Screening for Patent Quality:
Examination, Fees, and the Courts∗
Mark Schankerman†
Florian Schuett‡
December 2015
PRELIMINARY: DO NOT QUOTE WITHOUT PERMISSION
Abstract
This paper studies how government policy instruments can be used
to improve the quality of patent screening. We focus on four key policy instruments: patent office examination, application fees, activation
(renewal) fees and post-examination challenges in the courts. We show
that there are important complementarities among these policy levers
and identify conditions under which they can be used to achieve either
partial or complete screening. We also examine the welfare implications of different instruments, and the sensitivity of conclusions to the
way in which courts are modelled.
1
Introduction
The patent system is one of the main devices governments use to increase
innovation incentives. However, there is growing concern among academic
scholars and policy makers that patent rights are becoming an impediment,
rather than an incentive, to innovation. Critics claim that the proliferation of patents, and the fragmentation of ownership among firms, raise the
transaction costs of doing R&D and expose firms to holdup through patent
litigation (Heller and Eisenberg, 1998; Bessen and Maskin, 2009). These
dangers have been prominently voiced in public debates on patent policy in
∗
We are grateful to Jay Pil Choi, Vincenzo Denicolò, Bernhard Ganglmair, Patrick
Legros, and participants of the MaCCI Workshop “Economics of Innovation” in Bad
Homburg (2015) for useful comments and suggestions. All errors are our own.
†
London School of Economics and Centre for Economic Policy Research, E-mail:
m.schankerman@lse.ac.uk
‡
TILEC & CentER, Tilburg University. E-mail: f.schuett@uvt.nl
1
the United States (Federal Trade Commission, 2011) and recent decisions by
the Supreme Court (e.g., eBay Inc. v. MercExchange, L.L.C., 547 U.S. 338,
2006). Many of these problems, critics claim, arise from ineffective screening by patent offices, granting property rights to obvious inventions that do
not represent a substantial inventive step, especially but not only in new
areas such as business methods and software. In the presence of costly (and
probabilistic) review by courts, weak patents – obvious ones that should not
be granted – may end up being strong (Farrell and Shapiro, 2008).
There is no shortage of criticism about patentability standards being
too low, and the need to make screening more effective. But how does
one achieve this goal? The economic theory literature focuses primarily on
patent design features – e.g., duration and scope of patents (Scotchmer,
1999; Cornelli and Schankerman, 1999; Klemperer, 1990; Hopenhayn and
Mitchell, 2000) – but only recently have economists examined ways to enhance the effectiveness of patent screening. In a series of papers, Schuett
(2013a, 2013b) studies how patent examination intensity, examiner incentives, and application fees affect ex ante research choices of inventors. In
related work, Kou, Rey and Wang (2013) study how the non-obviousness
threshold for patenting affects adverse selection in ex ante R&D choices
by inventors.1 Legal scholars have written extensively on ways to improve
patent screening, including on the use of external peer review (Noveck,
2006), appropriate standard and application of the non-obviousness criterion (Eisenberg, 2004; Dreyfuss, 2008), and presumption of validity and
evidentiary standards for invalidation in the courts (Lichtman and Lemley, 2007). At the other extreme, it has been suggested that we should
move to a registration system for patents (with effectively no examination
for quality) and shift the entire burden of screening to the courts (Lemley,
2001). These proposals by legal scholars have not been subjected to formal
economic analysis, embedding them in an equilibrium framework in which
policy instruments affect optimal strategies of inventors and competitors.
In this paper we study how policy-makers can most effectively use the
instruments at their disposal to improve the quality of patent screening.
1
Other related studies include Caillaud and Duchene (2011) and Atal and Bar (2012).
2
We focus on four key screening instruments: the intensity of patent office
examination, application fees paid before patent examination, activation (renewal) fees paid by inventions that have passed examination, and review by
the courts for patents challenged by a competitor. For most of the analysis,
we assume that courts invalidate obvious inventions with certainty (we relax
this and study how results change with the characterization of courts later).
To our knowledge, we are the first to provide a theoretical analysis of this
full set of policy instruments, and to study how these instruments interact
with each other.
We develop a model in which an inventor faces a competitor. The inventor is endowed with an idea for an invention which can be either obvious
(‘bad type’) or nonobvious (‘good type’). The invention type is private information to the inventor. An obvious invention is profitable to develop in
the absence of a patent while a nonobvious one requires patent protection
to be profitable. Since patent protection increases the profit for both types,
however, owners of obvious inventions also have a private incentive to seek
a patent. There is a net social cost (benefit) of granting patents for obvious (non-obvious) inventions, so effective screening is important for welfare.
The inventor chooses whether to pay an application fee and, if subsequently
approved (screening by the patent office is imperfect), whether to pay the
activation fee. If the patent is activated, the inventor may choose to license the invention to the competitor and the competitor chooses whether
to challenge the validity of the patent in court. Formally, this is a signaling
game in which each decision by the inventor can reveal information about
the invention type, and the competitor Bayesian updates.
The key results from the analysis are as follows. First, we show that
the characterization of equilibrium turns on whether patent challenges are
credible, and this depends on the examination intensity (quality of patent
office screening) and the cost of going to court. If challenges are not credible,
bad types do not have to fear challenges; thus depending on the level of fees
and examination, they either pool with good types by applying for patents
and proposing a high license fee to the competitor, or they do not apply. If
challenges are credible, there is no pooling equilibrium. Instead, whenever
fees and examination intensity are such that the bad type would apply when
3
challenges are not credible, he also applies with strictly positive probability
when challenges are credible. The equilibrium is in mixed strategies, with
bad types either randomizing between high and low license fees or between
applying and not applying for patents. Over which decision they randomize
depends on the level of application and activation fees as well as on the
examination intensity and the cost of going to court. This highlights the
fact that the policy instruments interact in shaping the equilibrium.
Second, we show that if the patent office makes no examination effort (a
pure registration system), or if the activation fee is zero and examination
is imperfect, complete screening (where only the good type applies) cannot be achieved. This is important because it emphasizes that fees cannot
completely screen in a pure registration system. Complete screening can be
achieved by a combination of an application fee and an examination that is
sufficiently rigorous (even though not perfect). Moreover, the examination
intensity required to induce self-screening of inventors is increasing in the
activation fee (activation fees and examination are not substitutes). We also
show that, despite our assumption that courts are mistake-free, they cannot
eliminate all bad patents that are issued. This is because in equilibrium not
all bad patents are challenged by the competitor. This result raises serious
doubts about over-reliance on the court system to weed out bad patents.
Third, we perform a welfare analysis to further investigate the optimal
structure of fees, taking the examination intensity as exogenously given.2
The most interesting case arises when examination is not sufficiently rigorous for complete screening to be achievable. In that case, we show that a
social planner would always frontload fees, i.e., rely on application rather
than activation fees. The intuition for frontloading of fees is that, while
application and activation fees are perfect substitutes for the good type,
the bad type prefers activation fees, which are due only after having passed
examination.
When we relax our assumption that courts are mistake-free (i.e., always
invalidate obvious inventions) and allow courts to randomly uphold a fraction of patents (‘probabilistic patents’), we show that it is again possible
2
We have yet to complete the welfare analysis when the examination intensity is a
choice variable.
4
fully to screen out bad patents by a combination of application fees and sufficiently stringent examination intensity, but doing so requires more rigorous
examination by the patent office than when courts are mistake-free.
Our results about the virtues of frontloading fees call into question the
current structure of fees at the major patent offices around the world. Patent
offices often backload a substantial portion of their fees by charging a variety
of post-grant fees such as issuance and renewal or maintenance fees. At the
USPTO, for example, a patent application with three claims or less costs
the applicant a total of $1,740 in pre-grant fees. If the application is granted
and the resulting patent renewed to full term, the applicant pays a total of
$13,560 (ignoring discounting) in post-grant fees.3
It should be noted that there may be reasons outside of our model for
backloading fees. A system of renewal fees essentially ensures that more
valuable inventions receive longer protection. Scotchmer (1999) and Cornelli
and Schankerman (1999) identify conditions under which society wants to
give longer patents for more valuable inventions. In Scotchmer (1999), this
occurs if R&D costs are convex in value, while in Cornelli and Schankerman
(1999), it improves the incentives of the most productive inventors.
Throughout the paper, we take the existence of a patent system as given.
