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Organizations, as is true with social systems more generally, tend to be nearly, not fully, decomposable. However, analyses of nearly decomposable systems have tended to be at a single level of analysis and have generally neglected the vertical element of nearly decomposable systems. Critical to the notion of nearly decomposable systems is the property that the details of a particular subproblem may be encapsulated and captured by more aggregate parameters and that those subproblems interact in an aggregate way. We explore these issues in reference to the role of three canonical organizational structures in facilitating adaptation in the presence of near decomposability: a traditional hierarchy in which a subordinate reports to a single boss, an autonomous form in which the subordinate does not have a direct reporting relationship, and a multiauthority structure in which the subordinate reports to multiple bosses. Despite the ubiquity and potential benefits of multiauthority structures in coordinating highly interdependent tasks, our understanding of the mechanisms that determine the performance of those structures is still relatively modest. Scholars have noted conflicting empirical findings and have called for a more rigorous approach to study these organizational forms. To help address these issues, we develop an agent-based computational model that compares the performance of these three canonical types of organizational forms in settings characterized by different degrees of complexity and near decomposability.
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ORGANIZATION SCIENCE
Articles in Advance,pp. 1–18
http://pubsonline.informs.org/journal/orsc/ ISSN 1047-7039 (print), ISSN 1526-5455 (online)
When Two Bosses Are Better Than One: Nearly Decomposable
Systems and Organizational Adaptation
Daniel A. Levinthal,aMaciej Workiewiczb
aThe Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania; bESSEC Business School, 95021 Cergy-Pontoise, France
Contact:
dlev@wharton.upenn.edu,http://orcid.org/0000-0002-8740-6091 (DAL); workiewicz@essec.edu,
http://orcid.org/0000-0001-5745-719X (MW)
Received: July 10, 2015
Revised: July 25, 2016; January 25, 2017;
July 28, 2017
Accepted: September 16, 2017
Published Online in Articles in Advance:
April 2, 2018
https://doi.org/10.1287/orsc.2017.1177
Copyright: © 2018 INFORMS
Abstract. Organizations, as is true with social systems more generally, tend to be nearly,
not fully, decomposable. However, analyses of nearly decomposable systems have tended
to be at a single level of analysis and have generally neglected the vertical element of
nearly decomposable systems. Critical to the notion of nearly decomposable systems is the
property that the details of a particular subproblem may be encapsulated and captured by
more aggregate parameters and that those subproblems interact in an aggregate way. We
explore these issues in reference to the role of three canonical organizational structures in
facilitating adaptation in the presence of near decomposability: a traditional hierarchy in
which a subordinate reports to a single boss, an autonomous form in which the subordi-
nate does not have a direct reporting relationship, and a multiauthority structure in which
the subordinate reports to multiple bosses. Despite the ubiquity and potential benefits of
multiauthority structures in coordinating highly interdependent tasks, our understanding
of the mechanisms that determine the performance of those structures is still relatively
modest. Scholars have noted conflicting empirical findings and have called for a more
rigorous approach to study these organizational forms. To help address these issues, we
develop an agent-based computational model that compares the performance of these
three canonical types of organizational forms in settings characterized by different degrees
of complexity and near decomposability.
Supplemental Material:
The online appendix is available at https://doi.org/10.1287/orsc.2017.1177.
Keywords:
organizational design
organizational adaptation
near decomposability
matrix organization
1. Introduction
The mantra that one should “act locally but think glob-
ally” is not only a suggestion to social action but also
arguably a fundamental challenge for organizations.
Organizations are composed of a potentially broad set
of individuals engaged in a wide array of tasks, tasks
that are likely to have some degree of interdependence
given their colocation within the same organizational
entity. In that sense, a critical function of organizations,
and in turn organizational design, is to address the
dual challenge of taking advantage of the specializa-
tion of labor and needing to coordinate efforts. There
is an inherent conflict in this dual imperative. While
the division of labor allows individuals to develop an
enhanced level of expertise in a given problem domain,
the constraints of bounded rationality (Simon 1955)
that make it advantageous to focus on a limited prob-
lem domain also imply limits on the span of control
for those responsible for coordinating organizational
action, or “integrating” a set of more specialized actors
(Simon 1947). Organizational hierarchies help econo-
mize on these managerial bounds by encapsulating
many of the details of lower-level subsystems within
the broader organization (Chandler 1962, Williamson
1975). Higher-level managers make choices that both
influence the direction of the organization and set
the parameters under which lower-level actors operate
(Goold and Campbell 1987). However, organizations,
as is true with social systems more generally, tend to
be nearly, not fully, decomposable (Simon 1962). Thus,
a simple nested hierarchy of an organizational chart
is unlikely to capture fully the underlying interdepen-
dence within an organization.
One of the key premises in the organization design
literature is the idea that the structure of the under-
lying interdependencies should inform the appropri-
ate organizational form (Lawrence and Lorsch 1967,
Thompson 1967, Galbraith 1977). The fact that interde-
pendencies tend to be nearly decomposable facilitates
the delegation of authority over distinct task domains
(Baldwin and Clark 2000, Rivkin and Siggelkow 2003,
Siggelkow and Levinthal 2003, Ethiraj and Levinthal
2004a, Felin and Zenger 2014). However, analyses of
nearly decomposable systems have tended to be at a
single level of analysis and, correspondingly, have gen-
erally neglected the vertical element of nearly decom-
posable systems. In that sense, such analyses are effec-
tively studies of the power of modularity (Simon 1962,
Augier and Sarasvathy 2004). Critical to Simon’s (1962)
notion of nearly decomposable systems is the property
1
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Levinthal and Workiewicz: Nearly Decomposable Systems and Organizational Adaptation
2Organization Science, Articles in Advance, pp. 1–18, © 2018 INFORMS
that the details of a particular subproblem may be
encapsulated and captured by more aggregate param-
eters and that those subproblems interact in an aggre-
gate way. This suggests, as we develop more fully
in the subsequent section, a different representation
than the standard NK structure that has been used to
study the role of modularity and task decompositions
(Ethiraj and Levinthal 2009, Rivkin and Siggelkow
2007). We offer an enrichment of the standard NK
structure so as to better capture Simon’s (1962,2000)
conceptualization.
With regard to basic organizational structures, the
two forms highlighted in the management literature
are functional and multidivisional, or of the so-called
M-form (Chandler 1962, Williamson 1975). Yet quite
commonly we observe more complex structures, most
prominently matrix or network organizational forms
(Davis and Lawrence 1977, Ford and Randolph 1992,
Galbraith 2009, Burton et al. 2011). A fundamental
property of these more complex organizational forms
is the presence of multiauthority relations, or, put more
simply, many managers often face the situation of hav-
ing multiple bosses (Davis and Lawrence 1977). These
more complex forms address coordination challenges
that do not lend themselves to the more segmented
authority structures of a simple hierarchy. Prior work
suggests that such structures are particularly common
in project-based organizations (Ford and Randolph
1992, Sydow et al. 2004, Morris et al. 2011) and large
transnational companies (Bartlett and Ghoshal 1989,
Galbraith 2009, Guadalupe et al. 2013). The presence
of multiauthority relationships, in turn, poses poten-
tial challenges for managers, who may face the difficult
position of deciding which authority figure to follow
when their guidance and recommendations conflict.
While recognizing the potential for such challenges,
we also wish to understand the power and logic of
multiauthority relationships. Despite the ubiquity and
potential benefits of those forms in coordinating inter-
dependent tasks, our understanding of the mecha-
nisms that determine the performance of these struc-
tures is still relatively modest. In particular, scholars
have noted conflicting empirical findings regarding the
efficacy of these forms and have called for a more rigor-
ous approach to the study of these structures (Ford and
Randolph 1992, Greenwood and Miller 2010, Bolton
and Dewatripont 2013).
We examine the efficacy of the multiauthority
form in task environments characterized by different
degrees of decomposability. In particular, we seek to
examine the effects that the multiauthority form has on
the dual challenges of coordination and specialization
that are central to the process of organizational adap-
tation. The challenge of coordination privileges the
role of high-order authorities in specifying the general
strategic orientation that acts to guide and constrain
the search behavior of lower-level actors. By contrast,
the complexity of lower-level subsystems argues for
greater degrees of local autonomy.
To examine the tensions among these various forces,
we develop an agent-based computational model that
examines the performance of three canonical types of
organizational forms: a traditional hierarchy in which
a subordinate reports to a single boss, a multiauthority
structure in which the subordinate reports to multiple
bosses, and an autonomous form in which the subor-
dinate does not have a direct reporting relationship.
We consider these alternative forms in environments
characterized by different degrees of complexity and
near decomposability. First, we identify the properties
of the task environment, in particular the complexity
of the higher-order problem that superiors face, the
complexity of the problem environment of their sub-
ordinates, and the relative importance of the higher-
level strategy problem to the lower-level operational
challenges of the subordinates. We then examine the
robustness of these results to consider some of the pos-
sible pathologies of the multiauthority form, such as
the possible stalemate that might result from having
multiple bosses, the impact of changes in higher-level
policy on lower-level managers’ motivation, possible
biases in the saliency of higher-level strategic problems
in the minds of upper management relative to the more
operational changes of lower-level managers, and the
impact of alternative organizational forms on the speed
of adaptation.
