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A. Castiaux, “‘Inter-organisational learning -Lotka-Volterra modelling of different types of relationships”
International System Dynamics Conference — Oxford, July 2004
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Inter-organisational learning
Lotka-Volterra modelling of different types of relationships
Annick Castiaux
Business Administration Department, University of Namur
8 Rempart de la Vierge, B-5000 Namur, Belgium
Telephone: +32-81-724880 — Fax: +32-81-724840
E-mail: annick.castiaux@fundp.ac.be
Abstract
In this paper, we propose a simple model, based on Lotka-Volterra system, to simulate
knowledge building in various configurations of inter-organisational partnerships. This
model allows to differentiate the impacts of internal interactions and external
collaborations on knowledge growth in an organisation. Following the type of
partnership, i.e. competition, symbiosis or predation, we analyse the efficiency of inter-
organisational knowledge building on a long-term perspective. The only relationship
that demonstrates a long-term interest in the building of strictly new knowledge is
predation. This kind of relationship allows large and lean organisations to complete
their exploitative capabilities with explorative skills coming from small and agile
organisations. Through such a relationship, a balance between exploration and
exploitation can be found. This approach is a first step in a research dedicated to the
study of complex adaptive systems, a well-suited framework to analyse management
phenomena occurring at the edge of chaos, between stability and instability.
1 Introduction
More and more, accelerated environmental changes push organisations to evolve, adapt
themselves, innovate, be flexible, etc. Managers are faced with the emergency to create
newness more rapidly and efficiently than competitors. This race to innovation can only
be won through an efficient knowledge management that includes two main issues: the
exploration of new knowledge, in order to create variety and open the frontiers of the
organisation, the exploitation of newly acquired knowledge, in order to propose new
products to the market and to introduce new processes in the company (March 1991;
Levinthal and March 1993). The simultaneous management of both — exploration and
exploitation — is a strong paradox. Such a paradox has been called by other authors the
“productivity dilemma” (Benner and Tushman 2003). While exploitation requires
management skills focused on control (minimising complexity and uncertainty),
standardisation, repetition and incremental innovation, exploration calls upon opposed
capabilities as flexibility (with high complexity and uncertainty), creativity, variety and
radical innovation. In this perspective, the efficient management of knowledge
associated with innovation is a key issue (Hall and Andriani 2003; Patrucco 2002).
In this paper we use a theoretical framework borrowed from biology to study the
influence of this paradox on knowledge creation, in the particular configuration of two
interacting organisations. We focus our attention on the effect of this interaction
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A, Castiaux, “Inter-organisational learning —Lotka-Volterra modelling of different types of relationships”
International System Dynamics Conference — Oxford, July 2004
following the forms that it can take: competition, predation or symbiosis. We try to
understand which mechanisms could be more relevant following the organisations
respective management styles, exploration or exploitation oriented. We briefly
introduce complex adaptive systems as an interesting framework to understand such
management paradoxes and we show that our models are a first approach of this
formalism, based on the unstable equilibrium between a negative and a positive
feedback, leading to behaviours at the edge of chaos. Finally, we propose some
potential improvements of the models and research perspectives in this domain.
2 Context of the modelling
In this section, we explain the context of our modelling. First, we consider the recent
evolution of inter-organisational relationships. From lean supply chains to agile
networks of competencies, relationships are more and more flexible but also more and
more complex to manage. We briefly look at the place of knowledge building in this
inter-organisational context. Second, we try to understand the exploitation-exploration
paradox of knowledge building through the well-known similar paradox of
organisational learning. We use feedback loops representations to enlighten our
discourse and anchor our reasoning in system science (Forrester 1961). This leads us to
introduce briefly complex adaptive systems. We finally propose the theoretical
background of our modelling, a first approach of knowledge building as a management
phenomenon at the edge of chaos (Senge 1990).
