Patent Pools and Cross-Licensing
in the Shadow of Patent Litigation*
byJay Pil Choi 1
Michigan State University, U.S.A. and Yonsei University, Korea

Abstract
This paper develops a framework to analyze the incentives to form a patent pool orengage in cross-licensing arrangements in the presence of uncertainty about thevalidity and coverage of patents that makes disputes inevitable. It analyzes theprivate incentives to litigate and compares them with the social incentives. It showsthat pooling arrangements can have the effect of sheltering invalid patents fromchallenges. This result has an antitrust implication that patent pools should not be
permitted until after patentees have challenged the validity of each other’s patents if
litigation costs are not too large.

Shortened Title: Patent Pools and Litigation* Manuscript received December 2007; revised September 2008.
1 I thank the Co-Editor and two anonymous referees for very constructive comments and suggestions that helped

improve the paper significantly. I am also grateful to Robert Hunt, Corinne Langinier, Josh Lerner, GianCarlo
Moschini, Ines Macho-Stadler, Jennifer Reinganum, Santanu Roy, and participants in various conferences andseminars for helpful comments. Please address correspondence to: Jay Pil Choi, Department of Economics, 110
Marshall-Adams Hall, Michigan State University, East Lansing, MI 48824, U.S.A. Phone: (517) 353-7281. Fax:
(517) 432-1068. E-mail: choijay@msu.edu.

1. Introduction
This paper develops a model of patent pools/cross-licensing in which the
incentives to litigate are explicitly taken into account in the formation of patent pools.
The basic premise of the paper is that patent rights are inherently probabilistic and subject
to disputes. Even though the literature on patent protection has assumed ironclad patents
and no uncertainty regarding patent claims until recently, the reality is that the extent towhich protection is provided by the patent is not precise, and even the validity of thepatent itself can be challenged in the courts. 2 Moreover, as emphasized by Scotchmer(1991), the innovation process is typically cumulative with innovations building on eachother and requiring multiple patents for the practice of technology. 3 As a result, weobserve a myriad of patent infringement suits through which questions of utility, novelty,
and nonobviousness are independently ruled on by a court.4
The majority of these disputes, however, are settled out of court rather thanlitigated to a final resolution. 5 In fact, many patent pools and cross-licensing
arrangements arise as an attempt to settle disputes on conflicting claims in the litigation

2 For instance, the "doctrine of equivalents" entitles the patented invention to cover a certain range ofequivalents. However, the exact boundary of the equivalents is impossible to draw. The matter of
infringement can be reasonably assumed to be decided case by case. See Lemley and Shapiro (2005) for an
excellent survey of the burgeoning literature on probabilistic patents.
3 See also Green and Scotchmer (1995) and O’Donoghue, Scotchmer and Thisse (1998).
4 According to Allison and Lemley (1998), nearly half (46%) of fully litigated patents are declared invalid,

which illustrates the importance of court decisions on patent validity in infringement suits. See Lanjouw
and Schankerman (2001) for an empirical analysis of patent litigation.
5Lanjouw and Schankerman (2002) report that 95% of patent lawsuits are settled prior to a court judgment.

process or in expectation of impending litigation. 6 To reflect this reality, this paper
develops a simple framework to analyze the incentives to form a patent pool or engage incross-licensing arrangements in the presence of uncertainty about the validity of thepatents. It analyzes the private incentives to litigate and compares them with the social
incentives. It shows that pooling arrangements can have the effect of sheltering invalid
patents from challenges. This result has an antitrust implication that patent pools should
not be permitted until after patentees have challenged the validity of each other’s patents
if litigation costs are not too large.
To analyze patent pools with probabilistic patents, I adopt the framework
developed by Lerner and Tirole (2004) that can encompass the whole range ofrelationships between patents including perfectly substitutable and complementary
patents. It is shown that the scope for public policy can be very different depending on
the nature of relationship between patents. With ironclad patents, patent pools are procompetitive when the relationship is relatively complementary, as they correct anexternality that leads to excessive royalty rates. Social and private incentives to form apatent pool are completely aligned. The case with substitute patents is very different.
Patent pools tend to be anticompetitive and social and private incentives to form them
may be quite divergent.

6According to Shapiro (2003), “[v]irtually every patent license can be viewed as a settlement of a patentdispute: the royalty rate presumably reflects the two parties’ strengths or weaknesses in patent litigation in
conjunction with the licensee’s ability to invent around the patent. The same is true of cross-licenses,
where net payments reflect the strength of each party’s patent portfolio along with its commercial exposure
to the other’s patents.”

2

In the presence of litigation with uncertain patents, I make a distinction between
ex ante and ex post patent pools. Ex ante patent pools are formed when patents
considered for patent pools have not yet been contested in the court and thus theirvalidities are uncertain. Ex post patent pools are formed after the validities of patents inconsideration have been contested in court and thus there is no uncertainty about theirvalidities. The ex post optimal patent policy replicates the optimal rule with ironclad
patents. In contrast, the ex ante optimal patent policy depends on litigation incentives ofprivate parties when the ex ante patent pool is not allowed. It is shown that ex ante patentpools should not be allowed if private parties have incentives to litigate and the patent
policy is ex post optimal. However, if no firm has incentive to litigate, the optimal policy
is to allow patents if they are relatively complementary, as with ironclad patents. Since
private firms lack incentives to litigate each other when patents are weak, we derive aparadoxical result that paten pools should be allowed when patents have suspect value inthe case of complementary patents.
I also analyze patent disputes that concern the relative priority of patents to checkthe robustness of the results. Once again, I find that there is a divergence in private andsocial incentives in the formation of patent pools. In addition, I find a discrepancy
between private and social incentives to litigate when patent pools are not allowed.
Litigation occurs when patents are strong, while on welfare grounds litigation should takeplace when patents are weak.
This paper is closely related to Shapiro (2003) who also recognizes that IPR
associated with patents are inherently uncertain or imperfect, at least until they havesuccessfully survived a challenge in court. He proposes a general rule for evaluating3

proposed patent settlements, which is to require that “the proposed settlement generate atleast as much surplus for consumers as they would have enjoyed had the settlement notbeen reached and the dispute instead been resolved through litigation.” 7 He
convincingly argues that such a rule would fully respect intellectual property rights while
protecting the interest of consumers. However, his paper does not analyze the incentives
to litigate in the first place by just assuming that there would be patent disputes. My
paper points out that the most serious case arises when both firms have weak patents anddo not have any incentive to challenge each other. In such a case, public policy should begeared towards providing incentives for other concerned parties to challenge weakpatents. A recent paper by Farrell and Shapiro (2008) also analyzes the licensing ofpatents that may be invalid to licensees who compete in a downstream product market.
They show that weak patents can command surprisingly large per-unit royalties whenlicensed to a group of downstream oligopolists, and call for patent reform. 8 However,they do not explicitly analyze the incentives to litigate.
Lerner and Tirole (2004) build a model of a patent pool in which they provide anecessary and sufficient condition for a patent pool to enhance welfare. They extend
their model in several directions to analyze various issues related to patent pools. Theseissues include the evaluation of the “external test” that does not allow inclusion ofsubstitute patents in a pool, the rationale for the provision of automatic assignment of
future related patents to the pool, and the pool members’ incentives to invent around each
7 Shapiro (2003, p. 393). See also Priest (1977) for an early analysis of patent licensing as a disguise forcartel arrangements.
8 In particular, Farrell and Shapiro (2008) show that in a symmetric Cournot oligopoly with constantmarginal costs, the royalty rate for a weak patent is proportional to the number of downstream firms.