It is not a priori clear whether a patent system is the optimal mechanism
in the environment we consider; an alternative incentive mechanism such as
prizes may perform better. Since abolishing the patent system is not on the
table in the foreseeable future, we believe that exploring how to improve
the functioning of the existing system is a worthwhile endeavor in its own
right. Note also that a patent system with the patentability requirement we
will consider below may well place lower informational requirements on the
government than a prize system. A prize system requires the government
to know the R&D costs of the invention, its value, or the difference between
R&D costs and competitive profits, whereas the patent system we envisage
only requires knowledge of the sign of the difference between R&D costs and
competitive profits.
3
See
www.uspto.gov/learning-and-resources/fees-and-payment/uspto-fee-schedule,
accessed on 10 November 2015. Every claim in excess of three costs an additional $420
in pre-grant fees.
5
The paper is organized as follows. Section 2 presents the setup of the
model. Section 3 derives the equilibrium. Section 4 provides conditions for
full screening as well as some comparative statics, while Section 5 develops
the welfare analysis. Section 6 analyzes a number of alternative settings,
including exogenous challenges and a more general screening technology. We
conclude with a short summary of results and discussion of their implications
for policy (to be completed).
2
Model
There is a unit mass of inventors. Each inventor is endowed with an idea
(v, θ) for an invention. Inventions differ in two dimensions: value, indexed
by v, and R&D cost, indexed by θ. The characteristics (v, θ) of the inventor’s idea are his private information. Developing an idea into an invention
requires an R&D investment kθ . Once an invention has been developed,
the inventor can apply for a patent (i.e., patent applications can only be
submitted on inventions, not ideas).
Each inventor has a single competitor. Both firms are initially symmetric, and industry profits and consumer surplus prior to the invention are
normalized to zero. To fix ideas, consider a cost-reducing invention. In the
absence of a patent, once the invention has been developed it can be freely
copied (notice that this implies that the competitor learns v). Both firms
thus benefit from the cost reduction and obtain a profit πv > 0 each (i.e.,
total industry profit is 2πv ).4 Total welfare (gross of R&D costs) is 2πv + Sv ,
where Sv ≥ 0 is consumer surplus. If instead the invention is protected by a
patent the inventor obtains πv +∆v , where ∆v is the patent premium, which
will be endogenized below, and welfare is 2πv +Sv −Dv ≡ Wv , where Dv ≥ 0
is deadweight loss. We assume that Wv ≥ πv + ∆v for all v. This assumption says that the social returns exceed the private returns to R&D, which
is consistent with the evidence in Bloom, Schankerman and Van Reenen
(2013).
In what follows, we postulate that the requirement for an invention to be
4
For the inventor to benefit from the cost reduction even absent patent protection,
competition must not be too fierce. An example under which firms earn higher profits
post-invention is Cournot competition.
6
patentable is kθ > πv , i.e., R&D costs must be larger than the competitive
profits the inventor can obtain without a patent. Such a patentability requirement can be justified as follows. Consider a social planner maximizing
welfare. Which types of inventors does the planner want to give patents
to in our environment? From an ex post perspective, the answer is clearly
none at all, since patents create deadweight loss. From an ex ante perspective, the planner is still worried about deadweight loss, but also realizes that
some socially valuable inventions will not be developed in the absence of the
promise of a patent. But ideas with kθ ≤ πv are developed even without a
patent. Hence, due to deadweight loss, it cannot be optimal to give them a
patent. A second concern for the planner may be that giving patents to some
ideas with kθ > πv might lead to development of these ideas even though
they are not socially valuable, i.e., kθ > Wv . However, our assumption that
Wv > πv + ∆v rules this out, as it implies that ideas that are not socially
valuable are not privately valuable either.5
Our patentability requirement corresponds to the notion that patents
should be given only to those inventions that require the patent incentive
to be developed, and not those that society would have benefited from even
absent a patent. This is in line with the rationale courts and legal scholars
typically give for the nonobviousness requirement in patent law (see, e.g.,
Eisenberg, 2004).
In what follows, we simplify the analysis by considering a single v.6
5
A further objection to the patentability requirement we impose is that it encourages
high-cost inventions. This corresponds to a different environment, in which ideas are
endogenous. However, even in such an environment, the patentability requirement kθ > πv
can often be justified. To see this, suppose the inventor can choose (or influence, possibly
at a cost) θ but not (directly) v. Let v ∈ {L, H} and θ ∈ {G, B}, with kG > kB .
Assume θ is a signal of value: letting pθ ≡ Pr(v = H|θ), this implies pG > pB . We have
E(Wv |θ) = pθ WH + (1 − pθ )WL . If E(Wv |G) − kG > E(Wv |B) − kB , or
(pG − pB )(WH − WL ) > kG − kB ,
the planner wants to encourage the inventor to go for ideas with θ = G, which have
high R&D cost. That is, the planner would like to promote “ambitious” research. She
can achieve this by promising patents only to type θ = G. Depending on parameters
and information structure, it may or may not be optimal to base patentability on kθ − πv ,
rather than kθ only; however, in the simplified environment we consider in the basic model
below, these rules coincide.
6
The extension to multiple v has yet to be added, but is not fundamentally different as long as the competitor observes v; the signaling game then only involves private
information about θ.
7
Hence, we drop the index v from all expressions. Moreover, we consider
θ ∈ {G, B}, with kG > π > kB . Inventions of type θ = B occur with probability 1 − λ and will be referred to as obvious while inventions of type θ = G
occur with probability λ and will be referred to as nonobvious. Obvious inventions would be developed even in the absence of patent protection, while
nonobvious ones would not. Thus, society should award patent protection
only to nonobvious inventions. Because for an inventor whose idea is obvious the decision whether to develop does not depend on whether he expects
to obtain patent protection, we can normalize kB = 0 without loss of generality and assume kG = k > π. In order to ensure that patent protection
can provide sufficient incentive for nonobvious inventions to be developed,
we assume ∆ ≥ k − π.
We now endogenize the patent premium ∆ by considering an explicit
licensing game between the inventor and the competitor. Without a license
agreement, the firms compete with asymmetric costs, so that the inventor
earns π + ∆I and the competitor π − ∆C . Assume ∆I > 0 and ∆C > 0
(the patent benefits the inventor and hurts the competitor). With a license
agreement, so that both firms use the invention but are able to (jointly)
exercise market power, the inventor earns π + m + F and the competitor
π − F , where m ≥ 0 is the extra profit due to market power and F is the
license fee paid by the competitor to the inventor.7 Thus, total industry
profit becomes 2π + m. The parameter m can be interpreted as a measure
of how lenient or restrictive antitrust policy is towards license agreements
(e.g., which kind of pricing schemes are allowed – royalties or lump-sum fees
only). We assume that m + ∆C ≥ ∆I , which will ensure that the inventor
prefers to license his invention as long as he has sufficient bargaining power.
Hence, ∆ = m + ∆C .
Letting S − ∆S denote consumer surplus after innovation when there
is a patent, we have D ≡ ∆S − m. The assumption that deadweight loss
is positive amounts to ∆S ≥ m. We assume S + 2π − D ≥ kG , so that
investment in nonobvious innovation is socially valuable even if it comes at
7
Below we will assume that the inventor has all the bargaining power, so that it does
not matter how the extra profit m from reaching agreement is distributed between inventor
and competitor.
8
the expense of deadweight loss.
To obtain a patent, the inventor must submit an application to the patent
office and pay an application fee φA ≥ 0. The patent office then examines the
application. Nonobvious inventions always pass the examination. Obvious
inventions pass the examination only with probability 1 − e, where e ∈
[0, 1] represents the patent office’s examination intensity; with probability
e obvious inventions are detected and refused patent protection. Inventions
that pass the examination must pay a fee φP ≥ 0 in order to be issued
a patent. This payment thus occurs after the patent office has decided
whether to allow or reject the application, and has to be paid only in case
of allowance. We will refer to payment of φP as the inventor activating the
patent and to φP as the activation fee.8 If the inventor does not apply, does
not pass the examination, or does not pay φP , the invention falls into the
public domain.
An inventor holding a patent on his invention can enter into a license
agreement with his competitor. We assume that the inventor makes a takeit-or-leave-it offer to the competitor to license the cost-reducing invention
for a license fee of F .9 After receiving the inventor’s offer, the competitor
decides whether to accept or reject. If the competitor accepts, she pays the
license fee and can use the invention in production. If the competitor rejects
the license contract, she has the option of challenging the patent in court
at cost l.10 We assume l < ∆C ; otherwise, the competitor never has any
incentive to challenge. The court then determines the validity of the patent.
