Tsukuba Economics Working Papers
No. 2010-003	
 Complexity, Uncertainty, and Organizational Congruency
byNobuyuki Hanaki and Hideo Owan	 	 March 2010

UNIVERSITY OF TSUKUBA
Department of Economics
1-1-1 Tennodai
Tsukuba, Ibaraki 305-8571
JAPANComplexity, Uncertainty, and Organizational
Congruency
Nobuyuki Hanaki∗

Hideo Owan†

March 16, 2010

Abstract
Many scholars in the ﬁelds of organization theory and management strategy haveargued that there is a tension between the two types of organizational learning activities, exploration and exploitation. They appear to be substitutes: the greater theskill at one, the harder it is to do the other well. It is often argued that the two
activities compete for scarce resources when ﬁrms need diﬀerent capabilities and management policies to promote one over the other. We present another explanation that
attributes the phenomenon to the dynamic interactions among the activities, search,knowledge sharing, evaluation, and alignment within organizations relying on the NK
Landscape framework (Kauﬀman 1993). Our results show that successful organizations
tend to bifurcate into two types: those that always promote individual initiatives andbuild organizational strengths on individual learning and those good at aligning theindividual knowledge base and exploiting shared knowledge. Straddling between the
two types often fails. The intuition is that an equal mixture of individual search andorganizational alignment slows down individual learning compared to the ﬁrst organization type while making it diﬃcult to update institutionalized knowledge because
individuals’ knowledge base is not so suﬃciently aligned as in the second type. In
such “straddling” organizations, once individuals get stuck with locally-best solutionsin an uncoordinated manner, they cannot agree on how to improve the organizational
knowledge. Straddling is especially ineﬃcient when the operation is suﬃciently complex (in other words, the interdependency is high) or when the business environment
is suﬃciently uncertain.
Keyword: Congruency, Complexity, Uncertainty, NK Landscape∗

GREQAM, Université de la Méditerranée, and University of Tsukuba, nobuyuki.hanaki@univmed.fr andhanaki@dpipe.tsukuba.ac.jp†
Institute of Social Science, University of Tokyo, owan@iss.u-tokyo.ac.jp1

1

Introduction
I think our growth will end at only two or three times the current scale once
we undertake to increase routines. I think the biggest reason we don’t see“mega ventures” emerging in Japan is that every ﬁrm starts organizing androutinizing their processes too early. When I worked with American ﬁrms
such as Microsoft or Apple, I was always surprised to see disorder in many
aspects of their operations. They wouldn’t be called “ﬁrms” if they werein Japan. Their processes are not very routinized, but that is exactly why
they can continue to grow. Their workplaces are full of chaos, especiallycompared to their Japanese counterparts. However, creative people who canmake breakthroughs prefer working in such places. So it is with our company. We are paying the cost of disorganization and mistakes caused by
the chaos. . . But, it is impossible to have both creative workers and routine
workers in the optimal mix.
- Masayuki Makino, CEO, Works Applications, Inc.1

Tension between exploration and exploitation has been a central theme in the literature of organizational learning since March (1991). The issue is not a mere perception
held only by academics, but a real problem faced by many business executives, including the above-quoted CEO of one of Japan’s fast-growing business software companies.
Nevertheless, too few theories have been oﬀered to analyze the trade-oﬀs that are
creating this tension at the organizational level. In this article, we develop an agentbased model that formulates what we believe are four important steps of organizational
learning: search, knowledge sharing, evaluation, and alignment, through which organizational knowledge is updated. The model is useful for examining the origin of the
primary tension between exploration and exploitation.
We identify organizational congruency as a main driver of knowledge exploitation
rather than its result. Organizational congruency is formulated as the degree of alignment in knowledge base imposed on individuals. Higher congruency facilitates the
upgrading of organizational knowledge, which in turn accelerates exploitation in ourmodel. Key to our theory is the idea that knowledge diversity makes exploration more
eﬀective even as it impedes the updating of organizational knowledge, thus creating
1

Works Applications, Inc. (A) by Hideo Owan, Aoyama Business School case, November 2009.

2

an obstacle to exploitation. Although March (1991) has already argued that eﬀorts to
exploit existing knowledge eventually suppress exploration by reducing the diversityof knowledge, he does not illustrate the mechanism by which more exploration leads
to less exploitation or the reason the diversity of knowledge can discourage eﬀorts to
exploit it. The mechanism we illustrate in this paper goes beyond the usual argumentthat exploration and exploitation compete for scarce resources (March, 1991; Roberts,2004). Our theory suggests that the tension between exploration and exploitation
comes not necessarily from resource constraint, but rather from the substitutability
between initiatives and alignment.
Crossan, Lane, and White (1999) have expressed a view similar to ours: “Thistension (between exploration and exploitation) is seen in the feedforward and feedback
processes of learning across the individual, group, and organization levels.” According
to them, feedforward is the transference of learning from individuals and groups tothe organizational levels where ideas are embedded in the form of systems, structures,
strategies, and procedures. Feedback is the way in which this embedded or institutionalized learning aﬀects individuals and groups. Note that the feedback process relates
to exploitation where developing organizational knowledge assimilates learning and actions at the individual level. Although our view is similar to that of Crossan et al.
(1999), the tension arises endogenously in our model, whereas it is assumed as one of
the four key premises in their frameworks (Crossan et al. 1999: 523).
There are two important assumptions that drive the key results in our theory. First,
we assume that updating organizational knowledge requires a certain level of consensus.
In our model, organizational knowledge is successfully updated only when a majorityof high performers agree with the proposal to change it. This means that the mere
showing of new ideas to others is not enough for implementation at the organizational
level. Many others must have a similar view of the world and see common meaning in
the idea. This means that a certain level of organizational congruency is required topromote organizational learning.
Second, we assume that the organization’s management inﬂuences individuals’ time3

