Strategic Declaration of Standard Essential
Patents ∗Reiko Aoki†

Yasuhiro Arai‡

March 2018

Abstract
We examine how the ex-post assessment of standard essential patents (SEPs) affects the patent holder’s strategic incentive to declare SEPs. While declaration
guarantees inclusion in the standard, it requires commitment to license under fair,reasonable, and non-discriminatory (FRAND) terms. We consider two forms of essentiality assessment: (i) by an independent organization and (ii) by the courts
during a patent dispute or challenge initiated by a standard implementer. Assessment by an independent organization can eliminate declared patents whose
essentiality is low. Assessment through a dispute can decrease the number ofboth declared and non-declared (i.e., non-FRAND-encumbered) patents and thesedifferent trade-offs affect the rights holder’s strategic declaration incentive. We obtain the following results. First, there is less declaration when there is ex-post
assessment of either type compared with no assessment. Second, there is less declaration with assessment by an independent organization than with assessment
through disputes. We also show that a rights holder with high essentiality patents
sets a higher declaration rate than one with low essentiality patents.

Keywords: Standard; Standard Essential Patents; R&D
JEL Classification: O38; L15∗

This study is conducted as a part of the Project “Intellectual Property and Standardization—Strategy
and Policy” undertaken at Research Institute of Economy, Trade and Industry (RIETI). The authors are
grateful for helpful comments and suggestions by Luis Cabral (New York Univ.), Jorge Contreras (Univ.
of Utah), Anne Layne-Farrar (Charles River Associates), Mark Ramseyer (Harvard Univ.), Juichi Nagano(Nagoya Univ.), Sadao Nagaoka (Tokyo Keizai Univ.) and Discussion Paper seminar participants at RIETI.
All errors are our own.
†
Japan Fair Trade Commission. reiko_aoki669k@jftc.go.jp‡
Humanities and Economics, Kochi University. yasuhiro68i@gmail.com

1

1

Introduction

When a new technology is invented, the inventor needs to consider how to obtain revenue from the invention. Standardization is often necessary for the new technology to
be adopted widely. A standard is “a document, established by consensus and approvedby a recognized body, that provides, for common and repeated use, rules, guidelines
or characteristics for activities or their results, aimed at the achievement of the optimum degree of order in a given context”(ISO/IEC Guide 2:2004, definition 3.2). DVD
or WiFi are examples of such standards. Further, some standards are not set by arecognized body and are instead produced by a private firm, such as the Windows OS
and QWERTY keyboard. For example, Biddle et al. [2010] show that at least 251 interoperability standards are included in a modern laptop. Standardization thus plays animportant role in our lives.
With technology becoming more and more complicated, there are more instances inwhich standard implementers need to use patented technology. A patent that protects
an essential technology of a standard is called a standard essential patent (SEP). Under
SEPs, not only is the technology required but also no substitute technologies exist. By
definition, the SEP holder has strong bargaining power when it comes to agreeing
licensing contracts. To avoid problems and negative consequences, the SEP holder
must “declare’’(i.e., make public) that the essential patented technology is an SEP andcommit to fair, reasonable, and non-discriminatory (FRAND) terms of licensing forstandard setting organizations to include it in the standard.
Despite the growing importance of SEPs, analysis of a patent holder’s strategic
incentive to declare SEPs is scarce. The literature on SEPs can be divided into two
categories: analysis of the characteristics of SEPs and analysis of the strategic behavior
to obtain SEPs. For example, Rysman and Simcoe [2008] show that patents declared as
SEPs receive more citations than other patents in the same technology field. They also
argue that high value patents tend to be declared as SEPs. Pohlmann et al. [2016] focus
on the relationship between SEPs and the SEP holder’s financial performance. Theyfind an inverted U-shaped relationship between the number of SEPs and a firm’s ROA.
Lemley and Shapiro [2013] and Lerner and Tirole [2015], using a general framework,
show that ex-ante price commitments such as a FRAND terms improve efficiency.
The second category of the literature focuses on the strategic behavior to invent andpatent SEPs. Leiponen [2008] shows that firms can increase their contributions to thedevelopment of the new tehnical specification in the standard by joining the industry
consortia. Bekkers et al. [2011] show that participation in the standardization process
plays an important role in determining essential patent claims. Kang and Bekkers[2015] discuss the “just-in-time patenting strategy,” a practice where rights holders
apply for low value patents just before a standardization meeting and try to include
these patented technologies into the standard.
These studies implicitly assume that SEPs are essential to the standard and overlook
2

