ECONOMIC ANALYSIS GROUP

DISCUSSION PAPER

Innovation and Ex Ante Consideration of Licensing 

Terms in Standard Setting

by

 Tor Winston *

EAG 06-3 March 2006

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*

 Economist, U.S. Department of Justice. The views expressed are not purported to reflect the views of 

the U.S. Department of Justice.
Abstract

In an effort to produce interoperable products, firms frequently participate in Standard Setting 

Organizations (SSOs) to collaboratively set technical standards for products used by networks of 

consumers. Some SSO members say they suffer from a type of holdup: after they sink

technology-specific investments in developing and implementing a standard using a particular 

patented technology the patent owner can set licensing terms that exploit those investments. 

These members have called on SSOs to enhance competition between patent owners by

soliciting and considering licensing terms for competing technologies ex ante, before anointing 

one as “the standard.” However, more competitive licensing terms may dampen incentives to 

innovate. This paper analyzes the balance between the welfare benefits of the added competition 

and the welfare costs of reduced innovation. The model of R&D investment and standard setting 

predicts that both total welfare and consumer welfare are higher when an SSO considered

licensing terms ex ante as long as the cost of innovation is not “high.” The model also predicts 

that the welfare benefits of ex ante consideration of licensing terms grow as the costs of

innovation falls. However, when the cost of innovation is “high” the negative welfare effects are 

always small.
1 Introduction

Technical standards add tremendous value by enabling products to interoperate. A cell phone is valuable because it is compatible with a network of other

phones. Computer software is valuable, in part, because it allows us to create

documents that can be viewed by others. The technological standards that are

the foundation of such networks are commonly established through three mechanisms: 1) market competition, where ...rms produce incompatible products until

one ...rm’s technology becomes the de facto standard; 2) collaboration between

rival producers who agree to use the same (or compatible) technology; and 3)

government intervention.

1

There are many examples of each route to standardization. The triumph

of VHS technology over Betamax and the rise of Microsoft Windows are classic examples of the ...rst route. The second route was used to collaboratively

develop interpretability standards for the World Wide Web and Wireless Local

Area Networks (WLAN).

2 Similar standards for mobile broadband technology

are currently being developed by an industry group called the WiMAX Forum.

The third route was used when the quasi-governmental International Telecommunications Union (ITU) established the standard protocols for FAX machines.

The ITU also cut short a standards war between competing protocols for 56K

modems when it promoted one protocol as the industry standard. More recently, the US Federal Geographic Data Committee (FGDC) has led an e¤ort

to develop compatibility among Geographic Information Systems (GIS) software, and the Federal Communications Commission (FCC) has designated a

standard for high de...nition television (HDTV). See (Augereau et al. , 2004).

To ensure that their products are compatible, and thus more valuable, ...rms

frequently collaborate in Standard Setting Organizations (SSOs) to choose a

particular technology as the industry standard.

3 Traditionally, SSOs have been

1Economic theories of networks and standards have primarily focused on the competition

between ...rms to become the de facto industry standard. A 1992 Journal of Industrial Economics symposium on network industries (Gilbert, 1992), (Katz & Shapiro, 1986b), and (Katz

& Shapiro, 1986c) provided a theoretical foundation for an extensive literature on competition

in network industries and the implications of networks for investment and antitrust. Most

models that have considered de jure standard setting (standard setting within collaborative

standard setting organizations) have focused on the strategic issues surrounding coordination.

Firms might disagree over which technology the SSO should choose and some ...rms must decide between participating in collaboration or trying to establish their own de facto standard.

These issues are discussed by Joseph Farrell and various coauthors in (Farrell, 1996), (Farrell

& Saloner, 1988), and (Besen & Farrell, 1994). Two excellent summaries of the literature are

(Quelin et al. , 2001) and (David & Greenstein, 1990). (Tassey, 2000) provides useful general

background on technological standards.

2 The World Wide Web Consortium (3WC) has developed numerous protocols that support

the transfer of data, photos, video, and audio across the internet. Until recently, the 3WC

required that all proprietary technology incorporated in its standards be licensed "royalty

free." The Institute of Electrical and Electronics Engineers (IEEE) has also developed standard

protocols for wireless data transmission from computers to nearby internet connections.

3 SSOs are also used to develop quality standards that enable adherents to commit to

a certain level of quality. Examples of such standards are board certi...cation for medical

professionals and product safety standards.

2
populated by engineers who consider the technical merits of available alternative

technologies and select the "best" technology as the industry standard without

regard to what the licensing terms for any patented technologies might be. In

selecting one technology as the standard, the SSO members e¤ectively eliminate

their ability to substitute between the available technologies. When the selected

technology is under a patent, the intellectual property (IP) owner e¤ectively

becomes a monopolist.

Recently, some SSO members have complained that IP owners exploit their

positions as monopolists and set unfair or excessive licensing terms for technologies that the SSOs have adopted as industry standards.

4 Dissatisfaction with the

status quo system has prompted calls for SSOs to consider the licensing terms,

as well as the technical merits, of the available technologies before "anointing"

one as the standard because the current safeguards requiring "reasonable and

non-discriminatory" (RAND) licensing terms are insu¢cient to prevent IP owners from exercising any market power they gain from having their technology

selected by an SSO.

5

A simple hypothetical example helps to illustrate the point. An SSO wants to

develop a standard method of attaching peripheral devices to cell phones. There

are two possible ways to con...gure four metal pins on the plug that will attach

a device to a phone. The four pins can be aligned in a single row or they can be

arranged in two rows. Call these technologies X and Y respectively. Technology

X is marginally better than Y: Under the status quo system, the SSO would

choose X. Then the patent owner would be able to set its royalty knowing that

it no longer faced competition from technology Y: Under the proposed ex ante

system, the SSO would ...rst request licensing terms from both patent owners

and then select the best combination of technology and licensing terms. Thus,

4 Robert Skitol provides an excellent description of the problem and summary of related

legal literature and ...lings (Skitol, 2005). In 2002 the Department of Justice and the Federal

Trade Commission held joint hearings on "Competition and Intellectual Property Law and

Policy in the Knowledge-Based Economy." Two of the sessions focused speci...cally on the issues

of licensing technology implicated by de jure standards set by SSOs. Transcripts and written

testimony of the hearings are available at http://www.ftc.gov/opp/intellect/index.htm. Ex

ante licensing discussions were also at the center of a debate over the "Standards Development

Organization Advancement Act of 2004," a law which extended the "National Cooperative

Research Act" to limit the antitrust liability of registered SSOs as well as research joint

ventures. See (Schwartz & Gorman, 2004).