2. Nearly Decomposable Systems and
Organizational Forms
2.1. Specialization, Integration, and the
Organizational Challenge
The promise and challenge of organizations is the dual
imperative to reap the benefits of specialization of la-
bor and knowledge while at the same facilitating the
coordination of interdependent actions (Smith 1776,
Durkheim 1933, Puranam et al. 2012). Organizations
divide labor to allow their members to focus on smaller
partitions of their task environment and, in the process,
capture gains from specialization, which allows organi-
zational members to better meet the demands of their
local task environments (March and Simon 1958, Cyert
and March 1963, Dessein and Santos 2006). The divi-
sion of labor results in an architecture of tasks in orga-
nizations that takes on a nested hierarchical structure
in which the overall task environment is partitioned
into multiple subunits, and those subunits, in turn, are
divided into even smaller sub-subunits (Simon 1962).
However, as the tasks and related knowledge become
increasingly diversified and distributed, an organiza-
tion faces an increasing pressure to integrate the collec-
tive efforts of its members (Chandler 1962, Thompson
1967). This integration is necessary because of the
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Levinthal and Workiewicz: Nearly Decomposable Systems and Organizational Adaptation
Organization Science, Articles in Advance, pp. 1–18, © 2018 INFORMS 3
existence of spillovers between the activities of the sub-
units. The management literature has, for a long time,
recognized that while firms should strive to respond to
the demands of their local environments, they should
also maintain a close internal fit between the activities
of their members (Miller and Friesen 1984, Porter 1996,
Ghemawat 2007). The emergence of professional man-
agement roles in the 19th century was directly driven by
the need to achieve such an internal fit (Chandler 1962).
Acting as coordinators, managers assume responsibil-
ity for ensuring that the units under their control stay in
alignment with each other and fit the broader policies
of the corporation (Simon 1947, Mintzberg 1979, Noda
and Bower 1996). The challenge of organization design
can thus be represented as identifying a hierarchical
structure that balances the gains from specialization
within units with the gains from integrating and direct-
ing their efforts to some common purpose (Thompson
1967, Siggelkow and Levinthal 2003). The general rec-
ommendation stemming from this line of work is that
organizations that benefit primarily from a close align-
ment among subunits should pursue centralization of
decision making, while those organizations benefiting
primarily from local adaptation should decentralize
and leave the decision-making authority to the subunits
themselves (Fayol 1949, Goold and Campbell 2002).
Integrating many distributed and interdependent
subunits, each of them internally complex, would
surely overwhelm any boundedly rational manager,
who would have to consider every possible interac-
tion among the detailed decisions made by each of
the subordinates (Simon 1955). Fortunately, the inte-
gration problems managers face are made easier by the
fact that the systems of activities in organizations tend
to be nearly decomposable (Simon 1962, Rivkin and
Siggelkow 2003). While the task environments faced by
organizations are systems with complex interactions,
they can be divided into smaller subunits in such a
way that the intensity of interactions between the sub-
units is smaller than within those subunits (Goold and
Campbell 2002)—a key property of nearly decompos-
able systems (Simon 1962,2000). This perspective is
summarized by Simon (2000, p. 9) as follows:
Even more important, [near decomposability] allows us
to factor the system, so that we do not have to deal
with all of its complexity at once. Having determined
the behavior of subunits at one level, we can replace the
details of these subunits by a small number of aggregate
parameters, and use these to represent the system at
the next level above. Or, looking from the top down, we
can say that the behavior of the units at any given level
does not depend on the detail of structure at the next
level below, but only upon the steady state behavior, in
which the detail can be replaced by a few aggregated
parameters.
Studies of organizations confirm that near decompos-
ability is a prominent feature of organizational task
environments (Galbraith 1977, Goold and Campbell
1987, Baldwin and Clark 2000). Facing a nearly decom-
posable system, a manager only needs to understand
and tend to the aggregate interactions among the sub-
units. This greatly reduces the complexity of the inte-
gration challenge, allowing for a much easier com-
prehension of and coordination between the parts
of the system (Baldwin and Clark 2000, Ethiraj and
Levinthal 2004a).
What is equally important from the perspective of
organization design, near decomposability also allows
superiors to specify policy directives to guide and con-
strain the actions of their subordinates and to ensure
those actions fit the broader firm strategy through the
ability to replace the details of lower-level decisions
by an aggregate representation. Simon (1947), in dis-
cussing the mechanisms of coordination of special-
ized tasks in organizations, introduces the notion of
a decision premise to capture the nature of authority
in hierarchies. Superiors may set the broad parame-
ters under which their subordinates must operate, but
within those bounds, the subordinates are free to act
with discretion:
Influence, then, is exercised through control over the
premises of decision. It is required that the decisions
of the subordinate shall be consistent with premises
selected for him by his superior. ...Most often, influence
places only partial limits upon the exercise of discretion.
A subordinate may be told what to do, but given consid-
erable leeway as to how he will carry out the task.
(Simon 1947, p. 223, italics in original)
For instance, the top management of the organization
may specify the basic architecture of a business model
with regard to the fundamental way the firm wishes
to compete and what that implies for its overall prod-
uct development strategy, marketing effort, manufac-
turing strategy, and so on. Individuals responsible for
these areas need to develop more specific policies that
address their particular functional problem in a man-
ner consonant with this broader articulated strategy
(Rumelt 1974, Porter 1996).
The near decomposability of organizational task en-
vironments thus suggests that managerial decisions
will have different levels of abstraction, depending on
the level of hierarchy. Consistent with this perspective,
Mintzberg (1979) notes,
Managerial jobs do, however, shift in orientation as they
descend in the chain of authority. There is clear evidence
that the job becomes more detailed and elaborated, less
abstract and aggregated, more focused on the work flow
itself. (p. 29)
In a similar spirit, Martin (1956) examines the deci-
sion process at four levels of management and observes
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Levinthal and Workiewicz: Nearly Decomposable Systems and Organizational Adaptation
4Organization Science, Articles in Advance, pp. 1–18, © 2018 INFORMS
that, when moving upward in the hierarchy, the deci-
sions tend to be more abstract, general, and ambigu-
ous, while the planning horizon becomes longer and
the frequency of decisions lower.
Thus, given the nearly decomposable nature of orga-
nizational task systems, balancing specialization and
integration requires identifying the degree to which
the superiors’ needs for overall alignment should con-
strain the actions of their subordinates so as to facilitate
this overall fit while at the same time recognizing that
such constraints may inhibit these lower-level actors
achieving closer fit to their local environments.
2.2. The Role of Organization Design
While centralization and decentralization of decision
making can be achieved within a traditional hierar-
chy by placing authority at an appropriate level of
the organization, the complexity of some task envi-
ronments may require more complex organizational
forms, such as the matrix and the project-based orga-
nization (Davis and Lawrence 1977, Galbraith 1977,
Ford and Randolph 1992). These complex organiza-
tional structures introduce additional reporting lines
between the subordinates and their superiors to allow
for coordination among multiple dimensions, balanc-
ing the need for simultaneous specialization and inte-
gration, and achieving more robust information flows
(Knight 1976, Galbraith 2009, Burton et al. 2011). The
core feature of those more complex structures is the
fact that subordinates must report to multiple bosses.
We call those types of hierarchies, collectively, the mul-
tiauthority form to highlight the departure from the
traditional single lines of authority found in the func-
tional and the M-form.
Despite the promises of solving the integration ver-
sus specialization dilemma and being better suited to
deal with complex task environments, the support for
the efficacy of the multiauthority form has been mixed
(Larson and Gobeli 1987, Galbraith 2009). Conflicting
demands caused by having multiple superiors are one
of the key challenges associated with the multiauthority
form. Managers representing different organizational
dimensions, such as product or geographic domains,
compete for resources, authority, power, and influence
(Mintzberg 1979, Burton et al. 2011). Having multiple
bosses has been blamed for exacerbating the problem
of incompatible goals and objectives, with the situation
made more problematic by the presence of role conflict
and role ambiguity (Larson and Gobeli 1987).
The well-documented failures of the multiauthority
form and the mixed empirical evidence as to the ben-
efits of those structures have cast doubt on the form’s
effectiveness. Many researchers and practitioners have
concluded that those types of hierarchies should be
abandoned in favor of traditional and simpler ones
(Hamel and Prahalad 1996, Christensen 1997). But,
despite the widely professed disappointment with
the multiauthority form and the excessive bureau-
cracy it often tends to entail, recent empirical evidence
suggests that multiauthority forms are in fact quite
common among a broad spectrum of organizations
(Galbraith 2009, Morris et al. 2011, Guadalupe et al.
2013). The empirical prominence and our still incom-
plete conceptual understanding of the forces and ten-
sions present in these organizational forms suggests
the value of further, analytical consideration of the
multiauthority form and how it addresses the trade-off
between specialization and integration.
2.3. Modeling Organization Design and
Near Decomposability
Formal modeling has been shown to be a useful tool
in investigating the effects of organizational structures
on organizational adaptation in complex task envi-
ronments (e.g., Rivkin and Siggelkow 2003; Siggelkow
and Levinthal 2003; Siggelkow and Rivkin 2005,2006;
Ethiraj et al. 2008; Mihm et al. 2010). These studies
build on the premise that organizational members are
boundedly rational and thus engage in local experi-
mentation to improve their performance (March and
Simon 1958). We depart, however, from those studies in
three important ways: (1) the conceptualization of the
organizational task environment, (2) the role of supe-
riors, and (3) the effects of conflict in the presence of
multiple lines of authority.