SEP declaration as a strategic behavior. However, the essentiality of patents is notcontrolled by anyone. Firms can declare if they themselves judge the technology to be
essential. Declaration does not involve any assessment of the actual essentiality of thepatented technology. A firm can also choose not to declare a technology that is actually
essential.
Several studies conclude that fewer than 30% of patent families declared “essential”are actually essential in the telecommunication industry (Goodman and Myers, 2005;
Fairfield Resources International 2008, 2009). The rise in the number of declared SEPs
increases the costs of reaching a licensing agreement. In addition, efforts to disguiseinessential patents as SEPs results in a social cost. Therefore, policymakers such as
the European Patent Office pay attention to the declaration issue.
To the best of our knowledge, the only work that examines the strategic incentive todeclare is Dewatripont and Legros [2013]. They focus on the over-declaration of SEPs
and show that the rights holder has an incentive to over-declare to increase its profit
share from the standard. They assume that the rights holder focuses on the royalty
benefit from SEPs. However, according to a survey of patent owners conducted by
Blind et al. [2011], rights holders’ most important reason for obtaining essential IPRs
is to secure their freedom to operate (FTO), not generate license revenue. Dewatripont
and Legros [2013] assume that inessential patents do not benefit the holder at all,even though they can be profitable since they are not restricted by FRAND terms. In
our research, we take into account these factors not considered in Dewartripont andLegros’ analysis. Regibeau et al. [2016] suggest two approaches to mitigate the overdeclaration of SEPs. One approach is to make SEP declaration costly. The other is arandom assessment of the essentiality of declared patents. However, they do not go into
detail on how these approaches affect the rights holder’s incentives. In this research,
we analyze an effective policy for reducing the over-declaration of SEPs.
The remainder of the paper is organized as follows. Section 2 sets up the basicmodel and analyzes the two assessment approaches. Some extensions are presented
in Section 3. Section 4 concludes. All proofs are given in the Appendix.

2

Model

Our model features a rights holder (firm 1) and a standard implementer (firm 2). Firm
1 obtains profits from its patented technology. We assume that the number of firm
1’s patents is F . The rights holder can decide how many patents are declared as
SEPs by setting the declaration rate e ∈ [0, 1] to maximize its profit. We capture theessentiality of the rights holder’s F patents by assuming they are distributed according
to“essentiality”. By essentiality, we mean the probability that a patent passes the expost assessment. If the rights holder sets the declaration level e, the lowest probabilityof positive assessment (i.e., it is essential) of its declared patent is equal to 1 − p(e). We

3

assume that the probability that the patent is determined to be non-essential is p(e),and it satisfies the following conditions:dp (e)>0(1)
de
If the rights holder increases the declaration rate e, it needs to disguise the patents
whose essentiality is relatively low as SEPs. Then, p(e) is an increasing function of e.
p (0) = 0, p (1) = 1,

If there is no ex-post assessment of SEPs’ essentiality, the number of declared patents
is Dn = e × F .
The rights holder’s payoff π1 is given by

π1 = RF + RH − CD − CO .
The rights holder must commit to the FRAND licensing terms if it declares its patent
as an SEP. The profit from the FRAND royalty is given by RF , which is assumed to be
the function of the declaration rate e and number of inessential patents F :RF = D × rL .
D is the number of patents declared by firm 1 and rL is equal to the FRAND royalty
rate per patent. We assume that the profit from non-declared patents is RH . If therights holder does not declare its patents as SEPs, it can set a higher royalty rate thanthe FRAND condition or rely on profit from selling products including its inessential
patents. Revenue from non-declared patents, RH , is given by