We assume that during litigation the court learns the invention’s true type
θ. If the invention is obvious (θ = B), the court invalidates the patent and
both firms can freely use the invention. If the invention is nonobvious, the
court upholds the patent and the inventor can offer a new license contract
to the competitor.11
8
One can think of the activation fee as a renewal fee paid in lump sum, whereby the
inventor chooses to maintain his patent for some duration in exchange for payment of φP .
9
Elsewhere in the literature, this licence negotiation stage is sometimes referred to as
a settlement stage (see, e.g., Meurer, 1989).
10
In the baseline model we assume that the inventor does not incur litigation costs. This
simplifies the analysis and avoids multiplicity of equilibria. We relax this assumption in
Section 6.2.
11
In other words, courts do not make mistakes in assessing patent validity. In Section
9
Our equilibrium concept is Perfect Bayesian Equilibrium.
3
Equilibrium
3.1
Nonobvious inventions
We start by analyzing the problem of an inventor of type G. Consider first
the licensing stage. Suppose that it is common knowledge that the patent
is valid (θ = G), so that the competitor has no incentive to challenge.
Consider a license fee offer F . If the competitor rejects the license, the firms
will have asymmetric costs and earn π + ∆I and π − ∆C , respectively. If
the competitor accepts the license, they will have symmetric costs and earn
π + m + F and π − F . Thus the maximum license fee the competitor is
willing to pay is F = ∆C . At this fee, the inventor is better off licensing
than not if ∆I ≤ m + ∆C , which we have assumed to hold. This leads to
the following lemma.
Lemma 1. If it is common knowledge that the patent is valid, the inventor
will offer to license it at a fee of F G = ∆C , which the competitor accepts.
The inventor earns π + ∆ and the competitor earns π − ∆C .
Now suppose it is not common knowledge that θ = G. Let λ̃(F ) denote
the competitor’s belief that the patent is valid given that the inventor offers
her a license at fee F . Yet, regardless of the competitor’s beliefs, the type-G
inventor will offer the exact same license contract identified in Lemma 1.
The reason is that he does not care about the competitor challenging the
patent: he does not incur litigation costs, and he knows that in the event
of a validity challenge his patent will be upheld in court, after which the
outcome identified in the lemma will materialize.12
It follows that the behavior of an inventor of type G is simple and can
be summarized as follows.
Lemma 2. An inventor of type G will invest in R&D, apply for a patent,
pay the activation fee and offer a license at fee F G to the competitor if
∆ − (k − π) − φP − φA ≥ 0;
(1)
6.2, we examine a more general screening technology in which both patent office and courts
can make errors (of both type I and type II).
12
We relax both of these assumptions in Section 6.2.
10
otherwise he will not invest (and hence cannot apply for a patent).
3.2
Obvious inventions
Contrary to type-G inventors, type-B inventors care about challenges and
thus about the competitor’s beliefs. Suppose type G always invests, applies,
activates, and offers to license his patent at fee F G . Denote by α the probability that a type-B inventor applies for a patent. Similarly, denote by ρ
the probability that a type-B inventor activates the patent in case he passes
examination, and by y the probability that she offers a license contract with
fee F G . Indeed, all three of these decisions – whether to apply for a patent,
pay the activation fee, and which license fee to offer – potentially provide
information about the inventor’s type. In addition, the outcome of examination also provides information. The competitor’s belief that an activated
patent is valid when offered a license contract at fee F G is
λ̂ ≡ λ̃(F G ) =
λ
.
λ + (1 − λ)(1 − e)αρy
Now consider the competitor’s decision whether to challenge the patent when
offered a license contract at fee F G = ∆C . If she accepts the contract or
rejects it but does not challenge, her payoff is π − ∆C ; if she challenges, her
expected payoff is
λ̂(π − ∆C ) + 1 − λ̂ π − l.
With probability λ̂ the invention is nonobvious, in which case the court
upholds the patent, and the inventor holds the competitor down to a payoff
of π −∆C (see Lemma 1). With probability 1− λ̂ the invention is obvious, in
which case the court invalidates the patent, and the competitor obtains π.
In either case the competitor incurs litigation costs of l. Thus the competitor
prefers challenging to not challenging if and only if
1 − λ̂ ∆C ≥ l.
(2)
The lower bound on λ̂ occurs if the type-B inventor pools with the typeG inventor, i.e., if α = ρ = y = 1, and is denoted
λ(e) ≡
λ
.
λ + (1 − λ)(1 − e)
11
Because this is the lowest value that λ̂ can take it is the one that makes
challenges most attractive from the competitor’s point of view. If challenging
the patent is not worthwhile for the competitor under pooling, it will never
be worthwhile. Hence, we will say that a validity challenge is credible if and
only if
(1 − λ(e)) ∆C ≥ l.
(3)
That is, if the type-B inventor mimics the type-G inventor, challenging the
validity of the patent is a credible threat.
Remark: Note that (1 − λ(e)) is decreasing in e, implying that, as
the patent office steps up its examination efforts, it may crowd out private
challenges. The reason is that higher e makes it less likely that a type-B
inventor passes the examination, and therefore strengthens the competitor’s
belief that a successful patent applicant is of type G.
The following lemma characterizes the type-B inventor’s and competitor’s equilibrium behavior in the case where challenges are not credible.
Lemma 3. Suppose (3) does not hold. Then, the type-B inventor applies,
activates and proposes F G (i.e., α = ρ = y = 1) if
(1 − e) [∆ − φP ] − φA ≥ 0,
(4)
and does not apply otherwise. The competitor never challenges.
Proof. Since challenges are not credible, the type-B inventor can obtain the
same payoff as a type-G inventor once he passes the examination, which
is the highest payoff he could ever hope to secure. Thus we do not have
to consider deviations to other license fees, regardless of the competitor’s
beliefs λ̃(F ). The type-B inventor’s only relevant decision is whether to
apply. He prefers applying to not applying if and only if
eπ + (1 − e) [π + ∆ − φP ] − φA ≥ π,
which after rearranging yields (4).
When challenges are not credible, the type-B inventor either applies for
(and activates) a patent and then pools with the type-G inventor by offering
F = F G , or he does not apply at all. By contrast, when challenges are
12
credible, pooling with type G cannot be an equilibrium. The reason is that
the competitor would then have belief λ(e) and would therefore challenge
the patent with probability 1, in which case the type-B inventor would be
sure to have his patent invalidated. To avoid being challenged, the type-B
inventor can offer to license his patent at a fee that is low enough for the
competitor to prefer not to challenge. Consider a candidate equilibrium in
which type G proposes F G = ∆C and type B proposes F̃ < ∆C (i.e., a
separating equilibrium). The competitor correctly infers that λ̃(F̃ ) = 0.
For the competitor to prefer not to challenge although he believes that the
patent is invalid with certainty, it must be that π − F̃ ≤ π − l, or F̃ ≤ l.
The out-of-equilibrium belief most likely to support this as an equilibrium
is λ̃(F ) = 0 for any F ∈
/ {F G , F̃ }. Given these beliefs, the competitor’s best
response is not to challenge if F ≤ l; thus, the type-B inventor might as
well propose F̃ = l. This is not an equilibrium, however, as type B could
do better by deviating to F G . Observing F G would lead the competitor to
believe that the patent is valid with certainty, and therefore refrain from
challenging. Hence, the equilibrium can be neither pooling nor separating.
What this argument suggests is that, when challenges are credible, the
only equilibrium is a semi-separating one in which the type-B inventor randomizes over one of his decisions (applying, activating, license fee) and the
competitor randomizes over challenging and not when observing a license
offer at fee F G . To determine over which decision the type-B inventor will
randomize, suppose first that application and activation fee, φA and φP , are
sufficiently low (in a sense yet to be made precise). Then, type B always
applies and activates; the randomization will occur over the license fee to
propose. As in Meurer (1989), the type-B inventor will propose
∆C with probability y
FB =
l
with probability 1 − y,
where y is chosen so as to make the competitor indifferent between challenging and not. Denote by x the probability that the competitor challenges the
patent when faced with a license offer F = F G . The competitor chooses x so
as to make the type-B inventor indifferent between proposing ∆C and l. This
is an equilibrium if it allows type B to break even, i.e., if his payoff from applying exceeds his payoff from not applying: π +(1−e)(m+l−φP )−φA > π.
