Why do firms disclose knowledge and how does it matter ?
Paul Muller*, Julien Penin♦
Abstract
In this paper we provide a theoretical framework describing the formation of
innovation networks. Our main emphasis is put on the role played by open
knowledge disclosure on the formation of such networks. It is argued that
firms who widely disclose knowledge to other firms are more likely to enter
innovation networks and to acquire a central position within these networks.
Indeed, the act of disclosing knowledge triggers their reputation, which
constitutes the main criterion firms take into account when deciding whether
to start a cooperation with another firm. The higher the firm own reputation
the higher her chances of entering new R&D partnerships with other firms.
Our model provides therefore a rationale to behaviors of open knowledge
disclosure by showing that such strategies, although risky in the short run,
may pay in the long run by enabling firms to access external sources of
knowledge more easily.
Keywords: open knowledge disclosure, inter-firm cooperation networks,
reputation, network simulation.
JEL classification: D85 – L14 – L16 – L23.
*
BETA, University Louis Pasteur, 61 avenue de la Foret-Noire, 67085 Strasbourg, France
Email : [email protected]
♦
BETA, University Louis Pasteur, 61 avenue de la Foret-Noire, 67085 Strasbourg, France, and Université du
Québec à Montréal, Département des sciences économiques, case postale 8888, Succursale Centre Ville,
Montréal, Québec, Canada, H3C 3P8.
Email : [email protected]
-1-
I.
Introduction
The aim of this paper is to provide a theoretical framework describing the formation and
evolution of innovation networks. Specific attention is paid to the emergence of central agent(s) within
innovation networks and to the role of knowledge disclosure in giving rise to the emergence of these
central players. In short, we argue that disclosing information about the competences (by widely
disclosing knowledge) not only provides competitors with useful information about firms’ own
researches but also allows the disclosing firms to improve their external reputation. This, in turn helps
them to acquire a central status within innovation networks, enabling therefore disclosing firms to
increase the efficiency of their research.
We start from the observation that many firms tend to widely disclose some parts of the
knowledge they hold, which then become available to other firms, including to competitors. Firms
allow their researchers to publish in scientific journals, to attend conferences, they apply for patents
while not planning to use the exclusive property right associated with them, they release information
on their web sites, etc. (see Allen, 1983; Hicks, Ishizuka, Keen and Sweet, 1994; Hick, 1995).
Since such behaviors of open knowledge disclosure do not give rise to direct rewards, they
have for long time been considered as a puzzle by mainstream economics, which assumes that once an
innovation is implemented the only way to benefit from it is to exclude other firms from its use by
keeping it secret or at least by protecting it with a patent. However, nowadays, reasons underlying
such behaviors are well accounted for by standard economic theory (see Allen, 1983; von Hippel,
1987; De Fraja, 1993; Harhoff, 1996; Boivin, 2000; Eaton and Eswaran, 2001; Pénin, 2003; Harhoff,
Henkel and von Hippel, 2003).
Among others, behaviors of open knowledge disclosure may be triggered by reputation
motivations. Reputation may constitute an important effect for researchers who often value their
prestige as much as their salary. But reputation may also be profitable to firms and not only to
researchers. Indeed, acquiring a reputation as innovator may facilitate firms’ access to financing by
banks, stock exchange and venture capitalists, it may make easier to get public or private contracts,
grants and subsidies. Furthermore, and this is the point emphasized in this paper, a reputation as
innovator may allow a given firm to find competent R&D partners more easily. These effects stem
from the fact that, as brilliantly put by Hicks (1995), open knowledge disclosure (the fact that firms
publish in scientific journals for instance) enables firms to “signal un-publishable resources” to the
academic and industrial worlds.
Economic industrial theory has for long acknowledged that innovation is a collective process
involving several agents such as firms, universities, research institutes, venture capitalists, banks,
patent offices, government agencies, etc. (see, for instance, Gibbons, 1994). Being a member of an
innovation network (and a fortiori, having a central position in a network) is essential for firms
-2-
because first, it allows them to share the costs and the risks of doing research and second, it provides
access to knowledge held by other firms and which would not be available otherwise.
However, this collective process of innovation, the formation of R&D collaborations between
firms, occurs within an environment of incomplete information. It may be hard for firms, for instance,
to infer exactly the competences of potential partners. It follows that firms may sometimes think it a
profitable strategy to disclose some of their knowledge -even the most valuable- in order to break the
uncertainty with regard to their competences. In other words, because incomplete information impedes
collaboration processes, open knowledge disclosure constitutes a prerequisite to knowledge trading
within an innovation network. Reputation, by mitigating adverse selection problems, facilitates entry
into innovation networks and helps improve the position of the firm within those networks.
We propose in this paper a simulation model based on social Network Analysis aimed at
describing the emergence and the dynamics of innovation networks, with particular emphasis on the
role of knowledge disclosure within this process. At the start of the simulation, firms, symbolized by
nodes located on a empty graph, are endowed with different amounts of specific knowledge1 and with
different strategies in terms of knowledge disclosure (high frequency of knowledge disclosure and low
frequency).
The profit of a firm is positively related to the amount of specific knowledge she holds, which
in turn depends on the firm’s position within the network (since this position determines among others
the amount of external knowledge that the firm has access to and hence can absorb). It is also assumed
that firms’ activity of open knowledge disclosure increases their reputation, easing therefore the
building up of new connections. Firms have therefore to face the following trade-off : Either they
choose to frequently disclose knowledge to all the other firms (including to their direct competitors)
thus decreasing their current profit but also increasing their reputation (which may enable them to
enjoy in the future more inter-firm R&D cooperative relationships and to have access to extra sources
of external knowledge), or they decide to keep their knowledge secret, favoring their current
profitability but eventually impeding their ability to create new connections, since they will suffer
from a lack of reputation.
A major result of our simulation is the setting of a particular network shape where some firms
acquire a central position in the innovation network while other adopt more “peripheral” positions.
Moreover, we find that firms’ status within innovation networks and firms profitability are highly
sensitive to the strategy of open knowledge disclosure (low or high frequency) they adopt. It may not
only be the firms endowed with a higher amount of specific knowledge that acquire a central status but
1
By specific knowledge it is important to understand that we mean pieces of knowledge only held by the firms and not by
other members of the innovation network, i.e. specific knowledge corresponds here to secret or unrevealed knowledge rather
than to knowledge that can be used, that make sense, only in the firm context.
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also the most active in terms of knowledge disclosure. In other words, a reasonable strategy of open
knowledge disclosure enables firms to catch up with firms initially endowed with more specific
knowledge.
The paper is structured as follows: In the next part we explain the link between open
knowledge disclosure, the initiation of formal and informal R&D collaborations and the problems that
arise from incomplete information. We then present a simulation model aiming at stressing the role of
open knowledge disclosure in the formation of innovation networks. This is followed by a discussion
of the simulation results. We conclude with remarks and indications for further work.
II.
Open knowledge disclosure, R&D collaborations and incomplete information
II.1.
Innovation as a collective process
Innovation is usually perceived as a group of activities involving interaction and knowledge
exchanges between people and organizations. Innovation becomes thus the outcome of a system of
inter-personal and inter-organization interactions taking place continuously and everywhere. An
innovative firm can interact with many different actors: other firms (competitors, suppliers,
customers), universities, research institutes, venture capitalists, banks, patent offices, government
agencies, etc.
In other words, knowledge production or innovation is a collective process. In order to be
innovative, economic agents must cooperate, must set up formal research joint ventures (RSV) or
more informal innovation networks, in which they have the possibility to exchange knowledge and to
share specific competences (Gibbons’ mode II, 1994). Specifically, an innovation network2 can be
defined such as a reasonably stable set of partners who collaborate in order to improve their research.
More precisely, it is: “a set of reciprocal, reputational or customary trust and cooperation based
linkages among actors that coalesces to enable its members to pursue common interests, in this case on
respect of innovation” (Cooke, 2001, p. 953; see also Maskell and Lorenzen, 2003).