First, while many of the studies employing an NK
model structure have considered the patterns of inter-
actions between organizational tasks (Siggelkow and
Levinthal 2003; Ethiraj and Levinthal 2004a,b; Rivkin
and Siggelkow 2007; Ethiraj et al. 2008; Aggarwal et al.
2011), the difference between modularity and near
decomposability has not been fully addressed (Augier
and Sarasvathy 2004). Scholars have used the term mod-
ularity to describe patterns of interactions between indi-
vidual elements of a system in which most of the inter-
actions occur within the modules (within interactions),
with only relatively few interactions between elements
lying in different modules (between interactions). The
discussion of NK models often uses the terms “mod-
ularity” and “near decomposability” interchangeably
(e.g., Rivkin and Siggelkow 2007, Ethiraj et al. 2008).
However, these NK models, with block-diagonal inter-
actions, capture only a subset of the characteristics of
a nearly decomposable system and, in particular, do
not capture the idea of the encapsulation of subsystems
into higher-order elements and the aggregate nature of
interactions among these higher-order elements.
As proposed by Simon (1962), complex systems con-
sist of stable and nearly independent subsystems, in
which the interactions are governed by net inputs
and outputs of the other subsystems. Nearly decom-
posable systems are thus hierarchical in nature, with
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Levinthal and Workiewicz: Nearly Decomposable Systems and Organizational Adaptation
Organization Science, Articles in Advance, pp. 1–18, © 2018 INFORMS 5
Figure 1. Comparison of a Nearly Modular and Nearly Decomposable System
A. Near modularity
(only detailed interactions)
B. Near decomposability
(detailed and aggregate interactions)
Detailed, lower-level
interaction
Aggregate, higher-level
interaction
the interactions between subunits occurring on an
aggregate (higher) level (Simon 1962, p. 193). In such
systems, the interactions between modules not only are
fewer, but also happen at different timescales (Simon
2000). By contrast, in the standard NK structure, the
pattern of interactions, commonly called an interaction
matrix, is specified for a single vector of decision vari-
ables. This structure is quite appropriate to address
issues of modularity (Ethiraj and Levinthal 2004a), but
it does not lend itself to a consideration of organiza-
tions as hierarchical systems.
Figure 1provides a representation of the two ap-
proaches to modeling complex systems. Panel A in the
figure represents a traditional NK nearly modular sys-
tem, in which interactions occur on a single level; that
is, the same types of interactions happen between the
modules as within the modules. The only difference
is the relative number of interactions with variables
from within and outside a given module. In a nearly
decomposable system, on the other hand, the interac-
tions between the subsystems (dotted arrows) occur on
the level of aggregate representations of the subsys-
tems, not between the individual variables from differ-
ent subsystems.
Arguably both the standard NK treatment and
Simon’s (1962) conceptualization of nearly decompos-
able systems are extreme or limit cases. The for-
mer negates the possibility of interactions at a more
aggregate scale among subsystems, while the latter,
although incorporating interactions among detailed,
lower-level decisions within subsystems, negates the
presence of these detailed lower-level decisions across
subsystems. One could certainly consider a more gen-
eral structure that allowed for both sorts of interac-
tions. However, as Simon (1962) argues, these detailed
interactions between subsystems are highly disruptive
from the evolutionary point of view, and, over time,
systems (e.g., organizations) will evolve to eliminate
or encapsulate such interactions inside subsystems,
leaving only higher-level interactions that can be man-
aged more easily (Simon 1962). In sum, our aim is not
to replace the near modular (NK) view of complex sys-
tems but to complement it with a model that captures
additional characteristics of complex systems and, in
particular, organizations—properties that prior model-
ing approaches, building directly on the NK structure,
have omitted.
An additional consideration is that prior analyti-
cal treatments have investigated the role of superiors
in affecting organizational adaptation efforts through
either ex post evaluation of subordinates’ choices
(Rivkin and Siggelkow 2003; Siggelkow and Rivkin
2005,2006; Aggarwal et al. 2011) or choosing an advan-
tageous starting position for subordinates’ search based
on a prior cognitive model (Gavetti and Levinthal 2000,
Gavetti 2005). In our context, we consider a setting in
which the superiors are tasked with a parallel search
for a beneficial combination of higher-order policy deci-
sions. These policy decisions represent a task of find-
ing a superior strategy and setting the overall frame-
work for subordinates’ choices (Chandler 1962, Rumelt
1974, Porter 1996). Superiors thus guide and constrain
their subordinates via ex ante policy directives, as these
lower-level agents themselves search for new strategies
in their respective domains. In reflecting on the limi-
tations of their own approach, Siggelkow and Rivkin
(2006, p. 793) note that introducing such a parallel, mul-
tilevel search would be an important contribution.
Furthermore, prior work has focused on models
with unambiguous lines of authority, where every
subordinate reports to only one superior, following
the principle of unity of command (Fayol 1949). The
problem of multiple superiors has attracted little atten-
tion in the literature on organizational adaptation.
The challenge of multiauthority relationships emerges
when these lower managers face a dual reporting
relationship—say, in the case of a product manager in a
global enterprise who is under the dual authority of a
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Levinthal and Workiewicz: Nearly Decomposable Systems and Organizational Adaptation
6Organization Science, Articles in Advance, pp. 1–18, © 2018 INFORMS
country manager and a global product executive. Hav-
ing multiple bosses often leads to situations in which
a subordinate must satisfy multiple conflicting direc-
tives. Our key observation here is that reporting lines
are not simply channels that relay information across
the organization; they also direct and constrain the
actions of subordinates, often resulting in subordinates
receiving conflicting directives.
We argue that the concept of near decomposabil-
ity is central to our understanding of the benefits of
different organizational forms. An effective organiza-
tion design identifies the sets of highly interdependent
tasks and incorporates them into self-contained sub-
units to foster local adaptation, and, in addition, sets a
coordination structure to integrate the subunits’ joint
efforts (Goold and Campbell 1987, Burton et al. 2011).
The problem for an organization designer who is fac-
ing a nearly decomposable problem can be essentially
represented as identifying a hierarchical structure that
balances the benefits of specialization within the units
with integrating their effort at a higher level.
In our analysis, we examine three canonical organi-
zational forms, each representing a different type of
authority relationships. We divide this set of possi-
ble organizational forms into three groups based on
the number of subordinate–superior reporting rela-
tionships: (a) the single-authority form with only one
reporting relationship, (b) the multiauthority form with
two reporting relationships, and (c) the autonomous
form with no reporting relationships. We compare the
performance of these forms in environments character-
ized by different degrees of importance and difficulty of
specialization and integration problems.
3. Model
3.1. Organizational Task Environment
As argued above, the near decomposability of the
organizational task environment is an important con-
sideration in weighing the dual challenges of the
specialization and integration of organizational tasks.
Furthermore, the task environment can be character-
ized by the relative importance of achieving high lev-
els of specialization (i.e., the adaptation of subsystem
to its local context) and integration (i.e., the linkage
among the subsystems) and the complexity of both
challenges. These properties guide our modeling of the
task environment.
Consider a task environment consisting of a set of
binary detailed decisions (DDs), where each decision
can assume one of two possible values (e.g., 0 and 1).
These decisions are grouped into Npsubunits, each
consisting of Np,ddetailed decisions represented by
a vector fp,d{dp,1,... ,dp,Nd}. Each subunit has a
manager who is responsible for the DDs of that sub-
unit. Consistent with Simon’s (1962) characterization of
nearly decomposable systems, the DDs in each subunit
are assumed to jointly determine an aggregate behav-
ior, which we term a policy decision (PD). As in Gavetti
(2005), we use a simple majority rule to map the set
of lower-level DDs to a binary categorization at the
aggregate level. Specifically, a corresponding PD takes
on the value 0 if the lower-level DDs are mostly 0 (i.e.,
{0,0,0},{0,0,1},{0,1,0},{1,0,0}) or the value 1 other-
wise. Figure 2provides an illustration of the mapping
between the two levels in this hierarchical system. In
our baseline analysis, we set NPto 4 and Np,dto3for
all PDs.1
Consider a car manufacturer developing a new vehi-
cle. The company’s executives are facing several broad
policy decisions, such as what type of a vehicle to
develop (sport utility vehicle (SUV) or sports car),
which customer segment to target (families or young
males), which price category (luxury or budget), and
how to advertise it (TV or Internet). Each of those pol-
icy decisions can be further disaggregated into multi-
ple, more detailed decisions. For example, a manager
in the design department must decide on the type of
suspension (high, low), type of tires to use (low pro-
file, high profile), and shape of the body (tall, low).
Some of those characteristics are SUV-like (high sus-
pension, high-profile tires, and tall body shape) while
some are sports car–like (low suspension, low-profile
tires, low-body shape). Following the majority rule,
whenever the proposed vehicle has most of the charac-
teristics belonging to one of the two vehicle types, it is
said to represent that type.