RH = N × rH ,N is the number of non-declared patents. rH is the royalty rate per patent, which islarger than the FRAND royalty rate rL . N is given by
N = F × (1 − e).
We assume that a firm incurs declaration costs CD , including the cost of disguisinginessential patents as SEPs. CD is given by the following:

CD = α × F × e.
The declaration cost depends on the number of declared patents and cost parameter α.
The rights holder also has an incentive to secure its FTO by declaring SEPs. To
take this incentive into account, we introduce the operation cost CO . If the numberof declared patents increases, the rights holder can avoid the risk of being infringed.
Therefore, we assume that CO is4CO = (A − D) cO ,where A and cO are positive constants. We consider two types of ex-post assessments:
assessment by an independent organization (including a government) and assessment
by patent disputes or challenges initiated by a standard implementer. The timing of
the game is summarized as follows:
1. Firm 1 obtains the number of patents F .
2. Firm 1 decides the degree of over-declaration.
3. The number of patents decreases because of disputes or ex-post assessments.
Ex-post assessment is either by an independent organization or through a dispute. In
the next section, we consider the benchmark case that no ex-post assessment exists.

2.1

BenchmarkFirst, we consider the case of no ex-post assessment. We can rewrite the firm’s profit
as follows:

π1 = eF rL + F (1 − e)rH − αF e − (A − eF ) cO .

(2)

Firm 1 chooses the declaration rate e to maximize its profit. From this equation, we
can obtain the following lemma.
Lemma 1. When there is no ex-post assessment, firm 1 sets the optimal declaration ratee∗ as follows:(i) If rL + cO − α > rH , firm 1 declares all its inessential patents as SEPs (e∗ = 1).
(ii) Otherwise, firm 1 does not declare at all (e∗ = 0).
Proof. See the Appendix.
When the firm increases the declaration rate, it can increase the benefits from the
FRAND royalty rL and securing FTO cO . On the contrary, it needs to pay the declaration
cost and give up the high royalty rate rH . When rL +cO −α is larger than rH , the benefitof declaration is sufficiently large. Then, the firm has a strong incentive to declare its
inessential patents as SEPs. If the declaration cost α is too large or revenue from the
FRAND royalty and FTO is small, the firm has no incentive to lie.

2.2

Ex-post assessment by an independent organization

We next consider ex-post essentiality assessment by an independent organization. If
the independent organization assesses the declared SEPs, it can eliminate the SEPs

5

Figure 1: Expected number of SEPs with assessmentthat do not pass the assessment. A firm’s expected number of SEPs decreases becauseof the assessment. If the firm sets the declaration rate e, the number of declaredpatents without assessment is eF. When we take into account the ex-post assessment,
the number of expected declared patents Da is given by

Z e
Da = F ×(1 − p(t))dt.

(3)0

The shaded area in Figure 1 is equal to Da .
Firm 1’s profit with assessment is given byZ e
π1 = rL F ×Z e(1 − p(t))dt + rH F (1 − e) − αF e − A − F ×0
(1 − p(t))dt cO . (4)0From this equation, we can obtain the following lemma.
Lemma 2. When there is ex-post assessment by an independent organization, firm 1
sets the optimal declaration rate e∗A as follows:(i) If rL + cO − α > rH , firm 1 sets 0 < e∗A < 1 that satisfiesp (e∗A ) =rL + cO − α − rH.
rL + cO(ii) Otherwise, firm 1 does not declare at all (e∗A = 0).
Proof. See the Appendix.
When the declaration cost is sufficiently large, the declaration rate is equal to zero in
the same manner as Lemma 1. The ex-post assessment decreases the marginal revenueof declaration since the number of declared patents decreases. We assume that the6Figure 2: Optimal declaration rate with assessment
declaration cost is a quadratic form. The next proposition compares the declaration
rate in the benchmark with that in the ex-post assessment.
Proposition 1. A firm’s declaration rate decreases when there is ex-post assessment by
an independent organization.
Proof. See the Appendix.
The intuition of this proposition is shown in Figure 2.