4other ‘s patents. 9 However, litigation incentives are tangential to their analysis. My
paper and Lerner and Tirole (2004) focus on different aspects of patent pools and thus
should be viewed as complementary.
Finally, Gilbert (2004) reviews the history of patent pools and evaluates theperformance of courts through the lens of economic analysis. He makes an argument thatthe most important factor in the legal evaluation of patent pools and cross-licensing
arrangements should be the competitive relationships among the patents involved. In his
review of the legal cases, however, he finds that the most decisive factor in courts’
determination of whether patent pools have violated antitrust laws has been restrictive
licensing terms. Gilbert (2004) also points out that the social return from challenges to
weak patents is much higher than the private return and makes a recommendation that
antitrust agencies become more proactive in this area. This paper provides theoreticalsupport for both of his arguments.
The remainder of the paper is organized in the following way. In section 2, I set
up the basic model of patent pools/cross-licensing with multiple patents that takes placein the shadow of litigation. The model encompasses a wide range of relationships
between patents. This includes the two polar cases of perfect substitutes and perfectcomplements and the whole spectrum between them. The basic presumption in theliterature to date, enunciated in the Antitrust Guide Lines for the Licensing andAcquisition of Intellectual Property (1995), is that inclusion of complementary or
essential patents in a patent pool is pro-competitive, but assembly of substitute or rival

9 In a companion paper, Lerner, Strojwas, and Tirole (2003) empirically test the theoretical predictions

concerning the structure of patent pools by using a sample of 63 pools established between 1895 and 2001.

5

patents in a pool can eliminate competition and lead to elevated licensee fees. The
model in this paper provides theoretical support for such a presumption, but also provides
a few caveats in applying such a policy. In particular, section 3 makes a distinction
between ex ante and ex post patent pools, depending on whether patent validity has been
established in the court, and derives the optimal patent pool policy. Section 4 extends
and checks the robustness of the basic model by considering the possibility that theprobability of patents’ validity can be correlated. This case arises naturally if the natureof the patent dispute entails the relative priority of patents since one party’s validity
automatically implies the invalidity of the other patent. Concluding remarks follow insection 5.

2. The Model of Patent Pools under Validity Uncertainty
I consider a situation of multiple patents with dispersed ownership and potentiallyconflicting claims. For analytical simplicity, I assume that there are two patents, A andB, which are owned by two separate firms. The relationship between these two patents
could be either complementary or substitutable. Building on the framework developed
by Lerner and Tirole (2004), I present a model that can encompass both perfectly
substitutable and perfectly complementary patents and the full range between them. 10
There is a continuum of potential licensees/users of patents. They areheterogeneous in terms of their willingness to pay for licensing, which is indexed by θ.
Patents are assumed to be symmetric in their contributions to licensees’ willingness to

10 As emphasized by Lerner and Tirole (2004), patents are rarely perfect complements or perfect

substitutes.

6

pay. More specifically, I assume that licensee type θ’s gross surplus from using only
one and both innovations are given by v + θ and V + θ, respectively, with V ≥ v. 11 Thus,

Δ = V − v is the incremental value of the second patent and can be interpreted as aparameter representing substitutability/ complementarity of the two patents, with a higher

Δ representing a higher degree of complementarity. For instance, Δ =0 is a case of
perfect substitutes since it takes only one technology for the full benefit of V, whereas Δ=V is a case of perfect complements. 12
I assume that θ ∈ (-∞, 0], with the normalization that v and V represent thewillingness to pay for one and two patents for the highest type. Let F denote thecumulative distribution of θ. Then, the demand for the bundle of both patents at royalty
rate R can be written as:(1)

Q(R) = Pr (V + θ − R ≥ 0) = 1− F(R –V)

I make the standard assumption that the distribution of types satisfies the monotonehazard rate condition, that is, F´/(1−F) is strictly increasing:

11 The assumption of additive separability of user preferences is made to simplify the analysis. In

particular, it implies that all licensees select the same set of technologies in the market. See Lerner andTirole (2004) for a more detailed discussion of this assumption.
12 As example of the perfect complementary case would be two patents on technologies that are necessary

to make a microprocessor such as one patent on planar technology and the other on the microprocessor bus.
In this case, both patents have a stand-alone value of zero and a value of V when used together. An
example of symmetric intermediate cases would involve patents on two alternative video standards such as
Blu-Ray and HD-DVD. Each can be used alone with a value of v. Together, each standard can provide
some benefit to the other standard due to indirect network effects, which would raise its value to V.

7

(2)

F "⋅ (1 − F ) + ( F ') 2 > 0This assumption ensures that the patent pool’s objective function, RQ(R), is quasiconcave and the second order condition for the maximization problem is satisfied:
2Q′(R) + RQ′′ (R) = −2 ⋅ F '( R − V ) − R ⋅ F "( R − V ) < 0 . 13

(3)

The innovation in this paper is that I treat the intellectual property rights
associated with the patents as probabilistic and explicitly consider the uncertainty in theextent of protection a patent provides in the analysis of the incentives to form a patentpool. The uncertainty about the validity of the patents is represented by the parameters α
and β ∈[0,1], which are the probabilities that the court will uphold the validity of patents
A and B, respectively, if they are challenged. 14 I assume a symmetric information
structure in that α and β are common knowledge.
2. 1. Patent Pools with Ironclad Patents 15
As a benchmark, I first analyze a situation in which patent protection is ironclad
so the validity of the patents is not an issue.16 Without the possibility of patent litigation,
let rA and rB denote the royalty rates charged by firm A and firm B, respectively.
13

Using

the

first

order

condition,

we

can

−2 ⋅ F '( R − V ) − F "( R − V ) ⋅ [1 − F ( R − V )] / F '( R − V ) < 0 .

rewritethesecondorder

conditionas

The second order condition holds if the

distribution F satisfies the monotone hazard rate condition. This condition is a standard assumption in the
incentive literature and is satisfied by most widely used distributions; See Fudenberg and Tirole (1991, p.
267).
14 With probability (1-α)(1-β), for instance, both patents are invalidated. This may be the case if bothpatents did not reveal the relevant prior art in their applications and were awarded inappropriately.
15 This subsection closely follows Lerner and Tirole (2004) and replicates some of their results.

8As a first step in deriving the Nash equilibrium in the licensing market, consider ahypothetical situation in which licensees are constrained to purchase both patents. Thenfirm A solves the following problem given firm B’s royalty rate rB .
Max rA ⋅ Q(rA + rB ) .

(4)

rA

The first order condition for firm A’s optimal royalty rate rA is given by(5)

Q(rA + rB ) + rA ⋅ Q' (rA + rB ) = 0 ,which implicitly defines firm A’s reaction function rA = ΘA( rB ). Firm B’s reaction
function, rB = ΘB( rA ), can be derived in a similar way. The symmetric Nash equilibrium
royalty rates rˆA = rˆB = r̂ are at the intersection of these two reaction functions. The
stability and uniqueness of the Nash equilibrium in the royalty rates are ensured with themonotone hazard assumption of F. 17 The total royalty rate is given by R̂ = rˆA + rˆB =2 r̂ .
The solution above, however, is predicated on the assumption that potential
licensees are not allowed to license only one technology. Thus, we must check whether
the equilibrium derived will remain unchanged even if potential licensees are allowed to

16 Later I introduce uncertainty about the validity of patents and make a distinction between ex ante and ex

post patent pools. Ex ante patent pools are formed when patents considered for patent pools have not yet
been contested in the court and thus their validities are uncertain. Ex post patent pools are formed after thevalidities of patents in consideration have been contested in court and thus there is no uncertainty about
their validities. Thus, the patent pools considered in the analysis of this subsection correspond to ex post
patent pools.
17 The monotone hazard assumption implies that Q′(R) + RQ′′ (R) < 0.