SSO members have also voiced a related complaint: some participants have allegedly violated rules that require them to disclose any patents that might read on the standard being

developed. This has been the subject of several high pro...le lawsuits. See Micron v. Rambus,

189 F.Supp.2d 201(D.Del. 2002); Rambus v. In...neon Technologies, 318 F.3d 1081, Fed. Cir.

2003; and the FTC’s suit against Union Oil Company of California, In re Union Oil Company

of California, No. 9305, March 2003.

5 Relatively few disputes over "reasonable and non-discriminatory" licensing terms have

been settled by the courts. In one such case Rockwell International Corp. claimed that Motorola Corporation’s licensing terms for patented technology incorporated in the ITU standard

for 33.6K modems were "unreasonable." See (Shapiro, 2000). In another court case, Soundview Technologies charged that Sony and other members of the Electronic Industries Alliance

(EIA) violated antitrust laws by collectively ...xing royalties for Soundview’s patented technologies used in the "V-Chip," the standardized chip that the government requires to be

installed in all televisions to enable parents to block violent programming.

3
if the terms o¤ered for technology Y were su¢ciently superior, the SSO would

select technology Y as the standard.

This process would allow SSO members to bene...t from increased competition between substitute technologies before they commit to one technology.

Without such ex ante competition, the SSO members su¤er from a holdup

problem similar to that examined in (Williamson, 1989) and (Grossman & Hart,

1986): after SSO members have made asset-speci...c investments (speci...c to a

patented technology) in developing and implementing a particular standard, the

patent owner is able to extract rents from those investments.

6

Despite the potential advantages of ex ante competition, most large SSOs

have rules that explicitly prohibit any public discussions of licensing terms during the standard setting process and many of their members have vigorously

opposed any change.

7 At the 2002 Federal Trade Commission / Department of

Justice hearings on IP and antitrust, representatives from large ...rms spoke on

both sides of the issue; some downplayed the frequency and importance of such

licensing hold up while others insisted that it is a signi...cant problem.

8

Opponents of ex ante competition have argued that such licensing discussions are likely to extend into areas that would be per se violations of antitrust

laws, such as agreements on product prices.

9 Further, opponents contend that ex

ante competition would introduce many practical problems that would greatly

impede an already cumbersome standard setting process primarily because business people and lawyers would be required to negotiate licensing terms and

ensure that discussions do not violate antitrust laws. Proponents of ex ante

competition argue that SSOs create market power for the IP owner when they

select its patented technology and that the SSO should be able to counter that

arti...cial market power through joint ex ante consideration of licensing terms.

Citing the possible e¢ciency justi...cations, proponents have sought guidance

from the antitrust agencies on the issue.

10 Federal Trade Commission Chair6 Carl Shapiro provided a de...nition of "holdup" in this context in (Federal Trade Commission and Department of Justice, 2002a) pp. 15-16. An amicus brief ...led by Joseph Farrell and

other leading academics in the Federal Trade Commission’s Rambus proceeding also describes

holdup in the context of standard setting (Farrell, Joseph, et al., 2004).

7For example, IEEE policies state that "[t]he validity, terms, or cost of speci...c patent use"

should be avoided during standard setting meetings. However, the SSO rules do not explicitly

prohibit bilateral ex ante negotiations between an IP owner and a potential licensee. Even

so, to the extent that such bilateral negotiations are e¤ective they also dampen incentives to

innovate.

8For example, Scott Peterson of Hewlett-Packard spoke out in favor of allowing ex ante

licensing discussions. Carl Cargill of Sun Microsystems explained that RAND licensing terms

are not su¢ciently well de...ned. See (Federal Trade Commission and Department of Justice,

2002b) on pp.246-251 and pp. 109-111. They were opposed by Earle Thompson of Texas

Instruments and Richard Holleman of the IEEE.

9 See the testimony of Earle Thompson, Intellectual Asset Manager and Senior Counsel of

Texas Instruments and attorney Paul Vishny in (Federal Trade Commission and Department

of Justice, 2002a) pp.32-33 and p.44 respectively.

10

(Lemely, 2002) provides an excellent in-depth review of current legal issues surrounding

SSOs and IP rights. (Lemely, 2002), (Curran, 2003), and (Gi¤ord, 2003) all make the case

that ex ante licensing discussions have potential e¢ciency justi...cations and thus should be

subject to a rule of reason analysis. Scott Peterson, of Hewlett-Packard, and Robert Skitol

4
man Deborah Majoras has agreed that, "joint ex ante royalty discussions that

are reasonably necessary to avoid hold up do not warrant per se condemnation." (Majoras, 2005) This echoes the view expressed in June 2005 by outgoing

Assistant Attorney General for Antitrust R. Hewitt Pate.(Pate, 2005) The European Commission has also indicated that it will study the issue.(European

Commission, 2005)

Aside from the practical and legal issues surrounding ex ante discussions,

there is a concern that adopting the ex ante system may harm welfare by dampening innovation incentives. If SSO members extract more favorable terms from

IP owners by engaging in ex ante licensing discussions, then ...rms will likely

invest less in researching and developing technologies that could form the basis of new standards.

11 To analyze the e¤ects of adopting the ex ante system

one must assess both the social bene...ts of lower royalties and the social costs

of diminished innovation incentives.

12 This paper develops a model of R&D

investment and standard setting to analyze the e¤ects of adopting the ex ante

system on the surpluses enjoyed by IP owners who license technology to manufacturers, manufacturers who buy licenses in order to produce an end product,

and consumers who purchase the end product. The model predicts that greater

competition between IP owners under the ex ante system bene...ts both consumers and producers (manufacturers that buy licenses to use the technology)

as long as the cost of innovation is not "high." The model also predicts that

innovators (R&D ...rms) are harmed by the competition introduced by the ex

ante system.

