Week 5 - Assess an Organization's Structure and Propose Changes

Optimal Structure, Market Dynamism, and the Strategy of Simple Rules

Citation Davis, Jason, Kathleen M. Eisenhardt and Christopher B. Bingham "Optimal Structure, Market Dynamism, and the Strategy of Simple Rules." Administrative Science Quarterly, 54 (2009): 413–452

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Optimal Structure, Market Dynamism, and the Strategy of Simple Rules

Jason P. Davis

Massachusetts Institute of Technology

Kathleen M. Eisenhardt

Stanford University

Christopher B. Bingham

University of North Carolina

ii

ABSTRACT

Using computational and mathematical modeling, this study explores the tension between too

little and too much structure that is shaped by the core tradeoff between efficiency and flexibility

in dynamic environments. Our aim is to develop a more precise theory of the fundamental

relationships among structure, performance, and environment. We find that the structure-

performance relationship is unexpectedly asymmetric, in that it is better to err on the side of too

much structure, and that different environmental dynamism dimensions (i.e., velocity,

complexity, ambiguity, and unpredictability) have unique effects on performance. Increasing

unpredictability decreases optimal structure and narrows its range from a wide to a narrow set of

effective strategies. We also find that a strategy of simple rules, which combines improvisation

with low-to-moderately structured rules to execute a variety of opportunities, is viable in many

environments but essential in some. This sharpens the boundary condition between the strategic

logics of positioning and opportunity. And juxtaposing the structural challenges of adaptation for

entrepreneurial vs. established organizations, we find that entrepreneurial organizations should

quickly add structure in all environments, while established organizations are better off seeking

stable environments unless they can devote sufficient attention to managing a dissipative

equilibrium of structure (i.e., edge of chaos) in unpredictable environments.•

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A longstanding question in strategy and organization theory is how the amount of organizational

structure shapes performance in dynamic environments. Given its fundamental importance, this

question has been explored in a variety of research traditions, ranging from organizational

studies (Burns and Stalker, 1961; Hargadon and Sutton, 1997) and competitive strategy (Rindova

and Kotha, 2001; Rothaermel, Hitt, and Jobe, 2006) to network sociology (Uzzi, 1997; Owen-

Smith and Powell, 2003) and, more broadly, the complexity sciences (Kauffman, 1993;

Anderson, 1999). Although highly diverse, these literatures nonetheless highlight two

fundamental arguments.

The first argument is that a balance between too much and too little structure is critical to high

performance for organizations in dynamic environments. Organizations with too little structure

lack enough guidance to generate appropriate behaviors efficiently (Weick, 1993; Okhuysen and

Eisenhardt, 2002; Baker and Nelson, 2005), while organizations with too much structure are too

constrained and lack flexibility (Miller and Friesen, 1980; Siggelkow, 2001; Martin and

Eisenhardt, 2010). This tension produces a dilemma for organizations, as high performance in

dynamic environments demands both efficiency and flexibility. Research shows that high-

performing organizations resolve this tension using a moderate amount of structure to improvise

a variety of high-performing solutions (Brown and Eisenhardt, 1997, 1998). Overall, this

suggests an inverted U-shaped relationship between the amount of structure and performance, a

relationship often observed when tensions are at work.

The second argument is that achieving high performance with moderate structure is influenced

by the changing nature of environmental opportunities (Adler, Goldoftas, and Levine, 1999;

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Rindova and Kotha, 2001). Highly dynamic environments require flexibility to cope with a flow

of opportunities that typically is faster, more complex, more ambiguous, and less predictable

than in less dynamic environments. Research shows that high-performing organizations cope

with dynamic environments with less structure (Eisenhardt and Martin, 2000; Rowley, Behrens,

and Krackhardt, 2000). Conversely, less dynamic environments favor efficiency, and so high-

performing organizations have more structure in these environments (Pisano, 1994; Rivkin and

Siggelkow, 2003). Overall, this suggests that the optimal amount of structure decreases with

increasing environmental dynamism, a consistent finding within multiple literatures.