13
If type B cannot break even proposing l but could break even proposing ∆C ,
the randomization must instead occur over the application decision (or the
activation decision). The competitor then chooses the probability of challenges x so as to make type B indifferent between applying and not (or
between activating and not).
The following lemma characterizes the equilibrium. The lemma is based
on the condition for type G to invest, (1), being satisfied, which requires
in particular φP ≤ ∆. Below we examine under what assumptions the
various conditions characterizing type B’s behavior given in the lemma are
compatible with (1).13
Lemma 4. Suppose (3) holds. Then, the equilibrium behavior of the type-B
inventor and the competitor can be characterized as follows:
(i) If φA ≥ (1 − e)(∆ − φP ), the type-B inventor does not apply (α = 0),
and the competitor does not challenge (x = 0).
(ii) If φA < (1 − e)(∆ − φP ), the type-B inventor applies with strictly
positive probability (α > 0) and randomizes such that
λ(e)
∆C = l.
1−
λ(e) + (1 − λ(e)) αρy
(5)
The competitor always accepts when offered F = l (x = 0); she always challenges the patent when offered F ∈
/ {l, F G } (x = 1). When
offered F = F G she randomizes between accepting and challenging.
Specifically:
(a) for φP < l + m and φA < (1 − e)(l + m − φP ), the type-B inventor
chooses α = ρ = 1 and y ∈ (0, 1) solving (5). The competitor
challenges with probability x such that
(1 − x)∆ = l + m;
13
(6)
The uniqueness of the equilibrium is due to our assumption that the inventor does not
incur litigation costs. If litigation were costly to the inventor, there would be a continuum
of semi-separating equilibria with F G ≤ ∆C and (depending on parameters) also pooling
equilibria. Note, however, that a semi-separating equilibrium with F G = ∆C always
exists.
14
(b) for φP > l + m and φA = 0, the type-B inventor chooses y = 1
and (α, ρ) ∈ [0, 1]2 solving (5). The competitor challenges with
probability x such that
(1 − x)∆ = φP ;
(7)
(c) for max{0, (1 − e)(l + m − φP )} < φA < (1 − e) (∆ − φP ), the
type-B inventor chooses ρ = y = 1 and α ∈ (0, 1) solving (5).
The competitor challenges with probability x such that
(1 − e) [(1 − x)∆ − φP ] = φA .
(8)
Proof. For φA ≥ (1 − e)(∆ − φP ), type B’s payoff from applying is weakly
less than his payoff from not applying even if there are no challenges, so
(α = 0, x = 0) is an equilibrium, establishing (i). (This equilibrium is
unique for φA > (1 − e)(∆ − φP ).) In what follows, we first show that for
φA < (1 − e)(∆ − φP ), there is no equilibrium in which α = 0, ρ = 0, or
y = 0, that there is none in which α = ρ = y = 1, and that there is also none
in which x = 0 or x = 1, implying that the equilibrium must be in mixed
strategies. We then prove the more specific claims made in (ii.a)-(ii.c).
Suppose first there were an equilibrium with α = 0, ρ = 0, or y = 0
when φA < (1 − e)(∆ − φP ). Then the competitor’s belief would be λ̂ = 1,
and hence she would not challenge. But this means that the type-B inventor
could secure a strictly positive expected payoff of (1−e)(∆−φP )−φA > 0 by
applying, activating and offering F G , contradicting the optimality of α = 0
or ρ = 0. Moreover, by offering F = F G = ∆C type B obtains a higher
payoff than by offering F = l (because ∆C > l), contradicting the optimality
of y = 0. Hence, under the assumed condition on φA , in any equilibrium we
must have α > 0, ρ > 0 and y > 0. Next, suppose there were an equilibrium
with α = ρ = y = 1. Then λ̂ = λ(e), and by (3), the challenger would
always challenge. But then type B would be better off deviating in some
dimension. (If φP > 0, type B would be better off not activating or not
applying. If φP = 0 < l + m, type B would be better off offering F = l.)
Now consider the competitor’s decision to challenge. If there were an
equilibrium in which she never challenges (x = 0), then all type-B inventors
15
would apply, activate and offer F G (α = ρ = y = 1). But in that case, (3)
implies that the competitor would strictly prefer to challenge. If there were
an equilibrium in which she always challenges (x = 1), then type B would
prefer not to apply, in which case the competitor would be better off not
challenging.
Hence, the only equilibrium is in mixed strategies. For the competitor
to be indifferent between challenging or not, his beliefs about the type of
inventor he faces must be such that the payoff from challenging is the same
as the payoff from not challenging, i.e., (2) must hold with equality. Using
the definition of λ̂ yields (5). The conditions for the type-B inventor to be
indifferent depend on parameters and are specified below.
Claim (ii.a) [φP < l + m and φA < (1 − e)(l + m − φP )]: Because
the competitor always accepts the offer F = l, the type-B inventor can
guarantee himself a payoff of l+m following activation. Hence, if φP < l+m,
type B strictly prefers activating to not activating, implying ρ = 1. By
the same argument, if φA < (1 − e)(l + m − φP ), type B strictly prefers
applying to not applying, so α = 1. The only randomization variable that
remains is y. For the type-B inventor to be indifferent between offering
F = l and F = ∆C , both must procure him the same payoff. This requires
π + l + m = π + (1 − x)∆, or (6).
Claim (ii.b) [φP > l + m and φA = 0]: Because φP > l + m, the
inventor will never offer F = l, as he would be sure to make a loss then.
Hence, y = 1. In any equilibrium in which the type-B inventor is indifferent
between activating and not, which requires π = π +(1−e)[(1−x)∆−φP ], or
(7), his payoff from applying for a patent will be zero. Because φA = 0, he
will also be indifferent between applying and not. Hence, any combination
of α and ρ which (given y = 1) solves (5) constitutes an equilibrium.
Claim (ii.c) [max{0, (1 − e)(l + m − φP )} < φA < (1 − e) (∆ − φP )]:
Because (1 − e)(l + m − φP ) < φA , the type-B inventor cannot break even
offering F = l; hence, y = 1. To see that type B will necessarily randomize
over the application decision rather than the activation decision, suppose to
the contrary ρ < 1. This would require (1 − x)∆ = φP . But in that case,
type B’s payoff from applying would be zero, and given φA > 0 he would
prefer not to apply. Hence, ρ = 1. The only randomization variable that
16
remains is α. For type B to be indifferent between applying and not, it must
be that π = π + (1 − e)[(1 − x)∆ − φP ] − φA , or (8).
Let us denote
α̃ = ỹ ≡
λl
.
(1 − λ)(1 − e)(∆C − l)
That is, α̃ (ỹ) is the value of α (y) solving (5) when y = 1 (α = 1) and
ρ = 1. Notice that α̃, ỹ ∈ (0, 1) when challenges are credible. Furthermore,
let
x̃ ≡ 1 −
and
x̂ ≡
l+m
∆
(1 − e)(∆ − φP ) − φA
.
(1 − e)∆
That is, x̃ is the value of x solving (6) while x̂ is the value of x solving (8).
Notice that x̃ ∈ (0, 1) (because l < ∆C ) and x̂ ∈ (0, 1) when φP < ∆ and
0 < φA < (1 − e)(∆ − φP ).
Figure 1 depicts how the equilibrium that arises when challenges are
credible depends on φA and φP . The figure is drawn under the implicit
assumption that φA > 0 so that ρ = 1. In region 1, where φP ≤ l + m
and φA ≤ (1 − e)(l + m − φP ), fees are sufficiently low for the type-B
inventor to always find it worthwhile to apply and activate (α = ρ = 1) while
randomizing over the license fee to offer, with y = ỹ; the rate of challenges
is given by x̃. Moving toward the north-east into region 2, type B can no
longer break even by offering the low fee F = l; he now randomizes over
the application decision, applying with probability α = α̃ while activating
and offering the high license fee F G with certainty (ρ = y = 1). The rate of
challenges is given by x̂. As fees increase further and we reach region 3, the
type-B inventor no longer applies (α = 0) and the rate of challenges drops
to zero (x = 0).
The figure also shows the condition under which type G finds it profitable
to invest, (1). The φA = ∆−(k −π)−φP line is drawn under the assumption
that e > ē(0) (to be defined below), which implies existence of region 3.
If instead e < ē(0), then region 3 does not exist. That is, there is no
combination of φA and φP such that type G (invests and) applies and type
B does not. We investigate this point in more detail in the next section.