R&D collaborations with other firms or with universities are important for two reasons (i.e.
they allow an increase of the firm’s stock of knowledge via two channels):
(i) They increase the efficiency of the research, since they allow firms to share the tasks, the
costs and the risks of doing research. In other words, R&D cooperation allows a more efficient
division of researches by enabling firms to develop synergies with complementary partners;
2
A definition of an economic network is given by Kogut (2000, p. 407): “A definition of an economic network is the pattern
of relationships among firms and institutions. In this definition, an idealised market is a polar case of a network in which
firms transact at spot prices and are fully connected in potential transactional relations but are disconnected through their
absence of cooperative agreements. Few market exist of this type. Rather most markets consist of sub-sets of firms and
institutions that interact more intensely with each other on a long term basis. These patterns of interactions encode the
structural relationships that represent the network”.
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(ii) They open access to technical opportunities and to external sources of knowledge (which
would not have been available otherwise since, most of the time, knowledge is not a public good that,
once produced, becomes available to everybody, but is rather a sticky good that remains within the
organization or network that has produced it): a) by helping to recruit young researchers; b) by
providing access to new technologies and to sticky knowledge; and c) by enabling firms to gain early
warning of where things are starting to happen. To put it plainly, companies who are members of
innovation networks keep intellectual alert and are able to move quickly into new areas.
Being a member of innovation networks is important because networks exclude as well as they
include. If firms who are members of an innovation network have a privileged position to acquire
knowledge, outside firms can often not access the knowledge produced within the network. As argued
by Gibbons (1994), in a collective form of knowledge production, knowledge production and
knowledge appropriation converge, meaning that, in order to access the produced knowledge,
outsiders must first be granted access to the network. Firms who want to benefit from specific
knowledge must actively cooperate, they must first enter the network in which this knowledge is
enclosed. This still enhances the importance of membership.
II.2
How can firms identify potential fruitful R&D partnerships?
An important question that firms involved in this collective process of innovation have to
address is dealing with the problem of finding the most adequate partners. How can firms identify
potential fruitful partnerships? How can they distinguish between the different potential partners?
Collaboration has a cost, which implies that firms cannot collaborate with any other firm. Each firm
can only manage a finite number of collaborations. The importance of the selection of the partners is
still increased by the fact that collaboration often constitutes a risky strategy, since it usually means to
open access to the most precious knowledge of the firm to collaborators, who may often be rivals too.
Collaboration also requires sometimes to invest in the construction of common, specific assets
(Williamson, 1975), exposing firms to risks of hold-up. Furthermore, even if these considerations
about the cost of the collaboration can be neglected, it remains that firms are clearly more interested in
collaborating with other firms who are at the forefront of the technological frontier. All these elements
tend to support the view that firms must thoroughly select their partners.
But on which criteria can firms base their selection of partners? Which variables determine the
choice of collaborators? What happens at the initial stage of the collaboration? We see that this
problem of how to find the adequate partners is at the core of the collaboration problem and, as such,
at the core of the innovation process itself. But curiously, economic literature has not focused much on
this problem of the initiation of the collaboration. A notable exception being the work of Grosetti and
Bès (2002), who explored the ways through which 110 R&D collaboration between firms and public
labs in France were initiated.
They identify three main channels through which an R&D collaboration may start: The first
they call the “logic of market”, when the collaboration results from a link established through
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scientific publications or public conferences, meaning that partners have been connected, have heard
about each other, through a scientific publication for instance. The second they call “the logic of
personal network”, when collaboration results from former existing personal relationships between the
two entities (see, for instance, the work of Granovetter, 1973 and 1974, dealing with the importance of
weak ties in connecting people)3. In this case, the collaboration is initiated by a person who knows a
friend who has a friend working for a company involved in such an activity, etc. The third way to
initiate a collaboration is when this collaboration is organized and structured by a public institution
who puts the different actors in touch. Globally, their inquiry indicates that for 42 out of 110
collaborations the contact results from a “logic of market”, for 48 out of 110 collaborations from a
“logic of network” and for the remaining 20 collaborations from a “logic of the institutions”. The
“logic of market” to initiate collaborations has been proved to be specifically high when firms and labs
are not located in the same region. Indeed, when the partners are located in the same region “the logic
of network” applies in 60% of the collaborations and “the logic of market” in only 20%, while when
partners are not located in the same geographical region the logic of market applies in 59% of cases
and the logic of network in only 24%.
Our interest lies precisely in what Grosetti and Bès called “the logic of market”. More
specifically, we consider that the choice of a firm’s partner collaborating on R&D is based mainly on
its reputation, which is defined here as a set of information determining the decision of an agent to
form a new relationship with an other agent (see Muller, 2003). It follows that all the variables
influencing a firm’s reputation may also influence positively or negatively the firm’s attractiveness.
Firms who wonder whether or not to cooperate with a given firm may grant considerable attention to
the reputation of this firm. This consideration leads us directly to the “logic of market” quoted above,
since attending conferences, publishing in scientific reviews or applying for patents constitute ways to
improve the firm’s own reputation. One may hence conclude that the major role played by reputation
in the collective process of knowledge production may provide a convincing explanation to behaviors
which have often been misunderstood by mainstream economic theory, namely behaviors of open
knowledge disclosure (see Pénin, 2003).
II.3.
On open knowledge disclosure
Open knowledge disclosure is defined here as situations in which a firm chooses to voluntarily
disclose knowledge without being directly rewarded for this disclosure and without being able to
prevent some firms to have access to the disclosed knowledge (see Pénin, 2004). Channels through
which firms may openly disclose knowledge are scientific publications, patents, conferences, the
Internet, etc. To openly disclose knowledge means therefore to offer knowledge to other firms without
3
It should be noticed that in this case the personal network is already structured and nothing is said about how it was formed.
It is however quite likely that open knowledge disclosure, i.e. the logic of network, played an important role to help
developing the personal network of the firm.
-6-
any guarantee of direct rewards. On the other hand, such behaviors may involve important costs4.
These two features, high costs and uncertain benefits, explain why industrial economists have for long
considered such behaviors as puzzles.
Conventional wisdom suggests that behaviors of open knowledge disclosure remain marginal
and that firms who do not have a natural protection for their innovation (such as a lead time advance,
or complementarity with other assets, etc.) try most of the time to keep a tight secrecy over their
research (since open knowledge disclosure cannot pretend to any direct remuneration). On the
contrary, it seems that many firms decide to openly disclose part of their knowledge. In some
industries such behaviors are not marginal but are even the norm.
For instance, Hicks (1995) attempted to measure the tendency of firms toward scientific
publications. The figures suggested in her paper are sometimes impressive and, from a global point of
view, they convince the reader that firms do publish massively in many sectors. She concludes that:
“Firms such as Philips, Hitachi, ICI, Ciba, Siemens, Sandoz, Roche, Hoechst and Toshiba contribute
as much to the public literature as medium sized universities” (Hicks, 1995, p. 403). Furthermore,
these publications by firms seem to contain, at least to some extent, valuable knowledge since they are
not less quoted than publications written by researchers in universities. Hicks’ explanation to why
firms publish is very close to our view: She suggests that such publications may be targeted to signal
unpublishable resources to the academic and industrial worlds.
Other studies reach similar conclusions. For instance in the pharmaceutical industry (Koenig,
1983; Cockburn and Henderson, 1998) or in the case of copper interconnects technology in which it
has been shown that IBM published, from 1985 to 1997, twice as many publications related to this
technology as the most productive universities (Lim, 2000). Qualitative and quantitative evidence
regarding the publication activities of European and Japanese firms were also provided respectively by
Hicks, Ishizuka, Keen and Sweet (1994), Hicks, Isard and Martin (1996). Regarding the other
channels through which firms may openly disclose knowledge (conferences, the patent system and the
internet) empirical evidences are fewer than for publications but we nevertheless believe that these
channels are relevant. For instance, in the case of the patent system, it is more and often reported that
firms regard patents not only as a way to achieve an exclusive monopoly position but also as a tool to
improve their bargaining position in negotiations with other firms, which tend to support the
4
The most dissuasive cost being probably the one that comes from providing useful information to potential competitors,
which may sharply affect the firm profitability through her position in the competitive environment. Indeed, rival firms may
absorb and use the disclosed knowledge, which in turn enable them to improve their technology and hence to compete more
fiercely with the firm who disclosed. This sole cost may frequently deter firms from openly disclosing knowledge. Other
costs involve the codification of the disclosed knowledge (which must be articulated, expressed in a language and written
down on a support) or the fact that the support through which the diffusion is operated may not be free (patent application for
instance is very expensive).