allocation between exploration (i.e. experimenting with new ideas) and exploitation(i.e. copying organizational knowledge) at the individual level. The famous story of
3M’s mandatory rule that its technical people should be able to devote 15 percentof their time to any projects of their own choice rather than those they are oﬃciallyassigned to is a classic example. Management uses its authority and techniques forcontrol, such as process management, to aﬀect the way people achieve their targets.
Furthermore, individuals engaging in exploitation do not have the option of ignoring organizational knowledge. Each kind of monitoring and incentive mechanism encourages
individuals to take in institutionalized knowledge as their own knowledge base.
One important implication of our model is non-concavity in the optimization problem. As argued, for example, by Levinthal and March (1993) and Ghemawat andRicart i Costa (1993) among others, ﬁrms tend to end up with the “extremes” in thepresence of such non-concavities. According to our theory, successful ﬁrms tend tobifurcate into two types: those that always promote individual initiatives and build organizational strengths on individual learning and those good at aligning the individual
knowledge base and exploiting shared knowledge. Let us call the former high-initiative
organizations and the latter high-alignment organizations.
Straddling between the two types often fails. This bifurcation arises when the operation is suﬃciently complex (in other words, the interdependency is high enough)or the business environment is suﬃciently uncertain. The intuition is that an equal
mixture of individual search and knowledge alignment slows down learning throughindividual search compared to the high-initiative organization while making it diﬃcult to update institutionalized knowledge because individuals’ knowledge base is not
suﬃciently aligned. In such organizations, once members get stuck with locally bestsolutions at the individual level, they cannot agree on how to improve the organizational knowledge. We ﬁnd that the resultant ineﬃciency is especially large when tasks
are interdependent or when the environment continuously changes.
More formally, we develop a model of organizations that undertake tasks of varying
degrees of complexity. The complexity of a task is formulated as interdependency

4

among tasks in determining functional performance following the NK landscape model(Kauﬀman, 1993). We also introduce environmental uncertainties by allowing theperformance function to be redeﬁned randomly from time to time.
Each organization consists of several members who search independently for better
practices and also learn from the organizational knowledge. The organizational knowledge evolves over time as proposals from the members of the organization to modify it
are constantly evaluated by high-performing members. Speciﬁcally, in each period eachmember of an organization either conducts an individual search for a better conﬁguration (with probability λ) or adopts the conﬁguration from the organizational knowledge(with probability 1 − λ). After all the agents have either conducted individual searches
or learned from the organizational knowledge, each agent proposes, with probability
p, to modify the organizational knowledge. Each proposal will be evaluated by themembers of organization whose performance at the time of evaluation is higher than
the average one in the organization. If the majority of high-performing members agree
on a proposed modiﬁcation, the organizational knowledge is changed.2
The two parameters of the model, λ and p, represent the degree of organizational
congruency and the frequency of knowledge sharing within the organization, respectively. The lower λ is, the higher is the degree of organizational congruency. In otherwords, when λ is low, it is more likely that members of the organization follow practices
or procedures that embody the organizational knowledge, regardless of whether or not
adopting them results in higher performance. When p is high, every agent attempts tochange the organizational knowledge more frequently.
Through extensive simulations of the model, we ﬁnd that (1) frequent knowledge
sharing within an organization has positive inﬂuences on its performance and (2) there
exist non-monotonic relationships between the degree of organizational congruency
and the organizational performance, especially when tasks are either complex or theenvironment is uncertain. Namely, the performance of an organization is high when
there is a substantial, but not overly strong, degree of congruency (λ ≈ 0.2) or no2

In case of a tie, a proposal is approved with probability 1/2.

5

congruency at all (λ ≈ 1.0).
It is rather intuitive that too much congruency is counter-productive, since agents
do not search for better practices and since without such individual searches it is notpossible to improve the organizational knowledge from which agents learn. However,more detailed analyses may be required in order to understand the non-monotonisityof the relationship between congruency and performance. Our analyses reveal that theperformance of an organization with no congruency (i.e. λ = 1.0) is always better thanthat of any other organization in early periods. When the task is suﬃciently complex,
however, on average, the performance of an organization with a substantial degree ofcongruency and frequent knowledge sharing catches up with and exceeds that of theformer organization in later periods. This reversal of performance comes from thediﬀerence in the rate at which the organizational knowledge improves. When a task
is complex, each member of an organization may arrive at distinct but locally bestpractices and may fail to agree on how to change the organizational knowledge. Aslong as agents rarely follow the organizational knowledge, this is not a problem (justas in the case of an organization without congruency). However, an organization witha moderate degree of congruency suﬀers from such disagreements because they resultin its agents adopting practices that are not proven to generate high value.
The same phenomenon arises when environmental uncertainty is high. In such anenvironment, an organization needs to keep up with the changing environment by continuously modifying the organizational knowledge. However, when agents are equally
likely to be conducting individual searches and adopting practices from the organizational knowledge, they fail to agree on how to adjust the organizational knowledge and,as a consequence, organizational performance suﬀers.
When congruency is high but not overly strong (λ ≈ 0.2), such disagreements about
how to modify the organizational knowledge do not arise as frequently. Most membersof the organization share the same ideas and search in similar directions. Hence, organizational knowledge will improve continuously as long as there is suﬃcient knowledge
sharing within the organization. And, the performance of such organizations eventually6

exceeds that of organizations with a low or an intermediate level of congruency.
The rest of the paper is structured as follows: in Section 2 we present the modelstudied in this paper, in Section 3 we present and discuss the results of simulation, andin Section 4 we conclude the discussion.

