Eza-eeVol. 55, No. 4, Oct. 2004

:

The Consortium Standard and Patent Poolsi'

Reiko Aoki and Sadao Nagaoka

1

1. Introduction

In this paper we examine the currentpractices of a patent pool that is part of a

consortium standard. A consortium stan-dard is a collaborative venture of firms to

promote a new technical standard. It caneventually be adopted by national or inter-

national standard setting bodies (a de 1-ure

standard) or become the de facto standard

after winning the competition with other

possible standards. A collaborativeapproach to standardization has becomeessential in the information and communi-

cation technology areas where speed ofinnovation and the world wide reach of the

technologies have made compatibility andearly establishment of a standard critical.

Consortium standard is distinguished from

a standard sponsored by a single firm in

the following two respects. First, itinvolves multiple firms with differentinterests. Second, it often adopts openlicensing policy through its commitment to

standard bodies such as ITU and ISO.Since a majority of the recent standards

involve proprietary technologies, patentpools have become an essential feature of

consortiums. We look at the two sides of a

patent pool : interactions among membersand with users of the technology. A list of

recent prominent consortiums is providedin Appendix 2.

Since such a consortium often involves

collaboration among competitors, there is

the question of how such collaboration can

be designed to avoid becoming an anti-

competitive device. The critical rule in this

respect is whether it is for combining com-

plementary patents or not (see Lerner and

Tirole (2004) for the analysis of competi-

tion rules for a patent pool, such as thefreedom of bypassing the pool). The Cour-

not effect (Shapiro (2001)) means it is

socially beneficial to bundle complemen-tary patents. Recognizing this fact, theU.S. antitrust authority has stated that a

patent pool of essential patents are notanticompetitive2}. A patent is essential to a

standard if the standard is not possible to

implement without infringing it. Thusessential patents for a particular standard

are always complementary, implying it issocially desirable to have the set of patents

form a pools and be licensed as a bundle.

Bundling essential patents has addi-tional dynamic beneficial properties. Bun-

dling improves not only consumer welfarebut also the competitive position of a con-

sortium standard relative to the standardcontrolled by a single firm. (See Nalebuff

(2000) for a potentially huge competitive

disadvantage of uncoordinated pricing ofcomplements.) Second, the joint profit of

firms is larger when the patents are bun-

dled, since the unbundled prices exceed the

profit maximizing price. Thus return from

R & D investment will be greater whenpatents are bundled.

In spite of these beneficial properties,

such collaboration does not necessarilyoccur. An outsider of the patent pool can

emerge, who does not join in the pool and

licenses an essential patent independently

1

346 ff esfrom the pool. Although such a licensormay be still subject to the RAND (reason-

able and non-discriminatory) conditions

when it has participated in the standard

development, his Iicensing term is notbound by the licensing policy of the patent

pool. In the worst case, a "submarine"patent may emerge after the adoption ofthe standard. The outsider who suddenlysurfaces can charge whatever the marketbears, causing the hold-up problem in addi-

tion to double marginalization. Anotherpossibility is that a patent pool for a single

standard may split, so that a licensee must

obtain licenses separately from two ormore group of the patentees. In the case of

the DVD patent pool, a firm must obtain at

least two independent licenses, one each

from the 3C group and the 6C group. Such

breakdown of an integrated patent poolnot only raises the total price to be paid by

licensees but also reduces the joint profit

of the patentees.

The question is why we see the emer-gence of an outsider and the split of the

patent pool. In the next two sections we

identify two major sources:free riderproblem and bargaining failure due toheterogenous membership. In Section 4 we focus on how a patentpool interacts with its users. In particular

we examine the effectiveness of RAND aspart of the consortium standard. Standard

setting organizations which are willing to

accommodate standards with non-free pat-

ents require the firms to commit them-selves to licensing under RAND conditions(i. e., licensing under reasonable and non-

discriminatory terms) for members of the

organizations and often for the generalpublic3). However, the economic rationale

of RAND conditions has not been explicit-

ly specified and there are many ambigu-ities on what they mean. We analyzewhether non-discriminatory licensingensures ex-post efficiency and whetherthere are any good grounds for the govern-ment (e.g., competition policy authority)

m eeto control the level of royalty.

