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Inter-firm Assets Pooling
in Technology Generation and Transfer

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2/05 p:lCIRC/DateDue.indd-p.1

INTER-FIRM ASSETS POOLING
IN TECHNOLOGY GENERATION AND TRANSFER

By

Nanyun Zhang

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Economics

2006

ABSTRACT

INTER-FIRM ASSETS POOLING
IN TECHNOLOGY GENERATION AND TRANSFER

By

Nanyun Zhang

The first chapter was motivated by the observation that in the biotechnology
industry patent pools have long been advocated, but are rarely formed. I seek the answer
from the underlying innovation structures. In science-based industries patent holders
usually follow up on their initial discoveries and play leading roles in the applied
innovation research in cooperation with firms. Patent pools not only are created for the
purpose of cooperative marketing, but also serve as an information-sharing institution. By
studying both new product innovation and cost-reduction innovation, I model the tradeoff
faced by patent holders between gaining from the synergy effect or spillover effect
created by the information flows with a pool and gaining from the differentiation effect
without a pool. The conditions for the no-pool equilibrium are derived and in the end I
conduct a welfare comparison and find that consumers can be worse off with a patent
pool when the effort level of competing research units are strategic complements.

Chapter 2 explains why in contract to previous literature, incomplete patent pools
emerge in equilibrium. I discuss the patent pool equilibria structure in a price setting
under open and closed membership games and analyze how market dynamics,
competition effect and the relative strength of competing technologies determine firms’
pooling decision. Also, the paper sheds light on how the incomplete patent pools affect

technology transfer, technology generation, and ultimately, social welfare. The main

findings of this paper are: first, with open membership, multiple equilibria exist. Both
incomplete pools and individual structure can be equilibria, depending on the new market
size in the second period and the substitutability of competing technologies. But with
closed membership, only a complete pool can be equilibrium when the substitutability of
two technologies is low. Second, royalty rates are set lower in the earlier stage generally
so as to positively affect early technology adoption. Third, although incomplete pool
structure is associated with lower social welfare ex post, a complete pool structure may
reduce firms’ incentives to innovate in the first place, or induce the firm to foreclose;
thus, it is not socially desirable ex ante.

Intrigued by the phenomenon that different industries have different tendencies of
forming strategic alliances, I present a simple model in chapter 3 to show how the
interplay between technology uncertainty and product differentiation determines firms’
decisions on forming R&D alliances in developing a new product. I examine the stable
strategic alliance structure for four firms under open membership simultaneous move and
sequential move unanimity games in a quantity setting context. The major finding is
under the open membership game, only {22} and {1111} structure exist in equilibrium;
under the closed membership game, an asymmetric {13} structure also can be
equilibrium. The social welfare analysis shows when the probability of success for each
firm is small enough, a grand alliance is optimum. And the discrepancy between the
social optimum and the market equilibrium cannot be solved by further cooperation in the
product markets without sacrificing welfare, thus leading to a policy complication in

aligning the private and public interests in alliance formation.

Acknowledgements

First, I would like to express my gratitude to my committee chair, Dr. Thomas
Jeitschko, for his support, patience, and encouragement throughout my graduate studies.
His technical and editorial advice was essential to the completion of this dissertation; I
benefited a lot from invaluable insights he shared with me on the workings of academic
research in general.

I am also grateful to my advisors, Dr. Jay Pil Choi and Dr. Carl Davidson, for
their tremendous help throughout the course of writing these theses. They helped screen
many previous drafi of ideas and offered many valuable suggestions that improved the
model and the presentation of this dissertation. And I thank my outside committee
member Prof. Adam Candeub too for his interesting discussions on anti-trust law issues.

My thanks also go to those who are not in my committee but helped me with
encouraging comments or cooperation during my research on patent pools. Mr. Alfi'ed
Chaouat, Director Licensing of Thomson Multimedia and Mr. John Hanshaw, Licensing
Associate of MPEG LA, generously shared their observations and insights with me in the
beginning of the research. I also benefited from the discussions with Dr. Roger E.
Stricker, Intellectual Property Vice President of Lucent Technologies, Mr. Philip
McGarrigle, Chief Intellectual Property Counsel at Affymetrix, Inc., and Mr. James
Kulbaski, partner of Oblon Spivak McClelland Maier and Neustadt. Dr. Josh Lerner and
Dr. Nisval Erkal each read my drafts of some chapters and offered precious thoughts and

suggestions on the paper. I very much appreciate their time and inputs.

iv

TABLE OF CONTENTS

LISTS OF FIGURES ................................................................................ vi

CHAPTER 1

PATENT POOLING STRATEGIES IN UNIVERSITY-TO-INDUSTRY KNOWLEDGE

TRANSFER
1. Introduction ................................................................................... l
2. Model 1: the Case of New Product Innovation ......................................... ll
3. Model 2: the Case of Cost Reducing Innovation ....................................... 24
4. Concluding Remarks ....................................................................... 40
References ....................................................................................... 43
Appendix A ...................................................................................... 46

CHAPTER 2

INCOMPLETE PATENT POOLS
1. Introduction ................................................................................. 56
2. The Model ................................................................................... 6O
3. Equilibria Analysis ......................................................................... 7O
4. Extended Discussions ...................................................................... 79
5. Concluding Remarks ....................................................................... 85
References ....................................................................................... 88
Appendix B ...................................................................................... 89
Appendix C ...................................................................................... 91
Appendix D ...................................................................................... 94

CHAPTER 3

TECHNOLOGY UNCERTAINTY, PRODUCT DIFFERENTIATION, AND THE
ENDOGENOUS FORMATION OF STRATEGIC ALLIANCES

1. Introduction ................................................................................ 104
2. The Alliance Formation Model ......................................................... 109
3. Alliance Structure Equilibria Analysis ................................................ 120
4. Welfare Analysis .......................................................................... 127
5. Concluding Remarks ..................................................................... 129
References ...................................................................................... 132
Appendix E .................................................................................... 134

LIST OF FIGURES

CHAPTER 1:

Figure 1: Investment Level and Pooling Structure in Equilibrium ........................... l9
Firgure 2: CS and PS Comparison under Different Pooling Structures ..................... 21
Figure 3: SARS Vaccine Development Organizations ......................................... 23
Figure 4: How the Spillover Effects Influences x, Cost, R, P& TI ........................... 33
Figure 5: Equilibrium of Pooling Structures ..................................................... 36
Figure 6: CS and PS Comparison Under Different Regimes .................................. 38
Figure 7: Consumer Surplus Comparison Under Different Regimes ........................ 54
Figure 8: Producer Surplus Comparison Under Different Regimes .......................... 55
CHAPTER 2:

Figure 1: Relationship Between Firms, Patents and Products ................................ 60
Figure 2: Game Tree: Only One Choice for each firm ....................................... 64
Figure 3: Stable Equilibrium Under Open Pool Game ........................................ 71
Figure 4: Firms’ Foreclosure Decision in Equilibrium ........................................ 82
Figure 5: Welfare Comparison Between Complete and Incomplete Pools ................ 100
Figure 6: Firm C’s Gain from Innovating Product II ......................................... 102
Figure 7: Firm C’s Foreclosure Decision in Equilibrium .................................... 103
CHAPTER 3:

Figure 1: Nash Equilibrium under Open Membership Game ............................... 121
Figure 2: Coalition-proof Nash Equilibrium under Open Membership .................... 123

vi

Figure 3: Size Announcement Game .......................................................... 124

Figure 4: Equilibrium under Sequential Game ............................................... 125
Figure 5: Social Welfare Optimal Structure in Equilibrium ................................ 128
Figure 6: Profits Comparison between {112} and {22} structures ........................ 135
Figure 7: Profits Comparison between {112} and {13} structures ........................ 135
Figure 8: Profits Comparison between {G} and {13} structures ........................... 136
Figure 9: Profit Comparison between {112} and {1111} structures ....................... 137
Figure 10: Welfare Comparison between {112} and {1111} structures ................... 141
Figure 11: Welfare Comparison between {112} and {22} structures ...................... 142
Figure 12: Welfare Comparison between {G} and {22} structures ........................ 142

vii

CHAPTER 1
PATENT POOLING STRATEGIES IN

UNIVERSITY-TO-INDUSTRY TECHNOLOGY TRANSFER
I. Introduction

Patent pools have a long history of being employed as a means of resolving
patent disputes among competing firms. Their recent application in MPEG and
DVD technologies has been affirmed by the DOJ (Department of Justice), and its
efficiency aspect especially gained attention from the economics profession.
Among the recent literature on this topic, Choi (2002) shows why firms have the
incentives to form a patent pool in the presence of uncertainty about the validity of
patents that makes disputes inevitable; Shapiro (2003) proposes a specific antitrust
rule limiting the settlements of patent disputes including patent pools so that
consumers will be left as well off as they would have been from ongoing patent
litigation; Lerner and Tirole (2004) provide a necessary and sufficient condition
for patent pools to enhance welfare, and show that requiring pool members to be
able to independently license patents matters if and only if the pool is otherwise
welfare reducing.

All these papers focus on analyzing the pool’s behavior, assuming that a
patent pool is used in an industry. Will complementary patent holders in any
industry resort to patent pooling when facing patent disputes or numerous

transactions? Observations from the biotechnology1 industry give a direct answer:

 

‘ Any technologies related to biology can - in a broad sense — be referred to as biotechnology; thus
the biotechnology industry includes agriculture, medicine, cosmetics, and food preparation and
processing, etc. But in this paper, we adopt the concept used in Resnik (2003), which focuses on
the materials and methods related to genetic engineering that have been developed since the

No; despite patent pools having been advocated for several years for solving its
patent thicket problems. Why? In this paper I explore the intriguing discrepancy
between the theory and the real world phenomenon. But before analyzing the
patent pooling proposal, I briefly outline the patent thicket problem in the
industry.

In biotechnology, universities have been the most active players in
conducting basic research; and they are the major patent holders for scientific
discoveries on isolated and purified genes or DNA sequences and on methods for
cloning, isolating and manipulating DNA, RNA or proteins. Since the passage of
Bayh-Dole Act in 1984, federal/public firnded research institutions such as
universities are under more and more pressure to commercialize their scientific
discoveries. But universities rely on dedicated biotechnology firms2 (DBF) to
translate their discoveries into commercial products (Edwards, Murray and Yu
(2003)) through licensing. For example, based on an isolated gene discovered by a
university, a biotechnology firm can develop a process for making transgenic
plants that produce pharmaceutical compounds of interests and these
pharmaceutical compounds can be isolated and purified from the plant and then
administered to humans to treat deadly diseases (Mueller (2001)). During this

process, patent problem occurs to the biotechnology firms in license-in stage.

 

discovery of recombinant DNA techniques in the 19705. Biotechnology in this narrower sense
includes DNA/RNA cloning, gene transfer, genetic manipulation, the polymerase chain reaction,
gel electrophoresis, and other methods and materials used to create genetically modified
organisms, develop genetic therapies, or bioengineer pharmaceutical products such as synthetic
proteins or hormones.

Many DBFs are founded just to exploit a particular biotechnology discovery. Although some
DBFs are direct spin-offs of the university system, and some biotech subunits of the existing large
firms also participate in the transformation of the up-stream university technology, in this paper,
we treat them all as an “intermediate” chain in the innovation sequence in biotechnology industry.

Biotechnology firms usually need to use multiple fragments held by
different patentees in order to do the firrther research and ultimately innovate some
foreseeable commercial products, such as therapeutic proteins or genetic
diagnostic tests. Thus, they are forced to cope with “patent thickets” in situations
where multiple owners hold important underlying patents related to potential
innovations. In other words, they must bundle licenses from all patent holders to
avoid being charged with infiingement under multiple patents and this can be
frustrating to a small biotechnology firm in the very beginning. For example,
patents on receptors are useful for screening potential pharmaceutical products; to
learn as much as possible about the therapeutic effects and side effects of potential
products at the pre-clinical stage, firms want to screen products against all known
members of relevant receptor families. But if these receptors are patented and
controlled by different owners, gathering the necessary licenses may be difficult or
impossible. Unable to procure a complete set of licenses, firms choose between
diverting resources to less promising projects with fewer licensing obstacles and
proceeding to animal and then clinical testing on the basis of incomplete
information. (Heller and Eisenberg (1998))

Facing this problem, people have voiced two different solutions. One is at
the heart of the public debate these days, which is essentially against granting of
patents by the US Patent Office (U SPTO) to inventions in the biotechnology field,
especially to those involving genetic information. They argue that patenting
biotechnology inventions will not only prevent access to the technology needed

for the research and deve10pment necessary to develop new commercial products,

but also hinder further basic researches (Mueller (2001); Heller and
Eisenberg(1998) ). Another opinion is well represented by USPTO’s white paper3
on the use of “patent pools” in the biotechnology industry as a means of
reconciling the interests of both the public and private sector. According to
USPTO, patent pooling can
0 eliminate the problems caused by “blocking” patents or “stacking”
licenses,
Cl encourage the pool members to focus more on their core
competencies and thus spur innovation at a faster rate,
D reduce transaction costs related to uncertain litigation,
[:1 provide further innovation by enabling its members to share the
risks associated with R&D,
D institutionalize the exchange of technical information not covered
by patents so as to avoid overlapping efforts.
And the paper concluded that pooling is a “win-win” situation that could “serve
the interests of both the public and private industry.” With so many benefits patent
holders can get from pooling their patents, why hasn’t any patent pool been
formed in the biotechnology industry?4 I examine the industry’s innovation
structures and the characteristics of technology transfer that possibly underlie the

no-pooling strategy in the equilibrium of the implied game. Thus, the

 

3 Clark, Jeanne, Stanton, Brian and Tyson, Karin (2000).

‘ In January 2005 Essential Inventions Inc. proposed to WHO, UNAIDS and the Global Fund the
creation of an Essential Patent Pool for AIDS. This pool has not been formed yet. Even if the pool
is formed someday with the concerted effort from politicians and scientists, it is a non-profit pool
and its immediate focus is less on tackling innovation than on fairly disseminating the benefits of
drugs for Aids in developing nations. Thus its motivations and possible implications differ from
the issues addressed in this paper.

concentration of this paper is a departure from most patent pool related papers in
which the efficiency side of the role that an existing patent pool may play in the
transfer of technology is highlighted.

By innovation structure I refer to the ways in which technical advancement
proceeds in an industry. In Merges and Nelson’s on the complex economics of
patent scope (1990), four types of technology-advancing patterns are classified:
cumulative technologies, discrete technologies, a hybrid of these two, usually
found in the chemical industries; and the fourth type, science-based technologies.
According to their paper, the fourth type includes biotechnology, semiconductors
during the 19505, and the burgeoning new field of superconductivity. While their
paper emphasizes the discussion of how the broadness of patents affects the subtle
balance between the private and public spheres in the field, my research in
biotechnology exposed me to some major characteristics of the technology
transfer that differs from those industries where patent pooling applies, namely the
incomplete technology and the tacit knowledge transfer process.

First, concerning scientific discoveries, the pioneer inventions owned by
the patents holders to be transferred are not complete and they need further
innovation to be embodied in a final product and commercialized. For example,
universities can file applications on newly identified DNA sequences, including
gene fragments, before identifying a corresponding gene, protein, biological
function, or potential commercial product (Heller and Eisenberg ( 1998)). But the
characterization of nucleic acid sequence information is only the first step in the

utilization of genetic information. Significant and intensive research efforts are

required to glean the information from the nucleic acid sequences for use in the
development of pharmaceutical agents for disease treatment. Due to budget
constraints or lack of specific assets needed in further exploration, universities
usually license their technologies to dedicated biotechnology firms. This is
different from the cases of existing patent pools discussed where applicable final
technologies are the object of technology transfer.

Second, scientific discoveries are characterized by tacit knowledge that
would not be disclosed in a patent and cannot be fully revealed and transferred in
the licensing process. Thus, discovering scientists are often closely involved in the
subsequent innovation and patent holders have the right and option to decide on
the deepness of the technology transfer by choosing the research cooperation
effort or how much retained intellectual human capital they will release.5 This
aspect of technology transfer is usually ignored in the discussion of patent pools in
industries where the license for the right to use an invention is the major subject of
technology transfer.

These two characteristics set the stage for the two simple models that are
presented in this paper. Because of the incomplete technology and tacit knowledge
transfer during the applied innovation process, patent pools not only are created
for the purpose of cooperative marketing among patent holders, but also
potentially serve as an information-sharing institution. And the information
sharing mechanism within a pool may have different implications in different

types of innovations. The first model is applied to new product innovations, in

 

5 Further discussion and empirical work on this aspect can be found on Zucker, et al.,
“Commercializing knowledge: university science, knowledge capture and firm performance in
biotechnology”.

which the realization of the value of scientific patents is uncertain due to the
uncertainty in the applied research and the consequent final product market
structure. Moreover, it is assumed that information flows and coordinated research
within patent pools can help increase the chances of success. The second model is
applied to cost reduction innovations, in which information sharing can enhance
the spillover effect of R&D. In both cases, information sharing within a pool
results in a lowered differentiation level of final products. Thus, there is a tradeoff
facing scientific patent holders when deciding to pool their patents with their peers
or deciding to work separately with the downstream DBFs. It is shown that this
concern may provide enough disincentives to the initial patent holders in their
patent pooling decision that impedes the formation of patent pools under certain
conditions. Hence, patent pooling is a firnction of the industry innovation structure
and the characteristics of technology transfer.

This paper develops a better understanding of inter-organizational
cooperation behavior in general and university-to-industry knowledge transfer in
particular. As mentioned briefly in the beginning, this paper is related to the
literature on patent pooling, but a patent pools’ pricing decision or rules for
members are not the objectives of our analysis. Instead, I extended the study to
R&D cooperation among scientific patent holders as a natural result of their patent
pooling. A few papers on university—to-industry knowledge transfer in the
biotechnology industry are related to the model. Zucker, et al. (2001) examines
how the collaboration between university star scientists and firm scientists is a

crucial transfer mechanism and has a significant positive effect on firm

performance when knowledge has an important or large tacit component. Two
basic ideas from their paper inspired my research. First, “Difficulties inherent to
the transfer of tacit knowledge lead to joint research: Team production allows
more knowledge capture of tacit, complex discoveries by firm scientists.” Second,
“firm success was not the result of a general knowledge ‘spillover’ from
universities to firms but due to star scientists taking charge of their discoveries.”
And “university star scientists’ relationships with firms were governed by tight
contractual arrangements, academic scientists typically being ‘vertically
integrated’ into the firm in the sense of receiving equity compensation and being
bound by exclusivity agreements.”

Powell, et a1. (1996) discusses how inter-organizational collaboration
contributes to organizational learning and the emergence of the biotech industry.
They argue that when the knowledge base of an industry is both complex and
expanding and the sources of expertise are widely dispersed, the locus of
innovation will be found in networks of learning, rather than in individual firms.
The large-scale reliance on interorganizational collaborations in the biotech
industry reflects a firndamental and pervasive concern with access to knowledge.
Both of their findings support the basic assumption in my paper that vertical
cooperation between universities and DBFs are typical and important in
biotechnology and the application of patent pooling adds a new networking tool
and enhances information sharing between pool members.

Another strand of literature to which this paper belongs is on cooperative

and non-cooperative R&D. D’Aspremont and Jacquemin (1988), followed by

Suzurnura (1992) and Motta (1992), discusses how cooperative R&D agreements
between otherwise competing firms may internalize the adverse effect that
spillovers have on the incentive to invest in R&D. Brod & Shivakumar (1999) is
very closely related to the second model in this paper: they study how the
interplay between the spillover and the differentiation effects determine the
equilibrium in duopoly, but they only compare the full competition model with a
semi-collusive model where firms choose their R&D efforts non-cooperatively but
collude in the product market. Fraja and Silipo (2002) analyzes how R&D levels
and welfare depend on the interplay of the degree of product market competition,
the similarity of the research strategies and the cost of R&D under different
cooperative structures between duopolists. But in their paper, spillovers
specifically refer to technological spillovers and the firms’ probability of success
is independent of the cooperative structure. Molto, Georgantzis, and Ortz (2005)
shows how cooperative R&D induces firms to choose identical or very similar
R&D processes to maximize the total profit of the duopoly. In their model, the
spillover is endogenous and a high degree of spillover is equivalent to high
similarity of technologies.

Unlike the above papers, patent pools in this paper are similar to
competitive research sharing joint ventures, where research units share the
research results without commanding jointly optimal research efforts or profit

sharing.6 Greenlee and Patrick ' (2005) studies endogenous formation of

 

6 Pharmaceutical firms Human Genome Sciences and SmithKline Beecham initiated such a joint
venture in 1993. In it, each firm proposes research programs to a jointly staffed committee that
approves or rejects, and the partner performing an approved project assumes complete
responsibility for its execution and costs. Aside from initial feasibility studies, the committee

competitive research sharing joint ventures; but the differentiation effect is
missing in their paper. And their focus is how research sharing and joint profit
maximization provide different incentives to collaborate and how research sharing
firms form the coalition and how this influences the welfare for certain spillover
spaces.

Our first model also pertains to innovation management and games of
R&D cooperation. Erkal and Minehart (2005) studies how firms’ incentives to
share R&D results depend on how close they are to the completion of a project
and they examine the links between the uncertainty firms face during the research
process and that in the product market. Thus, the tradeoff in their paper is between
a higher probability of success brought by information sharing and longer
monopoly profits that are earned if there is no sharing.

The paper proceeds as follows. In Section H, the model that explains the
tradeoff between a higher probability of success and a higher differentiation level
of the final products in the new product innovation process is introduced. Section
111 contains the model that explains the tradeoff between a greater spillover effect
and a higher differentiation level of final products in the cost reducing innovation
process. Both section II and 111 include the analysis and comparison of the welfare

and policy implications. Section IV concludes.

 

neither develops nor assigns projects. A firm that successfully introduces a new collaboration
product pays its partner a modest royalty for the use of the partner’s intellectual property. Each
firm gains access to the existing and newly created knowledge of its partner, and can develop
commercial products employing that knowledge without being held up for additional royalty
payments. In addition, SmithKline Beecham has the right to locate personnel at its partner’s facility
in order to work alongside partner employees. Thus, the collaboration between Human Genome
Sciences and SmithKline Beecham neither cormnands jointly optimal research efforts directly, nor
provides strong profit sharing incentives to undertake them. Greenlee and Patrick (2005).

10

11. Model l—the case of new product innovation
Consider an environment with two upstream scientific research institutes,
U,-, i = A, B. UA and U3 can be universities, other non-profit research centers or

private research firms. For the simplicity of the discussion, they refer to

universities in this paper. UA and U3 each hold an equally essential patent, .71 and
B, respectively. The technologies or scientific discoveries disclosed in patent .511

and .‘B have no commercial value themselves. But researches combining fl and B

can potentially lead to certain product or process innovation and create
commercial benefit for patent holders.