17
φA
∆ − (k − π)
φ
A
(1 − e)∆
α = 0,
x=0
=
3
∆
−
(k
No investment by type G
−
π)
−
φ
P
α = α̃,
y = 1, x = x̂
(1 − e)(l + m)
φA
=(
2
1−
e)(
l+
m
α = 1, 1
−φ
P)
y = ỹ, x = x̃
0
l+m
φA
=(
1−
e)(
∆
−φ
P)
∆ − (k − π)
∆
φP
Figure 1: The equilibrium as a function of φP and φA when ē(0) < e < 1
4
Fees and screening
In this section we look at the effect of fees on screening of inventors, taking
the patent office’s examination intensity e as exogenously given. We first
study under what conditions we can achieve full screening, i.e., deterring
applications by type B without discouraging investment by type G. We
then derive comparative statics results for the case where full screening is
not possible.
4.1
Full screening
The two following propositions examine when and how it is possible to induce
complete self-screening of inventors, so that only nonobvious inventions are
applied for. The results show that the extent to which fees are effective
screening tools depends on the examination intensity e.
Proposition 1. If either e = 0 or φA = 0 and e < 1, there is no equilibrium
in which only the type-G inventor applies.
Proof. If e = 0, then by Part (i) of Lemma 4, deterring type B requires
18
φA + φP ≥ ∆. If φA = 0 and e < 1, then by Part (i) of Lemma 4, deterring
type B requires either e = 1 or φP ≥ ∆; since e < 1 by assumption, we
must have φP ≥ ∆. In either case, type G will not invest, as his payoff then
is ∆ − (k − π) − φP − φA ≤ −(k − π) < 0, where the last inequality is due
to the definition of a nonobvious invention.
This proposition makes two points. First, it underlines the importance
of patent examination. If there is no examination at all (e = 0), then
fees cannot completely screen out obvious inventions. This happens despite
the fact that we have assumed that courts are perfect at discriminating
between obvious and nonobvious inventions. One might have expected that
the resulting payoff differential at the litigation stage would suffice to screen
inventors through an appropriate choice of fees. The reason why this fails to
hold is that the competitor is Bayesian and updates her beliefs based on the
inventor’s equilibrium strategy. If there were an equilibrium in which only
type G applies, the competitor would rationally expect any applicant to be
of type G, and therefore refrain from challenging. But then, in the absence
of patent examination, type B would also find it worthwhile to apply, hence
such an outcome cannot be an equilibrium. Instead the equilibrium will
be in mixed strategies, implying that at least some type-B inventors apply.
In contrast to the competitor’s decision whether or not to challenge the
patent, the patent office examines all patents, regardless of the inventor’s
equilibrium strategy.
Second, we cannot rely exclusively on the activation fee φP if we want
to induce self-screening of inventors; screening relies crucially on the application fee φA being positive. This is related to the previous result. If
applications are costless (φA = 0) and examination is less than perfect
(e < 1), type-B inventors have nothing to lose from applying. But once
a patent passes examination, it is subject only to a possible challenge by the
competitor, whose decision depends on his beliefs, which in turn depend on
the inventor’s equilibrium strategy. Because of the mixed-strategy nature
of the equilibrium, completely deterring type B through the activation fee
is possible only by setting φP ≥ ∆, which also deters type G.
Proposition 2. For any activation fee φP < ∆ − (k − π), there exists an
19
application fee φA > 0 such that only the type-G inventor applies if and only
if e ≥ ē(φP ), where
ē(φP ) ≡
k−π
.
∆ − φP
(9)
Proof. By Lemma 2, investment by type G requires π − k + ∆ − φP ≥ φA .
By Part (i) of Lemma 4, deterrence of type B requires φA ≥ (1 − e)(∆ −
φP ). An application fee φA satisfying both inequalities exists if and only if
π − k + ∆ − φP ≥ (1 − e)(∆ − φP ), or
π − k + e(∆ − φP ) ≥ 0,
which can be arranged to yield e ≥ ē(φP ) defined in (9).
Proposition 2 says that complete screening of inventors is possible provided the examination intensity is sufficiently large. Note that, for any
φP < π + ∆ − k, the examination intensity required is strictly less than
one: the patent office does not have to be perfect. Exactly how rigorous the
patent office needs to be depends on φP , as the following corollary shows.
Corollary. The examination intensity required to achieve complete selfscreening of inventors, ē(φP ), is increasing in φP .
This result speaks to the relative effectiveness of application and activation fees in inducing inventors to self-screen. The higher the activation
fee φP , the higher the examination intensity needed for screening. In other
words, higher activation fees make it more difficult to induce inventors to
self-screen. The intuition is that, while application and activation fees are
perfect substitutes for type-G inventors, type-B inventors prefer activation
fees, which only need to be paid conditional on surviving examination. For
type G, all that matters is the sum φP + φA because he knows he will pass.
By contrast, for type B what matters is φA + (1 − e)φP .
A further result of our analysis is that despite the fact the courts are
mistake-free, they cannot eliminate all bad patents that are issued. To
see this point, note that eliminating all bad patents would require that
x = 1 whenever α > 0, i.e., all issued patents would need to be challenged.
Alternatively, type-B inventors would have to reveal themselves so that they
could be targeted by challenges. But as Lemma 4 shows, neither of these
20
is an equilibrium outcome. There is no equilibrium with α > 0 and x = 1.
There is also no equilibrium in which type-B inventors reveal themselves and
then get challenged. Although for φP < l and φA < (1 − e)(l − φP ), type
B sometimes reveals himself by offering F = l, the competitor optimally
responds to this by not challenging.
4.2
Partial screening
The previous subsection has shown that when e < ē(0), it is impossible to
achieve full screening. Nevertheless both application and activation fees can
be effective in achieving partial screening. In addition, fees and examination
will affect the rate of challenges and the licensing fees proposed by inventors.
The next proposition considers the effects of φA , φP and e on the equilibrium
variables α, x, and y.
Proposition 3. Suppose the type-G inventor invests and challenges are
credible, i.e., (1) and (3) hold. Then:
(i) An increase in φA or φP weakly decreases applications by type B (α),
weakly decreases the rate of challenges (x), and weakly increases the
license fee proposed by type B (y).
(ii) An increase in e has ambiguous effects on applications by type B (α),
the rate of challenges (x), and the license fee proposed by type B (y).
Proof. To be added.
Proposition 3 shows that an increase in fees unambiguously decreases
bad applications and challenges (in a weak sense). It also leads to higher
license fees, as type-B inventors switch from randomizing over the license
fee to randomizing over the application decision. Perhaps more surprisingly,
the effect of an increase in the examination intensity e has ambiguous effects
on applications by type-B inventors. Over some range, the application rate
of type-B inventors actually increases with e. The intuition is that more
rigorous examination makes it more likely that a granted patent is valid,
other things equal. That is, higher e raises the competitor’s posterior belief
λ̂. But in equilibrium, the competitor must be indifferent between challenging and not, which requires that λ̂ be held constant. Therefore, in region 2,
21
type B responds to an increase in e by adjusting the probability of applying
(α) upward.
5
Welfare
To be able to say more about the optimal structure of fees for a given e, let
us derive the expected welfare as a function of the equilibrium variables α,
x, and y.14 Assume that the cost of examining an application with intensity
e is γ(e). Denoting expected welfare by W , we have
W (α, x, y) = 2π + S + λ(−D − xl − k − γ(e))
+ (1 − λ)α (1 − e) (y(1 − x) + 1 − y)(−D) − xyl − γ(e) . (10)
With probability λ, the invention is nonobvious, in which case the inventor
always applies and society incurs the deadweight loss D, the cost of investment k and the cost of examination γ(e) with certainty, while it incurs the
cost of challenges l with probability x. With probability 1 − λ, the invention
is obvious, in which case the inventor applies with probability α. Conditional on application, society incurs the deadweight loss with probability
(1 − e)(y(1 − x) + 1 − y), the cost of challenges with probability (1 − e)xy,
and the cost of examination with certainty. To understand these probabilities, recall that with probability 1 − y, the type-B inventor offers F = l,
which is always accepted; with probability y, type B offers F = ∆C , which
is accepted with probability 1 − x and instead leads to a challenge with
probability x.