Because of the ex-post

assessment, the expected number of declared SEPs decreases. Then, the firm will
decrease its declaration rate since the marginal revenue of declaration decreases. The
next corollary shows the comparative statics of the optimal declaration rate with ex-post
assessment.
Corollary 1. If rL + cO − α ≥ rH , the optimal e∗A depends on each parameter as follows:

∂e∗A
∂e∗
∂e∗
∂e∗
≥ 0, A ≥ 0, A ≤ 0, A ≤ 0
∂rL
∂cO
∂α
∂rH
Proof. See the Appendix.
When the benefit from the declaration (FRAND royalty and FTO) increases, theoptimal declaration rate also increases. Figure 2 shows the intuition of this corollary.
If the declaration becomes costly or the non-FRAND royalty becomes large, the firm
loses its incentive to declare. When the firm increases the declaration rate, it canincrease the benefit from the FRAND royalty rL and securing FTO cO . On the contrary,it needs to pay the declaration cost and give up the high royalty rate rH . When rL +cO −α
is larger than rH , the benefit of declaration is sufficiently large. Then, the firm has astrong incentive to declare its inessential patents as SEPs. If the declaration cost α is
too large or revenue from the FRAND royalty and FTO is small, the firm has no incentive
to lie. In the intermediate range, the firm sets e∗ to solve this trade-off problem.
7

Figure 3: The expected number of patents with dispute

2.3

Ex-post assessment through disputes

The implementer can also decrease the number of declared patents by disputes orchallenges in court. The implementer can reduce not only the number of declaredpatents but also the number of non-declared patents. An inessential patent has a riskof not being able to set a high royalty rate since its intentional failure to declare may
be unfair competition because of firm 2’s dispute. Thus, we assume that the expected
number of patents that can obtain the non-FRAND royalty Nd depends on p(e), namely
the probability of the patent being considered to be inessential.

Nd is given by
Z 1
Nd = F ×p(t)dte

and is where in Figure 3.
We can obtain the number of declared patents with assessment through disputes
from equation (3). If the dispute fee CDI is sufficiently low, the implementer will decrease the number of both declared and non-declared patents to save the royalty payment. If the implementer resorts to disputes, firm 1’s profit is given byZ e
π1 = rL F ×

Z 1(1−p(t))dt+rH F ×

0



Z e
p(t)dt.−αF e− A − F ×(1 − p(t))dt cO . (5)e0From this equation, we can obtain the following lemma.
Lemma 3. When there is ex-post assessment through disputes, firm 1 sets the optimal
declaration rate e∗D as follows:(i) If rL + cO − α > 0, firm 1 sets 0 < e∗D < 1 that satisfies8p (e∗D ) =rL + cO − α.
rL + cO + rH(ii) Otherwise, firm 1 does not declare at all (e∗D = 0).
Proof. See the Appendix.
This result can be interpreted in the same manner as Lemma 2.

The imple-

menter’s challenge can defeat declared patents whose essentiality is low and nondeclared patents whose essentiality is high. Hence, firm 1 sets the declaration rate bytaking into account both eliminations. The next proposition compares the declaration
rate in the benchmark case with that in the case of assessment through disputes.
Proposition 2. When the profit from inessential patents is small, the rights holder’s
declaration rate decreases in the number of implementer’s disputes. Otherwise, disputes
increase the declaration rate.
Proof. See the Appendix.
The intuition of this proposition is clear. When the royalty rate from inessential
patents, rH , is high, the rights holder has a strong incentive not to declare in thebenchmark case. If we take into account the implementer’s dispute, the number of
non-declared patents decreases. This effect increases the incentive to declare to obtain
the profit from declared patents. When rH is small, the rights holder will set e =1 to enjoy the profit from inessential patents. The dispute decreases the marginal
revenue of declaration by eliminating the number of declared patents. Then, the optimal
declaration rate becomes smaller than in the benchmark case. The next corollary shows
the comparative statics of the optimal declaration rate with disputes.
Corollary 2. If rL + cO − α ≥ 0, the optimal e∗D depends on each parameter as follows:

∂e∗D
∂e∗
∂e∗
∂e∗
≥ 0, D ≥ 0, D ≤ 0, D ≤ 0.
∂rL
∂cO
∂α
∂rH
Proof. See the Appendix.