The process from scientific discoveries to commercialization of innovated
products requires intensive research, dispersed expertise, and huge financial
investment, which are beyond the capability of UA and U3. So universities license
their patents to the downstream research firms, F, j = 1, 2.7 F refers to Dedicated
Biotechnology Firms (DBFs) in this paper and I assume that F; and F2 are
identical and competing head-to-head. The technology transfer from UA and Us to
F1 and F2 includes two parts: a license for the right to use an invention, and
physical transfer of technologies along with valuable information”. The second

part refers to patent specific human capital in our paper and would not be

 

7 I assume that there are only two DBFs qualified for the applied research, which makes the patent
prices irrelevant in this simple model. This is actually an important difference comparing with
some electronic industries, such as DVD, where patent pools have been formed. In those cases,
patent holders can maximize profit by setting prices and influence market size of the technology.
But in biotechnology industry, the potential demand of pioneer inventions are constrained by the
research capability of research firms; the licensees can be few and unidentifiable sometimes, which
may make the demand function method irrelevant.

8 Gallini, N., 2002. P. 141

11

disclosed in a patent. To complete technology transfer and enhance the results of
applied research of DBFs, star scientists who own the pioneer invention in both
universities need to sign research cooperation contracts and work with DBFs. So,
vertical R&D cooperation is a necessary part of the story. What is optional is the
relationship between UA and U3.

Universities are facing the choices between forming a patent pool and
acting individually. If acting independently, each signs a research contract with
one of the DBFs and they compete in the further innovation. If forming a pool,
two universities agree to cooperate in applied research and maximize the pool’s
profit level. I assume that the differentiation level of the final products is big
enough so that market foreclosure is a dominated strategy in any situation. In other
words, the pool will work with both DBFs and two universities’ research resources
will be assigned to two firms. Although two DBFs will work competitively in the
further innovation, scientists in the patent pool are free to communicate and share
information regarding to the research process.

After two universities make the pooling decision, two firms decide on
investment/effort level and then compete in price in the final product markets.

Regarding to profit sharing rules, for simplicity, I assume that universities
and firms will split the profit evenly in the case of vertical R&D cooperation.
Also, I assume two universities have the same research strength and bargaining
power and they will split the profit evenly if a pool forms.9 There is no extra

transaction cost associated with forming and operating a patent pool.

 

9 We assume that the upstream scientific research entities, including universities, other non-profit
research centers and private firms, desire to profit from their pioneer inventions and are profit

12

I will present two simple models under the above scenarios in this paper.
In section II, I study the pooling strategy in an industry where two applied
research firms cooperate with scientific patents holders to innovate a new product.
In section III, the case of cost-reducing innovation is discussed.
1].] Setup

Two research units, paired between universities and firms, join the new
product innovation race and compete in the final product market. The result of
innovation is uncertain and the probability of success of unit 1’ depends on two
factors: unit i’s effort level x, and the pooling status of patent holders. Let x, be
the probability when there is no pooling between U A and U 3- The formation of
the pool can increase that probability to 6x,. 0 e[1, 2] and it measures R&D
coordination effect or the synergism created within the patent pool. In the final
product market, the differentiation level is y with a patent pool and dy without a
pool, where d 6 (0,1] is the substitutability of the final products and it inversely
measures the differentiation effect that firms can benefit from independent
research. The higher the d is, the more substitutable the final products are, the less

differentiation effect the independent research can have by conducting a non-

cooperative R&D. The aim of the model is to identify in which areas of the space

 

maximizers. Some may inquire about the profit maximization assumption applied to non-profit
organizations. One important observation is that although they are not profit-maximizers as to the
selection and irrrplementation of research project, they are trying to make as much money as
possible through the licensing management once they have held the patent. This is especially the
case after the passage of Bayn-Dole Act of 1980, which allowed universities to retain patent rights
and to offer exclusive licenses on inventions developed with federal funds. I think it is reasonable
to assume that university licensors are maximizing their profit in making patent management
decision.

13

of (6, d), the no-pooling strategy will dominate or be dominated by the pooling
strategy.

The timing of the game is as follows. In the beginning of the game, UA and
U3 make the pooling decision, and the universities and the firms pair up.

In stage one, firms are engaged in innovations. F1 and F2 first need to make
choices over the investment effort level, x. Then the R&D process begins and in

the end of this stage, with certain probability each innovation unit develops an
innovation. I use x,” and xip to denote the investment level of F, under no-pool

structure and pool structure, respectively.
In stage two, firms are involved in product market competition. Firms
compete in price if there are more than one product. Depending on the pooling

structure and the market structure, firms receive profit accordingly. I use
1‘1,” and Hf to denote the net profit of F ,~ under no-pool structure and pool

structure, respectively. The game can be illustrated by the following structures:

Pooling decisions Probabilities Payoffs
of events
(1-6'X. )(1-9x2) (0,0)
UPFI; 6x,(1—6x,) (21M, 0)
Pool UPF2 (1 — 19x, )ex, (0, n“)
Olex2 (7r: , all?)
UA, UB
(1 — x,)(1— x2) (0, 0)
Not pool 11,11:l (1 - x,)x1 (71M, 0)
UBF2 (1—x,)x, (0, 71M)
xix2 (”nDp , 7r 1: )

I will describe and solve the model using backward induction in the next part.

14

II. 2 Stage II of the game: products competition:
Consider an economy consisting of an industry with two firms competing

in prices by producing differentiated products, and a competitive numeraire sector

with an output qo. Firm i (i =1, 2) produces product i at quantity level q, and
charges at price p,. There is a continuum of consumers of the same type, and the

representative consumer’s preferences are described by the utility function

U(q.,q2)+qo, where U(q1,q2)= q. +612 -(c112 + 2617611612 +q§)/2.

In the utility function, the degree of product differentiation is measured by
y, y 6 (0,1) , and decreases in y. In my model, this differentiation level also varies
with the pooling structure, which is embodied in parameter d. d = 1 when there is
a patent pool. When there is no pool, less information is shared between the two

research units and the two products will be more differentiated, i.e. 0 < d < 1.

Consequently, in a duopoly market, U (q,,q2) yields linear inverse demand

functions as follows:

P1 =1-q, -d7q2 (1' =1, with a patent pool
P2 ‘31—‘12 “-61 7611’ d 6 (0,1), without a pool

Solve it to get demand functions:

1_pi—d(7_pjy)
1_d272

 

q,= i=l,2;j=l,2;i¢j

Assume the marginal cost of production is zero. Firm 1' has the following

objective function:

 

1— .-d — .
Max ”izpiqt:pi pl (7 P17)

,i=1,2; '=1,2;°¢ '
pr 1_d2)/2 J l J

15

Solving the Bertrand competition model, we get:

_ _l—d7
pl [)2 2-dy

D D___ 1-2517 (1)
(Z—dt’) (1+d7)

If the model degrades into a monopoly situation, the monopoly i will face
the following inverse demand function regardless of the pooling structure:
pi = 1 - qt

Solve the model, we have
(2)

Notice that in the market competition stage, firms’ profits solely depend on
the market structure. The only choice the firms have is to influence the market

structure by R&D investment in the first stage.

11.3 Stage I of the game: R&D investment:

In this stage, two firms join the innovation race. In the beginning of the

stage, each firm needs to choose the investment intensity xi. Combining with the

coordination effect 6, contingent on the pooling decision in the beginning of the

game, the probability of success of firm i is 6x,. I assume that there is a

2
decreasing return to scale in R&D; and the cost of investment x, is 52L.

Firm i maximizes the net profit 11,. for the research unit:

16

2

Max r1, = 19222sz" + 9x, (1 — oxjw’" — 52—

xi

2 l—dy 6xl.(l—9xj.) xi
xx}. + ——
(2—d7)2(l+dy) 4 2

 

The best response functions can be derived from the first order conditions

as follows:

:g_ (4—3dy+d2y’)dyi92 x

x=67rM+t97rD—7er .
' ( ( )’) 4 4(1+dy)(2—d7)2 ’

 

(3)

Since 7:0 < 7:” , x, and x j are strategic substitutes in the sense that an

increase in one firrn’s research investment level reduces the equilibrium choice of
its rival.

Solving the model, we have

 

 

67:” 6(1 + d y)(2 - dy)2
x1=x2 : M D 2 = 2 3 3 2 2 2 (4)
1+(7r —7r )6 16+4dy6 +(dy —3d 7 )(4+19)
x,2 62(1 + d y)2 (2 — c117)4
I11:1]2 =— (5)

 

2 = 2(16+ 4217192 +(d’y’ —3d272)(4 +192))2

II. 4 Pooling decision and equilibrium analysis:

With all the results I have calculated above, the two universities are able to
make a decision on pooling the patents or not. Since I have assumed that
universities will simply evenly split the profit with the firms that they cooperate

with in innovation, their interests are fully aligned. They will make the pooling

decision so that the net profit of the research unit, 1'1, , is maximized, i = l, 2.

17

Our comparative static analysis reveals the following results in the model.
Lemma 1. The investment level x, is increasing in 6 and decreasing in d.
Proof: see the Appendix A.

To understand the relationship between xi and 0, the key is how 6 affect
the marginal revenue and marginal cost in our model. Marginal cost is
independent of 6.

aMR _ 6(x,627r0 +9(l-x,6)7rM) _ 7r“ (l—Bzrr" +62%”)
66 649 l+¢92(7rM -7rD)

 

Since > 0 , the

marginal revenue increases in 6. Thus, with the increase of 6, firms have incentive
to increase the input level x,.

The increase of d means a decreasing differentiation level of two final

products, which results in a more fierce competition and lowers the duopoly

an” 6MR an”

<0, SO 67rD 6d <0- Similar to the above

 

 

 

 

profits. 6 D = x1399 > 0,
7r

argument, firms respond to increased (1 by reducing the investment level.
Lemma 2. The net profit IT. is increasing in 6 and decreasing in d.
Proof: See the Appendix A.

The result is intuitive: the increase in 6 can increase the marginal revenue
and lead to higher investment level, but it does not change the marginal cost. As a
result, the net profit increases. Similarly, the increase in (1 reduced the duopoly

profit and marginal revenue, thus reduced the net profit.

18

Proposition 1: For any given parameter y, 76(0, 1), there exists a unique function
6 = 6(d, 7) , such that:

when6 <6(d,y) , x,” > xip, and IT,” > Hf), i: 1,2 and no patent pool will be
formed; When6 > 6(d,y) , x,” < xip, and l'liw’ < Hf), i = 1,2 , patent pool will

be formed.

Proof is contained in the Appendix A. See Figure 1 for an illustration.

 

 

 

 

6 (Coordination Effect)
1
6 = 6(d,7) x?" < x.’
l—INP < HP
Pooling Zone
xiNP > xiP
I-INP > HP
No Poolirg Zone
0 l

d (Differentiation effect)
Figure 1: x,” and xip comparison and pooling structure

in equilibrium in relation to d and 6

Figure 1 gives the general idea about how d and 6 influence the investment
level of firms under different pooling structures, i.e., x,“ and x!) and the pooling

structure in equilibrium.

This result can be derived from Lemma 1. Since x, is increasing in 6 and

decreasing in d, pooling has a positive effect on x," due to the synergy effect and

19

non-pooling strategy has a positive effect on )6in due to the differentiation effect.
And the combination of the critical value (6*, d*) can form a continuous set such

that xiNP = xip. Any point beyond that combination will lead to a situation where

one dominates the other. Intuitively, firms choose the investment level that can
benefit most from the dominant effect under each pooling structure. Thus, the
optimal investment and pooling structures are simultaneously determined by the
(6*, d*) combination.

The characteristics of patents in biotechnology industry exactly illustrated
the spirit of proposition 1. Those gene patents or research patents held by
universities usually have very uncertain research and commercial values. Since
they have discrete characteristics even in the same field; patent pooling between
universities cannot generate enough synergy effect to enhance firms’ chances of
success in conducting the applied R&D. On the other hand, each research path has
the potential to lead to more differentiated product innovations if conducted

independently, which can earn the firms the competitive edge.

Proposition 2. Welfare analysis:

1. There exists a function 6 = 6(d,y) for any given parameter 7/, y€(0, 1),

such that when6>6(d,y), producer suplus is higher with a pool than
without.

2. For any (6, d) combination, consumer surplus is higher with a pool than
without regardless of the value of 7.

Proof. See the Appendix A.

20

Proposition 2 can be shown in figure 2. It says that no-pooling structure
can be more beneficial than pooling structure under certain circumstances to
producers. But from consumer’s point of view, patent pooling is always the
optimal structure. The intuition behind proposition 2-1 is simple. From producers’
perspective, with the decrease of 6 and d, firms are less attracted to the pooling
structure and more attracted to do independent R&D so that they can benefit from

the differentiation effect.

 

 

 

 

6 (Coordination Effect)
1
19 = 6(d, 7)
PS N” < PSP
NP P
CS < CS
PS W > PS P
0 l

d (Differentiation effect)

Firgure 2: CS and PS comparison under different pooling structures

Consumer surplus is calculated by total utility minus producer surplus.
Forming a pool reduced the differentiation level, which lower both total surplus
and the producer surplus. Since the producer surplus decreases faster than the total
surplus, consumer surplus is lower with a patent pool. On the other hand, pooling
enhances the probability of success, which increases both the total surplus and

producer surplus. Due to faster increase in total surplus, consumer surplus is

21

higher with a pool. Combining the two factors above, the net effect results in a
higher level of consumer surplus with a patent pool.

And when 7 increase, it adds benefit to producer’s surplus under no-
pooling structure because it increases the base that the firms can leverage from
differentiation effect.

Proposition 2 implies the possible policy conflict between consumers and
producers. As I discussed in the introduction part, even though consumers can
benefit from the “patent pools” in the biotechnology industry called on by
USPTO’s white paper, the no-pooling structure will still be the equilibrium if the

(6*, d*) combination falls into the no-pooling zone. And the threshold

6 = 6(d*, 7*) can be interpreted as the critical degree of the synergy effect created

by the patent pools.

An example can be found in the failure of forming a patent pool among
several entities that had sequenced parts or the whole of Sars-associated
coronavirus (Sars-CoV) in 2003. It would facilitate and even speed up the
discoveries of vaccine if the Sars IP holders could pool the patents and cooperate
with each other. But with the patents unpooled, the vaccine firms in the new or

optional vaccine marketlo will work hard to pick their own research approaches

 

'0 Generally, the buyers of the vaccine vary dramatically depending on the type of vaccines. In the
so-called "traditional EPI (Expanded program on immunization) vaccines" market, the requirement
or recommendation of the immunization created a mass market; and there are only limited number
of worldwide buyers, including UNICER (United Nations Children's Fund), PAHO (Pan American
Health Organization) and WHO, and some nations' governments. Since the bulk purchases have
given them significant negotiating powers, the prices are driven down to the marginal cost, which
is not the market discussed in this paper. My model applies to the market for the optional vaccines
such as flu vaccine and the newly patented vaccines. The buyers in those markets are mainly from
industrialized countries and the private sector in developing countries; and the vaccines are sold to
those who can afford it. The SARS vaccine that I used as an example here belongs to this second
type of vaccine. The reason is the threat of SARS is still regional and it could not possibly be so

22

and hence more likely get a differentiated vaccine. I borrow the following figure
fi'om a seminar in World Health Organization11 to illustrate the situation faced by

the patent holders such as Coronavative, HKU and CDC.

 

 

Vaccine License
Development Assembly

 

 

 

 

 

 

 

Vaccine Co 1 Coro-

Vaccine navative
Approach 1 \ %

Vaccine Co 2 - ‘ HKU
Vaccine ‘ /

h 2
Approac Vaccine Co 3 m\

. CDC
Vaccine /’ \
Approach 3 Vaccine Co 4

Figure 3: SARS Vaccine Development Organizations

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A similar scenario caused by IP fiagmentation, which was not solved by
patent pool, can be found in the cancer drug research. Ideally, if we can use a
DNA Microarray to arrange 300 cancer-associated genes and make a DNA chip,
we will have a simple diagnosis for many cancers. But such DNA Microarray
technology has never been put into real usage due to the patent thicket. Why?

Microarray technology promises to monitor the whole genome on a single chip so

 

those who can afford it. The SARS vaccine that I used as an example here belongs to this second
type of vaccine. The reason is the threat of SARS is still regional and it could not possibly be so
soon added to the EPI vaccine package; thus, even though the buyers are regional governments, it
is still a market that sells differentiated products or single product (if it is monopoly) to many
buyers.

11 Source: http://www.who.int/intellectualproperty/events/en/JamesSimon.pdf

23

genes simultaneously. That will definitely increase the chance of success in
finding the diagnosis of cancer. But a DNA chip that uses all the related genes
results in a homogeneous product in the final product market. As long as those
research companies and patent holders are still profit concerned, they would be
reluctant in accepting the idea of patent pool in cancer related genes. In both the
Sars-vaccine and cancer DNA chip cases, forming a patent pool is beneficial to the

consumers for sure; but firms’ choices fall into the no pooling zone.

III Model 2—the Case of Cost reducing Innovation

In some cases, the two patents held by the universities may be used to
innovate certain new products that can be produced at a lower cost level compared
to the existing ones. Cost-reducing R&D is a very important subject in
biotechnology. For example: in forestry biotechnology, trees are genetically
modified to grow in arid or saline conditions or to develop cold-tolerant species; in
agriculture, biologist works on developing bioengineered crops -- crops carrying
genes selected for resistance to certain insects or specific herbicides. And in
vaccine industry, current influenza vaccine production methods are based on 50-
year old technology and it takes 4~9 months for a production stage. While a
Plasmid DNA vaccine only takes 1 month to produce. So the major vaccine
companies are competing in developing new vaccine making technologies to
shorten the production periods and lower the producing costs. A simple model is

developed here to address the issues that arise from this situation.

24

III. 1 Set-up

The basic setting for the two universities and two firms will be the same as
in model except that there is no uncertainty issue. Suppose the two firms have
been producing two differentiated products and competing in price. Now with

fiirther innovation based on two universities’ atents, firms’ investment x. can be
1

directly transferred to a cost reduction. The pooling structure will influence the
competition in two ways: one is the cost reduction level of the production; another
is the product differentiation level in the final products.

If a patent pool is formed during the R&D period, there will be a spillover

effect, .9, s e(0,l) on the cost reduction between firms due to the information
sharing. More specifically, the unit cost is C,(xl,x2) = c—x, —sxj. And the
differentiation level of the two products is y, 76 (0,1). If two research units
separately do the R&D without forming a pool, they can innovate some products
with increased differentiation level d y, d 6 (0,1) , but produced at a cost without
spillover effect, C,(xl , x2) = c — xi.

The timing of the game is as follows: in the beginning, universities decide
whether to pool or not. Then firms pair up with universities. In stage 1, two firms
make decisions over R&D investment level and the cost reduction and further
differentiation level are determined consequently. In stage II, firms compete in

price in the final product market. Again, games are solved using backward

induction. I begin the discussion of the model with the last stage.

25

III. 2 Product market competition
The product market competition is determined by the demand function and
the cost fimction.

The demand function is derived from the utility function U (q1,q2)+q0,

where U(q,,q2) = q1 +q2 —(q12+ Zdyqlq2 +q§)/2 . Same as in the first
model, 3/ measures the degree of product differentiation, and it could be further
lower to (17 under the circumstance that no patent pool has been formed. Thus, in

the duopoly market, U (q,,q2) yields different linear inverse demand functions
corresponding to different pooling structures.

P1 :1_q1 ‘d742 d = 1, with a patent pool
P2 = 1‘ €12 -d7q, ’ d 6 (0,1), without a pool

The unit production cost is determined by two factors: the initial
production cost, c, which is set as given and is the same for both firms; and the
investment level, xi, i=1,2. The cost function Ci(xl,x2) also depends on the
pooling structure:

Cl.(xl,x2) = c—(x‘. +sxj),

s = O, with a patent pool . . , .
where , l=1,2;j=l,2;l¢j
s 6 (0,1], with a pool

Firm 1' faces the following problem:

1-p. -d(7-p_,7)
1_d2y2

 

Iii)?“ ”.=(p,-C.)q,=(p,-C,) ,i=1,2;j=1,7-;i¢f

26

Solving the production stage, we observe that profits from production are given by

 

_ (p, -C,)2
71',- ——1—y2d2 ,where,
2+2C, —-d2y2 —d(y—ij)
pi - 4-d2y2
(2 +(C, —l)dy—d272 + C(dzyz —2))2
Thus, 7t,= j i=1,2;j=1,2;i¢j

 

(4-d272)2(l-d272)

Plug in the cost function C; = c — x, - sx and we can rewrite it as follows:

j 9

2 +c(2 +dy)—dy—dzyz —(2 +dsy)x, —(2s +d7)xj
pi = 2 2
4—d y

 

(2+dy(c—1—sx,. --xj)-d2y2 +(c—xl. —sxj)(dz}/2 —2))2
fl" :
' (4-d272)2(1-d272)

 

i=1,2; j=1,2; i¢j (6)
111.3 R&D investment
In the R&D stage, firm i chooses an investment effort, x, , to innovate the

2
x.
product that is cheaper to produce. The cost for the investment is i. This R&D

cost function is convex and represents decreasing returns to scale for R&D
expenditure. It implies that the marginal cost of R&D investment of firm i is 1.

Combining (6) and R&D cost function, firms’ maximization problem is:

(2+dy(c—1-sx,-x.)-d272+(c—x‘.—sx.)(d2}/2—2))2 x?
Maxl'li(xl,xj)= j 2 2 2 2 2 j _—l-
x.- (4-d r ) 0—61 7) 2

 

i=1,2;j=1,2;i¢j (7)

27

In this model, both the revenue function and the cost function are convex.
To make it a well-defined maximization problem, the cost function must be more

convex than the revenue function, or the following conditions must hold.

2(2 - dys 4’72): <1
((172 -4)2(1 #1272)

 

Lemma 3: The second order condition of (7) holds if

 

4—272 —\/32—48y2 +18y“ —2y"
27

 

With a pool this condition is s > . Without a pool

 

7 —(53-6\/7—8)"’3 —(53 45M)“
3% '

 

the condition is d < \/

Proof. See the Appendix A.
The above restrictions will apply to the rest of the analysis of the model.
The best response functions can be derived from the first order conditions as

follows:

Z +2(2—dsy—d272)(d7 +d272s —2s)xj
x :
‘ d°y°—7d‘y“+4d3y3s+2d2y2(8+s2)—8dys-8

 

(8)

Where, Z = 2(2—dys —d2}/2)(d2y2 +d7-c(2-dy—d2y2)—2)
Notice that the relationship between x1 and x2 in (8) is ambiguous; it

depends on the pooling structure and the values of the parameters. I have found
that following lemmas hold.