2.1 Inter-organisational relationships and knowledge building
In this section, we analyse the recent evolution of inter-organisational relationships, as it
has been described by several authors (Choi, Dooley and Rungtusanatham 2001;
Huemer 2004; Tidd, Bessant and Pavitt 2001). We consider supply relationships that
could apply to our study if we consider that some organisations are knowledge
suppliers, while others are knowledge buyers.
As shown in Figure | (adapted from (Tidd, Bessant and Pavitt 2001, 204)), recent
decennials have seen a real transformation of the supply market. Until recently, buyers
were faced with a homogeneous supply market where they simply made a choice based
on market considerations. The choice of the supplier was formalised with a contractual
relationship in which both organisations (supplier and buyer) were uncoupled. In the
eighties, more and more companies realised that a strong coupling with their suppliers
could help them to reduce time-to-market and transactional costs and to enhance
quality. Suppliers favouring this coupling by providing the best interoperability (thanks
to information systems, standard products and processes) were thus preferred to others.
The supply market became differentiated, the organisations making strong partnerships
with their favourite suppliers in order to reach lean supply. For some years, this tight
coupling raises some issues: a flexibility issue, since strong partnerships have created
dynamic inefficiencies, an equity issue, since some buyers have abused from their
powerful position to completely control their suppliers, and an innovation issue, since
those partnerships are working as autarchic entities, on the basis of repetitive and
controlled processes, excluding the emergence of radical newness. Some organisations
have thus evolved to a lighter coupling, based on supply alliances where each partner
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International System Dynamics Conference — Oxford, July 2004
benefits from the others’ skills and knowledge to innovate. New inter-organisational
types appear as networks of co-innovation, where each organisation focuses its efforts
on its core business, finding well-suited partners to complement those assets (Prahalad
and Hamel 1990; Quélin 2000). This is particularly true when innovation is at stake and
new knowledge must be found and developed, since no organisation can develop
knowledge and competencies outside its core business without adequate partners.
Objectives 4
Loosely
coupled
Process and
product
innovation Tightly
coupled
Lead time,
quality
Cost
>
Homogeneous Differentiated Indeterminate Supply
market
Figure 1 - Evolution of inter-organisational relationships with the changes in the supply market
(adapted from (Tidd, Bessant and Pavitt 2001, 204))
Considering that the supply object is knowledge, these three supply forms also exist:
Contractual market relation: The buyer wants to obtain a given and well-defined
knowledge, available from various sources with an equivalent quality. The supply
market is homogeneous and the choice criterion is the price proposed by the various
possible suppliers. This kind of contractual relationship does not couple parts
together. There is no interest to model it with Lotka-Volterra system.
Lean supply through strong coupling: A supplier clearly differentiates itself with a
knowledge that is particularly well-suited for the buyer in a short-term perspective.
This knowledge will spare the buyer long and costly knowledge developments that
are of prime importance for his business quality. A tight coupling between the
supplier and the buyer takes place. We can distinguish between a tight symbiotic
behaviour, where partners are mutually very dependent to create their own new
knowledge, and a predation behaviour, where the buyer or the supplier benefits from
the relationship while the other partner looses part of its knowledge in the operation.
If the buyer is the predator, this behaviour can end in the integration of the supplier
inside the buyer organisation (for instance through a buyback). If the supplier is the
predator, this behaviour means that the buyer is captive of the supplier because of its
high dependence on the supplier’s knowledge.
Co-innovation through loose coupling: Suppliers have all their particular skills and
knowledge, complementary to the ones of the buyer. Each protagonist finds benefit
in the relationship without being prisoner of it. We find here a light symbiotic
relationship, generally concretised in a partnership network that evolves following
environmental changes. This kind of relationship can also be seen as a light
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International System Dynamics Conference — Oxford, July 2004
predation relationship if one of the organisations clearly exploits the knowledge the
other explores, each organisation evolving through this schema in its more adapted
mode. Examples of this are co-innovation alliances between big firms and small
start-ups (Gans and Stern 2003).