-7-
hypothesis of patent as being valuable both for the property right and the reputation it provides to its
holder.
Furthermore, since there is no contractual agreement between the sender and the recipients and
since, in most cases, the sender does not even know who the recipients are, behaviors of open
knowledge disclosure have often been misinterpreted. Mainstream economics usually refers to the
notions of altruism, irrationality or to intrinsic motivations to explain them. However, it can be shown
that such behaviors can find many rational explanations, meaning that there are many indirect
mechanisms through which they may pay. A wide range of extrinsic motivations may trigger firms to
openly disclose knowledge, starting from the willingness to force reciprocity, the willingness to trigger
network effects or pecuniary spillovers, the necessity to keep bright researchers working for the firm,
the willingness to enhance the reputation of the firm, etc. (see Allen, 1983; von Hippel, 1987; De
Fraja, 1993; Hicks, 1995; Harhoff, 1996; Eaton and Eswaran, 2001; Harhoff, Henkel and von Hippel,
2003). Most of the time there is therefore no need to refer to altruism, bounded rationality or intrinsic
motivations to explain behaviors of open knowledge disclosure.
To summarize, let us now go to the focus of this paper and shed light on the relationship
between open knowledge disclosure, the collective process of innovation and problems of incomplete
information. As soon as we take for granted that the innovation process requires the collaboration of
several actors and that this process of collaboration takes place within an environment of incomplete
information (i.e. agents do not know perfectly which partner it would be preferable to cooperate with),
one may suggest the following proposition: Open knowledge disclosure helps firms to find R&D
partnerships more easily. Indeed, behaviors of open knowledge disclosure constitute indisputably a
way to enhance reputation. And reputation, as it has already been stressed, constitutes a powerful
device in improving firms’ position on the “market to find R&D collaborations”. In other words, open
knowledge disclosure may be a way to solve at least in part the problems due to incomplete
information. It may be a way to show to potential partners what the firm is doing and what she is
looking for, and as such, it may be a powerful device in order to find competent partners to collaborate
in R&D with. Let us now present a simulation model aiming at exploring more in depth the existing
links between R&D collaborations and open knowledge disclosure.
III.
A model of innovation networks morphogenesis
To put it shortly, the model of network morphogenesis decomposes as follows. A population
of firms is located on an empty graph. This graph may symbolize an innovation network at its
beginning, when there are no connexions between firms. At the outset, each firm has a scalar
knowledge endowment which is composed of specific knowledge and of general knowledge (i.e.
knowledge shared by all the firms of the model). Since those firms are supposed to be knowledge
-8-
intensive, specific knowledge constitutes their main source of profits. Furthermore, at each time step,
firms engage in R&D activity, which is aimed at building up new pieces of specific knowledge. The
probability of success (the probability of producing a new piece of specific knowledge) depends on the
total level of knowledge a firm has access to (such knowledge may be internally mobilized as well as
may stem from external sources through inter-firm R&D agreements). After having performed such an
activity, each firm considers the decision whether to disclose or not a part of the specific knowledge
they hold which, if disclosed, would become general knowledge. Such an action, although it decreases
her current profit, allows the firm to build up her reputation. Then, periodically, a firm considers the
decision of linking up with an other firm. Such a connexion process is driven by reputation effects:
since reputation mitigates the uncertainty associated with a first interaction, firms aiming at connecting
with an other business tend to give priority to firms enjoying higher levels of reputation. The main
interest of being connected with an other firm is to be offered access to a part of the specific
knowledge held by this firm, through joint ventures or any type of cooperation agreement.
Connections therefore increase the stock of knowledge of connected firms, which in turn enhances the
performance of their R&D.
III.1. Basic assumptions of the model
At time t, n firms are located on a graph Gt = (V , Γt ) , where V = {1,…,n} is the set of firms
(vertices) and Γt = {Γ it , ∀i ∈ V } is the list of connections in the graph where Γit = { j ∈ V | {ij} ∈ Gt } ({ij}
represents the tie binding two firms i and j at time t) constitutes the neighbourhood of firm i at time t,
or, put differently, the set of R&D agreements enjoyed by firm i at time t. For t = 0, {Γ0} = {∅} , the
graph forming the innovation network is empty.
Broadly speaking, the model relies on the coexistence of two types of knowledge. The first
type of knowledge is accessible to all firms in the network and may therefore be qualified as
“general”. This general knowledge is constituted by knowledge contained in scientific publications,
but also, and this constitutes a main focus of the model, by knowledge openly disclosed by firms to all
the other firms. The second type of knowledge is assumed to be only held by each firm of the network
and not available to other firms. In this manner, this type of knowledge may be qualified as firm
specific. Such knowledge may be made of particular know-how, pieces of knowledge subject to
secrecy policies, etc.
A main input in the production of firm specific knowledge is constituted by knowledge itself.
More specifically, in order to produce new pieces of specific knowledge through R&D activity, each
firm has to rely on the knowledge it has access to. This knowledge might be internally mobilized as it
may come from other firms through joint-ventures or any other type of cooperation agreement.
However, a given firm may only make use of a part of the specific knowledge held by its partners.
This comes from the fact that, in the frame of cooperation agreements, partners try to only allow
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access to some pieces of knowledge which have been considered as not vital for the firm. Thus, firms
may only allow access to their complementary competences while forbidding access to their core
competences. Moreover, it is assumed that the knowledge produced and held by firms are perfect
complements. There are no redundancies between the knowledge held by each firm and their partners
of the innovation network. It follows that the total knowledge a firm may mobilize to perform R&D is
given by:
Gen
Spe
Spe
K iTot
, t = K i , t + K i ,t + β ∑ K j , t ,
0 ≤ β ≤1
j∈Γit
Where K iGen
represents the general knowledge held by firm i at time t, K iSpe
,t
, t , the specific knowledge
held by i at time t and β the share of specific knowledge made accessible by firm’s i partners to their
R&D collaborators5. It is assumed that this latter parameter is set as fixed and equal for every firm of
the network.
The objective of each firm is to generate profits. Revenues mainly stem from the monopolist
rents provided by the use of the specific knowledge each firm has produced through past R&D. Such a
rent might come from licensing agreements, patent rights, etc. But, on the other hand, firms have to
bear costs related to the production of knowledge. The first type of costs gathers internal R&D
expenditure as well as administrative costs, etc. The second type of costs stems from inter-firm
partnerships. This issue has been widely discussed, notably in the frame of Transaction Costs
Economics (Williamson, 1975). Indeed, any inter-firm relationship is characterized by the
mobilization of specific assets by both partners. The profit function of a firm i at time t is therefore
given by:
Π i ,t = γ K iSpe
, t − α ki , t − c
Where ki,t represents the degree (or, similarly, the number of partnerships) of firm i at time t. The
parameters γ, α and c represent, respectively, the income generated by 1 unit of specific knowledge,
the unitary cost of an inter-firm relationship and internal costs (R&D expenditure, administrative
costs…). For the sake of simplicity, those parameters have been set as fixed and equal for every firm
at any time.
Lastly, each firm i ∈V is characterized by a strategy concerning the decision of knowledge
disclosure which is assumed to be given and fixed over time. Such a strategy reifies through the
frequency ϕi at which firms choose to disclose knowledge. Firms may be of two types : firms of the
first type adopt an active strategy of knowledge disclosure, giving thus rise to high values for ϕi
5
Notice here that even if R&D partners would give a full access to their knowledge, other partners would still have to absorb
this knowledge. Hence
β
can also be viewed, in some sense, as representing the absorption capacity of partner firms and
not only the share of knowledge made available to them.
- 10 -
whereas firms of the second type tend to adopt a more passive strategy associated with low ϕi values.
As our results will confirm, firms adopting the latter strategy are thus giving priority to the
maximization of current profit whereas firms of the second type favour a more long term strategy.
