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Journal ArticleDOI

Patterned Interactions in Complex Systems: Implications for Exploration

01 Jul 2007-Management Science (INFORMS)-Vol. 53, Iss: 7, pp 1068-1085
TL;DR: Simple, intuitive rules of thumb are developed that allow a decision maker to examine two interaction patterns and determine which warrants greater investment in broad exploration, which validates prior comparative static results with respect to the number of interactions and highlights an important implicit assumption in earlier work.
Abstract: Scholars who view organizational, social, and technological systems as sets of interdependent decisions have increasingly used simulation models from the biological and physical sciences to examine system behavior. These models shed light on an enduring managerial question: How much exploration is necessary to discover a good configuration of decisions? The models suggest that, as interactions across decisions intensify and local optima proliferate, broader exploration is required. The models typically assume, however, that the interactions among decisions are distributed randomly. Contrary to this assumption, recent empirical studies of real organizational, social, and technological systems show that interactions among decisions are highly patterned. Patterns such as centralization, small-world connections, power-law distributions, hierarchy, and preferential attachment are common. We embed such patterns into an NK simulation model and obtain dramatic results: Holding fixed the total number of interactions among decisions, a shift in the pattern of interaction can alter the number of local optima by more than an order of magnitude. Thus, the long-run value of broader exploration is significantly greater in the face of some interaction patterns than in the face of others. We develop simple, intuitive rules of thumb that allow a decision maker to examine two interaction patterns and determine which warrants greater investment in broad exploration. We also find that, holding fixed the interaction pattern, an increase in the number of interactions raises the number of local optima regardless of the pattern. This validates prior comparative static results with respect to the number of interactions, but highlights an important implicit assumption in earlier work---that the underlying interaction pattern remains constant as interactions become more numerous.

Summary (2 min read)

1. Introduction

  • In the context of organizational, technical, and social systems, however, recent empirical work has shown that interactions are often very patterned.
  • Section 5 explains in an intuitive way the link between different interaction patterns and the number of local optima they create.
  • 23) points out, “The random network theory of Erdős and Rényi has dominated scientific thinking about networks since its introduction in 1959, also known as As Barabási (2002.

2. Types of influence matrices

  • Following a long tradition in the organization literature (e.g., Learned, et al. 1961) that has gained energy recently from empirical, prescriptive, and computational studies (e.g., Siggelkow 2002; Porter 1996; Levinthal 1997), the authors conceptualize firms as systems of interdependent choices.
  • A number of these decisions interact with each other.
  • Influence matrices can differ, however, in the total number of off-diagonal x’s, i.e., in the number of interactions among the decisions, and in the patterns of these interactions.
  • One method of creating networks that contain elements that are more central than others has been provided by Barabási and Albert (1999).
  • Starting with x’s along the main diagonal, this matrix is created by randomly adding x’s below the diagonal until the matrix contains a total of N*(K+1) interactions.

3. Creation of performance landscapes and firms that search on them

  • Firms are assumed to make N binary decisions about how to configure their activities.
  • Hence, an N- digit string of zeroes and ones summarizes all the decisions a firm makes that affect its performance.
  • Once a particular influence matrix is chosen, the computer generates a performance landscape based on this influence matrix.
  • In the decentralized firm, decisions are split between two managers, A and B. Manager A is responsible for the first N/2 decisions, while manager B is responsible for the remaining N/2 decisions.
  • After evaluating alternatives, each manager implements the alternative that she finds best (or maintains the status quo if no evaluated alternative has higher performance).

4. Landscape characterization

  • The authors use each of the ten different influence matrices to generate performance landscapes and determine a number of topological characteristics of the resulting landscapes.
  • As a result, since the authors are interested in comparisons across influence matrices, they do not investigate values larger than K = 6. 13 that landscapes based on the same number of total interactions but different interaction patterns can contain dramatically different numbers of local peaks.
  • On K = 2 landscapes, the number of local peaks ranges from 3.4 for landscapes based on centralized influence matrices to 129.0 for landscapes based on dependent influence matrices.
  • One immediate consequence of the different number of local peaks is that firms are much more likely to find the global peak in landscapes with centralized interaction patterns than in landscapes that have dependent interaction patterns.