Lemma 4:

 

4—272 —\/32—4872+1874—276 <S< y

With a pool, if
27 2-7

 

xI and x2 are

1 ’

strategic substitutes; if s > x, and x2 are strategic complements. Without

2 9

28

 

 

7 - (53— 6M)“ - (53 — 6%)“

a patent pool, as long as the SOC holds, d < J 3
7

x1 and x2 are strategic substitutes.

Proof: See the appendix A.
Strategic substitutes and complements reveal whether one firm’s marginal
profits increases or declines corresponding to another firm’s more “aggressive”

investment strategy. Lemma 4 shows that when there is no pool, x1 and x2 are

2
I

6xj6xj

 

simply strategic substitutes, that is < O, and the strategic effect of

investment is to make the competitor play less aggressively in the second period.
Once there is a pool, this strategic relationship will be contingent on the
magnitude of the spillover effect.

Before solving the model, I can write the output level as a function of
x] and x2 as follows:

2+23xj -d}/--dxj}/—d2}/2(1«l-SJCJ.)+c(d2}/2 +d}/-—2)—)cl.(d2}/2 +dsy—2)
i— 4—5al272+d“y4

 

6Q, _ -(dzr2 +dS7-2)
ax, 4—5d272 +d‘y“

 

 

Since > O, for anyd 6 [0,1],}! 6 [0, 1], s 6 [0,1] , the

investment increase has a positive effect on firms’ own output. The reason for this

is, x, in this model can directly reduce the production cost and thus intensify the

price competition. To offset the negative price effect on revenues, firms choose to

produce more. I summarize this result in Lemma 5.

29

Lemma 5: Firm i ’3 output levels, Q. , increases in its own investment level xi.

Now solving the maximization problem, we can obtain the following results:

x _ 2(c—1)(d2y2 +dys—2)
' (dy—2)2(d372+3d7+2)+2(s+1)(d2y2+dys—2)

 

” = (c-1)2(d272-4)2(l-d272)
‘ ((d7—2)2(d272 +3d7+2)+2(s+1)(d272 Mos—2))2

 

(c—l)’((d’72 -4)2(1-d’72)-2(d272 +d75 -2)2)

': 11
' ((dr - 2)2(d272 + My + 2) + 2(s +1)(d2y2 + d7, _ 2))2 ( )

 

d =1,and s 6 (0,1], with a pool
Where,
d 6 (0,1), and s = 0, without a pool

111.4 Pooling decision and equilibrium analysis

As in model one, the two universities share the net profit evenly. Thus, UA
and U3 will compare 1'1,” and 1'1? to decide whether to pool or not.

The model I have calculated above is basically a game based on the
interplay of the spillover effect and the differentiation effect. To understand the
final pooling decision in equilibrium, we need to find how those two effects
determine the investment level and the net profit first. Intuitively, when
competition intensifies, firms’ incentive to invest in R&D decreases because
consumers will gain most of the benefit from their investment. With the increase
of the differentiation level, firms can get more profit in the final product market.
Thus, the marginal revenue of each investment level increases, keeping all
parameters fixed. Higher investment level leads to more cost reduction, which will

increase the net profit. So we have Lemma 6:

3O

Lemma 6: Prices, the investment level and the net profit are all decreasing in the

. . . . 6P 5 H
differentiation effect, (I ; that is, —’ < O, 3'— < 0 and 2— < 0 , for any 7, 7 6 (0,1).
ad 6d 6d

Proof: see the appendix A.

Next I analyze how the spillover effect, 3 , can influence the investment
level, investment cost, revenue and the net profit. Since the change of the spillover
effect is relevant only under pooling circumstances, I set d =1 while doing the
following comparative analysis.

Lemma 7: Firm’s investment level x, and investment cost Cost, has the

following relationship with the spillover effect 5, for any 7, ye(0,l): if

 

 

 

 

_ 2 _ 2 6x. 6Cost.
s 2 4 27 + (7 2)\/2y(2 +3}, + y ) , then —' S 0 and ' S 0. Otherwise,
27 as 65
6x, 6Costl. . .
— and are posrtive.

as 63
Proof: See the appendix A.
The increase in spillover effect can directly reduce the production cost by
benefiting from the other firm’s investment; thus, firms have the incentive to
reduce its own investment level and the investment cost when such an effect is big

enough. That is the intuition behind lemma 7.

. 2- — 2 6P. 6R. .
Lemma 8: For any 7, ye (0,1), if s Z—g—L’ then -—’20 and -—'sO, i.e. the
7

as as

price is decreasing in the spillover effect, and the revenue is increasing in the

. 2 — — 2 6P 8R.
spillover effect. If s < ——7—}:- , then —’ < O and ——’ > 0.
27 as as

31

Proof: See the appendix A.

To understand how 5 affects P, let’s begin with the analysis of the

l

2—72—7+2C +yC
= 4 2' 2 , where C,(xl,x2)=c—(xi+sxj).
‘7

 

:0

equilibrium price

Since P. is increasing in C, and Q. is decreasing in s, spillover effect has a direct

negative influence on B. However, the spillover effect also influences B through
xi. From the above expression, we know thatP, decreases in x, , but x, has an

ambiguous correlation with s, as stated in Lemma 7. Combining the direct and

indirect influences, we can derive the sign of Z—P’. Similar analysis applies to
s

R _(2-7’-7+(7’—2)C,-+7Cj)2
' (4—7’)’(1—r’)

 

, with opposite influences though.

Lemma 9: Firm’s net profit III. has the following relationship with the spillover

effect 3: for any 7, ye(0,1): if szh(y), $2230; if s<h(y), EEL>O, where
s s

h(y) solves for 9511’— = O and is a function of y.
s

Proof: see the appendix A for the proof and h(7).

To understand Lemma 9, I use figure 4 to illustrate the influence of the
spillover effect on the investment level, investment cost, prices, revenue and net

profit, followed by a discussion.

32

Spillover effect 5 (1,1)
1

 

L5 L4 L3

L2

 

 

 

0 l 7
Figure 4: how the spillover effect influences x, Cost, R, P & H

(When changing 7 under pooling structure)

In figure 4, there are 5 lines:

 

4—272 —\/32—4872 +187‘ —27°

 

 

 

L1 is s = 2 and SOC holds above L1;
7

L2 is s = 2 7 2 and x1 and x2 are strategic compliments above L2, i.e. when

‘ 7
s > 7 2 . Any point between L1 and L2, xl and x2 are strategic substitutes.
L3 is s = h(7). Above L3, ~61; < 0. And below L3, 6_l'l,_ > O.

as as
2

L4 is nil—L. Above L4, 9520 and 53530.

27 as as

 

_ 2 _ 3 a 6Cost.
L5 is 3:4 27 +0, 2)\/2}I(2+37+7 .AboveLS, 35-30 and '<0.

27 as as

 

 

33

Note that above L5, investment level xi and investment cost begin to
decrease in s. But the total revenues continue growing and prices continue
dropping until 5 reaches L4. Above L4, cost decreases faster than the revenue and

we can still observe that 1'1, increases in s , but the influences of dropping x, on
the net profits have two possible directions to go. If s falls into the area above
both the L4 and L2, then x1 and x2 are strategic complements. Thus, a reduction

of investment level in one firm will induce the other firm to adopt the same
strategy and the dropping of the investment level will cause the net profit to

decrease in 5 once reaching 5 = h( 7). We can observe that L3 and L2 converge at
point (s,7)=(l,l). If 5 falls into the area above L4 and below L2, then
x1 and x2 are strategic substitutes. Therefore, a reduction of investment level in
one firm will induce the other firm to invest more. As a result, the investment level

will not drop too much and the net profit still increases in s.

If there is no such area as that above L3, then we can use the same method

as in the first model to obtain the equilibrium of the game. Combining 26%— < O

and fl>0, we can find a unique critical value of

as

s = G(d,7*) for any 7*6 (0,1), such that when s > G(d,7*) , firms pool their
patent; and when s < G(d, 7*), firms do not form the pool. To find .9 = G(d, 7*) ,

solve s for I'll” =1'If. I.e.

8—16d272 +7d"74 —d°76 _ 8+857—2(8+s2)72 —4s73 +774 —76
(4+4d7—4d272 —d373 +d’7’)’ (4+47+2527-472 — 73 + 7’ +2s(y2 + 7-2))2

 

 

34

The result in Lemma 8 stops us from making the conclusion too fast. We
need to worry about whether in the area above L3 the net profit with a pool
decreases so much that when reaching 5 = 1, it is even lower than the net profit of
the firms without forming a pool. Thus I must check the uniqueness of the
solution. Simply set d = 1 and s = l to compare the lowest net profit under no-
pooling structure and the pooling structure at s = 1. The latter could be the one that
has been increasing with s, or the lowered level ifs falls into above L3 area.

Since I'li(d =1)—H,(s =1)

_ 87’ +78 +4376 +10075 +12072 —2y'° —4677 4727‘ -87’ —327—16 <

0
72(4-3r+7‘°')2(4+47-472-7’+7’)2

 

I rule out the situation that multiple equilibriums exist. Concluding the above

analysis, we have:

Proposition 3: There exists a function s =s(d, 7) as a solution of Hf”) 21-1,? ,
for any 7 6 (0,1), such that when s > s(d,7) , Hf”) < Hf), 1': 1,2 firms pool their
patent; and when s < s(d, 7) , Hf”) > Hf), i = 1,2 and firms do not form the pool.

And E(y29d)>§(}/1961) {fl/2 >71 for any dad 6(0,1)

As shown in figure 5-1, line 5 =s(d,7) splits the whole space into two

areas in equilibrium: pooling zone and no pooling zone according to firms’
choices. Figure 5-2 illustrates how the equilibrium pooling structures change with

7. More specifically, the smaller 7 is, the lower the basic substitutability of the two

35

products, and the more reluctant patent holders are in forming a pool. In an
extreme case, 7 = 0 and the firms are doing research on independent products;

then they always choose to pool the patents and get benefit from the spillover

effect.

S

1 1 (1,1)

 

—Pooling zon

s = s(d,7)

No Pooling Zone

 

 

 

 

 

0 1 0 1
d d
Figure 5-1: Equilibrium of Pooling Structures Figure 5-2: Equilibrium Pooling Structures
(fiXing'Y) (71<72)
The last part of the analysis is welfare comparison under different pooling
structures. I use net profit as an index of producers’ surplus and by subtracting

producers’ surplus from the total social welfare, we obtain the consumers’ surplus.

I summarize our analysis in the following proposition.

Proposition 4: Welfare comparison.

1) There exists a function 3 = 3(d, 7) as a solution to CS N" = CS P such that

when s > s(d, 7), consumer surplus is higher under no pooling regime.

36

2) There exist values of the spillover effect and differentiation effect

combinations such that:

CSNP >CSP and TI” >I'IP (Region A)

CSNP > CS” and 11”” < 11” (Region B)

CSNP <CSP and 1'1”” >IIP (Region C)

CSNP <CSP and H” <I'IP (Region D)
Proof: see the appendix A.

Proposition 4—1) shows that consumers prefer no-pooling solution when the

spillover effect s is moderate to high. The explanation can be found in Lemma 8:

. . . . 2 — — 2 . .
prices increase in s if s 2 __}2_'_7' So, when s is moderate to high, consumers
7

will expect higher prices in product market and cannot benefit from firms’ patent
poohng.

To get proposition 4-2), I plot the curves of s = s(d, 7) and s = s(d, 7) in d
and 5 spaces as in figure 6.

As shown in Figure 6, the two functions intersect each other in the interior
of the unit square. Above the s = Em, 7) or in area A and B, consumers prefer the
no-pooling solution; and in area C and D, consumers prefer the pooling. For the
firms, they prefer the no pooling solution in area A and C, which is below
s = s(d, 7) and prefer the pooling solution when above s = s(d, 7), or, in region B

and D.

37

S (Spillover Effect)
1 (1,1)

Firms’ Pooling Zone

A

~ /
=d’
5“ all“
/

O l d
Figure 6: CS and PS comparison under different Regimes

 

(Approximate graph when setting 7 = 0.5)

An interesting finding in Proposition 4 is in region A both the consumers
and the producers prefer the no-pooling solution even though patents are
complements. In other words, we do not have as simple a relationship between
different pooling situations and the consumer surplus as in our first model. To
understand proposition 4-2), first let’s compare region A and B. In both areas,
consumers prefer the no-pooling solution, but the firms’ profit is higher only in
region B. The reason is, for fixed d , increasing synergy effect 3 will increase net
profit, according to Lemma 9. Thus firms have incentives to form pools to benefit
from higher spillover effect.

Now we compare region A and C. In both areas firms prefer the no-
pooling solution. According to Lemma 6, prices and profits both decrease in d if

there is no pool in the industry. Then why from A to C could consumers be better

38

 

off by forming a pool with the increase of d ? The key reason is, when s < 2 ,

2 - 7
x1 and x2 are strategic substitutes and firms, once with a pool, will overinvest to
make their competitor play less aggressively. Since output with a pool also
increases in investment, according to Lemma 5, consumers could benefit from
increased competition in the product market. Once the gain from firms’
overinvestrnent in R&D and increased competition with a pool surpasses the gain
from reduced prices with the increase of d without a pool, consumer surplus is
higher with a patent pool.

Compared with the first model, a big change is that in this model, the price
and the investment level are not only decreasing in the differentiation effect, but
also related to the spillover effect. The complication in welfare analysis arises
from a non-single relationship between firms’ R&D choices. Firms have a critical
value of spillover effect in mind, above which they react to the competitor’s
investment level as a strategic complement. They reinforce the investment cut and
output cut whenever their counterpart initiates it; that is why consumers actually
are worse off with a pool when the spillover effect is high.

Examples for the second model can be found in the vaccine industry when
firms make efforts in reducing the cost of producing gene-based vaccines. Since
different research units own different research tool patents, patent thicket problem
may impede the cost reducing innovation process as well. The policy implication
is, forming a patent pool can at least guarantee a higher consumer surplus in the
new product innovation case, but in the cost reducing innovation case, the

authority enforcing the formation of a patent pool runs the risk of making

39

consumers worse off. To avoid a situation that falls in region A where both
consumer and firms worse off with a pool, policy makers should have some basic
evaluation of the values of the spillover effect and the differentiation effect in a

given industry whenever they advocate patent pools as a solution.

IV. Concluding Remarks

This paper gives explanations for why — contrary to traditional economic
theory and government endorsements — there are no patent pools among
complementary patents in the biotechnology industry. The key reason lies in the
difference in characteristics of the underlying scientific knowledge between the
biotechnology industry and the industries with patent pools. Unlike the transfer of
embodied technologies in existing patent pools, inventions in the biotechnology
industry are disembodied and often held as patent specific knowledge by
researchers. Thus, technology transfer and further innovations can take place only
through the exchange or movement of human capital. In our models, that leads to
vertical cooperation between universities and dedicated biotechnology firms. The
question is, how has this innovation structure in the industry affected the
cooperation between initial inventors in universities and made patent pooling more
complicated than that applied to embodied technologies?

Forming pools for scientific discoveries can get patent holding scientists
more connected and thus provide more opportunities for information sharing. But,
I found that two tradeoffs arise and dampen the universities’ incentives for such

sharing. In the case of new product innovations, within a pool, research units may

40

choose closer R&D approaches or paths so they can maximize knowledge flows
between each other, which can weaken the originality of innovation and put the
two firms into more fierce competition in the product market. When a higher
differentiation level of products increases expected profit in the duopoly market by
more than profits increase due to the enhanced chances of getting innovation done
faster, universities will prefer to stay un-pooled.

In the case of cost reduction innovations, the industry benefits from more
spillover effects due to improved absorptive capacity among innovators, but firms
may suffer certain losses because the innovations are less likely to contribute to the

production of more differentiated products. If the industries are dominated by the latter
concern, then patent pooling will not be a choice in equilibrium.

In addition to offering theoretical implications, the analysis also suggests a
lesson for technology policy. Scientific innovation is much more costly to adopt
than are embodied technologies. Although “one-stop shopping” implied by a
patent pool looks beneficial to the patent owners and all the potential patent users,
a pool may intensify the competition to such an extent that it discourages patent
holders fiom pooling their patents. Forming a pool, and “thereby promoting R&D
and promoting competition,” can be realized in the biotechnology industry only if
the patent holders operate as non-profit organizations or a channel is created that
allows consumers to compensate the investors and innovators for the losses they
otherwise bear. As I show in the second model, even though firms compete in both
the product market and in R&D investment, patent pool can still make firms

and/or consumers worse off under certain parameter combinations. When the

41

situation arises that both consumers and producers are worse off by forming a
patent pool, advocating a patent pool is obviously not beneficial to society.

Our topic falls into the broader topic of inter-organizational cooperation. I
concentrate on the situation that universities and firms cooperate in transforming
scientific innovation into applied technology and try to understand under what
circumstances the horizontal cooperation (patent pooling) between universities is
comparable to their vertical cooperation with firms. There are several ways to
further this research that may generate some additional interesting results. One is
to relax the symmetry assumption of the firms. Firms differ in both their research
capacity and their absorptive capacity. If we allow for asymmetric synergy effects
or spillover effects in the model, we can illustrate how those asymmetries affect
the pooling decisions. The second path is to model the contribution of the patent
holders in the R&D cooperation process and endogenize the human capital input
level. Then we can relax the even-split profit assumption and that may change the
pooling decisions. Also, as there are only two universities in our model; it is still
unknown whether more patent holders make more options available among

participants in reaching pooling agreements.

42

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45

Appendix A

Lemma 1

67:“

1+ (7!” — 7:0 )(92

 

Proof: x. = x2 =

I

E): _ (1+62(7rD -7tM ))7rM _ (1—627rM +627rD))7rM
d6 — (1—192(7r" —7r’"))2 — (1—62(nD —7rM))2

1 ‘1
since 62 S 4, 7r” :1, l—B‘rtM 2 0.

6x. 93 M
’0: 2 if D 2>0,since7tM>7rD
67: (1+6 (72' —7r ))
a D 2 1— d2 2
7r _ 7( (17+ 7)<0

ad _ (d7-2)’(1+d7)2

 

 

 

We also have

So, —<0 Q. E. D.

Lemma 2:

— 62(7IM)2
1‘ 2 — 2(1+(7¢-M -JZ'D)62)2

 

dH. _ (—1—62(2r” —2r”))2r” _ (9an —1—1927r0))7?M > 0
d6 (62MB —7rM)—l)3 (620:0 -7t")_1)3

9

. 1
smce 62 S 4, 7r“ :2, 62”” -1S 0 and 7!” > 7!”.

611 (940!“ )2

l

= > 0, since 7r“ > n0
67:0 (1+ 920:“ - 7r0))3

 

67:0 _ 27(1—d7+d272) <0
6d (d7—2)3(1+d7)2

 

We also have

46

So, 3 < 0 Q. E. D.
6d

Proposition 1:

6(1 + d7)(2 — d7)2

2= 2 3 3 2 , , ,wecanset6=
16+4d76 +(d 7 -3d 7‘)(4+6‘)

 

Proof: from results (4), xI = x

 

A» (1+a’7)(2-a’7)2
1 d tX,.'= .Ad td=l, t
a“ ge 16+4d7+5(d373-3d272) n 86 wege
61+ 2— 2
xP ( 7X 7) . Solving the function

 

" _l6+4762+(73—372)(4+62)

(1+ d7)(2 - (1’7)2 _ 0(1 + 7)(2 - 7f .
3 3 2 2 - 2 3 2 2 , we can find the unique
16+4d7+5(d 7 —3d 7) l6+476 +(7 —37 )(4+6)

6 = f'(d) for any given 7*, 7*e(0, 1), such that when 6 < f(d,7*) , x,” > x? .
See appendix A for the whole expression 6 = f (d , 7*) .

Similarly, from results (5), we have

_ xf 62(1+a'7)2(2—d7)4

" 2 z2(16+4d762+(d’73—3d272)(4+62))2 '

 

(x,"”’)2 : (1+ d7)’(2 - d7)“
2 2(l6+4d7+5(d373—3d272))2

 

 

Set6=1,1_1;vp =

<fo = 6’(1+7)2(2-7)’
2 2(16+4762+(73—372)(4+62))2°

 

andsetd= 1, Hf=

(1+ 47)2 (2 - d7)‘ = «92(1 + 7)2(2 - 7)“
(16+4d7+5(d’7’ —3d272))2 (16+4762 +(73 -372)(4+ez))2 ’

 

Solve we have the

same unique function 6 = f '(d ) for any given 7*, 7*e(0, 1), such that when

6<f(d,7*), r1,” >rif.

47

9 =f"‘(d)=((7—2)(—32-8(2+d)7+2(8-2d+15d2)}’2 +d(4+15d—10d2)7’
—5d2(3+d)7‘ +5a’37’ + ,/1 + 7\/_(1024+512(d—2)7—1856d272 +32d(5d2 +
48d —12)73 + 4d(32 + 60d —128d2 + 265d3)74 — 8d2(10 — 33d + 72(12 + 7Sd3)75

+d’(—88 ~363d + 384a!2 +100d3)7" + d‘(121 + 162d — 64d2)77 -— 27d5(2 + (1)7"

+9d679)))/(27(d7 ‘2)2(1+d7)(4—37+72))

Q. E. D.

Proposition 2:

Proof: from utility function, U (q,, q,) = q1 + q2 — (q,2 + 2d 7qu2 + q22)/2 , we can

calculate the total social welfare under monopoly and duopoly market structure.

SW, = 3 SW, = 3+(2d—1)7—-2d272
8 (2+d7—d272)2

 

Incorporate the uncertainty issue, the expected social welfare is

(d7 — 2)262(12—6d373 +3d’7‘ —7192 “127W2 —9)+ 2d7(6 +62))
(16+ 4(17192 + ((1373 -3d272)(4+ 92))2

 

E(SW) =

The expected producer’s surplus:

2(d7 - 2)“ (9 + d719)2

E(PS)=2E(7Z’,.)= 2 3 3 2 2 2 2
(16+4d76 +(d 7 —3d 7 )(4+6‘))

 

2(d7—2)‘(1 + (17)2
(16+4d7+(d373 —3d272)5)2

 

Set 6 = 1, E(PS””) =

2(7 - 2)i (9 + 7&2

Setd=l, E(PS”)= 2 3 2 2 2
(16+476 +(7 —37 )(4+6 ))

48

Solve E (PS NP ) = E (PS P ) , we have the same solution of the function 6 = f '(d )
as in proposition 1.
The expected consumer surplus:

E(CS) .-. E(SW — PS)

_ (d7—2)262(4—2d’7’ +d’7“ —7192 +d’72(6—3)+2d7(2+62))
(16+ 421792 +(d37’ —3d272)(4+62))2

 

(d7—2)2(4—2d373 +d"74 —7—2d272 +6d7)
(16+4d7 +(d37’ -3d272)5)2

 

Set 6 = 1, E(CS”")=

Setd= 1, E(Cs”)=(7‘2) 9 (4‘27 +27 19 +2; (0-32)+227(2+6 ))
(16+476 +(}’ ‘37 )(4+9 ))

 

It can be shown that for any 7, 76(0, 1), we have E (CS P ) > E (CS NP ).

