Electronic copy available at: http://ssrn.com/abstract=2489709

Do More Patents Mean Less Entry?

(Patenting strategies in cumulative innovation under the

threat of litigation)

Henri de Belsunce∗

August 29, 2014

Abstract

This paper investigates the entry decision of a firm into a marketthat is protected by a patent. It shows how entrants use the possibilityto study existing prior art before taking their entry decision. Studyingprior art reduces the information asymmetry that arises due to thefact that patent strengths are private information. The paper analysesthe incumbent’s incentives to pursue a raising rivals’ cost strategy byexcessive patenting. The application of the model shows that the trebledamages doctrine reduces the incentives for an incumbent to patentexcessively.

Keywords: Strategic Patenting, Cumulative Innovation, Treble Damages,Litigation, Reading Patents, Design-Around

JEL Codes: K41, O31, L12

∗International Max Planck Research School on Competition and Innovation - Munich.Email: henri.de-belsunce@imprs-ci.ip.mpg.de. The usual disclaimer applies.

Electronic copy available at: http://ssrn.com/abstract=2489709

1 Introduction

Over the last decades, we have witnessed an explosion1 of the size of patentportfolios that firms demand through patent filings or acquire via financialtransactions. Among these, numerous patents are commercially and evenlegally worthless2.

The lack of standards at the patent office has been lamented by manyscholars, e.g. Gallini (2002), Shapiro (2001), Bessen (2003). Also, theUS Supreme Court has acknowledged the ”notorious difference between thestandards applied by the Patent Office and by the courts” (Meurer, 1989).As a result, a high number of patent disputes end up in court and almosthalf of the litigated patents are held invalid when contested in court (Alli-son and Lemley, 1998). Effectively, the true opposition of patents occurs incourt and firms innovate under the threat of litigation.

In case of litigation, the opposing parties contest the validity of a patent inlight of the existing knowledge, i.e. prior art. Prior art is often contained inmultiple patents and claims and thus in practice, the litigation process op-poses patent portfolios. The court rule in favour of or against an incrementalinnovation depends on the value-added of the new innovation relative to thevalue of the prior art, i.e. on both the quality of the new patent as well asthe strength of the patents composing the prior art (Llobet, 2003).

Although a patent is publicly available, its patent strength is private infor-mation. Thus, an information asymmetry arises between owners of differentpatent portfolios and the larger a portfolio, the stronger the informationasymmetry concerning that portfolio will be. Only a costly3 effort of search-ing and studying existing patents gives an indication of the strength of priorart.

These facts suggest the argument that firms use patents as strategic tools incompetition. This paper aims to respond to the following questions by ex-ploiting a model framework that explicitly simulates the litigation decisionof courts and respects the private character of the information on patent

1US patent grants have increased by 58% over the 5-year period from 2008 to 2013,the ratio of grants per applications was 47.8% in 2012 (Data from the US PTO PatentMonitor as of June 2014).

2Referring to patents that have no impact on profits and which would be invalidatedwith certainty if contested in court. For a detailed account on worthless patents, seeMoore (2005).

3Studying of a patent is costly in effort for any reader. Furthermore, ”not being engagedin the development process, a competitor is likely to know less about the content of theprior art (Meurer, 1989)”. Also, the mere search for prior art may be costly, since thedisclosed prior art in a patent is often insufficient. For critiques on the low performanceof disclosure in patents, see Merges (1999) and Kitch (1977).

1

qualities. First, do more patents mean less entry? Is it possible to ratio-nalise excessive patenting of low quality ideas? Second, when is it profitablefor incremental innovators to invest in the studying of competitor patents?

Furthermore, when a court adjudicates an infringement of prior art, theinfringer has to pay damages to the rightful owner of the intellectual propertyright. A discrepancy arises here between the US and European treatmentof infringement findings. In case of a wilful infringement, a US court maytreble the damages to be paid to the defendant (§284 United States Code 35,2006).

A famous concern about the treble damages doctrine is that it discouragesfirms from reading competitor patents (FTC, 2003; Lemley, 2008; Lemleyand Tangri, 2003). When firms stop reading existing patents, the information-sharing nature of the patent system is undermined and therefore costly tosociety4.

We are hence interested in a third research question, namely how does thetreble damages doctrine affect the strategic use of patents by existing andfuture patent holders? This question is specifically addressed in the appli-cation of the model in section 4.

This paper shows by comparative statics that the incumbent benefits fromreduced entry when it decides to patent excessively. This follows from araising rival’s cost argument by which screening costs of the entrant areaffected. When screening is imperfect, screening becomes more costly to theentrant as both false positive and false negative errors occur with positiveprobability in equilibrium. The two types of errors are unequally expensive.The discrepancy between the two types of errors increases the variability ofthe cost base that the entrant faces. This reduces, in proportional terms, thecost variation that the incumbent can induce using an excess patent.

The treble damages doctrine multiplies the cost of false positive errors only.Consequently, the treble damages doctrine reduces the marginal benefit ofan excess patent and, hence, the incentives to do so for the incumbent. Thereduction in excess patenting, however, comes at the cost of making thestudy of competitor patents less attractive to entrants.

The contribution of this paper is a simple and tractable model to analyse theeffects of excessive patenting on the screening and entry decision of potential

4“Failure to read competitors’ patents can jeopardize plans for a noninfringing businessor research strategy, encourage wasteful duplication of effort, delay follow-on innovationthat could derive from patent disclosures, and discourage the development of competition”(FTC, 2003).

2

rivals. The model is particularly suited to study the effects of the highlycontested treble damages doctrine. The application of the model allows toshed light on the policy trade-off that decision-makers face when debatingthe utility of treble damages.

It shows that treble damages have the positive effect of reducing the ex-cess patenting incentives of incumbents. This is notable if policy makers areconcerned about the strain on the patent office due to the flood of patent fil-ings. However, the reduction in excess patenting incentives comes at the ex-pense of the effectiveness of the patent system in sharing innovation-relatedknowledge. Consequently, positive externalities for society arising from theinformation-spreading nature of patents are reduced under a treble damagesregime.

This paper draws on multiple strands of both the legal and economic litera-ture. It provides a model on the economic implications of the treble damagesdoctrine in order to support a highly active legal debate. The model uses el-ements from the economic literature on probabilistic patents and litigation,searching and reading prior art, as well as entry deterrence.

A few papers a particularly notable for the modelling of probabilistic liti-gation, where our model generally differs in the sense that uncertainty inlitigation does not come from probabilistic patent strengths, but from theimperfect information concerning these strengths. Furthermore, the appli-cation of a theoretical framework to investigate the impact of treble damagesis novel.

Llobet (2003)’s market structure and modelling of the litigation procedureis adopted here. Llobet is interested in observing how the litigation and set-tlement opportunities affect the optimal licensing rate, where as this paperfocuses on how the structure of the patent system affects patenting strate-gies. Furthermore, this model assumes perfectly competent courts (no signalnoise in observing patent strengths) and no settlement possibility.

Green and Scotchmer (1995) use a similar setting to investigate the differ-ence between ex-ante and ex-post royalty setting between an incumbent andan infringing entrant. They focus on how the patent system can instil suf-ficient investment incentives for the incumbent to conduct R&D in the firstplace. This paper has a different focus, namely to investigate the inherentincentives of the patent system to use patents strategically and the use oftreble damages as a policy instrument.

Meniere and Parlane (2008) look at stochastic innovation and the opposi-tion of patent portfolios in litigation in order to derive optimal infringementpenalties. This paper differs in the sense that it respects the private charac-ter of patent strengths and investigates the trade-off for an entrant to invest

3

in learning the quality of the opponent’s portfolio strength as well as thetrade-off for an incumbent to pre-empt market entry by costly, excessivepatenting.

A second relevant strand of the literature for this paper is the one concern-ing the investigations into when firms invest in the reading of competitorpatents. This paper sets itself apart by investigating the search and studydecision in a strategic context of pre-emptive patenting. Its focus on thetreble damages doctrine is novel and contributes to a vibrant debate. Ataland Bar (2010) analyse the search and study incentives of innovators vis avis the patent office. Langinier and Marcoul (2007) focus on using the effortof patent examiners as a policy tool to improve prior art disclosure in patentfilings. Caillaud and Duchene (2011) study the overload of the patent officewhile focussing on examination fees and toughness as policy tools.

Moreover, the classical I.O. literature (initiated by Salop and Scheffman(1983)) on entry deterrence by means of raising rivals’ cost arguments de-serves a brief mention. The present model puts the traditional mechanismsinto the current institutional context of the patent system and investigatesthe response of players using such strategies with respect to treble damagesas a policy tool. In can hence be seen as a reinterpretation of the basic ideasfrom a raising rivals’ cost consideration a la Gilbert and Newbery (1982),where this paper uses a different set-up to focus on the private nature ofinformation on patent strengths. In contrast to their paper, we can thusrationalise the excessive patenting of worthless ideas by incumbents and seehow this strategy performs in a context where courts award treble dam-ages.

Other relevant papers are Meurer (1989) and the report by the FTC (2003)which motivate much of the analysis. Choi (1998) investigates the signallingeffect of litigation. The free information externality that arises when a firstentrant litigates a patent and reveals the strength of the incumbent’s patentto other potential entrants, results in suboptimal litigation incentives foroutsiders. We draw on this paper’s (and others’, which are mentioned whenneeded) insights in the discussion of our results.

The paper proceeds as follows: In section 2, the model set-up is proposed.Section 3 presents the results for both the settings of perfect and imperfectscreening. In section 4, we apply the model to shed light on the effect of thetreble damages doctrine on the behaviour of both incumbent and enteringfirms. Section 5 looks at extensions and robustness of the model, section 6discusses the results. Section 7 concludes.

4

2 Model set-up

The model opposes an incumbent (I) and an entrant (E). The model relieson two institutional aspects of the patenting system that were introducedin the introduction:

First, patent strength is private information, but publicly observable. Thismeans that a competitor must spend a costly effort S > 0 to study anexisting patent in order to learn its strength. However, the number of patents(N) that a competitor holds is observed for free.

Second, patents are granted by the patent office without proper scrutiny.In the model, the argument is taken at the extreme and any idea (evenworthless ones) will be granted a patent. The true opposition of patentsoccurs in court. Thus, cumulative innovation occurs under the threat oflitigation.