2. The Free Rider Problem

First we introduce the basic frame-work. A firm that receives the licenses of

all the patents necessary to implement the

technology for royaltycifor i-th patentwill pay total of2ici,Firm Es optimaloutput qh(Zici) maximizes its profit`).That is, it solves,

max qh (A(qk, q-k) -2ci- 7) ,

qk iwhere 7 is the non-license marginal costand I2le (qk, q-h) is k's inverse demand func-

tion given other firms are producing q-h=(qi,''',qh-i,qh+i,"'qn)5) when there are n

licensees in total. The total demand forlicenses will be,

q(l2i.]ci) == :i]qh(¥. ci).

Because the patents are essential, this is

also the demand for any one of the essen-

tial patents as well as demand for thebundle if the patents are bundled. Weassume that q'<O and q'+cq":{;O. Whenthe patents are priced as a bundle by the

patent pool, demand for the bundle will be

function of the single bundle price coinstead of 2ici.

The incentive to remain an outsider or

split away from a pool can be illustrated

using Figure 1 where co represents thelicense royalty set by a pool and ci theroyalty set by an outsider. The reactioncurve Ro(ci) shows how the pool's profit

(co(q(ci+co)) maximizing royaltychanges as the outsider's royalty changes.

Since q'+ cq"gO, it satisfies the first-order

condition,

q(co+ci)+coq'(co+ci) = O. (1)The reaction curve is negatively slopedsince the patents are complementary. Simi-larly, the reaction curve Ri (co) shows how

the royalty of the outsider changes as the

pool royalty changes. This satisfies

q(ci+co)+ciq'(ci+co) == O. (2)Since all patents (pool's and outsider's)

are essential, two curves are entirely sym-

/

C,

C'

c'

n

The Consortium Standard

Figure 1. Patent Pool and Outsider

Ro (Ci)

N nl

tl /N

c

jittt

t nl

and Patent

Ri (Co)

c'

metric, irrespective of the relative number

of the patents held by the pool and theoutsider. The intersection is a Nash equi-librium (ci", c6") (Point N in Figure 1.),

which gives the outsider and the pool equalrevenues since ci"= corv. The iso-profit curve

for the outsider at the Nash equilibrium is

denoted ni".

If the outsider joins the pool, the new

pool royalty c* that maximizes pool reve-

nue, cq(c), satisfies the following first-

order condition,

q(c")+c"q'(c*) == O.Equations (1) and (2) implies q(ci"+co")+ (c,"+ co") q'(ci"+ co") == co"q'(ci"+ cSg) < O

from which we have the Cournot effect,

c" < ci"+ co".

We can find the outsider's iso-profit

curve when it becomes a pool member byidentifying the appropriate point on theline co+ci==c". If there are n members(including the outsider) in the pool, the

c*relevant point is C where ci=

outsider's share o

corresponding iso-profitFigure 1 (assumes n2)3).

integration of the outsider,

fall and the joint profit

ever, if the pool's profit is

since the nf pool revenue is -III. The

't' curve ls zl ln As a result of the

royalty would would rise. How- distributed

Co

the standard6).

The incentive to1as identif

problem.

access to

ls, lt ls a

standard

public goodthey are patented

be controlled.

demand forwhich has an essential patent related to the

standardthe other suppliers of the standard technol-

ogies to impose royalty on th

standard techno

a user ofaccess toindirectly through licensing policy of the

pool members. That is, the pool memberscan demand reciprocity in licensing to the

outsider firm. It is important to note that

the DOJ explicitly allows such clause as a

device to support the viability of a patent

pool against outsiders in its businessreview letter. However, such a clause isnot effective at all on those outsiders who

are specialized in licensing with respect to

that standard.

Pools 347 equally among its members, the

profit of the outsider is most likely to fall significantly, espe-

cially when the number of the pool membership is large. (The

point C moves south east along ci + co == c* as n increases).

Thus, notjoining the pool is

profitable as a unilateral con-

duct. The disincentive for join-

ing the pool increases as the

number of complementary pat- ents increases, since the profit

share of a particular member of

the patent pool declines while

what it can collect as an out- sider increases with the value of

icense independentlyied above is due to the free rider

Free rider problem arises whenthe good is not excludable, that

public good. In the case of a specification patent pool, the

is not the technology, since

and access to them can

The public good is the the standard. The outsider

does not need permission from

e users of the logy. If the outsider is also

the standard technology, his the demand can be controlled

l

348 ff za

3. Heterogenous Membership

In this section we analyze the bargain-

ing failure inherent in patent pools andexplore possible solutions. Coalition for-

mation literature has shown that even with

open membership, the grand coalition may

not form in equilibrium when there isasymmetry among firms (Belleflamme(2002)). We do note that the premises of

his analysis is quite specific (firms are

Cournot competitors and coalitions reducemarginal costs), not applicable to extent

of asymmetry in our analysis. A simulation

analysis by Axelrod et. al (1995) of the

UNIX operating standard also suggestsfragmentation from heterogeneity.Together with the Belleflamme result, we

suspect a similar heterogeneity frompreventing some firms to join the patentpool.