The remainder of this section provides a brief review of the economic literature on licensing, which forms the foundation of the model presented in this paper. Section 2 outlines a three-stage model of R&D investment and collaborative

standard setting. Section 3 solves for the equilibrium innovation investments,

R&D pro...ts, producer pro...ts, and consumer surplus of the three-stage model

for two separate games: one without ex ante licensing competition, and one

with ex ante licensing competition. Section 4 compares the welfare outcomes of

the two games and Section 5 concludes.

1.1 Review of licensing literature

From its inception, formal modeling of optimal licensing has been concerned

with the relationship between licensing revenues and the amount of resources

allocated for innovation. Kenneth Arrow’s pioneering work relates an inventor’s

royalty revenues to the structure of the downstream market in which its licensees

compete (Arrow, 1962). In Arrow’s three-stage model, a single IP owner sets

call for Agency guidance in (Petersonn, 2002) and (Skitol, 2005).

11 See (Holleman, 2002). Joseph Farrell also comments on the issue in (Federal Trade Commission and Department of Justice, 2002a) pp. 47-48.

The same concern arises from some SSO policies that require participants to license any

patents covered by the standard royalty free or to transfer the ownership of covered patents

to the SSO itself.

12 The tradeo¤ considered here is similar to the tradeo¤ implicit in granting patent protections. Market power is the currency with which society purchases innovation e¤ort.

5
royalties for its cost-reducing innovation, then producers choose whether or

not to purchase a license, and ...nally producers compete downstream.

13

In

the 1980s, a series of papers began to apply variations of Arrow’s basic threestage model to questions about the optimal structure of licensing fees: Should

licensors charge lump-sum royalties, or per-unit royalties, or both? Should

licensors sell to all comers or limit the number of licenses they o¤er? Should

licensors auction o¤ a limited number of licenses?

14

In his Handbook of Game

Theory chapter (Kamien, 1992), Morton Kamien provides an excellent summary

of several extensions of Arrow’s basic model developed by himself and various

coauthors as well as by Michael Katz, Carl Shapiro, and others. See (Kamien

& Tauman, 1992), (Kamien & Tauman, 1986), and (Kamien & Tauman, 2002).

Also see (Quelin et al. , 2001) for a summary of the literature on technology

standards in network industries, including (Katz & Shapiro, 1986a) and (Wang,

1998). Some of the extensions developed incorporate an initial stage in which

the licensor must ...rst invest in R&D in order to develop the cost-reducing

technology.

15

This paper makes several modi...cations to the basic model established in

the literature to address the new question of which standard setting system

yields the highest pro...ts, consumer surplus, and total welfare. To compare the

two standard setting systems, this paper develops two parallel versions of the

same theoretical model: one models the status quo system of standard setting

where industry standards are chosen without open competition over licensing

terms, while the other allows for ex ante competition in licensing terms before

the standard is chosen. The two models have the same three stages. First,

research and development ...rms (R&D ...rms) invest in innovation to develop

new technologies. Second, an SSO selects one of the new technologies as the

industry standard. Third, the SSO members compete in a Cournot market selling the standardized product. The Subgame Perfect Nash Equilibrium (SPNE)

of each of these two models are solved through backward induction starting

with Cournot competition in the downstream market and the innovation e¤ort,

pro...ts, and welfare associated with each of the two games are compared.

The current model di¤ers from the literature in four important ways. First,

unlike the existing literature, where a single IP owner competes with an existing

free technology, the current model allows two R&D ...rms to behave strategically

when investing in R&D and setting their royalty rates, somewhat like ...rms engaged in a patent race.

16 Second, in the existing literature downstream ...rms

13 The model predicts that an owner of a cost-reducing innovation who charges a per-unit

royalty can earn higher pro...ts when the downstream market is competitive than when it is

monopolistic.

14

(Katz & Shapiro, 1986c) does not explicitly model the downstream competition among

licensees.

15A new generation of licensing models, pioneered by (Segal, 1999), focuses on bilateral

licensing contracts in an environment where licensees (and even the licensor) compete in the

downstream market.

16Much of the literature on investment incentives and innovation considers patent races

(See (Tirole, 1995) pp. 394-399), where the ...rst ...rm to develop the technology (and patent

it) gets a monopoly payo¤. The current model has a similar "winner-take-all" element which

6
can generally decline to license the new cost-reducing technology and to continue producing using the old, higher-cost (but royalty-free) production technology. This is not possible in the current model because a downstream ...rm

that chooses not to take a license simply cannot legally sell the standardized

product in the downstream market. Third, some of the existing literature allows

for ‡exible licensing structures, but the current paper considers only per-unit

licenses. While this may be a strong assumption, it is probably appropriate

in the context of an SSO where IP owners routinely commit to licensing on

"non-discriminatory" terms.

17 Fourth, the current model interprets innovation

as an advancement that increases a consumer’s willingness to pay (a common

interpretation of "quality"). Although most of the existing literature has interpreted innovations as reducing production costs, the basic Cournot model can

accommodate either interpretation.

2 A Model of R&D Investment and Collaborative Standard Setting

The model proceeds in three stages. In the ...rst stage, two R&D ...rms simultaneously invest e¤ort in developing new technologies. The results of the R&D

e¤ort are not deterministic. Instead, each of the two ...rms realizes an unidimensional innovation that is a random draw from a distribution determined by the

...rm’s innovation e¤orts. A ...rm that invests more draws its innovation from a

distribution that ...rst order stochastically dominates the distribution of a ...rm

that invests less. In the second stage, the R&D ...rms submit their patented

innovations to an SSO, whose members then decide which of the two innovations (technologies) to implement as the standard, and set per-unit royalty fees.

In the third stage, the licensees (producers) compete to sell the standardized

product in the downstream market.

The model is analyzed in the context of several important maintained hypothesis. 1) The SSO members are homogeneous. 2) The two R&D ...rms are

not SSO members. 3) Individual SSO members are not able to negotiate licensing terms bilaterally with the R&D ...rms either before or after the standard

has been set. 4) The SSO members make sunk investments in developing and

implementing the standard. 5) The patented technology is essential to implementing the standard. 6) There are no alternative uses for the technologies;

speci...cally, neither R&D ...rm is in a position to promote its technology as a

is common in models of patent races. In both the status quo model and the ex ante model,

the ...rm that produces the greatest innovation becomes the monopoly provider of licenses in

equilibrium. However, unlike the patent race models, innovation occurs simultaneously so

neither ...rm innovates ...rst.