2.1 Storyline

I earns profits from the sale of a product that generates an exogenous con-sumer valuation of vI . I’s market (or production technique) is protected bya patent portfolio of breadth b. Furthermore, I has a reputation to litigateon IP issues.

E has an idea to enter the market by engineering around5 existing IP. E’sentry generates a small exogenous increase in the consumer valuation vE . Egets a patent of quality qE for its alternative production technology6.

Given I’s commitment to litigate, E’s entry triggers litigation on infringe-ment of I’s patents. The court decides if infringement has occurred andwhether damages have to be paid. Market entry is only profitable for the Ewhen it wins in the legal process, i.e. the design-around does not infringethe existing patents of the incumbent.

2.2 Litigation

In litigation, we have an opposition of succeeding patents (infringementsuit). In the context of design-around market entry, both the incumbent’sand entrant’s patents describe different ideas to produce the same output.The entrant’s patent may not infringe on the claims of the incumbent patent,

5The invention of an alternative idea that produces the same output as a given patentedidea, while not infringing the original patent’s claims.

6The insights of the paper remain the same if the entrant does not obtain a patent,but merely produces the output using an alternative production technology.

5

i.e. the entrant’s quality qE must be sufficiently large the overcome thepatent breadth b of the incumbent’s patent portfolio. In other words, thecourt investigates whether the idea of E’s design-around is sufficient “far”away from I’s idea, which is protected by a patent portfolio of radius b. Inmodelling terms, this means that both b and qE are both drawn from thesame interval [0, q]. More on this in subsection 2.3.

During the legal process, the court observes the true qualities of the patentsin question and will decide in favour of the stronger patent. This is based onthe idea that for an infringement case, a better engineering around idea hasa higher chance of surviving the legal enquiry. In the same logic, a strongerincumbent patent (e.g. broader and more general claims) will reduce thesurvival chances of the entrant’s patent in court.

Given perfect courts, the litigation technology is deterministic. The proba-bility of the entrant’s patent not being invalidated is given by a thresholddecision rule:

m = P{qE > b} =

{1 if qE > b0 if qE < b

where b is the strength of the incumbent’s existing patent and qE is thestrength of the entrant’s patent. We have ∂m

∂qE> 0 and ∂m

∂b < 0.

Figure 1 shows the ex-post probability of validity of the entrant’s patentbased on the realised portfolio strength b of the incumbent.

m

qE

1

0 0 q _ b

½

Figure 1: Deterministic litigation technology

The court has a re-distributional character. Under litigation, the total sur-plus generated by the producers is dispatched. During the litigation, themarket structure generates payoffs as described below in the subsection 2.6.In case of infringement, the entrant has to compensate I for the lost profits(vI). This corresponds to single damages. The variation to treble damages isintroduced and analysed in the application of the model in section 4.

Furthermore, going to court is inefficient as litigation costs K > 0 arise andwill be borne by the loser of the case. This corresponds to the legal doctrineon the burden of litigation costs as practised in most European countriesand does not match the analysis of treble damages which is a US concept.

6

However, it simplifies the analysis and is thus used in this initial model. Therobustness of the model to this specification is shown in section 5.

2.3 Innovation

The general technology for innovating is as follows. The idea for an in-novation is obtained for free, but in order to realise the advantages of aninnovation, the innovator must develop the idea into a patent and implementit at a cost ci, i ∈ {I, E}. The quality of an innovation qi is drawn froma uniform distribution U(.) on support [0, q]: qi ∼U[0, q]. The distributionand its support are common knowledge.

For the entrant, this means that it learns the idea for a design-around and itsquality qE ∼U[0, q] for free. Implementing the design-around costs cE > 0.E knows qE since it knows the existing technology (which it is trying toimitate) and the direction in which it is engineering around. However, Edoes not know the breadth b of the patents which I holds to protect itsIP.

For the incumbent, this means the following: Its existing patent portfolioof size N is protecting its IP with a breadth of b. Implementation costs forthis portfolio are sunk. Although I knows the individual patent qualities qIof the patents that compose its protecting portfolio, it does not know thebreadth of the overall protection b which it actually enjoys, because entryby design-arounds can occur in many different directions and I does notknow in which direction to measure it. We therefore consider that b (theaggregate patent breadth of I) is drawn from the same distribution as qE(the quality of the entrant’s patent) since they read on the same distance,namely how “far” the design-around is “away” from the original idea. Thuswe have b ∼U[0, q], where I does not know its own “type”.

The excess patent for the incumbent is a particular case: I gets an ideato patent a commercially and legally worthless idea (qI = 0) at an imple-mentation cost cI > 0. Given that it is worthless, neither the aggregateportfolio strength b, nor the consumer valuation that I’s product generatesvI is affected. In equilibrium, E is aware that the additional patent is worth-less, however E cannot distinguish it from valuable patents ex-ante (e.g. theworthless patent was filed simultaneously with the valuable patents7).

7The excess patent can also be thought of as the costly effort by the incumbent to splita single patent claim into multiple patents of smaller complementary claims.

7

2.4 Screening

By studying (“screening”) its opponent’s patents, E can learn b, the strengthof the existing patent portfolio of I. This gives E an indication of theoutcome of the litigation in case entry occurs. Screening costs S(N) > 0and depends positively on the size N of the patent portfolio to be screened8

(∂S(N)∂N > 0).

When not screening, the entrant forms an expectation E[b] based on thecommon knowledge about the distribution that b is drawn from. The costlessestimate of the incumbent’s patent strength is given by

ˆb = E[b] =

∫ q

01dU(b) =

q

2

When E screens, it delays its entry decision and observes a signal (message)m : {b ; qE} → {1 ; 0} on how the courts will decide the infringement case.The action of screening is private9. Initially, we consider perfect screening:E observes m without imprecision.

m = m =

{1 if qE > b0 if qE < b

where m is the true information on the court decision. Therefore, paymentof the screening fee erodes uncertainty about I’s patent portfolio strengthand allows E to take a more informed entry decision.

A technical assumption is made to obtain that screening occurs with positive

probability in the baseline: S < S = ∆(

1− ∆vI+K

), which interprets as

screening is not prohibitively costly and where ∆ = vE − cE representsthe net benefit from non-infringing entry for E. This implies that avoidinginfringement by screening and then deciding not to enter is profitable: ∆−vI −K < −S.

8The story behind this asumption is that the entrant screens a subsample of I’s patentportfolio to learn a signal m. The precision of the signal depends on the proportion of thefull portfolio that is screened. A larger patent portfolio is thus more costly to screen forE, because either the entrant screens a larger subsample (thus paying more for screening)or the entrant does not increase the size of the screened subsample, but accepts a decreasein the precision of the signal m (which increases the likelihood of screening errors).

9This is realistic as patents are public and their study occurs in the absence of thepatent holder’s knowledge. This assumption is necessary to exclude the signal (of whetherscreening has occurred or not) to I in this model since it would reveal information aboutthe quality of E’s patent.

8

2.5 Mechanism

The channel of the effects goes through the screening of the entrant. Bydemanding an excess patent, I can increase the number of patents that Ehas to screen if it decides to do so. Screening costs to E therefore increasefrom S(n) = s to S(n+ 1) = s(1 + τ), τ > 0. In other words, I can use theexcess patent as a raising rival’s cost strategy.

2.6 Payoffs and notation

We assume Bertrand competition between the firms. From before, we havethat I generates a consumer valuation of vI . The unit consumer has utilityu(v) = v − p. We focus on the case where E’s entry marginally increasesthe consumer valuation by 0 < vE < vE = vI+K

2 + cE . The upper boundon vE ensures that, ex-post, market entry is only profitable for E when itsdesign-around technology is deemed non-infringing by the courts. Ex-ante,entry without screening is only profitable when infringement is sufficientlyunlikely: qE > E[b].

We simplify notation as follows: vI = v, cI = c. The Incumbent earnsΠMI (v) = v if it produces alone. If only the entrant produces, then it earns

ΠME (v,∆) = v + ∆. Under a duopoly, the profits are ΠD

I (v,∆) = 0 andΠDE (v,∆) = ∆. Under litigation, single damages payments lead to the fol-

lowing ex-ante payoffs:

ΠlE = ∆− (v +K)P{b > qE}

ΠlI = v − (v +K)P{b < qE}

2.7 Timing

The timing is as given by the game tree shown in figure 2 (cubic decisionnodes belong to nature):

1. The incumbent I has the option to demand the grant of a commerciallyand legally worthless patent. Thereby, its portfolio size increases fromN = n to N = n+ 1.

2. The entrant E obtains a design-around idea of quality qE for free.

3. E decides whether to screen I’s patent portfolio to learn a signal mabout the outcome of the litigation (b ≶ qE).

4. E decides whether to enter the market or reject the design-around.

5. If market entry occurs, litigation arises. The court adjudicates onwhether infringement has occurred and, if so, redistributes profits.

9

I

N=n

E

N=n

+1

with

scre

enin

g,

S

= s

I win

s (b

>qE)

E wi

ns

(b<q

E)

E q E

~ U

[0, q

]

with

scre

enin

g,

S

= s(1

+τ)

no

scre

enin

g,

S=

0

E en

try

(EN

) no

entry

(NE)

no

scre

enin

g,

S=

0

E en

try

(EN

) no

entry

(NE)

E en

try

(EN

) no

entry

(NE)

E en

try

(EN

) no

entry

(NE)

E en

try

(EN

) no

entry

(NE)

E en

try

(EN

) no

entry

(NE)

I win

s (b

>qE)

E wi

ns

(b<q

E)

_q E

~ U

[0, q

] _

Fig

ure

2:F

ull

gam

etr

ee

10

In the game tree, the entry subgame starts at t = 3. We differentiate theentry subgame absent an excess patent (N = n, right-hand-side of the gametree) and the entry subgame given an excess patent (N = n+ 1, left-hand-side of the game tree).

3 Model Results

All proofs are given in the Appendix, starting on page 29.

3.1 Under perfect screening

Assuming that the entrant can perfectly learn the strength of the opposingpatent portfolio when screening and, hence, does not make errors when an-ticipating the court’s rule, we obtain the following results.

Lemma 3.1 (Optimal strategy for the entrant)In the entry subgame absent an excess patent (N = n), the entrant has anoptimal, composite strategy (σ∗E) conditional on the realisation of the qualityof its idea (qE).

