] such that b¯ I b b˜ b b¯ NI ) a narrower rather than a broader patent breadth can lead to greater product differentiation. ¯ ˜ ¯ Proof. When there exists a b˜ a ( q*, e 1] such that b I b b b b NI the patentee can induce nonNI ˜ infringement by claiming b = b or infringement by claiming either b I = b˜ + e or b I = 1 N b˜ . When the patentee claims b NI = b˜ , the entrant locates at q eNI = b˜ (see Eq. (6)). When the patentee claims b I = b˜ + e or b I = 1, the entrant infringes and locates at q eI (b=b˜ +e) = (4a) (b˜ + e)/(9b) or q eI (b=1)=(4a)/(9b), respectively (see Eq. (9)). It is easily seen that q eNI N q eI (b = b˜ + e)8b z (4)/(9), a a (0, 1) and C e z 0. Also, q eNI N q eI (b = 1)8b z (4)/(9), a a (0, 1) and C e z 0. To see this, note that when C e = 0, q eNIY(8)/(9b) N 0 and q e I(b = 1)Y0 when aY0, while q eNIY(72b)/(16 + 81b 2) and q eI (b = 1)Y(4)/(9b) when aY1. Since (72b)/ (16 + 81b 2) z (4)/(9b)8b z (4)/(9), and recalling that (Bb˜ )/(Ba) b 0 and (Bb˜ )/(BC e) N 0, it is clear that a relatively narrower patent breadth, b˜ , will cause the entrant to locate further away in the quality product space. 5 Having determined the patentee’s expected profits when he induces infringement and non-infringement, the next step in the analysis is to determine whether the patentee will find it optimal to induce infringement or non-infringement.20 Fig. 6 depicts the possible outcomes of a comparison between the patentee’s expected profits when he induces infringement and his profits when he induces non-infringement, given that the optimal patent breadth when infringement is induced is either b I = b˜ + e (panel (i)) or b I = 1 (panel (ii)). As shown in Fig. 6, the patentee’s expected profits under infringement can be depicted by either curve AB or curve CD (the expected profits are drawn on the assumption that b˜ b b˘ I b 1). When the patentee’s expected profits under infringement are depicted by the curve AB, the optimal strategy for the patentee is to induce infringement (point A is higher than point E in panel (i) and point B is higher than point E in panel (ii)). When the patentee’s expected profits under infringement are depicted by the curve CD, the optimal strategy for the patentee is to induce non-infringement (point C is below point E in panel (i) and point D is below point E in panel (ii)). A complete analytical comparison of the patentee’s profits when he induces infringement and when he induces non-infringement is not possible without knowledge of the values of the exogenous parameters a, b, P pM , C e and C p. However, the impact of these parameters on the incentive to induce infringement can be determined. The starting 20 This same comparison is made in the case where relocation is costless. With costless relocation, monopoly profits do not enter the comparison, since the patentee cannot maintain the monopoly unless entry can be deterred. Nevertheless, the same fundamental trade-off is at work. Choosing to induce non infringement avoids trial costs but ensures that the entrant always locates at b˜ . Choosing to induce infringement (by choosing a larger patent breadth) opens the possibility that the patent will be found valid and thus creating higher profits (in the costless relocation case, the higher profits result because the entrant is forced to choose a higher quality); however, choosing a higher patent breadth also lowers the probability that the patent will be found valid.

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197

Fig. 6. The patentee’s expected profits under infringement and his profits under non-infringement under scenario C.

point for this analysis is the observation that as a approaches one and b approaches (4)/(9) with C p = C e = 0, b˜ approaches one and P pNI, E(P pI)bI = b˜ + e and E(PpI)bI = 1 approach the same value. Given this common starting point, the impact of changes in the exogenous parameters on these baseline values can be used to determine the conditions under which infringement or non-infringement is the desirable strategy. Table 1 presents the impact of the parameters b, a, P pM , C p and C e on the profits under no infringement (P pNI) and infringement (E(P pI)bI = b˜ + e and E(P pI)bI = 1). Note that the derivatives depicting the impact of the exogenous variables on profits in Table 1 apply over all values of the exogenous variables and not just those associated with the starting point. An examination of the results in Table 1 permits a number of conclusions to be drawn about the choice made by the patentee. Consider first the impact of the validity parameter a. As a falls from its maximum value, profits in the no infringement case rise (note that g a b 0). Assuming 2P pD (b˜ )
P pM N 0, profits will fall in the infringement case where b I = b˜ + e, providing |g a | b 1. Profits will also fall in the infringement case where b I = 1, since 2P pD (1)
P pM N 0 if 2P pD (b˜ )
P pM N 0 (duopoly profits are higher, the larger is the quality chosen by the entrant). Thus, under the parameter values discussed above, the Table 1 Impact of b, a, P M p , C p and C e on the patentee’s expected profits Exogenous