17 There is an ongoing debate about the legal meaning of "nondiscriminatory" in this context.

It appears that uniform per-unit licensing fees are not considered discriminatory whereas

combinations of lump-sum and per-unit fees may be considered discriminatory. IP is often

licensed as a percentage of sales. However, equilibria solutions to the games using a percentage

royalty become intractable.

7
de facto standard outside the structure of the SSO. 7) There is no uncertainty

regarding whether the R&D ...rms’ patents cover the technologies in question.

18

The ...rst two maintained hypotheses are probably the most critical abstractions. In reality, SSO members are often a diverse group with individual vested

interests in the competing technologies. For example, IP owners themselves are

often SSO members and they actively promote their own technologies during

the standard setting process. These two maintained hypotheses abstract from

the complicated internal decision making process common in most SSOs because

the homogeneous SSO members in the model all agree on which technology to

choose. The third maintained hypothesis may be somewhat redundant given the

...rst two, but it is important to point out that bilateral licensing arrangements,

especially cross licensing, are common. The remaining maintained hypotheses

simply ensure that there is an interesting holdup problem and abstract from

some potential issues that would limit the applicability of the model in some

cases.

3 Solving for the SPNE Both With and Without

Ex Ante Licensing Competition

Two di¤erent standard setting systems are modeled using the same ...rst and

last stages; the systems di¤er only in the structure of the second stage of the

model. Under the status quo "ex post licensing" game (G1); the SSO members

simply choose the best technology (the largest innovation drawn by the two

R&D ...rms) and then the winning R&D ...rm sets a revenue-maximizing royalty. Under the proposed "ex ante licensing" game (G2); the two R&D ...rms

commit to speci...c royalties before the SSO members choose one technology as

the industry standard. The di¤erent methods of selecting a standard induce

di¤erent equilibrium levels of investment, returns on R&D, pro...ts for the SSO

members, and consumer surpluses. Thus, the equilibrium outcomes of the two

parallel games can be compared to evaluate whether the welfare bene...ts of the

additional competition under the ex ante system exceed the harm of reduced

innovation. The SPNE equilibria can be found through backward induction,

starting with the third stage.

3.1 Stage Three: Downstream Cournot Competition

As is common in models of optimal licensing, consumer demand is given by the

simple inverse demand function

P = Æ ¡ Q; (1)

where P is the market clearing price and Q is the total quality of a homogeneous product. Although products are probably heterogeneous in reality, the

assumption of product homogeneity is somewhat plausible because the products

18 Similar assumptions were made in (Besen, 2002).

8
have to have at least one thing in common: they must adhere to the industry

standard. The parameter Æ represents the value that results from technological

innovations. As innovations improve the quality of the product, each customer’s

willingness to pay increases. The demand curve (1) suggests that di¤erent customers value the basic product di¤erently, but that they all value improvements

in the product equally.

When N  ̧ 2 producers compete in the downstream market their combined

Cournot equilibrium pro...ts are

o

C (Æ; r) =

N

(N + 1)

2

(Æ ¡ r)

2

; (2)

where r is the positive per-unit royalty.

19 The R&D ...rm receives r for each of

the Q units sold by the downstream Cournot competitors (SSO members) and

its equilibrium revenues are

o (Æ; r) =

N

(N + 1)

(Æ ¡ r) r: (3)

In Stage Two, the R&D ...rms choose r to maximize (3);the revenues that they

ultimately earn in Stage Three. Because G1 and G2 diverge in Stage Two, the

two games are considered separately in the next section.

3.2 Stage Two: G1

In the status quo game (G1) the SSO selects the best technology (the highest of

the two realizations of Æ) and the winning R&D ...rm sets its royalty to maximize

(3). Let H denote the winning ...rm and rM denote its monopoly royalty choice.

Setting the derivative of (3) with respect to r equal to zero yields the revenue

maximizing per-unit royalty rM =

ÆH

2

and corresponding licensing revenues

oM (Æj ) =

N

(N+1)

¡

ÆH

2

¢2

:

3.3 Stage Two: G2

Stage Two in the ex ante game (G2) is divided into two sub-parts. First the

R&D ...rms set their royalties, and then the SSO chooses which technology to

incorporate into the standard. The SPNE of the stage is solved by backward

induction, starting with the SSO’s technology choice and then considering the

R&D ...rms’ optimal royalties.

3.3.1 Technology Choice

When considering licensing terms ex ante, the SSO chooses the best combination

of technology (Æ) and per-unit royalty (r): To do so, the SSO members compare

19 This is the same downstream market structure that Kamien employs in his 1992 summary

of the literature (Kamien, 1992). In reality, licensing terms have many more dimensions than

just price. For example, the licensing terms may restrict the use of the technology or account

for cross licenses.

9
the total expected pro...ts of the N licensees, given the two (Æ; r) combinations

o¤ered by the R&D ...rms.

20 By inspection of (2), it is clear that downstream

industry pro...ts are higher when the SSO selects the R&D ...rm that o¤ers the

higher value of (Æ ¡ r):

21

3.3.2 Royalty Choice

In Stage Two of G2 the two R&D ...rms compete in a Bertrand setting, each

lowering its royalty to undercut the other’s (Æ ¡ r) value. Let L denote the

...rm with the lower innovation value. The ability of Firm H to extract pro...ts is

limited by the willingness of Firm L to price at marginal cost, a royalty of zero.

22

Let the superscript D indicate the duopoly royalty and pro...ts. However, when

the di¤erence between ÆH and ÆL is su¢ciently large, the SSO will choose Firm

H0s innovation even if Firm H charges the monopoly royalty. That is, Firm H

is e¤ectively a monopolist because Firm L would have to o¤er a negative royalty

to compete with it superior technology.

Proposition 1 In equilibrium, the R&D ...rm with the lesser innovation o¤ers

its license for free (equal to marginal cost). The R&D ...rm with the superior

innovation charges r

D = ÆH¡ÆL if ÆL >

ÆH

2

and charges rM =

ÆH

2

if ÆL ·

ÆH

2

:

The SSO chooses Firm H0s technology as the standard.