To represent the degree of complexity of the spe-
cialization problem in our task environment, we allow
for the DDs to be interdependent—that is, a change
in a single decision variable may affect the value of
a number of other decision variables within the same
subunit (at the single level of a system). To represent
the interdependencies between the decision variables
within the same subunit, we adopt the structure of the
NK model (Kauffman 1993, Levinthal 1997, Lenox et al.
2006). While the standard NK structure is used in the
model to represent the interactions at a given level of
the system, we build on this standard treatment and
incorporate a vertical structure whereby lower-level
choices are aggregated to higher-level polices, which
themselves interact to form a fitness surface at this
higher level.
The variable Kp,d∈(0,Np,d1)determines the num-
ber of other decision variables within the same subunit
that interact with the focal decision. When Kp,d0,
there are no interdependencies between any pair of
decisions dp,iand dp,j(where ij), and a superior fit
with the unit’s local environment (specialization) can
be easily achieved with local experimentation. When
Kp,d>0, the unit’s specialization challenge is said to be
complex, as each decision variable dp,iimpacts the effi-
cacy of Kp,dother variables. To highlight the contrast
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Levinthal and Workiewicz: Nearly Decomposable Systems and Organizational Adaptation
Organization Science, Articles in Advance, pp. 1–18, © 2018 INFORMS 7
Figure 2. The Representation of a Hierarchical Complex System
101
1
Aggregation
Aggregation
Aggregation
Aggregation
010
001 111 010
Superiors’ level
(PD)
Unit managers’ level
(DD)
Vector of policy directives
Unit 1
d1, 1 d1, 2 d1, 3 d2, 1 d2, 2 d2, 3 d3, 1 d3, 2 d3, 3 d4, 1 d4, 2 d4, 3
Unit 2 Unit 3 Unit 4
p1p2p3p4
between complexity at different levels of the organiza-
tion (across higher-level policy decisions and among
detailed decisions), we keep Kp,dthe same for all sub-
units but introduce a distinct parameter Kpto charac-
terize the level of interdependence between subunits.
The degree of fit of a subsystem with its local envi-
ronment V(fp,d)is a simple average of the contribu-
tions of each decision variable within that unit, where
the contribution of each decision variable is deter-
mined by taking into account the focal decision and the
Kp,ddecisions that interact with it,
V(fp,d)1
Np,d
Np,d
i1
V(dp,i,dp,i),where ii,(1)
where dp,iare the Kp,dother decision variables inter-
dependent with the focal decision variable. For each of
these possible combinations of V(dp,i,dp,i),wedrawa
value from a uniform distribution between 0 and 1.
We represent the problem of integration of the
actions of the subunits in a similar fashion. We start
with a vector of policy decisions fp{p1,...,pNp},
where each of the Npelements is an aggregate repre-
sentation of the corresponding subunit. The parame-
ter Kpdetermines the number of interactions between
each policy decision and thus tunes the difficulty of the
integration challenge. The fitness of the overall policy
vector is calculated as an average of the contributions
of each policy directive:
V(fp)1
Np
Np
i1
V(pi,pi),where ii.(2)
Thus Kp,dand Kpdetermine the complexity of the
specialization and integration challenges. To determine
the relative importance of the two problems, we intro-
duce the parameter α. This parameter tunes the relative
importance of the specialization and integration prob-
lems. The performance of the entire organization, π,is
thus a weighted average of the higher-level (fp)and the
lower-level (fp,d)contributions:
πα1
Np
Np
p1
V(fp,d)+(1α)V(fp),(3)
where fp,dand fpare the combinations of the lower-
and higher-level decisions, respectively. We wish to
separate the difficulty of solving the specialization and
integration efforts (Kpand Kp,d) from their relative
importance (α), as these are distinct characteristics of
an organizational task environment. Thus, while a sub-
unit may find it difficult to achieve a high degree of
alignment with its problem environment, finding a
more or less ideal solution to the specialization prob-
lem may not be that important from the point of view
of the organization.
The degree of near decomposability is therefore
jointly determined by the Kpand αparameters. When
Kpis greater than 0, there are interactions between
the policy decisions at the higher level, and thus
the higher-order problem is not fully decomposable.
However, a separate issue is the extent to which the
specification of the lower-level problem contributes
to overall organizational performance. The parame-
ter αallows us to tune the degree to which the
higher- and lower-level interactions can be ignored. As
αapproaches 1, the higher-level interactions can be
increasingly ignored, as they only slightly contribute to
the overall fitness of the system. As αapproaches 0, the
aggregate interactions become increasingly important,
and lower-level contributions cease to matter. Interme-
diate values of αcreate a task environment where nei-
ther level can be ignored and where the specialization
and integration problems are both important. Thus, α
speaks to the degree of decomposability in a “vertical”
sense, whereas the values of Kpand Kp,dinfluence the
degree of “horizontal” decomposability in that they
determine the degree of interdependence within each
level of the task environment.
Thus, both the higher-order problem and the indi-
vidual unit subproblems can be more or less com-
plex, meaning involving more or less interdependen-
cies among the choice variables associated with each
problem. However, a separate issue is the importance
of the two problems. For instance, there may be set-
tings where operational excellence within each sub-
problem is critical and the overall strategy problem is
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Levinthal and Workiewicz: Nearly Decomposable Systems and Organizational Adaptation
8Organization Science, Articles in Advance, pp. 1–18, © 2018 INFORMS
not that important. Consider, for instance, the corpo-
rate strategy problem for a conglomerate firm relative
to the importance of the business unit strategy problem
of the underlying operating units. Conversely, we can
have the reverse situation. For instance, for a closely
linked diversified firm, the higher-order strategy prob-
lem across business units has considerable importance.
Whether this higher-order strategy is a critical driver
of overall firm performance, as indicated by α,isa
separate issue of the complexity (Kvalue) of the high-
order or local problems. We do not make a claim about
the general empirical relationship between the diffi-
culty and importance of the lower-level and higher-
level problems. There may indeed be some correla-
tion between the difficulty and importance of a given
problem, but they are appropriately viewed as distinct
constructs.
3.2. Organizational Forms
We specify the formal organizational structure as con-
sisting of a hierarchy of decision makers and the deci-
sion rights assigned to them. We consider three canon-
ical types of organizational forms consisting of two
hierarchical levels. At the lower level, all three forms
are characterized in the same manner and consist of
four subunits, each having one manager assigned to it.
The managers’ objective is to find the superior com-
bination of DDs (the task of the specialized subunits).
The three forms differ, however, in their configuration
of the upper organizational level and thus the way
they pursue the integration challenge. First, consider a
single-authority hierarchy (SA) with only one superior
responsible for coordinating all PDs. This form adheres
to the unity of command principle (Fayol 1949). The
second form is an autonomous (AU) organization, and
it represents an extreme form of decentralization in
which direct integration mechanisms are absent. It rep-
resents an organization where superiors do not inter-
fere in the activities of their subordinates or where
there are no superiors, as in the case of many boss-
less organizations (Puranam and Håkonsson 2015).
By giving full autonomy to the units, the superior
expects them to pursue strategies that would other-
wise have been constrained by wider corporate influ-
ences (Bowman and Kogut 1995, Goold and Campbell
2002). The third organizational form is the multiau-
thority form (MA). This form has four superiors, each
one in charge of two of the subunits and where each of
the four subunits’ managers reports to two superiors
(see Figure 3). Each of the superiors is responsible for
a unique pair of subunits. (None of the four superiors
has the same pair of subunits under their control.) This
represents a simple matrix organization, with each pair
of superiors representing one of the dimensions of
coordination, such as geography, product, service, etc.
While managers care only about the performance of
their own subunits, superiors’ job is to integrate the
actions of the subunits reporting to them, and thus they
need to take into account the performance of the sub-
units themselves and the corresponding PDs. Specifi-
cally, a superior evaluates performance as a α-weighted
combination of the fitness levels of the subunits report-
ing to them and the PDs that characterize the behavior
of the subordinates under their authority.
Superiors have the authority to direct the actions of
the managers reporting to them. Because combinations
of DDs determine the PD vector (ultimately, it is the
actions of the subordinates that determine whether an
intended policy has been implemented), the superi-
ors can affect the PDs only indirectly by issuing pol-
icy directives. By setting a policy directive, superiors
can command their subordinates to search only among
the DDs conforming to the desired PD.2Keeping with
the auto industry example, when a superior orders the
engineering department to design a new SUV and that
policy directive is binding, the manager in charge of the
engineering department will search only among the
combinations of DDs that are mostly SUV-like. Policy
directives therefore not only guide but also constrain
the managerial search. In that sense, a policy directive
is analogous to Simon’s (1947) decision premise, as it
directs subordinates’ search but leaves some degree of
discretion as to how to satisfy the superior’s demands.
This indirect influence of authority allows superiors to
search for a better combination of the PDs and thus
achieve integration among the subunits.
While searching, the subunit’s manager in our model
must always conform to at least one policy directive.