To demonstrate we extend the basicmodel to three types of firms that differ by

vertical structure: insider manufacturingV-firm (vertically integrated firm), out-

sider manufacturing M-firm, and insiderresearch R-firm. Insider means a firm inthe patent pool, which collects specificroyalty c from licensees. The patent pool

has only 2 members, V and R firms, each of

which has an essential patent. There are

two licensees, V and M firms which pro-duce very different products: each firmproduces as a monopolist in respectiveseparate but identical markets. Thisallows us to focus only on significance of

vertical structure of firms'). Using the ini-

tial basic formulation, firm k's inverse

demand is, Rle(qk, q-k) = P(qh),

for any k. When the (total) royalty is c,

M-firm always produces the monopolyoutput when marginal cost is c, denoted qM(c).

Patent Pool and Independent Licensing When there is a patent pool chargingthe bundle price c, V-firm chooses output q

bl ee

to maxlmlze, q+qM(c), (P(q)-c)q+ 2 C･Reorganizing, we get

(P(q)--SL)q+ q"iC) c.

The V-firm produces as if the marginal

cost were -S-. We denote the maximum

profit achieved with q==qv(c) by nv(c).

When V- and M-firms are producingoptimally given c, R-firm's profit is,

- qv(c)+qM(c) 7b? (C)- 2 C･The pool sets royalty to maximize poolrevenue c(qv(c) +qM(c)). This also maxi-

mizes patent R-firm's profit.

When firms license independently,V-firm chooses cv and q simultaneously to

maximize its profit. It is equivalent tomaximizing8) 7rv = (P(qM(CR))-CR)qM(CR)

+qM(cv+cR)cv,and R-firm chooses cR to maximize 7t:R = (qV(CR)+qM(eR+CV))CR.

This is a non-cooperative game where thefirms choose royalty (firm's strategy)

simultaneously.

The following proposition character-izes the relationship between royalty set

by a patent pool and royalties set indepen-

dently.

Proposition 1. IWien c*,nt,zv* are thePatent Pool revenue meximizing rayaltyand Profts, and cAR, c-v, fiR, fiv are equilib-

n'um rQyalties and Profts when R- andVVirms set them independently, then

C* (i) C*<CAR+C-V, CAR>C-V, C-R> 2' (ii) fiR + rr-V< nt + ni fiV< rrV".

The proposition is summarized inFigure 2. (The proof is in Appendix 1.) Bv

and IeR are best-response correspondences

and are downward sloping since the roy-alties are strategic substitutes. R-firm's

response correspondence is steeperbecause its royalty effects outputs of both

1

I

:

The Consortium Standard and Patent Pools 349M- and V-firms. V-firm only gets revenue

from M-firm. Thus for the same increaseof rival royalty, R-firms reduces its royalty

less. Both firms charge the same royalty,

cm, if it were the sole licensor, equivalent

to O rival royalty9). This implies the Nash

equilibrium (point III) must be under the

45 degree line (cR==cv), i.e., c-R>c-v. In

addition, the sum of the royalties at point

IE exceeds the pool revenue maximizingroyalty, since each firm does not internal-

yze the negative spillover of its own roy-

alty increase on each other (Cournoteffect). This implies c*< c-R+ c-v.

Since R-firm's profit is proportional to

that of the patent pool revenue, the highest

level along 45 degree line is at c" (as

drawn in Figure 2). V-firm's profitdecreases monotonically in total royalty

along the 45 degree line and with rivalroyalty, cR, along its own best-responsecorrespondence. This implies fiv< nv". The

sum of R-firm and V-firms profits is(cR +cv) qM (cR + cv) +P(qv(cR)) qv (cR)

(3)The first term is decreasing in total roy-

alty in the relevant region and thus ishigher with patent pool royalty c*. The

second term is also decreasing in cR. Thus

aggregate profit will be larger with patent

pool royalty c*. R-firm's profit may be

c'

Cm

C'

2

higher or lower by licensing independently.

In Figure 2, R-firm is better-off (as in the

following case of linear demand). But the

equilibrium IE may be on a lower iso-profit line. R-firm always has incentive to

deviate from a patent pool but independent

licensing may make it worse off.