σ∗E =

No Screening, No Entry (NS, NE) if qE < q

SScreening, then Deciding (S, D) if q

S< qE < q

TNo Screening, ENtering (NS, EN) if q

T< qE

Figure 3 illustrates the composition of the strategy. The optimal strategy toE is given by the upper envelope of the strategy payoffs. In the graph, thethresholds have an additional upper index of 0 to indicate that they resultfrom the perfect screening specification.

For qualities less than qS , E will stay out of the market without screening.For qualities above qT , E will enter the market without screening. For inter-mediate qualities between qS and qT , E will screen I’s patent portfolio andenter only in case of no infringement (i.e. qE > b) and stay out otherwise.

Proposition 3.2 (More patents mean less screening)An excess patent by the incumbent increases screening costs for the entrantand reduces the range of qualities for which the entrant screens.The optimal strategy for the entrant given an excess patent (N = n + 1) is

11

Figure 3: Expected payoffs to E plotted against the quality of its idea qE

given by

σ∗E′ =

NS, NE if qE < q

S′

S, D if qS′< qE < q

T ′

NS, EN if qT ′< qE

where qS′> q

Sand q

T ′< q

T.

The impact of an excess patent is illustrated in figure 4. It becomes imme-diately visible that the induced increase in screening costs causes a constantdownward shift of the expected payoff function under screening. Thereby,it impacts on both thresholds qS and qT , which move closer together andreduce the range of qualities over which E screens.

In figure 4, A represents the range over qE for which E switches strategyfrom S,D to NS,NE, i.e. stays out instead of screening. B represents therange where E changes from S,D to NS,EN, i.e. from screening to entrywithout screening.

Proposition 3.3 (Less screening means less entry)In the setting of a design-around, where the entrant’s product generates onlya marginal increase in consumer valuation, less screening translates into lessentry:

|A| > |B|

12

A

B

Figure 4: Impact of an excess patent on E.

The graphical intuition behind proposition 3.3 is that A is measured di-rectly against the qE-axis (= E[ΠE |NS,NE]), where as B is measured againstE[ΠE |NS,EN] of increasing slope. Translated onto the qE-axis, B is smallerthan A, because the difference in slopes (between E[ΠE |S,D] and E[ΠE |NS,EN])is sufficiently large when infringement is sufficiently expensive for E.

Lemma 3.4 (Excess patenting incentives for the incumbent)The incentives for the incumbent to produce an excess patent for the purposesof raising rivals’ costs of screening are given by:

−c+Sτ

∆

v +K

2≥ 0

The condition interprets as follows: The cost c of demanding an excesspatent must be set off by the expected benefit v+K

2 that I gets from reducingE’s screening incentives times the probability Sτ

∆ that its strategy will havean impact on E.

13

3.2 Under imperfect screening

By introducing screening errors, we move away from the assumption thatthe entrant can perfectly anticipate the court’s decisions. This is morerealistic since perfect screening is likely to be prohibitively costly in reallife. This setting will be useful to analyse the treble damages doctrine sinceit yields the result that infringement occurs with positive probability inequilibrium.

The entrant now screens with an exogenous precision of g < 1. Id est, thesignal m that E observes on the patent portfolio strength of the incumbentis wrong with a probability (1−g). Consequently, E takes a misguided entrydecision with the same probability10.

Lemma 3.5 (Costs of screening errors depend on their type)Imperfect screening introduces type I (false positive) and type II (false negative)errors in the entrant’s entry decision post screening, where

E[Cost of a type I error] > E[Cost of a type II error]

Lemma 3.6 (Screening errors reduce the use of screening)In the entry subgame absent an excess patent (N = n), given screeningerrors, the entrant has an optimal, composite strategy (σ∗E) conditional onthe realisation of the quality of its idea (qE).

σ1∗E =

NS, NE if qE < q1

SS, D if q1

S< qE < q1

TNS, EN if q1

T< qE

where q1S> q

Sand q1

T< q

T. Id est, the entrant reduces the range of qualities

qE over which it screens before taking the entry decision.

Screening errors impose an additional cost on the screening strategy11 forthe entrant, similar to the excess patent analysed above. In line with theprevious interpretation, a downward shift of E[ΠE |S,D] occurs and the rangeover which the entrant screens decreases likewise.

10The error probability (1− g) is restrained to be sufficiently small such that the equi-librium strategies in the screening subgame (conditional on the reading signal m of I’spatent portfolio strength) are unchanged. For details see Assumption 7.1 on page 35.

11As in the perfect screening setting, screening costs are restrained to be sufficientlysmall to observe screening with positive probability in equilibrium, i.e. S < S. For theprecise condition under imperfect screening see assumption 7.2 on page 37.

14

Figure 5: Impact of screening errors on E.

However, an additional effect occurs due to the discrepancy between thecostliness of the two types of errors that can be made due to a false positiveor negative screening signal (m): The downward shift of E[ΠE |S,D] is left-side heavy, i.e. the expected payoffs fall more for low qualities and therebythe slope of the function increases.

The result is driven by the assumption that the design-around only marginallyimproves the consumer valuation for the product. Consequently, the errorof entering while liable for infringement is more expensive than the errorof staying out of the market when in fact no infringement would have beenadjudicated to I by the courts. The graph in figure 5 visualises this analysis.

Corollary 3.7 (Less screening means less entry)Given imperfect screening, Proposition 3.3 holds true.

The intuition behind Corollary 3.7 is that excess patents act as a substituteto screening imperfections since both factors represent an additional cost onscreening. As screening becomes relatively more expensive, it is used lessin equilibrium, leading to the reduction of entry when entrants switch fromscreening (and then deciding on entry) to staying out straight away.

15

Proposition 3.8 (Steeper slope reduces excess patenting incentives)Given imperfect screening, screening becomes more costly for the entrant andthus is used less by the entrant, resulting in less entry (Corollary 3.7). Con-sequently, the excess patenting strategy becomes less profitable for I, since

A1 < A

where A = qS′− q

S, and A1 = q1

S′− q1

S.

The incentives to excessively patent for the incumbent are given by(gSτ

g∆− (1− g)(∆− v −K))

)[v +K

2

]− c ≥ 0,

a condition which is more stringent than the one given in Lemma 3.4.

Proposition 3.8 yields that the effect of an excess patent is reduced in asetting with imperfect screening as compared to a perfect screening set-ting.

This is because the reduction in entry that the excess patent commands isreduced in a setting where the entrant makes screening errors. The shifts(termed A and A1) of the intercept of E[ΠE |S,D] with the qE axis deter-mine by how much entry is reduced when the incumbent demands an excesspatent.

As the slope of E[ΠE |S,D] increases under imperfect screening, the downwardshift of the function by a constant shift Sτ results in a smaller shift of q

Sto q

S′(given by the intersections of E[ΠE |S,D] with the qE axis). Figure 6

visualises this effect12.

The intuition behind this mechanism is that, when screening errors occur,the variability of the profits ΠE , that the entrant can earn, increases13.Given a larger range of expected profits (and consequently costs) for E, thesame constant increase of a single cost factor loses importance in the overallentry decision. In other words, E bases its entry decision not only on thescreening costs, but also on the cost of (the newly introduced) screeningerrors. The constant change in screening costs now makes up a smaller pro-portion of overall costs and, thus, the raising rival’s cost measure of excessivepatenting loses effectiveness.

12The increase in entry given by the shift of length B1 of the threshold q1T to q1

T ′ isneglected here in the text since under the considered European litigation cost regime,the strategy change from S,D to NS,EN has no profit implication for I. The results arequalitatively unaffected if a US cost regime is assumed. Robustness is shown in section 5.1.

13I.e. the range E[ΠE |S,D]∣∣qE=q

− E[ΠE |S,D]∣∣qE=0

increases.

16

A1 B1 A

B

Figure 6: Steeper slope reduces effect of an excess patent.

4 Application: Treble damages

4.1 Institutional framework

The proposed model framework allows to analyse the effect of the trebledamages (TD) doctrine. A quote14 from the FTC (2003) motivates thisapplication:

[Pursuant to 35 U.S.C. §284,] a court may award up to threetimes the amount of damages for a defendant’s wilful infringe-ment of a patent - that is, the defendant knew about and in-fringed the patent without a reasonable basis for doing so15.Some Hearings’ participants explained that they do not read

14Parts in square brackets [] have been sourced from a different part of the same source.15[Ryco, Inc. v. Ag-Bag Corp., 857 F.2d 1418, 1428 (Fed. Cir. 1988) (The test

is whether, under all the circumstances, a reasonable person would prudently conducthimself with any confidence that a court might hold the patent invalid or not infringed.)]

17

their competitors’ patents out of concern for such potential tre-ble damage liability16,17.

Furthermore, the FTC (2003) mentions that

recent data suggests that courts enhance damages in a significantpercentage of decisions that find infringement18. [Data] from therecords of all patent cases tried from 1983 through 1999, showa finding of willfulness in 39% of the 888 decisions that foundinfringement and enhanced damage awards in 70% of the 219cases in which judges considered enhancement issues.

Consequently, it attributes a “disproportionately large in terrorem effect”to the treble damages doctrine as testified by panelists.

4.2 Adapting the model set-up

In the model, the treble damages doctrine is translated as follows: When afirm screens and reads the wrong signal m on the outcome of the litigationprocess and enters, the courts will award treble damages to the incumbentas a compensation for the infringement.

Without going into the practical, legal details on how courts know that Escreened19, this application models the state of affairs of the US patent sys-tem as perceived by the firms in the market and described in the quotationsfrom the FTC (2003). It is hence assumed that a screening error can besanctioned with treble damages although entry is based on a screening errorand not on a deliberate decision to enter. Courts can here not distinguishbetween the two types of mal-entry. The provided quotations suggest thatfirms hold this belief in reality and adjust their strategies accordingly.

16[Panelists expressed considerable dissatisfaction with a state of affairs that in effectexposes firms to greater potential damages for trying to learn if they are infringing anypatents than if they keep themselves blissfully ignorant.]

17[Many firms discourage employees from reading patents out of fear of wilful infringe-ment.]