Patentee’s expected profit

Variable

P NI p (b˜ ga )/(9a) (b˜ g b )/(9b) 0 0 (b˜ g C e)/(9C e)

a b PM p Cp Ce

E(P Ip)bI = b˜ + e M ˜ b˜(2P D p (b)
P p )(1 + g a ) 2 ˜2 2 D ˜ ˜ (ab g b )(2P p (b )
P M p )/(b)
(4a b )/(81b ) 1
ab˜
1 M ˜ (ab˜g C e )(2P D p (b )
P p )/(C e)

E(P Ip)bI = 1 M 2P D p (1)
P p 2
(4a )/(81b 2) 1
a
1 0

Table entries indicate the change that occurs in expected profits for a change in the exogenous variables. P D p (b) are the duopoly profits earned by the patentee when the entrant enters and chooses the optimal quantity qIe = (4ab)/ (9b) associated with patent breadth b; g a = (Bb˜ )/(Ba)(a)/(b˜ ) b 0 is the elasticity of b˜ with respect to a; g b = (Bb˜ )/ (Bb)(b)/(b˜ ) b 0 is the elasticity of b˜ with respect to b; and g C e = (Bb˜ )/(BC e)(C e)/(b˜ ) N 0 is the elasticity of b˜ with respect to C e.

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smaller is the validity parameter a, the more likely is the patentee to set patent breadth so as to not induce infringement. However, this result is not robust since profits under the infringement cases can rise with a fall in a under the right set of parameter values (i.e., when 2P pD (b˜ )
P pM b 0). The impact of the parameter b on the patentee’s choice of b is even less clear-cut. A rise in the R&D cost parameter b from its minimum value results in smaller profits for the patentee if infringement is not induced (note that g b b 0); profits will also fall in the case where infringement is induced and the maximum patent breadth is chosen (b I = 1). For the case where infringement is induced and the maximum patent breadth is not chosen (b I = b˜ + e), a rise in b will always lower profits if 2P pD (b˜ )
P pM N 0, although profits can fall even if this condition does not hold. Since a comparison of the magnitude of these profit increases requires additional information on the other parameters in the system, no general statement can be made about the impact of b on the patent breadth chosen by the patentee. The greater are the monopoly profits P pM , the greater is the patentee’s incentive to induce infringement, with the increase greatest for the case where b I = b˜ + e. Thus, larger monopoly profits can be expected to result in the patentee inducing infringement, since the only opportunity the patentee has to realize monopoly profits (when entry cannot be deterred) is when his patent is infringed and its validity is upheld during the infringement trial. As expected, the greater are the patentee’s trial costs C p, the greater is the loss from inducing infringement and the more likely it is that the patentee will choose a patent breadth that induces non-infringement by the entrant. Intriguingly, the greater are the entrant’s trial costs C e, the greater are the profits earned by the patentee in the no infringement case and in the infringement case where b I = b˜ + e (assuming 2P pD (b˜ ) N P pM ). If duopoly profits are small and monopoly profits are large (compare 1/9 to a(2P pD (b˜ )
P pM )), larger trial costs for the entrant can be expected to cause the patentee to choose non-infringement. This result occurs because larger trial costs for the entrant require a higher patent breadth b I to induce infringement (recall that (Bb˜ )/(BC e ) N 0) and this larger patent breadth reduces the probability that the patent will be found valid. As the probability of patent validity declines, the likelihood that the patentee will be able to realize the monopoly (duopoly) profits declines (increases). Thus, when the entrant’s trial costs are large, the greater (smaller) are the monopoly (duopoly) profits, the greater is the reduction in the patentee’s expected profits from infringement and non-infringement becomes more appealing to the patentee.