If a manager reports to two superiors who issued
inconsistent policy directives, the manager can pursue
any combination of DDs—in effect, the constraints are
removed. This represents a relatively lenient approach
to conflict resolution and reflects the dilution of author-
ity when the unity of command is violated (Chi and
Nystrom 1998). The existing literature offers several
reasons for an increase in a subordinate’s autonomy in
the presence of multiple superiors. Some authors sug-
gest that a manager may skillfully negotiate between
multiple sources of power to gain more flexibility
(Davis and Lawrence 1977). Within the agency litera-
ture, it has been argued that an agent can benefit from
competition among multiple principals (Bernheim and
Whinston 1986, Dixit 1998). The superiors might also
be more lenient toward their subordinates, recognizing
the difficulty of obeying multiple sources of authority
(Davis and Lawrence 1977). Baier et al. (1986) further
observe that one common practice in resolving conflict-
ing goals in organizations is to increase the ambiguity
of policy decisions, thus making them more suscepti-
ble to flexible interpretation. Reviewing the empirical
literature on multiauthority organizations, Ford and
Randolph (1992) find evidence for an increase in subor-
dinates’ autonomy in the presence of multiple bosses.
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Figure 3. The Three Canonical Organizational Forms
Superior
Single authority
(SA)
Multiauthority
(MA)
Autonomous
(AU)
Manager
unit 1
Manager
unit 2
Manager
unit 4
Manager
unit 3
Superior
1
Superior
3
Superior
4
Superior
2
Manager
unit 1
Manager
unit 3
Manager
unit 2
Manager
unit 4
Manager
unit 1
Manager
unit 3
Manager
unit 2
Manager
unit 4
In our initial modeling, we incorporate this argument
that multiauthority relationships increase a subordi-
nate’s autonomy. We later relax this assumption and
investigate the opposite case, in which in the presence
of inconsistent policy directives a manager freezes up,
waiting until his superiors resolve conflicting policies
among themselves.
We thus have two types of lower-level (managerial)
search: “constrained” and “unconstrained.” When a
manager reports to a single superior or when the two
superiors are in agreement, their authority is bind-
ing, and the subunit’s manager can only search among
those combinations of DDs that are consistent with the
issued policy directive. When there are no superiors or
the superiors disagree, a manager can search among
all possible combinations of lower-level decisions.
3.3. Organizational Search
The basic sequence of the simulation starts with a
choice of policy directive by superior(s) and then a
subsequent search on the part of the managers. In
particular, each round of the simulation begins with
a selection, at random, of a particular superior who
then chooses at random a one-bit flip in one of the
policy directives under her control. This step repre-
sents superiors’ local search in the single- and mul-
tiauthority forms. Next, the manager of the selected
unit proceeds to search locally within his task domain
for a superior combination of DDs that correspond to
the policy directive issued by his superior(s), if that
directive is binding. The manager is bound by a policy
directive either when there is a single “boss” or, in the
case of the multiauthority form, when both superiors
agree and issue the same policy directive. If the policy
directives contradict each other or, when the manager
has no superiors, he proceeds to search without any
constraint.
The manager then chooses one of the DDs at random
and changes its value. If the manager is bounded by a
policy directive, the new choice must conform to it. He
then compares the fitness level of the new combination
with that of the previous one. If the new fitness level
is higher than the prior value, the new combination is
accepted; conversely, if the new fitness level is lower
than the prior one, then the status quo is maintained.
The manager repeats this process until no better com-
bination can be found, either because the combination
is a local peak or, in the case of constrained search, the
other, potentially better combinations are not consis-
tent with the policy directive. The new combination of
DDs is then reported to the superior who issued the
policy directive.3
This process captures the idea of different frequen-
cies of search between the levels of a nearly decompos-
able system (Simon 1962). For each step in the supe-
rior’s search, the manager takes several steps to search
locally for the best combination of DDs. The superior
waits for the manager to finish this search and to sub-
mit a proposal and uses the steady state of the lower-
level activity to determine the payoff associated with
the proposed PDs.
To initialize the simulation, a set of policy directives
are selected at random. Similarly, the manager starts
with a generation of a random initial combination of
DDs, which in the case of the constrained search are set
at random subject to the constraint that the resulting
set of decisions must be consistent with this initial pol-
icy directive. The resulting combinations of DDs and
corresponding PD vector constitute the starting point
for the subsequent search process.
Furthermore, we assume that managers are effi-
cient in their search. By “efficient,” we assume that
when a manager receives a given policy directive for
the first time, he proceeds to search locally for the
best combination of DDs consistent with this directive.
When the solution is identified, it is recorded along
with its fitness value. The next time that the manager
observes the same policy directive, instead of repeating
the search process from scratch, the previously found
combination of DDs is retrieved and submitted to the
superior.
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Levinthal and Workiewicz: Nearly Decomposable Systems and Organizational Adaptation
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We introduce memory in this sense in our model for
two reasons. First, in this hierarchical structure, mem-
ory gives the model the behavioral realism of lower-
level actors not wanting to “reinvent the wheel.” In
addition, in the absence of memory, or the reliable
reenactment of a set of lower-level choices in response
to a higher-order policy, adaptation at the higher level
becomes problematic, as such adaptation requires rel-
atively reliable lower-level building blocks to succeed
(Simon 1962). By contrast, in a standard NK model,
the presence or absence of memory simply impacts the
computation algorithm—that is, whether the program
stops evaluating local neighbors after all local combi-
nations have beenconfirmed to be inferior—but not the
resulting behavior.
In the case of the SA and MA forms, after receiving
the proposal from the manager, the superior observes
the α-weighted average of the PD and DD fitness lev-
els for which she is responsible. If the new fitness is
superior to the previous one, the new policy direc-
tive is accepted. Otherwise, the status quo is preserved
with the superior reversing the policy directive, and
the manager is required to return to the previous com-
bination of DDs. The simulation then proceeds to the
next round. We allow the organizations to search for a
solution to each of the projects until a steady state is
reached (no further improvements are made).4
For each type of task environment and for each orga-
nizational form that we consider, we simulate 100 orga-
nizations facing 100 structurally similar (i.e., based on
the same parameter values) task environments and
report the average performance values across these
runs for each type of organizational form in a given
structural setting or task environment. The set of 100
independent organizations of each type addresses any
possible idiosyncrasies associated with the initial seed-
ing of decision and policy values, while the set of 100
independent task environments addresses any effect of
a specification realization of a given task setting. The
reported fitness values are normalized by setting the
value of the best combinations of DDs and PDs to 1
and the worst combinations to 0. A detailed outline of
the organizational search algorithm can be found in
the online appendix (A1).
4. Results
We examine the conditions under which complex orga-
nizational forms with multiple lines of authority can
outperform alternative, more traditional forms in envi-
ronments characterized by near decomposability. We
begin by setting up three canonical organizational
forms: the single-authority, autonomous, and multiau-
thority forms. Next we turn to formulating a repre-
sentation of a nearly decomposable environment. Per
the discussion in Section 2.3, we need to specify three
parameters: (1) the level of interdependencies between
the policy decisions (Kp), (2) the level of interdepen-
dencies between the detailed decisions within the four
subunits (Kp,d), and (3) the parameter α, which spec-
ifies the importance of the detailed subproblems rel-
ative to the aggregate policy problem. For the two
levels of the task environment, we set both the inte-
gration and specialization challenges to be difficult
(Kp,d2,Kp3); that is, each of the superiors and man-
agers face multiple interdependent decision variables,
a setting that presents a complex task environment for
both the higher- and lower-order problems. We present
the results for alternative combination of variables in
the online appendix (A2).
Next, we consider values of αfrom 0 to 1 to cap-
ture task environments that put different weights on
the specialization and integration challenges. With
αapproaching 0, integration becomes increasingly
important, and as αapproaches 1, the overall fit-
ness depends primarily on attending to the special-
ization challenge and the policy-level interactions can
be increasingly ignored. Figure 4presents the main
results of the simulation.5The results show that there
exists a range of αwhere the MA form outperforms the
other two organizational forms. In short, the MA form
is superior when the specialization challenge becomes
more important (high α), while the SA form proves to
be the best choice whenever integration is key (low α).
What explains the superior performance of the MA
form in task environments where the specialization
Figure 4. The Performance of the Three Organizational
Forms for Different αLevels When the Integration and
Specialization Problems Are Difficult (Kp3,Kp,d2)
0.5
0.6
0.7
0.8
0.9
1.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Fitness (normalized)
Single authority
Multiauthority
Autonomous
Integration Specialization
AB
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challenge is difficult and important (α1)? The
answer lies in the way that the MA form addresses
solving the specialization challenge. Consider the local
task environment of a subunit manager. Because of
interdependencies between the DDs, the task environ-
ment resembles a rugged landscape with many seem-
ingly attractive but suboptimal solutions (Levinthal
1997). The unconstrained search is more efficient in
such an environment, as the managers are not con-
strained by the superiors’ policy directives. The policy
directives, when binding, introduce additional points
on the search landscape at which an agent may get
stuck in his pursuit of a better solution. A manager
who finds himself in such a spot may be aware of other
superior locations in his local neighborhood, but mov-
ing to them would mean violating the policy direc-
tive of the superior. In other words, a manager may
get stuck because his superior, while searching for a
solution to her global problem, directs and thus con-
strains the search of her subordinate. The superior
may not necessarily want the best possible solution
to the lower-level problem but instead may prefer an
inferior lower-level solution, because it fits better with
her higher-level strategy.