18See Kimberly A. Moore, Judges, Juries, and Patent Cases An Empirical Peek Insidethe Black Box, 11 FED. CIR. B.J. 209 (2001)

19“Plaintiff must prove willfulness by clear and convincing evidence. This is a higherdegree of persuasion than is necessary to meet the preponderance of the evidence standard.Plaintiff proves willful infringement if it shows that defendant (1) was aware of plaintiff’spatent and (2) had no reasonable basis for reaching a good faith conclusion that its making,using or selling its device avoided infringing the patent. Plaintiff may also prove willfulinfringement by proving that defendant did not exercise due care to determine whether ornot it was infringing plaintiff’s patent once the defendant had actual notice of plaintiff’spatent. Infringement is not willful and deliberate if defendant had a reasonable basis forbelieving that the patent is invalid or not infringed.” Quote from the 5th Circuit PatternJury Instructions - Civil under Chairman Judge Martin C. Feldman, 2006.

18

4.3 Applied model results

Lemma 4.1 (Treble damages multiply the cost of type I errors only)In a setting where screening is imperfect, the introduction of treble damagesacts as a multiplier on the cost of type I errors (false positives) only. Conse-quently, the slope of the payoff function from screening increases as it forcesa left-side-heavy translation of the expected payoff function under screening.

Graphically, the introduction of treble damages forces an increase in slopeof the screening payoff function similar to that described in figure 5. Thedifference is that the translation of the expected payoff function under trebledamages shifts down the intercept of E[ΠE |S,D] with the ΠE-axis, while itdoes not change the value of E[ΠE |S,D] at qE = q.

Corollary 4.2 (TD reduce screening and thereby entry by E)TD reduces the range over which E screens due to the (left-side-heavy) down-ward shift of the screening function.

The intuition behind corollary 4.2 is analogous to that of corollary 3.7,namely that the strategy of screening has become more expensive and is thusused less in equilibrium. In the present setting, the reduction of screeningleads to less market entry by potential rivals.

Corollary 4.3 (TD reduces excess patenting incentives for I)The LHS translation of the screening function increases its slope and thusdiminishes the reduction of entry that an excess patent can command (in-tercept on qE axis is reduced)

A1 > A1TD

Furthermore, treble damages increase expected profits to I when E screens,thus further decreasing excess patenting incentives.

Two effects come into play (even in the European litigation cost setting),when treble damages are introduced. This is because both shifts of thethresholds q2

S and q2T have a profit implication for I and are thus rele-

vant20.

Both effects go in the same direction and reduce the excess patenting incen-tives of I. The first is analogous to the one analysed before, namely that

20The superscript 2 refers to the case when TD are included.

19

the cost impact commanded by an excess patent is reduced. The secondand new effect is that treble damages increase the expected profit of theincumbent when the entrant has screened. Hence, the shifting together ofboth the left and right hand side boundaries of the screening interval is rel-evant. The shifts reduce the (now profitable for I) screening strategy by Eand thereby further reduce the incentives for the incumbent to excessivelypatent.

5 Extensions and robustness checks

5.1 US litigation cost setting

In the baseline model, EU litigation cost splitting has been considered. Thissimplifies considerably the terms of the calculations in the output.

With the European splitting of legal costs under single damages, the analysisis simplified since the switch by E from strategy S,D to NS,EN (representedby the shift B in the graph 4) has no profit implication for I.

Proposition 5.1 (Robustness against a US litigation cost setting)The model insights are robust to a US litigation cost setting since strategyconsiderations for I based on A dominate those based on B. However, excesspatenting is less profitable under the US regime.

In the US system, each party has to bear its own litigation costs. Themathematical expressions change, however the qualitative insights from themodel remain the same because the strategy considerations for I based onreducing entry (A) dominate those based on fostering entry (B).

Although the general case in the US is that each party bears its own litigationcosts, 35 U.S.C §285 allows for the recovery of reasonable attorney fees inexceptional cases. The baseline model analysed in the paper can hence beseen as the setting where recovery of attorney fees is presumed.

5.2 Valuable Patents

Incumbent’s patent value: For simplicity and as a lower bound, theincumbent’s additional patent was assumed to be of zero commercial andlegal quality (qn+1 = 0). The only effect from I’s additional patent was anartificial increase of I’s portfolio size, which translated into a raise of thescreening costs for the entrant.

20

Proposition 5.2 (Given excess worthless patenting, any valuable patentwill be realised by I)The baseline model represents a lower-bound on the excessive patenting ac-tivity by incumbents. When additional patents by I bear commercial or legaladded-value, the excess patenting constraint is relaxed and the model resultsare strengthened.

The intuition of the value effects of an additional patent for I is the following:Commercial value of effectively reduces the implementation cost cI for theadditional patent. Legal value increases the portfolio strength b and therebyimproves the probabilities for I to win in case of litigation. Both effectsrelax the constraint on the excess patenting incentive. More patents meanless entry is, hence, valid to a larger extend as the new patent can furtherreduce entry by affecting the survival chances of design-arounds in court.I.e. the raising rival cost aspect can become a by-product of the patentapplication for valuable ideas.

Since both effects of commercial and legal value go in the same direction(namely increase slack in the excess patenting condition) and any valuablepatent encompasses the increase in screening costs for the rival (because theportfolio size still increases for valuable patents), the baseline model can beviewed as a lower bound on the excessive patenting activity that we observein a market.

The general framework for analysing valuable, additional patents by I wouldbe identical to the one given in the game tree in figure 2 with the additionthat in t = 0, the incumbent does not obtain a zero quality idea, but oneof quality qn+1 drawn from the uniform interval on [0, q]: qn+1 ∼ U[0, q].Both I and E have the same ex-ante expectations about the additionalpatent. How the value of the additional patent affects b or vI is not yetspecified.

Entrant’s patent value: So far, the model assumes both commercial (vE)and legal (qE) value for the patent of the entrant. In order to obtain theresults of the baseline model, the latter may take any values in the interval[0, q], which corresponds to the full range. Commercial value of the entrant’spatent, however, was limited to the interval vE ∼ (0, vE ] corresponding onlyto a marginal increase in the exogenous consumer valuation.

The idea behind the technical assumption on vE in order to make the analysisinteresting is that entry should be unprofitable when infringement occurs.The sufficient condition for this is ∆ < v + K rather than the one used sofar: 2∆ < v + K, which is more stringent and results in a case restriction.When relaxing this condition to the sufficient one, the main results in the

21

analysis of treble damages are unchanged, however the intermediate stepsare less clear cut.

Proposition 5.3 (Larger commercial value of the design-around)When v+K

2 < ∆ < v + K, the large commercial value that the entrant cangenerate reduces its sensibility to a raising rivals’ costs of screening effortby the incumbent since the entrant relies less on screening. Consequently,the model results are attenuated under large vE.

It is logical that the less risky entry is, the cheaper is the uncertainty aboutthe competitor’s patent portfolio strength and the less screening will beused. Therefore, the baseline focuses on the case when screening is an in-tegral part of competition (∆ < v+K

2 ) and we check robustness here (inproposition 5.3). The analysis loses its interest when ∆ > v + K since theentry is profitable regardless of infringement. We neglect the last case.

5.3 Independent legal opinion

“Judges are more likely to find willfulness when the infringer does not presentan attorney opinion as a defense” (Moore, 2004). This hints at the fact thatin practice, firms can avoid findings of wilful infringement by securing acounselling letter by an independent legal counsel on the validity of the in-cumbent’s patents. The practice in question is as follows (FTC, 2003):

Other testimony indicated that when troublesome patents areidentified, firms frequently seek to show due care and dissipatewilfulness concerns by securing opinion letters regarding invalid-ity or non- infringement from outside counsel21. Some testimonyquestioned the value of that practice and noted that attemptsto inquire about or pierce the surface of opinion letters can raisethorny disputes over attorney-client privilege22.

This strategy can be modelled as a method to circumvent award of trebledamages, however further increases the costs of screening. I.e. it makes theconstant downward shift of the screening payoff stronger and hence increasesthe effectiveness of an excess patent.

Now, the treble damages doctrine does not have grip on wilful infringersanymore (if they can disguise their wrongdoing by legal counsel), however

21[See Sung 2/8 (Patent Session) at 147 (a competent, independent legal opinion, evenif incorrect, will usually help to rebut an allegation of wilful infringement).]

22[See, e.g, Thomas 10/25 at 155 (rather than getting quality advice from counsel...we’re getting sort of pats on the back that, you might as well continue and here’s yourshield from triple damages), 177-78 (not suggesting that patent bar will cynically dish outany kind of opinion); Gambrell 10/25 at 169; Taylor 10/25 at 160.]

22

it still has an externality on entrants since their screening costs have goneup in order to acquire additional legal advice. Screening and entry is thusstill adversely affected by the treble damages doctrine.

Furthermore, the excess patenting strategy gains in effectiveness, since thesteepening of the slope (volatility range that E faces when entering) of thescreening function is eroded and replaced by an increase of the constantdownward shift of the screening function due to a multiplication of the

screening costs. In technical terms, τ is increased, while∂ΠE |S,D

∂qEdoes not

increase (hence the slope remains unchanged).

Allowing firms to escape treble damages by obtaining legal counsel erodesthe impact of treble damages. This is not in the interest of the maker.However, Moore (2004) details some of the factors which reduce the use oflegal opinion letters:

There are two problems with disclosing attorney opinions dur-ing discovery. The first is that it gives the patentee a detailedblueprint as to likely defences early in the litigation process. Thesecond is that the patentee can use the opinion against the defen-dant if at any point the defendant pursues a litigation strategythat differs from the opinion.

For the above reasons, it is not uncommon for firms to refrain from legalcounselling and then the insights from the model application to treble dam-ages hold. What is necessary for the model insights to be relevant is thatthere exists a positive probability of treble damages adjudication in case ofinfringement by the entrant.

6 Discussion of the results

The model has shown that the entrant uses screening for intermediate entryideas’ qualities to reduce the costly uncertainty on the incumbent’s patentportfolio strength. Imperfect screening makes unsurprisingly the screeningincentives lower. However, the setting with imperfect screening provides thecorrect counterfactual to compare the setting with and without the trebledamages doctrine.

It is clear from the model that for the setting of engineering around, the tre-ble damages doctrine reduces the incentives of the incumbent to excessivelypatent. This is a good thing since it avoids society the wasteful spending ofefforts on patenting worthless ideas as well as it reduces the strain on thepatent office.