Q. E. D.
Lemma 3:

Proof: the second order condition of the objective function (7) is:

2(2 - ds7 —d272)2
(6122’2 - 4)2(1- 61272)

 

2(2-57-7’)2
(72 -4)2(1-72)

 

Under pooling circumstance, that is <1. Solve it, we get

 

> 4--272 —\/32—4872 +187’ —276

 

S

 

 

 

27
. . . 2(2-(IVY .
Under non-pooling Circumstance, the SOC is 2 2 2 2 2 <1 . Solve it
(d 7 -4) (1-d 7)
7— 53—6 78 "”— 53—6 78 ”3
we get d < ( f) ( f) . Q. E. D.
372

49

Lemma 4:
Considering an industry with a patent pool first. Set d = I .

The best response functions are:

z'+ 2(2 —sy— 72x7 + 723 —2s)xj

 

xi: 0 4 3 2 2
7 —77 +47 s+27 (8+s )—87s—8

(9)
where Z'= 2(2—s7—72)(7+72 +c(2—-7—72)—2)

In function (9), since (2 - s7 - 72) > 0 ,

(7+72s—2s)
—774+473s+272(8+s2)—87s-8

 

. dx .
Sign(;’)=81gn(y.

J

First, let’s decide the sign ((725 + 7 — 23))

 

 

 

d 2 -2
Note that ((7 S+7 S))=72—2<0
ds
Ifs> 7 (725+7—23)<0' ifs< 7 (723+7-23)>O
2— 2, 9 2- 2,

If s = Z—Z—Z’ (72s + 7 — 2s) = 0 ; then xI and x2 are independent.
“ 7

Next, we use A to denote the denominator 76 — 7 7" + 473s + 272(8 + s2 ) — 8 7s — 8

and decide the sign (A)

 

al(76 —774 +473s+272(8+52)—87s—8) < 0
ds

Note that

 

<4—272—J32—4872+187‘

2 _ 27 , A > 0; but SOC does not hold. We rule out
7

 

Ifs

this situation.

50

 

>4—272—\/32—4872+l87’
27

 

Ifs _27 ,A<O

We summarize the above analysis in Lemma 4. Q. E. D.

Lemma 5:

Proof: set s = 0 in function (7), we have the following best reaction function:

u 2 2
x. = Z +2(2—d 7 )d7xj
' d‘r’76 —7d’74 +16d272 —8

 

(10)
where Z": 2(2—d272)(d272 +d7—c(2—d7-d272)—2)

Note sign (5%) = sign (d676—7d474+16d272—8), since 2(2—d272)d7>0
j
for any (I and s.

6(d‘r’76 — 7cl’74 +16d272 —8)
5d

 

= 32d72 +6d576 —28d374 > 0

 

 

7 —(53—6fl)"” -(53-6J7§)"’
2

Solve d676—7d474+16d272—8=0,d=\/ 3
7

Thus, we can summarize the relationship between itl and x2 in Lemma 5.

Q. E. D.
Lemma 6:

The differentiation effect is effective only under non-pooling circumstance; s = 0.

at; _ (c-1)d72(24+127—16d272 —9d’y’ +2d‘y‘ +d575) < 0
ad (4+4al7—4a7272 -d373 +di74)2

 

an, _ 70-0212 -d7)(1+d7)(d’76 +3257: -d’7‘ 4W} '8) < 0
ad (4+4d7-4d272-d373+d474)3

 

 

51

3 __ (1 —c)7(2d575 —d"74 —8d373 +2d272 +8d7—8)

I

6d (4+4d7—4dz72—d373+d‘l74)2

 

<0 Q. E.D.

Lemma 7:

 

Qfl __ 2(1-C)(8—8(1+s)7+2(sz —6)72 +(6+4s)7’ +374 _75)
as (4+ 47 + 257-47’ -r’ + 7“ + 2.962 +7-2»2

aCost, _ 4(1 —c)2(2—s7— 72)(8-8(1 +s)7+ 2(s2 -6)72 + (6 + 4s)73 +37“ —7’)

 

 

as (4+47+2527-472—73+74+25(72 +7-2))’
. . _ _ . x, 6Cost,
Since the nominators are posmve, the Signs of both — and are same as
s s

(8—8(1+s)7+2(s2 —6)y2 +(6+4s)73 +374 —75).

Notice that (8 —8(1 + s)7 + 2(s2 -6)72 + (6+ 4s)73 +374 —75) is decreasing in s

 

4—272 +(r—2)fiy(2+37+72

2 , which is also the condition
7

 

and it’s negative if s 2

for 9+ S 0 and 6Cost, S 0. Q. E. D.

as 85

 

Lemma 8:

51? _ 2(c-l)(7’+72 -47'-4)(72 +7+237-2)
as (4+47+2327—472—73+7’+2s(7+72—2))2

 

Its sign is as same as that of (72 + 7 + 2s7 — 2), which is increasing in s.

2 _ _ 2
Wecangetifszu,£>0;ifs<g——7——y—,then gig-<0.

27 as 27 as

5R.- _ 4(c-l)2(72 -4)2(72 —1)(72 + 7+ 257-2)
as (4+47+2s27—472 —73 +74 +2s(7+72 —2))3

 

 

Its sign is as same as that of (2 — 7 — 257 — 72) , which is decreasing in s.

52

_ _ 2 __ _ 2
WecangetistZ—yi,§§L<0;ifs<2——y—Zl—,thenfl>0
27 63 27 as
Q.E.D.
Lemma9

6T1, __ 4(16—3272 +473 +23373 +247’ —75 -876 +78 +6s272(2.2 -2)+I
as (4+47+ 2s27—472 —73 +74 +2s(7 +72 -2))3

 

 

Where I = s7(27° — 75 -1174 + 673 + 2072 —87 —8).
The nominator is positive and the sign depends on the denominator. Constrained

by our assumption that s 6 (0,1) , there is only one valid solution 5 = h( 7) such

that ifs 2 h(7), iall S 0 and ifs < h(7), % > 0. The solution h(7) =
s s

 

 

2
7 2 _22 4 4 7 3 2“1 _ 3 .
((2472(2_7-)+ (7 )7 (27 + 7 +37 07 8)6(1+t\/3)

1
+2163 i+\/3 B
247’ B ( ) )

Where

 

B = (7—2)37‘5((2+37+72)m\/3(l676 +2475 —577’ —6773 +8772 +697—74)

+975 + 457‘ + 6373 —972 — 727 — 36))”3

Q. E. D.

Proposition 4:
From utility function, U (q,,q2) :2 q1 + q2 — (q,2 + 2d 7q1q2 + q,2 ) / 2 , we can

calculate the total social welfare. We use net profits as an index of producers’

surplus and subtract it from the total surplus to obtain the consumer surplus.

53

(c — l)(d272 — 4)T

Total Surplus = Y

_ 2 2 2_ 2 _ 2 2 — 2 2 _22
PS(d,s,7)=2ni = 2(c 1) ((d 7 4) (1 dyy ) 2(d 7 +d7s ) )

(0 -1)(T(d171 — 4) - 2(6 -1)((d271— 4)2(1- £1272) - 2(0’272 + d7s - 2)1))
Y

CS(d. s, 7) =
Where, Y = ((d7 — 2)2(al272 +3d7 + 2) + 2(s +1)(cl272 + d7s —2))2

T = 4 + 4d7 + 4d7sz — 7d27z —d373 + 2d’7‘ + 4s(d171 +d7 — 2) —c(d373 +d’72 —4d7 —4)
To compare the consumer surplus under no-pool and pool condition, we need to
solve function CS(d, 0, 7*) — CS (1, s, 7*) = 0 . And we denote the solution by

s = K (d , s, 7*). Setting 7 = 0.5, I conducted a simulation and the result is shown

in figure 7:

 

s = K (d, s, 7*)
Figure 7: Consumer Surplus Comparison Under Different Regimes
On this graph, Consumers surplus is higher without a pool in the area with light

blue squares. Similarly, we compare the producers’ surplus and get the function

54

s = G(d,s, 7*) as the solution of PS(d,0, 7*) — PS(1, s, 7*) = 0 . We can illustrate

the simulation result when 7 = 0.5 in the following graph.

 

s = G(d,s,7*)

Figure 8: Producer Surplus Comparison Under Different Regimes
On this graph, firms prefer not to pool their patents in the area with light blue
squares. Combining the solution 3 = G(d,s, 7*) and s = K (d, s, 7*) , we can get
the figure 6.

Q.E.D.

55

CHAPTER 2

INCOMPLETE PATENT POOLS

I. Introduction

In intellectual property (1P) law, a patent pool is a consortium of two or more
companies agreeing to cross-license patents and other IP rights relating to a particular
technology. Its recent applications include MPEG-2', DVD 6C2, DVD 4C3, and 13944
standard patent pools. In August 2005, a patent pool was formed by about 20 companies
active in the Radio Frequency Identification (RFID) domains. For the creation of these
large consortiums, competition law issues are usually a major concern; and these patent
pools all have been affirmed by the DOJ and the USPTO. In the field of economics,
patent pools’ efficiency aspect especially gained attention. It has been generally agreed
among economists, since the first study of Coumot (1838), that selling complements
separately will lead to higher prices than bundling and selling them by a monopolist,
because separate parties fail to incorporate the pricing extemality, i.e. the benefit of a

price cut on the other’s sales. Accordingly, since essential patents used in a technology

 

' The MPEG-2 patent pool was created in July of 1997. MPEG-2 includes the fundamental technology for
the efficient transmission, storage and display of digitized moving images and sound tracks on which high
definition television (HDTV), Digital Video Broadcasting (DVB), direct broadcast by satellite (DBS),
digital cable television systems, multichannel-multipoint distribution services (MMDS), personal computer
video, digital versatile discs (DVD), interactive media and other forms of digital video delivery, storage,
transport and display are based. The technology in MPEG-2 compresses digital information by reducing
spatial and temporal redundancies in the binary data streams, thereby conserving transmission resources
and storage spaces.

2 In this patent pool (1999), Hitachi, Ltd., Matsushita Electric Industrial Co., Ltd., Mitsubishi Electric
Corporation, Time Warner, Inc., and Victor Company of Japan, Ltd., agreed to license their present and
future essential patents for compliance with the DVD-ROM and DVD-Video formats to Toshiba
Corporation (Toshiba).

3 Under this patent pooling arrangement(l998), Sony Corporation of Japan (Sony) and Pioneer Electronic
Corporation of Japan (Pioneer) agreed to nonexclusively license all essential patents necessary for
compliance with DVD Standard Specification to Koninklijke Philips Electronics, N.V. (Philips). And LG
Electronics joined the pool recently.

4 The 1394 Standard is a new, very fast external bus standard that supports data transfer rates of up to 400
Mbps.

5 Wikipedia.org.

56

are complements, the social incentives and private incentives to form a patent pool are
completely aligned and we should observe that all essential patent holders are willing to
form one complete patent pool.

Although this is the very assumption used in the existing papers about patent
pools, that is not the case in reality. For example, Lucent Technology, as a leading firm in
MPEG technology, has not joined MPEG-2 patent pool; Thomson, owning many must—
have multimedia technologies, has not joined any DVD patent pool either; and
Qualcomm, with an extensive portfolio in CDMA technology, has been staying away
from any wireless patent pool. The obvious inconsistency between theory and phenomena
became a major source of motivation for my research on this topic. If pooling patents can
internalize the price extemalities, speed up technology adoption and benefit both the
licensors and licensees, why does not every essential patent holder jump into the pool?
What are the major concerns in deciding to form or join a patent pool? How is the
incomplete patent pool related to the technology transfer and generation and how will it
influence social welfare? This paper is an attempt to address these questions.

Two important simplifications in existing patent pool literature restricted our
understanding of incomplete pool phenomena: one is symmetric technology capacity and
the other is static patent market. Symmetric technology means that firms are competing in
the same markets and have symmetric reaction functions. In reality, however, asymmetry
regarding technology capacity and patent assets is more commonly observed. And static
market implies that firms are purely maximizing profit in either a price-setting or a
quantity-setting competition; and their current strategic choice will not influence their

market conditions in the fiiture. In licensing market, however, licensees are not entering

57

the market all at the same time. They may choose a later technology adoption concerning
either the current price or the future technology improvement; and some new application
of certain technology can generate new markets too. The licensors, on the other hand,
cannot and will not commit to a long-tenn contract, also based on the possible
technological improvement and market dynamics in the future. As we observe in real
cases, they will adjust the prices periodically and face a new market again and again.
Since the existing customers will usually reenter the same technology market in the next
period constrained by the switching cost, the size of earlier market will influence that of
the later market. Thus, licensors are not just competing in price; they must take into
account of the market share to make maximum profit in the long run.

The major contribution of this paper is to relax these two strong assumptions and
bring some new insights into the economic study of firms’ pooling decisions in marketing
their patents. The main findings of this paper are: 1) when asymmetry of firms’ stakes in
product markets and the market dynamics are incorporated into the maximization issue,
incomplete pool can be an equilibrium in a two-stage price setting game. 2) Royalty rates
are set lower in the earlier stage so as to positively affect early technology adoption; but
in the later stage, when licensors are less concerned with the market share, the prices are
set at a higher level. 3) Although incomplete pool structure is associated with lower social
welfare ex post, a complete pool structure may reduce firms’ incentives to innovate in the
first place, or induce the firm to foreclose; thus, it is not socially desirable ex ante.

I adopted the model from Economides and Salop (1992) and revised it into a two-
stage model. This paper is also closely related to Lerner and Tirole (2004). They provide

necessary and sufficient conditions for patent pool to enhance welfare and examine when

58

requiring pool members to be able to independently license allows the antitrust
authorities to use this requirement to screen out unattractive pools. A major difference is
that their model allows licensees to drop some essential patents to produce substitutes;
thus there is a competitive margin constraining each patent holder. In my model, essential
patents are perfect complements and production of final products is impossible if any of
them missing. Besides, Lerner and Tirole (2004) does not consider market dynamics.

Among other recent literature on this topic, Choi (2002) shows why firms have
incentives to form a patent pool in the presence of uncertain validity of patents that
makes disputes inevitable; Shapiro (2003) proposes a specific antitrust rule limiting the
settlements of patent disputes including patent pools so that consumers will be left as well
off as they would have been from ongoing patent litigation. We are using different
models in addressing different questions about patent pool.

The discussion of the pooling memberships in this paper also refers to the branch
of literature about coalition formation. We differentiated open membership and closed
membership rules. Yi (1995, 1997) and Bloch (1996) have analyzed those games in
detail. In this paper we applied the concepts defined in those papers in a new situation.
The profit maximization and split rules we used in this paper are from “The Shapley
value for n-person cooperative games with transferable utility (1953)” discussed in J .W.
Friedman’s book, Oligopoly and the Theory of Games (1977).

This paper is organized as follows. Section II is the basic model description.
Section 111 gives basic results and analysis on profit, prices and social welfare. Section IV
extends the model to discuss firms’ innovation incentives and foreclosure decisions under

different pooling structures, and the effect of profit split rules. Section V concludes.

59

II. The Model

[1.1 General setting and assumptions

Consider three firms, A, B and C, each holding patent fl, 8, C, respectively.

These patents form a Leontief fixed-proportions production technology and enable the

downstream firms to produce product I by using all of them. Firm C is different from the

other firms in that it also holds some patent or patent package D, either including patent c

or not, that is essential in producing product 11. Product I and II are substitutes. Thus, firm

C owns two competing technologies. See figure 1 for a general illustration.

 

 

 

 

Upstream
F irms: Firm A Firm B Firm C
Patents: 3‘ B C D

 

 

 

 

 

 

 

 

 

 

 

 

Final Product:

Figure 1: Relationship between firms, patents and products
Licensors are competing in a price setting. They do not produce themselves;
instead, they license the technology to the downstream licensees and collect the royalty
revenue. The licensees will produce at a marginal cost of zero. We assume that
downstream product market is perfect competitive, thus the product price will equal to
the total royalty rate paid by the licensees for the patents used in producing that product.
Licensees enter the licensing market sequentially due to the evolving technology

application or improvement. Since the licensors cannot commit to a long-term licensing

60

contract, they will sell their patents more than once during their lifetimes. Here we
assume the patents are put into market twice, so the game has two stages. And licensees
can choose to enter the technology market in either stage. We normalize the potential
market size for each product to 1 in the first stage. In the second stage, the market is
composed of two parts: the new licensees and the existing licensees from the first stage.
The new potential market size is a , which can be either smaller or bigger than 1; or
actually measures the perceived relative market size for certain technology. If a is
different between two technologies, then we may also generate some interesting insight
in understanding firins’ pooling decisions. And here, for simplicity, it is treated as an
exogenous variable and same for two technologies in this paper. The existing customers
of one technology will reenter the licensing market of the same technology, since we
assume that there are considerable switching costs between two production technologies.
So the total potential market in the second stage is the sum of a and the demand in the
first stage.

Besides pricing policy, each firm also has another strategic choice in the
beginning of the game: to form a patent pool with other firms or to compete individually.

And firms’ choices will determine the market structure in the upstream technology

markets and consequently the product price in the final product markets. Since patents fl,

8, and C are perfect complements, allowing firms to license individually does not change

the results and for simplicity of the model, we will rule out that case.6

Other important assumptions in this paper are:

 

6 Here I use the results from Lerner, Josh and Tirole, Jean (2003).

61

1) All licensors are maximizing total profit from two stages; none of them is
shortsighted; and discount rate is set at l.

2) Licensors cannot “poach” the current customers of their competitors by
offering them special discounts or other inducement to switch.

3) There is no price leader in the industry.

4) We assume that the pooling structure determined in the beginning of the first

stage game will remain unchanged in the second period of game.

11. 2 Timing, strategies and rules of the game

The timing of the game can be divided into three steps as follows: first, all firms
make decision about pool formation; second, based on the pool structure, firms or pools
make decision on prices charged in the first stage market and the second stage market;
and third, after two periods, profits accrue and are split among pool members.

The set of players is denoted by F; a pool M is a nonempty subset of three players
and we also denote the set of the pool member as M. More specifically, M = {A}, {B},

{C}, {AB}, {AC}, {BC}, {ABC}.

Definition 1: A pool (coalition) structure .0," ={M1, M2, M1}, m=1,2,3,4,5, is a

partition oftheplayer set] ={A, B, C}. For i373 M, O M]- : Zand ELM, = I.

The index 1' refers to the players, and the index m refers to the pool structure.
The set of all pool structures is denoted by Q. There are five possible coalition

structures in our model. That is Q ={Q], £22, (23, Q4, 05}, where Q] ={A, B, C}, Q;

62

={AB, C}, (23 ={ABC}, Q4 ={A, BC}, 95 ={B, AC}. Since A and B are identical, Q4
={A, BC}: 95 ={B, AC}.

We classify the above five structures into three categories: independent structure
— Q], complete pool — Q3 and incomplete pool — (22, Q4 andQs. Sometimes in the paper
we simplify them as IND, CP and ICP respectively. To further differentiate, Q4 and 05
are both asymmetric incomplete pool, or we call them AICP while (22 is symmetric
incomplete pool, SICP.

Gains from the game are described by a valuation v, which maps the set of pool
structures .0 into vectors of payoffs in V(.(2). The component v,(.(2,,,) denotes the payoff
obtained by player i if the coalition structure .(2 is formed.

Now let’s define the rules of the game for every step of the game described above.
11.2.1 Pool formation rules

The game will be analyzed under two pooling mechanisms: open membership and
closed membership. I assume that no firm can belong to more than one pool. Since there
are three firms in the game, only one pool can be formed.

Open membership game: under this regime, three firms in the first stage of the

 

model simultaneously announce whether they want to join a coalition. The resulting pool
consists of all firms who wish to enter.

Closed membership game: this is also referred to as exclusive membership game
and the firms in a pool are able to exclude rivals from their coalition. In our model we
require total unanimity as analyzed in Bloch (1996). The closed membership game is
usually modeled extensively by a sequential protocol of proposals and

acceptance/rej ection decisions.

63

In this model, the game begins with any of the three firms chosen randomly by
nature. For simplicity, we use the order alphabetically among firm A, B and C. So firm A
proposes a coalition T to which she belongs along with some of the firms. Firms
receiving the proposal are asked sequentially for their approval. If all firms accept, the
coalition is formed. If not, the first firm who did not accept will make a new proposal,
and so on. In order to guarantee the game to stop, we assume that every firm makes only
one proposal. If none of the proposals are successful, no coalition is formed. The game is

shown in the following tree (figure 2):

Figure 2: Game Tree: only one choice/decision for each firm

A
A ABC
AB AC
BC YBB/B\YC
C
Y N C 3 BC C C13BYB:[:\CNCY
{A}{BC} CIND c C {AB}{C}B B B AC C C {ABC}
C C N
[ND IND

64

To model the closed membership game, I apply two rules here: first, if a firm
claims to prefer to be a single firm, then she has to leave the coalition formation game
and will not be included in any other firm’s pool proposal. That is, a pool newly proposed
by a player F must be a subset of the remaining players to which F belongs. Second, if a
coalition structure available to a firm but not chosen in the earlier stage, it will never be
proposed in the later stage again by other firms — in other words, no firm has the second
chance to choose over the same coalition structure.

Notice that in this model three firms are not symmetric or ex ante identical. Thus,

we cannot reduce the game into a “size announcement” game.7

11.2.2 Profit maximization rules

The profit maximization rules need to be specified for this model because the
three players are not symmetric. For any singleton, profit maximization is always
pursued. But two issues can arise after a pool is formed: one is the anti-trust concern,
another is the potential conflict between asymmetric pool members over control right of
the pool. This paper makes the following assumptions on these issues: patent pool will
maximize the total profit as long as it does not violate anti-trust law. Since anti-trust law
generally does not allow substitute patents to form a pool, this assumption means that if
all three firms form a grand patent pool, they can only maximize the profit over product

or technology I and firm C must individually make price decision about patent (I. Also, if

 

7 According to Bloch(l996), the infinite-horizon Unanimity game of alliance formation yields the same
stationary subgame perfect equilibrium coalition structure as a “Size Announcement” game. In other
words, each firm’s proposal of alliance to which it wishes to be a member is equal to a partition choice. So,
I decide to use their results to solve the reduced game as shown on Figure l.