2

Model
Consider an organization that consists of M agents. Each agent undertakes anidentical task having N dimensions. The value that an agent generates depends on how
the agent conﬁgures each dimension of the task. The performance of the organization
depends on the values generated by the agents therein.
Let xij (t) ∈ {0, 1} be agent i’s conﬁguration of dimension j in period t,3 and X i (t) ∈{0, 1}N = {xi1 (t), xi2 (t), ..., xiN (t)} be i’s conﬁguration of the task in period t. The
corresponding value agent i generates, or the performance of agent i in period t, is
Πi (t) = π(X i (t)). The performance of the organization, Π(t), is deﬁned simply as the1 ∑imean performance of its members, i.e., Π(t) = Mi Π (t).
We formulate the performance function π(·) based on the N K Landscape model(Kauﬀman, 1993), which allows us to parameterize the interdependencies among N
dimensions with a parameter K. Namely, the ideal conﬁguration for dimension jdepends on i’s conﬁgurations of K other dimensions.4 Let Γj = {l1 , l2 , ..., lK } bethe set of these K dimensions that aﬀect the eﬀectiveness of xij (t), and Xji (t) ={xil1 (t), xil2 (t), ..., xilK (t)} ∈ {0, 1}K be i’s conﬁgurations of these K dimensions in period t. Then,1 ∑qj (xij (t), Xji (t))
NNπ(X i (t)) =j=1

3

The assumption that each dimension can be either zero or one is made for the sake of simplicity. One
can easily extend the model so that a dimension can be conﬁgured in many ways. If the number of possible
conﬁgurations of a dimension is c, then the number of possible conﬁgurations of the task becomes cN .
4
We assume that these K dimensions are chosen randomly from N − 1 other dimensions. One can also
consider many other possible structures of interdependencies. Rivkin and Siggelkow (2007) demonstrate thatthe structure of interdependencies, even controlling for K, aﬀects the complexity of the environment and theeﬀectiveness of various search strategies.

7

where qj (xj , Xj ) is deﬁned by assigning values drawn randomly from U [0, 1] to eachpossible xj and Xj . Every agent faces the same performance function π(·) or {qj }.
When modeled in this way, the number of possible conﬁgurations of the task is
2N , a potentially large space in which agents must search for better conﬁgurations.
The parameter K captures the complexity of the task. When K = 0, there is nointerdependency among dimensions; thus, changing the conﬁguration of one dimension
results in smooth changes in performance. The larger K is, the more interdependencies
there are among diﬀerent dimensions. When K is large, changing the conﬁguration of
one dimension has a non-additive eﬀect on the value generated by the agent.
To capture the uncertainty of the environment in which organizations operate,
we introduce a parameter µ ∈ [0, 1] such that, in each period and for each possible
conﬁguration of the task X, qj (xj , Xj ) is redeﬁned randomly to a value drawn fromU [0, 1] with probability µ. When µ is zero, the values associated with each possible
conﬁguration of the task remain constant over time. When the value of µ is higher,
these values can change quite drastically from period to period.
The NK landscape has been applied in the literature on organization theory. In theirseries of papers, Rivkin and Siggelkow have considered how to design a decision-making
process in hierarchical (or multi-level) organizations undertaking complex projects inuncertain environments (Rivkin and Siggelkow, 2003, 2007; Siggelkow and Rivkin, 2005,
2006). In particular, one of their foci has been to understand the relationship between
the levels of decision making when lower layers of hierarchy have narrower scope. Other
applications of NK landscape in management literature include, for example, Gavettiand Levinthal (2000). Gavetti and Levinthal (2000) consider the interplays between
a forward-looking “oﬀ-line” search and a backward-looking “on-line” search and theirimplications to organizational performance. Our analysis departs from the existing
literature in the following two respects: (1) we do not consider hierarchical organization, and (2) the focus of our analysis is on organizational congruency, which has
not been considered formally in the literature. We now turn to how the behaviors oforganizations are modeled.

8

2.1

Search, learning, and organizational congruency

We assume that each agent receives a randomly conﬁgured task initially; i.e.,xij (0) ∈ {0, 1} are randomly set for all i and j. Agents modify their conﬁgurations
over time by conducting individual searches and by learning from the organizational
knowledge. Let Ω(t) = {o1 (t), o2 (t), ..., oN (t)} where oj (t) ∈ {0, 1} represents the organizational knowledge at period t. We assume that Ω(0) is randomly set. We allow theorganizational knowledge itself to evolve over time as agents in the organization contribute their knowledge in the manner described below. Note that knowledge sharing
improves organizational performance because agents face the same {qj }.
In each period, each agent either conducts an individual search for a better conﬁguration (with probability λ) or learns from the organizational knowledge (with probability 1 − λ). The individual searches are conducted as follows: an agent chooses oneof the N dimensions randomly and ascertains whether changing its conﬁguration generates a greater value. If it does, he adopts the change. Otherwise, his conﬁguration
remains as before.
When an agent learns from the organizational knowledge, he randomly chooses adimension such that his current conﬁguration diﬀers from that of the organizational
knowledge and adopts the organizational knowledge for the chosen dimension. Copyinga part of the organizational knowledge in this manner gradually assimilates the individual knowledge base to the organizational knowledge if λ is suﬃciently low. We call thisprocess alignment because the assimilated knowledge base facilitates upgrading of theorganizational knowledge as explained later. When adopting the conﬁguration fromthe organizational knowledge, the agent does not check whether doing so generates ahigher value. We assume that the organization’s management institutes a monitoringand incentive mechanism to enforce the alignment of the organizational base.
On the one hand, when λ is low, agents tend to follow the conﬁgurations of theorganizational knowledge; thus, their practices are all aligned with each other. When λis high, on the other hand, since agents pursue individual searches, their conﬁgurations
may remain diverse. Therefore, we can interpret the parameter λ to represent the level9

