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\begin{center}
\begin{tabular}{c}
Innovation and \textit{Ex Ante} Consideration of Licensing Terms in Standard
Setting \\ 
by \\ 
Tor Winston* \\ 
EAG 06-3 \ \ March 6, 2006 \\ 
\end{tabular}
\end{center}

\bigskip

\bigskip

EAG Discussion Papers are the primary vehicle used to disseminate research
from economists in the Economic Analysis Group (EAG) of the Antitrust
Division. These papers are intended to inform interested individuals and
institutions of EAG's research program and to stimulate comment and
criticism on economic issues related to antitrust policy and regulation. The
analysis and conclusions expressed herein are solely those of the authors
and do not represent the views of the United States Department of Justice.

Information on the EAG research program and discussion paper series may be
obtained from Russell Pittman, Director of Economic Research, Economic
Analysis Group, Antitrust Division, U.S. Department of Justice, BICN 10-000,
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Recent EAG Discussion Paper titles are listed at the end of this paper. To
obtain a complete list of titles or to request single copies of individual
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\bigskip

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

\newpage

\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 \textit{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 considers licensing terms \textit{ex
ante} as long as the cost of innovation is not "high." The model also
predicts that the welfare benefits of \textit{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.}

\newpage

\setcounter{page}{1}\bigskip \pagebreak

\section{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
firms produce incompatible products until one firm's technology becomes the 
\textit{de facto} standard; 2) collaboration between rival producers who
agree to use the same (or compatible) technology; and 3) government
intervention.\footnote{%
Economic theories of networks and standards have primarily focused on the
competition between firms to become the \textit{de facto} industry standard.
A 1992 Journal of Industrial Economics symposium on network industries \cite%
{gilbert:92-JIE}, \cite{katz/shapiro:85-AER}, and \cite{katz/shapiro:86-JPE}
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 \textit{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 firms must decide between participating in collaboration or
trying to establish their own \textit{de facto} standard. These issues are
discussed by Joseph Farrell and various coauthors in \cite{farrell:96-WP}, 
\cite{farrell/saloner:88-RAND}, and \cite{besen/farrell:94-JEP}. Two
excellent summaries of the literature are \cite{quelin:01-JES} and \cite%
{david/greenstein:90-EINT}. \cite{tassey:00-RP} provides useful general
background on technological standards.}

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 first route. The second route was used to collaboratively
develop interpretability standards for the World Wide Web and Wireless Local
Area Networks (WLAN).\footnote{%
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.} 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 effort
to develop compatibility among Geographic Information Systems (GIS)
software, and the Federal Communications Commission (FCC) has designated a
standard for high definition television (HDTV). See \cite%
{augereauetal:04-NBER}.

To ensure that their products are compatible, and thus more valuable, firms
frequently collaborate in Standard Setting Organizations (SSOs) to choose a
particular technology as the industry standard.\footnote{%
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
certification for medical professionals and product safety standards.{}}
Traditionally, SSOs have been 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 effectively eliminate their ability to
substitute between the available technologies. When the selected technology
is under a patent, the intellectual property (IP) owner effectively 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.\footnote{%
Robert Skitol provides an excellent description of the problem and summary
of related legal literature and filings \cite{skitol:05}. 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 specifically on the
issues of licensing technology implicated by \textit{de jure} standards set
by SSOs. Transcripts and written testimony of the hearings are available at
http://www.ftc.gov/opp/intellect/index.htm. \textit{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 \cite%
{schwartz/gorman:04-LT}.
\par
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 profile lawsuits. See Micron v. Rambus, 189 F.Supp.2d
201(D.Del. 2002); Rambus v. Infineon Technologies, 318 F.3d 1081, Fed. Cir.
2003; and the\ FTC's suit against Union Oil Company of California, \textit{%
In re} Union Oil Company of California, No. 9305, March 2003.}
Dissatisfaction with the \textit{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 insufficient to prevent IP owners from exercising any
market power they gain from having their technology selected by an SSO.%
\footnote{%
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 \cite{shapiro:00-WP}. In another court case, Soundview
Technologies charged that Sony and other members of the Electronic
Industries Alliance (EIA) violated antitrust laws by collectively fixing
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.}

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 configure 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 
\textit{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 \textit{ex ante} system, the SSO
would first request licensing terms from both patent owners and then select
the best combination of technology and licensing terms. Thus, if the terms
offered for technology $Y$ were sufficiently superior, the SSO would select
technology $Y$ as the standard.

This process would allow SSO members to benefit from increased competition
between substitute technologies before they commit to one technology.
Without such \textit{ex ante} competition, the SSO members suffer from a
holdup problem similar to that examined in \cite{williamson:89-HBIO} and 
\cite{grossman/hart:86-JPE}: after SSO members have made asset-specific
investments (specific to a patented technology) in developing and
implementing a particular standard, the patent owner is able to extract
rents from those investments.\footnote{%
Carl Shapiro provided a definition of "holdup" in this context in \cite%
{DOJ/FTC:02-DOJFTC2} pp. 15-16. An amicus brief filed by Joseph Farrell and
other leading academics in the Federal Trade Commission's Rambus proceeding
also describes holdup in the context of standard setting \cite{farrell:04}.}

Despite the potential advantages of \textit{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.\footnote{%
For example, IEEE policies state that "[t]he validity, terms, or cost of
specific patent use" should be avoided during standard setting meetings.
However, the SSO rules do not explicitly prohibit bilateral \textit{ex ante}
negotiations between an IP owner and a potential licensee. Even so, to the
extent that such bilateral negotiations are effective they also dampen
incentives to innovate.} At the 2002 Federal Trade Commission / Department
of Justice hearings on IP and antitrust, representatives from large firms
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
significant problem.\footnote{%
For example, Scott Peterson of Hewlett-Packard spoke out in favor of
allowing \textit{ex ante} licensing discussions. Carl Cargill of Sun
Microsystems explained that RAND licensing terms are not sufficiently well
defined. See \cite{DOJ/FTC:02-DOJFTC1} on pp.246-251 and pp. 109-111. They
were opposed by Earle Thompson of Texas Instruments and Richard Holleman of
the IEEE.}