65

a pool includes any asymmetric firms, neither of them have the controlling power with
regards to the patent pool pricing policy.
I use the following notations:

H: the set of patent or packages for product I. H= {5"1, 8, C, 5’13, 5‘10, 8 C, and 5180}

7‘ 71,1, : the royalty rate for separately marketed patent or patent pool H j in period t, where
H j = 31, B, C, .3118, 51C, 8 C, and .7180 and t = 1 and 2. For complete patent pool flBC,
the price will be simply put as r‘.

I“; : the royalty rate for patent d in period t, t= 1, 2.

P1: : price of product k in period t respectively, k = I and II and t =1 and 2. And the price

of product equals to the sum of royalty rate related to that product. So, product II’s price
I 2
in the first period is always r d and in the second period rd , while product I’s price is

determined by the different pooling structure. P,’ (0",)=Z::1 7;,1 (QM) . For i773 H .- (l
H}. = gone 2):-1 H j = (31, B, o).

D; : demand of product k in period t, where k = I, II and t = 1, 2.

I assume the own-price elasticity of demand for each product is 1 and cross-price
elasticity of demand is e. Let 0 < c < 1 to make sure that product I and II are gross
substitutes. More specifically, the demand functions are:

In period t, t = 1, 2:

D; =(t-1)a+l-P,' +cP,;
Dj,=(t—1)a+1-P,;+cP,’

66

The above demand functions reflect the phenomenon that we observe that firms’
first period prices will not only determine the current market share, but also directly

influence the second period’s market size.
’11,. , r, rd, [1 , D, : benchmark royalty rates and prices when there is only one period. I
will use these notations to compare the two-period model with one-period model in
equilibria analysis.

Single firm or pool M,- chooses 7”], and/or rt; whenever relevant, where M, e {2",
to maximize the profit they can earn from one or two product markets.

The maximization problem can be generalized into three cases:
Case 1: only product I market is relevant. This applies to firm A and B in (21 ={A, B, C},
pool {AB} in Q; ={AB, C}, firm A in Q4 ={A, BC}, and firm B in (25 ={B, AC}.
117?}: vM(Q,,,) =Zf=1rih((t_l)a +1— 2le r]; + crd')
Case 2: only product 11 market is relevant. This applies to firm C in Q3 ={ABC}.

ng VM(Qm)=th_lr;((t—l)a+l-r;+621,17,11.)
rd __ I: l

Case 3: both product markets are relevant. This applies to pool {BC} in Q4 ={A, BC}

and pool {AC} in (25 ={B, AC}.

Max 714(5)...) =Z:l[r,',i ((t—l)a+1—Z:=lr,',i +crd')+r; ((z—1)a+1—p;; ”2:1 4', )1

The maximization problems under different pooling structure can be found in detail in

Appendix B.

67

II.2.3 Profit sharing rules.

In the real world, pool profit is often split over patents equally and the profit
earned by each member simply is calculated by profit per patent multiplying number of
patents held by each member. But this method ignored the strategy asymmetry issue in a
pool. Ideally, a value function should be found to assign each player a value that reflects
the contribution made by that player to all the pools of which she is a member. And we
apply the concept “marginal value of a coalition” studied in n-person cooperative games

with transferable utility by Shapley (1953)

Definition 2: The marginal value of a coalition M, where MeQm, equals vM(.Q,,,), the
characteristic function value of M, minus the values of all smaller coalitions contained in
M under prior coalition structure [2,", vM(.Q.,,,). I.e. MV(M) = vM(.(2,,,) — vM(.Q.,,,).

In order to split the profit of a pool, we first find the marginal value of each
coalition and split that marginal value equally among all players who are members. Then,
for one pool member, the value of the game is the sum of her share of marginal value of
the coalition and the value she earns before forming this coalition. It is important that we
define the prior coalition structure. For example, current coalition M =ABC and the
coalition structure is Q3 = {ABC}. The smaller coalition can be (21 ={A, B, C}, (22
={AB, C}, Q4 ={A, BC} or £25 ={B, AC}. Suppose the prior structure is (22 = {AB, C}.
If vM(.Q3) = 11, v (02): v ({AB})+v ({C}) = 6+2=8, then MV(M) = 11 — 8 = 3. The
marginal value of the grand coalition, 3, will then be divided equally among A, B and C
and each gets 1. The final division of profits will be: vA(.Q3) = vB(.Q3) = 4 and vc(.(23)=3.

In this model, profit sharing will be determined in the following ways:

68

Case 1: AB will split profit of the AB pool equally under (22 ={AB, C}, since AB are

identical firms and earn same profit under prior structure (21 ={A, B, C}.

Case 2: Under £23 ={B, AC}, the prior market structure is obviously Q] ={A, B, C}.

VB (Q3) 2 [VBC (93) _ vBC (Ql )] / 2 + 178(91)

vC(Q3) = [vBC(Q3) — 17M“), )]/ 2 + vC(Ql)

Similarly we can find how AC split the profit of AC pool under 05 ={B, AC}.

Case 3: If current structure is £23 ={ABC}, the prior structure can be any of the other four
structures. And which one to use depends on the need in finding the equilibrium. Here we
denote the prior structure as 9.5; then the profit for each firm shared can be calculated
by:

v,(Q,) = [v,,C(Q,)—v,,c(o_,)]/3+ v,(t2_,), i = A, B, C.

III Equilibria
I solve the game using backward induction. First, using first order conditions I get
the equilibria prices under different pool structures; then each firm makes the pooling

decisions based on the profit information. Refer to appendix C for the complete results.

69

111.] Pool Structure Equilibria

This part of the paper will analyze how open membership games and closed
membership games result in two different sets of equilibria of pool structure while firms
make the decisions about forming patent pool based on same profit maximization rules
and profit sharing rules as discussed above.

Definition 3: A stable pool structure in the industry is achieved when no firm is able to
make a profitable deviation.

Note that we use a definition that is stronger than “stand alone stable”8. As
studied in Yi (1997) and Brenner (2004), a general solution for pool equilibria is difficult
to derive. The appropriate equilibrium concept I will use below is the subgame perfect
Nash equilibrium. Now let us find the stable pool structure for both open and closed

membership games.

1. Open Patent Games.

Under this regime, all three individual firms decide simultaneously whether they
will join a pool or not; all firms who wish to join will form a pool. The essential
characteristic of this game is that the pool member has no control over the size of the

pool and no choice over with which they form the pool.

Definition 4: A subgame perfect Nash equilibrium of the open patent pool is a pool
structure [2,". if n“ (0",) > n” ([2,) for any single firm i, i = A, B, and C, for any m at n,

where .QmeQ, [2,, 6.0.

 

8 A pool structure is called stand alone stable if there is no firm willing to deviate from an pool to a
singleton firm.

70

This concept states that for a poor structure to be Nash Equilibrium, neither a poor
member nor a firm outside the pool can benefit from a unilateral move. As a result,
neither should a single firm outside of the poor have an incentive to join the pool, nor
should a pool member have an incentive to leave it, given the other firrns’ choices. I

apply this concept to derive the equilibria and get the following results:

Proposition l—Subgame perfect Nash Equilibria under open membership regime
(1) Q1 ={A, B, C} is a stable equilibrium when ore(0, 0.77) or a >12;
(2) When ore(0.77, 1.2), there exists two critical values c1(a) <c2(a), such that
when c1 (67) < c <1, Q2 ={AB, C} is a stable equilibrium;
when 0 < c < c,(a) , Q3 ={ABC} is a stable equilibrium;
When c,(a) < c <1, Q4 ={A, BC} is a stable equilibrium.

Proof: see the appendix D for details

The equilibria under different combination of or and c can be shown in figure 3:

(1

 

0

13

Figure 3: Stable equilibrium under open pool game

71

In blank area: Q1 ={A, B, C} is a stable equilibrium
In gray area: Q2 ={AB, C} is a stable equilibrium
In horizontally solid line area: Q4 ={A, BC} is a stable equilibrium

In brick shaded area: Q3 ={ABC} is a stable equilibrium

Since no firm can unilaterally deviate from the resulting structure and do any
better, given that the other two firms have chosen to be a singular firm in the first stage,
Q is Nash equilibrium. But, if joining the pool is a dominant strategy under certain
conditions for any two of the firms, Q1 cannot be stable Nash Equilibrium.

Without taking into account of the market dynamics, firm AB has no incentive to
form a pool in the first place, knowing that C will not join them. And their decision is
independent of the static market size or price elasticity. But once the market evolves in a
way that depends on the market dynamics and the first period relative market demand,
firm A and B may be willing to join a pool and internalize the pricing extemality between
the two firms so that they can benefit from the expanded future market. And such
willingness to form a pool depends on the relative market size in the future. If the fiiture
new market is comparatively much smaller, then the benefit from pooling patents is not
high attractive enough; but if the future new market is comparatively much bigger, then
the two firms’ benefit earned in the first period from pooling cannot compensate their
forgone profit in the second period if they compete as independent firms. So they still do

not want to pool.

72

2. Closed Patent Pools:

Under closed patent pool regime, what matters are not only the size of the pool,
but also the specific members of the pool; and the existing members must act
unanimously in forming a pool and rejecting the others. A fundamental characteristic of
closed membership pool is that any member’s deviation will destroy the stability of the

whole pool structure.

Definition 5: A Subgame perfect Nash equilibrium of the closed patent pool is a pool

structure .0": if IIM (.0,,,‘)>7rM (.0,,), for any n ¢ m, where .0,,,e.0, .0,, 6.0.

77M (.0,,,) and JIM (.0,,) denote the total profit of pool members in pool M under pool
structure .0", and .0”, respectively. Notice that under .0”, M is no long a pool. We applied

this concept to derive the equilibria and get the following results:

Proposition 2—Equilibria under closed membership regime: there exists a critical value
c(or), c,(a)<c(a)<c2(a), such that when c < c(or), Q3 ={ABC} is a unique stable
equilibrium.
Proof: See Appendix D

The major difference in stable equilibrium between open and closed membership
game is the former is directly influenced by both the market dynamics and competition
effect in the market, while the later is only directly by competition effect. The intuition of

proposition 2 lies in the fact that market coordination is much more feasible to achieve

73

under closed membership; and it is easier for members in a grand coalition to align their

interests with each other under less fierce competition in the final market.

Remark 1: The closed membership game also allows us to move to a stability concept
that allows deviations by a subset of firms, not just unilateral deviation. That is the idea
captured by coalition-proof Nash equilibria. According to Bemheim et a1. (1987), an
agreement characterized by coalition-proof Nash equilibrium is self-enforcing, and “no
proper subset of players, taking the actions of its complement as fixed, can agree to
deviate in a way that makes all of its members better off”. It is easy to show that, after
taking a recursion in proof, self-enforceability holds for the equilibrium achieved in

proposition 2; thus it is a coalition-proof Nash equilibrium.

Remark 2: Regardless of the types of the game, firm C’s incentive to join a pool is
always directly determined by substitutability of two technologies. Precisely, the model

6(vC(AB + C) — vC(ABC))

6 >0. That is, the more substitutable the two
c

 

shows that

technologies are, the less likely firm C will join AB’s patent pool and the more likely we
observe incomplete pool in equilibrium. In other words, firms are not afraid of more
fierce competition in markets. On the contrary, the more competitive firms prefer to face

the competition directly and a patent pool may get in the way.

[11.2 Price Eguilibria

The two period game setting in this model reveals some important pricing

behavior that may miss in a single period model. This is because when firms set the

74

current prices, they must take into account the future market size and this makes price
competition even fiercer in the first period. We compared the prices in equilibrium in

two-period model with one-period model and get the following results.

Lemma 1: There exists a critical value a‘(Qm), such that when a > a‘(Qm), r5} > 43,] ,
where H]: .71, B, C, 9’18, 51C, 8 C, and .7130

Proof: See Appendix D.

Lemma 2: r}, (ICP) < r; (IND) + rh'(IND) , where j,h e {.71, B, C}, j at h;t = 1,2

Proof: See Appendix D.

Lemma 2 shows that forming a pool can relieve the competition pressure faced by
the members so that the pool can charge a lower royalty rates comparing to what they
charge as individual competitors. But this does not necessary lead to lower prices of the

product under incomplete pool structure than that under individual structure.

Proposition 3- Price equilibria: comparison between two periods
(1) For any Q,” 6 Q,fl‘(Qm) < fl(Qm).
(2) For any Q». E Q, P13 (9") > Pl], (QM).
(3) For product I, Pf (Q5) > P,1 (Q5) . And there exists a', such that

P,2(Qm) > P,'(Qm) for all a > (7., where i = l, 2, 3, 4.

75

(4) For any omen, 0<&2(9,.)-11‘<o,,,»>0, anion-6'62...»

> 0 , where k
667 6c

 

 

= I, 11.

Proof: see Appendix D.

Proposition 1( 1) means both technologies are priced lower in the first stage than that in a
single-period game, under certain market structure. The intuition is, when there are more
than one period games, firms will lower their prices to obtain a better position in

competition for later period. And this

Lemma 3: P,"(Q2) =P,"(Q3) = [f(Q4), for anyk = I, II and t = 1, 2

Proof:

In the rest of the paper, we denote the prices of product I and 11 under incomplete pool
structure as P,"(ICP) , when k = I, II and t = 1, 2

Proposition 2 — Price equilibria: comparison between pool structures

(1) For product I in the lst period, there exists a function of c, f(c), such that
when a > f(c), 19,1 (CP) > P,1 (IND) > P,l (ICP);
when a < f(c), ID,l (IND) > P,1 (ICP) > P,1 (CP);
(2) For product I in the 2nd period, P,2(IND) > Pf(1CP)> Pf(CP) when a > 1.2 and
Pi (ICP) > Pf (IND) > 13,2(CP) when a < 1.2.
(3) For product 11 in the lst period, there exists a function of c, g(c), such that

when a > g(c), P,',(CP) > P; (IND) = P; (ICP);

76

when a < g(c), Pl (IND) = P) (ICP) > 131100).

(4) For product 11 in the 2nd period, P; (IND) = P5 (ICP) > P; (CP)

The intuition is that letting fiiture total market depends on the earlier stage demand will
give firms more incentive to reduce the price in the first stage so that they can exploit

more in the future. This will positively affect the earlier adoption of the technology.

111.3. Social welfare analysis

In this section I analyze how pooling structures may affect the social welfare in the
absence of foreclosure. The social welfare is measured by the sum of the consumer
surplus and the producer surplus; in this linear demand system, consumers’ payment will
be cancelled out with producers’ surplus, thus we ultimately need to calculate the total
utilities that consumers get from product purchase.

To derive the consumer surplus, we first obtain inverse demand functions as follows:

1+(t—1)a_ D; _cD,',

PKDLDL): l-c i—c2 1—c2

 

1+(t-l)a_ c1); _ D,’,

PIKDLDL): l—c l—c2 l—c

 

2 , where t =1,2

—_—> P,’ = (fl + 7111 +(t-11a1—70; -— 70;,

P: = (.6+7)11+(t —1)a1-7D; 70;,

C

 

1
Where =——, = .
'3 l—c2 7 l—c2

77

The above inverse demand functions imply that the utility function is given by:

U'<D;,D,',) = (7+7)11+<r—1>a1(0; + Ding-(D? + DID—70w;
U(D,',D},,Df,0f,)=U‘(D},D},)+Uz<0fan/>

My findings can be summarized in the following proposition:

Proposition 4: 1n the absence of foreclosure,
SW (CP) > SW (ICP) > SW (IND)

Proof: See appendix D.

This result is not surprising. Since two substitute technologies are not allowed to
be included in the complete pool, and the pool bundling perfect complementary patents
can “internalize” positive pricing extemalities and set royalty rate below the level the
three players should choose if acting independently. This will expand the pool’s sales and
make complete pool most desirable from social welfare’s point of view. Under the
independent structure, on the other hand, no firm will take into account the positive effect
on other firms’ sale when one firm cuts the royalty rate on the product I licensing market
which results in higher prices in final products and less sales, comparing to complete pool
and incomplete pool structures.

Does that mean complete pool is most desirable for a society? This leads to the

examination of firm C’s innovation incentives under different pool structures.

78

IV. Extended discussion
IV.1. Incentive for firm C to innovate competing technology 11

Suppose technology I is developed earlier in the industry. Does firm C have the
incentive to innovate technology 11? How will the alliance structure influence the
incentive?

If firm C does not innovate technology 11, then in the final product market, there
is only product I. The utility function then can be rewritten in the following way:

1+(t—1)a D, 1 D’2

AS Di] :0, U’(DI‘2DIII)=UI(D’I) = l—c l—2(1-Cz) I

 

 

r, _ dU(D;) __1+(t-l)a _ D,’
dD; l-c l—c2

:> D; = (l +(t—1)a)(1+c)—(1—c2)r’
Now firm C’s profit firm C can be calculated solely from product I under three

pool structures: the complete pool (CP or 9,), incomplete pool (ICP or 92), or

individual firms (IND, or Q) and we list the results below:

(1+c)2 +a(l+c)+at2

 

 

V(~(Q3) = 90—62)

V1192) = (1 +c)2 +0‘(1:C)+az
7(1—c )

”(1.1190 = (1+c)2 +a(]+c)+a2

 

13(1—c2)
We use 1(Qm)=vC(Qm)—vé(Qm) to measure the incentive to innovate the

competing technology 11 under pool structure Qm. Note that the positive value of

79

vC (Qm)—vé (QM) does not necessarily mean that firm C has enough incentive to
innovate. The firm must take into account the innovation cost. But it is safe to say that the
larger vC (Qm)—vé (Qm) is, the greater the incentive to innovate competing technology.
Also, If we assume that the innovation cost is independent of the pool structure, then
(vC(Qm)-—vé (Qm ))—(vC(Qm.)—vé(Qm.)) implies the difference in innovation incentives
structure that m and m ’ can provide.

The main results can be summarized in the following proposition:

Proposition 5.

Under the IND (Q1) and ICP (Q2) structure, firm C always has the incentive to innovate

a competing technology. Under the CP structure (93), there exists a critical function
2(a) , such that when c > 2(a), firm C chooses not to innovate the technology 11; and

when c < 6(a) , firm C chooses to innovate.

Proof: See Appendix D for detail.

Firm C’s incentive to innovate is directly determined by the profit it can earn
under each market structure. Under the individual market and the incomplete pool
structure, although the new product will bring some competition into the final market,
firm C is free to set the royalty rate of patent C and D so as to mitigate the competition
and benefit from the multi-market operation. But, under the complete pool structure, firm
C does not have the control right in pricing patent C. If the new product it innovates
intensifies too much competition, firm C’s loss cannot be compensated by the benefit

from internalizing pricing extemalities; thus C chooses not to innovate.

80

V1.2. Foreclosure
Will firm C foreclose the rival firms by withdrawing patent c from product I
market? If that is the case, firm C becomes a monopolist in the final product market and it

can earn:

(l+c)2+a(l+c)+a2

v" (C) = 3(1 —c2)

 

Comparing this monopoly profit with the profit C earns under different market structures

with two products, we have the following finding.

Proposition 6:
Under incomplete pool and individual structures, firm C will not foreclose the product I
market regardless of the value of c and 0.

Under complete patent pool, foreclosure is more likely to occur. There exists a critical

function 6(a), such that when c>C(a), firm C chooses to foreclose; and when

c < C(a) , firm C chooses not to foreclose.

Proof: see Appendix D.

The intuition behind proposition 6 is the same as proposition 5. F inn C gain more
benefit from increased market size by operating in both product markets, as long as it can
set the prices for its two patents so that to internalize the price extemalities as it can be
realized under incomplete and individual patent pooling structures. If under the complete
patent pool, foreclosure became a conditionally profitable strategy for firm C when c is

getting bigger. More precisely, the new market size a must be increasing in c to prevent

81

firm C from foreclosing for c 6 (045,087). When c > 0.87, firm C chooses to foreclose
for sure.
Combining the findings stated in proposition 5 and 6, we can illustrate them in the

following graphs (figure 4). On the right of 2(a) , firm C will choose to foreclose product

I; and the area on the right of 2(a) is the zone when firm C will not have enough
incentive to innovate product 11. The foreclosure zone is larger because firm C can
become the monopoly of product 11 after foreclosure; instead, if it fails to innovate

product II, it needs to share the monopoly profit with firm A and B.

New market size (a)
0.87 2

 

Foreclosure zone

/7

1.2

C(a)

 

6(a)
/V No innovation of tech. 11

 

 

_

 

o 0.45 0.94 1 Products substitution (c)

Figure 4: Firms’ foreclosure decision in equilibrium

82

V1.3. Profit split rules

Through the paper, we built the model on a key assumption that pool members
will split the profit based on the calculation of marginal value of the pool. This situation
is ideal; in the real world, we more often observe that pool members split the profit
evenly according to the number of patents each owns within a pool. How may the profit
split rules in the real world change the results we get from the model?

A major difference that evenly split rule can make is, if firm C has to split the
profit it made with a partner, it’s actually sharing freely its market power gained from
owning two competing technology, which definitely reduces C’s incentive to form pools
with firm B. Thus, asymmetric patent pool will never be a stable equilibrium.

I conclude this finding in the following proposition:

Proposition 7: Asymmetric patent pool A+BC or B+AC structure cannot be a stable
equilibrium under evenly profit-splitting rules.
Proof:

vC(A +BC)—vC(A + B+C)

__1274+566c+2a(625+318c)+a2(1277+517c)
3174(1—c)

 

_ 1021+ 661c + 2a2(512 + 329c) + a(976 + 706C)
2523(1— c)

 

_ 8784 + 223332c + 2a(-9321+106036c)+ a2(9435 + 261367c)
2669334(1- c)

 

<0, ifce(0,1)anda >0

83

When evenly profit split rules provide the opportunities to some smaller
companies to free ride the market power owned by the multi-technology firms, the latter
may choose to stay away from the patent pools. This may give hints in explaining why

companies like Lucent does not join MPEG patent pool.

V1.4. Relative strength of competing technologies

Suppose in the second period, technology I has a new market sized at a, but
technology 11’s new market is sized at la, where a >0and 2>0. So we use A to
measure the relative prosperity or strength of two technologies in dynamics. After

running the whole simulation model, we get the following results:

Proposition 8: For any substitutability level, the greater the relative strength of
technology 11, 7t, the more incentives firm C has in joining AB pool and the more likely
we observe a complete pool, regardless of the open or closed game.