Bargaining Failure We investigate the relationship fur-ther by assuming the product market haslinear demand P(q)==1-q. Profits withpatent pool royalty c are,

rr. (c) = t- 3iC62 , nbe (c) = g(i-ic),

rr(c) - t+g-kc2,

where n(c)=nv(c) +7b? (c). Note that the

V-firm has the same incentive as theM-firm in that it wants c to be as low as

possible. Of course this will not be desir-

able for the R-firm. Although the R-firmwould not like the royalty to be too highsince it reduces demand, it finds its profit

increasing in c when c is small. That is, 7be

(c) is increasing in c for csgg and

decreasing for larger c's.

We can highlight the trade-off bydrawing a curve in (nbe, nv) space by plot-

ting (7be(c), rrv(c)) for OKcSl. We will

Figure 2. Patent Pool and Independent Licensing

Cv 19R . nv

""'''--- ----.."R.Y..

..x i '/ i

"i iP i/ te t1 t1 tP t/ / C'[ / -[ / 2:

it tt

E n'R Bv

Cm c'CR

refer to this as the frontier(Figure 3). The frontier is on

the vertical axis when c=Osince nk(O)=O. Raising royalty

benefits R-firm and hurts theV-firm. However the trade-offis not one to one because theV-firm will adjust output. It is

downward sloping until c={}.

Then it is upward sloping until

the curve ends at (-5H, -il6L) corre-

sponding to c=1. Making roy-alty too high is not good forboth firms.

If the pool sets royalty to

11

i

350 wa zamaximize revenue, then the royalty should

be c'=-g-. In this case,

rrv* - rrv(g) = t' nt

- nk(g) - t･

.*-n(g)-t･ 'outputs will be -l;- for M-firm and -ii- for

V-firm. This would be most desirable roy-

alty for the R-firm. The frontier is vertical

at this point. (This is point RY in Figures

2 and 3).

If the pool sets royalty to maximizethe joint profit of the V-and R-firms, n(c),

then the royalty is cPF ==-g-. Profits are,

..pF = ..(g) = 12o3s, rfF = lk(g) = it,

npR = z(g) = e/･

This is the point farthest from the originon the frontier. (This is point PF in Figure

3).

If the firms license independently, the

Nash equilibrium royalties are,

- 2 .. 3 Cv= 7T, CR=7･Recall that royalty rates are strategic sub-

stitutes for essential patents. The equilib-

rium profits are,

Figure3. Patent Pool Frontier

c=onv

C=1

PF

RY

SQ

IE

M ee fiv = ?t, jiR = zR}-, fi = t/ < n'*.

The point is marked IE in Figures 2 and 3.

V-firm has lower profit than the R-firm.R-firm is better off than the patent pool.

If R-firm moves first, then it will set

1royalty level cfi=-2-. V-firm chooses cSv--

1T･ Profits are,

7riQ=-iiiltT, rfQ= ;t, rrSQ == JiiltT.

R-firm's profit increases but V-firm Ioses

out. This corresponds to point SQ in Fig-

ure 3.

Both points IE and SQ are outside the

frontier. Independent licensing is moreattractive to the R-firm than a patent pool

while the V-firm always prefers the pool.

We also note that revenue maximizing isnot the best option for the patent pool as a

whole. The aggregate profit is largest when c=cPF. Both simultaneous independent and

R first mover licensing result in smaller

total profit. The total profits are even

lower than with the revenue maximizingroyalty, c*. This means that the V-firmwould be better off if it give what R-firm

would achieve as a first-mover to induceR-firm to join the pool. Because point SQ

is outside the frontier this allocation that ' guarantees R-firm enough to join cannot be achieved by splitting the pool revenue according to patents. It must be achieved in form of a transfer payment.

Discriminatory Licensing Rule The pool frontier is con-

strained by the non- discriminatory licensing rule. Without this constraint, it is pos-

sible to increase joint profit even

more. Specifically, the pool chooses two royalty rates, cM and

cv, cooperatively to maximize n. Jomt profit (3). This is achieved

The Consortium Standard and Patent Pools 351

with cfi=-li- and cvC=O. The insider (V-

firm) pays zero royalty. The joint profit

achieved is -g-. The Nash Bargaining Set

(feasible set) is,

(g ( 7z:i? , rrv) l z'v + n:R f{:-).

The disagreement point is the independentlicensing point (fiR, fiv). Then the Nash

Bargaining Solution is,

7u9[B-;g2, z.NB-;gi.