III.2. The dynamics of the model
The aim of this model is to show that, for knowledge intensive firms, signalling through open
knowledge disclosure constitutes a way to improve the performance of their R&D (and, in fine, their
profitability) by allowing enlarged access to knowledge resources external to the firm through the
binding of partnerships. The dynamics of the system lies thus at the individual level. The dynamics of
the model decomposes into 3 main steps, namely, knowledge production, knowledge disclosure and
partnership binding. A summary of the dynamics of the model is presented in figure 1.
that it
At each time step, each firm is characterized by a certain level of total knowledge K iTot
,t
can mobilize in the perspective of increasing the stock of firm specific knowledge through the
undertaking of R&D activity. Knowledge creation is here considered as a stochastic process : under
the assumption of constant R&D expenditure, a new unit of knowledge is created with a probability
pi,t. Since knowledge constitutes the main input of R&D, the probability of creating a new knowledge
unit is positively correlated with K iTot
, t . This probability is given by the distribution function of an
exponential law:
Spe
Tot
Tot
⎤
pi ,t ⎡⎣ K iSpe
,t = K i ,t −1 + 1⎦ = F ( K i ,t −1 ) = 1 − exp ( − λ ⋅ K i ,t −1 ) with λ > 0
∂F
∂2 F
> 0 and
< 0,
∂K
∂K 2
One may therefore observe that, for R&D expenditure set as equal, the function of knowledge
production is increasing with knowledge but with decreasing returns to scale.
During the second stage of the process, each firm considers the decision whether to openly
disclose or not a fraction of the specific knowledge it holds. This action of knowledge disclosure is
turned towards all other firms of the network. Once disclosed, this fraction of firm specific knowledge
turns general: the amount of disclosed knowledge transfers from the firm’s stock of specific
knowledge to the stock of general knowledge, decreasing thus its current profit. But, on the other
hand, knowledge disclosure induces an increase in the reputation of each emitting firm.
- 11 -
During that stage of knowledge disclosure one important constraint is put on the firms, namely
the fact that their funding6 after having disclosed a fraction of the specific knowledge has to be
positive. Firms who violate this survival condition are removed from the simulation. Moreover, a
firm’s strategy ϕi plays here a crucial role by influencing the decision to engage into the knowledge
disclosure process. Indeed, firms having adopted active strategies of knowledge disclosure disclose
knowledge more frequently than firms having adopted a more passive strategy. Indeed, by interpreting
the parameter ϕi as i’s propensity to disclose knowledge (as expressed in a quantitative way), the
frequency at which i discloses knowledge is proportional to ϕi.
6
t0
For a firm i, her funding at time t0 is given by the sum of her past profits and her initial funding : Ψ i ,0 + ∑ Π i ,t
t =1
where Π i ,t corresponds to firm i’s profit at time t and Ψ i ,0 firm i’s initial funding.
- 12 -
Figure 1: Dynamics of the model
At time t = 0, an empty network where the nodes figure firms. Firms differentiate through 2
dimensions :
A stock of knowledge (general and specific).
A disclosure strategy.
At time t, each firm is characterized by a stock of knowledge
i
K Tot = K Gen + K Spe + β
K Spe , 0 ≤ β ≤ 1 , with Γt being firm’s i neighbourhood at time t and β the
i ,t
i ,t
i ,t
∑
j ,t
j∈Γit
share of knowledge held by the i’s partners that it has access to, as well as by a profit function:
Π t = γ K ispé
, t − α ki , t − ct , α > 0.
Production
Each firm produces a new piece of knowledge with a probability based on an exponential law:
Spe
Tot
Tot
⎤
pi ,t ⎡⎣ K iSpe
,t = K i ,t −1 + 1⎦ = F ( K i ,t −1 ) = 1 − exp ( − λ ⋅ K i ,t −1 )
Disclosure
Specific knowledge disclosure: firms disclose a
share δ out of their specific knowledge
The disclosed pieces of specific
knowledge become general
(decrease in instant profit)
Choice of the partner
according to its reputation :
R j ,t
P [ij ] =
∑ Rk ,t
k
No
Yes
Increase of 1 unit in firm i’s
reputation Ri,t .
Linking
Drawing of a firm i wishing to engage
in a partnership (drawing depending
on the disclosure strategy)
Survival conditions.
If ∑ Π j < 0 the firm goes bankrupt and will be left out for the rest of the simulation run.
j <t
Periodically, the third stage of the process takes place corresponding to partnership binding.
During that stage, one firm has to link up a partnership with an other firm of the network, according to
the reputation of the latter. The probability of picking the firm initiating the partnership depends on the
firm’s strategy ϕi ; firms endowed with an active strategy being more likely to be picked than less
active firms. Indeed, the main goal of an active knowledge disclosure strategy is to increase the firm’s
reputation. This increases the likelihood of binding numerous inter-firm partnerships. But the same
type of reasoning may be turned the other way round. Whereas, in the former case, a firm endowed
- 13 -
with a high reputation might be the recipient of partnership proposals, active firms may also be more
motivated to initiate new partnerships than passive firms.
To summarize, whereas a firm’s strategy plays a central role in the process of relationship
initiation, reputation plays a crucial role in the process of partnership binding. Indeed, a firm initiating
a new partnership links up with an other firm of the network with a probability proportional to the
reputation of the latter. It follows that the probability Pini(i) for a firm i to initiate a new relationship is
given by:
Pini ( i ) =
ϕi
∑ϕ j
j∈V
And, for a firm i initiating a new inter-firm relationship, the probability of i to choose an other firm j
belonging to the network (but not to i’s set of current partners) is given by:
P ⎡⎣{ij} ∈ Gt | {ij} ∉ Gt −1 ⎤⎦ =
Rt j
∑
{ }
k∈V −
Rtk
Γit −1
With Rt j the reputation of firm j at time t.
III.3
Numerical analysis
Since network models are particularly hard to deal with in an analytical way, the methodology
provided by numerical simulation will be applied. Ultimately, our interest lies in the evolution of an
innovation network and the condition under which, starting from a situation where no firms are
connected to each other, such a network develops (through the accumulation of inter-firm partnership
agreement).
Statistics
Our main interest lies in the emergence of inter-firm differentials arising from differences in
knowledge disclosure strategies (either active or passive). Hence, we focus on inequalities indicators
related to the performance of firms in terms of their ability to generate profits. Our interest also lies in
assessing to what extent such a strategy of knowledge disclosure benefits the whole economy. In this
manner, statistics dealing with knowledge growth of the industry will be computed.
The first indicator, related to inequalities in firms performance, is provided by Herfindahl Index
t0
for funding. The funding of firm i at time t0 is given by : Ψ i ,t = Ψ i ,0 + ∑ Π i ,t , where Π i ,t corresponds
0
- 14 -
t =1
to firm i’s profit at time t and Ψ i ,0 to firm i’s initial funding. Herfindahl Index for funding at time t is
then given by:
⎛
Herf ( Ψ t ) = ∑ ⎜ Ψ i ,t
i∈V ⎝
⎞
Ψ j ,t ⎟
∑
j∈V
⎠
2
In order to focus on the link between firms’ performances and their disclosing strategy, we also
use indicators comparing the average profit of firms according to their strategies. In this manner, we
compute a ratio comparing the average profit for active firms with the average profit for passive firms
(Average Profit Ratio - APR). Moreover, in order to assess the relative position between highly
disclosing firms versus slightly disclosing firms in the network, we also compute an other statistics
comparing the average degree for highly disclosing firms versus the average degree for slightly
disclosing firms (Average Degree Difference - ADD).
1
∑ i∈I Π it
APRt = n − m
,
1
∑ Π jt
m j∈J
ADDt =
1
1
k − ∑ j∈J k jt ,
∑
i∈I it
n−m
m
where k represents the number of R&D partnerships of the firm, I is the set of firms who reveal a high
amount of knowledge (n-m firms) and J the set of firms who reveal a weak amount of knowledge (m
firms). One can observe that an APR superior to one indicates better average performance of
disclosing firms compared with non disclosing firms. Similarly, a positive ADD statistic indicates that
disclosing firms have built on average more links than non disclosing firms.
Settings
We consider an economy with n = 100 firms. For the sake of simplicity in the interpretation of
the effects, some individual parameters are set as equal for all firms. Those parameters are provided in
table 1. Such parameters may be merged into two main categories. The first type of parameters deals
with the performance of R&D activity and might therefore be coined as “knowledge parameters”. The
second class of parameters is linked to the generation of profit. They may therefore be viewed as
“financial parameters”.