4. Concluding remarks The escalation of patent litigation in high technology industries and the increasing concern that the USPTO grants dweakT patents render the innovator’s patent breadth choice an important decision. The paper develops a simple game theoretic model to describe the patenting behavior of an innovator who, having invented a patentable drastic product innovation and having decided to seek patent protection, determines the breadth of protection that maximizes the innovation rents enabled by the patent. The starting point for

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this paper is the recognition that choosing the maximum patent breadth can increase the probability of the patent being found invalid. As a consequence, patent breadth becomes a strategic decision for the innovator. To determine the optimal breadth of patent protection claimed, the patentee chooses the breadth of protection that induces the desired behavior by the entrant. The patentee is foresighted and anticipates that he may have to incur costs to enforce and/or defend his patent rights. The model shows that the breadth of patent protection that maximizes the innovator’s innovation rents depends on the entrant’s R&D cost structure, the patentee’s and the entrant’s trial costs and the effect that patent breadth has on the probability that the validity of the patent will be upheld during an infringement/validity trial. These results are shown to be fairly robust to assumptions regarding the costs of relocation for the entrant. Contrary to what it is traditionally assumed, this paper shows that it is not always optimal for the patentee to claim the maximum patent breadth possible. The patentee will claim the maximum patent breadth if he cannot deter entry and the entrant always finds it optimal to not infringe the patent. When the entrant’s R&D costs are low and the effect of patent breadth on patent validity is small, infringement by the entrant is generally not optimal, even when the patent breadth is large and the entrant’s trial costs are low. Thus, under these conditions, the innovator is likely to choose the maximum patent breadth, since doing so results in reduced market competition (to not infringe, the entrant must choose maximum product differentiation, which relaxes competition). Maximum patent breadth protection may also be claimed under certain conditions (relatively small monopoly profits, intermediate entrant R&D costs) where the entrant will infringe the patent. The paper shows that maximum patent breadth is rarely associated with entry deterrence. If the patentee can deter entry, it is always optimal to do so—in almost all cases, this deterrence can be accomplished with a patent breadth that is less than the maximum breadth possible. Entry deterrence, however, is only possible when the entrant’s trial costs are high and her R&D effectiveness is low, implying that patents can only be used to justify modeling an industry as a monopoly under a very specific set of conditions. Our results are in contrast to the findings of entry deterrence models with endogenous capacity where large capacity can either deter entry or has no marginal value if entry occurs. In our model, a broad patent can, in most cases, invite entry while a relatively narrower patent can deter it. When entry cannot be deterred, the analysis shows that, in many cases, the choice of a narrower patent breadth can lead to the entrant choosing a product that results in greater product differentiation (and hence greater profits for both players) compared to a situation where a broad patent is chosen. This result occurs because when the entrant has high R&D costs and low trial costs a broad patent provides an incentive for infringement by the entrant, thus leading to dunder-locationT in the quality product space. The paper also shows that the consideration of socially optimal patent breadth needs to be restructured. While government can affect patent breadth, it can only do so through the resources that are made available to the Patent Office and through decisions made regarding R&D incentives and the nature of R&D court trials. An examination of the optimal government behavior would focus on the trade off between the resources spent on these factors and the impact they have on the industry participants.

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Further work is required to fully understand the patent breadth decision and its implications. For instance, the analysis assumes a trial always occurs if the entrant infringes the patent, regardless of the entrant’s location choice. However, if it is possible for the entrant to select a location so that a trial does not occur, then the entrant’s choice of location has an additional strategic element, namely whether to induce the patentee to initiate a trial. Knowledge of the entrant’s behavior will in turn affect the patentee’s patent breadth decision, thereby linking the patent breadth decision to patent litigation decisions. In addition, the analysis is performed under the assumptions of a single potential entrant and no ex ante or ex post licensing. The relaxing of these assumptions pose additional research questions concerning the mode of market entry (simultaneous or sequential), the patenting and patent breadth decisions of the potential entrants, as well as the strategic use of licensing as a substitute for patent litigation. For instance, while in our single entry model (or under a model of multiple simultaneous market entry) the entrant is always better off when the incumbent’s patent is invalidated, under a model of multiple sequential market entry, the first entrant might prefer licensing to having the incumbent’s patent revoked since patent invalidation could invite additional entry. The examination of the above issues is the focus of future research. Acknowledgement We would like to thank Rich Sexton for useful comments on earlier versions of this article and the editor Stephen Martin and an anonymous reviewer for helpful suggestions. A contribution of the University of Nebraska Research Division, Lincoln, NE, 68583. Journal Series No. 14632. This research was supported in part by funds provided through the Hatch Act. Appendix A A.1. Existence of patent breadth b˜ If a patent breadth b˜ that makes the entrant indifferent between infringing and not infringing the patent, while still generating positive profits for the entrant, exists, it NI ˜ I ˜ should satisfy the conditions b˜ a ( q*, e 1] and P e (b ) = E(P e (b )) N 0. The solution of 2 2 NI ˜ I ˜ ˜ ˜ P e (b ) = E(P e(b ))Z ((8a )/(81b) + (b)/(2))b
C e = 0 in terms of b˜ yields 
p(4)/(9)b ffiffipffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 9 4bF 2 b 16Ce a2 þ8bþ81Ce b2 . The root b˜ 1 ¼ the following two roots: b˜ 1;2 ¼ 16a2 þ81b2  pffiffipffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 9 4b
2 b 16Ce a2 þ8bþ81Ce b2 V0 8bN 49 ; aað0;1Þ1Ce z0 and it is thus rejected since q*e b 16a2 þ81b2  pffiffipffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2  9 4bþ 2 b 16Ce a2 þ8bþ81Ce b z0 8bN 49 ;aað0;1ÞCe 0 and it is accepted b˜ V 1. The root b˜ 1 ¼ 16a2 þ81b2  pffiffipffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 9 4bþ 2 b 16Ce a2 þ8bþ81Ce b2 as a possible solution. If b˜ ¼ exists, it should also satisfy the 16a2 þ81b2 I ˜ ˜ conditions q*e b b˜ Vp1, P eNI(b˜ ) N 0 and E(P  e(b)) N 0. The condition b N q e* is satisfied since pffiffi ffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 9 4bþ 2 b 16Ce a2 þ8bþ81Ce b2
4 N 0 8 b N 4 ; a a ð0;1Þ1Ce z 0. The condition b˜
q*e ¼ 2