Proof:

0(v(.(ABC)-v(.(AB+C)) > 0
62

 

It can be shown that:

In other words, when technology 11 is more promising in the future, firm C is
more likely to join AB and form a complete pool structure. A more promising technology
11 means firm C can gain more from coordination effect generated by patents pooling;
when firm C ‘8 gain from head-to-head competition is big, high relative strength can
offset part of those competition effects and thus makes joining a complete pool more

appealing to firm C. This could explain why a multi-technology firm such as Lucent is

84

reluctant to join MPEG patent pools. Lucent may own some competing technologies with
MPEG; but none of those shows superior strength in future markets. Thus, it still benefits

more from direct competition than from market coordination.

Remark 3: How the relative strength of technology 11 influences the formation of an

G(VA(A+BC)-VA(ABC))
6x1

 

asymmetric pool A+BC? It can be shown that < 0. That is, the

more promising technology 11 is, the more likely A will join BC’s pool and form a
complete patent pool. The intuition behind firm A’s strategy is, A is able to benefit from
two types of free riding: one is to stay alone and take advantage of the positive
extemalities the BC pool can create; another is to join the BC pool and take advantage of
the mitigation of competition due to the market power of firm C. When product H is
relatively competitive and promising, the latter advantage will be bigger than the former

one and firm A will tend to join the BC and form a complete pool.

VI. Concluding Remarks

This paper tries to explain the phenomenon of incomplete patent pools that
contradicted the existing theories. Two assumptions are relaxed from the existing
literature: symmetric patent assets and static games. Instead, the paper deals with the
situation where patent holders are asymmetric regarding to technology capacity and
strength and extends the model into a two-stage game setting. The interplay between
dynamic market size change and the substitutability of two competing technologies will

determine the equilibrium pooling structures.

85

The model shows, under open membership game, firms’ pooling decisions are
constrained by both market dynamics and the substitutability of two competing
technologies and both incomplete pools and individual structure can be equilibria,
depending on the new market size in the second period and the substitutability of
competing technologies. But closed membership relaxed firms from the constraint of new
market size and only a complete pool can be equilibrium when the substitutability of two
technologies is low. It’s also proven that royalty rates are set lower in the earlier stage
generally so as to positively affect early technology adoption; but in the later stage, when

licensors are less concerned with market shares, the prices are set at a higher level.

From technologies marketing point of view, this paper shed insights on two
important observations. First, firms with competing technologies are reluctant in joining a
patent pool, and this is especially the case when the competing technologies are close
substitutes to the counterpart. To those firms, it is more appealing to market the two
technologies directly in the market and joining a patent pool may get in the way of firms’
inter-sectional decision. Second, firms with superior technologies are less concerned
about the free-riding issue of less competitive firms and thus a complete pool is more

likely formed in equilibrium.

The model also shows that although incomplete pool structure is associated with
lower social welfare ex post, a complete pool structure may reduce firms’ incentives to
innovate and suffocate competing technologies in the first place, and, thus, it is not

socially desirable ex ante in this setting.

86

Following further researches and extensions are worth pursuing. First, pooling
structures are fixed after it is formed in the beginning of the game; letting the members
update pooling structures may generate interesting theories to explain how the pooling
structures evolved in the real world. Second, this model can be generalized to more than
three players and used to explain the phenomenon of competing patent pools as existing
in DVD industry; the two-stage game setting may also have restricted the results of this
paper. Relaxing it may bring us more insights into patent pool issues. Also, firms’
technology asymmetry can be in different forms among the three players and changing

the assumption made here may leads to new results of the model.

87

References:

Aghion and Tirole (1994): “On the Management of Innovation’, Quaterly Journal of Economics,
109, pp. 1185-1207.

Bloch, Francis (1996): “Sequential Formation of Coalitions in Games with Extemalities and
Fixed Payoff Division”, Games and Economic Behavior.

Brenner, steffen (2004): “Stable patent pools”, working paper.

Chang, Howard (1995): Patent scope, antitrust policy, and cumulative innovation. Rand Journal
of Economics, Vol. 26, No 1, Spring 1995. Pp. 34~57.

Choi, Jay (2002): A dynamic analysis of licensing: The “Boomerang” effect and grant-back
clauses. International economic review, vol. 43, No, 3. August 2002.

Choi, Jay (2002): Patent pools and cross-licensing in the shadow of patent litigation. Preliminary
working paper.

Choi, Jay (2003): Antitrust analysis of mergers with bundling in complementary markets:
implications for pricing, innovation, and compatibility choice

Cournot, Augustine (1883): “Researches into the Mathematical Principles of the Theory of
Wealth”(in French), translated in 1927.

Economides and Salop (1992): Competition and Integration among complements, and network
market structure. The journal of industrial economics, Vol. XL.

Friedman, J.W.(l977), Oligopoly and the Theory of Games.

Fudenberg and Tirole: “Customer poaching and brand switching”, the Rand Journal of
Economics, winter 2000.

Jaffe, Adam and Josh, Lerner (2001): Reinventing public R&D: patent policy and the
commercialization of national laboratory technologies. Rand Journal of Economics, Vol. 32, No
1, Spring. Pp. l67~198.

Lerner, Josh and Tirole, Jean (2004): EFFICIENT PATENT POOLS. AER Vol. 94, No. 3,
June 2004.

Pepall and Norman (2001): Product differentiation and upstream-downstream relations. Journal
of Economics and Management strategy, Vol. 10, summer 2001.

Shapiro, Carl (2001): Navigating the patent thicket: Cross Licenses, patent pools, and standard-
setting. Innovation policy and the economy, vol. 1, MIT press, 2001.

Shapiro, Carl (2003): Antitrust limits to patent settlements. Rand Journal of Economics, Vol. 34,
No 2, Summer 2003. Pp. 391~411.

Yi, Sang-Seung (1997): “Stable Coalition Structures with Extemalities”. Games and Economic
Behavrior 20, 201-237.

88

Appendix B:

Maximization problems under each pool structure

Case I: Q, ={A, B, C}, all firms compete independently

The firms’ maximization problems are:

FirmA:
l l l l l 2 l l l l 2 2 2 2
Max ra(1—(ra +rb +rc)+crd)+ra (a+1-(ra +7, +rc)+crd —(ra +rb +rc )+crd)
r0
FirmB:

Max rb'(1—(ral +rbl +rcl)+crdl)+rb2(0t+1—(ral +rb1 +rc')+crdl —(ra2 +rb2 +rcz)+crd2)
’b

FirmC:

1 1 1 1 1 2 1 1 1 1 2 2 2 2
Max 76(1—(70 +rb +rc)+crd)+rc (a+1—(ra +rb +rc)+crd——(ra +rb +rc)+crd)
rurd

+ra:(1—rdl+c(ral +1}: +rcl))+ra,2(a+l—rdl +c(ra1 +rbl +rc‘)—rd2 +c(ra2 +rb2 +rcz))

Case 11: Q; ={AB, C}, symmetric incomplete pool structure.

This is the case that two symmetric firms form a pool. Now product 1’s prices
t t t
arezpl = rub +7} ,t= 1,2.
Pool {AB}:

1 l l l 2 l l l 2 2 2
Max rab(1—(rab +rc)+crd)+rab(a+l—(rab +rc)+crd —(rab +rc )+crd)

rab’rab

FirmC:
M 1 1 1 1 2 1 1 1 2 2 2
ax rc(l—(rab+rc)+crd)+rc (a+l—(rab+rc)+crd —(rab+rc )+crd)
rc,rd

+r; (l-rd1 +c(ra'b +rc'))+ra,2(cr+l—rdl +c(ralb +rc1)—rd2 +c(razb +rcz))

89

Case 111: Q, ={ABC} a complete mo]

In this case, the pool will act as a monopoly in product 1 market and firm C sets the price

for patent D individually.

1 . . .
The pool chooses r' , and firm C chooses royalty rate r , t=1, 2, to maxrmize their

profit from both periods:

p001 ofABc;Ma.2x VABC(Q3) = r‘(1—rl +crd‘)+r2((a+l—rl +crdl)—r2 +crd2)

Firm C:

Ma} vC(Q3) =[VABC(Q3)—v/,BC(Q_3)]/3+r(}(l—rdl +crl)+rd2(a+1—rd2 +cr2)

rdrrd

Cfle IV: (AL =1AJC} or = B AC as mmetric incom [etc 001 structure

In this case, the multi-technology firm C pools its patent C with patent B or A. When
assets pooling between asymmetric firms occurs, we assume the pool will maximize the whole
profit from both markets. By using this assumption, firms in BC pool or AC pool gain the highest
profit under this pooling structure. Still, asymmetric patent pools are dominated. So relaxing this
assumption will not influence the results we get in this paper.

Also, this assumption is consistent with Aghion and Tirole (1994). The former paper
argues that control rights will be assigned so as to maximize the value of the final output as long
as the R&D firm has sufficient financial resources.

Pool BC: (or Pool AC)
1 l l l 2 l l l 2 2 2
Max (rbc(l—(rbc +ra)+crd)+rbc(a+l—(rbc +ra)+crd —(rbc +ra )+crd)
bc’ d
l l l I 2 l l l 2 2 2
+rd(l—rd +c(rbc +ra))+rd (a+1—rd +c(rbc +ra)—rd +c(rbc +ra ))

Firm A:

l l l l 2 l l l 2 2 2
Max 70(1—(rbc+ra)+crd)+ra (a+l—(rbc+ra)+crd —(rbc+ra )+crd)
(1’0

90

Appendix C: Results of the model
Royalty Rates, product prices and firm profits:

Case 1: Q. ={A, B, C} IND structure

21—3a+8c—26ac
87—87c

 

rJ(01>=r.'(0.>=7'2’—9“, r.‘(0.>=

63 — 34c + a(9 + 20c)

 

PKQ) =rJ(Q.)+ri(Qt)+r.'(Q.)=

 

87(1-c)
2(l+4a) 6+24a+23c+34ac
2(2 = 2(2 =-——-—,er =
r“( ') r”( ') 29 ‘( ') 87-87c

18+72a+11c-14ac)

 

P,2(Q,) =rj(o,)+r,2(s2,)+r§(§2,) =

 

 

87(1—c)
, 1+2a
rJ(Q)= P,,(Q)=3—(1_),rj(0.)= 1",,(0)=3 _3c
60+45a+61a2
VA(Q,)=V,.(Q.)= 84]

1021+ 661C + 2a(512 + 329a) + a2 (976 + 706C)

v" (9‘) = 2523(1— c)

B(91)=;4——"(31_),B,(0.>= -2c

 

Case 2: Q2 ={AB, C} SICP structure

_—7 2a _21—6a+2c—17ac

 

42—a(12+11c)-—19c

 

P,‘(=Q) r‘,(o,)+r',(o)=

 

69—69c
3_(__1+3a) 9+27a+l4c+19ac
M 2) 23 m 2) 69—69c

91

7.1m)=B}(Q)=3—(——1_a),r.;(9)=P13(Q#13:

 

18+54a+5c—8ac
69—69c

 

172(92) = a211(02)+rc2(92) =

72 + 64a + 736172
1058

 

v..<n.>=v.<n.>=%vstnz>=

745+313c+a2(758+3100)+a(721+337c)
1587(l-c)

 

VC (S2,) =

8(02)=P,(Q.)=—— 4 6 8:19) B,(Q.>=-2—_1

(61— c’) 2c

Case 3: Q3 ={ABC} Complete pool structure
r'(03)= P,‘ (0.) =

3(648 — 774c2 — 90c3 + 363C4 +1 1 lo5 — 56c‘5 - 24c7 — a(648 + 648C — 342C2

-594C3 - 87c4 +14lcS + 4066 — 8C7 )) / 5832 — 631802 + 287164 — 80166 +10468
rd] (Q3) =PIII (03) =

(1944 + 648C — 2214c2 — 810C3 +1089c4 + 537C5 —180c6 —104c7 — 3a(648 + 648C

—414c2 —582c3 —39c“ +113cS + 32c6))/5832—6318c2 + 2871c“ —801c6 +104c8
72 (03)= 132(93)=

-(6 (—3+c’) (108+ 108c—3c2-39c3-8c4+4cs+a(216+108c-Jl4c2
-758 +11c4+16c5))) / (5832-6318c2+28'71c4- 801c6+104c8)

(are: (n.>=

-(4 (-3+c2) (—3 (-54-54c+3c2+16c3+5c‘) +2a(162+108c:-9ot:2
-72 c3+9c‘+13 c5))) / (5832-6318 c2+2871c‘—801c‘+104 c8)

92

The profits of three firms under complete rule depend on the prior market structure. We
have three versions of profit set, but we skipped numbers here for the long expression.

V193) = [VABC(Q3) — VABC(QI )] / 3 + V1621)
V1103) : [VABC (Q3) _ vABC (Qz )] / 3 + V1 (92)

V1193) = [vABC (Q3) - VABC (Q4 )] / 3 + vi (Q4)
Where i = A, B, C.

3(2+c) PQ( )_ 3+2c
43c(— 1’” 3 265-8)

 

P1623):—

Case 4: Q, ={A, BC} AICP structure
(Q5 ={B, AC} is the same case, skipped)

7—2a r'(Q )_ 21—6a+2c—17ac
__ 3 _

I
o = ,
r“( 4) 23 ”‘ 69—69c

 

42—a12+11c -19c
a'tn.)=r.:<90+r.:.<o.>= ( )

 

 

69—69c
31+3a 9+27a+14c+19ac
rim.) =——( ).r,:.<n.> =
23 69—69c

18+54a+5c—8ac

 

P126241) : r02(Q3)+rb2C(Q4) =

 

 

69—69c
1+2a
r1<04)=ni(0.)=3——(1_“)rim.)=11f(0)=3_3€
72+64ar+73a2
v Q = =2 Q
,1( 4) 529 VA( 2)

745 +313c+a(721+337c)+a2(748+310c)
1587(1—c)

 

vBC (94) =

93

v.62.) = 30mm.) wire.» + v.62.)

_ 72+64a +730:2
1058

 

= V3 (02)
v.10.)=30.49.78.101»+410.)

_ 1274+842c+ 2a(625+433c)+a2(1277+839c)
3174(1-c)

 

Appendix D: Proofs of Lemma and Proposition
Lemma 1:

Proof:

2(l+4a)_ 7-a _ -5+9a
29 29 29

 

 

raz(Ql)-ral(Ql)=rb2(Ql)_rbl(Ql)= >Oifa>g

6+24a+23c+34ac_21—3a+8c—26ac

 

r.’1,(02)-r.‘.(02)=

 

 

87(1—c) 87(1—c)
—5+9a+5c+20ac . 5-5c
= > 0 ifa >
29(1-c) 9+20c

9+27a+14c+19ac_ 21—6a+2c-17ac

 

 

r32(Q2)—rc'(Q2)=

 

 

69(1- 0) 690— c)
—4+11a+4c+12ac , 8—8c

= >0Ja>
23(1- c) 22 + c

3(1+3a)_7-2a _ —4+11a
23 23 23

 

r.:(Q.>—r;.<nz>= >070»?1

94

9+27a+14c+19ac_21—6a+2c—l7ac

 

'13. (94) - ’1'.- (Q4) =

 

 

69(1 — c) 69(1 — c)
—4+11a+4c+12ac , 8—8c

= >0fa>
23(1- c) 22 + c

3(1+3a)_7—2a _ —4+11a
23 23 23

 

r02(Q4)—ra'(Q4)= >0 ifa>fi

 

rj(o,)—r;(o,)=1+2a—1'a= 0‘ >0ifa>0,i=1,2,4,5.
3—3a l—c l—c
Lemma2:

Case 1: symmetric incomplete pool of ab

, 2(7—a) 7—2a ll9+12a
: — : >

raI + rbl — rub 0
29 23 667

 

, 4(1+4a)_3(1+3a) _ 5+107a >

fi+fi-%= 0
29 23 667

 

 

Case 2: Asymmetric incomplete pool of bc

i 1 1_

7—a _21—3a+8c—26ac_21—6a+2c—17ac _ 119+12a >
29 87(1—c) 69(1—c) 667

0

 

2 2(1+4a)+6+24a+23c+34ac_9+27a+14c+19ac _ 54-10707 >

r,2 + 732 — rm. = 0
29 87(1— c) 69(1— c) 667

 

Proposition 1:
We can solve the following functions to find the conditions for Q to be Subgame Perfect
Nash Equilibrium.

v, (Q, (A, B, C)) > v3(Q,(AB, c»

v,3 (Ql (A, B, C)) > v,3 (Q2 (AB, C))

95

vA(QI(A,B,C)) > vA(Q4(A,BC))

v8 (Q,(A, B, C)) > vB(Q4(A, BC))
(2) For Q; ={AB, C} to be an equilibrium, the following conditions must all be satisfied:

v, (Q,(AB,C)) > vA(Q,(A,B, C))
v,(o,(AB, C)) > mo, (A, B, C))

vC (QZ(AB,C)) > vC (Q3(ABC))
And for Q4 ={A, BC } to be an equilibrium, the following conditions must all be satisfied:

vA (Q4(A,BC)) > vA(Q3(ABC))
v3 (Q4(A, BC)) > v3 (Q,(A,B, C))

vC(Q4(A,BC)) > vC(Ql(A,B,C))

Solving these functions, we can get the conditions of equilibrium, as stated in proposition.

And we can show that the following conditions necessary for Q3 ={ABC} to be an equilibrium
are not satisfied simultaneously under any value of on and c:

v, (Q,(ABC)) > v, (Q,(A, BC))
vB(Q3(ABC)) > v, (525(A C, 3))

vC(Q,(ABC)) > vC(Q,(AB, C))

Proposition 2:

Q3 ={ABC} is a stable equilibrium when the following conditions are satisfied simultaneously:

v,,c(o,(ABC)) > 12mm, (A, B, C))

vABC(Q3(ABC)) > v,,,c(o,(AB, C))

96

vABC(Q3(ABC)) > vABC(Q4(A,BC))
By calculation, vABC (Q3(ABC)) > Vac“): (A,B,C)) when c < 0.49

vABC(Q3(ABC)) > vmm, (AB, C))

and when 0 < 0.4.

vABC(Q3(ABC)) > vABC(Q4(A,BC))
Combining the solution, when c < 0.4, (23 ={ABC} is a stable Nash equilibrium.
Now we need to eliminate the possibility that Q. ={A, B, C}, Q; ={AB, C} and Q4 ={A,

BC} can be stable equilibria.

The following conditions must all be satisfied in order for 01 ={A, B, C} to be stable
equilibrium:

vABC(Q,(A,B,C)) > vABC(Qz(AB,C))
vABC.(Q,(A,B,C)) > vABC(Q4(A,BC))

vABC(Q,(A,B,C)) > vABC(Q3(ABC))
But we find that

vABC(Q,(A,B,C)) —vABC(Qz(AB,C))

_1381+301c+2a2(695+146c)+2a(623+218C)
2523(1—c)

_961+97c+a2(967+91c)+a(913+145c)
1587(l-c)

 

_ 25884+ 362336! + 2597902 < O

_ 444889

 

Which is enough to show that Q, ={A, B, C} is unstable.

For Q; ={AB, C} to be an equilibrium, the following conditions must hold:

97

VAB (92(AB9 C)) > vAB (Q! (A9 B9 C))
VA,9 (Q,(AB,C)) > vAB (Q3(ABC))

vAB(QZ(AB,C)) > vAB(Q4(A,BC))
Since

72+64a+ 73a2 _ 3(72+64a+73a2)

r2 AB,C — o A,BC =
v,,,( 2( )) v..,,( .( )) 529 1058

 

_ 72 +646: + 73612 <
1058

 

Q; ={AB, C} cannot be a stable equilibrium.
For (24 = {A, BC} to be an equilibrium, we must have:

vBC(Q4(A, BC» > vBC(Q, (A, B, C))
vBC(Q4(A, BC» > vBC(QZ(AB, C))
v,C(Q,(A, BC» > vBC(QS(AC, B»

vBC (Q4(A, BC)) > vBC (Q3(ABC))
It should suffice to prove that (2., = {A, BC} is not a stable equilibrium by showing that

vBC (04 (A, BC)) — vBC (Q2 (AB, C))

_ 745+313c+a2(748+3106)+a(721+337C)
1587(l—c)

 

_l706+410c+a2(1715+401c)+2a(817+241C)
3174(1—c)

 

_ 72 + 64a + 7361!2 <
1058

 

98

Proposition 3:

Case 1: Q, ={A, B, C} IND structure

B](Ql)-P/(Qi) =

 

 

87(1—c) 4(1—c) _ 348(1—c)

l—a _ 1 __1+2a<
3(l—c) 2—2c 6(l—c)

 

 

PMQ.)-Pu(01)=

for anyc e (0,1),a > 0
Case 2: 02 ={AB, C} (same as Q, ={A, BC} and 95 ={B, AC})

42—a12+11c-19c 4—c
Etna—13(02): ( ) —

 

 

69—69c 6(1-c)
_8+150+a(24+22c) < O
138(1—c)
l—a 1 1+2a

 

 

B’(Qz)—B’(Qz)= 3(1—c)— 2—2c =_6(1—c) <

for anyc e (0,1),a > 0
Case 4: Q3 ={ABC} Complete pool structure
1’,‘(93)-1’,(93) =

3(648 — 774a2 — 90c3 + 3635‘ +1 1 1c5 — 56c6 — 24¢? — a(648 + 648C — 342c2

—594c3 —87c“ +141c5 +40c6 —8c7))/5832—6318c2 + 2871c“ —801c6 +104c8

3(2 + c)

———<0, oran ce 0,1 anda>0
4(3_C2) f y ( )

Pill (Q3)_PII(QJ) =

99

63-34c+a(9+20c)_ 3—c __9+49c+4a(9+20c) <

O

(1944 + 648C — 2214c2 — 810c3 +1089c4 + 53705 — l 8006 —104c7 — 3a(648 + 648C

—4l4c2 — 582c3 -— 39c4 +113c5 + 32c6 )) / 5832 — 6318c2 + 2871c4 — 801C6 +104c8

3+2c

<0, oran ce 0,1anda>0
2(3_cz) f y ( )

Proposition 4: sw (CP) > sw (ICP) > sw (1ND)

2(9a2 (—419904 +1329696c2 + 272160c3...) + ...832cl6

 

 

 

SW (CP) — 2 4 5 s 2
(1— c)(5832 — 6318c + 2871c —801c +104c )
_ 2
SW (ICP) = 11035 + 2719c + 2a(4769 + 521c) 2a (1759 + 8860)
9522(1- c)
_ 2
SW (1ND) = 15541 + 6325c + 4a(3358 + 8476) a (4862 + 3548c)

l 5 l 3 8(1 ~ c)
First I compare SW (CP) and SW (ICP). The result of SW (CP) —SW (ICP) can be shown as a
surface that is strictly above a zero plane, as shown in the following graph. So we can conclude

that sw (CP) >sw (ICP).