of organizational congruency (i.e., high λ indicates low organizational congruency).
It is of our interest to discover the relationship between the degree of organizational
congruency represented by λ and organizational performance under various levels ofcomplexity and uncertainty.
At the end of each period, with probability p, each agent proposes to modify theorganizational knowledge. When an agent proposes to modify the organizational knowledge, he randomly chooses one dimension such that his conﬁguration diﬀers from thatof organizational knowledge. And, he proposes to change the conﬁguration of the chosen dimension in the organizational knowledge so that it will be the same as his current
conﬁguration. Whether the proposal is accepted or not depends on voting by agents inthe organization. It is accepted if the majority of the agents whose performance is noless than the performance of the organization5 conﬁgure the dimension as proposed.6
The parameter p can be interpreted as the frequency of knowledge sharing within theorganization. The higher the value of p is, the more quickly organizational knowledge
improves.
The model presented here is similar to that of March (1991), which studies the relationship between exploitation of existing knowledge and exploration of new knowledge
in an abstract model. In particular, both our model and that of March (1991) consider
interactions between individual search and learning within an organization throughcommunications among its members. Our model diﬀers, however, from that of March(1991) in its assumption of the underlying conﬁguration space. While the latter assumes the existence of a unique conﬁguration that an organization needs to discover,
our model employs the NK landscape so that there can be many distinct locally-best
conﬁgurations when a task is complex. We are not aware of existing research thatformally attempts to understand the eﬀect of organizational congruency in the face ofsuch multiplicities of locally-best conﬁgurations.

5
6

That is, we consider the majority of those agent k such that Πk (t) ≥ Π(t).
In the case of a tie, a proposal is approved with probability 1/2.

10

1. Set parameter values, and give a random seed
2. Initialize NK landscape, agents, and organizational knowledge
3. for 1 ≤ t ≤ 1000(a) for each agent 1 ≤ i ≤ M(i) Search (λ) or Copy (1 − λ)(ii) update the agent’s conﬁguration and performance(b) Update performance of organization(c) for each agent 1 ≤ i ≤ M (in random orders)(i) Propose (with prob. p) or not.
(ii) If proposes, evaluate the proposal(iii) update organizational knowledge(c) if µ > 0, update NK landscape, the performances of agents and the organization(d) Back to (a)Table 1: Pseudo Code3

Results
There are six parameters in our model. The task is deﬁned by its size N and its

complexity K. The environmental uncertainty is captured by µ. The organization ischaracterized by the number of agents, M , the frequency of knowledge sharing among
them, p, and the level of organizational congruency, λ. In all the simulations, we ﬁx
N and M to be 100 and 20, respectively, and vary other parameters to investigate theeﬀect of congruency and communications on the performance of organizations undervarious degrees of complexity and uncertainty.7
For each set of parameter values, the payoﬀ function, π(·), initial conﬁguration for
individual task X i (0), and organizational knowledge, Ω(0), are generated. Then, weallow organizations to operate in the manner described in the Model section for 1000
periods. Table 1 shows the pseudo code of the simulations.
To summarize the performance of an organization over time, we mainly focus onpresent discounted values (PDVs) of organizational performance over these 1000 pe∑triods: namely, Π = 1000
t=1 δ Π(t) where δ is a discount factor. Below, we will set thediscount factor to be δ = 0.999.8 This discount factor gives the payoﬀ for the last
7

The appendix shows the results from M = 10 and M = 30, which are similar to the results from M = 20.
If we set the discount factor too low, the payoﬀ at t = 1000 will be given a negligible weight comparedto those for earlier periods. For example, if δ = 0.95, the weight for the payoﬀ at t = 1000 will be less than
811

(A) K = 0 and µ = 0.0(B) K = 8 and µ = 0.0

425

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0.0(D) K = 8 and µ = 0.005

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PDV 360
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λ

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9
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Figure 1: Average PDVs of organizational performances for various p and λ in four combinations of complexities (K = 0 (left) and K = 8 (right)) and uncertainties (µ = 0.0 (top) andµ = 0.005 (bottom)). Discount factor is δ = 0.999. Data are generated by taking averageover 100 simulation runs for each set of parameter values.

period a weight that is 0.37 of that for the ﬁrst period. We also take the average over
100 simulation runs based on varying random seeds.

3.1

Eﬀect of p and λFigure 1 shows the PDV (shown by height) for various degrees of activeness ofcommunication p (the horizontal axis) and of control λ (the vertical axis) under fourcombinations of complexities, K ∈ {0, 8}, and uncertainties, µ ∈ {0.0, 0.005}. Recall
that a higher λ represents weaker organizational control (or congruency).
0.01% of the payoﬀ at the period t = 1. Since it is possible for performance to take a long time to level oﬀ,
we would like the payoﬀ at t = 1000 to have enough weight compared to the initial payoﬀs.

12In all four panels in Figure 1, one can see that organizational performance measured
by PDV becomes higher as we move along the horizontal axis from left to right. Thatis, the more frequently individuals engage in knowledge sharing, the higher their organizational performance, regardless of task complexity and environmental uncertainty.
While the ﬁgure exhibits a monotonic relationship between PDV and frequencyof knowledge sharing, p, the relationship between PDV and level of organizational
congruency, λ, is not monotonic in three out of four cases shown in Figure 1. Except
for cases in which the task is simple and there is no environmental uncertainty (Panel(A)) or the level of knowledge sharing in the organization is very low (low p), theperformance of the organization has two peaks: (1) when organizational congruency isvery low, i.e, λ ≈ 1.0; and when there is a substantial, but not overly strong, degree ofcongruency, λ ≈ 0.2. We call the former, a high-initiative organization and the lattera high-alignment organization. When λ is very small (so that individual searches
are seldom conducted) or has intermediate values of around 0.5 or 0.6, performance
becomes low.
The non-monotonic relationship between λ and organizational performance can bebetter seen in Figure 2. For the same four combinations of K and µ as in Figure 1,
Figure 2 plots PDVs against various values of λ for three values of p: p = 0.0 (solid
black), p = 0.5 (solid gray), and p = 1.0 (dashed black). One can see from the ﬁgurethat for λ ≈ 0.2 to generate as high a level of performance as λ ≈ 1.0, the eﬀorts toshare knowledge must be persistent (i.e., high p). Another point indicated by Figure 2 isthat in the case of complex tasks (K = 8), organizational performance declines sharply
as one moves away from the state of full individual search, i.e., λ = 1.0, while there
is a wider range of λ with values around λ = 0.2 that maintains high performance.
This suggests that when knowledge sharing activities are suﬃcient, any shift fromfull exploration (i.e., λ = 1.0) may require a substantial leap toward a state of highcongruency.9

9Figure 2 also shows that when the task is simple (K = 0), the introduction of a small degree of congruency
can improve performance compared to the case of no congruency.