Opponents of \textit{ex ante} competition have argued that such licensing
discussions are likely to extend into areas that would be \textit{per se}
violations of antitrust laws, such as agreements on product prices.\footnote{%
See the testimony of Earle Thompson, Intellectual Asset Manager and Senior
Counsel of Texas Instruments and attorney Paul Vishny in \cite%
{DOJ/FTC:02-DOJFTC2} pp.32-33 and p.44 respectively.} Further, opponents
contend that \textit{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 \textit{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 artificial market
power through joint\textit{\ ex ante} consideration of licensing terms.
Citing the possible efficiency justifications, proponents have sought
guidance from the antitrust agencies on the issue.\footnote{\cite%
{lemely:02-CALR} provides an excellent in-depth review of current legal
issues surrounding SSOs and IP rights. \cite{lemely:02-CALR}, \cite%
{curran:03-CHG}, and \cite{gifford:03-IDEA} all make the case that \textit{%
ex ante} licensing discussions have potential efficiency justifications and
thus should be subject to a rule of reason analysis. Scott Peterson, of
Hewlett-Packard, and Robert Skitol call for Agency guidance in \cite%
{peterson:02} and \cite{skitol:05}.} Federal Trade Commission Chairman
Deborah Majoras has agreed that, "joint ex ante royalty discussions that are
reasonably necessary to avoid hold up do not warrant per se condemnation." 
\cite{majoras:05} This echoes the view expressed in June 2005 by outgoing
Assistant Attorney General for Antitrust R. Hewitt Pate.\cite{pate:05} The
European Commission has also indicated that it will study the issue.\cite%
{ec:05}

Aside from the practical and legal issues surrounding \textit{ex ante}
discussions, there is a concern that adopting the \textit{ex ante} system
may harm welfare by dampening innovation incentives. If SSO members extract
more favorable terms from IP owners by engaging in \textit{ex ante}
licensing discussions, then firms will likely invest less in researching and
developing technologies that could form the basis of new standards.\footnote{%
See \cite{hollerman:02}. Joseph Farrell also comments on the issue in \cite%
{DOJ/FTC:02-DOJFTC2} pp. 47-48.
\par
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.} To analyze the effects of
adopting the \textit{ex ante }system one must assess both the social
benefits of lower royalties and the social costs of diminished innovation
incentives.\footnote{%
The tradeoff considered here is similar to the tradeoff implicit in granting
patent protections. \ Market power is the currency with which society
purchases innovation effort.} This paper develops a model of R\&D investment
and standard setting to analyze the effects of adopting the\textit{\ 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 \textit{ex ante} system
benefits 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 firms) are harmed by the
competition introduced by the \textit{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 profits, producer profits, and consumer surplus
of the three-stage model for two separate games: one without \textit{ex ante}
licensing competition, and one with \textit{ex ante} licensing competition.
Section 4 compares the welfare outcomes of the two games and Section 5
concludes.

\subsection{ 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 \cite{arrow:62-NBER}. In Arrow's three-stage
model, a single IP owner sets royalties for its cost-reducing innovation,
then producers choose whether or not to purchase a license, and finally
producers compete downstream.\footnote{%
The model predicts that an owner of a cost-reducing innovation who charges a
per-unit royalty can earn higher profits when the downstream market is
competitive than when it is monopolistic.} In the 1980s, a series of papers
began to apply variations of Arrow's basic three-stage 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 offer? Should licensors
auction off a limited number of licenses?\footnote{\cite{katz/shapiro:86-JPE}
does not explicitly model the downstream competition among licensees.} In
his \textit{Handbook of Game Theory }chapter \cite{kamien:handbook}, 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 \cite{kamien/oren/tauman:92-JME}, \cite%
{kamien/tauman:86_QJE}, and \cite{kamien/tauman:01-MS}.\ Also see \cite%
{quelin:01-JES} for a summary of the literature on technology standards in
network industries, including \cite{katz/shapiro:86-QJE} and \cite%
{wang:98-ELetters}. Some of the extensions developed incorporate an initial
stage in which the licensor must first invest in R\&D in order to develop
the cost-reducing technology.\footnote{%
A new generation of licensing models, pioneered by \cite{segal:99-QJE},
focuses on bilateral licensing contracts in an environment where licensees
(and even the licensor) compete in the downstream market.}

This paper makes several modifications to the basic model established in the
literature to address the new question of which standard setting system
yields the highest profits, 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 \textit{status quo} system of
standard setting where industry standards are chosen without open
competition over licensing terms, while the other allows for \textit{ex ante}
competition in licensing terms before the standard is chosen. The two models
have the same three stages. First, research and development firms (R\&D\
firms) 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 effort, profits, and welfare associated
with each of the two games are compared.

The current model differs 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 firms to behave
strategically when investing in R\&D and setting their royalty rates,
somewhat like firms engaged in a patent race.\footnote{%
Much of the literature on investment incentives and innovation considers
patent races (See \cite{tiroleIO:95} pp. 394-399), where the first firm to
develop the technology (and patent it) gets a monopoly payoff. The current
model has a similar "winner-take-all" element which is common in models of
patent races. In both the \textit{status quo} model and the \textit{ex ante}
model, the firm that produces the greatest innovation becomes the monopoly
provider of licenses in equilibrium. However, unlike the patent race models,
innovation occurs simultaneously so neither firm innovates first.} Second,
in the existing literature downstream firms 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 firm 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
flexible 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.\footnote{%
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.} 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.

\section{A Model of R\&D Investment and Collaborative Standard Setting}

The model proceeds in three stages. In the first stage, two R\&D firms
simultaneously invest effort in developing new technologies. The results of
the R\&D effort are not deterministic. Instead, each of the two firms
realizes an unidimensional innovation that is a random draw from a
distribution determined by the firm's innovation efforts. A firm that
invests more draws its innovation from a distribution that first order
stochastically dominates the distribution of a firm that invests less. In
the second stage, the R\&D firms 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 firms are
not SSO members. 3) Individual SSO members are not able to negotiate
licensing terms bilaterally with the R\&D firms 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; specifically, neither R\&D firm is in a position to
promote its technology as a \textit{de facto} standard outside the structure
of the SSO. 7) There is no uncertainty regarding whether the R\&D firms'
patents cover the technologies in question.\footnote{%
Similar assumptions were made in \cite{bessen:02}.}

The first 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 first 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.

\section{Solving for the SPNE Both With and Without \textit{Ex Ante}
Licensing Competition}

Two different standard setting systems are modeled using the same first and
last stages; the systems differ only in the structure of the second stage of
the model. Under the \textit{status quo} "\textit{ex post} licensing" game ($%
G1),$ the SSO members simply choose the best technology (the largest
innovation drawn by the two R\&D firms) and then the winning R\&D firm sets
a revenue-maximizing royalty. Under the proposed "\textit{ex ante}
licensing" game ($G2),$ the two R\&D firms commit to specific royalties
before the SSO members choose one technology as the industry standard. The
different methods of selecting a standard induce different equilibrium
levels of investment, returns on R\&D, profits for the SSO members, and
consumer surpluses. Thus, the equilibrium outcomes of the two parallel games
can be compared to evaluate whether the welfare benefits of the additional
competition under the \textit{ex ante }system exceed the harm of reduced
innovation. The SPNE equilibria can be found through backward induction,
starting with the third stage.