We must add a fourth relationship pattern, which is not related to supplier-buyer
relationship: the competition relationship, where every protagonist tries to develop new
knowledge more rapidly than the other.
2.2 Positive and negative feedbacks in organisational learning
Exploration environment
o Unknown structure
o Dynamic complexity
co Time delays
© Inability to conduct controlled experiments
Exploitation environment
Known structure
Variable level of complexity
Controlled experiments
Decisions Information feedback
Exploration Exploitation Exploitation Exploration
© Radical innovation || 0 Improvements o Structured © Selective perception
© Project management || 0 Product management information © Missing feedback
© Agility paradigm co _Leanness paradigm © Complete, accurate, |] o Delay
co Extemal learning o _ Internal learning immediate feedback || o — Bias, distortion, error
© Long-term survival }\o Short-term survival Ambiguity
f
Mental models
Mapping of feedback structure
© Disciplined application of scientific
reasoning
© Discussability of group process,
defensive behaviour
Strategy, structure, decision rules
o Balance between exploitation and
exploration
© Simulation used to infer dynamics
of mental models correctly
Figure 2 - Double learning loop including both exploitation and exploration processes
(adapted from (Sterman 2000, 34))
In the introduction, we have underlined the influence of exploitation-exploration
balance on both the intra-organisational and inter-organisational rates of knowledge
growth or decline. The feedback structure proposed at Figure 2 helps to understand this
influence. This feedback structure is based on the famous double loop learning model
developed by Argyris (Argyris 1977). This framework has demonstrated its interest to
understand the factors influencing systematic organisational learning. Recently,
Sterman (Sterman 2000) proposed an interesting adaptation of this double loop learning,
differentiating the feedback influence of
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A, Castiaux, “Inter-organisational learning —Lotka-Volterra modelling of different types of relationships”
International System Dynamics Conference — Oxford, July 2004
e the virtual world to which the organisation can easily refer as “formal models,
simulations, or ‘microworlds’, in which decision makers can refresh decision-
making skills, conduct experiments and play” (Sterman 2000, 34);
e the real world, uncertain, dynamically complex, beyond control.
We have adapted this feedback structure to discriminate between the feedback due to an
exploitation environment (that can be assimilated to Sterman’s virtual world) and an
exploration environment (similar to Sterman’s real world). Considering that the result of
a learning loop is the acquisition of knowledge, the exploration environment would
provide new knowledge, through mainly external relationships, while the exploitation
environment would give the necessary feedback to select, control and exploit newly
acquired knowledge, through efficient internal and external interactions with known and
assessed partners. On one hand, the exploration environment opens the knowledge
perspectives of the organisation, bringing newness and variety. On the other hand, the
exploitation environment limits knowledge expansion, eliminating useless or obsolete
knowledge and codifying useful knowledge to allow its transfer to operational personnel
and its transformation in definite processes and/or products.
Using an analogy from physics, we can say that the exploration of new knowledge
increases the entropy of the organisation (i.e. its uncertainty and its complexity) to
maintain it alive and make it evolve, while the aim of exploitation is to keep the
organisation entropy at a sufficiently low level to diminish the management risks
associated with uncertainty and complexity.
One should underline here, as it is indicated by the arrows between exploitation and
exploration environments in Figure 2, that both environments are not independent.
Exploration environment will invade exploitation environment, changing the
perspectives for usual and controlled business, while exploitation environment will
condition and bias exploration environment, in order to diminish uncertainties and
threats. We are in a dynamic context, where definite borders can difficulty be designed.