Proof. When Firm H sets a royalty rate of rH = ÆH ¡ ÆL and Firm L sets a

rate of 0; then neither ...rm can pro...tably deviate if ÆL >

ÆH

2

: Firm L will earn

zero pro...ts at any positive royalty because it will not be selected by the SSO

and could only earn negative pro...ts from setting a negative royalty. Firm H

can increase its royalty (and thus pro...ts) up to ÆH ¡ÆL and its technology will

still be selected by the SSO. If Firm H sets a royalty greater than aH ¡ ÆL the

SSO will choose Firm L

0

s technology and Firm H will earn zero royalties.

However, if ÆL ·

ÆH

2

; then aH ¡ÆL would exceed the monopoly royalty rate

ÆH

2

: Thus Firm H would maximize pro...ts by setting its royalty to

ÆH

2

: Firm L

could not pro...tably deviate for the same reasons described above.

Substituting r

D into (3) yields Firm H0

s Stage Two equilibrium licensing

revenues

o

D (ÆH) =

N

(N + 1)

ÆL (ÆH ¡ ÆL) if ÆH <

ÆL

2

: (4)

Firm L

0

s equilibrium licensing revenues are zero because it is not selected by

the SSO. The R&D ...rms consider the Stage Two pro...ts of G1 and G2 when

deciding how much e¤ort to invest in innovation e¤ort in Stage One.

20 Because members of the SSO are homogeneous, this decision rule could be de...ned in

terms of aggregate or individual downstream pro...ts.

21Letting L denote the ...rm with the lower innovation value, the SSO maximizes industry

pro...ts by choosing Firm H if (ÆH ¡ rH) < (ÆL ¡ rL) :

22

It is assumed that the costs of abandoning the chosen standard are su¢ciently high that

they do not constrain the winning R&D ...rm’s royalty choice.

10
3.4 Stage One: Expected Pro...ts

The ...rst stages of G1 and G2 are essentially the same; the forward-looking

R&D ...rms make their innovation investment decisions in Stage One based on

the equilibrium royalty revenues they expect to earn in the subsequent stages.

23

This decision depends on the relationship between the cost of innovation e¤ort

and the corresponding expected licensing revenues. In equilibrium, each R&D

...rm chooses an innovation e¤ort that is a best response to the other’s choice.

Because the R&D ...rms’ expected pro...ts depend on the cost of the innovation

e¤ort they expend, it is necessary to establish the innovation process before fully

characterizing pro...ts.

3.4.1 The Innovation Process

The development of new technologies is an inherently uncertain process. Large

innovations may result from only a small amount of e¤ort just as large amounts

of e¤ort may yield only small innovations. However, in general, a ...rm that

expends more e¤ort can expect to produce a larger innovation. To re‡ect the

uncertainty of the process, a ...rm’s innovation, Æ; is modeled as a random draw.

Let j denote an R&D ...rm.

24 Firm j0

s innovation, Æj ; is drawn from

f (Æj j ̧j ) =  ̧j (Æj )

 ̧j¡1

; (5)

a family of probability density functions de...ned over the support Æj 2 [0; 1] :

The di¤erent distributions in the family are distinguished by Firm j

0

s innovation

e¤ort,  ̧j : It is useful to note that E [Æj j ̧j ] =

 ̧j

1+ ̧j

: Thus, the expected marginal

product of innovation e¤ort  ̧j is positive and decreasing.

25 Finally, let the cost

of innovation e¤ort be speci...ed as a linear function of e¤ort, C ( ̧j ) = c ̧j :

26

3.4.2 Expected Pro...ts

R&D ...rms choose their innovation e¤orts in Stage One to maximize their expected pro...ts from royalties earned in subsequent stages. These expected royalties depend on three factors: whether the ...rm generates the best of the two

innovations (if it does not, it gets no future royalties in equilibrium); the absolute level of its innovation (the greater its innovation, the more royalty revenue

it will earn); and, in the case of G2, the relative level of the ...rm’s innovation

compared to the other R&D ...rm’s innovation. These factors are captured in the

23 The R&D ...rms are assumed to be risk neutral.

24 The j and ¡j subscripts replace the H and L subscripts because the ...rms’ actual innovations are not realized until the end of Stage One.

25

It is easy to extend the model to account for di¤ering levels of productivity of innovation

e¤ort. If innovations are drawn from f (Æj j ̧j ) = 1⁄2 ̧j (Æj )

1⁄2 ̧j¡1

; then marginal changes in

 ̧j have a greater e¤ect of moving probability from the lower end of the distribution to the

higher end of the distribution when 1⁄2 is higher.

26 This linear speci...cation indicates that the R&D ...rms have no monopsony power in the

market for innovation e¤ort (hiring engineers) and that there are no lumpy or sunk costs

associated with innovation e¤ort.

11
following expected pro...t functions that integrate royalties over the two R&D

...rms’ distributions of Æ:

Expected Pro...ts: G1 In the equilibrium of G1 Firm j earns the monopoly

royalty, oM (Æj ); conditional on the fact that it draws a higher innovation value

than its rival. Thus the expected pro...t for Firm j is

E[o

G1

j

( ̧j j ̧¡j )] =

Z 1

0

μZ Æj

0

o

M (Æj ) f (Æ¡j j ̧¡j ) dÆ¡j

¶

f (Æj j ̧j ) dÆj¡C ( ̧j );

(6)

where the subscript ¡j denotes the other R&D ...rm. The inner term of the

double integral integrates the monopoly royalty revenues of Firm j (with innovation Æj ) over the truncated distribution of Æ¡j 2 (0; Æj ): In this range,

Firm j

0

s technology would be selected by the SSO in equilibrium and Firm j

would earn royalties. The outer term integrates over the entire distribution of

Æj : Substituting the functional forms of f (Æj j ̧j ); oM (Æj ); and C ( ̧j ) into (6)

and solving the integral yields

E[o

G1

j

( ̧j j ̧¡j ; N)] =

1

4

N

(N + 1)

 ̧j

(2 +  ̧j +  ̧¡j )

¡ c ̧j : (7)

Before turning to the equilibrium innovation e¤orts in G1 consider the expected

pro...ts in G2:

Expected Pro...ts: G2 The expected pro...t function for G2 is more complex

because the R&D ...rm with the higher innovation will set the monopoly royalty

if its innovation is su¢ciently superior and the duopoly royalty if it is not. Thus

in (8) the inner term of the double integral is split into two terms. The ...rst

is similar to the inner term in (6). However, (8) only integrates the monopoly

royalty revenues over the range Æ¡j 2

¡

0;

Æj

2

¢

; the outcomes when Firm j would

price as a monopolist due to the superiority of its innovation. The second

integrates the duopoly royalty revenues over the truncated distribution of Æ¡j 2

¡ Æj

2

; Æj

¢

; the outcomes when Firm j

0

s technology would still be selected by the

SSO but the ...rm would be constrained to price as a duopolist. Again, the outer

term integrates over the entire distribution of Æj : Thus Firm j

0

s equilibrium

pro...ts are

E[o

G2

j

( ̧j j ̧¡j )] =

Z 1

0

Ã R Æj

2

0

oM (Æj ) f (Æ¡j j ̧¡j ) dÆ¡j+

R Æj

Æj

2

o

D (Æj ; Æ¡j ) f (Æ¡j j ̧¡j ) dÆ¡j

!

fj (Æj j ̧j ) dÆj¡C ( ̧j ):

(8)

Substituting the functional forms of f (Æj j ̧j ); oM (Æj ); o

D (Æj ; Æ¡j ); and

C ( ̧j ) into (8) and solving the integral yields

E[o

G2

j

( ̧j j ̧¡j ; N)] =

N

(N + 1)

 ̧j

¡

1 + 2

1+ ̧¡j  ̧¡j

¢

2

1+ ̧¡j (1 +  ̧¡j )(2 +  ̧¡j )(2 +  ̧j +  ̧¡j )

¡ c ̧j :

(9)

12
3.5 Equilibrium Innovation E¤orts

The expected pro...t functions (7) and (9) imply that each game (G1 and G2)

has a unique symmetric SPNE level of innovation e¤ort in Stage One. This

result is established by setting the ...rst order conditions (FOCs) of the expected

pro...t functions (taken with respect to  ̧j ) equal to zero and then solving the

resulting system of two equations and two unknowns.

27

Proposition 2 The unique symmetric SPNE of G1 is given by

N

(N + 1)

3

2 +  ̧

G1

 ́

16

3

1 +  ̧

G1

 ́2 = c: (10)

Proof. In G1; Firm j maximizes its expected pro...ts by choosing  ̧

¤

j

to satisfy

N

(N + 1)

(2 +  ̧¡j )

4

¡

2 +  ̧

¤

j +  ̧¡j

¢2 = c: (11)

In equilibrium both ...rms’ FOCs must be satis...ed and thus, by inspection of

(11),  ̧

¤

j must equal  ̧

¤

¡j

: Denote this symmetric equilibrium e¤ort as  ̧

G1

: Substituting  ̧

G1

for both  ̧

¤

j and  ̧

¤

¡j

in (11) yields (10).

Proposition 3 The unique symmetric SPNE of G2 is given by

N

(N + 1)

3

1 + 2

1+ ̧

G2

 ̧

G2

 ́

2

3+ ̧G2

3

1 +  ̧

G2

 ́3 = c: (12)

Proof. In G2; Firm j chooses  ̧

¤

j

to satisfy

N

(N + 1)

¡

1 + 2

1+ ̧¡j  ̧¡j

¢

2

1+ ̧¡j (1 +  ̧¡j )

¡

2 +  ̧

¤

j +  ̧¡j

¢2 = c: (13)

Both ...rms’ FOCs are satis...ed when  ̧

¤

j =  ̧

¤

¡j

:

28 This symmetric equilibrium

must be unique. Because

3

1+2

1+ ̧¤

j  ̧

¤

j

¥

2

 ̧¤

j (1+ ̧¤

j )

is monotonically decreasing in  ̧

¤

j

(for

27Only interior pro...t maximization solutions are considered here. The Appendix provides

a proof that corner solutions to the pro...t maximization problem can not be Nash equilibria

in either G1 or G2 if

1

8

N

(N+1) < c and neither ...rm will invest in innovation if

1

8

N

(N+1)  ̧ c:

28

If both ...rm’s FOCs hold then

μ

1+2

1+ ̧¤

¡j  ̧

¤

¡j

¶

2

 ̧¤

¡j

3

1+ ̧¤

¡j

¥ =

μ

1+2

1+ ̧¤

j  ̧

¤

j

¶

2

 ̧¤

j

3

1+ ̧¤

j

¥ : Because

μ

1+2

1+ ̧¤

j  ̧

¤

j

¶

2

 ̧¤

j

3

1+ ̧¤

j

¥

is monotonically decreasing in  ̧

¤

j

, no two values of  ̧

¤

j

yield the same value of

μ

1+2

1+ ̧¤

j  ̧

¤

j

¶

2

 ̧¤

j

3

1+ ̧¤

j

¥ :

Thus  ̧

¤

¡j =  ̧

¤

j

is the SPNE of G2:

13
 ̧

¤

j > 0) there can be only one value of  ̧

¤

j

corresponding to any given  ̧

¤

¡j

:

Substituting the symmetric equilibrium e¤ort,  ̧

G2

; for both  ̧

¤

j

and  ̧

¤

¡j

in (13)

yields (12).

As predicted, the equilibrium level of e¤ort is lower under the ex ante licensing system.

Proposition 4 The equilibrium innovation e¤ort in G1 exceeds the equilibrium

innovation e¤ort in G2; or  ̧

G1 >  ̧G2

:

Proof. The value of the left-hand sides of (10) and (12) are monotonically

decreasing functions of  ̧

G1

and  ̧

G2

respectively. Thus, if the left-hand side

of (10) exceeds the left-hand side of (12) when  ̧

G1 =  ̧G2

; then when the lefthand sides of (10) and (12) are both set to c; it must be true that  ̧

G1 >  ̧G2

:

Following a proof by contradiction, suppose that (10) evaluated at  ̧ is smaller

than (12) evaluated at  ̧: This implies that

¡

2 ¡  ̧ +  ̧

2

¢

< 2

1¡ ̧

; (14)

which does not hold for  ̧ > 0: For  ̧

G1 =  ̧G2 > 0 the left-hand side of (10)

must exceed the left-hand side (12): Thus  ̧

G1 must exceed  ̧G2 when (10) and

(12) hold.