\subsection{Stage Three: Downstream Cournot Competition}

As is common in models of optimal licensing, consumer demand is given by the
simple inverse demand function%
\begin{equation}
P=\alpha -Q,  \label{D}
\end{equation}%
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 have to have at least one thing in common: they must adhere to
the industry standard. The parameter $\alpha $ 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 $\left( \ref{D}\right) $ suggests that different customers value the
basic product differently, but that they all value improvements in the
product equally.

When $N\geq 2$ producers compete in the downstream market their combined
Cournot equilibrium profits are 
\begin{equation}
\pi ^{C}\left( \alpha ,r\right) =\frac{N}{(N+1)^{2}}\left( \alpha -r\right)
^{2},  \label{C ds profits}
\end{equation}%
where $r$ is the positive per-unit royalty.\footnote{%
This is the same downstream market structure that Kamien employs in his 1992
summary of the literature \cite{kamien:handbook}. 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.}
The R\&D firm receives $r$ for each of the $Q$ units sold by the downstream
Cournot competitors (SSO members) and its equilibrium revenues are%
\begin{equation}
\pi \left( \alpha ,r\right) =\frac{N}{(N+1)}\left( \alpha -r\right) r.
\label{C licensing R}
\end{equation}%
In Stage Two, the R\&D firms choose $r$ to maximize $\left( \ref{C licensing
R}\right) ,$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.

\subsection{Stage Two: \textit{G}1}

In the \textit{status quo} game $\left( G1\right) $ the SSO selects the best
technology (the highest of the two realizations of $\alpha )$ and the
winning R\&D firm sets its royalty to maximize $\left( \ref{C licensing R}%
\right) $. Let $H$ denote the winning firm and $r^{M}$ denote its monopoly
royalty choice. Setting the derivative of $\left( \ref{C licensing R}\right) 
$ with respect to $r$ equal to zero yields the revenue maximizing per-unit
royalty $r^{M}=\frac{\alpha _{H}}{2}$ and corresponding licensing revenues $%
\pi ^{M}\left( \alpha _{j}\right) =\frac{N}{(N+1)}\left( \frac{\alpha _{H}}{2%
}\right) ^{2}.$

\subsection{Stage Two: \textit{G}2}

Stage Two in the \textit{ex ante} game $\left( G2\right) $ is divided into
two sub-parts. First the R\&D firms 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 firms' optimal royalties.

\subsubsection{Technology Choice}

When considering licensing terms \textit{ex ante}, the SSO chooses the best
combination of technology $\left( \alpha \right) $ and per-unit royalty $%
\left( r\right) .$ To do so, the SSO members compare the total expected
profits of the $N$ licensees, given the two $\left( \alpha ,r\right) $
combinations offered by the R\&D firms.\footnote{%
Because members of the SSO are homogeneous, this decision rule could be
defined in terms of aggregate or individual downstream profits.} By
inspection of $\left( \ref{C ds profits}\right) $, it is clear that
downstream industry profits are higher when the SSO selects the R\&D firm
that offers the higher value of $\left( \alpha -r\right) .$\footnote{%
Letting $L$ denote the firm with the lower innovation value, the SSO
maximizes industry profits by choosing Firm $H$ if $\left( \alpha
_{H}-r_{H}\right) <\left( \alpha _{L}-r_{L}\right) .$}

\subsubsection{Royalty Choice}

In Stage Two of $G2$ the two R\&D firms compete in a Bertrand setting, each
lowering its royalty to undercut the other's $\left( \alpha -r\right) $
value. Let $L$ denote the firm with the lower innovation value. The ability
of Firm $H$ to extract profits is limited by the willingness of Firm $L$ to
price at marginal cost, a royalty of zero.\footnote{%
It is assumed that the costs of abandoning the chosen standard are
sufficiently high that they do not constrain the winning R\&D firm's royalty
choice.} Let the superscript $D$ indicate the duopoly royalty and profits.
However, when the difference between $\alpha _{H}$ and $\alpha _{L}$ is
sufficiently large, the SSO will choose Firm $H^{\prime }s$ innovation even
if Firm $H$ charges the monopoly royalty. That is, Firm $H$ is effectively a
monopolist because Firm $L$ would have to offer a negative royalty to
compete with it superior technology.

\begin{proposition}
In equilibrium, the R\&D firm with the lesser innovation offers its license
for free (equal to marginal cost). The R\&D firm with the superior
innovation charges $r^{D}=\alpha _{H}-\alpha _{L}$ if $\alpha _{L}>\frac{%
\alpha _{H}}{2}$ and charges $r^{M}=\frac{\alpha _{H}}{2}$ if $\alpha
_{L}\leq \frac{\alpha _{H}}{2}.$ The SSO chooses Firm $H^{\prime }s$
technology as the standard.
\end{proposition}

\begin{proof}
When Firm $H$ sets a royalty rate of $r_{H}=\alpha _{H}-\alpha _{L}$ and
Firm $L$ sets a rate of $0,$ then neither firm can profitably deviate if $%
\alpha _{L}>\frac{\alpha _{H}}{2}.$ Firm $L$ will earn zero profits at any
positive royalty because it will not be selected by the SSO and could only
earn negative profits from setting a negative royalty. Firm $H$ can increase
its royalty (and thus profits) up to $\alpha _{H}-\alpha _{L}$ and its
technology will still be selected by the SSO. If Firm $H$ sets a royalty
greater than$\ a_{H}-\alpha _{L}$ the SSO will choose Firm $L^{\prime }s$
technology and Firm $H$ will earn zero royalties.