The MA form benefits from unconstrained search,
freeing the unit managers from the constraints of
authority whenever the superiors issue inconsistent
policy directives. By contrast, in the SA form, man-
agers are always searching under the constraint of a
single boss and therefore frequently become stuck on
authority boundaries—locations that are not locally
optimal but where further improvements would neces-
sitate disobeying their superior. Specifically, for a sin-
gle local search attempt, a constrained manager has
only a 35.5% chance of finding the global peak, com-
pared with a 60.5% chance for an unconstrained man-
ager. A constrained manager is stopped in his improve-
ment efforts by a policy directive 34.4% of the time,
and the length of his local search is shorter by 39%
compared with that of an unconstrained manager.
Considering the above discussion, one may ask why
the AU form does not perform better than the MA form
when αapproaches 1. Since there are no superiors to
constrain the managers from pursuing specialization,
it is reasonable to speculate that the AU form would
outperform the MA form in difficult tasks requiring
specialization. The answer to this puzzle highlights a
particular benefit of formal authority. When dealing
with satisficing managers, the shift in policy directive
by a superior induces more search on the part of the
subordinate (manager). As a result, authority can lead
to better results in such situations by producing more
search, even if that managerial search is handicapped
by the constraints of that authority. Thus, the SA and
MA forms hold an advantage over the AU form by
inducing each of its managers to search more, while
the managers in the AU form perform only a single
unconstrained search.
Consider the types of problems for which the MA
form does not excel. Figure 4shows that the SA
form is superior whenever integration of managers
actions becomes more important than local special-
ization (α0). The reason for this is fairly intuitive.
While the SA form has a single superior in charge of all
policy decisions, the MA form splits the formal author-
ity between four superiors, with each controlling only
a subset of PDs each, and this authority is exerted
over overlapping policies. Each of the four superiors
does not attend to the negative spillovers that her local
improvement efforts create for her peers, which may
lead to acceptance of choices that are suboptimal from
the point of view of the entire organization. These
spillovers increase the breadth of search efforts, but
they may also result in the organization failing to per-
sist in good policy solutions (Rivkin and Siggelkow
2003, Siggelkow and Levinthal 2003, Knudsen and
Levinthal 2007). Achieving superior integration is nev-
ertheless not guaranteed for the SA form. For α0, the
SA form is able to achieve a performance level of only
about 0.873, compared with the MA’s 0.848. The locally
searching single superior in the SA form can still get
stuck on a suboptimal peak.
To sum up, the superiority of the MA form stems
from its use of a mix of unconstrained and constrained
search by subunit managers. The SA form, while being
best at solving the integration problem, sacrifices effi-
cacy of the specialization efforts of its managers. The
AU form releases its managers from the bounds of
authority, but it forgoes integrating their efforts and
lacks an additional inducement to search stemming
from policy directives. The MA form thus offers a com-
promise. It benefits from an occasional use of uncon-
strained search and therefore outperforms the SA form
with respect to the challenge of specialization, while at
the same time it tends to the integration challenge. In
addition, relative to the AU form, it induces mangers
to search more.
4.1. Testing the Limits of the Multiauthority Form
Our results suggest that the MA form should be
a preferred form for many organizations, especially
when the integration problems are less important. This
result contrasts somewhat with the findings of prior
research that when the task environment favors spe-
cialization over integration, authority should be dele-
gated to the bottom of the organization (Christensen
1997, Goold and Campbell 2002). Furthermore, in many
instances, the implementations of the more complex
organizational forms have led to disappointing results
and numerous pathologies (Davis and Lawrence 1977,
Larson and Gobeli 1987, Galbraith 2009). While some of
those failures can be attributed to faulty or incomplete
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Levinthal and Workiewicz: Nearly Decomposable Systems and Organizational Adaptation
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implementation of the desired form, we are interested
in identifying and analyzing formally the sources of
limitations of the multiauthority form that may prevent
it from achieving its latent potential. We wish to explore
whether our representation of the multiauthority form
may have been overly optimistic in that issues that nat-
urally arise in such complex organizations have been
assumed away. We subsequently investigate the impact
that some of the key assumptions have on the efficacy
of specialization and integration efforts in the MA form
with the additional experiments that follow.
A general consensus in the literature has emerged
that the neglect of informal factors in the function-
ing of the multiauthority form is responsible for
its disappointing performance (Bartlett and Ghoshal
1989, Galbraith 2009). One of the key realizations is
that the same property that gives the MA form its
unique character—the existence of multiple lines of
authority—can be the source of some of its biggest
shortcomings. In particular, there is the issue of pos-
sible conflicts between multiple superiors. The exis-
tence of multiple viewpoints often leads to pursuing
incompatible goals and objectives. Furthermore, mul-
tiple bosses are more likely to have different exper-
tise and educational backgrounds (engineers, market-
ing, or finance), leading to problems with finding a
common language (Knight 1976, Barker et al. 1988,
Bechky 2003).
While the existence of conflict is natural to most
organizations (Cyert and March 1963), breaking the
unity of command by the multiauthority form makes
the situation especially severe, often causing paraly-
sis and stalling decision making (Davis and Lawrence
1977, Larson and Gobeli 1987). Employees in those
organizations often report lower motivation and
greater stress because of the ambiguity related to
resources (who owns what), authority (who is respon-
sible for what), promotions (who decides about future
career progression), and evaluation criteria (how will
employees be assessed for promotion) (Ford and Ran-
dolph 1992, Galbraith 2009).
In the subsequent analysis, we modify the model
structure to incorporate a sense of what these poten-
tially negative effects of multiauthority, or authority in
general, have on actions of the superiors and managers.
In particular, we look at four factors that have been
highlighted in the literature: (a) conflict resolution, (b)
employee motivation, (c) policy bias, and (d) slower decision
making (Davis and Lawrence 1977, Larson and Gob-
eli 1987, Ford and Randolph 1992, Chi and Nystrom
1998, Doz and Kosonen 2008, Galbraith 2009). By so
doing, we are able to examine the possible effects each
of those factors has on the performance of the multiau-
thority form. As in the previous analysis, we present
the results for the case where specialization and inte-
gration are both complex (Kp3,Kp,d2).
4.1.1. Conflict Resolution. First, we test the role of the
conflict resolution mode between the policy directives
in the MA form. As discussed earlier, the MA form
is unique in exposing subunit managers to multiple
policy directives, thus occasionally exposing the man-
agers to conflicting demands. This is a direct result
of the violation of the unity of command principle
(Fayol 1949). A manager exposed to conflicting policies
might either fear punishment for not carrying out both
commands or carry out whichever option he prefers
(Simon 1947, p. 141). Galbraith (1977) attributed differ-
ent approaches to solving conflicts between multiple
superiors to the problem-solving climate in an orga-
nization. In our initial analysis, we assumed that in
the presence of conflicting policy directives the man-
agers were unconstrained as there would always be at
least one superior who would back the manager’s pro-
posal. However, such conflicts might result in a stale-
mate or turf war (Bartlett and Ghoshal 1989, Doz and
Kosonen 2008), and in such a situation, the unit’s man-
ager may have to wait until the superiors resolve their
differences and issue a consistent joint policy directive.
To gauge the impact of this phenomenon, we simu-
late an alternative MA form (referred to as multiau-
thority (a), or MA-a, to distinguish it from the origi-
nal version), where the subunit managers only search
when the policy directives from both of their superi-
ors are consistent. When the policy directives are in
agreement, the managers’ search is constrained by the
double-authority relationship.
Figure 5(a) presents the results of this experiment.
With α0, there is no difference between the previ-
ous (MA) and the current (MA-a) version; because the
search on the lower level does not matter in this case,
the MA-a form performs at the same level as the MA
form. However, with higher levels of α, where pur-
suing specialization becomes increasingly important,
the MA-a form’s performance begins to suffer com-
pared with that of the MA form. Since in the MA-a
form the unit managers’ search is constrained, this
form achieves the same outcome in solving the spe-
cialization challenge as the SA form. The MA-a form’s
performance is thus dominated by the SA form, since
the SA form remains better in solving the integration
challenge.
4.1.2. Employee Motivation. Next, we investigate the
effects of reduced motivation on organizational search.
In our initial analysis, we assumed that the subunit
managers search for the best solution to their superiors’
policy directives. The managers are assumed to be moti-
vated to consider many possible alternative combina-
tions of DDs that satisfy their superiors’ requests. While
this is a plausible assumption, studies of organizations
reported that depriving subordinates of decision rights
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Levinthal and Workiewicz: Nearly Decomposable Systems and Organizational Adaptation
Organization Science, Articles in Advance, pp. 1–18, © 2018 INFORMS 13
Figure 5. Comparing the Effects of Different Conflict Resolution Mode, Employee Motivation, Policy Bias, and Time
Constraints (Kp3,Kp,d2)
(a) Dysfunctional conflict resolution (b) Employee motivation
(c) Policy bias (d) Time constraints
0.5
0.6
0.7
0.8
0.9
1.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Fitness (normalized)
Single authority
Single authority (b)
Multiauthority (a)
Multiauthority (b)
Integration Specialization
0.5
0.6
0.7
0.8
0.9
1.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Fitness (normalized)
Integration Specialization
ABC
0.5
0.6
0.7
0.8
0.9
1.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Fitness (normalized)
Single authority (c)
Multiauthority (c)
Integration Specialization
ABC
0.5
0.6
0.7
0.8
0.9
1.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Fitness (normalized)
Single authority
Integration Specialization
Autonomous
Autonomous
Autonomous
Autonomous
Multiauthority
Notes. In panel (a), the subunit managers only search when the policy directives from both of their superiors are consistent. In panel (b), the
subunit manager only nominally complies with superiors’ second request. In panel (c), the superior overestimates the contributions of her
own decisions to the overall performance of the organization. In panel (d), we measure the fitness of the organization after 10 rounds.
can have adverse effects on employee motivation and
creativity (Hamel and Prahalad 1996, Chi and Nystrom
1998). As Gibbons (2005, p. 206) remarks, “The cost of
control is the loss of initiative.” Many executives rec-
ognize the importance of managers’ motivation and
strive to create a high-performance culture to avoid sit-
uations where the subordinates only do the bare min-
imum required of them (Goold and Campbell 2002).