23

However, the treble damages doctrine itself represents a burden on the en-trant since it exacerbates the cost of type I (false positive) errors. Conse-quently, it can be seen as a substitute for the incumbent’s excessive patentingstrategy that reduces entry itself, but avoids wasteful activity by the incum-bents. Policy should note these points.

The model implicitly assumes that entry post screening will result in theadjudication of treble damages. This is not perfectly accurate in real life,but the qualitative insights from the model remain valid as long as firms facea positive probability in equilibrium to be condemned for treble damages ifthey screen. Seaman (2011), Lemley and Tangri (2003) and Moore (2004)discuss the effects of the wilfulness doctrine pre and post the 2007 Seagatedecision23 and present the facts that treble damages have been awarded bothbefore and after Seagate in a significant (and similar) proportion of litiga-tion cases, with an especially high number of treble damages adjudicationswhen the court cases were decided by a jury. This lends validity to themodel as it suggests that treble damages apply in unpredictable situations24

and supports the idea that firms shy away from activities sanctioned bytreble damages where commonly cited defence tools (e.g. legal opinions oninfringement or validity of prior art) have no statistically significant powerin avoiding enhanced damages (Seaman, 2011).

In the same line of thought, the model can be seen as providing differen-tiated predictions based on the nature of an industry. For example in thepharmaceutical industry, patent claims can be very precise with the protec-tion of a molecular formula, whereas in other industries the limits of claimsare more blurry. If wilful infringement is more likely to be found in case ofinfringement in specific sectors, then the model results gain importance inthat field.

When treble damages are granted, the court may in addition also award at-torney’s fees to the prevailing plaintiff (Moore, 2004). This is equivalent topassing a US court case under a European litigation costs splitting, equal tothe main setting presented in this paper. This strengthens the results fromthe model since it increases the amount of the damages. The case withoutattorney’s fee awards is compared in section 5.1, the qualitative insights ofthe model remain valid.

23by the Federal Circuit in the US which toughened the standard applied to determinea wilfulness finding, for details see re Seagate Tech., LLC, 497 F.3d 1360, 1365

24E.g. the following factors had no significant predictive ability of wilfulness findings inSeaman (2011): opinions of counsel, attempts to design around the patent, re-examinationat the PTO, and bifurcation of wilfulness from liability at trial.

24

The model and its application have a strong validity in the context of tech-nologies that rely on the bundling of patents from different stake holders.This fragmentation of patent rights is also known as patent thickets25. Wheneach individual patent holder of a fragment of the composite technology ownsIP protection for this fragment in the form of patents, then each of theseright-holders may have an incentive to excessively patent. The accumulationof excess patents exacerbates the effect of the raising rival’s cost argumentas compared to the setting of a single incumbent. The insights of this modelthus give an additional rationale for incumbent firms to invest in creating adense web of overlapping patent rights a la Shapiro (2001).

In the context of multiple entrants, a reasoning a la Choi (1998) is appli-cable. In his paper, patent litigation serves as an information transmissionmechanism where the costs of transmitting are borne by the first plaintiff.Other firms interested in the free information transmitted by the litigationprocess have a free-riding incentive to wait and let another entrant initiatecostly litigation. The threshold for the first player to litigate is thus in-creased. In the current setting, it would apply by increasing the thresholdto enter for the first entrant. Subsequent entrant would learn for free thequality of the incumbent’s portfolio. Therefore, entry would occur after alonger time lag, but then all entrants with higher quality ideas than theincumbent would enter.

The current paper is particularly suited to explain excess patenting, how-ever also applies to other situations, where a raising rival’s cost strategyworks by the mechanism of furthering information asymmetries. The basicconsiderations of a raising rival cost strategy are widely discussed in the eco-nomics literature, even their existence in patenting (Gilbert and Newbery,1982). This paper sets itself apart from the previous literature in the sensethe the set-up allows to investigate the impact of the treble damage doc-trine and respects the private information character of patent strength. Byintroducing the novel screening mechanism on patent qualities, this paper isable to rationalise the excessive patenting of even commercially and legallyworthless ideas. This is in contrast to Gilbert and Newbery (1982), wherepreemptive patenting steals the legal and commercial value of the entrant’sidea in a patent race. Our setting does not need to rely on valuable preemp-tive patenting to reduce market entry, a result that seems to fit strongly theobserved explosion of low quality patent filings at the patent office.

Finally, it is useful to detail what is meant by “more patents” in the titleof this paper when talking about reducing entry. The model insights ap-

25For accounts on thickets, see Galasso and Schankerman (2010); Graevenitz et al.(2011).

25

ply to all raising rival’s cost strategies which have an effect on the entrantthrough the channel of increasing screening costs. Next to a mere additionalpatent, the following strategies fit the model set-up: (1) Introducing ambi-guity in patent claims (Chiang, 2012) and thereby blurring the boundariesof the claim, (2) Citing irrelevant prior art (Means, 2013) and thereby blur-ring the limits of entrant’s affirmative duty to read all relevant patents, (3)Monitoring entry in order to warn and inform potential entrants of patent in-fringement (Crampes and Langinier, 2002) thereby focussing their resourceson the study of patents that they would otherwise not be aware of.

7 Conclusion

This is a first paper looking at the incentives of firms to flood the marketwith patents and their interaction with treble damages as a policy tool. Thepredictions of this model are testable since both patent numbers and entryare easily observable. The screening decision, on which read intermediateresults, is not observable, but the account by the FTC (2003) matches theresults of the model.

The model is able to put the treble damages doctrine into an analysis thatprovides policy recommendations depending on the public goal. If a policyobjective is the fostering of the mutual reading of competitor patents (e.g.if large positive externalities are to be expected from this activity), then thetreble damages doctrine should be removed to re-incentivise firms to screencompetitor patent portfolios. If, however, the reduction of excess patentingof worthless ideas by the industry is the goal (e.g. because the stress onthe patent office shall be reduced), then the maintenance of the treble dam-ages doctrine ensures reduced incentives for firms to so. This effect howevercomes at the expense of a reduced information-sharing ability of the patentsystem as entrants will read less.

26

References

Allison, John R. and Mark A. Lemley (1998), “Empirical evidence on thevalidity of litigated patents.” AIPLA QJ.

Atal, Vidya and Talia Bar (2010), “Prior art: To search or not to search.”International Journal of Industrial Organization, 28, 507–521.

Bessen, James (2003), Patent thickets: Strategic patenting of complex tech-nologies.

Caillaud, Bernard and Anne Duchene (2011), “Patent office in innovationpolicy: Nobody’s perfect.” International Journal of Industrial Organiza-tion, 29, 242–252.

Chiang, Tun-Jen (2012), “Forcing patent claims.” Michigan Law Review(Forthcoming), 113.

Choi, Jay Pil (1998), “Patent litigation as an information-transmissionmechanism.” American Economic Review :, 1249–1263.

Crampes, Claude and Corinne Langinier (2002), “Litigation and settlementin patent infringement cases.” RAND Journal of Economics, 258–274.

FTC, Federal Trade Commission (2003), “To promote innovation: Theproper balance of competition and patent law and policy.” 1–315.

Galasso, Alberto and Mark Schankerman (2010), “Patent thickets, courts,and the market for innovation.” The RAND journal of economics, 41,472–503.

Gallini, Nancy T. (2002), “The economics of patents: Lessons from recentus patent reform.” The Journal of Economic Perspectives, 16.2, 131–154.

Gilbert, Richard J and David MG Newbery (1982), “Preemptive patentingand the persistence of monopoly.” The American Economic Review, 514–526.

Graevenitz, Georg von, Stefan Wagner, and Dietmar Harhoff (2011), “Howto measure patent thickets – a novel approach.” Economics Letters, 111,6–9.

Green, Jerry R and Suzanne Scotchmer (1995), “On the division of profit insequential innovation.” The RAND Journal of Economics, 20–33.

Kitch, Edmund W. (1977), “Nature and function of the patent system, the.”JL & Econ.

27

Langinier, Corinne and Philippe Marcoul (2007), “Patents, search of priorart and revelation of information.”

Lemley, Mark A (2008), “Ignoring patents.” Mich. St. L. Rev., 19.

Lemley, Mark A and Ragesh K Tangri (2003), “Ending patent law’s willful-ness game.” Berkeley Tech. LJ, 18, 1085.

Llobet, Gerard (2003), “Patent litigation when innovation is cumulative.”International Journal of Industrial Organization, 21, 1135–1157.

Means, Samuel Chase (2013), “The trouble with treble damages: Ditchingpatent laws willful infringement doctrine and enhanced damages.” Uni-versity of Illinois Law Review, 1999–2045.

Meniere, Yann and Sarah Parlane (2008), “Innovation in the shadow ofpatent litigation.” Review of Industrial Organization, 32.2, 95–111.

Merges, Robert P (1999), “As many as six impossible patent before break-fast: Property rights for business concepts and patent system reform.”Berkeley Tech. LJ, 14, 577.

Meurer, M. J. (1989), “The settlement of patent litigation.” The RANDJournal of Economics, 77–91.

Moore, Kimberly A (2004), “Empirical statistics on willful patent infringe-ment.” Fed. Cir. BJ, 14, 227.

Moore, Kimberly A. (2005), “Worthless patents.” Technical report, GeorgeMason University School of Law Working Papers Series : 27.

Salop, Steven C. and David T. Scheffman (1983), “Raising rivals’ costs.”The American Economic Review, 73, pp. 267–271.

Seaman, Christopher B (2011), “Willful patent infringement and enhanceddamages after in re seagate: an empirical study.” Iowa L. Rev., 97, 417.

Shapiro, C. (2001), “Navigating the patent thicket: Cross licenses, patentpools, and standard setting.” Innovation Policy and the Economy, 119–150.

United States Code 35, §284 (2006), “Supp. 3 - title 35 - patents part iii- patents and protections of patent rights - remedies for infringement ofpatent, and other actions - damages.” Bills and Statutes.

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Appendix: Proofs

Proof of Lemma 3.1We solve the game by backwards induction. In the screening subgame (ex-cerpt shown in figure 7), E has a dominant strategy to play depending onthe relative strength of its patent (qE) against that of the incumbent (b).

E screen

I wins (b>qE) E wins (b<qE)

E E

entry (EN)

no entry (NE)

entry (EN)

no entry (NE)

Figure 7: Perfect screening subgame tree

Post-screening, payoffs to E are given by

ΠE |S, D =

−S if qE < b and E stays out ←∆− v −K − S if qE < b and E enters∆− S if qE > b and E enters ←−S if qE > b and E stays out

where the arrows indicate the dominant strategies to be played dependingon whether the quality qE ≷ b.