However, if $\alpha _{L}\leq \frac{\alpha _{H}}{2},$ then $a_{H}-\alpha _{L}$
would exceed the monopoly royalty rate $\frac{\alpha _{H}}{2}.$ Thus Firm $H$
would maximize profits by setting its royalty to $\frac{\alpha _{H}}{2}.$
Firm $L$ could not profitably deviate for the same reasons described above.
\end{proof}

\bigskip Substituting $r^{D}$ into $\left( \ref{C licensing R}\right) $
yields Firm $H^{\prime }s$ Stage Two equilibrium licensing revenues%
\begin{equation}
\pi ^{D}\left( \alpha _{H}\right) =\frac{N}{(N+1)}\alpha _{L}\left( \alpha
_{H}-\alpha _{L}\right) \ \text{if}\ \alpha _{H}<\frac{\alpha _{L}}{2}.
\label{Duopoly Profits}
\end{equation}%
Firm $L^{\prime }s$ equilibrium licensing revenues are zero because it is
not selected by the SSO. The R\&D firms consider the Stage Two profits of $%
G1 $ and $G2$ when deciding how much effort to invest in innovation effort
in Stage One.

\subsection{Stage One: Expected Profits}

The first stages of $G1$ and $G2$ are essentially the same; the
forward-looking R\&D firms make their innovation investment decisions in
Stage One based on the equilibrium royalty revenues they expect to earn in
the subsequent stages.\footnote{%
The R\&D firms are assumed to be risk neutral.} This decision depends on the
relationship between the cost of innovation effort and the corresponding
expected licensing revenues. In equilibrium, each R\&D firm chooses an
innovation effort that is a best response to the other's choice. Because the
R\&D firms' expected profits depend on the cost of the innovation effort
they expend, it is necessary to establish the innovation process before
fully characterizing profits.

\subsubsection{The Innovation Process}

The development of new technologies is an inherently uncertain process.
Large innovations may result from only a small amount of effort just as
large amounts of effort may yield only small innovations. However, in
general, a firm that expends more effort can expect to produce a larger
innovation. To reflect the uncertainty of the process, a firm's innovation, $%
\alpha ,$ is modeled as a random draw. Let $j$ denote an R\&D firm.\footnote{%
The $j$ and $-j$ subscripts replace the $H$ and $L$ subscripts because the
firms' actual innovations are not realized until the end of Stage One.} Firm 
$j^{\prime }s$ innovation, $\alpha _{j},$ is drawn from 
\begin{equation}
f\left( \alpha _{j}|\lambda _{j}\right) =\lambda _{j}\left( \alpha
_{j}\right) ^{\lambda _{j}-1},  \label{C pdf}
\end{equation}%
a family of probability density functions defined over the support $\alpha
_{j}\in \left[ 0,1\right] .$ The different distributions in the family are
distinguished by Firm $j^{\prime }s$ innovation effort, $\lambda _{j}.$ It
is useful to note that $E\left[ \alpha _{j}|\lambda _{j}\right] =$ $\frac{%
\lambda _{j}}{1+\lambda _{j}}.$ Thus, the expected marginal product of
innovation effort $\lambda _{j}$ is positive and decreasing.\footnote{%
It is easy to extend the model to account for differing levels of
productivity of innovation effort. If innovations are drawn from $f\left(
\alpha _{j}|\lambda _{j}\right) =\rho \lambda _{j}\left( \alpha _{j}\right)
^{\rho \lambda _{j}-1},$ then marginal changes in $\lambda _{j}$ have a
greater effect of moving probability from the lower end of the distribution
to the higher end of the distribution when $\rho $ is higher.} Finally, let
the cost of innovation effort be specified as a linear function of effort, $%
C\left( \lambda _{j}\right) =c\lambda _{j}.$\footnote{%
This linear specification indicates that the R\&D firms have no monopsony
power in the market for innovation effort (hiring engineers) and that there
are no lumpy or sunk costs associated with innovation effort.}

\subsubsection{Expected Profits}

R\&D firms choose their innovation efforts in Stage One to maximize their
expected profits from royalties earned in subsequent stages. These expected
royalties depend on three factors: whether the firm 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 firm's innovation compared to the other R\&D
firm's innovation. These factors are captured in the following expected
profit functions that integrate royalties over the two R\&D firms'
distributions of $\alpha .$

\paragraph{Expected Profits: \textit{G}1}

In the equilibrium of $G1$ Firm $j$ earns the monopoly royalty, $\pi
^{M}\left( \alpha _{j}\right) ,$ conditional on the fact that it draws a
higher innovation value than its rival. Thus the expected profit for Firm $j$
is 
\begin{equation}
E[\pi _{j}^{G1}\left( \lambda _{j}|\lambda _{-j}\right) ]=\int_{0}^{1}\left(
\int_{0}^{\alpha _{j}}\pi ^{M}\left( \alpha _{j}\right) f\left( \alpha
_{-j}|\lambda _{-j}\right) d\alpha _{-j}\right) \text{ }f\left( \alpha
_{j}|\lambda _{j}\right) d\alpha _{j}-C\left( \lambda _{j}\right) ,\text{ }
\label{ExPrG1}
\end{equation}%
where the subscript $-j$ denotes the other R\&D firm. The inner term of the
double integral integrates the monopoly royalty revenues of Firm $j$ (with
innovation $\alpha _{j})$ over the truncated distribution of $\alpha
_{-j}\in \left( 0,\alpha _{j}\right) .$ In this range, Firm $j^{\prime }s$
technology would be selected by the SSO in equilibrium and Firm $j$ would
earn royalties. The outer term integrates over the entire distribution of $%
\alpha _{j}.$ Substituting the functional forms of $f\left( \alpha
_{j}|\lambda _{j}\right) ,$ $\pi ^{M}\left( \alpha _{j}\right) ,$ and $%
C\left( \lambda _{j}\right) $ into $\left( \ref{ExPrG1}\right) $ and solving
the integral yields%
\begin{equation}
E[\pi _{j}^{G1}\left( \lambda _{j}|\lambda _{-j},N\right) ]=\frac{1}{4}\frac{%
N}{\left( N+1\right) }\frac{{{\lambda }_{j}}}{\left( 2+{{\lambda }_{j}}+{{%
\lambda }_{-j}}\right) }-c\lambda _{j}.  \label{CExPrG1}
\end{equation}%
Before turning to the equilibrium innovation efforts in $G1$ consider the
expected profits in $G2.$