Yet although these arguments are widely understood in general, unresolved issues remain. First,

the empirical evidence that supports an inverted-U shaped relationship is modest. It primarily

consists of qualitative case comparisons (Mintzberg and McHugh, 1985; Brown and Eisenhardt,

1997) and quantitative confirmations such as statistical tests of quadratic relationships and

interaction effects that are not sufficiently precise to identify a specific functional form (Bradach,

1997; Gibson and Birkinshaw, 2004; Rothaermel, Hitt, and Jobe, 2006), such as an inverted-U.

Rather, the evidence simply points to a unimodal shape for the relationship between structure

and performance that increases on one side and decreases on the other. So the evidence does not

rule out other shapes (e.g., broad plateau or inverted-V) and related functional forms. The shape

of the structure-performance relationship has consequential theoretical and managerial

implications. For instance, if the relationship is a broad plateau with a wide range of optimal

structures, then balancing between too much and too little structure is easy and unimportant. In

contrast, if the shape is an inverted-V, in which the optimal structure is a narrow peak,

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sometimes called an “edge of chaos,” then balancing between too much and too little structure is

challenging and crucial.

Second, the theory that underlies the relationship between the amount of structure and

performance is incomplete. As sketched above, the basic theoretical argument is that

organizations with too much structure are too inflexible, while organizations with too little

structure are too inefficient. Although appealing, this argument neglects key factors such as

limited attention, time delays, and the fleeting and varied nature of opportunities that might

influence this tradeoff. So, for example, the theory does not consider that, although less structure

enables flexible improvisation, improvisation is an attention-consuming and mistake-prone

process (Hatch, 1998; Weick, 1998). As a result, the theory fails to clarify precisely how

structure influences efficiency and flexibility, and thus the exact nature of the efficiency-

flexibility tradeoff, including whether it is advantageous to err toward too much or too little

structure.

Third, the theory that underlies the argument that environmental dynamism influences the

optimal structure is imprecise. In particular, environmental dynamism is a multidimensional

construct (Dess and Beard, 1984), and yet the theory does not unpack how the dimensions of

dynamism operate. The empirical literature also reflects this imprecision, as studies often mingle

dimensions such as complexity, velocity, unpredictability, and ambiguity (Eisenhardt, 1989;

Pisano, 1994) that may have distinct effects. Understanding the influence of different dimensions

is important because they may have unexpected implications for theory and practice. For

example, it may be that only one or two dimensions shift optimal structure or that the structure-

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performance relationship has distinct shapes in specific environments, such as highly ambiguous

nascent markets and high velocity “bubble” markets.

Overall, these unresolved issues suggest a lack of specific understanding in diverse literatures of

the fundamental relationships among structure, performance, and environment. This is the gap

that we address by exploring the relationship between structure and performance, the underlying

tradeoff between efficiency and flexibility, and the influence of environmental dynamism. There

are many definitions of structure, with varied attributes such as formalization (e.g., rules,

routines), centralization (e.g., hierarchy, use of authority, verticality), control systems (e.g., span

of control), coupling and structural embeddedness (e.g., tie strength, tie density), and

specialization (e.g., role clarity) (Weber, 1946; e.g., Burns and Stalker, 1961; Pugh et al., 1963;

Galbraith, 1973; Mintzberg, 1979; Granovetter, 1985; Scott, 2003). But although the definitions

include varied attributes, they all share an emphasis on shaping the actions of organizational

members. Entities are more structured when they shape more activities of their constituent

elements and thus constrain more action. Conversely, entities are less structured when their

constituent elements have more flexibility in their behavior. Thus we define structure broadly as

constraint on action.