2.4

Comparison

We are now ready to compare disputes with ex-post assessment. The next proposition
compares the optimal declaration rate under both schemes.
Proposition 3. The declaration rate with assessment through disputes is larger thanthat with assessment by an independent organization.
Proof. See the Appendix.

9The interpretation of this proposition is straightforward. The reduction in the number of declared patents decreases the marginal revenue of declaration. With the independent organization assessment, the rights holder’s profit from inessential patents
becomes relatively large since the assessment only decreases the number of declaredpatents. Therefore, the optimal declaration rate with ex-post assessment decreases
considerably. When we consider assessment through disputes, the implementer candecrease both declared and non-declared patents. This reduces the profit from inessential patents.

Compared with assessment by independent organizations, the rights

holder sets a higher declaration rate since the profit from inessential patents decreases.

3

Extensions

The preceding section compared the two assessment schemes from the viewpoint of
the declaration rate. In this section, two extensions of this model are considered:essentiality of patents and welfare analysis.

3.1

Essentiality of patents

In the real world, the essentiality of firms’ patents is distributed in various ways. In thissubsection, we consider how the distribution of essentiality affects the rights holder’sstrategy. We analyze two cases, namely when the essentiality of patents is high andwhen it is low. When essentiality is relatively high, we assume that p(e) satisfies thefollowing conditions:

dp(e)
dp(e)
d2 p (e)> 0, lim= 0, lim= ∞.
(6)2
e→0 dee→1 dedeIf equation (6) is satisfied, p(e) is illustrated as in Figure 3. When essentiality isrelatively low, p(e) needs to satisfy
d2 p (e)
dp(e)
dp(e)
< 0, lim= ∞, lim= 0.
2
e→0 dee→1 dedeIf equation (7) is satisfied, p(e) is illustrated as in Figure 4.

(7)

From Lemmas 3 and 2, we know that the optimal declaration rate depends on thecharacteristics of p(e). The next proposition shows how the distribution of essentiality
affects the firm’s declaration strategy.
Proposition 4. The optimal declaration rate of a firm whose essentiality is low e∗L issmaller than those with high essentiality e∗H .
Proof. See the Appendix.
The intuition of this proposition is shown in Figure 5.

10Figure 4: Essentiality of patents is relatively low

Figure 5: Comparison of the optimal declaration rate11

When essentiality is low, the risk of not being able to set a high royalty rate is also
low since the firm’s patents are less involved in the standard. Then, the rights holder
can easily obtain a high royalty by decreasing the declaration rate.

3.2

Welfare analysis

The existing literature does not pay attention to the welfare implications of the overdeclaration of SEPs. In this subsection, we consider how the over-declaration of SEPs
affects social welfare. To calculate social welfare, we shed light on the standard implementer’s profit. For simplification, only one standard implementer, firm 2, can makestandard products by using firm 1’s patents and sell them to consumers1 . The timing of
the game is summarized as follows. First, the rights holder (firm 1) decides the degreeof the over-declaration of SEPs. After that, firm 2 chooses the quantity of standard
products. Firm 2’s profit function is as follows:

π2 = q × (p − DrL − N rH ) − γD,
where q is the quantity of standard products. We assume that firm 2 needs to pay alicense fee DrL + N rH per product to the rights holder. The last term means that firm
2’s transaction cost is an increasing function of the number of declared patents D 2 .
We assume that the marginal cost of standard products is equal to zero. The inverse
demand function is p = T − q . Firm 2 tries to maximize its profit by controlling thequantity of products. From the first-order condition, firm 2’s optimal quantity q ∗ isgiven byq∗ =T − N rH − DrL.
2

To focus on social welfare, we must redefine the rights holder’s profit function as follows:

π1 = q × (DrL + N rH ) − αD − (A − D)cO .
The first term is the benefit from the royalty, the second term is the cost of overdeclaration, and the last term is the operation cost. If we consider the case that no
ex-post assessment exists, the number of declared patents D is eF . Firm 1 tries tomaximize the following equation by controlling the declaration rate e:
1

The results remain essentially unchanged if there are a number of producers of standard productsin the market and they are engaged in price competition.
2
Blind et al. [2011] quote from two interviewees. “For anyone wishing to adopt a standard, it is adaunting task to analyze all the claims and come up with an opinion which patents are truly essential”
and “There is a very large amount of uncertainty; nobody really knows what is actually essential ornot. . . .”It is thus clear that a rise in the number of declared patents increases the transaction cost of
standard implementers.