4 The E¤ect of the Ex Ante System on Equilibrium Surpluses and Welfare

The equilibrium innovation e¤orts in each game determine the expected surpluses of the R&D ...rms, the downstream ...rms, and consumers. (The formulas

for the producer and consumer surpluses are constructed in the same manner

as the expected R&D ...rm pro...t functions described above and are given in

the Appendix.) After solving for the equilibrium innovation e¤orts and ...nding

the corresponding surpluses, it is possible to evaluate the model’s predictions

regarding the e¤ects of adopting the ex ante licensing system on each group’s

surplus (and the total surplus) by comparing the G1 and G2 equilibrium results.

One would expect that adopting the ex ante system would decrease the

pro...ts of the R&D ...rms because it introduces an additional element of competition. Further, one would generally expect that consumers and downstream

...rms would bene...t from the additional competition among R&D ...rms.

29 The

equilibrium outcomes of the two games are generally consistent with these expectations. The model predicts that both consumers and downstream ...rms are

better o¤ with the ex ante system unless the costs of innovation are "high" and

that R&D ...rms are always worse o¤ with the ex ante system. The model also

predicts that the bene...ts of the ex ante system to consumers and downstream

29

It is theoretically possible that additional competition among R&D ...rms would induce

them to invest even more in innovation.

14
...rms (and the harm to R&D ...rms) are inversely related to the cost of innovation

e¤ort.

Ideally, one could analytically solve for the equilibrium innovation e¤orts

in each game (as functions of N and c) and then use those ...ndings to solve

for the surpluses enjoyed by consumers, downstream producers and R&D ...rms.

However, such a straightforward analytical approach is not possible in this case

because general analytic solutions for the equilibrium innovation e¤ort in G2 do

not exist. (Analytic solutions exist for particular combinations of the parameters. For example, when N = 2 and c =

5

192

then (12) holds for  ̧

G2 = 1:)

However, if one ...xes the value of N it is possible to perform comparative

statics on the welfare e¤ects of adopting the ex ante system for di¤erent values

of c by expressing each of the surpluses in G1 as a function of  ̧

G2

: This can

be done by ...rst inverting (10) to solve the G1 equilibrium condition for  ̧

G1

as a function of c and then replacing c with the left hand side of (12); the

G2 equilibrium condition.

30 The result gives  ̧

G1

as function of  ̧

G2

: Finally,

this  ̧

G1

3

 ̧

G2

 ́

can be substituted into the G1 surplus functions. Although

conceptually simple, this process produces algebraic monstrosities. Thus, it is

necessary to illustrate the resulting comparative statics using graphs. In the

graphs below N = 2:

Before doing so, it is useful to review the mechanics of this process, which

are illustrated in Figure 1. In the ...rst panel of Figure 1, the horizontal axis

measures equilibrium innovation e¤ort and the vertical axis measures the cost

of innovation e¤ort. The curves labeled G1 and G2 plot the costs of innovation

that are associated with each equilibrium level of innovation e¤ort, as given by

the equilibrium equations (10) and (12).

30 Solving (10) for  ̧

G1 yields

 ̧

G1 =

¡(2μ ¡ 1) +

p

(2μ ¡ 1)

2 ¡ 8μ

2μ

;

where μ = 16

N

N+1

c:

15
Consumer Surplus and Costs in G1 and G2

0 0.2 0.4 0.6 0.8 1 1.2 1.4

. Innovation Effort in G2

0.02

0.04

0.06

0.08

0.1

r e musnoC sul pr uS

A'

B'

G1

G2

0 0.2 0.4 0.6 0.8 1 1.2 1.4

0.02

0.04

0.06

0.08

0.1

noit avonnI t soC

A

B G1

G2

Figure 1

For example, the intersection labeled A indicates that when  ̧

G2 =1 then c =

0:026: Despite the fact that it is on the vertical axis, c is clearly the independent

variable, not the dependent variable. Because (10) can be inverted to express

 ̧

G1

and a function of c, one can ...nd the  ̧

G1

associated with the cost given

by intersection A. The intersection labeled B gives this point as  ̧

G1 1⁄4 1:3: In

the second panel of Figure 1, the curves labeled G1 and G2 plot the consumer

surplus associated with the equilibrium level of e¤ort in each of the two games,

as given by (15) and (16) in the Appendix. By comparing the heights of the

intersections labeled Ap and Bp; which give the consumer surpluses associated

with  ̧

G2 =1 and  ̧G1 1⁄4 1:3; which are in turn associated with c = 0:026, it is

clear that consumer surplus is greater under the ex ante system when c = 0:026:

Using the substitution process described above, Figure 2 illustrates the equilibrium consumer surplus for a range of G2 equilibrium e¤orts. Because  ̧

G2

depends on the cost of innovation e¤ort one can use this ...gure to compare con16
sumer surplus over a range of possible values of c even though the results do

not allow for a direct algebraic relationship between changes in c and changes

in consumer surplus.

31

The line labeled G2 in Figure 2 simply plots the equilibrium consumer surplus (equation (16) in the Appendix) for each equilibrium level of innovation

e¤ort,  ̧

G2

. The line labeled "Cost" relates each level of c to the resulting e¤ort

in G2: Exploiting the equilibrium conditions (10) and (12) as described above to

...nd  ̧

G1

3

 ̧

G2

 ́

, the line labeled G1 plots the equilibrium consumer surplus in

G1 for each  ̧

G2

: For any particular c; the Cost curve yields the equilibrium effort,  ̧

G2

(c): The G2 curve gives consumer surplus in G2 when e¤ort is  ̧

G2

(c):

Finally, the G1 curve gives consumer surplus in G1 when e¤ort is  ̧

G1

3

 ̧

G2

(c)

 ́

:

In words, the G1 curve gives the consumer surplus from the equilibrium e¤ort

that R&D ...rms would make in G1 when costs are such that R&D ...rms would

make e¤ort  ̧

G2

(c) in G2:

Figure 2 illustrates that the consumer surplus in G2 exceeds the consumer

surplus in G1 for most levels of c: However, careful examination of the G1 and

G2 curves near the origin reveals that the consumer surplus generated in G1 is

actually slightly greater than in G2 when  ̧

G2

is very low, which occurs when the

cost of innovation e¤ort is "high." The straight dashed lines highlight the ...nding

that the two systems result in the same consumer surplus when c = 0:064:

For innovation costs above that level (but less than

1

8

N

N+1

) G1 yields slightly

higher consumer surplus. The graph also reveals that the di¤erence between

the consumer surplus generated in G2 and the consumer surplus generated in

G1 increases as costs fall below 0:064: Thus the model predicts that, as long

as the costs of innovation e¤ort are not "too high," the expected bene...ts to

consumers of the additional competition between the R&D ...rms, under the ex

ante system, outweigh the costs of having less expected innovation. Moreover,

the absolute e¤ect of introducing more competition is larger when innovation

costs are smaller and expected innovations are larger.