We conducted this research using simulation methods, which are effective for research such as

ours in which the basic outline of the theory is understood, but its underlying theoretical logic is

limited (Davis, Eisenhardt, and Bingham, 2007). In this situation, there is enough theory to

develop a simulation model, yet the theory is also sufficiently incomplete that it warrants

examination of its internal validity (i.e., the correctness of its theoretical logic) and elaboration of

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its propositions through experimentation, which are both strengths of simulation (Sastry, 1997;

Zott, 2003). Simulation is also a particularly useful method for research such as ours when the

focal phenomenon is nonlinear (Carroll and Burton, 2000; Rudolph and Repenning, 2002;

Lenox, Rockart, and Lewin, 2006). Though statistical and inductive methods may indicate the

presence of nonlinearities, they offer less precise identification, particularly of complex ones

such as tipping points and skews. Simulation is also a particularly useful method when empirical

data are challenging to obtain (Davis, Eisenhardt, and Bingham, 2007). For example, simulation

enables us to study mistakes that informants might be reluctant to reveal (Carroll and Burton,

2000; Finkelstein, 2003) and to unpack environmental dimensions that may be difficult to

disentangle in actual environments (Dess and Beard, 1984). Finally, simulation is especially

effective for research such as ours that involves longitudinal and process phenomena because

such phenomena can be studied over extended time periods that would be difficult to observe

with empirical data (March, 1991; Zott, 2003). Using these methods, we seek to understand the

effects of varying amounts of structure on performance in different environments.

ORGANIZATIONAL STRUCTURE AND ENVIRONMENTAL DYNAMISM

Several research streams focus on the fundamental relationships among structure, performance,

and environment. One general argument is that organizations with too little structure are too

confused and lack efficiency, while organizations with too much structure are too constrained

and lack flexibility. By contrast, moderate structure balances between these two states and so is

likely to be high performing (Weick, 1976; Brown and Eisenhardt, 1997). Support for this

general argument emerges in several literatures. Studies in network sociology point to the

“paradox of embeddedness” wherein moderately connected actors outperform those who are

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either less or more connected (Uzzi, 1997; Baum, Calabrese, and Silverman, 2000; Owen-Smith

and Powell, 2003). Uzzi (1997) found that firms in the garment industry that combined more and

less structured partnerships were more effective than those firms that used only one type.

Similarly, studies of partially connected technology standards (Garud and Jain, 1996) and

“leaky” networks in the Boston-area biotechnology field (Owen-Smith and Powell, 2003)

suggest that balancing too much and too little structure improves industry-level performance.

The argument for structural balance is also supported in areas of organizational studies in which

loose coupling, ambidexterity, and improvisation are key, including creativity (Amabile, 1996),

innovation (Davis, 2009), group problem solving (Bigley and Roberts, 2001; Okhuysen and

Eisenhardt, 2002), organizational change (Tushman and O'Reilly, 1996; Gilbert, 2005), and

organizational learning (Tripsas, 1997; Hansen, 1999). For example, Brown and Eisenhardt

(1997) found that high-tech firms with a moderate number of simple rules (i.e., semi-structure)

are more flexible and efficient—quickly creating high-quality, innovative products while

responding to market shifts—than firms with more or fewer rules.

In the strategy literature, there is also support for this argument in studies of vertical integration

(Schilling and Steensma, 2001; Rothaermel, Hitt, and Jobe, 2006), loose internal coupling

(Galunic and Eisenhardt, 2001; Williams and Mitchell, 2004; Martin and Eisenhardt, 2010),

innovation (Katila and Ahuja, 2002; Fleming, Sorenson, and Rivkin, 2006), and moderately

structured capabilities with simple rules (Burgelman, 1996; Bingham, Eisenhardt, and Furr,

2007). Rindova and Kotha (2001) found that Yahoo’s initially high performance in a dynamic

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environment was partially due to its simple-rules structure for the critical process capabilities of

acquisitions and alliances.