\paragraph{Expected Profits: \textit{G}2}

The expected profit function for $G2$ is more complex because the R\&D firm
with the higher innovation will set the monopoly royalty if its innovation
is sufficiently superior and the duopoly royalty if it is not. Thus in $%
\left( \ref{ExPrG2}\right) $ the inner term of the double integral is split
into two terms. The first is similar to the inner term in $\left( \ref%
{ExPrG1}\right) $. However, $\left( \ref{ExPrG2}\right) $ only integrates
the \textit{monopoly} royalty revenues over the range $\alpha _{-j}\in
\left( 0,\frac{\alpha _{j}}{2}\right) ,$ the outcomes when Firm $j$ would
price as a monopolist due to the superiority of its innovation. The second
integrates the \textit{duopoly} royalty revenues over the truncated
distribution of $\alpha _{-j}\in $ $\left( \frac{\alpha _{j}}{2},\alpha
_{j}\right) ,$ the outcomes when Firm $j^{\prime }s$ technology would still
be selected by the SSO but the firm would be constrained to price as a
duopolist. Again, the outer term integrates over the entire distribution of $%
\alpha _{j}.$ Thus Firm $j^{\prime }s$ equilibrium profits are 
\begin{equation}
E[\pi _{j}^{G2}\left( \lambda _{j}|\lambda _{-j}\right) ]=\int_{0}^{1}\left( 
\begin{array}{c}
\int_{0}^{\frac{\alpha _{j}}{2}}\text{ }\pi ^{M}\left( \alpha _{j}\right)
f\left( \alpha _{-j}|\lambda _{-j}\right) d\alpha _{-j}+ \\ 
\int_{\frac{\alpha _{j}}{2}}^{\alpha _{j}}\text{ }\pi ^{D}\left( \alpha
_{j},\alpha _{-j}\right) f\left( \alpha _{-j}|\lambda _{-j}\right) d\alpha
_{-j}%
\end{array}%
\right) \text{ }f_{j}\left( \alpha _{j}|\lambda _{j}\right) d\alpha
_{j}-C\left( \lambda _{j}\right) .  \label{ExPrG2}
\end{equation}%
Substituting the functional forms of $f\left( \alpha _{j}|\lambda
_{j}\right) ,$ $\pi ^{M}\left( \alpha _{j}\right) ,$ $\pi ^{D}\left( \alpha
_{j},\alpha _{-j}\right) ,$ and $C\left( \lambda _{j}\right) $ into $\left( %
\ref{ExPrG2}\right) $ and solving the integral yields%
\begin{equation}
E[\pi _{j}^{G2}\left( \lambda _{j}|\lambda _{-j},N\right) ]=\frac{N}{\left(
N+1\right) }\frac{{{\lambda }_{j}}\left( 1+2^{1+{{\lambda }_{-j}}}{{\lambda }%
_{-j}}\right) }{2^{1+{{\lambda }_{-j}}}\left( 1+{{\lambda }_{-j}}\right)
\left( 2+{{\lambda }_{-j}}\right) \left( 2+{{\lambda }_{j}}+{{\lambda }_{-j}}%
\right) }-c\lambda _{j}.  \label{CExPrG2}
\end{equation}

\subsection{Equilibrium Innovation Efforts}

The expected profit functions $\left( \ref{CExPrG1}\right) $ and $\left( \ref%
{CExPrG2}\right) $ imply that each game ($G1$ and $G2$) has a unique
symmetric SPNE level of innovation effort in Stage One. This result is
established by setting the first order conditions (FOCs) of the expected
profit functions (taken with respect to ${{\lambda }_{j}}$) equal to zero
and then solving the resulting system of two equations and two unknowns.%
\footnote{%
Only interior profit maximization solutions are considered here. The
Appendix provides a proof that corner solutions to the profit maximization
problem can not be Nash equilibria in either $G1$ or $G2$ if $\frac{1}{8}%
\frac{N\,}{\left( N+1\right) }<c$ and neither firm will invest in innovation
if $\frac{1}{8}\frac{N\,}{\left( N+1\right) }\geq c.$}

\begin{proposition}
\bigskip The unique symmetric SPNE of $G1$ is given by%
\begin{equation}
\frac{N}{\left( N+1\right) }\frac{\left( 2+{{\lambda }^{G1}}\right) }{16{%
\left( 1+{{\lambda }^{G1}}\right) }^{2}}=c.  \label{Eq G1}
\end{equation}
\end{proposition}

\begin{proof}
\bigskip In $G1,$ Firm $j$ maximizes its expected profits by choosing ${{%
\lambda }_{j}^{\ast }}$ to satisfy%
\begin{equation}
\frac{N}{\left( N+1\right) }\frac{\left( 2+{{\lambda }_{-j}}\right) }{4{%
\left( 2+{{\lambda }_{j}^{\ast }}+{{\lambda }_{-j}}\right) }^{2}}=c.
\label{G1 FOC}
\end{equation}%
In equilibrium both firms' FOCs must be satisfied and thus, by inspection of 
$\left( \ref{G1 FOC}\right) $, ${{\lambda }_{j}^{\ast }}$ must equal ${{%
\lambda }_{-j}^{\ast }}.$ Denote this symmetric equilibrium effort as ${{%
\lambda }^{G1}.}$ Substituting ${{\lambda }^{G1}}$ for both ${{\lambda }%
_{j}^{\ast }}$ and ${{\lambda }_{-j}^{\ast }}$ in $\left( \ref{G1 FOC}%
\right) $ yields $\left( \ref{Eq G1}\right) $.
\end{proof}

\begin{proposition}
\bigskip The unique symmetric SPNE of $G2$ is given by%
\begin{equation}
\frac{N}{\left( N+1\right) }\frac{\left( 1+2^{1+{{\lambda }^{G2}}}{{\lambda }%
^{G2}}\right) }{2^{3+{{\lambda }^{G2}}}{\left( 1+{{\lambda }^{G2}}\right) }%
^{3}}=c.  \label{Eq G2}
\end{equation}
\end{proposition}