2.3 Between stability and instability: complex adaptive systems
New shared
models
Stability (negative feedback)
2 A249
Self-
oA organization
“Limited Instability” or “Edge of Chaos” itd
Complex - Relations between agents
Adaptive o - Agents’ relations with their environment =)
Systems - Information flow
- Cultural diversity (shared and individual models)
Instability, chaos (positive feedback)
Figure 3 - The organisation as a complex adaptive system (adapted from (Chiva~-Gomez 2003))
Complex adaptive system theory finds its roots in evolutionary biology, non-linear
dynamical systems and artificial intelligence. Such systems adapt themselves
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International System Dynamics Conference — Oxford, July 2004
spontaneously to the changing environment and influence this environment, with the
objective to co-evolve as harmoniously as possible. A CAS is characterised by a series
of dynamic capabilities that can be sorted under three foci (Choi, Dooley and
Rungtusanatham 2001): its internal mechanisms, its environment and the co-evolution
between the system and its environment.
As explained in Figure 3, a complex adaptive system can evolve to stability if negative
feedback prevents the emergence of newness and variety. This stability often means the
death of the system. It can also evolve to instability or chaos if positive feedback
prevents a minimal control of variety growth. This instability also means the death of
the system or, at least, the impossibility to manage it. Finally, a CAS can evolve to a
balanced state between stability and instability, at the edge of chaos. In this state, it
presents complex dynamic capabilities that allow it to self-organise in order to co-
evolve with its environment in a flexible way.
If we consider the double side of knowledge building that we have developed through
the double loop learning model in the previous section, it is obvious that CAS
formalism is well-suited to study knowledge creation in organisations. As described in
Figure 4, new knowledge creation is regulated by a negative feedback loop, due to the
necessary control on knowledge growth to make its exploitation possible, as well as a
positive feedback loop, due to exploration of new knowledge. This leads the
organisation in a state between stability and instability. Following the strategic
orientation of the organisation — more oriented towards exploitation or exploration —
negative or positive feedback can be dominant. Respectively, the organisation will ten
evolve more or less rapidly to a stable or unstable state. From a knowledge building
viewpoint, stability means that the organisation subsists on the basis of its existing
knowledge and competencies and does not seek new knowledge, while instability
means that the organisation cumulates more and more new knowledge that it cannot
manage anymore.
Exploration 4 + +, Exploitation
ete fo ee
i ©) on:
New
& - Feedback
Feedback knowledge from
eiploation y . exploitation
environment ~® Exploration Exploitation énvironment
+ emergence control
Figure 4 - Positive and negative feedbacks in new knowledge creation
The formalism of complex adaptive systems is considered in recent literature as a
powerful tool to understand complex behaviours in highly uncertain management
problems as product development (Chiva-Gomez 2003), organisational networks (Choi,
Dooley and Rungtusanatham 2001) or ecological economics (Ramos-Martin 2003). In
the next section, we present Lotka-Volterra system as a first approach of this formalism
and explain the pertinence of this approach to analyse knowledge building in the context
of two interacting organisations.
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International System Dynamics Conference — Oxford, July 2004
2.4 A first approach through Lotka-Volterra system
2.4.1 Generalised Lotka-Volterra system
In the twenties, the American Lotka (1925) and the Italian Volterra (1926) proposed a
model to describe the evolution of two populations interacting in such a way that one of
them — the predator population — feeds itself from the other — the prey population. If we
name P,, the predator population and P,, the prey population, the equations governing
their co-evolution are Lotka-Volterra well-known system:
#. = Pl, +¢,,P,)
ie (Eq. 1)
7 =P le, +enP.)
where the a; coefficient gives the endogenous growth rate of population P;, negative for
the predator population and positive for the prey population, whereas the cj coefficient
represents the growth effect of population P; on population P;, positive for the predator
population and negative for the prey population.
To take into account intra-population interactions that can have a positive impact on
growth (mutual assistance of the population members) or a negative impact on growth
(internal competition due, for instance, to the lack of space or scarcity of resources),
these equations can be generalised to the following system:
dP.
“=P(a,+b,P,+¢,P,)
dt
(Eq. 2)
dP.