5. Intuition

  • Even if the total number of interactions among decisions is held constant, performance landscapes can differ markedly in the number of local peaks they contain.
  • For each of these two, the authors describe the shapes of the resulting landscapes as well as the underlying intuition for the number of local peaks that arise.
  • Because decisions 4-12 are uninfluential, the alteration of each does not affect the contributions of the other decisions, and this simple procedure produces the greatest possible performance conditional on decisions 1-3.
  • This is especially likely when many decisions are uninfluenced, causing all configurations to have a similar underlying level of performance and permitting small differences to create numerous local optima.
  • If the authors fill one row of this influence matrix with x’s, i.e., make one decision’s contribution dependent on all other decisions, the number of local peaks increases sharply to 58.

6. Performance consequences

  • In prior sections, the authors have asserted that the proliferation of local peaks increases the value of, and need for, broad exploration.
  • In each firm, managers evaluate two alternatives per period.
  • The column labeled “random” replicates the finding of Rivkin and Siggelkow (2003), which used random influence matrices.
  • For low levels of K, the hierarchical firm significantly outperforms the decentralized firm, while for high levels of K, the decentralized firm significantly outperforms the hierarchical firm.

7. Discussion and Conclusion

  • In management science, the study of complex systems has recently gained momentum as simulation tools, originally developed in biology and physics, have been applied to organizational, social, and technological settings.
  • Many simulation models in this field of inquiry have two parts: a problem space (a performance landscape, an environment, etc.) and entities that search (or move, or live) in the problem space.
  • The interaction patterns that produce very few local peaks are marked by a handful of highly influential decisions and a large number of uninfluential decisions.
  • These patterns produce landscapes that are easy to search: once the handful of core decisions are made, other choices fall into place naturally.
  • Patterns of interaction, however, may affect not only the power of exploration across discrete modules, but also the ability of managers to explore possibilities within each module.

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Patterned Interactions in Complex Systems:
Implications for Exploration*
Jan W. Rivkin Nicolaj Siggelkow
239 Morgan Hall 2211 Steinberg Hall-Dietrich Hall
Harvard Business School Wharton School
Boston, MA 02163 Philadelphia, PA 19104
(617) 495-6690 (215) 573-7137
jrivkin@hbs.edu siggelkow@wharton.upenn.edu
* Special thanks to Howard Brenner for computer programming and to Monica Yan and Gavaskar
Balasingam for research assistance. We are grateful to the Mack Center for Technological Innovation and
the Division of Research of Harvard Business School for generous funding. Errors remain our own.

Patterned Interactions in Complex Systems:
Implications for Exploration
Abstract: Scholars who view organizational, social, and technological systems as sets of interdependent
decisions have increasingly used simulation models from the biological and physical sciences to examine
system behavior. These models shed light on an enduring managerial question: how much exploration is
necessary to discover a good configuration of decisions? The models suggest that, as interactions across
decisions intensify and local optima proliferate, broader exploration is required. The models typically
assume, however, that the interactions among decisions are distributed randomly. Contrary to this
assumption, recent empirical studies of real organizational, social, and technological systems show that
interactions among decisions are highly patterned. Patterns such as centralization, small-world
connections, power-law distributions, hierarchy, and preferential attachment are common. We embed
such patterns into an NK simulation model and obtain dramatic results: holding fixed the total number of
interactions among decisions, a shift in the pattern of interaction can alter the number of local optima by
more than an order of magnitude. Thus, broader exploration is far more valuable in the face of some
interaction patterns than in the face of others. We develop simple, intuitive rules of thumb that allow a
decision maker to examine two interaction patterns and determine which requires greater investment in
broad exploration.