\begin{proof}
\bigskip In $G2,$ Firm $j$ chooses ${{\lambda }_{j}^{\ast }}$ to satisfy%
\begin{equation}
\frac{N}{\left( N+1\right) }\frac{\left( 1+2^{1+{{\lambda }_{-j}}}{{\lambda }%
_{-j}}\right) }{2^{1+{\lambda }_{-j}}\left( 1+{{\lambda }_{-j}}\right) {%
\left( 2+{{\lambda }_{j}^{\ast }}+{{\lambda }_{-j}}\right) }^{2}}=c.
\label{G2 FOC}
\end{equation}%
Both firms' FOCs are satisfied when ${{\lambda }_{j}^{\ast }}={{\lambda }%
_{-j}^{\ast }}.$\footnote{%
If both firm's FOCs hold then $\frac{\,\left( 1+2^{1+{{\lambda }_{-j}^{\ast }%
}}\,{{\lambda }_{-j}^{\ast }}\right) }{\,2^{{{\lambda }_{-j}^{\ast }}}\left(
1+{{\lambda }_{-j}^{\ast }}\right) }=\frac{\,\left( 1+2^{1+{{\lambda }%
_{j}^{\ast }}}\,{{\lambda }_{j}^{\ast }}\right) }{2^{{{\lambda }_{j}^{\ast }}%
}\,\left( 1+{{\lambda }_{j}^{\ast }}\right) }.$ Because $\frac{\,\left(
1+2^{1+{{\lambda }_{j}^{\ast }}}\,{{\lambda }_{j}^{\ast }}\right) }{2^{{{%
\lambda }_{j}^{\ast }}}\,\left( 1+{{\lambda }_{j}^{\ast }}\right) }$ is
monotonically decreasing in ${{\lambda }_{j}^{\ast }}$, no two values of ${{%
\lambda }_{j}^{\ast }}$ yield the same value of $\frac{\,\left( 1+2^{1+{{%
\lambda }_{j}^{\ast }}}\,{{\lambda }_{j}^{\ast }}\right) }{2^{{{\lambda }%
_{j}^{\ast }}}\,\left( 1+{{\lambda }_{j}^{\ast }}\right) }.$ Thus ${{\lambda 
}_{-j}^{\ast }}={{\lambda }_{j}^{\ast }}$ is the SPNE of $G2.$} This
symmetric equilibrium must be unique. Because $\frac{\left( 1+2^{1+{{\lambda 
}_{j}^{\ast }}}{{\lambda }_{j}^{\ast }}\right) }{2^{{{\lambda }_{j}^{\ast }}%
}\left( 1+{{\lambda }_{j}^{\ast }}\right) }$ is monotonically decreasing in $%
{{\lambda }_{j}^{\ast }}$ (for ${{\lambda }_{j}^{\ast }>0}$) there can be
only one value of ${{\lambda }_{j}^{\ast }}$ corresponding to any given ${{%
\lambda }_{-j}^{\ast }}.$ Substituting the symmetric equilibrium effort, ${{%
\lambda }^{G2},}$ for both ${{\lambda }_{j}^{\ast }}$ and ${{\lambda }%
_{-j}^{\ast }}$ in $\left( \ref{G2 FOC}\right) $ yields $\left( \ref{Eq G2}%
\right) $.
\end{proof}

As predicted, the equilibrium level of effort is lower under the \textit{ex
ante} licensing system.

\begin{proposition}
The equilibrium innovation effort in $G1$ exceeds the equilibrium innovation
effort in $G2,$ or ${{\lambda }^{G1}}>{{\lambda }^{G2}.}$
\end{proposition}

\begin{proof}
The value of the left-hand sides of $\left( \ref{Eq G1}\right) $ and $\left( %
\ref{Eq G2}\right) $ are monotonically decreasing functions of ${{\lambda }%
^{G1}}$ and ${{\lambda }^{G2}}$ respectively. Thus, if the left-hand side of 
$\left( \ref{Eq G1}\right) $ exceeds the left-hand side of $\left( \ref{Eq
G2}\right) $ when ${{\lambda }^{G1}}={{\lambda }^{G2},}$ then when the
left-hand sides of $\left( \ref{Eq G1}\right) $ and $\left( \ref{Eq G2}%
\right) $ are both set to $c,$ it must be true that ${{\lambda }^{G1}}>{{%
\lambda }^{G2}.}$ Following a proof by contradiction, suppose that $\left( %
\ref{Eq G1}\right) $ evaluated at ${\lambda }$ is smaller than $\left( \ref%
{Eq G2}\right) $ evaluated at ${\lambda .}$ This implies that%
\begin{equation}
\left( 2-{\lambda }+{\lambda }^{2}\right) <2^{1-{\lambda }},
\label{Condition 1}
\end{equation}%
which does not hold for ${\lambda >0.}$ For ${{\lambda }^{G1}}={{\lambda }%
^{G2}>0}$ the left-hand side of $\left( \ref{Eq G1}\right) $ must exceed the
left-hand side $\left( \ref{Eq G2}\right) .$ Thus ${{\lambda }^{G1}}$ must
exceed ${{\lambda }^{G2}}${\ when }$\left( \ref{Eq G1}\right) $ and $\left( %
\ref{Eq G2}\right) $ hold.
\end{proof}

\section{The Effect of the \textit{Ex Ante} System on Equilibrium Surpluses
and Welfare}

The equilibrium innovation efforts in each game determine the expected
surpluses of the R\&D firms, the downstream firms, and consumers. (The
formulas for the producer and consumer surpluses are constructed in the same
manner as the expected R\&D firm profit functions described above and are
given in the Appendix.) After solving for the equilibrium innovation efforts
and finding the corresponding surpluses, it is possible to evaluate the
model's predictions regarding the effects of adopting the \textit{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 \textit{ex ante} system would decrease
the profits of the R\&D firms because it introduces an additional element of
competition. Further, one would generally expect that consumers and
downstream firms would benefit from the additional competition among R\&D
firms.\footnote{%
It is theoretically possible that additional competition among R\&D firms
would induce them to invest even more in innovation.} The equilibrium
outcomes of the two games are generally consistent with these expectations.
The model predicts that both consumers and downstream firms are better off
with the \textit{ex ante} system unless the costs of innovation are "high"
and that R\&D firms are always worse off with the \textit{ex ante} system.
The model also predicts that the benefits of the \textit{ex ante} system to
consumers and downstream firms (and the harm to R\&D firms) are inversely
related to the cost of innovation effort.

Ideally, one could analytically solve for the equilibrium innovation efforts
in each game (as functions of $N$ and $c$) and then use those findings to
solve for the surpluses enjoyed by consumers, downstream producers and R\&D
firms. However, such a straightforward analytical approach is not possible
in this case because general analytic solutions for the equilibrium
innovation effort in $G2$ do not exist. (Analytic solutions exist for
particular combinations of the parameters. For example, when $N=2$ and $c=%
\frac{5}{192}$ then $\left( \ref{Eq G2}\right) $ holds for ${{\lambda }%
^{G2}=1.)}$