13

(A) K = 0 and µ = 0.0(B) K = 8 and µ = 0.0
PDV

PDV

420

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Figure 2: Average PDVs of organizational performances for various λ in four combinationsof complexities (K = 0 (left) and K = 8 (right)) and uncertainties (µ = 0.0 (top) andµ = 0.005 (bottom)). In each ﬁgure, results for three distinct ps are reported: p = 0.0 (solid
black), p = 0.5 (solid gray), and p = 1.0 (dashed black). Discount factor is δ = 0.999. Data
are generated by taking average over 100 simulation runs.
Why do successful organizations, in the face of complex tasks and uncertain environments, bifurcate into two types: high-initiative (λ = 1.0) vs. high-alignment(λ ≈ 0.2)? In other words, why do we obtain non-monotonic relationships between
λ and organizational performance? To answer this question, we turn to dynamics ofperformance over time.

3.2

Dynamics

Figure 3 shows the dynamics of organizational performance for four values of λ,λ ∈ {0.0, 0.2, 0.6, 1.0} (shown in solid black, solid gray, dashed black and dashed gray,respectively), for the four combinations of K ∈ {0, 8} and µ ∈ {0.0, 0.005} consideredin Figures 1 and 2. These four λs are chosen because they correspond approximately
to the local maxima and minima of organizational performance measured by PDV.
Knowledge sharing within an organization is assumed to be very frequent, p = 1.0,

14

(A) K = 0 and µ = 0.0(B) K = 8 and µ = 0.0

<Pt >

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100 200 300 400 500 600 700 800 900 1000t
100 200 300 400 500 600 700 800 900 1000

0.58
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(C) K = 0 and µ = 0.005(D) K = 8 and µ = 0.005

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t

100 200 300 400 500 600 700 800 900 1000

100 200 300 400 500 600 700 800 900 1000

Figure 3: Average performance over time for two levels of complexity, K = 0 (left) andK = 8 (right), and two degrees of environmental uncertainty, µ = 0.0 (top) and µ = 0.005(bottom). Four values of λ are considered: λ = 0.0 (solid black) ,λ = 0.2 (solid gray), λ = 0.6(dashed black), λ = 1.0 (dashed gray). The communication is active (p = 1.0). The datais generated by taking the average per period organizational performance for each block of
100 periods. The average from 100 simulation runs is reported.

15

which corresponds to the dashed black curves in Figure 2.10 Figure 3 reports theaverage per-period organizational performance for each block of 100 periods, i.e., fort ∈ [1, 100], t ∈ [101, 200] and so on.
When the task is simple and there is no environmental uncertainty, organizations
with lower degrees of congruency (i.e., higher λs) demonstrate faster improvements inperformance (Panel (A)). When K = 0, the best conﬁguration for the task can be foundthrough a local search procedure, such as the individual searches considered in thispaper. Therefore, all the agents in an organization will eventually ﬁnd the unique best
conﬁguration as long as λ > 0.0. (Note that when λ = 0.0, there is no individual search,so that agents never ﬁnd the best conﬁguration). Once everyone in an organization
has found the best conﬁguration, there is no further improvement in organizational
performance. When all the agents in an organization only conduct individual searches
and do not copy from organizational knowledge (i.e, λ = 1.0), each agent rapidly ﬁnds
the best conﬁguration. Organizations that employ full individual search (λ = 1.0)
are not especially superior to organizations with higher levels of congruency (λ < 1.0)
because organizations can achieve very good performance provided knowledge sharing
takes place frequently enough and organizational knowledge is improved rapidly. As
knowledge sharing becomes less frequent (i.e., lower p), however, higher congruency
imposed on individuals (i.e, lower λ) would instead disturb individual searches andretard organizational performance.
When the task is complex, the results are quite diﬀerent, even in the complete
absence of environmental uncertainty. Panel (B) of the ﬁgure shows that a higher
value of λ corresponds to a higher performance only at early periods, namely the ﬁrst
100 periods. In later periods, for example for t ∈ [101, 200], while λ = 1.0 (dashed gray)exhibits the highest performance, the performance of λ = 0.6 (dashed black) is lower
than that of λ = 0.2 (solid gray). Eventually, the performance of λ = 0.2 exceeds thatof λ = 1.0. This case demonstrates the possible trade-oﬀ between the performances in

10

As we have seen above, a lower value of p results in lower performance for an organization with λ smaller
than one.