= P.(a, +b,P, +e,P.)
dt
where the 5; coefficient gives the growth effect of internal interactions in population P;,
positive in case of mutual assistance, negative in case of competition. In this last case,
the most realistic, if K; is the maximal capacity of population P;, b; equals a; / K;. This
maximal population level is due to the finiteness of material resources available for each
species (space, food).
Finally, if we consider N interacting populations, we obtain a system of N coupled
differential equations that can be written as:
y
i= ofa, ar} Vi=1,N (Eq. 3)
where c;; = b;.
These equations have recovered interest in the recent management literature since they
constitute a simple model helping to understand phenomena as technology substitution
(Morris and Pratt 2003; Pistorius and Utterback 1997), organisational change (Modis
1997) or organisational learning (Zangwill and Kantor 2000).
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International System Dynamics Conference — Oxford, July 2004
2.4.2 Lotka-Volterra system and inter-organisational knowledge building
Our aim is to understand mechanisms governing new knowledge creation when
organisations are interacting. Considering Lotka-Volterra system given at (Eq. 2), this
means that the population levels P, and P, represent knowledge levels respectively in
organisation x and in organisation y. In this respect, the meaning of coefficients and the
factors influencing their value are different of those that could be used when the interest
variable is a physical population level. Let’s see how we can interpret endogenous
growth rate a,, intra-population (internal) interaction rate b;, and inter-population
(external) interaction rate cj.
Endogenous growth rate: This is the intrinsic rate of knowledge building (or
knowledge destruction) inside the organisation. It corresponds to the rate of
knowledge creation (or destruction) that would exist if the organisation had no
contact with the other organisation under study and if the groups and individuals
composing the organisation were not interacting. Factors influencing positively the
value of the endogenous growth rate are, for instance, creative orientation of the
individuals, hiring of new persons, collaborative contacts with other creative
organisations as universities, microscopic interactions of individuals inside a given
team or group, existence of an R&D department, continuous training of individuals,
etc. Factors influencing negatively the value of the endogenous growth are, for
instance, personnel departures due to retirements or job changes, short-time view
and lean strategy. As it has been demonstrated in the empirical literature (Kazanjian
2000; Leenders, van Engelen and Kratzer 2003; McAdam and McClelland 2002),
organisational practices concerning individual motivation, creativity, training and
collaboration management will strongly influence these factors.
Internal interaction rate: This is the rate at which knowledge is created or destroyed
in the organisation through interactions between the groups and persons composing
the organisation. In inter-species interaction, this coefficient is generally negative
since it reflects the existence of a maximal level for population density due to
material resource constraints (space, food). When knowledge is considered,
conservation properties that govern physical variables do not hold any more. The
theoretical maximal limit to knowledge creation can hardly be defined. A positive
value of the internal interaction coefficient allows to take into account the non-
conservative property of knowledge. However, the archiving, maintenance and
exploitation of knowledge will introduce limits to its growth. If it is negative, this
internal interaction rate reflects the necessity for the organisation to use internal
interactions to control, sort and limit knowledge in order to be able to exploit it. The
more the organisation has developed a control culture, focusing the majority of its
efforts on exploitation, the more this factor will be negative. If it is positive, this
internal interaction rate reflects the important place of emergent matters in the
organisation. The more the organisation gives place to exploration and flexibility,
the more this factor will be positive. It should be mentioned here that both extreme
situations (exclusive exploitation or exclusive exploration) are damageable for the
organisation: focusing only on exploitation, the organisation will miss opportunities
brought by emergent knowledge, while focusing on exploration, it will not benefit
from learning to enhance the profit of exploitation. The internal interaction rate can
be considered as a measure of the balance between exploitation and exploration
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International System Dynamics Conference — Oxford, July 2004
inside the organisation. This concept has been illustrated in previous sections.
Factors influencing the value of this coefficient are, for instance, the management
style of the organisation (exploitation, exploration), the openness of individuals to
newness, cross-functional communication, strategic importance of R&D, etc.