However, if one fixes the value of $N$ it is possible to perform comparative
statics on the welfare effects of adopting the \textit{ex ante} system for
different values of$\;c$ by expressing each of the surpluses in $G1$ as a
function of ${{\lambda }^{G2}}.$ This can be done by first inverting $\left( %
\ref{Eq G1}\right) $ to solve the $G1$ equilibrium condition for ${{\lambda }%
^{G1}}$ as a function of $c$ and then replacing $c$ with the left hand side
of $\left( \ref{Eq G2}\right) ,$ the $G2$ equilibrium condition.\footnote{%
Solving $\left( \ref{Eq G1}\right) $ for $\lambda ^{G1}$ yields 
\begin{equation*}
\lambda ^{G1}=\frac{-(2\theta -1)+\sqrt{(2\theta -1)^{2}-8\theta }}{2\theta }%
,
\end{equation*}%
where $\theta =16\frac{N}{N+1}c.$} The result gives ${{\lambda }^{G1}}$ as
function of ${{\lambda }^{G2}.}$ Finally, this ${{\lambda }^{G1}}\left( {{%
\lambda }^{G2}}\right) $ 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 first panel of Figure 1, the horizontal
axis measures equilibrium innovation effort and the vertical axis measures
the cost of innovation effort. The curves labeled $G1$ and $G2$ plot the
costs of innovation that are associated with each equilibrium level of
innovation effort, as given by the equilibrium equations $\left( \ref{Eq G1}%
\right) $ and $\left( \ref{Eq G2}\right) $.

%Figure 1:  Consumer Surplus and Costs in G1 and G2
%This figure depicts two stacked graphs.  The horizontal axis in each graph
%is identical, and shows innovation effort in G2, ranging from 0 to 1.5.  
%In the top graph, innovation cost is denoted on the vertical axis, and 
%two convex to the origin parabolas follow similar tracks from an innovation 
%cost of about 0.08 near the origin to about 0.02 and the end of the graph.
%The top parabola is labeled G1, and intersects a horizontal line at a cost
%of 0.026 and an innovation effort in of about 1.3.  
%This point is labeled B.  The bottom parabola is labeled G2, and 
%intersects the same cost level an innovation value of 1.  
%This point is labeled A.  
%
%The bottom graph in the figure again shows innovation effort in G2
% on the horizontal axis and Consumer surplus on the vertical axis.  
%Two curves starting at the origin and proceeding up and to the right show
% consumer surplus increasing with innovation effort.  The top curve 
%is labeled G2 and the bottom curve is labeled G1.  In the bottom graph, 
%a vertical line at the value of 1 shows the same innovation level in G2 
%as in the top graph, and relates that to a value of consumer surplus of 
%about 0.5.  This point is labeled A.  The value of innovation at 1.3 
%is also identified, and shows consumer surplus in G1 is approximately 0.03.  This point is labeled B on the G1 curve.

\bigskip

For example, the intersection labeled $A$ indicates that when ${{\lambda }%
^{G2}=}1$ 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 $%
\left( \ref{Eq G1}\right) $ can be inverted to express ${{\lambda }^{G1}}$
and a function of $c$, one can find the ${{\lambda }^{G1}}$ associated with
the cost given by intersection $A$. The intersection labeled $B$ gives this
point as ${{\lambda }^{G1}}\approx 1.3.$ In the second panel of Figure 1,
the curves labeled $G1$ and $G2$ plot the consumer surplus associated with
the equilibrium level of effort in each of the two games, as given by $%
\left( \ref{ECSG1}\right) $ and $\left( \ref{ECSG2}\right) $ in the
Appendix. By comparing the heights of the intersections labeled $%
A^{\shortmid }$ and $B^{\shortmid },$ which give the consumer surpluses
associated with ${{\lambda }^{G2}=}1$ and ${{\lambda }^{G1}}\approx 1.3,$
which are in turn associated with $c=0.026$, it is clear that consumer
surplus is greater under the \textit{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 efforts.
Because $\lambda ^{G2}$ depends on the cost of innovation effort one can use
this figure to compare consumer 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.\footnote{%
As discussed in the Appendix, if $c\geq \frac{1}{8}\frac{N}{N+1}$ then
neither R\&D firm invests in innovation effort in either game's equilibrium,
and thus consumer surplus is zero in both games.}

The line labeled $G2$ in Figure 2 simply plots the equilibrium consumer
surplus (equation $\left( \ref{ECSG2}\right) $ in the Appendix) for each
equilibrium level of innovation effort, $\lambda ^{G2}$. The line labeled
"Cost" relates each level of $c$ to the resulting effort in $G2{.}$
Exploiting the equilibrium conditions $\left( \ref{Eq G1}\right) $ and $%
\left( \ref{Eq G2}\right) $ as described above to find ${{\lambda }^{G1}}%
\left( {{\lambda }^{G2}}\right) $, the line labeled $G1$\ plots the
equilibrium consumer surplus in $G1$ \underline{for each $\lambda ^{G2}$}${.}
$ For any particular $c,$ the Cost curve yields the equilibrium effort, $%
\lambda ^{G2}\left( c\right) .$ \ The $G2$ curve gives consumer surplus in $%
G2$ when effort is $\lambda ^{G2}\left( c\right) .$ Finally, the $G1$ curve
gives consumer surplus in $G1$ when effort is ${{\lambda }^{G1}}\left(
\lambda ^{G2}\left( c\right) \right) .$ In words, the $G1$ curve gives the
consumer surplus from the equilibrium effort that R\&D firms would make in $%
G1$ when \text{costs }are such that R\&D firms would make effort $\lambda
^{G2}\left( c\right) $\text{ in }$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 $\lambda
^{G2}$ is very low, which occurs when the cost of innovation effort is
"high." The straight dashed lines highlight the finding that the two systems
result in the same consumer surplus when $c=0.064.$ For innovation costs
above that level (but less than $\frac{1}{8}\frac{N}{N+1}$) $G1$ yields
slightly higher consumer surplus. The graph also reveals that the difference
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 effort are not "too high,"
the expected benefits to consumers of the additional competition between the
R\&D firms, under the \textit{ex ante} system, outweigh the costs of having
less expected innovation. Moreover, the absolute effect of introducing more
competition is larger when innovation costs are smaller and expected
innovations are larger.

%Figure 2:  Consumer Surplus is Greater in G2 when c < 0.064
%
%This graph shows Innovation Effort in G2 on the horizontal axis, and 
%Consumer Welfare on the vertical axis.  Beginning at the origin, 
%two curves labeled G1 and G2 proceed up and to the right, with G2 
%everywhere at or above G1.  A third line labeled Cost is a downward 
%sloping parabola, starting near the vertical axis at around the value 
%0.08 and decreasing steadily to a value of approximately 0.02.  
%A point on the cost curve is identified where Cost = 0.064, and a 
%vertical line drops from this point in the cost curve to indicate the 
%point on the G1 and G2 curves where the value of consumer surplus for
% G1 and G2 is located.  Although G2 is at or above G1, the two curves
% are almost identical at this point in the graph, showing a value of 
% consumer welfare of less than 0.01.  

