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Article Excerpt
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 (Ulrich and Eppinger 2007, Baldwin and Clark 2000), and the design of individual and organizational learning processes (Ashby 1960, Argyris and Schon 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). How, however, 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, 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 trade-off--systems that are responsive and creative, yet stable and orderly, neither frozen nor chaotic (e.g., Langton 1990, Kauffman 1993). Among the complex adaptive systems 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 firm to undertake more exploration in order to escape those optima (Kauffman 1993, Levinthal 1997, Rivkin and Siggelkow 2003). Decisionmaking processes that focus on incremental change run out of improvement possibilities quickly when choices are intertwined, so broader search becomes vital.
By embedding recent empirical results in a simulation model, this paper takes the NK model's insights on optimal exploration an important step further. Past modeling efforts have looked exclusively at how the degree of interaction among a firm's choices affects appropriate exploration. Much less attention has been placed on the pattern of interaction among these choices. Indeed, in most NK analyses it is assumed that interactions among choices have a random pattern. This made sense in the biological context, where the interactions were among genes and it was "useful to confess our total ignorance and admit that, for different genes and those which epistatically affect them, essentially arbitrary interactions are possible" (Kauffman 1993, p. 41). In the context of organizational, social, and technological systems, however, recent empirical work has shown that interactions are often very patterned. Our paper exploits this newly gained knowledge in three ways. First, we examine how commonly observed patterns of interactions affect the proliferation of local optima and, accordingly, the appropriate amount of long-run exploration. We find that systems of choices with the same number of total interactions but different patterns of interactions can display very different numbers of local peaks. Second, we study the relationship between the number of interactions and the number of local peaks, holding the pattern of interaction constant. This analysis sheds light on the question of whether prior comparative static results with respect to K, derived from random interaction patterns, are likely to hold for other patterns as well. Third, we identify easily observable characteristics of interaction patterns beyond the overall degree of interaction that in many cases allow one to look at two patterns of interaction and tell immediately which one generates more local optima and warrants greater investment in broad exploration. This can enable managers to convert their knowledge of the interactions among the choices they face into concrete guidance for optimal exploration.
For insight into real patterns of interactions, we rely on empirical work conducted in diverse domains. Detailed work at the level of individual firms (e.g., Porter 1996, Siggelkow 2002), and at the level of individual product systems (e.g., Eppinger et al. 1994, Ulrich and Eppinger 2007, Baldwin and Clark 2000), has yielded a number of explicit maps that show the interdependencies among the various system elements, allowing us to start seeing patterns. Likewise, recent network analyses, such as work on small-world networks (Watts and Strogatz 1998), has generated a great deal of research describing the patterns of real-world networks of interactions. As most of these studies show, networks tend not to be random, but are highly patterned. (1) Specifically, recent empirical work led us to study 10 different interaction patterns: a small-world interaction structure (Watts and Strogatz 1998), which includes as extreme cases the random structure and the local structure; the preferential attachment and the scale-free structures, two structures currently under intense investigation (e.g., Barabasi 2002); and the centralized, hierarchical, block-diagonal, diagonal, and dependent structures, which capture various patterns observed in product design and studies of firms.
We emphasize the implications of interaction patterns for optimal exploration. Prior research has shown that interaction patterns affect other organizational phenomena as well, including the ability of a firm to adapt to environmental change, to imitate the effective configurations of other firms, and to replicate one's own effective configurations (e.g., Levinthal 1997; Rivkin 2000, 2001). We speculate below on how interaction patterns may influence these phenomena. Moreover, firms might be able to affect interaction patterns through system design decisions (Levinthal and Warglien 1999, MacCormack et al. 2006). Our findings suggest how firms might design systems to be more readily searchable.
This paper is structured as follows: Section 2 describes in detail the 10 interaction patterns we analyze. Section 3 outlines how we create decision problems with these different underlying interaction patterns. The results in [section]4 characterize the local optima that arise from the various interaction patterns. Section 5 explains in an intuitive way the link between different interaction patterns and the number of local optima they create. The different numbers of local optima, in turn, affect the benefit of broad organizational exploration, as [section]6 shows. Section 7 concludes.
2. Types of Influence Matrices
While the model we study is general enough to encompass a wide range of organizational, social, and technological systems, for expositional purposes we focus on firms as our system of interest. A long tradition in the organization literature (e.g., Learned et al. 1961), reinforced recently by empirical, prescriptive, and computational studies (e.g., Siggelkow 2002, Porter 1996, Levinthal 1997), leads us to conceptualize a firm's management team as facing a number of interdependent decisions. Each firm must choose, for instance, whether to distribute broadly or through narrow channels, whether to advertise in mass media, whether to invest in large-scale production facilities, etc. These decisions might interact with each other. For instance, broad distribution might make mass-market advertising more attractive.