External interaction rate: This is the rate at which knowledge is created or
destroyed in the organisation through interactions with the other organisation. This
rate can be positive if the interaction brings new knowledge to the organisation or
negative if the organisation looses knowledge during the interaction with the other
organisation. Factors influencing positively the value of this coefficient are, for
instance, trust between the organisations, interactions between their research
departments, common objectives or interests, cultural proximity... Factors
influencing negatively the value of this coefficient are, for instance, competition
between the organisations, size and/or stability differences between the
organisations, information retention, loss of intellectual property, personnel moves
from one organisation to the other...
To summarise, mechanisms that bring new knowledge in the organisation are:
Endogenous growth (positive part of rate a,), due to creativity of individuals or
teams, knowledge transfer from the environment (excluding the other organisation);
Constructive internal interactions (positive part of rate bj), allowing to build
architectural knowledge when individuals from different groups collaborate and
build new knowledge on the basis of their particular knowledge;
Constructive interactions with the other organisation (positive part of rate cj),
favouring knowledge transfers from an organisation to the other.
Mechanisms that remove new knowledge from the organisation are:
Endogenous decline (negative part of rate aj), due to standardisation of individuals,
absence of knowledge transfer from the environment, departures of key persons;
Destructive internal interactions (negative part of rate b;), often necessary to be able
to exploit new knowledge efficiently with limited resources;
Destructive interactions with the other organisation (negative part of rate cj), where
knowledge is stolen or transferred with negative consequences on one of the
organisations, for instance with key personnel transfers.
3 Modelling patterns of relationships
3.1.1 Competition
Very often, competition situations lead to complete annihilation of both competitors or
to instability. Here we have analysed situations where equilibrium can be reached. We
consider that both organisation have some creativity (positive a;) and must control their
knowledge to exploit it (negative b;). Organisation x is more creative and less
exploitation oriented than organisation y.
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International System Dynamics Conference — Oxford, July 2004
Low competition
Values of interaction coefficients are set to relatively weak values, with a necessarily
lower value for organisation y if we want to give it a chance to build knowledge.
Competition is low. However organisation y is better than organisation x at this
competition game. As shown in Figure 5, such systems are very sensitive to the initial
conditions since a very small variation of those leads to opposite final states. Initially
both knowledge levels tend to the equilibrium point and almost reach it, then they
diverge from it to reach one of the extinction points (extinction of P, or extinction of
P,). During a long time period, the system seems stable. However, at t = 90, divergence
from the equilibrium occurs. Since the system fakes equilibrium during a rather long
time, organisations are not rapidly aware of the threat from their competitors.
Concerning knowledge evolution, this situation is not profitable for any of the
organisations, excepting once the equilibrium is abandoned. There, one of the
organisations takes advantage from the other until this one does not possess any more
interesting knowledge. The relationship is then of no interest.
Initial conditions leading to the extinction of P,
Phase diagram
Time evolution
Initial levels
a
=|
z
a
= a
“D. L014.
. + : ; : eg
0 7 4 so t00 20140 :
Time (au) : Pir
Initial conditions leading to the extinction of P,
Time evolution Phase diagram
Initial levels
a NN
=i
z \
fH a S
z RO
A
3 a
“D.. L015.
r 7 f " " So
0 7 400 so 10020140 g
Time (au) : Pe
Figure 5 — Effect of low competition on knowledge creation and transfer
(a,=0.5, b,=-0.01, ¢,
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Strong competition
This time we choose higher values for the interaction coefficients, in order to simulate a
strong competition. Organisation y, less creative and more exploitative, is more
aggressive to obtain new knowledge from organisation x. The same kind of behaviours
can be met as for low competition. As can be seen in Figure 6, the difference lies in the
acceleration of the process, due to higher competition. If a stagnation period appears, it
is shorter that for low competition. Rapidly, one of the competitors has the advantage
and the other sees all his knowledge disappear to the benefit of the first. Here also, when
stability is reached, the relationship between both organisations has no interest any
more.