We now look at the entry subgame. In t=4 and given I’s commitment tolitigate, E will enter iff:

ΠE ≥ cEE has the option to choose a strategy σE among the three pure strategies{(NS, NE),(NS, EN),(S, D)}, where the abbreviations stand for “‘Not Screen &Not Enter”, “Not Screen & ENter” and “Screen & then Decide on entry”respectively.

For any given strategy, E’s payoffs under litigation increase monotonely withthe quality of its own patent: ∂ΠE

∂qE> 0. This relationship comes from the

fact that the ex-ante probability of winning litigation P{qE > b} increaseswith qE . Hence, entry is defined by a threshold argument where E realisesall ideas above a certain threshold q.

29

The outside option is always to “Not Screen, Not Enter”, which yields payoff

Eb[ΠE |NS, NE] = 0

Without screening, ex-ante profits to E from entering are as follows:

Eb[ΠE |NS, EN] = E

b[P{b < qE}(∆) + P{b > qE}(∆− v −K)]

= Eb[∆− (v +K)P{b > qE}]

= ∆− (v +K)

∫ q

qE

1dU(b)

= ∆− (v +K)

(q − qEq

)where NS, EN refers to the strategy of “Not Screening, then ENtering”. Eenters the market when Eb[ΠE |NS, EN] ≥ 0. In order words, E realises allideas of quality qE ≥ qNS

, where qNS

is defined by:

qNS

= q

(1− ∆

v +K

)Given screening efforts at a total cost S, E observes a signal (message)m : {b ; qE} → {1 ; 0} on how the courts will decide the infringement case.In the baseline, the message is precise m = m. By screening, the entranthas delayed the entry decision and can now take this entry decision givenmore information about the outcome of the litigation. Ex-post screening,profits of the dominant strategies to E are given by:

ΠE |S, D =

{−S if qE < b and staying out∆− S if qE > b and entering

where S, D refers to the strategy of “Screening, then Deciding”. Ex-ante,before learning the true strength of I’s patent, E’s payoff is given by:

Eb[ΠE |S, D] = E

b[P{b > qE}(−S) + P{qE > b}(∆− S)]

= Eb[−S + ∆P{qE > b}]

= −s+ ∆

∫ qE

01dU(b)

= −s+ ∆

(qEq

)Absent the strategy of entry without screening (NS,EN), E will thus screenand then decide whether to enter when Eb[Π|S, D] ≥ 0. At equality, this

30

defines the threshold qS above which ideas will be realised.

qS = q( s

∆

)Between the strategies S, D and NS, EN, E goes for the latter wheneverEb[ΠE |NS, EN] ≥ Eb[ΠE |S, D]. This inequality defines at equality the thresh-old qT above which ideas’ qualities must lie for E to realise them withoutscreening:

∆− (v +K)

(q − qEq

)≥ −S + ∆

(qEq

)⇔ qE(∆− v −K) ≤ q(∆− v −K + S)

∴ qT = q

(∆− v −K + S

∆− v −K

)

The thresholds are ordered in the following way: 0 < qS≤ q

NS≤ q

T< q.

To show that the thresholds are in increasing order, two steps: First showthat the single crossing property holds for any two of the payoff functions ofE: E[ΠE |S, D], E[ΠE |NS, EN] and E[ΠE |NS, NE]. Second, find the conditionfor E[ΠE |S, D]|qE=qNS

> 0 to hold.

The derivatives with respect to the quality of the E’s idea are (both constantin qE):

∂ E[ΠE |NS, EN]

∂qE=v +K

q,

∂ E[ΠE |S, D]

∂qE=

∆

q

⇒∂ E[ΠE |NS, EN]

∂qE>∂ E[ΠE |S, D]

∂qE

∀v > ∆ and the single crossing property is verified.

For the ordering to be as requested above (and not the other way round),it suffices to show that E[ΠE |S, D]qE=qT > 0. Simplifying, it yields therequirement that the screening cost S must be sufficiently small for screeningto occur with positive probability in the baseline equilibrium. The precisecondition is given by: S < S = ∆(1− ∆

v+K ).

Hence in t = 3 and when E has the option to choose between the threestrategies σE = {(NS & NE), (NS, EN), (S, D)}, E will use a different strategyconditional on the quality qE of its idea.

σ∗E =

No Screening, No Entry if qE < q

SScreening, then Deciding if q

S< qE < q

TNo Screening, ENtering if q

T< qE

31

Thus, E has a dominant strategy, conditional on the quality of its innovationopportunity. Screening of competitor patents will occur only for mediocrequality ideas (not the best, nor the worst ones). �

Proof of Proposition 3.2In t = 1, I decides develop a legally and commercially worthless patent. Theadditional patent has no impact on either revenues (consumer valuation vIremains unchanged) or litigation probabilities (b remains unchanged). Theonly effect of the excess patent is to raise the entrant’s costs when decidingto screen the incumbent’s patent portfolio by a factor τ .

Thus, given the excess patent, the ex-ante (t = 3) expected payoff to E fromthe strategy (S,D) is altered to :

Eb[ΠE |S, D, n+1] = −S(1 + τ) + ∆

(qEq

)which corresponds to a constant, linear downward shift of the curve by −Sτas shown in figure 4. The payoffs of the strategies NS,NE and NS,EN areunaffected.

As becomes immediately visible from the graph, the induced increase inscreening costs has an impact on both thresholds qS and qT , which movecloser together. The new thresholds (indicated by the dash on the subscript)are given by

qS′ = q

(S(1 + τ)

∆

)> q

(S

∆

)= qS

and qT ′ = q

(1− S(1 + τ)

|∆− v −K|

)< q

(1− S

|∆− v −K|

)= qT

The new optimal composite strategy for E, given an excess patent by theincumbent is:

σ∗E′ =

NS, NE if qE < q

S′

S, D if qS′< qE < q

T ′

NS, EN if qT ′< qE

The differences |qS′ − qS | = q(Sτ∆

)= A and |qT ′ − qT | = q

(Sτ

|∆−v−K|

)= B

represent by how much screening decreases given the excess patent. Theassumptions ∆ > 0 and |∆ − v − K| > 0 ensure that both A and B arepositive, hence yielding that more patents mean less screening. �

32

Proof of Proposition 3.3From Proposition 3.2, we have expressions for A and B.

We have |A| > |B|:

|A| > |B|

⇔ qSτ

∆− qSτ

|∆− v −K|> 0

⇔ qSτ

[−(2∆− v −K)

(∆)(|∆− v −K|)

]> 0

⇔ |∆− v −K| > ∆ (1)

which is always satisfied by assumption since we restrict our analysis todesign-arounds yielding only marginal increases in consumer valuation, v +K > 2∆. Hence, less screening is synonymous with less entry. �

Proof of Lemma 3.4Given the impact of an excess patent on E’s strategy, it is now possibleto analyse the excess patenting incentives of the incumbent26. The incum-bent has two strategies, namely to produce an excess patent (ExP) or not(NP), σI = {ExP, NP}. Depending on the strategy that I plays, E will beconfronted to a patent portfolio of size N = n+ 1 or N = n, respectively.

Without the excess patent, I’s payoff is:

E[ΠI |σ∗E , n] =

v if qE < q

SP{b > qE}(v)−K P{b < qe} if q

S< qE < q

TP{b > qE}(v)−K P{b < qe} if q

T< qE

Less screening by E due to an excess patent affects the ranges over qE forwhich the E plays a different strategy (according to σ∗E). It becomes clearthat under the EU litigation cost setting, only the variation of q

Sby a

distance A has an impact on I’s profits.

Therefore, it is profitable for I to develop the excess patent if the followingcondition holds:

EbEqE

[−c+ P{q

S< qE < q

S′}[v − v P{b > qE}+K P{b < qE}]

]≥ 0

⇔ EbEqE

[−c+

A

q(v +K)P{b < qE}

]≥ 0

26This part simplifies considerably due to the European setting for litigation costs.The consequence is that the switch by E from strategy S,D to NS, EN,D has no profitimplication for I.

33

⇔ −c+Sτ

∆

(v +K)

2≥ 0 (2)

For completeness: The full game can now be solved for the Nash equilibriumin the baseline scenario, when no screening errors are made by E. Assumingthat the incentive constraint for excess patenting in equation 2 is satisfied,the NE(σ∗I , σ

∗E) of the full game under perfect screening is

NE[ExP, σ∗E′ ]

If the excess patenting condition is not satisfied, then the NE of the fullgame is the following: NE[NP, σ

∗E ]. In the following, we will focus on the

former out of interest. �

Proof of Lemma 3.5When introducing imperfect screening, the entrant has a positive probabilityto misread the patent strength of the incumbent and hence to take the wrongdecision: EN when in fact E infringes (b > qE) and NE when in fact it doesnot infringe (b < qE). This error is set to happen with probability (1−g) > 0,where g = P{no screening error}.

As a consequence, both type I (false positives) and type II (false negatives)errors can occur with the same probability (1 − g) = P{b > qE |b < qE} =P{b < qE |b > qE}.

The corresponding screening game tree is as given in figure 8. It is reducedin the sense that the probability of a correct or wrong signal is incorporatedin the entry decision of E. This is done to allow better comparison with thebaseline screening subgame tree in figure 7.

E screen

I wins (b>qE) E wins (b<qE)

E E entry [correct signal]

no entry [wrong signal]

(g)

entry [wrong signal]

no entry [correct signal]

(1-g) (1-g) (g)

type II error type I error

Figure 8: Imperfect screening subgame tree (reduced)

34

Screening errors occur with a positive probability in equilibrium, however,their likelihood is restrained to be sufficiently small such that the opti-mal strategies in the screening subgame remain unchanged in the imperfectscreening setting.

Assumption 7.1 (Condition on the likelihood of screening errors)The screening errors occur with probability (1−g) in both directions, i.e. forboth false positive and false negative signals. The condition on the probabilityof “no error”:

g ≥ g = max

{1− ∆

v +K,

∆

v +K

}ensures that the optimal screening strategies for the entrant in the screeningsubgame remain unchanged, conditional on reading the signal m.