9

purchase only one technology. To prevent potential licensees from purchasing only one
technology, the following condition should hold:(6)

V − R̂ ≥ v − r̂ , that is, Δ ≥ r̂In this case, the demand margin binds for patent holders. 18 However, if condition (6) isviolated, the competitive margin binds. Consequently, potential licensees will purchase
only one technology if both firms charge the royalty rate of r̂ , and the excluded firm will
have incentives to cut its price below that of the competitor. Then, the only equilibriumthat can be sustained is rA = rB = Δ.
Thus, the equilibrium royalty rate is given by r * = min (Δ, r̂ ), with both firms having
positive sales.
In contrast, if firms A and B form a patent pool and practice package licensing,the optimal royalty rate is derived by solving(7)

Max R ⋅ Q(R )R~~
Let R * be the optimal royalty rate for the pool. 19 Then, R * satisfies the following firstorder condition:
(8)

~
~
~
Q ( R*) + R * ⋅Q ' ( R*) = 0

Proposition 1 shows that with the formation of patent pools, the overall royalty rate forthe licensees can be either lower or higher depending on the relationship between the two

18 The demand margin binds when an increase in one firm’s price induces a reduction of its demand, but

not to the exclusion of its technology from users’ choice of technologies.
19 Variables associated with (ex post) patent pools are denoted with a tilde.

10technologies; patent pools tend to be procompetitive as patents become more
complementary.

Proposition 1 (Lerner-Tirole, 2004). There is a critical level of Δ such that R* = rA * +~~rB * > R * if and only if Δ > Δ *, where Δ *= R */2.

That is, the total royalty rate~
decreases with the formation of the patent pool if and only if Δ > Δ *= R */2. In such acase, social incentives and private incentives to form a patent pool are aligned.
Otherwise, patent pools reduce social welfare. 20
Proof. If Δ ≥ r̂ and the demand margin binds, the Nash equilibrium royalty rates rA *= rB * = r̂ satisfy
2 Q( rA * + rB * ) + (rA * + rB *) ⋅ Q' (rA * + rB *) = 0
Evaluating the first order condition for the patent pool (8) at R* = rA * + rB * yields

Q( rA * + rB * ) + (rA * + rB *) ⋅ Q' (rA * + rB *) = −Q( rA * + rB * ) < 0~This implies that R* = rA * + rB * = 2 r̂ > R *.

If Δ < r̂ and the competitive margin binds, the Nash equilibrium royalty rates rA *~= rB * =Δ, with R* = 2Δ. Since 2 r̂ > R *, we have the desired result that that R* = rA *~~+ rB * = 2Δ > R * if and only if Δ > Δ *= R */2. See also Figure 1. Q.E.D

20 The analysis of patent pooling implicitly assumes that the two members of the pool are not permitted toissue licenses for their own patents independently of the package license for both patents from the pool.
Some patent pools explicitly allow this independent licensing. If members of the pool can and do license
independently, then the pool cannot lower welfare. See Lerner and Tirole (2004) for more details.

11

2 r̂

Royalty Rate without Patent Pool~
R*

Royalty Rate with Patent PoolΔ~

Δ *= R */2 r̂Competitive
Margin Binds

Welfare Reducing
Patent Pools

Demand Margin Binds

Welfare Enhancing
Patent Pools

Figure 1. Patent Pools with Ironclad Patents
As an example, consider a case where θ is uniformly distributed between minus
infinity and zero with population density of one. This generates a linear demand curvefor licensing, Q(R) = V− R. It can be easily verified that the optimal royalty rate for the~patent pool, R *, is given by V/2 in this case. Without a patent pool, the competitive12

margin binds and the symmetric equilibrium royalty rate is given by r* = Δ, if Δ < V/3.
Otherwise, the demand margin binds and the equilibrium royalty rate is given by r* =V/3. The critical value of Δ is given by Δ *= V/4.
The result that patent pools can be welfare enhancing when technologies become
more complementary and the demand margin binds is a generalization of the well-known
result that dates back to Cournot’s (1927) analysis of the complementary monopoly
problem. When the demand margin binds, without coordination in pricing each patentee
does not internalize the increase in the other patentee’s profits when the demand for the
package is increased by a reduction in its price. Thus, a patent pool can decrease theoverall royalty rates for the package and simultaneously increase both patentees’ profitsand consumer surplus. Consequently, social welfare also increases. As a result anargument can be made for lenient treatment of a patent pool due to its pro-competitiveeffects with complementary patents. In the next subsection, however, I consider the casewhere patent protection is not perfect. In this case, I show that more caution is needed in
granting blanket immunity even towards patent pools comprised of complementary
patents, especially when weak patents are involved.

2. 2. Uncertain Patents and Litigation Incentives in the Absence of Patent Pools
To investigate implications of uncertain patents, I now consider the possibility
that the scope of the patent is not exact and that the validity itself can be challenged. Let
me analyze each firm’s incentives to challenge the validity of the other firm’s patent. If
one firm, say A, challenges firm B’s patent, it is assumed that it is optimal for firm B tocounterattack by challenging the validity of firm A’s patent. This assumption will hold13

if there are economies of scope in litigations since the counter-suit will not significantly
add to the cost of litigation beyond that of defending its own patent. In fact, in litigation
cases where the accused also has patents, the accused party invariably lodges a countersuit against the challengers. This assumption implies that attacking another firm’s patentvalidity or infringement creates a risk of having one’s own patent invalidated in theprocess. For instance, when Hewlett-Packard recently sued data storage company EMC
Corp. for infringing some of its patents, EMC countersued H-P with its own patent
infringement claims. 21
I assume that the probability of validity of each patent is independent of the other.
This would be an appropriate assumption with complementary patents or if thetechnologies of the two patents were developed by taking completely different research
approaches in the case of substitute patents. As an example, consider a gene therapy
product to treat a disease. There are two alternative methods developed to get genes into
cells. Sandoz developed the ex vivo process in which cells are removed form the body,the genetic material is inserted, and the cells are returned to the body. Ciba Geigy, incontrast, developed the in vivo process in which the genetic material is inserted while the21 Another example is the recent patent dispute between Nikon and ASML involving lithographyequipment, which is used to print circuits on silicon wafers that become semiconductors or chips. When
Nikon filed a complaint against ASML claiming the Dutch company infringed on seven Nikon patents,
ASML responded by claiming that the respective Nikon patents in question were invalid, and acounterclaim was filed alleging that Nikon infringed on four ASML patents (see Chappell, 2002).