- 15 -
Table 1: Simulation - General parameters
parameter
Definition
Value
Knowledge parameters
K
gen
i ,0
β
δ
λ
γ
α
C
Fundi,0
Firm’s i (∀i=1,…,100) endowment in general knowledge at time t=0.
Share of specific knowledge held by a firm’s partner which is made
accessible through R&D agreement
Fraction of specific knowledge disclosed to the industry
Coefficient for the exponential law providing the probability of generating
1 new unit of specific knowledge through R&D.
Financial parameters
Marginal income steming from the use of specific knowledge
Unitary cost for maintaining an inter-firm relationship
Fixed costs
Firm’s i (∀i=1,…,100) monetary endowment at time t=0.
500
0.5
0.1 %
10-5
0.75
0.3
5
2000
Each simulation runs for 40,000 periods during which knowledge production and open
knowledge disclosure processes as well as periodical inter-firms relationship binding are performed.
Such a process is performed on average every 40 periods. The reason behind such a periodicity lies in
the fact that, for the simulation to provide significant results, the graph has to feature the sparseness
condition7. Such a condition is met since, at the end of the simulation, the graph contains 1,000 distinct
ties (for a complete graph, the total number of edges would be of 9,900 ties, so that only 10 % of the
connections are active).
The parameters we vary are three. First, in order to assess the consequences of open
knowledge disclosure on firms’ strategies, we vary the frequency of open knowledge disclosure for
firms having adopted an active strategy of knowledge disclosure as well as the proportion of such
“active” firms in the economy (by comparison with “passive” ones having adopted a less aggressive
strategy of open knowledge disclosure). In a second series of simulation runs, we wish to estimate the
robustness of such a strategy of open knowledge disclosure. In doing so, we set the proportion of
active firms as fixed and we introduce differences in firms’ initial endowments in specific knowledge
(comparing highly endowed firms vs. slightly endowed firms). The different values of those
parameters are presented in table 2.
7
The sparseness condition states that Dfull >> Dsparse where Dfull corresponds to the density of a fully connected
graph and Dsparse the density of a sparsely connected graph (see Watts, 1999).
- 16 -
Table 2: Simulation - specific parameters
Definition of the parameter
Values
Frequency in open knowledge disclosure for low disclosing firms
0.1 %
Frequency in open knowledge disclosure for high disclosing firms
0.5 % - 0.7 % - 1 %
-2%
Proportion of high disclosing firms in the economy
6 % - 26 % - 47 %
Initial endowment in specific knowledge for slightly endowed firms
5
Initial endowment in specific knowledge for highly endowed firms (the
proportion of active firms in the economy is set to 26 %)
10 – 100 – 500
Proportion of highly endowed firms
29%
Finally, during the second series of simulation, we are confronted with 4 types of firms: High
disclosing firms with a high knowledge endowment, high disclosing firms with a low knowledge
endowment, low disclosing firms with a high knowledge endowment and low disclosing firms with a
low knowledge endowment. The number of firms with respect to the previous typology is given in
table 3.
Table 3: Number of firms by type
Strategy of open knowledge
disclosure
Initial
endowment in
specific
knowledge
IV.
High
Low
High
6
23
Low
20
51
Simulation results and discussion
IV.1. When firms only differ in their disclosure strategy
Let us first consider the case in which firms only differ in their disclosure strategy. For each
simulation run we have two types of firms: the LD firms (as low disclosing firms) and the HD firms
(as high disclosing firms). One may hence be able to observe the evolution of the industry and the
individual performances of firms according to different values of the gap between HD and LD firms
and according to different proportion of these two types of firms. Specifically, this may enable us to
draw some conclusions regarding the role of open knowledge disclosure on firms’ performance.
- 17 -
Figure 1: Herfindhal of firm’s funding
diff max = 0.5%
diff max = 0.7%
0,013
0,013
0,012
0,012
0,011
0,011
0,01
0,01
1
27
53
79
105
131
157
1
26
diff max = 1%
51
76
101
126
151
126
151
diff max = 2%
0,013
0,013
0,012
0,012
0,011
0,011
0,01
0,01
1
26
51
76
101
126
1
151
26
51
76
101
Legend: Proportion of HD firms: thin and dark: 0%; thick and dark: 6%; thick and clear: 26%; thin and clear: 47%
Figure 1 provides some first indications toward this goal, since it describes the evolution of the
inequalities in firms’ performances (approximated by the Herfindhal of the funding). First, Herfindhal
Index for funding raises sharply at the very beginning of the simulation and this for all disclosure
strategies and proportions of HD firms, indicating that inequalities between firms emerge quickly but
somehow are not linked to the presence of HD firms. Second, the presence of HD firms starts to affect
the differential of performances between firms only half through the simulation. In general, the
presence of HD firms tends to increase performance inequalities (this point will be confirmed later
when comparing the performances of HD firms with those of LD firms). Third, when HD firms
disclose low amount of knowledge (i.e. the gap between HD and LD is low), inequalities tend to raise
with the proportion of HD firms. One may however note that, when the amount of disclosed
knowledge is low, the proportion of HD firms does not have an important effect on the inequalities
between firms performances. Conversely, when HD firms disclose a high amount of knowledge,
- 18 -
inequalities tend to decrease with the proportion of HD firms. For instance, the Herfindhal Index for
funding takes its highest values (reflecting strong inequalities) when HD firms are few (10% of the
total) but disclose a high amount of knowledge (2%).
Figure 2 depicts the average number of R&D partnerships set up by HD firms versus LD firms
by computing the evolution of the ADD statistics. All along the simulation, the difference between the
average number of R&D agreements set up by HD firms increases compared to those set up by LD
firms. Not surprisingly, this strongly suggests a positive effect of disclosure strategy on the formation
of R&D partnerships. HD firms tend to develop more research agreements than other firms. This point
is confirmed while observing the graphs in Appendix 1, which represent the evolution of the network
of R&D relationships all along the simulation (after 4,000, 12,000, 20,000 and 40,000 periods). Even
if conclusions based upon these 4 graphs must be taken with the greatest care, they nevertheless tend
to indicate that HD firms acquire a central position in the network compared to LD firms, and this
from the start of the simulation (the central position tend to get stronger as the simulation goes on).
Figure 2 also stresses the role played by the intensity of open knowledge disclosure on the
average degree difference between HD and LD firms. This average degree difference increases when
the intensity of the disclosure is increased from 0.5% to 0.7%, 1% and 2%. In other words, it comes
out that the more firms disclose knowledge the higher the number of R&D agreements in which they
are implied. However, average degree difference increases only very slowly with the intensity of
knowledge disclosure. Only when firms disclose 2% of their knowledge and when the proportion of
HD firms is 10% does this augmentation really start to be significant.
It is interesting to remark that the average degree difference decreases with the proportion of
HD firms. The less numerous the HD firms the higher the degree difference and this whatever the
intensity of the disclosure. This point can easily be explained in the frame of our model: Indeed, we
consider knowledge disclosure as a signal of competence that aims to identify potential R&D partners
to cooperate with. When firms think of establishing a new link with another firm, they include in their
decision the reputation of the other firms, a reputation which is positively linked with the disclosing
strategy of these firms. Hence, when too many firms disclose knowledge, it becomes harder for one
disclosing firm to be distinguished from other firms. It follows that disclosing firms will be able to
enter fewer R&D agreements. Put differently, when too many firms disclose knowledge, disclosing
firms cannot display their differences and hence the disclosure strategy looses some of its interest
since its primary aim is to be distinguished from other firms. Conversely, if only few firms reveal,
these firms will attract all the R&D agreements and hence on average will have far more R&D
partnerships.
- 19 -
Figure 2: Average degree difference of high disclosing firms versus low disclosing firms
diff max = 0.5%
diff max = 0.7%
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
0
5000
10000
15000
20000
25000
30000
35000
0
5000
10000
15000
20000
25000
30000
35000
40000
diff max 2%
diff max 1%
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
0
5000
10000
15000
20000
25000
30000
35000
0
5000
10000
15000
20000
25000
30000
35000
40000
Legend: Proportion of HD firms: thick and dark: 6%; thick and clear: 26%; thin and dark: 47%.