16

earlier periods and those in later periods.11 It should also be noted that the average
performance in all three cases except for λ = 0.0 converge to the same level in the ﬁnal
100 periods as shown in the Panel (B) of the ﬁgure.
In the presence of uncertainty (Panels (C) and (D)), the performance of the organizations with λ = 0.2 and λ = 1.0 exhibit a similar pattern, as seen in the case shownin Panel (B). Namely, initially, the organization with λ = 1.0 demonstrates higher
performance than the one with λ = 0.2, but in the later periods the performance of thelatter exceeds that of the former. The dynamics of the performance for λ = 0.6 (solid
black) is quite diﬀerent in the face of environmental uncertainty than in its absence.
That is, when there is suﬃcient uncertainty, performance does not improve much overtime (in the case of a complex task, Panel (D)) or can even deteriorate (in the case ofa simple task, Panel (C)). Note that due to the environmental uncertainty organizational performance in an individual simulation run demonstrates ups and downs overtime. Such volatilities are hidden, however, in Figure 3, where we plot the averaged
performance in each block of 100 periods and further take averages across 100 simulation runs. Nonetheless, deterioration of average performance appears for λ = 0.6 after
period 200. This puzzling outcome deserves more careful analyses.
Why does the reversal of relative performance between λ = 0.2 and λ = 1.0 takeplace during the course of organizational learning? And, why does performance for
λ = 0.6 in an uncertain environment with a complex task deteriorate after an initial
improvement?
Looking at the dynamics of diversity of individual conﬁgurations and the dynamics
of the value of organizational knowledge, π(O(t)), helps us to answer these questions.
The former is plotted in Figure 4 and the latter in Figure 5.
The diversity of the individual conﬁgurations, D(t), is measured by the average
distance between individual conﬁgurations and their means. The mean conﬁguration of∑dimension j at period t is x̄j (t) = i xij (t)/M . The distance between conﬁgurations of

11

Therefore, if we set the discount factor δ too low, we pick up only performance in earlier periods andfail to capture this trade-oﬀ.

17

(A) K = 0 and µ = 0.0(B) K = 8 and µ = 0.0

D
D

50

D

40
800

30

D

12

600

20
400

35

10
10

200

30

8

t

t

25

100 200 300 400 500 600 700 800 900 1000

100 200 300 400 500 600 700 800 900 1000

6

20

4

15
10

2
5

t

t

100 200 300 400 500 600 700 800 900 1000

100 200 300 400 500 600 700 800 900 1000

(C) K = 0 and µ = 0.005(D) K = 8 and µ = 0.005

D

D

800
800

D

600

D

175
400

100

150
125

600
400
200

200

80

t

t

100

100 200 300 400 500 600 700 800 900 1000

60

100 200 300 400 500 600 700 800 900 1000

75
40

50
20

25

t

t

100 200 300 400 500 600 700 800 900 1000

100 200 300 400 500 600 700 800 900 1000

Figure 4: The diversity within an organization for two levels of complexity, K = 0 (left) andK = 8 (right), and two degrees of environmental uncertainty, µ = 0.0 (top) and µ = 0.005(bottom). The communication is active (p = 1.0). Four values of λ are considered: λ = 0.0(solid black), λ = 0.2 (solid gray), λ = 0.6 (dashed black), λ = 1.0 (dashed gray). For the
clarity of exposition, only λ ∈ {0.0, 0.2, 0.6} are shown in the main ﬁgure. See the insets
for all the four λs. The extent of diversity is measured based on the discrepancy between
individual conﬁgurations and their means. The data is generated by taking the average perperiod diversity for each block of 100 periods. The average from 100 simulation runs isreported.

18

(A) K = 0 and µ = 0.0(B) K = 8 and µ = 0.0<ΠHOHtLL><ΠHOHtLL>

0.66

0.7

0.64
0.65

0.62
100 200 300 400 500 600 700 800 900 1000t
100 200 300 400 500 600 700 800 900 1000

0.58

t

0.55

0.56
0.54

(C) K = 0 and µ = 0.005(D) K = 8 and µ = 0.005<ΠHOHtLL><ΠHOHtLL>
0.64

0.65

0.62

0.625

0.6
0.58

0.6

0.56

0.575

0.54

0.55

0.52

0.525
100 200 300 400 500 600 700 800 900 1000t

100 200 300 400 500 600 700 800 900 1000t

Figure 5: The dynamics of the average value of organizational knowledge for two levels ofcomplexity, K = 0 (left) and K = 8 (right), and two degrees of environmental uncertainty,µ = 0.0 (top) and µ = 0.005 (bottom). Four values of λ are considered: λ = 0.0 (solid black),λ = 0.2 (solid gray), λ = 0.6 (dashed black), λ = 1.0 (dashed gray). The communicationis active (p = 1.0). The data is generated by taking the average per period value of organizational knowledge for each block of 100 periods. The average from 100 simulation runs isreported.
∑i
individual i and the mean conﬁgurations at period t is therefore Di (t) = N
j=1 |xj (t) −∑ix̄j (t)|/N . The diversity for an organization in period t is D(t) = M
i=1 D (t).
As in the case of organizational performance shown in Figure 3, we took the averageover each block of 100 periods.12 The results for four combinations of complexities
K ∈ {0, 8} and uncertainties µ ∈ {0.0, 0.005} are plotted. Four values of λ, λ ∈{0.0, 0.2, 0.6, 1.0} (shown in solid black, solid gray, dashed black, and dashed gray,respectively) are shown. p = 1.0 is assumed.
When the task is simple and there is no environmental uncertainty, the diversity
measure converges to zero for all types of organizations plotted in Figure 4 (Panel (A)).
The lower λ is, the faster is convergence. The reason even an organization with λ = 1.0(dashed gray, shown only in the in-sets) demonstrates zero diversity in the later period
12

Figure 3 reports the results obtained from taking the average of these averaged per-period diversities
across 100 simulations.