14

cells remain in the body. Therefore, it would be a reasonable assumption that theprobability of validity of each patent is independent of the other. 22
One issue to consider in my analysis is if the firms in patent disputes have legal“standing to sue.” This issue does not arise for substitute patents. For complementary
patents, one natural way to interpret the situation is to consider a case of potentially“blocking” patents. For instance, technology A is a broad patent on a basic research tool
whose commercial value is zero in itself. Technology B is an application of technology
A that enables commercialization of the latter with a value of V. Thus, B is a subservient
patent which cannot be practiced without a license from the holder of patent A if B isfound to infringe on patent A. In such a scenario, we have a case of perfectcomplementarity: the value of each patent alone is zero (v = 0) whereas they generate thevalue of V taken together (Δ =V). Such a blocking relationship may confer the patentholder A standing to sue B (or the users of technology B if they do not pay for A, for thatmatter). Once A lodges a patent suit against B, the optimal response of B is to invalidate
patent A. 23

22 In the next section, I consider the case where disputes are mainly on the issue of priority and one party’s

validity means the other party’s patent being revoked.
23 Our main results on the lack of incentives to litigate would not change even if we assume only the users

who license both patents have standing to sue. When a user challenges and invalidates a patent, the entire
cost of litigation is borne by the challenger, but the benefits of invalidation could accrue to all users. Thisis due to the Supreme Court’s 1971 decision in Blonder-Tongue that if a challenger successfully invalidates
a patent, other potential infringers of the patent can rely on this and need not pay royalties (Blonder-Tongue
Laboratories, Inc. v. University of Illinois Foundation, 402 U.S. 313 (1971)). The free-riding problem
created by Blonder-Tongue could limit the incentives for a user to invalidate weak patents. This also15

Let ΠM and ΠD, respectively, denote the patent-holder’s profits when it is the
only firm who has a patent and when it is one of the two firms who have patents. Noticethat both profits depend on Δ. If a firm is the only patent holder after the other patent isinvalidated and now freely available, potential licensees will buy the technology if andonly ifV + θ − r > max [v + θ, 0]Thus, the demand for the monopolistic supplier of the patent is given by:⎧Q(r ), if r ≤ Δ
q M (r ) = ⎨if r > Δ⎩0,This implies that the pricing decision for the monopolistic supplier of the patent is~constrained by the existence of the other freely available technology if Δ < R *. The

optimal price for the monopolist is given by:⎧⎪Δ, if Δ < R *rM = ⎨⎪⎩ R *, if Δ ≥ R *The profit for the monopolistic supplier of the patent is given by:⎧⎪ΔQ (Δ ),if Δ < R *
ΠM = ⎨⎪⎩ R * Q ( R *), if Δ ≥ R *If both firms hold a patent,

implies that the distortion identified in this paper would increase if we have more patentees in the model. I
thank an anonymous referee for this observation. See also Farrell and Shapiro (2008) and Choi (1998).

16

⎧ΔQ(2Δ),
Π D = r * ⋅Q(2r*) = ⎨ˆ (2rˆ),⎩rQ

if Δ < rˆ
if Δ ≥ r̂

It can be easily verified that ΠM > ΠD for all values of Δ∈[0, V].

Let the legal costs oflitigation be denoted by χ, which are assumed to be the same for both firms.
Each firm’s profits without litigation are given by:
V ANL = V BNL = ΠD

If there is litigation concerning the validity of the patents, each firm’s profits are given by

V AL = α [β ΠD + (1−β) ΠM] − χ , V BL = β [α ΠD + (1−α) ΠM] − χFirm A will have an incentive to litigate if(9)Λ A = V AL − V ANL = {α [β ΠD + (1−β) ΠM] − χ} − ΠD ≥ 0

It can be easily verified that∂Λ A
= β ΠD + (1−β) ΠM > 0∂α∂Λ A= α [ΠD − ΠM] < 0.
∂βThus, firm A’s incentives to litigate increase with the strength of its own patent anddecrease with the strength of the other firm’s patent. Given the other firm’s patent
strength, β, firm A will litigate if(10)

α ≥ ψA(β) =ΠD + χ
βΠ D + (1 − β )Π M

It can be easily verified that ψA(β) is upward sloping and convex in β.
Similarly, firm B will have incentive to litigate if

17

(11)

Λ B = V BL − V BNL = {β [α ΠD + (1−α) ΠM] − χ} − ΠD ≥ 0

Given the strength of firm A’s patent, α, firm B will initiate litigation if(12)ΠD + χ
β > ψB(α) =αΠ D + (1 − α )Π M

Let L A and L B denote the set of (α, β) that satisfies conditions (10) and (12),respectively, i.e.,(13)

L A = {(α, β) ∈ [0,1]2 | α [β ΠD + (1−β) ΠM] − χ > ΠD}
L B = {(α, β) ∈ [0,1]2 | β [α ΠD + (1−α) ΠM] − χ > ΠD}

Litigation will take place if either firm has an incentive to litigate, i.e., (α, β)∈L, where L= L A ∪L B. There will be no litigation only when neither firm has any incentive tolitigate. This is when α and β are low, that is, both firms have weak patents and(α, β)∈NL, where NL = L C = [0,1]2 − L.
Now let me analyze social incentives to litigate. Let CS(R) be the level ofconsumer/user surplus when the royalty rate for the bundle of both patents is given by R,
V

V

R

R

where CS(R) = ∫ Q( p)dp = ∫ [1 − F ( p − V )]dp and CS′ (R) < 0. If there is litigation, thedownstream market price depends on the outcome of the litigation. For instance, if theoutcome of litigation is that both patents are invalidated, both technologies are freely
available at the royalty rate of zero. Instead, if both patents are deemed valid, the royalty
rate would be R* = rA * + rB * as in the case of no litigation. If only one of them isdeemed valid, the holder of the valid patent will set the royalty rate at r M = Δ if Δ < R *and r M = R * if Δ ≥ R * .

18

Let me follow the standard practice of using the sum of consumer surplus andindustry profits as a measure of social welfare. Let WM, WD and WC denote the welfare
levels when the (upstream) market structures are monopoly (i.e., only one patent isdeemed valid), duopoly (both patents are valid), and perfectly competitive (both patents
are invalidated), respectively.
(14)

if Δ < R *⎪⎧ΔQ (Δ ) + CS (Δ ),WM = Π M + CS (r M ) = ⎨⎪⎩ R * Q ( R *) + CS ( R *), if Δ ≥ R *⎧2ΔQ(2Δ) + CS (2Δ),
WD = 2 ΠD + CS(R*) = ⎨ˆ (2rˆ) + CS (2rˆ),⎩2rQ

if Δ < rˆ,
if Δ ≥ rˆ

WC = CS(0)~We have WD < WM < WC since r̂ < R * < 2 r̂ . That is, social welfare increases as more

patents are invalidated and become freely available.
Without a patent pool, the expected social welfare associated with litigation is
given by
(15)

SW L = [α β WD + (α −2αβ+β)WM + (1− α)(1−β)WC ] − 2χIf there is no litigation and no patent pool, the market price at the downstream

stage is R* = rA * + rB *. Social welfare without litigation is then given by(16)

SW NL = WD = 2 ΠD + CS(R*)

Therefore, the social incentive to litigate is given by(17)Λ S = SW L − SW NL = (1−αβ) [WM −WD ] + (1− α)(1−β) [WC − WM ] − 2χ

It is not expected that private incentives to litigate would coincide with social incentives.
In particular, if the cost of litigation (χ) is relatively low Λ S > 0, and patent disputes

19through litigation are socially beneficial since they can lead to invalidation of patents andless market power. This implies that when both patents are weak the private and social
incentives will always diverge since lim Λ A = lim Λ B = − ΠD < 0. We can conclude
α →0
β →0

α →0
β →0

that when patents are weak, there will be a serious lack of incentives to litigate among
patent-holders since they accommodate each other by adopitng the policy of “live and letlive.”