This allocation is acceptable to the R-firm.

But can be achieved only by having thepool charge different prices. This is very

attractive to the R-firm but not to theV-firm since rrv"B < rri

Note that c">cRC+cvC. Discriminatory

treatment of R and V firms result in lower

royalty than the revenue maximizing non-

discriminatory royalty payment. Howeverit is higher than the non-discriminatoryprofit maximizing royalty. With discrimi-

natory royalty, V firm pays no royalty.With non-discriminatory royalty, burden is

shifted from M firm to V firm'O).

4. Analysis of RAND Conditions

In this section we explore what theRAND condition achieves, given that thecooperation among firms for a standard is

secured.

We start with the model with threetypes of firms:V, M and R. We nowassume the number of firms of each typeare v, m and r respectively. Both V and M

-firms must obtain a license from the pool

to produce. We denote T-firm's output byqT, price by PT, and profit by zT. Vertical

firm's profit comes from both royalty and

production :

cQ rrv = (Pv-c)qv+ v+r'where Q=vqv+mqM is the total output.M-firm has no royalty revenue : 7Tha = (PM rm C) qM,

while R-firm has only royalty revenue :

cQ 7CR === v+r'We assume the same type of firms behaveidentically.

We consider a two stage game: theroyalty fee c is set by the pool in the first

stage. In the second stage, firms that manu-

facture choose prices (outputs) non-cooperatively. We assume zero manufac-turing cost so that the only cost will be the

Iicense royalty, c. We consider twoextreme cases : when products are perfect

substitutes (homogeneous product) andwhen each firm is a local monopolist. The

first case would correspond to the case

where the firm specific complementaryassets, i.e. assets complementary to the

standard technology such as manufactur-ing know-how, are not important. Thesecond case would correspond to the case

where the standard can support a number

of applications for which each firmdevelops specialized complementaryassetsii>.

Perfect competition in manufacturing Here we assume that there is no verti-cally intetrated firm (v=O) for simplicity.

In this case, Bertrand competition with

homogeneous goods results in marginalcost pricing,

PM = C.Given marginal cost pricing in manufactur-

ing, there is no markup so that there is no

inefficiency due to double marginalization

when a patent pool is successful in bun-

dling all complementary patents. Theprofit of a research firm is given by,

- cQ 7tk ･ rThe pool chooses the royalty rate (c") to

maximize Qc subject to competition withalternative standards. The RAND condi-tions require the pool to apply the rate c"

to all licensees. In the case of Bertrand

competition in manufacturing, this nondis-

criminatory application of the royalty rate

insures the efficient manufacturing. Only a

352 ff esfirm with the lowest manufacturing costserves the market. It also generates the

maximum profit for R & D. Thus, non-discrimination is feasible and efficient.

Let us go back one step further andconsider the member firm i's R & D invest-

ment decision (lei). We assume that such

investment improves the quality of thestandard. Each firm has the following ex-

ante profit:

max Q(ki, k2, ''', kr) c - fe,.

rUnder the revenue sharing scheme whererevenue is divided equally among mem-bers, each firm can obtain only one r-th of

the increased' licensing revenue from qual-

ity improvement of the standard as result

of investment. Thus such a scheme causes

a large scale underinvestment in R & Dcompared to what is collectively opti-mal'2). The degree of underinvestment will

be very large when the pool membership is

large. This inefficiency obviously handi-

caps the consortium standard relative to a

closed standard sponsored by a single firm.

The only solution is to allocate pool reve-

nue according to contribution to the pool

revenue. Some scheme to evaluate the con-

tribution of each patent must be devised to

address this underinvestment problem.Given such an underinvestment problem,there is no economic ground for a govern-

ment to suppress the royalty rate agreedby the pool'3). Such intervention only exac-

erbates the underinvestment problem.

Local monopoly Assume that each firm serves its ownmarket, i.e., each firm is a monopolist in its

own market. Each firm chooses the profitmaximization price, for a given royalty c.

Thus there is a positive markup for amanufacturing firm and for a manufactur-ing operation of a vertically integrated

firm. Any positive per use charge causesthe problem of double marginalization.

In this case, non-discriminatory licens-

ing does not ensure ex-post manufacturing

blF ee

efficiency. The perceived marginal cost is

lower for an insider vertically integrated

firm than the outsider manufacturing firm,

since it perceives the gain from outputexpansion both from its sales of output and

through royalty income :

gqrrV. = oZ. (P (qv) qv) -(1- ,t . )c･

Thus, the non-discriminatory applicationof royalty in fact does not insure the effi-

cient entry in manufacturing. However, the

advantage of being an insider becomessmaller as the number of the members ofthe patent pool increases. In the case where

a number of firms supplying technologiesto a patent pool is large, this effect can be

negligible.