More broadly, research in the complexity sciences also examines the tension between too much

and too little structure. A repeated finding is that moderately structured computational systems

evolve more effectively than systems with too little or too much structure (Kauffman, 1989;

Langton, 1992; Gell-Mann, 1994). A related finding is that systems tend to fall away from the

optimal “edge-of-chaos” amount of structure into catastrophes without constant intervention

(Anderson, 1999; Eisenhardt and Bhatia, 2001). In the language of nonlinear dynamics (Strogatz,

2001), the optimal structure is often an unstable or dissipative critical point that is difficult to

maintain. Overall, these literatures suggest the following well-known proposition:

Proposition (P1): Performance has an inverted-U shaped relationship with the amount of

structure.

Several streams of research also focus on how environmental dynamism influences the

relationship between the amount of structure and performance. The general argument is that as

the environment becomes more dynamic, it becomes advantageous for the organization to be

more flexible and so less structured. Conversely, as the environment becomes less dynamic,

greater efficiency and so more structure are preferred. This general argument finds extensive

support in a number of literatures. Contingency theory (Lawrence and Lorsch, 1967; Thompson,

1967; Galbraith, 1973) is particularly prominent. In an early study, Burns and Stalker (1961)

found that a more structured mechanistic organization (e.g., role specialization, centralization,

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and formalization) is high performing in stable environments because it is highly efficient in

these routine situations. In contrast, a less structured organic organization (e.g., decentralized

decision making, broader and more fluid roles, wider span of control) is high performing in

dynamic markets because it enables flexible action. Similarly, Eisenhardt and Tabrizi (1995)

found that more structure (e.g., planning, numerous and well-defined process steps,

specialization) is faster and more effective for innovation processes in the stable mainframe

computing industry, whereas less structure and more improvised action (e.g., prototyping) is

better in the dynamic personal computing industry. Pisano (1994) found a similar contrast for

new process development in the dynamic biotech industry vs. the stable chemical industry.

The argument is supported by strategy research that has found less structured emergent strategies

to be higher performing in dynamic environments, whereas more structured deliberate strategies

work better in stable ones (Mintzberg and McHugh, 1985). Similarly, network studies have

shown that that loosely coupled networks are more effective in highly dynamic industries

(Tushman and Katz, 1980; Uzzi, 1997; Ozcan and Eisenhardt, 2008). Rowley, Behrens, and

Krackhardt (2000) observed that the high-performing firms in the dynamic semiconductor

industry have loosely coupled alliance networks, whereas high-performing firms in the stable

steel industry have more structured dense networks. Overall, these literatures suggest the

following well-known proposition:

Proposition 2 (P2): As environmental dynamism increases, the optimal amount of structure

decreases.

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Central to the underlying theory of these two propositions is the insight that the amount of

structure influences both efficiency and flexibility, but in opposite directions (Gibson and

Birkinshaw, 2004). By efficiency, we mean the rapid, less costly, mistake-free execution of

opportunities like new products, new market entry, or new acquisitions (Miller and Friesen,

1980; Adler, Goldoftas, and Levine, 1999). Structure creates the framework that enables reliable,

rapid, smooth execution in well-grooved routines that is efficient. In contrast, flexibility refers to

open, fluid execution of these opportunities (Weick, 1993; Sine, Mitsuhashi, and Kirsch, 2006).

Removing structure creates latitude for improvisation that is flexible. In dynamic environments,

high performance depends on balancing the tradeoff between flexibility and efficiency.

But though these general theoretical arguments are widely understood, unresolved issues remain.

First, the empirical evidence for an inverted-U shaped relationship is modest, consisting of

qualitative case comparisons (Brown and Eisenhardt, 1997; Gilbert, 2005), and quantitative

statistical tests of quadratic functions or interactions between efficiency and flexibility that are

not precise enough to determine that the relationship is, in fact, an inverted-U (Hansen, 1999;

Gibson and Birkinshaw, 2004; Rothaermel, Hitt, and Jobe, 2006). The evidence does not rule out

other shapes and functional forms that may have critical theoretical and practical consequences.