2.3. Patent Pools in the Presence of Uncertain Patents
The analysis in the previous subsection applies to the case where the formation ofa patent pool is not allowed, say, due to restrictions by antitrust authorities. If theformation of a patent pool is allowed without any restrictions, the only role of litigation isto set “threat points” for negotiating licenses. The terms of patent pools are negotiated in
the shadow of what would happen otherwise, and in this way the expectation of litigation
outcomes determines how the royalties are shared between pool members.
Let me analyze the private incentives to form a patent pool and how royalty
income is divided between the two firms. I assume that the surplus from negotiation isequally split between the two firms as in Green and Scotchmer (1995). When theparameters (α, β) belong to the set NL, such that both firms have no incentive to litigate,~
both will get the same royalty rate R */2 regardless of their relative patent strengths.

When (α, β)∈L, there will be litigation in the absence of a patent pool. In this case, thedivision of the royalty income reflects the relative strength of the patents. Let κ and20

(1−κ) denote the proportions of the royalty income that accrue to firm A and B,
respectively. Then, the bargaining solution with equal surplus implies that(18)κΠM − {α [β ΠD + (1−β) ΠM] − χ} = (1−κ) ΠM − {β [α ΠD + (1−α) ΠM] − χ}.

This yields κ =1+α − β.
2

Proposition 2. Under bargaining with equal surplus, the royalty rates are the same for~both firms at R */2 when both firms have weak patents, that is, (α, β)∈NL . If (α, β)∈L

and at least one of the firms has incentives to litigate, the royalty rates reflect the relative
strength of the patents (i.e., the probability of patent’s validity) in the pool.

Example. Once again, consider a case where θ is uniformly distributed between minus
infinity and zero with density one, which generates a linear demand curve for licensing,
Q(P) = V− P. Assume that Δ=V/2. In this case, the profits for the monopoly and
2

2

V
V
duopoly are given by ΠM =and ΠD =, respectively. For simplicity, assume that49

the cost of litigation is negligible with χ =0. Suppose that β=1/5. Then, it can be easily
verified that firm B has no incentive to initiate litigation, and firm A will have an
incentive to litigate if and only if α ≥1/2. Thus, firm A and B will share the monopoly
profit equally and the division of royalty income is invariant in α as long as α <1/2.
However, if α ≥1/2 the division of royalties reflects the relative strength of the twopatents. As can be seen in Figure 2, the value of patents can be discontinuous in patent
strength at the point of regime change.

21

9/10

κ=

13/20

1+α − β2

1/2(α, β)∈NL(α, β)∈L A

α

1/2

1

Figure 2: Firm A’s Share of Royalty Income as a function of α with β=1/5

In a model of patent dispute, Shapiro (2003) also points out the possibility that thevalue of a patent is not linear in patent strength when settlement is possible. However,
the reason for non-linearity is completely different. He considers a patent dispute
between the incumbent who holds a patent and the entrant who challenges it. Thus, there
is only one patent involved in the dispute. More importantly, his paper does not analyze
the incentives to litigate in the first place. The value of a patent is always continuous
and increasing in patent strength even though it is non-linear. My model indicates thatthe consideration of litigation incentives introduces a discontinuity in the division ofroyalty incomes.

223. Optimal Antitrust Policy on Patent Pools

I now consider the optimal antitrust policy concerning patent pools in a situation
where the social planner’s only decision is whether to approve patent pools or not. With
probabilistic patent rights, I need to make a distinction between ex ante and ex post
policy, depending on the information available at the time of the policy decision. Ex ante
policy decisions are the ones made when patents considered for patent pools have not yet
been contested in the court and thus their validities are uncertain. In contrast, ex post
policy decisions are the ones made after the validities of patents in consideration havebeen contested in court and thus there is no uncertainty about their validities. 24 I will callpatent pools formed before a patent validity check in court ex ante patent pools. Patentpools formed after litigation are called ex post patent pools.

3. 1. Ex Post Optimal Patent Pool Policy
Once patents in consideration are contested in court, they are either held valid orinvalidated, eliminating any uncertainty about their validities. It is obvious that the expost optimal patent pool policy requires that no invalidated patents be included in thepool. Thus, the only relevant case to consider is the one in which both patents are held
valid. Notice that this case is equivalent to the case of ironclad patents we analyzed
earlier. Since ex post decisions are made with respect to ironclad patents, the analysis of
24 There is no presumption here that litigation delivers the right answer concerning the validity of patents

disputed. Courts will certainly make errors and cannot be perfect in their verdicts. However, all that isrequired for the main results of this paper is that litigation eliminates uncertainty about the validity ofpatents. If we also consider the incentives to innovate for patents, potential errors by the courts would
matter and should be taken into account.

23

subsection II.1 applies. That is, the optimal ex post patent pool policy is to allow patent~pools if and only if Δ > Δ *, where Δ *= R */2 (see Proposition 1).

This implies that with the optimal ex post patent policy in place, each firm’s expost profit and social welfare when both patents are found to be valid are respectively
given by:⎧ D⎪⎪Π = r * ⋅Q (2r*) = ΔQ(2Δ ),
D

Π =⎨


⎪ R * Q( R*) ,⎪⎩2

if Δ < Δ* =R*(< rˆ)
2

if Δ ≥ Δ *⎧⎪W D = 2Π D + CS ( R*) = 2ΔQ (2Δ ) + CS (2Δ ), if Δ < Δ *W D = ⎨if Δ ≥ Δ *⎪⎩ R * Q( R *) + CS ( R *),3. 2. Ex Ante Optimal Patent Pool Policy
Now I turn my attention to ex ante optimal policy. Obviously, the analysis of ex
ante policy depends crucially on a counterfactual analysis of what would happen in themarket if the patent pool is not approved. In particular, it depends on if any firm would
have an incentive to litigate in the absence of ex ante patent pools, which in turn depends
on ex post patent pool policy, i.e., what is allowed if both firms’ patents are validated. I
assume that ex post patent policy is optimal; that is, a patent pool is allowed ex post if
and only if both patents are upheld to be valid and Δ > Δ *. 25

25 In the previous version of the paper, I assumed no ex post patent pool and derived qualitatively the same

results. See Choi (2003) for more details.

24

To analyze the social incentives to form ex ante patent pools, I need to consider
firms’ incentives to litigate in the absence of an ex ante patent pool. By proceeding as insubsection II.2, I can easily derive the condition for firm A to litigate as(10)′ (β) =α≥ ΨAΠD + χ
, D + (1 − β )Π M
βΠwhere a tilde above variables signifies that ex post optimal patent policy is reflected in
the litigation decision. Similarly, firm B will initiate litigation if(12)′ (α) =β≥ ΨBΠD + χ
 D + (1 − α )Π M
αΠLet LA and LB denote the set of (α, β) that satisfies conditions (10)′ and (12)′,
respectively, i.e.,(13)′

 D + (1−β) ΠM] − χ > ΠD}
LA = {(α, β) ∈ [0,1]2 | α [β Π
 D + (1−α) ΠM] − χ > ΠD}
LB = {(α, β) ∈ [0,1]2 | β [α ΠOnce again, litigation will take place if either firm has an incentive to litigate, i.e.,(α, β)∈ L , where L = LA ∪ LB .
I consider two cases to analyze the social incentives to form ex ante patent pools.

Case 1. (α, β)∈ L
In this case, if the ex ante patent pool is not allowed there will be patent litigation

k denote the level of social welfare
challenging the validity of each other’s patent. Let SW
that prevails with the formation of an ex ante patent pool. With a patent pool, the royalty~
rate for the bundle of both technologies is given by R *, regardless of Δ. This implies

k = W M , where W M = R * Q( R *) + CS ( R *)that SW.
25

Therefore, ex ante patent pools should be allowed if(19)

k − SW L = W M − {[α β W D + (α −2αβ+β)WM + (1− α)(1−β)WC] − 2χ}SW= α β[ WM − W D ] − (1− α)(1−β)[ WC − WM] + [ W M − WM ] + 2χ > 0

Lemma. If the patent policy is ex post optimal and the litigation cost is negligible (i.e.,χ ≈ 0), ex ante patent pools should not be allowed.