12
π1 (e) =T − (1 − e)F rH − eF rL2


× ((1 − e)F rH + eF rL ) − αeF − (A − eF )cO .

From the first-order condition of this equation, we can obtain firm 1’s optimal declaration rate e∗ as follows:e∗ = 1 −(rH − rL ) (T − 2rL F ) − 2(cO − α).
2F (rH − rL )2(8)

If firm 1 declares its inessential patents as SEPs, it has to give up the high royalty
rate rH . On the contrary, it can increase the quantity of standard products q ∗ bydecreasing its royalty. In addition, firm 1 can obtain the benefit of FTO. To satisfy

0 < e∗ < 1, the following condition is satisfied:(rH − rL ) (T − 2rL F )(rH − rL ) (T − 2rL F )− 2F (rH − rL )2 < cO − α <.
22We are now ready to consider the socially optimal declaration rate. The social planner
desires to maximize social welfare, which is the sum of π1 + π2 and consumer surplus

CS . To maximize social welfare, we can obtain the socially optimal declaration rate e∗∗
as follows:e∗∗ = 1 −4γ − 4(cO − α) − (rH − rL ) (T + rL F ).
F (rH − rL )2(9)

From equations (8) and (9), we can obtain the following proposition.
Proposition 5. The social over-declaration of SEPs occurs when γ is larger than (3T (rH −rL ) + 6(cO − α))/8. Otherwise, the social under-declaration of SEPs occurs.
Proof. See the Appendix.
The intuition of this proposition is clear. From the view of society, the declarationof SEPs has two welfare-enhancing effects. First, the declaration of SEPs decreases thetotal royalty payment of the standard implementer since the royalty rate of declaredpatents needs to be reasonable. Therefore, the over-declaration of SEPs decreases theprice of standard products and increases the consumer surplus. Second, firm 1 cansave the operation cost by increasing the number of declared SEPs. The declaration of
SEPs also has two welfare-reducing effects. If the number of declared SEPs increases,
the standard implementer needs to pay the transaction cost γD . Firm 1 needs to
pay the declaration cost αD to disguise inessential patents as SEPs. Firm 1 does notinternalize the standard implementer’s transaction cost. Then, if γ is sufficiently large,
the declaration rate set by firm 1 becomes larger than that set by the government.
In this case, the mitigation of the problem of the over-declaration of SEPs by using
ex-post assessment is socially beneficial. This proposition also indicates when social
over-declaration tends to happen. We can obtain the following corollary.
13

Corollary 3. Social over-declaration tends to happen when
1. The downstream market is small (T is small).
2. The difference between the FRAND royalty and non-FRAND royalty is small (rH −rL
is small).
3. The declaration cost is large (α is large).
The intuition of this corollary is clear. If the downstream market is small or the
royalty difference is small, firm 1 cannot obtain sufficient revenue from non-declaredpatents. Then, it has an incentive to declare SEPs to enjoy the benefit from FTO. Whenthe declaration cost is large, the social planner’s incentive to over-declare decreases.
In addition, the social planner must take into account the standard implementer’stransaction cost. Then, the socially optimal declaration rate tends to be smaller thanthe private optimal rate. These results show the conditions under which ex-post assessment that decreases the declaration rate becomes socially desirable. As we noted
before, Regibeau et al. [2016] suggest a random assessment of the essentiality of declared patents to mitigate over-declaration. However, when the downstream market
is large and the rights holder can set a higher royalty rate for its inessential patents,
ex-post assessment may harm social welfare.

4

Conclusion

We discussed how ex-post assessment affects the rights holder’s declaration incentive.
We considered two types of ex-post assessment: one that does not affect non-declaredpatents (independent organization) and one that does (through disputes).