Let us look at the determination of the

level of royalty. As analyzed in Section 3,

three types of firms have different interests

regarding the level of royalty, c. Sinceprice is chosen optimally for each c, by the

Envelope Theorem, we have, 1 0(Qc) arr. a. =-qV+v+r oc ' We can make several observations.First the outsider manufacturing firmwants the minimal price, since the second

term does not exist. The insider research

firm wants a higher price, since there is no

first term. The vertically integrated firm is

in the middle ground. It wants to balance

its production profit and royalty revenue.

The outcome would mainly depend on thenegotiations between insider manufactur-

ing firms, and insider research firms, as

well as on competition with the other stan-

dards.

Secondly, higher royalty increasesreward to R & D but exacerbates theproblem of double marginalization. Thezero price for technology is the most effi-

cient price ex-post but it gives no return on

R & D by research firms. Thus, there is a

clear trade-off between ex-post efficiency

and ex-ante incentive. Given the dilution

problem of R & D incentive identifiedabove, there seems to be no good ground

l

The Consortium Standard and Patent Pools 353for a government to suppress the royalty

even though it is high due to double mar-

ginalization. The solution to the tradeoff

cannot come from the government inter-vention in pricing. Instead, a lump-sumpayment to the insider research firm mayalleviate the above inefficiency. Buy-out of

the IPR of the research firms would be an

alternative, although such financingscheme may not be easily available for atechnology coalition.

While we discussed the effect on man-

ufacturing efficiency of non-discri-minatory licensing policy, we have notdiscussed why this might be beneficial in

the context of dynamic competition. Car-lton and Gertner (2003) have argued that

one advantage of an open source system to

a proprietary system is that it makes it

possible for anyone to make improve-ments. The system is able to improve orpermutate according to needs more easily.

Although a consortium standard dependson patented technology, its commitment to

give access to anyone who requires at a"reasonable" price allows outsiders toimprove the technology as with the open

system.

5. Conclusion

We have identified two possible obsta-

cles to a successful implementation patent

pools : free riding and bargaining failure.

Once the standard has been established, it

is not possible to exclude a firm with an

essential patent from accessing thedemand for the standard (i.e. collecting

royalty from the users of the patent).Patents can only be used to control access

to the technologies implementing the stan-

dard. We have also shown that the non-cooperative outcomes of licensing are not

achievable by transfer of rents by perpatent split. This is because the royaltyalone cannot both increase patent revenue

and allocate rents among heterogeneousmembers at the same time. Thus, while it is

easy to argue why a patent pool bundling

complementary patents are socially desir-able, the reality is that patent pools can be

difficult to organize and to maintain.

Our results suggest that both theRAND licensing scheme and the way toallocate rents among pool members needto be changed to accommodate the hetero-

geneous membership. The heterogeneity of

membership makes the "reasonable" roy-alty policy more difficult to implement.This is because the relationship between

royalty rate and revenue differs betweenresearch firms that only have patent reve-

nue and vertically integrated firms that

also have production profit as well aspatent revenue. One might think that char-

ging sufficiently high royalty will transfer

production profit from vertical firms toresearch firms in addition. Unfortunately

this transfer also reduces the size of the

total pool revenue by compounding theharm of double-marginalization. Thus it is

impossible to transfer enough revenue tomake it profitable for a research firm to

join a pool instead licensing independently.

This result suggests that there should be

extra distribution to research firms tocompensate for the lack of productionprofits. Requiring all members of the pool

to be treated equally could be a source of

patent pool's failure.

The system of allocating pool rentsaccording to patent numbers is also detri-

mental to innovation. Firms may signifi-cantly underinvest in quality of the stan-

dard since it is unable to obtain appropri-

ate return on its R & D investment. Im-proving the dynamic incentive of the con-

sortium standard will be important, since

it may have to compete with a ciosedproprietary standard, which may have ahandicap in innovation but has an clearadvantage in appropriation.

Finally let us turn to policy issues.Although it is very important for a compe-

tition authority to deter the formation of a

pools which are anticompetitive, it would

be detrimental to competition and innova-

1

354 me estion for a government to condition theapproval of the pool on low royalty rate.