Derivation of Assumption 7.1 In the screening subgame post screening,for EN to remain optimal when observing signal m = [b < qE ], need:

g(∆− S) + (1− g)(∆− v −K) > −S∆− (v +K)(1− g) > 0

g > g =∆− v −K−v −K

In the screening subgame post screening, for NE to remain optimal whenobserving signal m = [b > qE ], need:

−S > g(∆− v −K − S) + (1− g)(∆− S)

∆− g(v +K) < 0

g > g =∆

v +K

Thus, screening errors must be sufficiently small for equilibrium strategiesto remain unchanged. This implies that g > 1

2 and, in other words, meansthat the signal must be informative for screening to be profitable. �

The imperfect screening affects the expected payoff of E when it screens.

E[ΠE |S,D] =E[P{b > qE}[P{b > qE |b > qE}(−S)]

+ [P{b > qE |b < qE}(∆− v −K − S)] ← Type I error

+ P{b < qE}[P{b < qE |b < qE}(∆− S)

+ P{b < qE |b > qE}(−S)]]

← Type II error

= −S + (1− g)(∆− v −K)

(q − qEq

)+ (g)(∆)

(qEq

)

35

The costs of both types of errors are given by:

CI = E[Cost of type I error] = (1− g)(∆− v −K)

CII = E[Cost of type II error] = (1− g)∆

The cost of a type I error exceeds that of a type II error ∀ v + K > 2∆,which is satisfied by assumption.

⇒ CI > CII .

Furthermore, the slope of the expected payoff function under screening in-

creases from∂ E[ΠE |S,D]

∂qE= ∆

q under perfect screening (g = 1) to

∂ E[ΠE |S,D]

∂qE=

1

q

g∆ + (1− g)(|∆− v −K|︸ ︷︷ ︸>∆

)

under imperfect (g < 1) screening. �

Proof of Lemma 3.6For E, only the screening payoff is affected by the screening errors. Strate-gies NS,EN and NS,NE remain unaffected. Consequently, the threshold qNS(intersection of the latter two functions) is also unaffected.

The new thresholds, that define the range (over qE) for which E screens,are given by q1

S and q1T .

q1S is defined by the intersection of E[ΠE |NS,NE] and E[ΠE |S,D]:

−S + (1− g)(∆− v −K)

(q − q1Sq

)+ (g)(∆)

(q1S

q

)= 0

Reordering yields the threshold: ⇔ q1S =q [S − (1− g)(∆− v −K)]

g(∆)− (1− g)(∆− v −K)

q1T is defined by the intersection of E[ΠE |NS,EN] and E[ΠE |S,D]:

−S + (1− g)(∆− v −K)

(q − q1Tq

)+ (g)(∆)

(q1T

q

)= ∆− (v +K)

(q − q1Tq

)

Reordering yields the threshold: q1T =q [S − (1− g)(∆− v −K)]

g(∆)− (1− g)(∆− v −K)

36

Both thresholds q1S and q1

T are in the same ordering as before (0 < q1S <

qNS < q1T < q), when screening occurs with positive probability in equilib-

rium.

Assumption 7.2 (Screening occurs with positive probability)Screening occurs with positive probability in equilibrium when screening costsare sufficiently low: S < S. In the case of imperfect screening, the precisecondition is given by:

S =

(∆− v −Kv +K

)[−g(∆) + (1− g)(∆− v −K)] + (1 + g)(∆− v −K)

Derivation of Assumption 7.2 For screening to occur in equilibrium, Emust be able to generate positive profits by screening when it obtains a qual-ity qE = qNS , which is the indifference threshold between entering withoutscreening and staying out.

E[ΠE |S,D]

∣∣∣∣qE=qNS

> 0

⇔ −S + (1− g)(∆− v −K)

(q + q∆−v−K

v+K

q

)+ g(∆

(−q∆−v−K

v+K

q

)≥ 0

Simplifying and reordering the last line at equality yields the threshold costof screening S. �

The optimal, composite strategy to E is given by :

σ1∗E =

NS, NE if qE < q1

SS, D if q1

S< qE < q1

TNS, EN if q1

T< qE

where the definitions of the thresholds are given above.

The shift of the thresholds is given by the following distances (Note: theupper index 1 refers to the effect due to screening errors, the dash (′) on thesubscript refers to the effect of an excess patent):

q1S− q

S=q [S − (1− g)(∆− v −K)]

g(∆)− (1− g)(∆− v −K)−(qS

∆

)> 0

q1T− q

T=

(q [S − (1− g)(∆− v −K)]

g(∆)− (1− g)(∆− v −K)

)− q

(∆− v −K + S

∆− v −K

)< 0

q1S− q

Srepresents the decrease in entry of entrants as they switch strategies

from S,D to NS,NE. q1T− q

Trepresents the increase in entry due to switching

from S,D to NS,EN. Both thresholds qS

and qT

move closer together, hencethe range of qualities for which E will screen is reduced. �

37

Proof of Corollary 3.7We have that screening errors reduce the range of screening. The thresholdsqS and qT , which define the range of screening, move together.

Threshold qS moves to the right to q1S , a shift of distance q1

S− q

S, which

represents a decrease in entry since firms who screened before, now stay outof the market without screening.

Threshold qT moves to the left to q1T , a shift by distance q1

T− q

T. This shift

represents an increase in the market since firms who previously screened (andpossibly stayed out after reading a signal of I’s patent portfolio strength),now enter the market without screening.

The net effect of increased and decreased entry is an entry reduction if :

|q1S− q

S| > |q1

T− q

T|

⇔(g − 1)q

(−∆2 + ∆(K − 2S + v) + S(K + v)

)(−∆ +K + v)(∆ + g(−2∆ +K + v))

+q((g − 1)K + (g − 1)(v −∆)− S)

∆− 2∆g + (g − 1)(K + v)> 0

which is always true27 given the assumptions made so far on screening er-rors (Assumption 7.1) and screening costs (Assumption 7.2) in addition tothose made in the baseline model of perfect screening. �

Proof of Proposition 3.8An excess patent by the incumbent increases screening costs for the entrantand reduces the payoffs for the screening strategy.

Visually, as before, the excess patent results in a constant downward shiftof the screening payoff function. The threshold by which entry reduction isaffected is given by A1 = q1

S′− q1

S. This change in E’s strategy is beneficial

to I in terms of profits.

On the other hand, the entry increase, due to entrants who enter withoutscreening instead of screening first (given by B1 = q1

T− q1

T ′), is without any

profit implication for I since litigation costs are borne by the loser of thecase.

The profits to I given E’s optimal strategy σ∗E are:

E[ΠI |σ∗E , n] =

v if qE < q1

SP{b > qE}(v) + P{b < qE}[g(−K) + (1− g)(v)] if q1

S< qE < q1

TP{b > qE}(v) + P{b < qE}[g(−K) + (1− g)(v)] if q1

T< qE

therefore only A1 has profit implications for I.

27Mathematica file available upon request.

38

The intercept on the qE-axis that an excess patent generates determines howprofitable such a move is. In the case of imperfect screening, the slope of thescreening function has increased. This is due to a left-side-heavy translationof the curve, because of the cost discrepancy of type I and II errors.

The shift is given by:

A1 = q1S′− q1

S

=q [S(1 + τ)− (1− g)(∆− v −K)]

g(∆)− (1− g)(∆− v −K)− q [S − (1− g)(∆− v −K)]

g(∆)− (1− g)(∆− v −K)

=qSτ

g(∆)− (1− g)(∆− v −K)<

qSτ

∆= A

Thus the entry reduction that can be obtained by an excess patent hasdecreased.

The full expression capturing the incentives to excessively patent for I isgiven by

EbEqE

[−c+ P{q1

S< qE < q1

S′}[v − P{b > qE}(v)

− P{b < qE}[g(−K) + (1− g)(v)]]]≥ 0

⇔ −c+ EqE

[P{A}][v − v

2−1

2[g(−K) + (1− g)(v)]] ≥ 0

⇔ EqE

[P{A}][g (v +K)

2]− c ≥ 0

⇔ gSτ

g(∆)− (1− g)(∆− v −K)

[v +K

2

]− c ≥ 0 (3)

The incentive contraint such that excess patenting is profitable in equation3 is more stringent than the one of Lemma 3.4. Consequently, the incentiveto excessively patent goes down for I as the slope of the screening payofffunction increases. �

Proof of Lemma 4.1The screening subgame under the introduction of treble damages is shownin figure 9.

Introducing treble damages, the expected costs of errors are given by:

CTDI = E[Cost of a type I error] = (1− g)(∆− 3v −K)

CTDII = E[Cost of a type II error] = (1− g)(∆)

⇒ CTDI � CTD

II

39

E screen

I wins (b>qE) E wins (b<qE)

E E entry [correct signal]

no entry [wrong signal]

(g)

entry [wrong signal]

no entry [correct signal]

(1-g) (1-g) (g)

type II error type I error

Figure 9: Treble damages screening subgame tree (reduced)

Comparing to the single damages setting, we have CTDI > CI > CII = CTD

II .By the same argument as in the proof of Lemma 3.5, we have an increase of

the slope∂ E[ΠE |S,D]

∂qE. �

Proof of Corollary 4.2Identical argument as in the proof of Lemma 3.6 and Corollary 3.7. �

Proof of Corollary 4.3Identical argument as in the proof of Proposition 3.8, where the expectedcosts of screening errors are as given in the proof of Lemma 4.1.

Furthermore, treble damages have a profit implication for I. The expectedprofits to I given E’s optimal strategy σ∗E are:

E[ΠI |σ∗E , n] =

v if qE < q1

SP{b > qE}(v) + P{b < qE}[g(−K) + (1− g)(3v)] if q1

S< qE < q1

TP{b > qE}(v) + P{b < qE}[g(−K) + (1− g)(v)] if q1

T< qE

Therefore, now both of the shifts of the thresholds A2TD′ = q2

S′ − q2S and

B2TD′ = q2

T − q2T ′ affect I’s incentives to excessively patent.

B2TD′ represents a shift from S,D to NS,EN, which is payoff costly to I.