More generally, the lack of autonomy has long been
also recognized as damaging to employee motivation
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Levinthal and Workiewicz: Nearly Decomposable Systems and Organizational Adaptation
14 Organization Science, Articles in Advance, pp. 1–18, © 2018 INFORMS
in the organizational psychology literature (Turner
and Lawrence 1965, Herzberg 1966, Hackman and
Oldham 1976).
To reflect the possible adverse effects of reduced
autonomy on the motivation of subordinates, we con-
sider the following modification of the model. Within
the SA and MA forms (single-authority (b), or SA-b,
and multiauthority (b), or MA-b), we limit the search
performed by the managers. In particular, when asked
to perform their first search, the subunit managers
behave just as in the original specification. However,
when their superiors issue new policy directives to
induce more search, the managers comply only nom-
inally with the new request. Specifically, they look for
the closest combination of DDs from their current posi-
tion that satisfies the new policy directive and report
it back to the superiors. We report the results of this
robustness analysis in Figure 5(b).
The results indicate that the SA-b and MA-b forms
experience a drop in performance. While in task envi-
ronments favoring integration we observe no change,
the efficacy of specialization is lower for both forms.
The performance of the AU form remains intact.
Because the managers in the SA-b and MA-b forms
search only once and merely comply with the second
request, the two forms lose their advantage over the
autonomous form. While the MA-b form still manages
to outperform the SA-b in task environments favoring
more specialization (Figure 5(b), areas B and C), the
AU form is now superior for the highest values of α
(area C).
4.1.3. Policy Bias. In the next experiment, we consider
what happens when we introduce a bias between how
much importance the superiors assign to their actions
vis-à-vis the true importance of integration. Superiors
routinely tend to overestimate their own knowledge
and contributions and underestimate those of their
subordinates (Goold and Campbell 2002). Ghemawat
(2007), for example, discussed the case of Coca-Cola
in this regard. Under the leadership of the chief exec-
utive officer Roberto Goizueta, Coca-Cola introduced
a highly standardized strategy that underappreciated
the individual differences of the geographical markets
in which the firm operated (Ghemawat 2007, p. 17).
This tendency to underappreciate the local specializa-
tion efforts has often been cited as an argument in favor
of decentralization of decision rights and for giving
authority to those managers who are best positioned
to evaluate the merits of business decisions. We exam-
ine the impact of such a bias by introducing a new
parameter, α, to symbolize the relative weight that
superiors attribute to the importance of the specializa-
tion challenge faced by their subordinates. In general,
it is reasonable to assume that αis less than the actual
αvalue. In the analysis shown here, we set αto be
half of the actual αvalue. Thus, in the new single-
authority and multiauthority (SA-c and MA-c, respec-
tively) forms, the superiors perceive the importance
of their decisions to be higher than they really are.
For example, when the true α0.4, the environment
assigns 40% and 60% of the contribution to solving the
specialization and integration challenges, respectively.
A biased superior, however, may evaluate decisions
based on weights of 20% and 80% for specialization
and integration, respectively.
The results presented in Figure 5(c) demonstrate that
the bias for policy importance has an adverse effect
on the performance of the SA-c and MA-c forms.6
As the true importance of specialization increases, so
does the cost of underestimating it by the superiors.
We observe that the performance of both hierarchi-
cal forms declines, giving the AU form a performance
advantage in tasks demanding mostly specialization
(Figure 5(c), area C). But even when superiors have a
distorted understanding of the importance of the inte-
gration task, it is still not in general true that authority
should be delegated to the lower-level managers.
4.1.4. Decision Speed. Finally, we investigate the ef-
fects of timing as an additional criterion by which
to consider the performance of the three forms. The
MA form has been often accused of fostering exces-
sive bureaucracy that slows down decision making
and leads to prolonged stalemates among executives
(Davis and Lawrence 1977, Galbraith 2009). In the anal-
yses up to this point, we have examined performance
as characterized by the steady-state value. However,
the time needed to arrive to the steady-state solution
varies among the three forms. The AU form is the
fastest, as it performs only one search per each sub-
unit. The SA form requires a little more time, as the
single superior searches for the best possible combi-
nation of PDs, while the MA form takes the longest,
as the progress is slowed when the superiors reverse
each other’s decisions.7To demonstrate the effects of
the timing of the adaptive process, we compare each
form’s performance after only 10 rounds. We present
the results in Figure 5(d). We observe that the SA and
MA forms are prevented from reaching their steady-
state average performance. For α0, it takes the SA
and MA form 43 and 392 rounds on average, respec-
tively, to reach the steady state. For α0.5, the steady
state is reached in rounds 46 and 321 for SA and MA,
respectively, and it takes the MA form 261 time peri-
ods to overtake the SA form. For α1, the SA form
reaches the steady state in round 34, while for the MA
form it takes 139 rounds, and it takes the MA form
30 time periods to outperform the SA form. In sum,
in environments that require quick reaction time, the
multiauthority form finds itself at a disadvantage.
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Levinthal and Workiewicz: Nearly Decomposable Systems and Organizational Adaptation
Organization Science, Articles in Advance, pp. 1–18, © 2018 INFORMS 15
Thus, our additional analysis, while not exhaustive,
highlights several potential limitations of the multiau-
thority form. Factors such as the approach to resolving
conflicting policy directives, subordinates’ motivation,
superiors’ possible bias for the importance of their pol-
icy problem, and time constraints need to be taken
into account for a fuller understanding of the potential
efficacy of the multiauthority form and may help to
explain the divergence from the promise of this form
articulated by enthusiasts and the, at times, disappoint-
ing results associated with such forms.
5. Discussion and Conclusion
Organizations often need to coordinate among differ-
ent subunits either to realize the benefits of positive
spillovers or to avoid the negative ones. The charac-
ter of those interdependencies depends on a particular
setting. A multinational company may want to coor-
dinate between subsidiaries operating in neighboring
countries and offer the same product in each market
(Chi and Nystrom 1998, Ghemawat 2007). A multidi-
visional company may coordinate efforts of its sub-
sidiaries in the same country to either share costly assets
or represent them jointly in contacts with the local gov-
ernment (Bartlett 1982) or the local suppliers and dis-
tributors (Bartlett and Ghoshal 1989). Multibusiness
firms may also coordinate between divisions to con-
strain their competitive behavior when they interact
with the same competitor in several markets (Sengul
and Gimeno 2013).
By linking the idea of near decomposability to the
specialization and integration challenges organizations
face, our model illustrates the effects of different orga-
nizational structures on balancing the efficacy of search
at the lower and higher levels of an organization. We
represent an organizational task environment as a hier-
archical complex system, where variables at a higher
level of the system are represented by aggregated
lower-level variables. The existence of such loosely cou-
pled levels has important implications for managing
organizations. It allows a superior to abstract from the
detail of the lower level and thus overcome the limi-
tations of bounded rationality, enabling coordination
of tasks by issuing ex ante policy directives that direct
and constrain the actions of subordinates.
Our model also contributes to a wider discussion
regarding nearly decomposable complex systems. It
has been customary to represent near decomposability
of such systems as a decomposition of an interaction
matrix into modules (subsets of individual decision
variables) according to the number of interactions a
given variable has with other variables within and out-
side the module. While such representation has been
useful in pursuing many interesting questions, it leaves
out an important property of nearly decomposable
systems commonly found in organizations—namely,
hierarchy. A common feature of administrative hierar-
chies is that decisions become more general and less
precise as one moves upward (Mintzberg 1979). The
decision-making process, either top-down or bottom-
up, includes disaggregation of higher-level decisions
into finer-grained lower-level ones, or aggregation of
detailed decisions into fewer more general ones for fur-
ther processing. Per Porter’s (1996) example of South-
west Airlines, a high-level policy directive to purchase
the same model of an aircraft for the entire fleet does
not specify every single characteristic of such an air-
craft, but it directs and constrains actions of the subor-
dinate managers who are tasked with finding the best
solution that satisfies that directive. A subordinate,
by finding the best configuration of aircraft model,
interior configuration, and technical options, enacts
the desired policy directive. That high policy directive
of having a homogeneous fleet subsequently interacts
with other high-level policies to produce quick airport
turnarounds and low operating costs.