The sensitivity to initial conditions is even higher than in low competition. Very similar
initial conditions lead to the extinction of P, or P,.
Initial conditions leading to the extinction of P,
Time evolution Phase diagram
Initial levels
~ a
5 = —
4 ‘fas
3 \
a Pei mi
% | s
g al
3
2
dP () i dt=0
° 6 8 = 100120140 — —
Time (au) : PO
Initial conditions leading to the extinction of P,
Time evolution Phase diagram
Inivial levels
z PO SL
g |
3 Ss)
z Cera
¢ 6
2
2
HPO
$ + - : ' en aP()/ a=0
0 2 840 © ao t00 20140 =a —
Time (au) ’ rc)
Figure 6 - Effect of strong competition on knowledge creation and transfer
(a,=0.5, B=-0.01, Cy=-0.4, a)=0.3, by=-0.02 , Cy =-0.25)
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3.1.2 Symbiosis
A lot of symbiotic patterns are completely divergent or lead to annihilation of both
knowledge levels. Some patterns also lead to chaotic behaviours (Pistorius 1995). We
present here two cases that converge. It must be noted that both cases are weak
symbiotic relationships.
Similar partners
Time evolution Phase diagram
a
Bad Initial levels
4 ata?
& — / pot
& 4 ee
3 a
z
A
2 s
,
¥
Ce ee ee ee ¥
Time (a.u) Pe
Figure 7 - Symbiotic pattern of knowledge creation and transfer between equilibrated partners
(a,=0.2, by=-0.04, C)=0.015, a,=0.25, by=-0.05 , ¢,=0.02)
We first assume that both organisations have the same characteristics: similar levels of
creativity and exploitation orientation. Their collaboration will thus be based on a rather
equilibrated exchange of knowledge.
We see on the graphs of Figure 7 that both knowledge levels converge rapidly to an
equilibrium state from which they do not evolve any more. At this point, the
collaboration does not bring any new knowledge to any of our interacting organisations.
It is thus without interest in the context of a knowledge building partnership.
Very different partners
Time evolution Phase diagram
> -
=) < Initial levels
2 ee 20
es 7 fat
5 PO = / no)
% Ss ees 4
Bl / ce
%
2
so c
b
i ¥
— S
° 30 6) 120 150 18020 s
Time (a.u) PO
Figure 8 - Symbiotic pattern of knowledge creation and transfer between very different partners
(a,=0.15, b,=-0.05, ¢,=0.01, a,=-0.1, by=-0.012 , C.=0.05)
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Now, we assume that one of the organisations looses knowledge, while the other is
creative. The organisation that is not creative will use the partnership to gain
knowledge, while the gain of the creative organisation is supposed to be lower.
We see in Figure 8 that, as in the previous example, both knowledge levels converge to
the equilibrium point. The rate of progression to the equilibrium is however well slower
that in Figure 7. If the equilibrium point is higher than the initial levels, both
organisations learn from each other all along the time interval. Once this equilibrium is
reached, the relationship does not bring any new knowledge to the partners.
3.1.3 Predation
Internal interactions leading to convergence towards the equilibrium state
Time evolution Phase diagram
°
7
fs
S
g
PQ)
Initial levels
Knowledge levels (a.i)
dP) (di=0
o 2 4 6 8 10 120 140
Time (a.u) PO
Internal interactions leading to divergence from the equilibrium state
Time evolution Phase diagram
=0
$
=
Knowledge levels (a.u)
PQ
Fain
aPQyide=0 _
o 2 4 6 8 100 120 140
Tr ;
Hime (a.u) 2
Figure 9 - Prey-predation pattern of knowledge creation and transfer
(a,=0.5, b,=0.01 (upper case) or b,=0.012 (lower case), Cy=-0.25, a,=-0.2, B,=-0.01 , ¢.=0.125)
We consider that organisation x is creative and has an exploration orientation (both a,
and b, positive), while organisation y looses knowledge and has an exploitative culture
(both a, and b, positive). So the predator is organisation y, which needs the knowledge
of organisation x to evolve and survive. We consider here that the predation is light in
order to allow a co-evolution of both organisations’ knowledge. This means that
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International System Dynamics Conference — Oxford, July 2004
organisation y just takes a part of organisation x knowledge in order to evolve slowly, in
compliance with its exploitation orientation.