Expression (10) highlights several important points. First, holding everything else constant, welfare is decreasing in the application rate of type-B
inventors, α. This implies that welfare is maximized with complete screening (where α = x = 0). Second, if α > 0, the effect of the rate of challenges
x on welfare is ambiguous. Differentiating W with respect to x yields
∂W
= −λl + (1 − λ)(1 − e)αy(D − l).
∂x
(11)
On the one hand, challenges help society get rid of invalid patents (which
increases welfare provided deadweight loss exceeds litigation costs, D > l),
14
We are focusing on the case ρ = 1, i.e., we neglect situations in which φA = 0.
22
but on the other hand, they create wasteful litigation of valid patents. Third,
assuming deadweight loss exceeds litigation costs, welfare is increasing in y.
Taking the derivative of the term in square brackets with respect to y, we
obtain x(D − l), which is strictly positive for x > 0 and D > l.
Let e ≡ [k − π − (∆C − l)]/(l + m). If e < e, only region 1 is attainable,
and in region 1 welfare is unaffected by φA and φP because α = 1, x = x̃,
and y = ỹ, none of which depend on fees. To make the problem interesting,
assume in what follows that e < e < ē(0), so that both region 1 and region
2 are attainable but region 3 is not (i.e., full screening cannot be achieved).
Geometrically, region 3 in Figure 1 disappears as the φA = (1 − e)(∆ − φP )
line now shifts above the φA = ∆ − (k − π) − φP line. The social planner’s
problem is to choose φA and φP to maximize welfare subject to type G
investing, taking e as given:
max W (α, x, y)
(φA ,φP )
subject to φA ≤ ∆ − (k − π) − φP .
Although welfare does not depend directly on φA and φP , it depends on
them indirectly through their effect on the equilibrium values of α, x, and y.
The following proposition characterizes the welfare-maximizing combination
of fees.
Proposition 4. If e < e < ē(0) and ∆C > D > l, welfare is maximized for
φP = 0 and φA = ∆ − (k − π).
Proof. Notice that within region 1, welfare does not depend on either φA or
φP , as α = 1, x = x̃, and y = ỹ are all constant in φA and φP . Similarly,
within region 2, welfare depends on φA and φP only through x = x̂(φA , φP )
(which we make explicit by including the fees as arguments) and not through
α = α̃ or y = 1. Thus the welfare maximization problem is reduced to
a choice between W (1, x̃, ỹ) and maxφA ,φP W (α̃, x̂(φA , φP ), 1). Notice also
that αy is the same in regions 1 and 2, as αy = ỹ in region 1, αy = α̃ in
region 2, and α̃ = ỹ.
The proof proceeds as follows. We first show that, keeping αy fixed,
welfare is decreasing in α. Second, we show that fixing αy at its equilibrium
value in regions 1 and 2 (α̃ = ỹ), welfare is decreasing in x. Third, we show
that x̃ ≥ x̂(φA , φP ) for any (φA , φP ) in region 2. Together these claims
23
imply that the solution to the welfare maximization problem is obtained by
solving minφA ,φP x̂(φA , φP ) subject to φA ≤ ∆ − (k − π) − φP .
Claim 1: For any (α, y) ∈ (0, 1)2 and (α0 , y 0 ) ∈ (0, 1)2 such that αy =
α0 , y 0 , W (α, x, y) ≥ W (α0 , x, y 0 ) if and only if α ≤ α0 . Rewriting W we have
W (α, x, y) = 2π + S − λ(D + xl + k + γ(e))
+ (1 − λ) (1 − e)αyx(D − l) − α[(1 − e)D + γ(e)] . (12)
For αy = α0 y 0 , we have W (α, x, y) − W (α0 , x, y) = (1 − λ)(α0 − α)[(1 − e)D +
γ(e)] ≥ 0 if and only if α ≤ α0 .
Claim 2: (∂/∂x)W (α, x, y)|αy=α̃ < 0. Replacing αy by α̃ = λl/[(1 −
λ)(1 − e)(∆C − l)] in (11) yields
D−l
∂W = λl
− 1 < 0,
∂x αy=α̃
∆C − l
where the inequality follows from the assumption that l < D < ∆C .
Claim 3: x̃ ≥ x̂(φA , φP ) for any (φA , φP ) such that (1 − e)[l + m − φP ] ≤
φA (1 − e)[∆C + m − φP ]. Since x̂ is decreasing in φA and φP , its maximum
x̂max is attained for (1 − e)[l + m − φP ] = φA . We have
x̂max =
∆C − l
= x̃.
∆C + m
Hence, x̂(φA , φP ) < x̃ for (1 − e)[l + m − φP ] < φA .
Having established these claims, we now solve for the welfare-maximizing
fees, i.e., the fees that minimize x̂ subject to type G investing:
min x̂(φA , φP )
φA ,φP
subject to φA ≤ ∆ − (k − π) − φP .
Since x̂ is decreasing in φA , the constraint must bind at the optimum. The
problem becomes
min
φP
(1 − e)(∆ − φP ) − (∆ − (k − π) − φP )
k − π + e(φP − ∆)
=
.
(1 − e)∆
(1 − e)∆
Since this increases with φP , the minimum is reached at φP = 0, implying
φA = ∆ − (k − π).
This proposition shows that, if examination is not rigorous enough to
allow for full screening, the planner should set activation fees to zero and
24
use only application fees. The intuition is that, as discussed above, type B
prefers fees to be backloaded while type G is indifferent between application
and activation fees. Here, keeping the sum of fees φA + φP fixed, the rate
of challenges x decreases as we frontload fees, because fewer challenges are
necessary to make type B indifferent between applying and not. Moreover,
the planner should set application fees at the highest level compatible with
investment by type G. Again, this is related to the fact that higher fees
decrease x, which the proof shows to be welfare enhancing.
6
Alternative settings
6.1
Exogenous challenges
It is instructive to compare the results we have obtained when challenges
are endogenously triggered by a fully Bayesian competitor to the case where
challenges are exogenous. Specifically, suppose that all patents get challenged at a constant rate x̄ ∈ (0, 1) (independently of the inventor’s type θ)
and that courts do not make mistakes in determining validity.15 Then, the
type-G inventor activates iff ∆ ≥ φP while the type-B inventor activates iff
(1 − x̄)∆ ≥ φP . Clearly, for ∆ > φP > (1 − x̄)∆ and φA + φP ≤ ∆ − (k − π)
(which can both be satisfied provided x̄ is sufficiently large and φA sufficiently small), the activation fee screens out type-B inventors without dissuading type-G inventors. Moreover, no minimum level of patent examination is required to achieve this.
While this argument does not provide a reason why the activation fee
would be a better screening tool than the application fee, it is easy to construct an example where this is the case. To do this, let us extend the
basic model by introducing learning about the gains from patenting over
time. Suppose the type-G inventor does not know whether the gains from
patenting are high or low until after applying for a patent. For concreteness,
assume that the gains are either ∆ (with probability ν) or 0 (with probability
1 − ν). The type-B inventor knows his gains from patenting already at the
moment of applying. Assume that the application fee needed to screen out a
15
One could obtain similar results by assuming that challenges are more likely for type
θ = B and courts are random.
25
type-B inventor with high gains from patenting, φA = (1−e)[(1− x̄)∆−φP ],
is so large that the type-G inventor earns a negative expected profit from
investing even if φP = 0:
π + ν∆ − k − (1 − e)(1 − x̄)∆ ≤ 0,
or
k − π ≥ [ν − (1 − e)(1 − x̄)]∆
(13)
At the same time, assume that if φP is set so as to screen out the type-B
inventor, φP = (1 − x̄)∆, then it is profitable for the type-G inventor to
invest if φA = 0: ν[∆ − (1 − x̄)∆] ≥ k − π, or
ν x̄∆ ≥ k − π.
(14)
Inequalities (13) and (14) can only ever be simultaneously satisfied if
ν x̄∆ > [ν − (1 − e)(1 − x̄)]∆,
or
e < 1 − ν.
Thus, if patent examination is not too rigorous, then there exists a range
of values of (k − π) such that we can screen out type-B inventors through
the activation fee. At the same time, by construction, screening through the
application fee is not possible.
6.2
A more general screening technology
Many observers argue that patents are “probabilistic” in nature (Lemley and
Shapiro, 2005), suggesting that court decisions are subject to some amount
of randomness. We have so far assumed that courts do not make mistakes
in assessing validity. In this section, we look at a more general screening
technology whereby both patent office and courts sometimes make mistakes.