An equivalent (unreported) graph shows a similar pattern for the aggregate
surplus of the downstream producers, which (given the Cournot construction)
is simply $\frac{2}{N}$ times the consumer surplus. Unsurprisingly, an
equivalent graph also reveals that R\&D firm surplus is higher in $G1,$ when
there is no \textit{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 firms are always better off without the \textit{ex ante} system.

As one would expect, equivalent graphs of consumer surplus using larger
values of $N$ reveal that consumers benefit from increased downstream
competition. Such graphs also indicate that consumers gain more from the 
\textit{ex ante} system when $N$ is larger: the downstream firms pass on a
greater share of the reduction in royalties achieved through the \textit{ex
ante} system. Although, the break-even level of innovation effort
(approximately 0.166 in Figure 2) is independent of $N$, that effort level
is associated with higher $c$ when $N$ is larger.

It is worth noting that the SSO members would not favor the \textit{ex ante}
system if they knew that innovation costs were "high." However, the actual
cost of innovation effort is probably unknown. Thus it would be appropriate
to consider the expected welfare effects of adopting the \textit{ex ante}
system taken over a distribution of possible innovation costs. Given that
the \textit{ex ante} system has a very small social cost over a small range
of possible realizations of $c$ and much larger benefits over all other
(smaller) realizations of $c,$ it seems most plausible that adopting the 
\textit{ex ante} system would have a positive expected welfare effect.

\section{Conclusion}

There has been heated debate over whether SSOs should engage in \textit{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 \textit{ex ante} licensing competition argue that
it would diminish social welfare by reducing incentives to innovate.
However, the welfare effects of reduced innovation should be weighed against
the welfare benefits of increased competition among IP owners. To assess the
relative magnitudes of the competition effect and innovation effect on
social and consumer welfare, this paper develops a simple three stage model
that can be used to analyze both the \textit{status quo} system (without 
\textit{ex ante} licensing competition) and the \textit{ex ante} system
(with \textit{ex ante} licensing competition). The model predicts that the 
\textit{ex ante} system generally results in lower innovation effort and
lower profits for R\&D firms, but higher consumer surplus and profits for
downstream licensees.\pagebreak

\section{Appendix}

\begin{proof}
There are no equilibria where ${{\lambda }_{-j}}=0$ and ${{\lambda }_{j}}>0$
in Stage One of either $G1$ or $G2$ if $c<\frac{1}{8}\frac{N\,}{\left(
N+1\right) }.$

Suppose that Firm $-j$ chooses ${{\lambda }_{-j}}=0.$ Then Firm $j^{\prime
}s $ profits in the two games are equivalent (given by $E[\pi
_{j}^{G1}\left( \lambda _{j}|0,N\right) ]$ and $E[\pi _{j}^{G2}\left(
\lambda _{j}|0,N\right) ])$ and can only be positive if 
\begin{equation*}
\frac{1}{4}\frac{N}{\left( N+1\right) }\frac{1}{\left( 2+{{\lambda }_{j}}%
\right) }>c.
\end{equation*}%
This condition cannot hold for positive ${{\lambda }_{j}}$and $c<\frac{1}{8}%
\frac{N\,}{\left( N+1\right) }.$
\end{proof}

\begin{corollary}
If $c>\frac{1}{8}\frac{N\,}{\left( N+1\right) }$ then ${{\lambda }_{-j}}={{%
\lambda }_{j}}=0$ is the only equilibrium in Stage One of $G1$ or $G2.$
\end{corollary}

\subsection{Equilibrium Expected Consumer Surplus}

Consumer surplus in Stage Three is given by $\frac{1}{2}\left( \alpha
-P\right) Q$ where $\alpha $ is the value of the technology selected by the
SSO. Substituting in the Stage Three equilibrium values of $P$ and $Q$
yields 
\begin{equation*}
CS\left( {\alpha ,}r\left( \alpha \right) \right) =\frac{1}{2}\left( \frac{N%
}{N+1}\left( \alpha -r\left( \alpha \right) \right) \right) ^{2}.
\end{equation*}%
The expected values of equilibrium consumer surplus can be found by first
replacing $\pi ^{M}\left( \alpha _{j}\right) $ and $\pi ^{D}\left( \alpha
_{j}\right) $ in $\left( \ref{ExPrG1}\right) $ and $\left( \ref{ExPrG2}%
\right) $ with $CS\left( {\alpha ,}r\left( \alpha \right) \right) $, with
the appropriate equilibrium value of $r\left( \alpha \right) $. This yields
the expected consumer surplus when Firm $j^{\prime }s$ technology is
selected by the SSO in $G1$ and $G2,$ respectively. To find the total
expected consumer surplus one must add the expected consumer surplus when
Firm $-j^{\prime }s$ technology is selected by the SSO in each game.
Substituting the equilibrium innovation efforts chosen by both R\&D firms
into the expected equilibrium consumer surpluses of each game yields%
\begin{equation}
E\left[ CS^{G1}\left( \alpha ,r\left( \alpha \right) \right) |{{\lambda }%
^{G1}},{{\lambda }^{G1}}\right] =\frac{1}{8}\left( \frac{N}{N+1}\right) ^{2}%
\frac{{{\lambda }^{G1}}}{\left( 1+{{\lambda }^{G1}}\right) }  \label{ECSG1}
\end{equation}

\bigskip and%
\begin{equation}
E\left[ CS^{G2}\left( \alpha ,r\left( \alpha \right) \right) |{{\lambda }%
^{G2}},{{\lambda }^{G2}}\right] =\frac{1}{2}\left( \frac{N}{N+1}\right)
^{2}\left( \frac{\left( 1+\left( {{\lambda }^{G2}}\right) 2^{1+{{\lambda }%
^{G2}}}\right) }{2^{1+{{\lambda }^{G2}}}\left( 2+{{\lambda }^{G2}}\right) }%
\frac{{{\lambda }^{G2}}}{\left( 1+{{\lambda }^{G2}}\right) }\right) .
\label{ECSG2}
\end{equation}%
Because the combined Cournot profits of the downstream firms are simply $%
\frac{2}{N}$ times $CS\left( {\alpha }\right) ,$ the equilibrium downstream
profits can be found directly from $\left( \ref{ECSG1}\right) $ and $\left( %
\ref{ECSG2}\right) .$\pagebreak

\bibliographystyle{authordate1}
\bibliography{econ}
\pagebreak

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\end{document}