  
 
  
  

 
   

.0 7 I.
~~.%=:1" _. _
45.. fiwflfio
*wfiwfi
“(9)—mug), .0 053%.]?

  

100

Figure 5: Social welfare comparison between complete and incomplete pooling structures

_ 2
SW (ICP) — SW (IND) = 58847 + 50885a 21480a > O for any reasonable value of 0.

444889

 

Combining the above results, we obtain:
SW (CP) > SW (ICP) > SW (IND)
Proposition 5:

Firm C’s profits without innovating product 11 are:

(1+c)2 +0t(1+c)+a2

 

 

v(_.(Q3)= 9(1—c2)

14(02): (1+6)2 +a(l:—c)+a2
7(1-c)

Vclr(Qi)= (1+c)2 +a'(1+c)+oz2

 

13(1 - c2 )
Compare them with firm C’s profits from both product markets. We get the following results:

VC(Qz)—VC{(QZ) > O, for any a and c
VC(Q,)—VC'(Q,) > O, for any a and c

VC(Q, ) — VC’ (0,) > 0, when c > 2(a)

3(a) is shown as below:

101

 

Figure 6: Firm C’s gain from innovating product H

Proposition 6: Foreclosure

Proof:

Vé’(FC)-vc(91)

_(1+c)2+a(l+c)+a2 1021+661c+a(976+706c)+2a2(512+329c)
3(1— c2) 2523(1— c)

 

_180(c2 —1)+a2(183+1682c+658c2)+a(l35+841c+706c2) <0
2523(c2 -1)

 

vg(FC)—vC(Qz)

(l+c)2+a(l+c)+a2 745+313c+a(721+337c)+a2(748+310c)
3(1—c2) 1587(1—c)

 

_ —216(c2 —1)+a(l92+529c+337c2)+a2(219+1058c+310c2) < 0
1587(c2 —1)

 

102

VZ-I(FC)—VC(Q4) =Vg(FC)"VC(Qs)

_ (1+c)2 +o:(1+c)+ar2 1274+842c+2a(625+433c)+a2(1277+839c)
3(1—02) 3174(1—c)

 

 

_ 216(c2 —l)+2a(96+529c+433c2)+a2(219+2116c+839c2) < o

 

3174(c2 - 1)
vC(Q,) — vg (FC)
_ 12(6909708864 + ...a2(... + 4596800c”» (1+ c)2 + a(l + c) + a2
4761(c —1)(5832 — 6318c2 + 2871c‘ — 801C“ +104c“)2 3(1— c2 )

See the simulation results shown below:

   

Foreclosure area

Figure 7: F irm C’s foreclosure decision in equilibrium

103

CHAPTER 3

TECHNOLOGY UNCERTAINTY, PRODUCT DIFFERENTIATION
AND THE ENDOGENOUS FORMATION OF STRATEGIC ALLIANCES
I. Introduction

A wave of forming strategic alliances1 has been observed in business world since
198052. Alliances are usually created for specific strategic purposes, such as setting
standards, reducing cost, filling gaps in capabilities or developing a new product. These
alliances are called strategic in the sense that they are formed in the first stage in order to
influence the behavior of all game players in the following stages. The difference
between the strategic alliance and merged firms is, although they share control over the
pooled capabilities of the group in achieving the goals they agree upon, the members
within the alliance still compete with each other in the product market.

This paper focuses on the R&D alliances that are formed to develop a new
product. The member firms can either be the current competitors in the same market or
from different industries. The alliances aim to combine each member’s limited resources
or technological competencies to increase the chance to succeed in the R&D activities so
as to enhance the member firm’s market position.

One of the classic papers in the same topic is D’Aspremont and Jacquemin

(1988). They addresses the question--does cooperation between firms definitely suppress

 

1 For details about different organizational forms of strategic alliance, see appendix 1.

2 During the 19705, about 750 new commercial strategic alliances were recorded. Possibly, more existed.
The annual rate of strategic-alliance formation grew from around 100 to about 2,000 over the decade of
the 19808. By mid-decade (19905), the average annual rate of alliance formation had exceeded 10,000
worldwide. It is anticipated that eh rate will more than double by the turn of the century. Freidheim, C.
(1998), p. 37.

104

competition -- and draws a conclusion that firms’ cooperation at the precompetitive3
stage is closest to the social optimum, in the context of duopoly with spillovers. Kamien,
Muller and Zang (1992) examines the effects of R&D cartellization and research joint
ventures on firms that engage in competition in their product market. They show that
creating a competitive research joint venture reduces the equilibrium level of
technological improvement and increases equilibrium prices compared to when firms
conduct R&D independently; and a research joint venture that cooperate in its R&D
decisions yields the highest consumer plus producer surplus under Coumot competition.

My paper adopted the same setting of the game that firms cooperate in a
precompetitive R&D and compete in product market. But I differ from them in three
important ways.

First, I concentrate on the endogenous formation of strategic alliance, while those
two papers assume all firms either join one research joint venture or research cartel or
remain singletons and focus on the effect of R&D cooperation on the welfare. But grand
R&D alliance is an unrealistic assumption. The evidence from many industries suggests
that there are often more than one alliance groups in an industry, especially in the high-
technology industries. For example, in competing against a single firm Intel, during
19805 to 19905, at least five large alliances group were formed, led by Mips, Sun
Microsystems, Hewlett-Pachard (HP), IBM and Motorola respectively. In automobile
industry, GM’s partners’ include Isuzu, Suzuki, Toyota and newly, Fiat; Ford is allied
with Mazda, Nissan and Kia; and Daimler-Chrysler with Mitsubishi. Actually, these

phenomena have caused more concerns in the recent papers in this field.

 

3 In general, precompetitive research can be thought of as work where companies are not adverse to their
competitors having equal access to the results.

105

Second, their papers examine the case that R&D cooperation is directed to reduce
unit cost and, but this paper applies to the case that R&D cooperation is conducted to
develop a new product.

Cooperation in developing new products is becoming a more and more common
phenomena with the fast grth of technology after 19805. Firms form alliance to do
R&D for the following reasons. First, they may be driven by the great uncertainty
regarding both the demand and the technological success. Usually firms are reluctant to
put all the investment on one project and willing to find some partner to share the risk.
Second, many new products are born from the convergence of more than one industries
and firms must combine their competencies to make the research possible. Third, firms
need the alliance to help them get a product to market quickly and set technical standards
that would sustain their market position as the industry matured.

One example is the development of PDA (Personal Digital Assistant) in the early
19905. This field potentially combines technology from four industries—computer
hardware, computer software, telecommunications and consumer electronics. Major
companies in each of these areas are ambitious to launch a new product based on a
different vision. But each firm was only strong in one aspect of the emerging business
and lacked other needed technological competencies. IBM, Apple and HP approached the
PDA business from their experience in computer hardware; Microsoft and Lotus, from
computer software; AT&T, Tandy and Amstrad, fi'om consumer electronics. In Mueller
and Tilton (1969), they tried to explain that neither large absolute size nor market power
appears to be a necessary condition for successful development of most major

innovations.

106

The third difference: in their paper the success is certain in the sense that the
investment level can solely determine the cost reduction effect, but my model takes into
account of uncertainty issue. As a matter of a fact, in high technology industries,
uncertainty exists in any new product innovation process, regardless of the investment
level.

The questions this paper is intrigued to tackle are: How can the fundamental
factors determine the alliance formation in developing a new product? Why do the firms
in some industry form R&D alliances while those in others do not? Why do we see more
symmetric alliances in one industry than in another? How will the stable equilibrium
alliance structure differ between a simultaneous move game and the sequential unanimity
game? How is social welfare under different market equilibria? This paper aims to shed
some lights in understanding these questions.

My paper is also closely related to the strand of literature that examines the
coalition formation.

Bloch (1995) formally models how to determine endogenously the structure of
association that emerges from a non-cooperative sequential game of association
formation; and he finds that in equilibrium, the firms form two asymmetric associations.

In the recent effort by Brown and Chiang (2002), the conjecture that increasing
market volatility leads to larger coalitions in an oligopoly is first studied and they find
that “the conjecture generally fails in a small oligopoly whose firms play a unanimity
game but it is validated in an oligopoly that allows open membership. However, it is

valid in a small oligopoly if market volatility is sufficiently high, whatever the rule of

107

membership.” The difference between my paper and theirs is that I focus on the
uncertainty of R&D.

Yi (1997) studies how the sign of external effects of coalition formation provides
a useful organizing principle in examining economic coalitions. My paper reveals a
situation that a positive and a negative extemality may coexist in the external effects of
coalition formation. R&D research cooperation may enhance the members’ chance of
success and impose a threat to the competitors, which is called a negative extemality
according to Yi (1997). On the other hand, a successful R&D alliance will cause more
fierce competition among members in the final product market, which is an example of
negative extemality. And I study how the net extemality influences the result as the
major factors change.

Pepall and Norman (2001) tries to answer the question that how product
differentiation is actually achieved through either alliances among upstream firms or
integration between upstream and downstream firms. They examine the relationship
between the downstream and upstream sectors, when the upstream market supplies
specialized and complementary inputs to a downstream product-differentiated market.

What makes a difference in this model is the interplay between technological
uncertainty and differentiation level will jointly shape the stable equilibrium of the
industrial structure. Two effects arise from forming a R&D alliance: on the one hand, a
firm can derive value from a cooperative activity than from going it alone due to the
increased opportunity to launch the new product, which is called “synergy effect”; on the

other hand, the alignment reduces the degree of product differentiation and increases the

108

competition within an alliance, which is called “competition effect”. The tradeoff
between these two factors underlies frrms’ decision making strategies in forming alliance.

The paper is arranged as follows. Part H describes the setting and the assumptions
and introduces the model. Also, based on the solution of the model, a comparative static
analysis is conducted. Part III finds the equilibrium of the structure under open and

closed membership. Part IV provides social welfare analysis. Part V concludes.

[1. The alliance formation model
11. 1. Description of the settings

This is a simple model with four-finn oligopoly. All firms plan to engage in an
R&D to develop a new product. To simplify the analysis, I assume these four firms are

symmetric in the sense that they have same R&D productivity and investment budget.

11.1.1 Technological Uncertainty
Suppose that the results of R&D are uncertain in the industry. The probability of
its success is a function of the total investments in R&D. Here I use a specific function to

describe the production function of the investment:

1

Probability of success = f (,B,m) = B; , ,6 6 (0,1)

B measures the uncertainty level of result to the best of current R&D ability under
the investment constraint. Given that the technological development capabilities are
symmetrically distributed among four firms, ,8 is same for all firms. m is the number of
firms that decide to pool their resources in R&D. I assume that the investment level is

exogenous and fixed, so is the corresponding probability of success.

109

R&D results are fully shared within alliances. Between alliances or competitors,
however, the R&D process is well isolated and R&D outcome is well protected so that
there is no spillover effect. In the real world, firms can take advantage of their
competitors’ success by imitation after the product is introduced into the market, even if
they fail in their own initial R&D activity. Since there is only one period in product

market competition in my model, I rule out the imitation issue.

11.1.2 Product differentiation

If an R&D project succeeds, then the firms that conduct it will be able to produce
a product at zero marginal cost. But the products can be horizontally differentiated in this
model. You can imagine that this product can be developed from different R&D avenues,
each of which can lead to a product that is symmetrically differentiated among research
units. I use 7 to measure the differentiation level among products.

I made three assumptions about the production differentiation.

First, if some firms pool their R&D resources, they have direct purpose to take
advantage of the enhanced probability of success; they do not try to mimic the singleton
firms and use the resource separately in different avenues. Also, the R&D avenue is the
only way to differentiate a product. Firms have no chance to do any further work after
R&D is done. This assumption implies that firms will produce homogenous goods if and
only if they are from the same alliances and their R&D succeeds.

Second, all the information about R&D avenues picked by each research units is

public; and firms always choose an R&D avenue that is different from the potential

110

competitor. As a result, the products between competing players will always be
differentiated in the market.
Third, the number of competing parties in the R&D stage will not change the

differentiation level 7.

11.2 The game

I analyze a two-stage game of strategic alliance formation. In the first stage, all
firms decide simultaneously or sequentially about the size of the alliance they want to
join; and the alliances structure is endogenously determined in the end of this stage under
different membership rules; the investment in R&D is realized. In the second stage, R&D
researches are conducted and all firms being successful in R&D will compete in quantity
in a market sized 1 against each other; then the equilibrium price is realized.

There will be no restrictions on the number of alliances that will be formed,

although no firms are allowed to join more than one alliance at the same time.

Definition 1: An alliance structure .0, ={A ,, A 2, A5}, t=1,2, 3,4,5, is a partition of the

player set F ={F1, F2, F3,F4}. For i ¢j, A,- H Aj = Zand Z; A, = F.

There are 5 possible alliance structures that can be formed in the first stage. Type
1 is called “individual structure”, i.e., all firms decide to remain as a singleton and
compete with each other independently in the product market. Type 2 is another extreme
case, a “grand alliance”, in which case all four firms decide to join one single R&D

alliance and then compete in the product market if the R&D succeeds. The third type is in

111

{2, 2} form, where two alliances are formed and each contains two firms. The fourth
type is in {1,3} form, where one firm remains as a singleton, while all the other three
decide to form an alliance. The fifth type is in {1, 1, 2} form, where, two firms remain as
singletons and the other two decides to form an alliance.

Since the four firms are symmetric, I do not differentiate them in the last three
types of structures. What matters is the position a firm end up with under certain
structure; and it does not matter which firm is in that particular position. Also, I only list
the cases when there are some firms in product market; the case that all firms fail results
in zero profit for all firms.

With the extemality that an alliance will create for nonmembers, different alliance
structure will lead to varying product market equilibrium price and profit distribution
among firms. To solve the game, I use the backward induction. In the following part, I
solve the model of stage H when firms compete in quantity in the product market after the

alliances have been formed in the first stage.

11.2.1 Individual Structure — 01 = {{F;}, {F2}, {F3}, {F4}}

Since four firms conduct the R&D independently, each firm will succeed with
probability 0. In the final product market, there can be one, two, three or four firms in the
market. And the products must be differentiated if more than two firms succeed in
launching the product.

I will use the notation in the form of {N, .0,- I success status} to describe a firm in
different scenario under each alliance structure. Here N = I, II, III, IV is to represent the

number of firms in an alliance; [.3 denotes the different alliance structures, j =1 , 2, 3, 4, 5.

112

I will show success status by listing all the successful alliances represented by their sizes.
For example, q{I, .Q, II,I,I,I} refers to a single firm’s quantity when all firms succeed
under independent competition in R&D; q{III, .04 II, III} denotes to a member’s quantity
within a three-firm alliance when both the singleton firm and the alliance succeed under
alliance structure .04. I use 72' to denote the profit of a single firm and 1'1 the profit of the
industry. A single price in the market will be denoted as P; and I use p to denote different
prices. Without loss of generality, the investment cost is normalized to 1 and can be
dropped when calculating the expected profit.

Case 1: Only one firm succeeds. This happens with probability B(1-B)3.

Firm i solve: A?“ 0“]: ‘7qu)qi , i= 1, 2, 3, 4

jati

Solving the problem, we have:
1 1 1
(1(1,QII1}=—, P(I,Ql|1}=- ”(1,Q.l1}=(-)
2 2 4
Case 2: Two firms succeed. This happens with probability B2(1- B)2.

Firrnisolve: Ianx (1_qr ‘l’ZqJ-)qi,i= 1, 2.

jti
Solving the problem, we have:

1

q(I,Ql 1,1} =—, P(I,QI
2+r

 

1 2
L1}—(;)

 

 

1,1} = —1— ”(1,0,
2 + r
Case 3: Three firms succeed. This happens with probability B’ (1- B).

Firm i solve: A’gax (l—q, “YZqJ-)qi,i= 1, 2, 3.

jtl

Solving the problem, we have:

113

1

1
1,0 ’PI,Q 1,1,1 : 1,1,1 : ————Z
q( ' 2+2r ( 'l } } (2+2r)

 

 

 

1,1,1} = ”(1,0,

2+2r,

Case 4: All four firms succeed. This happens with probability B4.

Firm i solve: 4110-75 (l-q, —7Zq,-)q,,i= l, 2, 3, 4

 

j¢i
Solving the problem, we have:
(IQIIII}-—1—— P(IQIIII}-1 7r(IQIIII}-(—1——)2
q 91999 2+3)“, 91999 2+3)“, 91999 2+3r

 

 

 

So the expected profits for each firm in a {2, structure can be written as:

E Q = .34 3530-5) 3,320-5)2 _ 3 l
(“I I) (2+3y)2+(2+27)2 + (2+r)2 +0 '6) ,3(4)

11.2.2 Grand Alliance—Q; = {{F1234}}

Under grand alliance, firms can combine their investment to do R&D. As a result,

1
the probability of success is B“. But firms now either all produce some homogenous

goods or produce nothing.

If R&D succeeds, then firm i solves: ll/{Iax (1 —zq,)q,- , i = l, 2, 3, 4

The solutions of this game are:
1 1 1
q(1V,Q,|/V} = g’ P(1V,Q,|1V} = 3., ”(114921 IV} = E

If they fail, then no firm can produce anything and each gets zero profit.

So, the expected profits for each firm in a .(22 structure can be written as:

114

l 1 1 1 1
E Q = 4_ _ 4 __:_ 4
(nl 2) fl(25)+(1 [no (25m

11.2.3 Alliances in the form of {2, 2}-—Q3 = {{Frz}, {Fad}

Under this structure, we have two identical R&D alliances, A1 and A2, each

1
containing 2 firms and can succeed with probability B 2 . And notice that firms within an

alliance will produce homogenous goods, but will compete with a differentiated good

with another two firms, if both alliances succeed in R&D.

Case 1: Both alliances succeed. It happens with Probability B 5 B 5 =B.

I use the superscript of 1 and 2 to represent the groups and the subscript to differentiate

the firms if there is more than one firm in a group.

A representative firm i in alliance A1 will M51115 (1" qil " qj' " 7(in + qu')ql

l

2 2 l l 2
A representative firm i in alliance A2 will M 9x (1‘ qt " q j _ 7(qi + q j )qi

qt
Solve the equations, we get:

1
3+2r’

__1_
3+2r’

 

q(II,Q,|II,II} = P(11,Q_,|11,11} = 7r(II,Q,|II,II} = (3—12-—)2
+ r

Case 2: Only one of aflmce succeeds. It happens with Probability B 5 (1- B 5 ).

Then the firms within the alliance that succeeds will act as duopolists in market and
provide the homogenous goods. And we have:

9(11903|11}=% P(11,Q3|Il}=-:15—,7r(II,Q3|II}=-;—

The expected profit for any one firm under the above structure is:

115

1 1 l
E(n|Q3)=flzlflz(3———+lzy)+(1-fi2)(91)]=(+——€—7)2+(,35-fl)§

11.2.4 Alliances in the form of {1, 3}—Q4 = { {F1}, {F234}}

1 b

1
Case 1: Both alliances succeed. It happens with Probability BB 3 = B 3 .

1 2 2 2 1
Then the singleton firm will Mlax (1" q, _ 7(qi +qj +qk )qi

(It

2 2 2 1 2
A representative firm i in alliance A2 will M52“ (1" q.- “ q j — qr — 7‘11”,-

(Ii
Solve the functions, we get:

437 37

—_:,_,p(1,o,|1,111}=.g:.§.r_ “(10 4 _37

,2)
,2

 

q,(Io,

           

           

2

 

 

q(III, Q

         

p(III, r2

           

, ”(111,52,

         

     

—3r 2 ’
1

Case 2: Only the singleton succeeds. It happens with Probability B(1—B3). And the

winner earns a monopolistic profit %; and the price and the quantity in the market is -;—.

n(1,Q,|1} = l

1

Case 3: Only the three-firm alliance succeeds. It happens with Probability (l — B) B3 .

In this case, three firms each produce 21;, the market price is ‘11- and the profit of each

firm is 116' To describe it formally, 7r(III,Q4 [111} = i

So the expected profit for the singleton firm is:

116

E(tt{1l124})=/3[fl(: —_—-337,’) +-(1 ’6’) i]

The expected profit for a member in the three-form alliance is:

_§ fiLz _ 1
E(rt{III|.Q4 })—fl [ms—3%) +(1 31161

11.2.5 Alliances in the form of {1, l, 2}—Qs = {{Fl}, {F2}, {F341}

| VI

1
Case 1: All three partres succeed. It happens with Probability BBB 2 —B. 2

I use the superscript of 1, 2, 3 to represent the groups and the subscript to

differentiate the firms if there is more than one firm in a group. Then one of the two

singletons will A?“ (1" q] " 7(‘12 ‘1' 413 + ‘1'?)‘1l

A representative firm i in alliance A3 will ng (1" 7(‘I1 ’ qz ) - q? — q:- >913

1'

Solve them we have:

          

            

3—27 3—27
1.0, =———, 1,0 1,1,11 :—
q( - —4r2 p( 5' } 6+3y—4r2
2—7 2—y
111,12 1,1,11 = , (111,12 -—
q( 5' } 6+ —4r2 p ’ 6+37—4r2
3—2
”(1,9, 7 ,2,)zz,(1110,|1,,=111} (6—2—-7’—-,-)2
6+37—4r 6-+37 4r‘

            

Case 2: Only one of the singleton firm and the alliance succeed. It happens with

Probability 13(1- pm? =(1— 11m? .

Then the singleton firm will M51135 (1‘ ‘1' " 7(‘113 + (1391
q

117

A representative firm i in alliance A; will Max (1 - 7‘1l — 913 _ q; )q,

l

Solve them we have:

 

 

 

          

 

 

        

—2 3— 2
q(1,Q,|1,11}= 7, , p(1,o, 7,,,zr(Io, |1,11}= ( 7 )

—r-) —r) 2(3 -r)
«11.0. 2". .p(II.Q.|I,II}= 2 . .2019 II II} (2—217712

3— ') 2(3——r‘) 23—( r)

1

Case 3: Only the two singletons succeed. It happens with Probability BB(1— B 2 ).

Firrnisolve: Max ((1— qi yij)qi,1= 1, 2.

j¢i
Solving the problem, we have:

1 1 1 ,
q(19Qs|19l}=—_—9 P(19Q5|19I}:_9 ”(I9QSII9I}:(_)-
' 2+r 2+r 2+r

1

Case 4: Only the two-firm alliance succeed. It happens with Probability (1 - B)2 B 2 .
Then each firm will have:

q(II, Q,|11}=— ,,P(II Q,|11}=— ,,7r(II Q,|11}—— _

Case 5:Only one singleton succeeds. It happens with Probability (1— B)(1— B 2 ) B.