A2TD′ represents the shift of E from S,D to NS,NE. When v > P{b >

qE}(v) + P{b < qE}[g(−K) + (1 − g)(3v)], we always have A2TD′ < A1

TD′

which makes the excess patent less profitable than before. If v < P{b >qE}(v) +P{b < qE}[g(−K) + (1− g)(3v)], then screening entrants are moreprofitable to I than excluded rivals. All effects go in the same direction andtherefore, the introduction of treble damages reduces the excess patentingincentives of the incumbent. �

40

Proof of proposition 5.1In the US system, each party has to bear its own litigation costs. Conse-quently, the switch by E from strategy of screening (S,D) to no screening(NS,EN) due to an excess patent now has a profit implication for I, namelythat I has to bear its own litigation costs when defending its market againstentry in litigation.

The shift B represents the range over which E switches from S,D to NS,EN.When the entrant has an inferior patent (qE < b) and I can defend itsmarket in litigation, the incumbent must pay its own litigation costs K.Under screening, E would have stayed out and saved I the defence costs. Inthe European litigation cost setting, the strategy change of S,D to NS,ENby E was costless for I.

The exact mathematical expressions change, but the model insights are qual-itatively unchanged due to the following: The negative profit implication onI due to increased entry by high quality entrants (represented by the shiftB) is outweighed by the positive profit impact from reduced entry of lowquality entrants (represented by the shift A). The reason being that theratio of profit changes due to A versus B is given by

|Impact due to A||Impact due to B|

=v +K

K> 1.

Furthermore, we have from proposition 3.3 that |A| > |B|, i.e. the proba-bility that the affected entrant will switch strategy to staying out exceedsthe probability will switch to entry without screening. Thus, strategy con-siderations based on A dominate those based on B.

Consequently, the baseline analysis focussing on the shift A yields qualita-tively the same insights as one which would have taken both A and B intoaccount.

For completeness and as a comparison, we provide the expressions of somemilestones in the calculations of the model. The condition for less screeningto mean less entry is given by

|A| − |B| = qsτ

∆−K− qsτ

|∆− v −K|> 0

⇔ qsτ

[−v

(∆−K)(|∆− v −K|)

]> 0 (4)

and compares to condition 1.

41

The excess patenting incentive for I under the US cost regime:

EbEqE

[−c+ P{q

S< qE < q

S′}[v − v P{b > qE}+K P{b < qE}]

+P{qT ′< qE < q

T}[−K(1− P{b < qE})

]≥ 0

⇔ −c+Sτ

∆

(v +K

2

)+

Sτ

|∆− v −K|

(−K

2

)≥ 0 (5)

Inequality 5 compares to inequality 2 and indicates the tightening of theexcess patenting condition under the US litigation cost setting. Inequality5 can also be rewritten in the form of

1

2[P{A}[v +K]− P{B}[K]]− c ≥ 0

where P{.} interprets as the probability that qE falls in the range of A orB. We easily see that v + K > K, ∀ v > 0 and combined with inequality 4that the strategy considerations based on A dominate those based on B.

The analysis of the impact of treble damages is slightly more involved. Anincrease in the slope of the screening function causes A1 < A as given byproposition 3.8, but we also obtain B1 > B, where B = q

T− q

T ′and

B1 = q1T− q1

T ′. This means that the entry reduction commanded by the

excess patent is reduced under treble damages, but at the same time theentry fostering effect (represented by B) is enhanced. Both effects reducethe excess patenting incentives. The trade-off that the incumbent faces whendeciding on the excess patent is as presented in condition 5.

�

Proof of proposition 5.2We now show that the solved baseline model can be seen as a limiting case,which represents the lower bound on the incentives to excessively patent.

Introducing commercial (increase vI) or legal (increase b) value, the excesspatenting incentives are satisfied more easily. Hence, the baseline models’results encompass those for the case when I can patent a valuable idea.

Commercial value (increase in vI :) When additional patents by theincumbent increase the consumer valuation vI by a factor ζ > 0 for theproduct that I’s patent portfolio generates, then the payoff to I from the

42

additional patent is given by:

EbEqE

−c+ P{qS< qE < q

S′}[(v(1 + ζ) +K)P{b < qE}]︸ ︷︷ ︸

> payoff from condition (2)

+P{qE < qS}[vζ]︸ ︷︷ ︸>0

+P{qE > qS′}[vζ P{b > qE}]︸ ︷︷ ︸>0

> 0 (6)

When comparing condition 6 to condition 2, which represents the excesspatenting incentives for worthless patents, we see that commercial patentvalue introduces slack in the excess patenting condition, because ζ > 0 andI benefits from it as long as no entry occurs.

Furthermore, commercial value of the additional patent affects the entrant incase of damages payments, thereby increasing the threshold qS for screeningunder imperfect screening, i.e. the magnitude of the shift A is increased.This contributes in further making the first line of condition 6 larger thanits corresponding condition 2 under worthless excess patents.

Moreover, commercial patent value decreases the distance B by which en-try increases when an additional patent is supplied to the market. Entryincrease occurs from entrants switching strategy from S,D to NS,EN. Therange of entrants who switch strategies is reduced if the commercial value ofthe additional patent is positive, because increased damage costs are borneby E in case of infringement. The effect is that the threshold qT ′ increases.This counterbalances the effect of less screening due to increased costs.

Hence, commercial value has a strictly positive impact on the additionalpatenting incentives of the entrant since both effects of enhanced entry de-terrence (in A) and reduced entry fostering (in B) play to the benefit of theentrant.

Legal value (increase in b:) When the additional patent by the in-cumbent bears legal value, the litigation probabilities are affected. Thiscorresponds to an increase of b in the model.

For the entrant, entry under litigation is more expensive since infringementbecomes more likely, i.e. the probability of no-infringement by the entrant’spatent (m) decreases28. We separate the impact of an additional patent

28Technically speaking, the expected payoff functions for S,D and NS,EN become moreconvex as b increases. For ease of exposition, we only discuss on the intuition of the effects.

43

again in the entry reduction and fostering effects, we focus on the formerfirst.

The shift A represents the change of the threshold qS due to the additionalpatent. As m decreases, entry becomes simultaneously more expensive forE and A is increased above the level from the baseline model: qS′LV > qS′ .Consequently the excess patenting condition is relaxed for I thanks to astronger entry reducing effect.

The shift B represents the effect of increased “blind” entry (i.e. NS,EN)due to more expensive screening following the additional patent. When I ispayoff indifferent to E’s strategy switch between S,D and NS,EN, then onlythe former effect is relevant and plays in favour of I.

When the entry increase in B is payoff relevant for I, the entry increasingeffect of the additional patent affects the excess patenting incentives. Theeffect of entry fostering is reduced by the additional patent if the slope differ-ential between the expected payoff functions of S,D and NS,EN is increased29

at the intersection of the curves. This strengthens the anti-competitive ef-fects of the additional patent and hence relaxes the excess patenting con-straint. If, however, the slope differential reduces due to decreased m, thenthe incentive effect on B goes counter the effect of A and the overall effectof legal value is ambiguous.

Consequently, legal value of the additional patent strengthens the entry re-duction that an additional patent can command, while its effect on the entryincrease is ambiguous. As long as the effect of A dominates the effect of B(similar to proposition 3.3 in the baseline case) for the legal value, both legaland commercial value relax the excess patenting incentives as compared tocondition 2 and play to the benefit of the incumbent. Therefore, any valu-able idea will be patented by the incumbent whenever the excess patentingcondition is satisfied for completely worthless patents. �

Proof of Proposition 5.3When v+K

2 < ∆ < v + K, two effects occur: First, the expected payofffunction of S,D has a larger slope. The slopes of the payoff functions ofthe outside option as well as the strategy NS,EN remain unaffected. Higher∆ allows E to take more risks ex-ante (E can face a stronger I without

29Technically speaking, this corresponds to a condition on the convexity of the payoffsfunctions. The equivalent condition is the linear setting of worthless excess patents is thefact that the slope of the NS,EN function exceeds twice the slope of the S,D function.This is guaranteed in the baseline by the difference in consumer valuations that firms cangenerate: v + K > 2∆. This part links to the robustness discussion of proposition 5.3

44

screening) and will result in more entry without screening (for lower valuesof qE).

The argument of the effect of the increased increase is identical to the oneof the analysis of the treble damages doctrine. Due to the increased slope,the entrant’s sensitivity to an excess patent goes down because the raisingrivals’ cost impact is relatively smaller.

The second effect is that due to the decreased slope differential between theexpected payoffs of the S,D and NS,EN function, we do not validate theresult of proposition 3.3: |A| ≤ |B|. Consequently, less screening does notmean less entry anymore. This is because the relative magnitudes of theshifts A and B have changed, however the directions of the shifts remain asbefore (i.e. thresholds move together given an excess patent).

In the European litigation cost setting, the main results are unaltered sincethe shift B is payoff irrelevant for I. Hence, whether |B| is larger or smallerthan |A| is irrelevant for I consideration to excessively patent or not. Merelythe slope increase discussed above reduces the excess patenting incentives.

In the US litigation cost setting, the analysis is a little more involved sincethe shift |B| is payoff relevant: From section 5.1, we know that the excesspatenting incentive for I is a trade-off of the costs of the excess patentversus the benefits from the payoff of reducing entry. In the case of minorcommercial value: vE <

v+K2 − cE , the payoff considerations from A always

outweighed those of B since the change in strategy by an entrant from S,Dto NS,NE was both more profitable and more likely than a change fromS,D to NS,EN. Given larger vE , this is not so clear cut anymore and thetrade-off is tighter since the switch of an entrant from S,D to NS,NE isstill more profitable than a switch from S,D to NS,EN, but not necessarilymore likely. Hence, large commercial value of the entrant’s design-aroundintroduces ambiguity in the trade-off that the entrant faces when decidingon its strategy.

What is clear from the robustness analysis is that additional commercialvalue for the entrant’s patent will reduce E’s sensibility to excess patent-ing since E relies less on screening. Consequently, the model results areattenuated under large vE as the incumbent faces a tighter excess patentingcondition and excessive patenting has become less profitable.

Even though the intermediate result of proposition 3.3 may not be robustto large vE , excessive patenting may still occur when the excess patentingconstraint under treble damages30 is satisfied. The main results on theanalysis of treble damages then still holds against large commercial valuesince the impact of the treble damages doctrine (namely multiplying the cost

30Equivalent to condition 5 when replacing v by 3v

45

of type I errors) remains unchanged. For the main insights from corollary4.3 to remain valid, it is only necessary that the cost of type I errors exceedsthat of type II errors, which seems likely when the damages for type I errorsare trebled. �

46