For example, if the shape is a broad plateau, such that there are a variety of high-performing

structures, then it is easy and unimportant to find the optimal structure. Conversely, if the shape

is an inverted-V, such that there are only a few high-performing structures, then the optimal

structure is challenging to find and crucial to maintain. An inverted-U relationship also requires

very specific functional forms, the simplest being that structure has linear relationships (and

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opposite slopes) with efficiency and flexibility. But there is no clear theory for why these

relationships would be, for example, linear.

A second unresolved issue is that the theory underlying the relationship between structure and

performance is incomplete, particularly the theoretical logics tying structure with efficiency and

flexibility.1 Neglected considerations such as attention limits, mistakes, and the fleeting, varied

nature of opportunities suggest that these relationships are more complex than extant theory

indicates. For example, structure improves efficiency by constraining the behaviors of

organizational members within well-established guidelines determined by rules, roles, reporting

relationships, and other forms of structure (Feldman and Pentland, 2003; Rivkin and Siggelkow,

2003). Siggelkow’s (2001) study of Liz Claiborne provides an illustration. Here, executives

created organizational structures (e.g., hierarchies, rules, roles) to address a series of product

opportunities in the apparel industry. Rules were a particularly key form of structure that guided

basic decisions. For example, rules about apparel design stipulated that each season’s clothing

line comprise four to seven concept groups, sizes should be the same across styles, and colors

should not change across years. Together, these and other structures constrained organizational

actions and enabled Liz Claiborne to be highly efficient. Moreover, because Liz Claiborne

executives fit these structures to match specific environmental opportunities focused on a

growing number of professional women, the firm was able to execute a series of lucrative and

very related opportunities consistently, quickly, cheaply, and with few mistakes (Siggelkow,

2001).

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Although greater structure improves efficiency, the rate of improvement often declines, and the

range of opportunities that can be captured narrows as well. So organizations may be able to

execute specific opportunities efficiently but not diverse or higher-payoff ones. Brown and

Eisenhardt (1997) described a highly structured product development process that could rapidly

and flawlessly capture similar product opportunities but could not flexibly adjust to capture

highly profitable, new product opportunities. Similarly, Gilbert (2005) described how highly

structured, traditional newspaper firms were too rigid to execute new Internet opportunities,

whereas more loosely coupled ones were more successful. The key point is that increasing

structure can trap organizations in a few or low-payoff opportunities with a declining rate of

efficiency improvements. Organizational action becomes frozen, approaching a non-adaptive

state that complexity theorists call a “complexity catastrophe” (Kauffman, 1993; Anderson,

1999).

Similarly, the relationship between structure and flexibility is likely to be more complicated than

extant theory suggests. Decreasing structure increases flexibility because it gives executives

more degrees of freedom to operate (Weick, 1998; Gilbert, 2005). There is greater latitude of

action and thus a wider range of possible opportunities that can be addressed as managers

combine some structured actions and some actions improvised in real-time (Miner, Bassoff, and

Moorman, 2001; Davis, 2008). But in reality, improvised actions consume more attention than

rule-following actions because they require managers to figure out what actions to take (Hatch,

1998; Miner, Bassoff, and Moorman, 2001). Likely mistakes pose further demands on attention.

Because attention is constrained (March and Simon, 1958; Ocasio, 1997), it limits the number of

possible actions in a given time period. In other words, the benefits of flexibility depend on

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having enough attention to figure out what to do (Weick, 1998; Okhuysen and Eisenhardt, 2002).

As an example, Brown and Eisenhardt (1997: 15) described a high-tech firm with few rules,

priorities, and formal roles that “reveled in the excitement of panicked product development” but

engendered “enormous time wasting” and many mistakes. Though some participants enjoyed the

“Silicon Valley organic management,” this firm ultimately generated too many ineffective

products that were behind schedule. Thus limits of attention complicate the structure-flexibility

relationship.

Similarly, the fleeting nature of opportunities complicates the structure-flexibility relationship.