Now the singleton will enjoy a monopoly profit.
q,(I Q ,|=1} %,,p(1 Q ,|1}= — 2,,571(IQ [1}:—

The expected profit under the fifth type of alliance structure is:

130111105 })=

 

33—27

3113“ +B(1- B2)(—- 72) +(1-13)(1-B;) 41

21—
6+ 32—42)2 ’6( fl)(2(3_277_) )

118

1 2 2’7 2 2‘7 2 21
EIIQ=2‘————21———1—-
(21 | 5}) 131mm, _4 ,> + B( 31(2(,_7,)) +< 21(9)]

From the above results, we have shown that the firm’s payoff depends on the

alliance structure and the position that each firm has, although they are ex ante identical.

Further, by doing some comparative static calculation, I can derive the following result:

Lemma 1: Given 7, there exists a critical value B( 7), such that when B > B(7), the
singleton firm has no incentive to join an existing alliance; and B( 7) is increasing in 7.

Proof. See the appendix E, where I show that

E(7r |o,) — E(7r[1 |Q, ]» < 0
E(71[111|Q4])- E(rr[l |o, ]) < o

E(7l' |Q, ) — E(7r[1 |o, ]) < 0

When B > B09
E(7r[11 |Q, 1) - E(7r[1 1o, 1) < 0

Lemma 1 says: given the possible differentiation level a singleton firm can achieve, it
prefers staying as a singleton to joining an alliance if the probability of success is big
enough. That is because higher probability of success will give more weight on firm’s
decision to stay alone in avoiding the more fierce competition with the alliance.

Lemma 1 also reveals that when 7increases, singleton firm’s incentive to join an
existing pool increases. The reason is that it is more difficult for a single firm to make a
difference in product market with a bigger 7. In order to offset the differentiation effect,
the singleton must observe a higher probability of success to deviate from an existing

pool.

119

111. Alliance structure equilibrium

In this part, I solve the first stage of the game and find the alliance structures in
equilibrium. In the first stage, the firms form alliance to strategically influence the
behavior and performance in the second stage of the game. There are two types of rules
for alliance formation, namely, a simultaneous game with open membership and a

sequential game with closed membership.

[11.1 Simultaneous Game with Open Membership

Definition 2: In this game, each player F,- announces an action choice simultaneously
from its action space B = {b2, b2, b,,}. For each 4-tuple of announcements B = { B2, B2,
B3, B4} 68 EB] x B2 x B3 x B4, the resulting alliance structure is .0, ={A,, A2,
A,}, where F 2 and F}- e A, if and only if bi: bj.

To simplify the game, I assume that only one single deviation is allowed in the

alliance formation.

Definition 3: A Subgame perfect Nash equilibrium of the open membership game is an
alliance structure .0,” if 71’ (.(2,*) > n" ({2,) for any single firm, where

t¢s, (2,60, and (2560.

Thus, a subgame perfect Nash Equilibrium is a stable alliance structure since no

single firm is able to make a profitable unilateral deviation. Note that I use a definition

120

that is stronger than “stand alone stable”4 but weaker than the coalition proof Nash

Equilibrium. The equilibrium is derived based on the above concept and the stable

strategic alliance in equilibrium is summarized in the following result.

Proposition 1: Under membership without consent game, there exist two critical lines:
L1 connects point (0.09, 0) and (0.22, l), and L2 connects (0.19, 0) and (0.20, 1). The two
lines divide the unit square into three areas, such that:

On the right area of L2, Q = {F1F2F3F4} is the Subgame perfect Nash equilibrium.

On the area left to both L1 and L2, Q2 = {F 1234} is the Subgame perfect Nash equilibrium;
Between L1 and L2 and on the left of L2 Q3 = {{Ft 2}, {F34}} is the Subgame perfect Nash
equilibrium.

Proof: see figure 1 as an illustration; refer to the appendix E for proof details.

 

 

 

 

 

(Substitutability)
y 0.2 0.22
{22
{21
Q3
0 0.09 0.19 l B (Probability of Success)

Figure l: Equilibrium under Games without Consent

 

4 An alliance structure is stand alone stable if there is no firm willing to deviate from an alliance to a
singleton firm.

121

Proposition 1 shows how the probability of success in the industry and the
possible substitutability of final products jointly determine the equilibrium strategic
alliance. Intuitively, with the increase of the chances of success, firms’ incentives to
attend an alliance decrease; and with the increase of the difficulty for a firm to make a

difference in the final product, firms are more likely to stay in an alliance.

Remark: Cooperative Refinements of Nash Equilibrium
So far, I used the stability concept that only allows deviation by individual firms.
Suppose now a group of firms’ deviation is allowed. Then I need to apply coalition-proof

Nash equilibrium (CPNE) to refine the result.

Definition 4: An agreement is coalition-proof if and only if it is Pareto-efficient within
the class of self-enforcing agreements; in turn, an agreement is self-enforcing if and only
if no proper subset of players, taking the actions of its complement as fixed, can agree to

deviate in a way that makes all of its members better off. 5

Proposition 1’: Under membership without consent game, a line that connects (0.19, 0)
and (1, 0.22), L2, divide the unit square into two areas, such that:

On the left area of L2, Q3 = {{F12}, {F34}} is a coalition-proof Nash equilibrium;

On the right area of L2, Q = {F .F 2F 3F4} is a coalition-proof Nash equilibrium.

Proof: see the appendix E for details.

 

5 Bemheim et al. (1987)

122

y (Substitutability)
1 0.20

 

[23 Q]

 

 

 

 

0 0.19 l B (Probability of Success)

Figure 2: Coalition—proof Nash Equilibrium under Open Membership Game

There are two implications for the Pr0position 1’. First, no grand alliance is
possible once group deviation is allowed. Second, in equilibrium, only symmetric
alliance could exist. These results confirm most phenomena that we observed. In the real
world, grand alliance is rarely formed unless there is a government support; and
symmetric alliances are frequently observed in automobile and electronic industries
where firms compete in groups in R&D when the risk is high. For many industries with

higher probability of success in inventing new products, individual structure prevails.

111.2 Sequential Game

I adopt the same concept of an infinite-horizon sequential game with unanimity
rule as Bloch (1996). The game proceeds in the following ways. First, F1, which is
chosen by nature, makes a proposal for an alliance, e.g. {F1, F3, F4}. Then the player on

Ft’s list (not including F1) with the smallest index — here, it is F3 either accepts or rejects

123

the pr0posal. If F3 accepts, it is F4’s turn to make the decision. If F4 accepts it too, then, a
three-finn alliance is formed, which leaves a structure of Q4. If any of the potential
members rejects F 1 ’s proposal, then the current proposal is thrown away. F2 has a chance
to make a proposal, until any one of the players’ proposals is accepted and the remaining
players repeat the game in the same way. One assumption here is that once an alliance is
formed, no firm can leave and no new member can be accepted.

With four firms in the game, it involves a lot of calculation in the formal way to
find an equilibrium if following the above concept. Fortunately, according to
Bloch(l996), the infinite-horizon Unanimity game of alliance formation yields the same
stationary Subgame perfect equilibrium coalition structure as a “Size Announcement”
game. In other words, each firm’s proposal of alliance to which it wishes to be a member
is equal to a partition choice. A reduced game tree is shown in Figure 3.

Figure 3: Size Announcement Game: a Simplified Unanimity Sequential Game

{Grand}

 

F3 {1,2,1} {1,3} {2,1,1} {2,2}

{1,1,1,1} {1,1,2}

124

Solving the model by backward induction, we can get the following result; note

that the order of the asymmetric alliances matters.

Proposition 2: Under sequential game, there are two lines that split the unit square into
three areas. Lt connects (0, 0.11) and (0.09, 1); L2 connects (0.19, 0) and (0.20, 1); such
that:

On the left of L1, {24 {{Fl23}, {F4}} is the Subgame perfect Nash equilibrium;

Between L1 and L2, {23 {{F12}, {F34}} the Subgame perfect Nash equilibrium;

On the right of L2, {2, {{Fl}, {F2}, {F 3}, {F4}} is the Subgame perfect Nash equilibrium.
Proof: see the Appendix E. The proposition 2 can be illustrated as in the following figure.
(Substitutability)

y (Substitutability)
(0,1) 0.09 0.20 (1,1)

011,? '

 

Q3 0]

 

 

 

 

 

(0,0) 1 (1,0)
0 0.19 1 B (Probability of Success)

 

Figure 4: Equilibrium under Sequential Game

125

In the sequential move game, firms can choose whether to form or join a specific
alliance or stay as a singleton. Both the alliance and the singleton can exclude the
outsiders. Intuitively, an alliance is formed only when the members’ gain from enhanced
probability of success is more than the loss of the increased competition among alliance
members. Comparing the closed game with the refined open game, the only difference
lies in the equilibrium structure around the comer of point (0, 1). Since the probability of
success is very low for each firm and the product differentiation is also unlikely in the
final product market following a success, firms can gain more from R&D cooperation at
a lower cost of product competition. So, the first firm to propose will choose to form a
three-firm alliance and the two other members will accept this proposal. The fourth firm,
unlike in the open game, cannot join the existing alliance even it will make it better off.

Proposition 2 also implies that except on the occasion when the probability of
success for single firm is very low and the final products substitution is very high, there is

no first mover advantage in a sequential game.

Definition 5: .Q ={n1, n2, nm} is a concentration of!) ’= {n1’, n2’, ..., nmt’}, where m ’2
m, if and only if one can obtain {2 from {2’ by a finite sequence of moving one member at
a time from an alliance in .Q’ to another alliance of equal or larger size.

Remark: Under closed membership game, the decrease of B and the increase of 7will

lead to a more concentrated alliance structure.
On the unit square from comer (l, 0) to comer (0, 1), the probability that a single

firm can succeed in R&D declines and the final products produced by different alliances

126

are getting more substitutable. As a result, firms are more willingly to join an existing

alliance. So the equilibrium structures change from {1111}, to {22}, and to {13}.

IV. Welfare Analysis

In this section, I calculate the social welfare under different strategic alliance
structure and find the optimal structure under different combination of the probability of
success and the substitution level. The social welfare is measured by the sum of the
consumer surplus and the producer surplus, which is the same as the total utilities that
generated in the utility function. 1 first derive the inverse demand firnctions; then get the
utility function that is implied by the inverse demand function. The major finding is
summarized as follows.

Proposition 3: Social welfare corresponding to different alliance structures change with
the combination of B and 7. There exist three critical lines: L1 connects (0, 0.08) and
(0.23, 1); L2 connects (0.35, 0) and (1, 1); L3 connects (0.78, 0) and (l, 1); such that, from
social welfare perspective:

On the left of L1, .02 {{F1234}} is the optimal alliance structure;
Between L1 and L2, [)3 {{F12}, {F34}} is the optimal alliance structure;

Between L2 and L3, {)5 {{Fl}, {{F2}, {F34}} is the optimal alliance structure;

On the right of L3, {2, {{Fl}, {F2}, {F3}, {F4}} is the optimal alliance structure.

Proof: see the Appendix E.

Comparing the social welfare optimal structure in equilibrium with the Subgame
perfect Nash equilibrium under both open and closed game, a major difference is: .05

{{Fl}, { {F2}, {F 34}} is the optimal alliance structure from social welfare point of view

127

for a big area of combination of B and 7, but it can never survive as equilibrium in the

business world. See figure 5 for an illustration.

 

 

 

 

 

y (Substitutability)
(o 1) 023 (1,1)
92
.Q
3 05
01
(0,0) (1,0)
0 0.08 0.35 0.78 l B (Probability of Success)

Figure 5: Social Welfare Optimal Structure in Equilibrium

Also, note that in both the sequential game and refined open game, a grand
alliance cannot exist in equilibrium. That means, in this model, the enhanced probability
of success can never be big enough to compensate the expected loss from increased
competition in the final product market.

Proposition 3 clearly disclosed the discrepancy between the social motive and the
private motive in forming an R&D alliance. Firms fail to form an alliance mostly in fear
of the fierce competition in production market. Can the cooperation in production market
among alliance members eliminate the discrepancy? Morasch (2000) introduces a model
where alliances serve as output commitment device. The idea is that member firms can
establish a production joint venture for certain intermediate product. The joint venture

then sells those products to each member at an agreed transfer price. In the end of the

128

game, all alliance members share the profit or loss of the joint venture evenly. Morasch
(2000) shows that forming a production joint venture with an appropriate transfer price is
formally equivalent to signing an alliance contract with output based payments that are
financed equally by all other member firms.

Suppose government adopts this idea and allow firms form a grand alliance when

the probability of success is small enough. Now the profit function of firm i in the grand

alliance is given by: a,(Q,,2)=(1—(2qj)—q,)q,+11q,-/12qj/3, where it is the
1 1

agreed transfer fee based on output.

The game was solved and the results were compared with the {23 {{F12}, {F 34}}
structure without production alliance contract. It is shown that grand alliance will survive
as equilibrium when B is small, which is the favored result suggested by earlier social
welfare analysis.

The problem is, even though the production joint ventures would not be banned
by the antitrust legislation, it results in a lower social welfare comparing with both the
grand alliance and the .03 {{Ft 2}, {F34}} structure without production alliance contract.
Thus, from social welfare point of view, strategic alliance serving as output restriction
device is not a good solution to the discrepancy between socially optimal equilibrium and

the market equilibrium.

V. Concluding remarks.
This paper develops a simple model to explain firms’ alliance formation patterns
in different industries in the precompetitive R&D cooperation. Based on the conjecture

that the interplay between technology uncertainty and product differentiation determines

129

firms’ decisions on forming R&D alliances in developing a new product, I examine the
stable strategic alliance structure for four firms under open membership simultaneous
move and closed membership sequential move games in a quantity setting context. The
major findings are: first, under the open membership game, only {22} and {1111}
symmetric alliance structures exist in equilibrium; under the closed membership game, an
asymmetric {13} structure also can emerge in equilibrium. Second, Social welfare
analysis shows when the probability of success for each firm is small enough, a grand
alliance is optimum. But the discrepancy between the social optimum and the market
equilibrium cannot be solved by alliance member’s further cooperation in the product
markets without sacrificing welfare.

When allowing strategic alliance to serve as an appropriate commitment device,
Morasch (2000) proves that in a linear Coumot oligopoly with at most five firms only
one alliance forms. The model shows that for the R&D strategic alliance formation, their
result does not hold.

Brown and Chiang (2002) study the conjecture that increasing market volatility
leads to larger coalitions in an oligopoly. They found that if market volatility starts at a
low level and proceeds to a moderate level, do not expect a general increase in coalition
size. But if it is sufficiently large, coalition size rises with market volatility,
independently of the coalition forming rules. Although this paper is dealing with R&D
uncertainty, the results are quite similar to theirs.

There are two limitations on the methodology. First, the model used a specific
R&D cooperation function that relates the number of firms in the alliance with the

increased probability of success. It is unclear whether and how a different form of

130

cooperation productivity function will influence the equilibrium results. Second, there are
four symmetric firms in this game. Although it facilitates the analysis of different types
of alliance structures without using any constrainté, the assumption weakened the model.
A natural extension of the model will be to introduce n firms with certain asymmetric
aspects and see whether my findings can sustain. Also, fi'om public policy point of view,
how to provide incentives to induce the socially optimal alliance structure remains to be
pursued. A further research on this subject also includes studying the alliance formation

within Bertrand price-setting oligopolies.

 

6 A typical assumption used in existing literature when dealing with 11 firms is there are only two coalitions
can form. See Belleflamme (1997).

131

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133

Appendix E:
Range of Inter-firm Links7

Inter-firm Links
I
I l
Contractual Agreements Equity Arrangements
1

l

 

ll'raditional Nontraditional No New Entity Creation of limity Dissolution

 

 

 

 

 

Contracts Contracts I of Entity
_l I 1
_ Arm’s-length _Joint R&D _ Minority Nonsubsidiary JV
Buy/sell Equity JV 5 Subsidiaries
Contracts ' Joint Product Investments of MNCs
Development
* Franchising ’ Long-term - Equity ' Fifty-fifty M&A
Sourcing Swaps JV
Agreements
- Licensing - Unequal
‘ Joint Manufacturing Equity
_ Joint Marketing JV
— Cross-
Licensing r Shared Distr./Service

 

_ Standards Setting/
Research Consortia

Strategic Alliances

Proofs of Lemmas and propositions:

Lemma 1:

1) E(71|Q3) — E(7t[I|Q,])) < 0 when B > 13(7)
E(7rI03)-E(Ir[1|051))— — 54412—1211 —

(3 2)

3 3—27
32 ____)
Bl (6+37-4 47

 

+fl5(1—Bx-2————33 +-B(l 35x, :y)’+(1-B)(l-B5)-:;l

(32)“)

 

7 See Yoshino and Rangan (1995), p. 8

134

      
  
   
    
 

n(Q,)—n(I/Q'5(i'°5 1
-0.1
—o.15 ,
-o.2 L”
o \‘a.

\.

0.25

Figure 6: Profits Comparison between {112} and {22} structures
1 2— 1
2) E(7r[1111941)-E(fl[11951)=fl’[fl(#)2 41-2131 —

3—27 , 1 3-27 , l 1 , l 1
.____._ Z _ _— _ 1 1__ 1_ 2 _
6+3r—47’) +fl (1 flX2(3_7,)) +130 fl X2”) +( fix [3 )4]

 

121m

n(3/Qs)-n(I/Q4) '°'°5 1,

-0.2 1 ‘

l\

\\
0.5 \-\
13 \,_,
0.75 "\

Figure 7: Profits Comparison between {112} and {13} form

135

s1E1n|Q.)—E1211|12.1)

1 4 3 _ 3—
(EW —1(8B[B—37,z_))+(1B)41

 

Figure 8: Profits Comparison between {G} and {13} structures

4) E(7r[11 |Q,]) — E(7r[I|Q,]) < o

251212—45 +2B(1— 12)1-(2—— )+11— 1311— )1-
6+37 :2)

B‘ ,3/2’11—11) ,33211—2)’
(2+37)2 (2+27)2 (2+r)2

 

3111—21731?

136

 

Figure 9: Profit Comparison between {112} and {1111} structures

Proposition 1:
Proof: For each strategic alliance to be Subgame perfect Nash equilibrium, no single
firm can benefit from a single deviation. So I compare the current profit of the firm with
the profit after possible deviations. The following conditions must hold.
For 9, (F,,F,,F,,Fj,) to be Equilibrium: ”(12) > 7r(II|Q,)
For Q2 (G) to be equilibrium: ”(92) > 71(1 |Q,)
For Q3 (14';2 ,F‘,,) to be equilibrium:

71(1),) > ”(1195)

”((23) > ”(111 |Q,)

For (2.. (Fl, F234) to be equilibrium:

137

7r(I|Q4) > ”(92)
”(111|Q,) > 2(1),)

map» > 71(1 |12,)
For Q5 (F, , F2, F,4)to be equilibrium:

71(1|Q,) > ”(111|12,)
71(1|Q,)> ”(12, )

”(11 |Q,) > ”((2)
Solving these functions, I get the conditions of equilibrium as stated in Proposition 1.
Proposition 1’:
Proposition 1’: Under membership without consent game, a line that connects (0.19, 0)
and (1, 0.22), L2, divide the unit square into two areas, such that:
On the left area of L2, Q3 = {{F12}, {F34}} is a coalition-proof Nash equilibrium;
On the right area of L2, Q1 = {F1F2F3F4} is a coalition-proof Nash equilibrium.
Proof:

E(7IIQ,) - 15020402 ]»

 

= fl 5- l—i 5 0 d1 f d
(3+27)2+(fl fl)9 (25W > ’regar esso flan 7'

So, if firms are allowed to deviate in groups, {22} form dominate the grand alliance on
the whole unit square in my model.

Proposition 2:

138

Proof: For Q1 ={Fi, F2, F 3, F4} to be stable equilibrium, the following conditions must

hold simultaneously:

1'I(Q,) > II(Q,)

32(1),) > 1‘1(111|1),)

2741),) > n(11|1),)

271(1), ) > n(11|1),)

It is shown in my calculation that all these conditions hold
when 272(Q,) > 1'I(II |Q,) , which is the area on the right of L2 that connects (0.19, 0) and

(0.20, 1);

Q2 ={F1234} is a stable equilibrium when the following conditions are satisfied

I1(02) > 11621)
1'1(Q2) < 11(Q3)
1'1(Q,) > 1'1(Q,)
simultaneously: , but the calculation shows that I'I(Q,) < II(Q,).
11(0)) > 11(01)
I1(02) < H(Q,)
1'I(Q2) > 1'I(Q,)

It concludes that Q2 = {F1234} is a dominated structure in equilibrium.
For Q3 ={Ft2, F34} to be an equilibrium, the following conditions must hold:

n(11|1),) > 2741),)
n(11|1),) > 22(1),)

H(11|1),) > 22(1),)

139

It’s shown that when II(II |Q3) > 271(Q,) , which is the area on the left of L2 that connects

(O. 19, 0) and (0.20, 1), all the three conditions hold.

For Q4 ={F1, F234} to be an equilibrium, we must have:

11(111|1),) > 37r(1),)
n(111|1),) > 32(1),)
H(111|1),) > 32(1),)

H(111|1),) > 32(1),)

It’s shown that on the left of L; that connects (0, 0.11) and (0.09, 1), all these conditions
hold.

For Q5 ={F1, F2, F34} to be an equilibrium, we must have:

n(11|1),) > 271(Q,)
n(11|1),) > 2n(111|1),).

n(1|1),) > map»

It is shown in the calculation that Q5 ={F 1, F2, F34} is dominated by Q1 ={F 1, F2, F3, F4}
when B is medium and big, and by Q3 ={F12, F 34} when B is medium and small.
Proposition 3:

First, I calculate the expected social welfare under each alliance structure and get the

following result.

E(SW(Q. )1 = 31” ((1-3); , 8112—1) 1313+» _ 3(2—w 13+27) +16/2’ (1+7)

8 (2 + 7)’ (1+ 7)2 (2 + 37)2

 

)

140

E1SW1122» = 122’;

 

E1SW1123» = 317? mnfl

 

B7(448 —3367 —9672 + 8173))

E1SW19.»=-3331“315+412“ (84,2).

17? —1),6’(3 + 7)

E1SW112.» = 31112 —1)ZJZ+%(JB-1Xfl-W" (2+ )1

(B-1)fl”’(59-447 —872 +873) , 12””(43 —197— 2472 +1273)
4125—31 ’ 1682—4751
Next, I compare each of them and find the optimal structure for the each combination of

the parameters.

 

Figure 10: Social Welfare Comparison between {112} and {1111} structures

141

 

51(92) -Sfl (93)
-o.2 1

 

Figure 12: Social Welfare Comparison between {G} and {22} structures

142