Proof. I prove this by showing that condition (19) can never be satisfied if χ ≈ 0. To
demonstrate this, I consider three sub-cases depending on the magnitude of Δ.
~(i) Δ< R */2 (< r̂ )With a negligible litigation cost, condition (19) can be rewritten as:
(20)

β>

[W M − W M ] + (1 − α )[W C − W M ]α [W M − W D ] + (1 − α )[W C − W M ]~Notice that we have WC > WM > W D = W D > W M for Δ< R */2. Therefore, the RHS ofinequality (20) is larger than 1. As a result, condition (20) cannot be satisfied. Thisimplies that if the two technologies are very close substitutes (more precisely, if~
Δ< R */2), patent pools should never be allowed. The reason is that even in the worst

possible scenario under litigation, which is both patents being held valid, social welfare is
still higher than when under an ex ante patent pool. This result is consistent with theconventional wisdom that patent pools should not be allowed for close substitutes.
~~(ii) R */2<Δ< R *In this case, we have WC > WM > W D = W M > W D . Therefore, with χ ≈ 0,

k − SW L ≈ − (1−α β)[ WM − W D ] − (1− α)(1−β)[ WC − WM] < 0.
SW

26

~
(iii) Δ ≥ R *~For Δ ≥ R *, we have WC >WM = W M = W D . This implies that with χ ≈ 0,

k − SW L ≈ − (1− α)(1−β)[ WC − WM] < 0.
SW
Sub-cases of (ii) and (iii) indicate that ex ante patent pools should not be allowed~
even if the two technologies are complementary (more precisely, even if Δ> R */2) aslong as the litigation costs are negligible. In other words, patent pools should be allowed
only after the validities of all patents are certified in courts and they are sufficiently~
complementary (i.e., Δ> R */2). 26 Thus, provided that the ex post optimal patent pool

policy is in place, the only way to justify ex ante patent pools is significant litigation
costs.
jCase 2. (α, β)∈ NL

In this case, if the ex ante patent pool is not allowed, there will be no patent
litigation, assuming that the ex post patent policy is optimal. Since no one has any
incentive to litigate to invalidate each other’s patent, the situation is as if all patents were
ironclad. Thus, policy concerning patent pools should be the same as that under ironclad
patents analyzed before. The social welfare without a patent pool is given by SW NL =26 The previous version of the paper (Choi, 2003) considers a more limited patent pool policy in which thepatent pool decision cannot be contingent on the outcome of patent litigation and is made only at the exante stage. In such a case, there are cases in which ex ante patent pool should be allowed. In particular,
with the linear demand example considered earlier, I show that if Δ ≥ V/2, patent pools should be allowed
when β ≥

1−α
.
2
1− α
9

27

WD = 2 ΠD + CS(R*) whereas the social welfare with a patent pool is W M . This implies~
that patent pools should be allowed in this case if Δ > Δ *= R */2 (see Proposition 1).

The following proposition summarizes the optimal patent pool policy.

Proposition 3. If (α, β)∈ L and the litigation cost is negligible, ex ante patent pools

should not be allowed. Ex post litigation, patent pools should be allowed only if bothj , ex ante patent pools should be
patents are found to be valid and Δ > Δ *. If (α, β)∈ NL

allowed if Δ > Δ *.

To be more concrete, let me again consider a specific example of uniform
distribution which yields a liner demand for the bundle of the two technologies, Q(P) = V− P. Here, firms A and B will set the royalty rate of rA * = rB * = Δ if Δ<V/3, and rA *= rB * = V/3 if Δ ≥V/3. If one of the patents is invalidated, the other patent-holder as amonopolist sets the royalty rate of r M = Δ if Δ < V / 2 , and r M = V / 2 if Δ ≥ V / 2 . The~
optimal royalty rate under a patent pool is given by R * = V/2. The critical value Δ * is

V/4. This leads to⎧⎪ Δ (1 − Δ ),
ΠM = ⎨ 2⎪⎩V / 4,

if Δ < V / 2⎧ Δ (V − 2Δ ), D = ⎪⎨
Π2⎪⎩V / 8,

if Δ < V / 4

if Δ ≥ V / 2⎧⎪Δ (V − 2Δ ),ΠD = ⎨ 2⎪⎩V / 9,if Δ < V / 3
if Δ ≥ V / 3

if Δ ≥ V / 4⎧V 2 Δ 2,⎪ −WM = Π M + CS (r M ) = ⎨ 2
2⎪3V 2 / 8,⎩

if Δ < V / 2
if Δ ≥ V / 228

WC = CS(0) = V 2 /2

W M = R * Q( R *) + CS ( R *) = 3V 2 / 8
⎧ D
V2
D
W
=
Π
+
CS
R
=
− 2Δ 2 , if Δ < V / 4
2
(
*)
⎪
D

W =⎨
2
⎪ R * Q( R *) + CS ( R *) = 3V 2 / 8,
if Δ ≥ V / 4⎩

To demonstrate the divergence in social and private incentives to form ex ante
patent pools, consider the case where Δ ≥ V/2. In this case, it easily be shown that
litigation takes place with negligible litigation costs if β ≥8
9 − 2αor α ≥

8
9 − 2βholds.

The areas of incongruence between the social and private incentives are represented as
dotted ones in Figure 3. In the dotted areas, social welfare increases with litigation andone of the two firms will have incentives to litigate if patent pools are not allowed. Thus,
the optimal policy is to disallow patent pools whereas private firms would always prefer
to form patent pools.
Proposition 3 indicates that when no firm has incentive to litigate, we have a~paradoxical result with complementary patents (i.e., Δ > Δ *= R */2): patent pools shouldbe allowed and the monopoly be preserved exactly when the patents are most suspect andhave little value (the shaded area in Figure 3). The reason is that unless there is a third
party that has a stake in the invalidation of the patents the alternative is the perpetuationof duopoly, which is worse than monopoly in the case of complementary patents. Public
policy in this case should be geared towards providing incentives for third parties toinvalidate weak patents.

29β (β ) =α =Ψ
A89(2 − β )

1

8
9

LB

 (α ) =β =Ψ
B

Litigation by B23

89(2 − α )

4
9

LA

j
NL

Litigation by A

No Litigation

0

4
9

2
3

8
9

1

α

Figure 3: Discrepancy between Private and Social Incentives to Litigate (Δ ≥ V/2)
My discussion so far has focused on the case in which litigation costs are
negligible. The consideration of litigation costs changes my welfare results in a
predictable way. In particular, there can be regions of parameters in which ex ante patentpools are welfare-enhancing especially when litigation costs are significant. However, it
does not change the main message of the paper, which is that ex ante patent pools should
not be allowed for patents of suspect validity if firms have incentives to litigate.