In the context of modeling search behavior of firms, the NK framework assumes that a firm faces N decisions, each of which can be configured in a number of different ways (two, in our simulations). The contribution of an individual decision to a firm's overall performance depends on the resolution of that decision, and possibly other decisions. It is common to think of the space of decisions and the payoffs from combinations of choices as defining a "performance landscape:" each of the N decisions corresponds to a "horizontal" dimension, while the payoff is represented on the "vertical" axis.
An influence matrix records which decisions affect each decision. If a firm makes N decisions, then an influence matrix is an N * N matrix whose entry (i, j) is set to an x if the resolution of column decision j affects the value of row decision i. Because each decision affects itself, all influence matrices have xs along their diagonal. Influence matrices can differ, however, in the total number of off-diagonal xs, i.e., in the number of interactions among the decisions, and in the patterns of these interactions. In the original NK setup (Kauffman 1993), it was assumed that each decision is affected by exactly K other decisions, i.e., each row contained K off-diagonal xs. Thus, in total, an NK influence matrix contained N * (K + 1) interactions. While a number of studies have investigated various consequences that arise when K increases in a random influence matrix (e.g., Kauffman 1993), we are interested in the effect of different patterns of interactions holding K fixed. Hence, to allow for comparisons of different types of interaction structures, we keep the total number of interactions fixed at N * (K + 1), but alter the pattern of interactions among the decisions.
Even for relatively small values of N and K, many possible interaction structures exist. In particular, N * K (off-diagonal) interactions can be placed in [N.sup.2] - N locations (the N diagonal elements are always filled), creating
([N.sup.2] - N)!/(N * K)!([N.sup.2] - N - N * K)!
possibilities. For N = 12 and K = 2, for instance, this yields 1.36 * [10.sup.26] possible influence matrices. For all our analyses, the labeling of individual decisions does not matter (i.e., columns and corresponding rows can be rearranged). (2) This reduces the number of patterns by a factor as large as N!, the number of ways that N decisions can be reordered. For N = 12 and K = 2, this reduction still leaves a lower bound of 2.84 * [10.sup.17] different patterns. Given this vast space of possibilities, it is helpful to consider different types of interaction patterns. In particular, we focus on 10 types that were culled from current work on networks, from studies that depict firms as deploying systems of interdependent activities, and from product design analyses.
Influence matrices arise frequently in these contexts even though the term "influence matrix" might not have been used there. The representation of a network as an influence matrix is straightforward (Wasserman and Faust 1994). Each row corresponds to a node of a network, as does each column, with an entry in row i, column j denoting that node j has a link to (and affects) node i. The work on firms as systems of interdependent activities generally has represented firms as consisting of a network of activities that are linked by interactions among them (Porter 1996, Siggelkow 2002). Again, these networks can easily be transformed into influence matrices. Most directly, the product design literature has developed the tool of a "design structure matrix" (DSM) (Steward 1981, Eppinger et al. 1994, Baldwin and Clark 2000), which corresponds to an influence matrix by our definition. A DSM contains all design decisions (e.g., concerning particular design parameters) that have to be resolved. The DSM has an entry in row i, column j if the design choice of element j has an impact on the optimal design choice of element i. For instance, the choice of engine power (element j) might have an impact on the optimal design of the brake system (element i). Table 1 examines all activity system maps that have been published in the literature (Porter 1996; Siggelkow 2001, 2002) and all DSMs that were published on the DSM home page (www.dsmweb.org), which is hosted by Steven Eppinger, Daniel Whitney, and Ali Yassine. For the firm activity systems, N ranges from 18 to 48, and K, calculated as the number of off-diagonal interaction effects divided by N, from 2.2 to 3.5. For the DSMs, N varies from 13 to 111, with K ranging from 1.4 to 6.8.
The 10 different types of influence matrices we explore can be divided into two groups. For five types, each decision is affected by exactly K other decisions. That is, each row of the influence matrix contains exactly K off-diagonal entries. The other five types allow for more heterogeneity among the decisions. For instance, some decisions are allowed to be affected by many other decisions, while other decisions might depend only on themselves.
Random. In a random influence matrix, exactly K xs are placed at randomly chosen off-diagonal positions in each row. For one example with N = 12 and K = 2, see Figure 1A. This specification is one of the two original specifications of the NK model (Kauffman 1993) and is the setup most commonly used in the organization literature (e.g., Westhoff et al. 1996, Rivkin 2000).
Local. In a local influence matrix, the other original specification, each decision i is assumed to be influenced by its K/2 neighbors on either side of it (Figure 1B). For instance, if K = 2, decision 3 is affected by decisions 2 and 4. Decisions are assumed to lie on a "ring," i.e., if K = 2, decision 1 is affected by decision 2 and decision...
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