This leads to the traditional prey-predator curves, as presented in Figure 9, where we see
regular peaks of knowledge created by organisation x, than transferred to organisation y
for exploitation. This seems an interesting pattern for both organisations: we can see
organisation x is a “knowledge lab”, acquiring radically new knowledge thanks to its
contacts and creativity, while organisation y is the “knowledge plant”, with sufficient
resources to exploit part of this new knowledge that it consider as strategically
important. In the upper case of Figure 9, as it is shown in the phase diagram, both
knowledge levels are circularly converging towards their equilibrium point, at the
intersection between the equilibrium lines of both knowledge levels (dP,/dt=0 and
dP,/dt=0). This convergence to a stable state is due to the negative sign of b,, generating
a negative feedback (stabilisation). However, this convergence is slow and the
relationship can be interesting during a rather long period. It can even be balanced by a
higher value of b, (i.e. a more explorative organisation), as proposed in the lower case
of Figure 9, where the spiral pattern of the phase diagram is divergent from the
equilibrium point, evolving slowly towards an instable state.
This spiral pattern can be linked to Nonaka’s knowledge spiral (Nonaka 1994) where
four mechanisms of knowledge conversion between tacit and explicit modes lead to a
cyclic creation of knowledge in the organisation. Tacit mode corresponds to a more
explorative state while explicit mode leads to the exploitation of knowledge into
products and processes. This predation relationship between an exploitative and
established organisation and a flexible and creative organisation gives us an inter-
organisational knowledge spiral.
4 Conclusions and perspectives
We have proposed Lotka-Volterra set of equations as a possible model to study business
systems including a management paradox. In particular, we have modelled the effect of
different inter-organisational relationships on new knowledge creation in the
organisations. Our two-dimensional models have shown that symmetry between both
organisations (as it is the case for competition or symbiotic patterns) is not favourable to
new knowledge creation, since it leads to stability through negative feedback or to
instability through excessive positive feedback. On the other hand, asymmetric patterns
as prey-predator relationships appear as being more interesting for new knowledge
creation. An adequate balance between negative feedback — essentially brought by the
predator — and positive feedback — essentially due to the prey — leads to repeated
creation of new knowledge by the prey, followed by the transfer of part of this new
knowledge to the predator. We can see this pattern as the focusing of each partner on its
management style and core competencies, complementary to the one of the other
partner: the predator entity, on its exploitation capabilities, and the prey entity, on its
exploration skills. Understanding the importance of complementarities in knowledge
building, some organisations have implemented new management methods to favour
radical innovation while still managing their existing competitive advantages. A
successful case in the Japanese telecommunication industry is based on the creation of a
dedicated and independent creative department and its collaboration with the traditional
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A, Castiaux, “Inter-organisational learning —Lotka-Volterra modelling of different types of relationships”
International System Dynamics Conference — Oxford, July 2004
organisation (Kodama 2003). Such a collaboration is precisely the “predation” strategy
that we have recommended in this paper.
Our models are a basic approach of the complex adaptive system paradigm. We see a lot
of perspectives in such research. First, our models should be complemented with
additional feedback structures in order to take into account the “adaptive” quality of
organisations. As a matter of fact, if an organisation realises that its level of creativity is
falling, it will react with several possible mechanisms as becoming more flexible,
encouraging creativity, favouring informal communications, etc. This could be added in
the models. A next step would also be to consider more than two interacting
organisations and progressively model a network behaviour as it is more and more
observed. Progressively, we want to understand complex adaptive systems, model them
and use these models to have a better insight in management issues at the edge of chaos.
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