With this formalization of the integration and special-
ization challenges as a backdrop, we test the efficacy of
three canonical organizational forms—multiauthority,
single authority, and autonomous—in adapting to
task environments characterized by different degree of
importance of the integration and specialization chal-
lenges. Our results suggest that whenever the inte-
gration is of high importance, because of the interde-
pendence of the set of decisions across subunits, the
single-authority hierarchy will result in the highest per-
formance. At the other extreme, however, when special-
ization is important, the multiauthority form appears
to be a better choice. We would therefore expect to
see the multiauthority form perform better in situa-
tions requiring dual foci—where an organization needs
to coordinate multiple subunits while simultaneously
allowing those subunits to pursue local adaptation. The
increased level of autonomy in the multiauthority form
stemming from the possibly mixed nature of superi-
ors’ directives frees the subunit managers to search
unconstrained and to arrive at potentially superior solu-
tions. Even though the existence of crossing reporting
lines within this form creates complexity for superiors
and conflicting directives for subordinates, the multi-
authority form attends to the challenges of both coordi-
nating the separate parts of the organization and facili-
tating the relatively effective specialization of the units.
This finding corresponds to the propositions raised by
the literature on the project-based and multinational
organizations (Bartlett and Ghoshal 1989, Chi and
Nystrom 1998, Galbraith 2009), which have proposed
similar benefits of the matrix form. While organiza-
tions could balance local and global challenges through
cycling between single-authority and autonomous
forms (Nickerson and Zenger 2002, Siggelkow and
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Levinthal and Workiewicz: Nearly Decomposable Systems and Organizational Adaptation
16 Organization Science, Articles in Advance, pp. 1–18, © 2018 INFORMS
Levinthal 2003), the multiauthority structure offers a
similar compromise between the two objectives with-
out the need for frequent reorganizations.
Our model also further highlights the limitations
of the multiauthority form, which may help explain
some of its observed failures and inconsistent empir-
ical findings. The results presented in Section 4.1 in
particular speak to the multitude of additional factors
that can impact the relative performance of alternative
organizational forms. The analysis also serves as a cau-
tionary tale, alerting students of organizations to the
complex web of interactions between different organi-
zational features that can obfuscate the true efficacy
of alternative organizational designs and thus frustrate
further empirical investigations. First, we find that the
effects of conflicting directives on subordinates’ search
are an important condition impacting performance of
the multiauthority form. The other two forms avoid
ambiguity by either preserving the unity of command
or eschewing superiors altogether. Only the multiau-
thority form exposes its managers to potentially con-
flicting decision premises, and therefore the mode of
resolution of such a conflict is crucial in producing
desired results. One method to deal with conflicting
policy directives in multiauthority forms is to forge
ahead with an initiative, despite the conflict, using the
fact that there is at least one superior who can act as a
sponsor. While both modes of conflict resolution even-
tually lead to a decision, when approval of only one
of the bosses is required, the manager can search sub-
ject to less constraint, which, in expectation, leads to a
higher chance of finding a better solution to the lower-
level “specialist” problem. A further possible conse-
quence of the loss of autonomy in both the multiau-
thority form and the single-authority form is a loss of
motivation for proactive search efforts on the part of
lower-level actors.
The multiauthority and single-authority forms are
also sensitive to bias in the perception of the impor-
tance of the superior’s policy problem of integra-
tion relative to subordinates’ specialized subproblems.
Since this effect is absent in the fully autonomous form,
to the extent this effect is present, it tends to favor
the autonomous organizational form. In addition, this
effect further highlights the importance of different
approaches to decision making and data sharing in
organizations that can counter such biases.
Finally, our model highlights the importance of
time constraints. Depending on the time horizon, the
multiauthority form may be inferior to either the
single-authority or the autonomous form, which more
quickly arrive at satisfactory solutions to organiza-
tional challenges. The multiauthority form intention-
ally increases the incidence of conflicts by exposing
subordinates to multiple sources of authority. Those
conflicts, regardless of how they are resolved, require
time and attention and thereby slow down the adap-
tive efforts of an organization. We would thus expect
the multiauthority form to be prevalent in environ-
ments where the information processing requirements
arise because of interdependencies within and between
subunits; however, in “high-velocity” environments
(Eisenhardt 1989), where the speed of decisions takes
on more importance, their performance may suffer.
While extending our conceptualization of organi-
zational forms in some respects, our approach natu-
rally has a number of limitations, stemming in part
from the inherent abstraction of any given modeling
effort. In particular, while we consider such factors as
conflict resolution mode, employee motivation, policy
bias, and timing, we have not considered other issues
such as informal communication, internal social net-
works, or organizational culture. By so doing, we do
not presume that those factors do not matter. They
most certainly do, but the focus of the current work
is to consider a single mechanism in isolation, formal
authority, and how it affects the efforts of an orga-
nization to address the specialization and integration
challenges.
In sum, our work engages the suggestion in the liter-
ature that multiauthority forms are better suited than
traditional, single-authority hierarchies in addressing
challenges where issues of local specialization and
global integration have to be taken into account. We
expand on this general perspective and offer some
insight regarding some specific mechanisms that are
at play. We also examine some of the boundary con-
ditions for the efficacy of the representative organiza-
tional forms in environments characterized by com-
plexity and hierarchy. Authority structures are central
to organizations, impacting both the challenges of inte-
gration and control in complex task settings. However,
for most managers, “authority” is plural, not singular.
Oftentimes, in practice, these complex relationships are
viewed as particularistic and possibly pathological. We
suggest that neither property may be true. Rather, mul-
tiauthority relationships reflect some of the fundamen-
tal tensions that are characteristic of organizations of
any substantial scale or scope. While the label “matrix
organization” may have some sense of transience in its
popularity and its usage, the underlying phenomenon
is enduring, and as a result, these structures form an
important agenda item for management scholars—an
agenda to which we hope the current work makes some
contribution.
Acknowledgments
The authors’ names are in alphabetical order. The authors
thank Thorbjorn Knudsen and two anonymous reviewers
for their thoughtful and helpful comments. The paper also
benefited from feedback from Phanish Puranam, Metin Sen-
gul, Gabriel Szulanski, Peter Zemsky, and the seminar par-
ticipants at INSEAD, the Frankfurt School of Finance and
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Levinthal and Workiewicz: Nearly Decomposable Systems and Organizational Adaptation
Organization Science, Articles in Advance, pp. 1–18, © 2018 INFORMS 17
Management, the University of Southern Denmark, Bocconi
University, the Rotterdam School of Management at Erasmus
University, HEC Paris, and the 2015 Theoretical Organization
Models Society conference in Venice. Errors and omissions
remain the authors’ own.
Endnotes
1We have tested the model with different values of Npand Np,d,
and the qualitative results hold. Clearly, Np,dmust take on an odd
number value to allow aggregation by a simple majority.
2We distinguish between policy decisions and policy directives, as a pol-
icy directive is an ex ante choice made by a superior that may or may
not lead to the actual policy being implemented by the subordinates.
3We have also ran analyses where we limited managerial search to
only one trial per round, thus preventing him from reaching a steady
state. This reduced the overall organizational performance, but the
qualitative results are preserved.
4For Kp>0, the MA form often experiences an ongoing process of
mutual perturbation (Siggelkow and Levinthal 2003), where the mul-
tiple superiors keep switching their policy directives while pursu-
ing their own performance improvements. Thus, to obtain a reliable
measure of performance of the MA form, we run the simulation for
600 periods, where in all cases the performance trajectory reaches
a stable pattern of oscillation if not a steady-state value. We then
record the average performance of the last 50 rounds to remove fur-
ther stochastic artifacts. Thus, the steady-state solution is reached
when the fitness value is at or fluctuates around the long-term mean.
5The U shape of the fitness lines of the one-boss and multiauthority
organizations is a result of the normalization procedure. We first
scaled the fitness values of the PD and DD vectors so that the lowest
possible fitness level corresponds to 0 and highest to 1. We then
combined the two fitness values per Equation (2). The dip for the
intermediate values of αis caused by the fact that the combination
of the DD decision variables may not correspond to the optimal
aggregate value of the PD vector. For example, the global peak on
the DD level is produced by a vector of decision variables (0,0,0),
while the PD yielding superior fitness is 1.
6We also ran additional analyses where, instead of setting αto
half the value of the true α, we set a random αU(0,1). For high
values of α, we observed results similar to those reported here,
since, on average, the superiors were undervaluing the importance
of specialization. Conversely, for low levels of α, the superiors were,
on average, undervaluing the benefits of integration, which nega-
tively affected performance of the single- and multiauthority forms.
The relative advantages of one form over another, however, were
preserved.
7The search in the MA form may never actually stop for α1as
there is the ongoing possibility of superiors reversing each other’s
decisions. We can, however, identify a time period after which the
average expected performance reaches a plateau.
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Maciej Workiewicz is an assistant professor of man-
agement at ESSEC Business School in France. He received
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... Second, MNE-subsidiary studies explicitly assume that subsidiary development is characteristic of a network structure (Birkinshaw, 1998;Decreton et al., 2019;Johnson & Medcof, 2007;Schmid et al., 2014), which allows the subsidiary a certain level of autonomy and entrepreneurial opportunities. This perspective discounts the scope for other structural possibilities through which subsidiaries may develop, such as an intermediary or a mandated unit, or a matrix structure, which are the most complex and studied mainly in terms of their coordinating and controlling characteristics (Egelhoff, 2020;Egelhoff & Wolf, 2017;Egelhoff et al., 2013;Goold & Campbell, 2002;Levinthal & Workiewicz, 2018). ...
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