We dis-cussed the over-declaration of SEPs in a model wherein (1) the rights holder controls
the declaration rate to maximize its expected profit by incurring certain costs and (2)the rights holder can enjoy a FRAND royalty and FTO from the declared patents and ahigh royalty from non-declared patents. We obtained the following results. First, thelevel of declaration is lower under ex-post assessment, which eliminates those patents
whose essentiality is low. Consequently, ex-post assessment decreases the marginal
benefit of declaration. Second, the level of declaration with ex-post assessment by anindependent organization is smaller than that with assessment through disputes by
an implementer. Assessment through disputes decreases the total number of patents.
Then, the rights holder will place greater weight on non-declared patents with assessment by an independent organization compared with assessment through disputes. We
also showed that a rights holder with high essentiality patents sets a higher declaration
rate than one with low essentiality patents. Our analysis thus suggests that changes
should be made to the direction of modern standardization policy.
We close with thoughts on future extensions of this model. First, we need to consider
the welfare analysis carefully. In this model, we focused on how to mitigate the overdeclaration of SEPs. However, it is not clear which assessments are socially desirable,14

by disputes or by an independent organization. Second, in our setting, the numberof patents, F , is exogenously given. The R&D incentive is, of course, affected by expost assessment. A framework within which firms make R&D decisions is therefore
necessary to analyze how assessment policy affects the R&D incentive.

5

Proof

Proof of Lemma 1
We can easily show that the declaration rate affects the rights holder’s profit fromequation (2) as follows:∂π1= F (rL + cO − α − rH ).
(10)∂eWhen the profit from inessential patents is large (rL +cO −α < rH ), the rights holder
does not declare at all. Otherwise, it chooses full declaration (e = 1).
Proof of Lemma 2
Firm chooses the declaration rate e to maximize its profit. We can obtain the firstorder condition from equation (4) as follows:∂π1= F (rL + cO − α − rH ) − F p (e) (rL + cO ) = 0.
∂e

(11)

We can easily show that the second-order condition is satisfied as Follows:∂ 2 π1= −F p0 (e) (rL + cO ) ≤ 0.
2∂e
From equation (11), the optimal declaration rate e∗A needs to satisfyp(e∗A ) =rL + cO − α − rH.
rL + cO(12)

Proof of Proposition 1
From (12), it is clear that p(e∗A ) is smaller than 1 when rL + cO − α + rH is positive.
Proof of Corollary 1
We assume that p(e) is an increasing function of e. If the right-hand side of (12)increases, the declaration rate also increases. From (12), we can obtain the following
results:∂p(e∗A )∂p(e∗A )∂p(e∗A )∂p(e∗A )
≥ 0,
≥ 0,
≤ 0,
≤ 0.
∂rL
∂cO
∂α
∂rH
Proof of Lemma 3
The firm chooses the declaration rate e to maximize its profit. We can obtain thefirst-order condition from equation (5) as follows:

15

∂π1
= F (rL + cO − α) − F p (e) (rL + cO + rH ) = 0.
∂e

(13)

We can easily show that the second-order condition is satisfied as Follows:∂ 2 π1= −F p0 (e) (rL + cO + rH ) ≤ 0.
∂e2
From equation (13), the optimal declaration rate e∗D needs to satisfyp(e∗D ) =rL + cO − α.
rL + cO + rH

(14)

Proof of Proposition 2
From (14), it is clear that p(e∗D ) is smaller than 1 when rL + cO − α is positive. When0 < rL + cO − α < rH , we find that e∗D > e∗ = 0.
Proof of Corollary 2
We assume that p(e) is an increasing function of e. If the right-hand side of (14)increases, the declaration rate also increases. From (14), we can obtain the following
results:∂p(e∗D )∂p(e∗D )∂p(e∗D )∂p(e∗D )
≥ 0,
≥ 0,
≤ 0,
≤ 0.
∂rL
∂cO
∂α
∂rH
Proof of Proposition 3
From (12) and (14), it is clear that e∗D > e∗A when rL + cO − α > rH . When 0 <rL + cO − α < rH , we find that e∗D > e∗A = 0.

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