19

is that, as discussed above, when K = 0 and µ = 0.0, every agent in the organization
eventually ﬁnds the unique best conﬁguration through individual searches unless λ iszero. And, since everyone eventually agrees on the best conﬁguration, organizational
knowledge will also be conﬁgured accordingly. Therefore, the value of organizational
knowledge shows rapid improvement, as shown in Figure 5 (Panel (A)). When λ = 0.0(shown in solid black), this is not the case. Although the diversity measure goes tozero as well, the value of organizational knowledge shows little improvement. Diversity disappears because everyone adopts conﬁgurations from the same organizational
knowledge. However, because agents never search for better conﬁgurations, they do
not have new information necessary to improve organizational knowledge.
When there is no uncertainty but the task is complex (K = 8, µ = 0.0), as shownin Figure 4 (Panel (B)), diversity remains high for organizations with λ = 1.0 (dashedgray, shown only in in-set) for long periods of time, while the diversity measures in
the organizations with λ = 0.0 and λ = 0.2 quickly converge to zero. In the case of
λ = 0.6, the diversity measure declines much more slowly than in the cases of smaller
values of λ.
The high diversity for organizations with λ = 1.0 under the complex task is due tothe existence of many distinct but locally-best conﬁgurations. And, since such locallybest conﬁgurations vary from one another, diversity among the individual conﬁgurations remains high and agents in the organizations do not agree on how to improveorganizational knowledge. As a result of the inability to aggregate information andchoose the best among many local optima, the value of organizational knowledge remains low (Figure 5, Panel (B)). Although the value of organizational knowledge forthe λ = 0.0 organization also shows little improvement, this is due to the complete
absence of individual searches.
Panel (B) of Figure 5 also shows that an organization with λ = 0.6 is much slower
in improving organizational knowledge than one with λ = 0.2. Recall that, in ourmodel, in order to modify organizational knowledge, not only must new proposals be
submitted, they must also be approved. In the model considered here, a proposal

20

is approved when a majority of better-performing agents conﬁgure the dimension as
proposed. Also, as discussed above for the case of λ = 1.0, when a task is complex,
individual searches may lead to various distinct conﬁgurations that are local optima.
If many agents search in diﬀerent directions, it is more diﬃcult for them to agree on
how to modify organizational knowledge. The insuﬃcient alignment of the individual
knowledge base resulting from lower congruency creates a bottleneck to improvement oforganizational knowledge, which in turn slows down the improvement of organizational
performance.
The inability to improve organizational knowledge can be detrimental when the environment is changing. In such an unstable environment, the quality of organizational
knowledge itself can deteriorate over time, as one can see from Panel (C) of Figure 5.
Note that an organization with λ = 1.0 is not capable of improving organizational
knowledge when the task is complex, but it does not suﬀer from the bad organizational
knowledge because agents never adopt bad conﬁgurations of the organizational knowledge. However, when λ = 0.6, an intermediate level, agents can still have suﬃciently
diﬀerent knowledge conﬁgurations, which in turn hinders organizational knowledge
from improving, as shown in Panel (C) of Figure 5. This explains why the average
performance in organizations with λ = 0.6 deteriorates, as can be seen in Panel (C) of
Figure 3.

3.3

Optimal degree of congruency

So far we have considered four combinations of complexities of task (K ∈ {0, 8})
and uncertainties of environment (µ ∈ {0.0, 0.005}). We have seen that when theenvironment is uncertain or the task is complex, successful organizations bifurcate into
two types: high-initiative vs. high-alignment organizations. We have also noted thatfor the latter to be successful, very frequent knowledge sharing within the organizationis required to improve and maintain the quality of organizational knowledge. We
would also like to ﬁnd out the conditions under which a high-alignment organization
outperforms a high-initiative one. Figure 6 illustrates which of the organizations with

21

(A) λ ∈ {0.2, 0.6, 1.0} or those with (B) λ ∈ {0.2, 0.6, 0.95} performs best under various
levels of complexity of the task (K) and various degrees of environmental uncertainty(µ). We assume very frequent knowledge sharing p = 1.0. We introduce λ = 0.95
instead of λ = 1.0 in Panel (B) of the ﬁgure to test robustness of the results fromthe comparison. As we have seen above, in the face of complex tasks, organizational
performance declines very sharply as one moves away from λ = 1.0, while there exists
a wider range of λ around 0.2 that generates high performance.
In Panel (A) of the ﬁgure, the white (black) cells in the ﬁgure show the combinationsof K and µ where an organization with λ = 1.0 (λ = 0.2) performs the best. For Panel(B), the white cells represent the combinations where λ = 0.95 performs the best.13
The gray cells without the indication “ND” show the cases where λ = 1.0 (or λ = 0.95
in the case of Panel (B)) and λ = 0.2 perform equally well and are both better thanλ = 0.6. The gray cells with the indication “ND” are the region where all three λperform equally well.
One can see from Panel (A) that when uncertainty is low (µ < 0.001), a highinitiative organization (λ = 1.0) exhibits superior performance even when the task isquite complex.14 The advantage of a high-initiative organization disappears once aslight degree of alignment is introduced (Panel (B)), unless the task is simple. Overall,our results are not robust for µ < 0.005. In other words, there is not much signiﬁcant diﬀerence between high-initiative and high-alignment organizations in a relatively
stable environment.
As the environment becomes more uncertain but not overly so (µ = 0.005 or 0.01),
a high-alignment organization (λ = 0.2) demonstrates its advantage assuming thatthe task is reasonably complex. When the environment becomes extremely unstable13

We have performed two-sample t-test based on PDVs generated by 100 simulations for each set ofparameter values. Depending on the results of a variance comparison test, unequal variance or equal varianceis assumed in performing t-test. One organization is said to outperform the other if the mean PDV issigniﬁcantly greater at 5% signiﬁcance level in a one-tailed test.
14
Note that we are measuring performance with PDVs that put higher weights on earlier periods thanlater ones. As seen in the previous section, if we compare the average performance in later periods (or place
more weight on the performance of later periods by using a higher discounting factor δ), in cases of veryfrequent knowledge sharing, λ = 0.2 is better than λ = 1.0.