16a2 þ81b

9b

9

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b˜ V 1 is satisfied for certain combinations of b, a and C e. To determine the combinations of b, a and C e values which satisfy the condition b˜ V 1, the pairs of b, a and C e values that satisfy the above constraint as an equality (b˜ = 1) are determined first. The solution of b˜ = 1 16a2
72bþ81b2 with respect to C e yields Ce ¼ . The combination of b and C e values, for a 162b given a value, for which b˜ = 1 is represented by the locus b˜ = 1 in Fig. 3. The area to the right of the locus b˜ = 1 represents all combinations of b and C e values, for a given a value, for which b˜ b 1. If b˜ exists it must also satisfy the conditions P eNI(b˜ ) N 0 and E (P eI (b˜ )) N 0. Thus, b˜ must violate the entry deterrence condition—b˜ must take values in the interval b˜ I b b˜ b b¯ NI when b z (8)/(9) (i.e., when b¯ NI exists) or in the interval b¯ I b b˜ when (4)/(9) b b b (8)/(9) (i.e., when b¯ NI does not exist). To determine the combination of b, a and C e values for which b¯ I b b˜ b b¯ NI, the locus b¯ I = b¯ NI must first be determined. The qlocus ffiffiffiffiffiffiffiffiffiffi 8 b¯ I = b¯ NI depicted in Fig. 3 refers to the pairs of b, a and C e values for which ¼ 81C2e b 9b

8a

holds true. Solution of the above condition with respect to C e yields: C e = (512a 2)/ (6561b 3). All combinations of b and C e values, for a given a value, below the locus b¯ I = b¯ NI and to the right of locus b = (8)/(9) are such that b¯ I b b˜ b b¯ NI while all combinations of b and C e values, for a given a value, below the locus b˜ = 1 and to the left of locus b = (8)/(9) are such that b¯ I b b˜ . Given the above, b˜ exists for all combinations of b and C e values, for a given a value, in the area below the locus b˜ = 1 and below the locus b¯ I = b¯ NI represented by the vertically hatched area in Fig. 3. This case is also depicted in Fig. 2, panel (iv). A.2. The effect of b, a and C e on b˜

pffiffiffi

  pffiffiffi  2 2 pffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Ce 16a þ 81b2 þ 8 2 2b þ b 16Ce a2 þ 8b þ 81Ce b2 9 16a2
81b2 Bb˜ ¼ V0 pffiffiffipffiffiffi 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffi Bb 2 b 16a2 þ 81b2 16Ce a2 þ 8b þ 81Ce b 4 8bN ;aað0;1Þ1Ce z0: 9

pffiffiffi  pffiffiffi pffiffiffi  pffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 144a b 2Ce 16a2 þ 81b2 þ 8 2 2b þ b 16Ce a2 þ 8b þ 81Ce b2 Bb˜ ¼
b0  2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffi Ba 16a2 þ 81b2 16Ce a2 þ 8b þ 81Ce b 4 8bN ;aað0;1Þ1Ce z0: 9

pffiffiffi Bb˜ 9 b 4 ¼ pffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffi N0; 8bN ;aað0;1Þ1Ce z0: BCe 9 2 16Ce a2 þ 8b þ 81Ce b

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