31As discussed in the Appendix, if c  ̧ 1

8

N

N+1

then neither R&D ...rm invests in innovation

e¤ort in either game’s equilibrium, and thus consumer surplus is zero in both games.

17
0 0.2 0.4 0.6 0.8 1 1.2 1.4

. Innovation Effort in G2

0.02

0.04

0.06

0.08

0.1

r e musnoC er afl e W

Consumer Surplus is Greater in G2 when c 0.064

G1

G2

Cost

Cost 0.064

Figure 2

An equivalent (unreported) graph shows a similar pattern for the aggregate

surplus of the downstream producers, which (given the Cournot construction)

is simply

2

N

times the consumer surplus. Unsurprisingly, an equivalent graph

also reveals that R&D ...rm surplus is higher in G1; when there is no ex ante

competition in licensing terms, than in G2 for all levels of c: Thus, comparing

the total welfare results of the two systems yields the same qualitative result:

total welfare is greater under G2 except for when c is "high." The break-even c

for total welfare is slightly lower than 0:064 because total welfare incorporates

the fact that R&D ...rms are always better o¤ without the ex ante system.

As one would expect, equivalent graphs of consumer surplus using larger values of N reveal that consumers bene...t from increased downstream competition.

Such graphs also indicate that consumers gain more from the ex ante system

when N is larger: the downstream ...rms pass on a greater share of the reduction

in royalties achieved through the ex ante system. Although, the break-even level

of innovation e¤ort (approximately 0.166 in Figure 2) is independent of N, that

e¤ort level is associated with higher c when N is larger.

It is worth noting that the SSO members would not favor the ex ante system if they knew that innovation costs were "high." However, the actual cost

of innovation e¤ort is probably unknown. Thus it would be appropriate to consider the expected welfare e¤ects of adopting the ex ante system taken over a

distribution of possible innovation costs. Given that the ex ante system has a

very small social cost over a small range of possible realizations of c and much

larger bene...ts over all other (smaller) realizations of c; it seems most plausible

that adopting the ex ante system would have a positive expected welfare e¤ect.

18
5 Conclusion

There has been heated debate over whether SSOs should engage in ex ante discussions of licensing terms before selecting among the alternative technologies.

In addition to many practical and legal arguments, some who oppose the introduction of ex ante licensing competition argue that it would diminish social

welfare by reducing incentives to innovate. However, the welfare e¤ects of reduced innovation should be weighed against the welfare bene...ts of increased

competition among IP owners. To assess the relative magnitudes of the competition e¤ect and innovation e¤ect on social and consumer welfare, this paper

develops a simple three stage model that can be used to analyze both the status quo system (without ex ante licensing competition) and the ex ante system

(with ex ante licensing competition). The model predicts that the ex ante system generally results in lower innovation e¤ort and lower pro...ts for R&D ...rms,

but higher consumer surplus and pro...ts for downstream licensees.

19
6 Appendix

Proof. There are no equilibria where  ̧¡j = 0 and  ̧j > 0 in Stage One of

either G1 or G2 if c < 1

8

N

(N+1)

:

Suppose that Firm ¡j chooses  ̧¡j = 0: Then Firm j

0

s pro...ts in the two

games are equivalent (given by E[o

G1

j

( ̧j j0; N)] and E[o

G2

j

( ̧j j0; N)]) and can

only be positive if

1

4

N

(N + 1)

1

(2 +  ̧j )

> c:

This condition cannot hold for positive  ̧jand c <

1

8

N

(N+1)

:

Corollary 5 If c >

1

8

N

(N+1)

then  ̧¡j =  ̧j = 0 is the only equilibrium in Stage

One of G1 or G2:

6.1 Equilibrium Expected Consumer Surplus

Consumer surplus in Stage Three is given by

1

2

(Æ ¡ P) Q where Æ is the value of

the technology selected by the SSO. Substituting in the Stage Three equilibrium

values of P and Q yields

CS (Æ;r (Æ)) =

1

2

μ

N

N + 1

(Æ ¡ r (Æ))

¶2

:

The expected values of equilibrium consumer surplus can be found by ...rst

replacing oM (Æj ) and o

D (Æj ) in (6) and (8) with CS (Æ;r (Æ)), with the appropriate equilibrium value of r (Æ). This yields the expected consumer surplus

when Firm j

0

s technology is selected by the SSO in G1 and G2; respectively. To

...nd the total expected consumer surplus one must add the expected consumer

surplus when Firm ¡j

0

s technology is selected by the SSO in each game. Substituting the equilibrium innovation e¤orts chosen by both R&D ...rms into the

expected equilibrium consumer surpluses of each game yields

E

h

CS

G1

(Æ; r (Æ))j ̧

G1

;  ̧

G1

i

=

1

8

μ

N

N + 1

¶2

 ̧

G1

3

1 +  ̧

G1

 ́ (15)

and

E

h

CS

G2

(Æ; r (Æ))j ̧

G2

;  ̧

G2

i

=

1

2

μ

N

N + 1

¶2

0

@

3

1 +

3

 ̧

G2

 ́

2

1+ ̧

G2

 ́

2

1+ ̧G2

3

2 +  ̧

G2

 ́

 ̧

G2

3

1 +  ̧

G2

 ́

1

A :

(16)

Because the combined Cournot pro...ts of the downstream ...rms are simply

2

N

times CS (Æ); the equilibrium downstream pro...ts can be found directly from

(15) and (16):

20
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