HD firms tend to develop more R&D agreements than LD firms. The next step is to explore
the consequences of this feature in terms of profit. Does this tendency of HD firms to develop more
R&D agreements materialise into profit? Or, put it differently, are disclosing firms also more
profitable than LD firms? undoubtedly, if we trust figure 3, the answer to this question is yes. In the
long run, HD firms tend to be more profitable than LD firms, which is not necessarily the case in the
short run.
- 20 -
Figure 3: Average profit ratio of high disclosing firms versus low disclosing firms
diff max = 0.5%
diff max = 0.7%
3
3
2
2
1
1
0
0
0
5000
10000
15000
20000
25000
30000
35000
0
5000
10000
diff max = 1%
15000
20000
25000
30000
35000
40000
diff max = 2%
3
3
2
2
1
1
0
0
0
5000
10000
15000
20000
25000
30000
35000
0
5000
10000
15000
20000
25000
30000
35000
Legend: Proportion of HD firms: thick and dark: 6%; thick and clear: 26%; thin and dark: 47%.
Indeed, in all cases, i.e. whatever the intensity of the disclosure and the proportion of
disclosing firms, it seems that in the short run a disclosure strategy is not profitable. Figure 3 clearly
shows that at the very beginning of the simulation the average profit ratio is always less than one,
indicating that HD firms are less profitable than LD firms. We can see further that this profit ratio is
sometimes negative because HD firms may even experience losses in the short run. This result,
pointing out the risk of a disclosure strategy, is still reinforced by analysing the mortality of HD firms
versus LD firms. It appears indeed that LD firms never disappear while on average 1 or 2 HD firms
die at the very beginning of the simulation. Moreover, the more firms disclose knowledge, the higher
their death probability. In the extreme case where HD firms disclose an amount of knowledge higher
than 2% (situation which we did not present in our graphs) and where only 10% of firms are of HD
type, all of them disappear quickly. This point stresses the risk of too active a disclosure strategy,
which is harmful for the firm in the short run.
- 21 -
However, if open knowledge disclosure is a risky strategy in the short run, it becomes a
profitable strategy in the longer scale (for firms who manage to remain alive). In all our simulations
one may observe that, after 8,000 time steps, the average profit ratio becomes higher than one,
indicating that, in average, HD firms become more profitable than LD firms. Hence, the following,
apparently robust, proposition can be made: knowledge disclosure leads to profit reduction in the short
run but may lead to higher profits in the long run. This result is consistent whatever the intensity of the
disclosure and the proportion of disclosing firms.
It appears that the proportion of disclosing firms influences sharply their performances. We
pointed out earlier that the less numerous the disclosing firms and the more they set up R&D
agreements. It comes out here that the less numerous the HD firms, the more profitable they become.
This indicates that the fewer the number of highly disclosing firms, the more profitable the disclosing
strategy. Further, the intensity of the disclosure does not seem to really influence firms’ profitability.
HD firms are, on average between 2 and 3 times more profitable than LD firms and this almost
independently of the disclosure intensity. The intensity of knowledge disclosure seems to have a
marginal effect on profit.
Our last focus lies in the total sum of knowledge produced by firms in the industry. This
statistic proxies the pace of technological progress and could even be considered as a first indicator of
the effect of open knowledge disclosure on social welfare.
Figure 4 allows us to observe two phenomena. First, the evolution of knowledge follows an
exponential trend, which is in line with the theoretical view that knowledge production follows
increasing returns. Knowledge is considered as a cumulative good, meaning that the more knowledge
an economy holds the more knowledge it will produce (see Scotchmer, 1991). Second, one can clearly
see that open knowledge disclosure tends to accelerate this process. Higher knowledge disclosure
intensity and higher proportion of disclosing firms, enhance the production of knowledge in the
industry. This indicates a strong positive effect of disclosure strategies on the stock of knowledge of
the industry. Interpreting this result as evidence that open knowledge disclosure is welfare increasing
and, as such, constitutes a socially desirable behavior may appear quite pretentious, but at least our
result does not discard this possibility.
- 22 -
Figure 4: Total sum of knowledge in the economy
diff max = 0.5%
diff max = 0.7%
600000
600000
500000
500000
400000
400000
300000
300000
200000
200000
100000
100000
0
0
0
5000
10000
15000
20000
25000
30000
35000
0
40000
5000
10000
diff max = 1%
15000
20000
25000
30000
35000
40000
diff max = 2%
600000
600000
500000
500000
400000
400000
300000
300000
200000
200000
100000
100000
0
0
0
0
5000
10000
15000
20000
25000
30000
35000
5000
10000
15000
20000
25000
30000
35000
40000
40000
Legend: Proportion of high disclosing firms: thin and dark: 0%; thick and dark: 6%; thick and clear: 26%; thin and clear:
47%.
IV.2. When firms differ both in their disclosure strategy and in their initial
endowment of specific knowledge
In this second part, we allow firms to differ in their initial endowment of specific knowledge,
which means that there are now 4 types of firms: small (in the sense of low initial endowment of
specific knowledge) high disclosing firms, small low disclosing firms, big (in the sense of a high
initial endowment of specific knowledge) low disclosing firms and big high disclosing firms8. It is also
8
For the sake of simplicity we use the following notations in the remainder of the paper : small and high disclosing firms=
SH ; small and low disclosing firms= SL ; Big and high disclosing firms= BH ; big and low disclosing firms= BL.
- 23 -
worth noticing that in order to focus more clearly on the comparison between high disclosing and low
disclosing firms and on big and small firms we fix the proportion of high disclosing firms at 26% (see
table 3).
Our aim is to compare the performances of firms according to their disclosing strategy and to
their initial endowment of specific knowledge. We wish to explore more in depth the consequences of
open knowledge disclosure on firms’ performances and to compare the effects of this strategy
relatively to other variables that may affect firms’ profitability. Specifically, we expect that BH firms
perform better both in terms of profitability and in terms of R&D partnerships than other firms. As we
put it in our model, initial endowment in specific knowledge should matter for long run firms’
profitability, since firms endowed with high level of specific knowledge enjoy higher probability to
produce further specific knowledge. Hence higher initial endowment in specific knowledge should
provide firms with a self-reinforcing advantage through time, firms with high level of specific
knowledge producing more specific knowledge than others. But here our interest rather lies in the
comparison of the performances of SH firms versus BL firms. This comparison may allow us to draw
some conclusions regarding the relative importance of knowledge disclosure as compared with merely
“being big”. Hopefully we will show that, whereas enjoying a low initial endowment in specific
knowledge is indeed a handicap for long run profitability, it can be compensated by adopting an active
strategy of open knowledge disclosure.
Figure 5 displays firms’ average profitability according to their type. One may observe, from
the two upper graphs, that while firms’ differences in their initial endowment of specific knowledge
remains low, long run profitability is mainly determined by the disclosure strategy. In the first periods
of the simulation both BH and BL firms exhibit higher profits than SH and SL firms, but quickly firms
who disclose a low amount of knowledge are outperformed by those who disclose a high amount.
After 6,000 time steps, SH firms catch up with BH as well as with BL firms. Then the SH and BH
firms follow exactly a similar pattern of evolution, indicating that, when differences in initial
endowment are low, long run profitability is mainly determined by the intensity of knowledge
disclosure. This feature is confirmed by analysing the path followed by the BL and SL firms: Before
the end of the first 10,000 time steps the profitability of the two types of firm converges and follows
roughly the same trend until the end of the simulation. One may also observe that differences in
average profitability between BL and SL firms on the one hand and BH and SH firms on the other
hand are increasing slightly but steadily. This, again, indicates that for the long run profitability of
firms it is mainly the disclosing strategy that matters. Finally, one can notice that this conclusion
seems to hold even for strategies of low knowledge disclosure, since there is not much difference
between the two upper graphs i.e. between a situation in which high disclosing firms disclose 0.5% of
their specific knowledge and a situation in which they disclose 2% of their specific knowledge.