Once the pool is judged to be a bundle of

complementary patents, it should be free to

set the royalty rate. On the other hand, a

government intervention may be warrant-ed to prevent the free riding on the pool by

an outsider which surfaces after the stan-

dard is set.

(The Institute of Economic Research, Hitotsubashi University, and Department of Economics, University of Auckland /Institute of Innovation Research, Hitotsubashi University)

Appendix 1 : Proof of Proposition 1

Propotition 1. waen c*, nt, zv* are thePatent Pool revenue maximizing mpally andProfts, and c-R, cA- frR, jiv are equilibrium

mpalties and Pwfits when R- and Vtfirms set

them indePencienteL then

c* (i) C"< C-R+ C- V, C'SR> C- V, CAR> 2 ,

(ii) fiR + fiv< nt + nv*, itv< fi v*.

Let the inverse demand be P(q). Wedenote by qm(7) the monopoly profit whenmarginal cost is 7. That is, it is the solution

to the first-order condition,

max (P (q) - 7) q･ qWe denote by cm, the royalty rate that maxi-

mizes revenue 7'qm(7). We assume that thesecond-order condition,

2cqin(c)+qh'(c)gO, (4)so that it satisfies, the first-order condition,

q.(cm)+cmqh(cm) = O. (5) The profits of R- and V-firms when theyconstitute the patent pool are,

7u? (c) - -S-(qm(c) +qm(-S')),

rrv (c) - -S-qm(c) +(P(qm('S')--S)qm(mS-)･

Royalty c* maximizes pool revenue and sat-isfies,

c'(qh(c') +tqh( C2" ))+qm (c")

+q.( C2*)-O. (6)Claim 1.

cm<c*<2cm.Proof. It follows from (5) and (6). Z The profits when the two firms set roy-

- eealties independently are,

ztf(cR, cv) = cR (qm(cR +cv) +qm(cR)),

n"(cR, cv) = cvqm(cv+cR)+(P(qm(cR))-cR) qnt(cR).

Denote by BR(cv) and Bv(cR) the best-response correspondences when firms setroyalties independently. They are solutions to

the two first-order conditions

07i)6 == cR(qh(cR+cv)+qh(cR)) 0CR +qm(cR+cv)+qm(cR) == O, (7) orre = cvqh(cR +cv) +qm(cR +cv) = O. OcvClaim 2.

-1<Bk(c,)<O, -1</3e(c.)<O.Proof.

027uS = qh(cR + cv) + cRqm(cR + cv) KO, 0CVOCR 02ntf = cRqh' (cR + cv) +2qh(cR +cv) Ocft

+cRqh'(cR)+2+2qh(cR)<O. The inequalities follow from (4). Since

Bk=-oc02,o7rfc.1Oo2c7i.f2,

and qh(cR +cv) <O, so that the ratio must be

greater than -1. D CIaim 3. Bv (O) == cm, BR (O) = cm. Proof. Substituting cR =cnt and cv=O into (7)

yields

2qm (cm) + cm2qh(cm) . This is zero from (5) implying BR(O)=cm.

Similarly for Bv. D CIaim 4. (i)cR=BR(cv) intersects the line cR

+cv=c' below the line cR=cv (45 dagree line).

(ii) cv=Bv(cR) intersects the line cR==cv

c* above cR=Cv= 2･

(iii) inte7section of cR==BR(cv) and the line cR =cv is northeast (higher along the 45

degree line) of intersection of cv=Bv(cR)

and the line cR=cv. Proof. We first show 66caj lc.-c.-s' = c"qin(c")+ C2' qh( C2' )qm(c*)

+q.( C2' )- C2* qh(c") - - C2' qh(c*) >O.

The last inequality follows from (6). This implies part (i).

Denote the intersection of cR=:19R(cv) and line cR+cv=c* by (c-R, c*- c-R). Since

this is on BR,

The Consortium Standard and Patent Pools

22 7r;S( c-R, c- v) + na c-R, cA v)

= ( cAR+ c- v) qm( c-R+ c- v)

+P(qm ( cAR) ) q. ( cAR) .

Since c"< cm, the first term is an increasing

function on the interval (c-R+ cAv, c*). The

second term is a decreasing function and c-R

c*>

qm (c*) + c'Rqfu (c") + c-Rqh( c-R) +q. ( c-R)

- o.Since c-R< cm, the sum of the last two termsis positive from(5). The sum of the first two

terms must be negative and we have

4m(C") C-R < - qh(c*) '

c*Since < c"R, we have 2 oacrr.Vi 1,.=..=s* = q.(c*) + C2* qh(c*) >o.