This technology encompasses both the basic model (with perfect courts) and
completely random courts (where the probability that a patent is upheld
does not depend on the inventor’s type θ) as special cases.
Suppose the patent office and the courts review applications with intensity e1 and e2 respectively. The intensity of review equals the probability
26
Table 1: Probability of acceptance and rejection at review stage i by type
Type G
Type B
Acceptance
ei + (1 − ei )qi
(1 − ei )qi
Rejection
(1 − ei )(1 − qi )
ei + (1 − ei )(1 − qi )
that they find out the inventor’s true type. With probability 1 − ei , i = 1, 2,
they find no strong evidence either way, in which case the patent office allows the application with probability q1 while the courts uphold the patent
with probability q2 . This leads to stage-i probabilities of acceptance and
rejection for each type of inventor given in Table 1, with i = 1, 2, stage 1
corresponding to patent office review and stage 2 corresponding to court
review. Our basic model is a special case of this setup with e1 = e, q1 = 1,
and e2 = 1.
In addition, suppose that both the inventor and the challenger incur
litigation costs. The inventor’s litigation costs are lI while the challenger’s
are lC . Assume (1−e2 )(1−q2 )∆C < lC < (e2 +(1−e2 )(1−q2 ))∆C ; otherwise
the competitor either would not want to challenge even when being sure of
facing a type-B inventor or would want to challenge even when being sure of
facing a type-G inventor. Everything else is the same as in the basic model.
6.2.1
Random courts
Before considering the full-fledged generalization, let us look at the special
case in which e1 = e, e2 = 0, and q1 = q2 = q ∈ (0, 1). That is, courts
are random: the probability that a patent is upheld does not depend on the
inventor’s type. This implies that, once they pass the examination at the
patent office, both inventor types are equivalent, in the sense that they have
the same continuation payoff. Thus, either both or neither of the inventor
types activate the patent, and if they do, both types offer the same license
fee F . Assume also that lI = 0 and lC = l. The competitor’s payoff from
accepting then is π − F , while her payoff from rejecting and challenging is
q(π − ∆C ) + (1 − q)π − l. Hence, the competitor challenges iff F > l + q∆C .
If (1 − q)∆C < l, challenges are not credible; therefore the inventor
charges F = ∆C and earns the same payoff as the type-G inventor in the
27
baseline model. If instead (1 − q)∆C ≥ l, challenges are credible. The
inventor then faces a choice between asking for F = l + q∆C , which avoids
a challenge and yields π + m + l + q∆C , or asking for F > l + q∆C , which
triggers a challenge and yields q(π + ∆) + (1 − q)π. The inventor’s payoff
from activating the patent is thus V = max{q∆, l + m + q∆C }. It follows
that both types of inventors activate their patents iff V ≥ φP . As one might
expect, when courts cannot distinguish valid from invalid patents, activation
fees are ineffective as a screening tool.
The type-G inventor invests iff π + V − φP − φA − k ≥ 0. Assuming
challenges are credible, i.e., that l ≤ (1−q)∆C , we have l+m+q∆C ≤ ∆, and
hence V ≤ ∆. Thus, the type-G inventor earns a lower payoff with random
courts than with mistake-free courts. Not surprisingly, probabilistic patent
enforcement by the courts is a drag on innovation. The type-B inventor
applies for a patent iff (1 − e)[V − φP ] − φA ≥ 0. We therefore obtain the
following result.
Proposition 5. Suppose courts randomly uphold a fraction q of patents,
independent of θ, and that (1 − q)∆C ≥ l. For any activation fee φP <
π + V − k, there exists an application fee φA > 0 such that only the type-G
inventor applies if and only if
e≥
k−π
≥ ē(φP ).
V − φP
Proof. The threshold on e can be found using the same argument as for
Proposition 2, replacing ∆ by V . The inequality (k − π)/(V − φP ) ≥ ē(φP )
follows from the fact that, if (1 − q)∆C ≥ l, then V ≤ ∆.
Thus, while it is still possible to induce inventors to self-screen, doing so
requires more rigorous examination by the patent office than when courts
are mistake-free.
6.2.2
Imperfect but non-random courts
Now consider the full-fledged generalization. Type G’s expected payoff from
investing (and then applying for and activating the patent, if granted, and
28
offering a license at fee F G ) is
h πG = (e1 +(1−e1 )q1 ) x (e2 +(1−e2 )q2 )(π+m+∆C )+(1−e2 )(1−q2 )π−lI
i
+ (1 − x)(π + m + F G ) − φP + (1 − e1 )(1 − q1 )π − k − φA , (15)
where x is the rate of challenges given F G . To understand this expression,
note that the application is allowed by the patent office with probability
(e1 + (1 − e1 )q1 ), in which case the patent is either challenged (probability
x) or not (probability 1 − x). In the event of a challenge, the patentee wins
with probability (e2 + (1 − e2 )q2 ), in which case she earns π + m + ∆C ,
and loses with probability (1 − e2 )(1 − q2 ), in which case she earns only the
competitive profits π. In either case she incurs litigation costs of lI . If there
is no challenge the patentee earns π +m+F G . The application is rejected by
the patent office with probability (1 − e1 )(1 − q1 ), in which case the patentee
earns only π.
Suppose type G invests and applies; moreover, suppose that if he is
successful in obtaining a patent, he activates it and charges a license fee
F G = ∆C (we will later examine under what conditions this is an equilibrium). The competitor’s belief that an activated patent whose holder offers
a license fee of F G is valid is
λ̂ =
λ(e1 + (1 − e1 )q1 )
,
λ(e1 + (1 − e1 )q1 ) + (1 − λ)(1 − e1 )q1 αρy
where α, ρ, and y are the probabilities that type B applies, activates, and
offers to license at fee F G , respectively. The lower bound of λ̂ is attained at
αρy = 1 and given by
λ=
λ(e1 + (1 − e1 )q1 )
.
λ(e1 + (1 − e1 )q1 ) + (1 − λ)(1 − e1 )q1
Challenges are credible if and only if
π − ∆C ≤ λ [(e2 + (1 − e2 )q2 )(π − ∆C ) + (1 − e2 )(1 − q2 )π]
+ (1 − λ) [(1 − e2 )q2 (π − ∆C ) + (e2 + (1 − e2 )(1 − q2 ))π] − lC
(16)
[1 − (1 − e2 )q2 − e2 λ]∆C ≥ lC .
(17)
or
29
Consider the behavior of type B in the case where challenges are credible, i.e., (17) holds, and fees are sufficiently low as to make applying and
activating profitable (i.e., α = ρ = 1); we will later make this statement
more precise. Let us look for an equilibrium in which type B randomizes
over the license fee FB as follows:
G
F = ∆C
FB =
F̃
with probability y
with probability 1 − y,
where F̃ is chosen such that the competitor does not find it worthwhile to
challenge.
The competitor’s beliefs on the equilibrium path are λ̃(F G ) = λ̂ and
λ̃(F̃ ) = 0. The out-of-equilibrium belief most likely to support the equilibrium is λ̃(F ) = 0 for F 6= F G , F̃ . For the competitor to refrain from
challenging when observing F 6= F G despite assigning probability 1 to the
patent being invalid, it must be that
(1 − e2 )q2 (π − ∆C ) + (e2 + (1 − e2 )(1 − q2 ))π − lC ≤ π − F.
The highest fee that satisfies this inequality is
F = lC + (1 − e2 )q2 ∆C .
Let s(F ) ∈ [0, 1] denote the competitor’s probability of challenging the
patent when observing a license fee offer F . Sequential rationality requires
s(F ) = 0 for F ≤ F and s(F ) = 1 for F > F , F 6= F G . Thus, F̃ = F . We
also have s(F G ) = x, which depends on λ̂. For the type-B inventor to be
indifferent between offering F G and F̃ , it must be that
π + m + F̃ = x[(1 − e2 )q2 (π + m + ∆C ) + (e2 + (1 − e2 )(1 − q2 ))π − lI ]
+ (1 − x)(π + m + F G ).
Simplifying and using F G = ∆C yields
x=
(e2 + (1 − e2 )(1 − q2 ))∆C − lC
≡ x̃.
(e2 + (1 − e2 )(1 − q2 ))(m + ∆C ) + lI
For the competitor to be willing to randomize between challenging and
not, it must be that (16) holds with equality when replacing λ by λ̂. After
simplifying we thus need
λ̂ =
(e2 + (1 − e2 )(1 − q2 ))∆C − lC
.
e 2 ∆C
30
Using the definition of λ̂, substituting α = ρ = 1, and solving for y yields
λ(e1 + (1 − e1 )q1 )
lC − (1 − e2 )(1 − q2 )∆C
y=
≡ ỹ.