1
1. Introduction
How much should an organization invest in the broad exploration of new possibilities? This enduring
question arises in a wide array of contexts, including the management of production processes (Abernathy
1978), the search for new technologies (Wheelwright and Clark 1992; Fleming 2001), the structuring of
organizations (Tushman and O’Reilly 1996), the design of products (Baldwin and Clark 2000), and the
design of individual and organizational learning processes (Ashby 1960; Argyris and Schön 1978; March
1991). The question poses a managerial dilemma. On one hand, managers of an organization must
embrace the exploration of new possibilities. Otherwise, the organization fails to innovate. On the other
hand, managers must contain exploration because it competes for resources with another crucial
organizational process, the exploitation of known opportunities (March 1991). It is widely acknowledged
that effective organizations strike a healthy balance between exploration and exploitation, even though it
is organizationally difficult to accomplish both (Ghemawat and Ricart i Costa 1993; Tushman and
O’Reilly 1996; Benner and Tushman 2003). But how can one know whether a particular balance is
healthy? Under which conditions is it essential to rein in exploration, and when must one unleash it?
Studies of complex adaptive systems (CASs), set initially in the physical and biological sciences,
have begun to shed light on this issue. Many of these studies seek systems that relax the exploration /
exploitation tradeoff – that are responsive and creative yet stable and orderly – neither frozen nor chaotic
(e.g., Langton 1990; Kauffman 1993). Among the CAS frameworks that have made the transition to
management science, the NK model from theoretical biology (Kauffman and Levin 1987; Kauffman and
Weinberger 1989; Kauffman 1993) has become a particularly popular platform for studying organizations
as complex adaptive systems (e.g., Levinthal 1997; McKelvey 1999; Gavetti and Levinthal 2000; Rivkin
2000; Sorenson 2002; Ethiraj and Levinthal 2004). The model grants a researcher control over the
interactions among the elements that make up a system. Results of the model have shed light on the
question of optimal exploration: as the degree of interaction among a firm’s choices rises, the poor local
optima that can disrupt a firm’s search efforts proliferate and it becomes preferable, ceteris paribus, for a

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Abstract: Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.

39,297 citations


"Patterned Interactions in Complex S..." refers background in this paper

  • ...The organizational implications of this feature have been discussed by Levinthal (1997), Rivkin (2000), and others....

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Journal ArticleDOI
15 Oct 1999-Science
TL;DR: A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
Abstract: Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

33,771 citations


"Patterned Interactions in Complex S..." refers methods in this paper

  • ...2003), memberships in underwriting syndicates (Baum et al. 2003), firmalliance networks (Schilling and Phelps 2004), career networks of artists (Uzzi and Spiro 2005, Guimera et al. 2005), and collaboration networks of scientists (Newman 2001). Following the algorithm by Watts and Strogatz (1998), we create small-world influence matrices in two steps....

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Journal ArticleDOI
TL;DR: In this paper, a simple model based on the power-law degree distribution of real networks was proposed, which was able to reproduce the power law degree distribution in real networks and to capture the evolution of networks, not just their static topology.
Abstract: The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them. Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other. The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.

18,415 citations

Journal ArticleDOI
TL;DR: In this paper, the authors consider the relation between the exploration of new possibilities and the exploitation of old certainties in organizational learning and examine some complications in allocating resources between the two, particularly those introduced by the distribution of costs and benefits across time and space.
Abstract: This paper considers the relation between the exploration of new possibilities and the exploitation of old certainties in organizational learning. It examines some complications in allocating resources between the two, particularly those introduced by the distribution of costs and benefits across time and space, and the effects of ecological interaction. Two general situations involving the development and use of knowledge in organizations are modeled. The first is the case of mutual learning between members of an organization and an organizational code. The second is the case of learning and competitive advantage in competition for primacy. The paper develops an argument that adaptive processes, by refining exploitation more rapidly than exploration, are likely to become effective in the short run but self-destructive in the long run. The possibility that certain common organizational practices ameliorate that tendency is assessed.

16,377 citations

Book
01 Jan 1967

11,087 citations

Frequently Asked Questions (2)
Q1. What contributions have the authors mentioned in the paper "Patterned interactions in complex systems: implications for exploration" ?

Scholars who view organizational, social, and technological systems as sets of interdependent decisions have increasingly used simulation models from the biological and physical sciences to examine system behavior. The authors develop simple, intuitive rules of thumb that allow a decision maker to examine two interaction patterns and determine which warrants greater investment in broad exploration. This validates prior comparative static results with respect to the number of interactions, but highlights an important implicit assumption in earlier work—that the underlying interaction pattern remains constant as interactions become more numerous. The models suggest that, as interactions across decisions intensify and local optima proliferate, broader exploration is required. 

This is a speculation that deserves investigation in future research. An exciting question for future research is, what interaction patterns will prevail over time ? Patterns of interaction, however, may affect not only the power of exploration across discrete modules, but also the ability of managers to explore possibilities within each module. Because optimization of high-dimensional systems with many interdependencies is usually a difficult task, it may be very helpful to design a system in a way that smoothes performance landscapes and facilitates the search for good solutions.