This implies part (ii).

Suppose cR=BR(cv) intersects line cR=cv at cR=cv=z. It must satisfy (7) :

qm (2z) +zqh(2z) +qm (z) +zqh(z) = O.

The sum of last two terms must be positivesince z< cm. Thus we have one lc.-c.-z=qm (2z) +zqh(2z) <O. 0cv

This shows part (iii). D The proceeding claims are summarizedin Figure 2. The part (i) of the proposition

follows : Nash Equilibrium lies below the 45

c*degree line, it is above the line cR+cv= 2,and to the left of the point RY. To show part (ii) of the proposition, we

first calculate the total of the firm profits:

z)? (c*) + nv (c*) = c*qm (c*)

+P(qm( C* ))q.( C* ),

2c- v) + 7ve( c-R

ity of

To

note

. This implies 7o? (c') + zv (c') > zi5( cAR,

, cAv). This implies first inequal-

proposition's part (ii) .

show the second inequality, first wethat n<-S-, -S-) is decreasing in c:

orr(s･g)

0c

= 7}(q

This implies

c== cv =-2- (45

h

7Z'f(CR, Cv)

degree line)

(C) C+ q. (c) -q.( C

at the intersection of 45 line and B

7

is decreasing along cR

.So profit is lower

v than at cR

))<o.

355

C*=cv= 2.Since ne(cR,cv) is decreasing in

cR along Bv, profit is lower at iE than at the

intersection. Thus we have the second in-equality.

Notes 1) We are indebted to comments from Yoshi-hito Yasaki, Akira Okada and other participants of

"IT Innovation Workshop," Hitotsubashi Univer-

sity, March 2004, and Institute of EconomicResearch Seminar as well as research assistance of

Naotoshi Tsukada. 2) See Klein (1997) for the recent articulation

of the policy of the US antitrust authority towardpatent pools. See Gilber (2002) and Priest (1977)

for a historical overview of the U. S. policy toward

patent pools.

3) There is an example of a standard bodywhich maintains free IPR policy such as W3C. SeeLemley (2002) for a comprehensive review of licen-

sing policies of standard bodies.

4) For instance, if the product market is a Cournot

duopoly with linear demand 1-Q, Q, total output,

then qh(Zici+r)=(1-Zici-2r+r')/3 where 7and 7' are this firm and rival's respective firmspecific non-license marginal costs.

5) We write Rle(qk, q-k) for generality, includ-

ing heterogenous goods. If firms producedhomogenous goods, then q-h=2."-=i"-.k qJ.

6) The above analysis assumed the Nash equi-librium of simultaneous pricing by the pool and the

outsider. It is possible that the outsider moves first

in price setting, since there is a first mover advan-

tage. This is explored in Section 3.

7) There is no market interaction between M

and V firms: V-firm has no incentive to raiseroyalty to raise rival's cost. See end of this section

for details.

8) V-firm's royalty revenue comes only fromthe M-firm and does not include own output. SoV-firm chooses output equal to the monopoly out-put when marginal cost is cR, i. eo, qM(cR) and not

qv(cR).

9) Exact definition is in the proof.

10) Of course these trade-offs will differ when

there is downstrearn market interaction. For adiscussion of downstream oligopoly, see ?

11) Rernarks regarding the case of downstream

oligopoly at end of previous section would applyhere also.

12) The benchmark is the investment when thestandard is controlled by a single firm. Such firm

may overinvest or underinvest in the quality of the

standard, depending on the relationship betweenthe valuation of a marginal consu;ner and that of a

average consumer. 13) Note that any dynamic concern of pricing,

such as penetration pricing for promoting the diffu-

'

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1

The Consortium Standard and Patent

sion of a standard, can be internalized by a patent

pool.

14) The licensing of certified essential patents

will be undertaken by separate licensing companies

("Platform Companies") which are specific to a

particular radio access technology e. g. W-CDMA,

cdma2000, TD-CDMA, etc. The members of thePlatform Companies are the owners of certifiedessential patents,

15) The Platform Company for the 3G systems

based on the W-CDMA technology was formed inSeptember 2003 (PlatformWCDMA Limited or"PlatformWCDMA"). PlatformWCDMA willoffer licenses under the W-CDMA Patent Licensing

Programme which was launched officially on the 24

March 2004. The W-CDMA Patent Licensing Pro-gramme became effective 1 January 2004.

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ft ma fi ce (2OO2) FNg}Meeue fx- cJ) ii):¥manJt]J : .{7F- tz

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