- 24 -
Figure 5: Firms’ profits according to knowledge disclosure intensity and to initial endowment of
specific knowledge
diff max = 0.5% / speknow = 5-10
diff m ax = 2% / speknow = 5-10
10000
10000
1000
1000
100
100
10
10
1
250
5250
10250
15250
20250
25250
30250
1
250
35250
0,1
5250
10250 15250 20250 25250 30250 35250
0,1
diff max= 0.5% / speknow = 5-500
diff max= 2% / speknow=5-500
10000
10000
1000
1000
100
100
10
10
1
250
5250
10250 15250 20250 25250 30250 35250
1
250
5250
10250 15250 20250 25250 30250 35250
0,1
0,1
Legend: type of firms: thin and dark: BH; thick and dark: SL; thick and clear: SH; thin and clear: BL.
Note: The scale is logarithmic
How does this conclusion evolve when differences in initial endowment in specific knowledge
increase? By comparing the two upper with the two lower graphs above, one observe that previous
conclusions change but not that much. Indeed, the main evolution while increasing differences in
firms’ initial endowment of specific knowledge deals with the time needed for SH firms to catch up
with BL and BH firms. This point put apart, the results previously emphasized do not change
significantly. SH firms still become relatively quickly more profitable than SL firms, they still catch
up and even outperform BL firms and they still tend to catch up in the very long run with BH firms,
- 25 -
even if they never outperform them. Similarly, SL and BL firms’ profitability still converge in the long
run, even if BL firms manage to keep a slightly higher profit.
How importantly does the increase in the initial endowment of specific knowledge affect the
time needed for catching up? All we can say is that the impact can be consequent. Indeed, by
switching from the two upper graphs to the two lower graphs, we see that the trajectories of SL and
SH firms do not change that much: their paths diverge after 5,000 time steps, with the SH firms
becoming increasingly profitable (the disclosing strategy starts to pay off). But on the other hand, the
time SH firms need to outperform BL firms increases tremendously: SH firms become more profitable
than BL firms only after approximately 25,000 time steps. It is however worth noticing here that the
type of disclosing strategy adopted by firms will slightly affect the time needed to catch up. We indeed
observe that SH firms catch up more quickly when they disclose 2% of their knowledge than when
they disclose 0.5% but the differences does not appear too important.
To summarize, by allowing firms to differ both in their disclosing strategy and in their initial
endowment of specific knowledge, one can make the following propositions: Initial endowment in
specific knowledge does not play an important role to explain firms’ long run profitability compared
to firms disclosing strategy. But it may nevertheless affect firms profitability in the short run (and even
longer) quite consequently. The process of catching up may be very hard and long for firms who
started with a relatively low endowment in specific knowledge. But, in general, our simulations tend to
indicate that disclosing firms will catch up with highly endowed firms. Further, it seems that the
higher the disclosure and the smaller the initial difference in specific knowledge, the faster the
catching up.
Prior to conclude, it is worth to emphasise an important assumption of the model, which may
explain alone most of the above results. It has indeed been assumed here that firms disclose a fraction
of the specific knowledge they held but, whatever the “quantity” or the “quality” of knowledge that is
being disclosed, their reputation increases always of one unit. Hence we assume that it is only the act
of disclosing knowledge that counts in order to build the firm’s own reputation and not “what” is
disclosed. Notice that in order to support this assumption, it can be argued that firms while assessing
other firms’ reputation only value the act of disclosing knowledge because the other indicators are
more time consuming and expensive.
- 26 -
Figure 6: Firms’ degree according to knowledge disclosure intensity and to initial endowment of
specific knowledge
diffmax = 0.5% / speknow = 5-10
diffmax = 2% / speknow = 5-10
50
50
40
40
30
30
20
20
10
10
0
0
250
5250
10250
15250
20250
25250
30250
35250
250
diff max = 0.5% / speknow = 5-500
10250
15250
20250
25250
30250
35250
diff max = 2% / speknow = 5-500
50
50
40
40
30
30
20
20
10
10
0
5250
0
250
5250
10250
15250
20250
25250
30250
35250
250
5250
10250
15250
20250
25250
30250
35250
Legend: type of firms: thin and dark: BH; thick and dark: SL; thick and clear: SH; thin and clear: BL.
However, this assumption alone may be sufficient to explain why SH firms always tend to
catch up with big firms. Indeed, if reputation is only based on the act of disclosing, it implies that
reputation of SH and BH firms, on the one hand, and of BL and SL firms, on the other hand, follow
exactly the same trend, which means that these two types of firms (low and high disclosing firms)
develop a similar number of partnerships (since R&D partnerships are mainly function of firms’
reputation). Figure 6 below clearly confirms that firms’ degree depends mainly on their disclosing
strategy and is almost independent of their initial endowment in specific knowledge (notice about
figure 6 that BL and SL curves follow the same path i.e. only one curve appears on the graph). If it
- 27 -
was assumed that reputation was a function not only of the act of disclosing knowledge but also of the
quantity of disclosed knowledge, BH firms would see their reputation grow faster than SH firms and it
is hence probable that the latter would have more difficulties to catch up. It would also become harder
for SH firms to catch up with BL firms since the latter hold initially more knowledge than SH firms,
which implies that the quantity of knowledge they disclose, although they do not disclose a high
fraction of their knowledge, may be more important than the quantity of knowledge disclosed by SH
firms and hence that their reputation may grow faster than the one of SH firms. However, this point
will have to be tested in another paper.
V.
Conclusion
This paper aimed to provide a theoretical model describing the formation of innovation
networks by allocating a central role to behaviors of open knowledge disclosure. We started from the
basic assumption that innovation is a collective process and hence that a major challenge for firms
involved in this collective process is to identify adequate partners. It has then been conjectured that the
presence of incomplete information within the innovation process may induce the most competent
firms to disclose widely some parts of their knowledge in order to signal their competences and to
facilitate cooperation with other competent actors. According to us, it is hence possible to regard
behaviors of open knowledge disclosure as a signal of competences sent by competent firms to the
industrial and academic worlds and hence as a strategy enabling them to find R&D partnerships more
easily. The empirical finding of Grosetti and Bès (2002), that roughly one third of the collaborations
they studied have been triggered after a patent, a conference or a scientific publication, seems to
confirm that open knowledge disclosure play a central role in helping to identify potential partners and
hence in giving rise to R&D collaborations.
More generally the model exposed in this paper is concerned with the fact that a strategy of
open knowledge disclosure constitutes not only a gift made by disclosing firms to other firms, but also
contributes to an increase in the performance of disclosing firms in terms of knowledge creation,
allowing them thus to increase their individual profitability. Firms are therefore confronted with the
following trade-off: Actively disclosing knowledge is penalising on the one hand, since it provides
competitors with valuable knowledge, but on the other hand, it is profit increasing since disclosing
firms are also more prone to form new links with other firms, to join innovation networks, enabling
them to access external sources of knowledge.
Some implications of our model have then been tested by using numerical simulations. To
summarize, let us emphasise the following results that have emerged from these simulations: (i) Open
knowledge disclosure increases the inequalities in the industry (measured in terms of profitability); (ii)
open knowledge disclosure tends to increase the number of R&D partnerships for high disclosing
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firms as compared with low disclosing firms; (iii) open knowledge disclosure is a risky strategy in the
short run, since it leads to profit reduction and sometimes it jeopardises the survival of the firm, but on
a longer scale it is profit increasing, as compared with strategies of low knowledge disclosure; (iv)
open knowledge disclosure is a more profitable strategy if few firms tend to adopt it; (v) open
knowledge disclosure favours rapid technological progress, allowing a fast increase in the total
production of knowledge in the industry; (vi) adopting a strategy of open knowledge disclosure allows
firms to catch up with and to outperform (in terms of profitability) firms who started with higher
endowment of specific knowledge and who adopted a strategy of low knowledge disclosure. It also
allows them to catch up with (but not to outperform) firms who started with higher endowment of
specific knowledge and who adopted a strategy of high level of knowledge disclosure, tending to
support the view that to explain firms’ long run profitability the disclosure strategy counts more than
the initial endowment in specific knowledge; (vii) the higher the disclosure intensity (within the limit
of the survival condition) and the smaller the initial difference in specific knowledge, the faster the
catching up.