30

According to a recent survey by the American Intellectual Property Law
Association, typical patent litigation costs are estimated to be around $1 million throughthe discovery stage and $2 million through any appeal process for cases in which thestakes are between $1-25 million. 27 Figure 4 describes a typical case with litigation
costs that illustrates the discrepancy between private and social incentives to form ex ante
patent pools, with the assumption that litigation costs are about one tenth of the profits D ). 28 Under this assumption on
the firms can receive as a patent pool member (χ =.1 Πlitigation costs, it can be shown that LA = {(α, β) ∈ [0,1]2 | α > Ψ A ( β ) =LB = {(α, β) ∈ [0,1]2 | β > Ψ B (α ) =when β ≥ 1 −

89
} and
90(2 − β )89}, and patent pools should be allowed only
90(2 − α )1if (α, β)∈ L .
5(1 − α )27 American Intellectual Property Law Association, Report of the Economic Survey 2003. See also Miller(2004).
28 If the stakes in patent litigation are measured by the difference in the expected payoffs between the casein which its own patent is validated and the case in which it is invalidated, they also depend on theprobability that the other firm’s patent is validated. Assuming that the other firm’s patent is upheld withprobability ½, the figure essentially assumes that the litigation costs are approximately 6.7% of the stake inlitigation, which seems to be roughly consistent with the ratio of average litigation costs to stakes in thesurvey by the American Intellectual Property Law Association.

31

β
89
90
1

 (α ) =
β =Ψ
B

4
5

89
90

89
90(2 − α )LB (β ) =
α =Ψ
A

89
180

j
NL

β = 1−

89
90(2 − β )15(1 − α )No Litigation

LA
0

89
180

4
5

1

α

Figure 4: Discrepancy between Private and Social Incentives to Litigate (Δ ≥ V/2)
with Litigation Costs

4. Disputes over Priority and Correlation in the Probability of Validity

Up to now I have assumed that the probability of validity of each patent is
independent of any others. This would be an appropriate assumption in the case ofcomplementary patents. If the dispute concerns substitute patents, it would be areasonable assumption if the technologies of the two disputed patents were developed bytaking completely different research approaches. For instance, in the case of EPO used32

for treating anemia, Genetics Institute had a patent on a method for purifying EPO fromnatural sources while Amgen had a patent on a process for using recombinant DNA to
make EPO (Viscusi, Vernon, and Harrington, 1995). However, in the case of substitutepatents, there could be situations in which both patents essentially cover the same productand the dispute is on priority. Then, the validity of these two patents would be correlated
since only one firm can prevail in the court. In this section, I consider an extension andcheck the robustness of the model to changes in the nature of disputes and the possibilityof correlation in the probability of patent validity.
To be more precise, consider a situation where two firms, A and B, are involvedin a patent dispute. These two firms have conflicting patents for a new product in that therelative priority of their patents is at stake. 29 The discovery process of the patent suit
may reveal certain earlier inventions suggesting that these two firms’ claims are notsufficiently novel to satisfy patent law standards of patentability. One possibility of thepatent suit, therefore, is that both patents are held invalid. This type of uncertainty in theoutcome of a patent suit is captured by a probability α that the disputed patents satisfy thenovelty requirement. 30 For simplicity, let me assume, conditional on these patentssatisfying the novelty requirement, that the probability of one firm’s patent having
priority over the other is the same across the two firms, with each firm being equally
likely to win in the suit. In other words, these two firms have the same probability of

α/2 that their patents will be upheld if they are contested in court. With the remaining

29 Disputes over priority are known as patent interferences.
30See Scotchmer (1991) for an economic analysis of the novelty requirement in a model of sequential

innovations.

33

probability of (1-α), both patents are held invalid. These probabilities are assumed to be
known and shared by both parties.
In this case with substitute patents, it is clear that the optimal ex post patent pool
policy is not to allow patent pools. By Proposition 3, we also know that ex ante patentpools should not be allowed if firms have incentives to litigate in the absence of ex antepools and the litigation is negligible. If firms do not have any incentives to litigate, theex ante optimal policy is the same as the ex post optimal policy, that is, no ex ante patentpools should be allowed.

Proposition 4. In the case of substitute patents with uncertainty concerning novelty

requirement and priority, neither ex ante nor ex post patent pools should be allowed.

Given the simplicity of the optimal patent policy in this case, we now focus on thediscrepancy between private and social incentives to litigate. For simplicity, let me
assume away any legal costs involved in the litigation process. Then each firm in disputehas the following expected payoff from the patent suit.

(21)

V AL = V BL =

α
2

ΠM

If these two firms choose to coexist, each firm has a duopoly profit of ΠD for sure,assuming no further entry:(22)

V ANL = V BNL = ΠD

Therefore, they will litigate if α ≥

2Π D
.
ΠM

34

Now let us analyze the incentive to litigate from a social planner’s viewpoint.
Assume that industry structure becomes perfectly competitive due to free entry when thepatents are invalidated. Then, the social welfare resulting from the patent suit is:(23)

SW L = α WM + (1−α) WC

The social welfare without litigation is given by:(24)

SW NL = WD

Therefore, litigation is preferred from the social planner’s viewpoint if α ≤W C −W D.
W C −W M

Notice that when the patents are substitutes and the nature of disputes is relative priority,
invalidation of one patent does not imply that the technology is freely available. In fact,
invalidation of only one patent leads to a monopoly situation. Thus, it is natural toassume that WC > WD > WM in this case.
As an example, consider Cournot competition with linear demands and constantmarginal costs: P = a − Q and MC = c, where a > c. It can be easily verified that
litigation is privately optimal if α ≥ 8/9, whereas litigation is socially optimal if α ≤20/27. Unless α ∈ [20/27, 8/9], there is a conflict between the social and private
incentives to litigate. In particular, private firms prefer to litigate when the probability ofvalidity is high whereas the social planner prefers litigation when the probability ofvalidity is low.
The example above also demonstrates the inadequacy of the Shapiro rule (2001)
proposed for patent settlement once we account for incentives to litigate. It is easy to seethat with substitute patents unrestricted negotiation between the two patentees will
always lead to a collusive outcome with social welfare loss. Thus, any licensing

35

arrangement involving substitute patents should be subject to restrictions on thecontractual terms. Shapiro (2003) recommends a general rule for evaluating proposed
patent settlements, which is to require that “the proposed settlement generate at least as
much surplus for consumers as they would have enjoyed had the settlement not beenreached and the dispute instead been resolved through litigation.” 31 The rationale forsuch a rule is that it fully respects intellectual property rights while protecting the interestof consumers.
To show the non-applicability of the Shaprio Rule when both patents are weak,
consider the Cournot competition example above with a linear demand. Let CSM,
CSC denote consumer surplus when the market structures are monopoly (patents satisfy
the novelty requirement and one of the firms wins the priority suit) and perfectlycompetitive (both patents are invalidated):2(25)(a − c)(a − c), CSC =
CSM =
2
8

2

This implies that the expected consumer surplus from ongoing litigation is(26)

CS = αCSM + (1−α) CSC=

4 − 3α(a − c)28

Let p denote the price that results from the settlement between the two firms. Then, tomaintain the expected consumer surplus from litigation CS , the maximum settlement
price allowed would be

31 Shapiro (2003), p. 393.

36

(27)

p = kc + (1-k)a, where k =4 − 3α432

A natural way to implement the outcome would be a cross-licensing arrangement with a
per-unit royalty rate. More specifically, with a royalty rate of r, each firm’s marginal cost
becomes c + r. With Cournot competition and the linear demand curve, each firm
produces [a − (c + r)]/3 and the market price is [a + 2(c + r)]/3. Thus, the royalty rate ofr = [1 − (3k / 2)]( a − c ) will induce the market price of p = kc + (1-k)a.
The Shapiro rule is certainly a sensible rule once firms are already engaged inpatent disputes. The problem is that the rule has no bite when their patents are weaksince neither of them will have an incentive to litigate in the first place. Instead, theywould prefer to maintain the status quo without challenging each other’s patents. Moreprecisely, if they litigate and the Shapiro rule is enforced for settlement, each firm’s profit
would be [(1-k)(a-c)] 2. In contrast, if they adopt the strategy of coexistence without
challenging each other, they can secure the duopoly profits of (a-c) 2/9. Thus, whenk>2/3, or equivalently if α < 20/27, neither firm has an incentive to challenge the other’s
patent. As a result, the distortion due to the weak patents will not be corrected throughthe litigation process.