22

(A) Comparison amongλ ∈ {0.2, 0.6, 1.0}
0.0001 0.0005 0.001

0.005

0.01

0.05

0.0

0.0001 0.0005 0.001

0.005

0.01

0.05

12

12

12

12

10

10

10

10

8

8

8

8

6

6

6

6

4

4

4

4

2

2

2

2

0

0

0

ND
0.0

ND

ND

0.0001 0.0005 0.001
μ

0.005

0.01

K

K

0.0

(B) Comparison amongλ ∈ {0.2, 0.6, 0.95}

0.05

ND
0.0

0.0001 0.0005 0.001
μ

0

0.005

0.01

0.05

Figure 6: Comparison of PDV of (A) λ ∈ {0.2, 0.6, 1.0} and (B) λ ∈ {0.2, 0.6, 0.95} forvarious degree of complexity K and uncertainty µ. p = 1.0 and discount factor is 0.999
in calculating PDVs. White and black areas indicate λ = 1.0 (λ = 0.95 in panel B) and
λ = 0.2 demonstrate the highest performance, respectively. Gray areas indicate no diﬀerence
between λ = 1.0 (λ = 0.95 in panel B) and λ = 0.2, and both are better than λ = 0.6. Gray
areas with “ND” indicate that all three λs perform equally well.

23

(µ = 0.05), though, a high-alignment organization loses its relative advantage and ahigh-initiative organization tends to perform better.
This exercise reveals that institutionalizing knowledge in the form of routines, procedures, strategies, and systems generally creates advantage when the business is reasonably complex and uncertain. The cost of institutionalizing knowledge is the delaycaused by the aggregation of individual knowledge. Furthermore, the assimilation of theindividual knowledge base could also hinder the improvement of organizational knowledge by reducing the range of individual searches when the environment changes drastically. Potential costs discussed above make it suboptimal to choose a high-alignmentorganization in an extremely unstable environment.

4

Conclusion
This work demonstrates the origin of the primary tension between exploration andexploitation and conditions in which choosing an “extreme” type of organizational
learning is optimal. We identify important roles played by organizational congruency
in facilitaing organizational learning. Our results show non-concavity in the optimization problem of organization design and imply that two types of organization with
distinct natures could emerge. A high-initiative organization promotes individual initiatives to experiment with new ideas and build its strength on individual learning. A
high-alignment organization, in contrast, assimilates the individual knowledge base andaccelerates organizational learning through frequent knowledge sharing among individuals. An organization with a more equal mix of individual initiatives and knowledgealignment tends to perform worse, and especially so when the operation is reasonably
complex (in other words, interdependency is high enough) and/or the business environment is reasonably uncertain. Although a high-alignment organization tends to befavored in a moderately uncertain environment, a high-initiative organization tends tobe favored when the environment becomes extremely unstable.
There are two remaining issues to be considered. First, how robust are the results24we have illustrated in this paper to changes in the assumptions? Speciﬁc rules andprocesses of updating organizational knowledge in our model must be relaxed to examine whether our bifurcation results continue to hold under diﬀerent assumptions.
Second, we did not consider the possibility that the degree of organizational congruency changes as time goes by. Such a question is especially formidable if parametervalues, such as complexity of operation K, were to change in the course of a ﬁrm’s
growth. We believe that these questions can be successfully addressed by extending
the basic framework we employed in this paper, but will leave them to future research.

25

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26

A

Results from M = 10 and M = 30
The main text concentrated on discussion of the results for M = 20. This appendix

presents the simulation results from M = 10 and M = 30, which are qualitatively thesame as the results in the main text. Figure 7 shows, in the same format as in Figure 1,
PDV with discount factor δ = 0.999 for various values of p and λ for four combinationsof K and µ. M = 10 is on the top row and M = 30 is on the bottom row. As one
can see from comparing Figure 7 and Figure 1, the main results do not change as wechange the number of agents in the organization. What does change is the range ofvalues of λ < 1.0 that maximizes performance.

M = 10K=0

K=8µ = 0.0µ = 0.005

380

400
PDV

µ = 0.0

1.0
0.9
0.8
0.7
0.6

380
360
340
320
0.0

340
320

0.3
0.5
P

0.7
0.9
1.0

325
0.0

0.5
P

0.7
0.9
1.0

340
320
0.0

0.5

0.1

Λ
0.3
0.5

Λ
0.3

0.7

0.5

0.9
1.0

0.2

0.6
P

0.1

0.8

0.0

0.3

0.4

0.2

0.6
P

0.4

0.2

0.3

0.4

0.1

0.8

0.0

1.0
0.9
0.8
0.7
0.6

360

0.4

0.2

0.2

0.6

380
PDV

0.5

0.1

0.3

0.4

0.1

0.8

350

Λ
0.3

0.2

0.6

1.0
0.9
0.8
0.7
0.6

375

0.4

0.2

0.3

0.4

400
PDV

0.5

0.1

Λ
0.4

0.2

400

425
1.0
0.9
0.8
0.7
0.6

360

0.0

0.5

0.1

PDV

µ = 0.005

0.7

0.1

0.8
0.9

0.0

1.0

0.0

M = 30K=0

K=8µ = 0.0µ = 0.005µ = 0.0

380

400
1.0
0.9
0.8
0.7
0.6

PDV 375
350
325
0.0

Λ
0.4

0.2
0.3

0.3

0.4
0.5

0.2

0.6
P

0.7

0.1

0.8
0.9
1.0

0.0

400

425
1.0
0.9
0.8
0.7
0.6

PDV 360
340
320
0.0

0.5

0.1

µ = 0.005

0.3
0.5
0.7
0.9
1.0

0.3
0.5

0.2

0.6
P

0.1

0.8

Λ
0.4
0.7

0.1

0.8
0.9

0.0

1.0

0.0

380

1.0
0.9
0.8
0.7
0.6

PDV
360
340
320
0.0

0.5
0.4
0.3

0.2

0.6
P

325

0.2

0.3

0.4

350

0.1

Λ
0.4

0.2

1.0
0.9
0.8
0.7
0.6

375

0.0

0.5

0.1

400
PDV

0.5

0.1

Λ
0.4

0.2
0.3

0.3

0.4
0.5

0.2

0.6
P

0.7

0.1

0.8
0.9
1.0

0.0

Figure 7: Present Discounted Values of organizational performance for M = 10 (top) andM = 30 (bottom) for four combinations of K ∈ {0, 8} and µ ∈ {0.0, 0.005}

27