(1 − λ)(1 − e1 )q1
(e2 + (1 − e2 )(1 − q2 ))∆C − lC
Finally, we need to check that the type-G inventor has no incentive to deviate. The best deviation would be to F = F̃ . But since x is chosen so as to
make the type-B inventor indifferent between F G and F̃ , and type G has a
higher probability of winning in court, type G must strictly prefer F G to F̃ .
The above equilibrium was derived under the assumption that fees are
sufficiently low for the type-B inventor to find it profitable to apply. Since
the type-B inventor’s payoff in this equilibrium is equal to his payoff when
offering F̃ , this requires
(1 − e1 )q1 [m + lC + (1 − e2 )q2 ∆C − φP ] > φA .
(18)
Suppose instead (18) does not hold. Then, the above strategy profile cannot
be part of an equilibrium. However, if the type-B inventor’s payoff from
applying is positive when there are no challenges, i.e.,
(1 − e1 )q1 [m + ∆C − φP ] > φA ,
(19)
then – rather than randomize over the license fee to offer – type B will randomize over the decision to apply.16 Since in equilibrium type B’s probability of applying (α) must be such that the competitor is indifferent between
challenging and not, we will have
lC − (1 − e2 )(1 − q2 )∆C
λ(e1 + (1 − e1 )q1 )
≡ α̃ = ỹ.
α=
(1 − λ)(1 − e1 )q1
(e2 + (1 − e2 )(1 − q2 ))∆C − lC
The competitor chooses x to make the type-B inventor indifferent between
applying and not:
π = (1 − e1 )q1 x[(1 − e2 )q2 (π + m + ∆C ) + (e2 + (1 − e2 )(1 − q2 ))π − lI ]
+ (1 − x)(π + m + ∆C ) + (e1 + (1 − e1 )(1 − q1 ))π − φA .
Solving for x yields
x=
m + ∆C − φP − φA /[(1 − e1 )q1 ]
≡ x̂.
(e2 + (1 − e2 )(1 − q2 ))(m + ∆C ) + lI
16
As in the basic model, there is also the possibility of randomizing over activation, but
this can only be part of an equilibrium for φA = 0. In what follows we neglect this special
case.
31
If (19) is not satisfied, type B does not apply.
Now let us check whether type G finds it profitable to invest in R&D.
The expression for πG in (15) can be rewritten as
πG = (e1 + (1 − e1 )q1 ) (1 − x(1 − e2 )(1 − q2 ))(m + ∆C ) − xlI − φP
− (k − π) − φA .
This expression highlights several important points. First, the assumption
that m + ∆C > k − π no longer suffices to ensure that the type-G inventor
wants to invest when fees are zero. To see this, suppose φA = φP = 0.
Then, we have x = x̃ (i.e., the rate of challenges in region 1). Type G’s
profit becomes
πG = (e1 + (1 − e1 )q1 ) m + ∆C
[(e2 + (1 − e2 )(1 − q2 ))∆C − lC ][(1 − e2 )(1 − q2 )(m + ∆C ) + lI ]
−(k−π).
−
(e2 + (1 − e2 )(1 − q2 ))(m + ∆C ) + lI
Even if the patent office does not wrongly reject applications (q1 = 1) and
courts are perfect (e2 = 1), as in the basic model, the presence of litigation
costs means that πG ≥ 0 if and only if
m + ∆C −
(∆C − lC )lI
≥ k − π.
m + ∆C + lI
An even more important difference with the basic model emerges as we let
fees increase to the point where x depends on φA and φP (region 2). Suppose
x=
m + ∆C − φP − φA /[(1 − e1 )q1 ]
,
(e2 + (1 − e2 )(1 − q2 ))(m + ∆C ) + lI
which is the equivalent of x̂ (i.e., the rate of challenges in region 2). We
then have
(e1 + (1 − e1 )q1 )e2 (m + ∆C )
(m + ∆C − φP ) − (k − π)
(e2 + (1 − e2 )(1 − q2 ))(m + ∆C ) + lI
(1 − e2 )(1 − q2 )(m + ∆C ) + lI
e1 + (1 − e1 )q1
− φA 1 −
(1 − e1 )q1
(e2 + (1 − e2 )(1 − q2 ))(m + ∆C ) + lI
πG =
Hence, the type-G inventor’s profit is decreasing in φP but not necessarily
in φA . To see this, notice that we can further simplify the expression in
square brackets as
(e2 (1 − e1 )q1 − e1 (1 − e2 )(1 − q2 ))(m + ∆C ) − e1 lI
.
(e2 + (1 − e2 )(1 − q2 ))(m + ∆C ) + lI
32
If
(e2 (1 − e1 )q1 − e1 (1 − e2 )(1 − q2 ))(m + ∆C ) − e1 lI > 0,
(20)
πG is decreasing in φA , but if (20) is violated, πG is actually increasing
in φA . The intuition as to why this can happen is likely related to the
argument in Atal and Bar (2011): increasing fees raises the perceived patent
quality, which benefits patent holders. However, while this argument is made
in a reduced-form way in Atal and Bar, here we endogenize the benefits
from higher perceived patent quality. In our setup, higher perceived patent
quality leads to fewer challenges. Under some conditions, the indirect effect
through a decrease in the rate of challenges can dominate the direct effect
of higher fees.
A necessary (but not sufficient) condition for (20) is that
e2
e1
<
.
(1 − e1 )q1
(1 − e2 )(1 − q2 )
(21)
The next result shows that this inequality can be linked to certain features
of the system of patent review, as discussed below.
Lemma 5. Suppose q2 ≥ q1 ≥ 1/2 and e2 > e1 . Then, there exists lI∗ such
that πG is decreasing in φA if and only if lI < lI∗ .
Proof. Suppose first that q1 = q2 = 1/2. Then (21) simplifies to
e1
e2
<
,
1 − e1
1 − e2
(22)
which is equivalent to e1 < e2 . The condition q2 ≥ q1 ≥ 1/2 implies q1 ≥
1−q2 . Dividing the left-hand side of (22) by something larger than its righthand side preserves the inequality. Thus, if the conditions in the lemma are
satisfied, (20) holds for lI = 0, while for lI → ∞, (20) can never be satisfied.
By continuity, there exists lI∗ as claimed.
The condition q2 ≥ q1 can be interpreted as the courts applying a presumption of validity: in the absence of strong evidence of obviousness, they
are (weakly) less likely to deny patent protection to an inventor than the
patent office. The condition q1 ≥ 1/2 means that most of the time also the
patent office does not reject an application without strong evidence. The
condition e2 > e1 says that the courts are more likely to find out the true
33
nature of an invention than the patent office. Hence, according to Lemma 5,
if patents benefit from a presumption of validity and courts are better at distinguishing obvious from nonobvious inventions than the patent office, the
type-G inventor’s profit is decreasing in φA if litigation costs are sufficiently
low.
In what follows we assume that (20) holds so that πG decreases with φA .
We then have πG ≥ 0 if and only if
φA ≤
(e1 + (1 − e1 )q1 )e2 (m + ∆C )(m + ∆C − φP )
(e2 (1 − e1 )q1 − e1 (1 − e2 )(1 − q2 ))(m + ∆C ) − e1 lI
− (k − π) [(e2 + (1 − e2 )(1 − q2 ))(m + ∆C ) + lI ] .
Let us check how the slope of the right-hand-side term in φP compares to
that of the corresponding condition for type B, i.e., (19). That is, we want
to know whether the following inequality holds:
(e1 + (1 − e1 )q1 )e2 (m + ∆C )
> (1 − e1 )q1 .
(e2 (1 − e1 )q1 − e1 (1 − e2 )(1 − q2 ))(m + ∆C ) − e1 lI
A sufficient condition for this is
e2 (m + ∆C ) ≥ (e2 (1 − e1 )q1 − e1 (1 − e2 )(1 − q2 ))(m + ∆C ),
which is always satisfied since (1 − e1 )q1 < 1. We conclude that, as in the
basic model, φA and φP are closer substitutes for type G than for type B.
That is, fixing φA + φP , type B prefers fees to be backloaded (in activation
fees) more strongly than type G. In fact, type G may even prefer fees to be
frontloaded.
34
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36