This work was only a first step in our attempt to describe the formation of innovation networks
by putting the main emphasis on the relationship between open knowledge disclosure and the creation
of new R&D partnerships. In our next researches, many points would deserve a more in depth
treatment. Here are some suggestions for further developments (this list is far from being exhaustive):
First, we may consider a different reputation function that would take into account the “quantity” of
knowledge that is disclosed and not only the act of disclosing. This, as it has been discussed shortly
above, may change in a non marginal way some of our results.
Then it may also be necessary to allow firms to put an end to some of the links they have
established when they assess that the return of these partnerships is too low. Including this possibility
of breaking R&D relationships may hence be a way to stress the distinction between a firm’s
reputation (which is based on the beliefs that other firms have regarded the competences of the firm)
and the actual level of competence of this firm. In other word, it may allow firms who have made
mistakes in the assessment of other firms’ reputation to correct this mistake by putting an end to the
collaboration (of course we will have to take into account that to break a link is often costly since, for
instance, many assets may be specific to the collaboration).
Third, it may be necessary to explore how our conclusions evolve when we change the value
of α, which is the unitary cost of maintaining a link with another firm. An important assumption of our
model is that α is constant. While it may as well be that this cost is increasing with the number of
relationships since it may more and more expensive for a firm to maintain her network when the latter
is increasing. Our guess is that to include this feature in our model may lead to put into perspective our
strong conclusion regarding the effect of knowledge disclosure on firms’ profitability.
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Fourth and last point, it may be worthwhile to lay more emphasis on behaviours of closed
knowledge disclosure, which we define as situations in which disclosing firms make their disclosed
knowledge available only to the members of their own network (closed knowledge disclosure is
therefore different from open knowledge disclosure in the sense that in the latter case the disclosed
knowledge is made available to all firms, not only to firms members of the network). In our model, it
appears clearly that we regard open knowledge disclosure as a prerequisite to closed knowledge
disclosure, as a first step that allows the firm to join innovation networks and hence, that may lead to
knowledge trading within the innovation networks that have been joined. But we do not really focus
on the role of knowledge trading. While, it may be interesting to explore how these two types of
knowledge disclosure, open and closed, co-evolve in the development of innovation networks.
References
Allen R. C (1983), “Collective Inventions”, Journal of Economic Behavior and Organization, vol. 4,
pp. 1-24.
Boivin C. (2000), “Protection et Partage des Connaissances dans l’Economie du Savoir”, paper
presented at L’Economie du Savoir : Enjeux Economiques et Enjeux de Gestion, école
des HEC, Montréal, 5-6 mai 2000.
Cassier M., Foray D. (1999), “The Sharing of Knowledge in Collective Spontaneous or Collusive
Forms of Invention”, colline wp 01.
Cockburn I., Henderson R. (1998), “Absorptive Capacity, Coauthoring Behavior, and the Organisation
of Research in Drug Discovery”, The Journal of Industrial Economics, vol. 46, pp. 157-182.
Cooke P. (2001), “Regional Innovation Systems, Clusters and the Knowledge Economy”, Industrial
and Corporate Change, vol 10., pp.
De Fraja G. (1993), “Strategic Spillovers in Patent Races”, International Journal of Industrial
Organization, vol. 11, pp. 139-146.
Eaton B.C., Eswaran M. (2001), “Know-how Sharing with Stochastic Innovations”, Canadian
Journal of Economics, vol. 34, pp. 525-548.
Gambardella A. (1992), “Competitive Advantage from In-House Scientific Research: The US
Pharmaceutical Industry in the 1980s’”, Research Policy, vol. 21, pp. 391-407.
Gibbons M. (1994), The New Production of Knowledge: The Dynamics of Science & Research in
Contemporary Societies, London ed.
Granovetter M. (1985), “Economic Action and Social Structure: The Problem of Embeddedness”,
American Journal of Sociology, vol. 91, pp. 481-510.
Granovetter M. (1974), Getting a Job: A Study of Contacts and Careers, Cambridge, Mass.:
Harvard University Press.
- 30 -
Granovetter M. (1973), “The Strength of Weak Ties”, American Journal of Sociology, vol. 78, pp.
1360-1380.
Grindley P., Teece D. (1997), “Managing Intellectual Capital: Licensing and Cross-Licensing in
semi-conductors and electronics”, California Management Review, vol. 39, pp. 8-41.
Grosseti M. and Bès M-P. (2002), “Proximité Spatiale et Relations Science-Industrie: Savoirs Tacites
ou Encastrement (‘Polanyi ou Polanyi’)?” Revue d’Economie Rurale et Urbaine, n° 5., pp.
777-788.
Hagedoorn J. (1995), “Strategic Technology Partnering during the 1980s’: Trends, Networks and
Corporate Patterns in Non-Core Technologies”, Research Policy, vol. 24, pp. 207-231.
Hall B. H., Ziedonis R. H. (2001), “The Patent Paradox Revisited: An Empirical Study of Patenting in
the US Semiconductor Industry, 1979-1995”, Rand Journal of Economics, vol. 32, pp. 101128.
Harhoff D. (1996), “Strategic Spillovers and Incentives for R&D”, Management Science, vol. 42, pp.
907-925.
Harhoff D., Henkel J., von Hippel E. (2003), “Profiting from Voluntary Information Spillovers: How
Users Benefit by Freely Revealing their Innovation”, Research Policy, vol. 32, pp. 1753-1769.
Henderson R., Cockburn I. (1994), “Measuring Competence? Exploring Firm Effect in Pharmaceutical
Research”, Strategic Management Journal, vol. 15, pp. 63-84.
Hicks D. (1995), “Published Papers, Tacit Competencies and Corporate Management of the
Public/Private Character of knowledge”, Industrial and Corporate Change, vol. 4, pp. 401424.
Hicks D., Ishizuka T., Keen P., Sweet S. (1994), “Japanese Corporations, Scientific Research and
Globalization, Research Policy, vol. 23, pp. 375-384.
von Hippel E. (1988), The Sources of Innovation, Oxford University Press.
von Hippel E. (1987), “Cooperation Between Rivals: Informal Know How Trading”, Research
Policy, vol. 16, pp. 291-302.
Koenig M. (1983), “A Bibliometric Analysis of Pharmaceutical Research”, Research Policy, vol. 12,
pp. 15-36.
Kogut B. (2000), “The Network As Knowledge: Generative Rules and the Emergence of Structure”,
Strategic Management Journal, vol. 21, pp. 405-425.
Lim K. (2000), “The Many Faces of Absorptive Capacity: Spillovers of Copper Interconnect
Technology for Semiconductor Chips”, working paper 4110, MIT Sloan School of
Management.
Maskell P., Lorenzen M. (2003), “The Cluster as Market Organization”, Druid working paper 200314.
Meagher K., Rogers M. (2004) “Network Density and R&D Spillovers”, Journal of Economic
Behavior and Organization, vol. 53, pp. 237-260.
- 31 -
Muller P. (2003), “The role of authority in the governance of knowledge communities”, Paper
presented at DRUID Winter 2003 PhD Conference, Hotel Comwell Rebild Bakker, Aalborg,
Denmark, January 16-18.
Pénin J. (2004), “Open Knowledge Disclosure: An Overview of the Empirical Evidences and the
Economic Motivations”, presented at the third EPIP meeting in Pisa, 2-3 april, 2004.
Pénin J. (2003), “Endogénéisation des Externalités de Recherche: Le Rôle de la Capacité d’Emission
des Connaissances”, Revue d’Economie Industrielle, vol. 102, pp. 7-28.
Scotchmer S. (1991), “Standing on the Shoulders of Giants: Cumulative Research and the Patent
Law”, Journal of Economic Perspectives, vol. 5, pp. 29-41.
Spence M. (1973), “Job Market signalling”, Quarterly Journal of Economics, vol. 87, pp. 355-374.
Watts D. J. (1999), Small Worlds: The Dynamics of Networks Between Order and Randomness,
Princeton University Press.
Williamson O. (1975), Markets and Hierarchies: Analysis and Antitrust Implications, New York, Free
Press.
- 32 -
Appendix I: Network of R&D relationships
(HD firms (2%) are in blue and represent 26% of the total number of firms, while LD firms (0.1%) are
in red)
after 4000 periods:
after 12000 periods:
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after 20000 periods:
after 4000 periods:
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