32 Let CS (p) be the level of consumer surplus when the market price is p. With the linear inverse demand

curve of p = a − Q, CS(p)= (a − p)2/2. Thus, p is defined by CS( p ) = CS , which yields the expressionin equation (27).

375. Concluding Remarks

In this paper I have developed a simple model of patent pools that take place inthe shadow of patent litigation. I analyzed private incentives to litigate and comparedthem with the social incentives. It was shown that pooling arrangements can have theeffect of sheltering invalid patents from challenges. In addition, antitrust implications ofpatent pools were considered. In particular, patent pools should not be permitted until
after patentees have challenged the validity of each other’s patents if litigation costs are
not too large.
The analysis of the paper points out, inter aila, the serious lack of private
incentives to weed out patents of suspect value through litigation. This is especiallytroubling in view of the recent explosion of patent awards triggered by U.S. patent reformin the last two decades and escalating litigation costs. 33 This development has led somecommentators to even question whether the proliferation of patent awards may impede
rather than promote innovation (Gallini, 2002). Considering ex parte relationships
between patent applicants and examiners, it is important to subject patents of dubious
merit to adversarial contests in the court. The current patent system, however, suffersfrom a free-rider problem. To mitigate the problem, we may seriously consider adopting
a European style administrative opposition procedure in the US system and/or allowing
the participation of third parties through pre-grant publication of patent applications. 34

33 See Lerner (1995) for an empirical analysis of patent litigation. He estimates the costs of patent

litigation started in 1991 at about $1 billion, which amounts to 27 percent of basic R&D expenditures by
US firms in the same year.
34 See Jaffe and Lerner (2004) and Choi (2005) for more discussion on patent system reform.

38

I conclude by mentioning a few avenues of research to extend the simple model inthis paper. First, I have assumed a symmetric information structure in which all potential
litigants have the same beliefs about the validity, scope, and enforceability of the patents
considered. This assumption can be suspect if the patentee has better information
regarding validity since she may know the potential weaknesses of the patent (Meurer,1989). Without symmetric beliefs, mutual optimism concerning the outcome of litigation
could lead to patent disputes in court. Out-of-court settlement then can be explained by
the revelation of a new piece of information that leads to shared beliefs. Consideration ofsuch private information introduces a whole new set of problems and allows much richer
dynamics. The mere decision to bring a suit, for instance, can have informational content
especially when out-of-court settlement is possible. In addition, if there is private
information held by either of the disputing parties regarding the validity of the patent,
litigation behavior in court can have signaling value and potentially influence the termsof licensing just as predatory behavior of the incumbent can affect the terms of a merger
with the entrant (Saloner, 1987). This is an important agenda for future research.

Michigan State University, U.S.A. and Yonsei University, Korea

39

References

Allison, J. R. and M. A. Lemley, “Empirical Analysis of the Validity of LitigatedPatents,” American Intellectual Property Law Association Quarterly Journal 26(1998), 185-275.
Chappell, J., “Legal Snafus Abound,” Electronic News (September 2, 2002).
Choi, J. P., “Patent Litigation as an Information Revelation Mechanism,” American
Economic Review 88 (1998), 1249-1263.

Choi, J. P., "Patent Pools and Cross-Licensing in the Shadow of Patent Litigation"
CESifo Working Paper Series No. 1070, November 2003.

Choi, J. P., “Live and Let Live: A Tale of Weak Patents,” Journal of European Economic
Association 3 (2005), 724-733.

Cournot, A., Researches into the Mathematical Principles of the Theory of Wealth,originally published in French (1838), translated by N. Bacon (New York:
Macmillan, 1927).
Farrell, Joseph and Shapiro, Carl, “How Strong Are Weak Patents?” American Economic
Review 98 (2008), 1347-1369.

Fudenberg, D. and J. Tirole, Game Theory (Cambridge, MA: MIT Press, 1991).
Gallini, N. T., “The Economics of Patents: Lessons from Recent U.S. Patent Reform,”
Journal of Economic Perspectives 16 (2002), 131-154.

Gilbert, R. J., “Antitrust for Patent Pools: A Century of Policy Evolution,” Stanford
Technology Law Review 3 (2004), also available at

http://stlr.stanford.edu/STLR/Articles/04_STLR_3/
Green, J. and S. Scotchmer, “On the Division of Profit in Sequential Innovation,” Rand

40

Journal of Economics 26, (1995), 20-33.

Jaffe, A. B. and J. Lerner, Innovation and Its Discontents: How Our Broken Patent
System is Endangering Innovation and Progress, and What to Do About It(Princeton, NJ: Princeton University Press, 2004).
Lanjouw, J. O. and M. Schankerman, “Characteristics of Patent Litigation : A Window
on Competition,” Rand Journal of Economics 32 (2001), 129-151.
____ and ____, “Enforcing Intellectual Property Rights: Suits, Settlements and the
Explosion in Patent Litigation,” unpublished manuscript, June 2002
Lemley, M. A. and C. Shapiro, “Probabilistic Patents,” Journal of Economic Perspectives
19 (2005), 75-98.
Lerner, J., “Patenting in the Shadow of Competitors,” Journal of Law and Economics 38(1995), 463-495.
____ and J. Tirole, “Efficient Patent Pools,” American Economic Review 94 (2004), 691711.
____, M. Strojwas and J. Tirole, “Cooperative Marketing Agreements between
Competitors: Evidence from Patent Pools,” Harvard NOMO Working Paper No.
03-25, April 2003.
Meurer, M. J., “The Settlement of Patent Litigation,” Rand Journal of Economics 20(1989), 77-91.
Miller, J. S., “Building a Better Bounty: Litigation-Stage Rewards for Defeating Patents,”
Berkeley Technology Law Journal 19 (2004), 667-740.

O’Donoghue, T., S. Scotchmer and J.-F. Thisse, “Patent Breadth, Patent Life and thePace of Technological Progress,” Journal of Economics and Management41

Strategy 6 (1998), 1-32.

Priest, G. L., “Cartels and Patent License Arrangements,” Journal of Law and Economics
20 (1977), 309-377.
Saloner, G., "Predation, Mergers and Incomplete Information," Rand Journal of
Economics 18 (1987), 165-186.

Scotchmer, S., “Standing on the Shoulders of Giants: Cumulative Research and the
Patent Law,” Journal of Economic Perspective 5 (1991), 29-41.
Shapiro, C., “Navigating the Patent Thicket: Cross Licenses, Patent Pools, and Standard
Setting,” in A. Jaffe, J. Lerner, and S. Stern, eds., Innovation Policy and theEconomy, Vol. 1, (Cambridge, MA: MIT Press, 2001), 119-150.

____, “Antitrust Limits to Patent Settlements,” Rand Journal of Economics 34 (2003),
391-411.
U.S. Department of Justice and the Federal Trade Commission, Antitrust Guide Lines for
the Licensing and Acquisition of Intellectual Property, 1995.

Viscusi, W. K., J. M. Vernon and J. E. Harrington, Economics of Regulation andAntitrust, 2nd edition (Cambridge, MA: MIT Press, 1995).

42