Although organizations could take enough time to engage in extensive trial-and-error actions to

capture any opportunity, opportunities actually have limited time windows in which they are

viable (D'Aveni, 1994). Moreover, mistakes during improvisation introduce time delays that are

particularly damaging because opportunities are fleeting (Tyre and Orlikowski, 1994; Perlow,

Okhuysen, and Repenning, 2002). Figuring out successful improvised actions becomes

especially difficult with low structure because so much is changing that it is hard to get

everything right at once (Moorman and Miner, 1998; Bingham, Eisenhardt, and Davis, 2009). As

structure decreases, action becomes increasingly chaotic, approaching a non-adaptive state that

complexity theorists call an “error catastrophe,” in which organizations make too few correct

actions to succeed (Reynolds, 1987; Kauffman, 1993).

A third unresolved issue is that the theory underlying the argument that more environmental

dynamism lowers the optimal structure is imprecise. Specifically, environmental dynamism is a

multidimensional construct. For example, environmental dynamism includes velocity—the speed

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or rate at which new opportunities emerge (Eisenhardt, 1989). The Internet bubble is a good

example of a high-velocity environment (Goldfarb, Kirsch, and Miller, 2007). But dynamism

also includes ambiguity—lack of clarity, such that it is difficult to interpret or distinguish

opportunities (March and Olsen, 1976). Nascent markets like nanotechnology are examples of

environments with high ambiguity (Santos and Eisenhardt, 2009). It also refers to

unpredictability—disorder or turbulence, such that there is no consistent pattern of opportunities.

Growth markets such as Web 2.0 and wireless services often have unpredictable opportunities.

Environmental dynamism can also include complexity—the number of opportunity

contingencies that must addressed successfully. Opportunities within “green” power, for

example, involve many scientific, regulatory, safety, and commercial aspects and so are highly

complex (Sine, Haveman, and Tolbert, 2005).

Although environmental dynamism is multidimensional, existing theory does not unpack how

different dimensions operate. Empirical research reflects this imprecision. Some research focuses

on specific environmental features such as unpredictability (Lawrence and Lorsch, 1967) and

ambiguity (March and Olsen, 1976). Other research mixes several dimensions together, such as

ambiguity and complexity, to describe environmental dynamism in an industry (Pisano, 1994).

Still other research uses a single term such as velocity but then actually combines multiple

dimensions such as unpredictability, ambiguity, and velocity (Eisenhardt, 1989). Adding to the

imprecision, these dimensions are often correlated in many actual environments. For example,

high-velocity environments can be unpredictable (Eisenhardt, 1989), and complex environments

can involve multiple ambiguities (Gavetti, Levinthal, and Rivkin, 2005). Unpacking the

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dimensions of environments, as we do in our simulation study, will provide a better

understanding of optimal structure in different environments.

METHODS

We used stochastic process modeling to study the structure-performance relationship in distinct

environments. This approach enables a custom design of the simulation because it is not

constrained by an explicit problem structure (e.g., cellular automata) (Davis, Eisenhardt, and

Bingham, 2007). Rather, it allows the researcher to piece together processes that closely mirror

the focal theoretical logic, bring in multiple sources of stochasticity (e.g., arrival rates of

opportunities), and characterize them with a variety of stochastic distributions (e.g., Poisson,

Gamma) (Law and Kelton, 1991).

Stochastic modeling is an effective choice for our research because the problem structure does

not fit well with any structured approach. This enables more accurate representation of our

phenomena rather than force-fitting them into an ill-suited structured approach.2 Further,

because our baseline theory is well established in the empirical literature, we enhance the

likelihood of realism by building a model from the ground up (Burton and Obel, 1995) and thus

mitigate a key criticism of simulation. This approach also enabled us to include several sources

of stochasticity that are theoretically important (e.g., improvisational action, opportunity flow)

and to experiment flexibly with theoretically relevant environmental dimensions (e.g., velocity,

ambiguity). Stochastic process modeling also has an influential tradition in our focal literatures,

such as the garbage can model (Cohen, March, and Olsen, 1972), dynamics of culture (Carroll

and Harrison, 1998), and exploration versus exploitation (March, 1991)3.

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Modeling Organization Structure and Environment

Our simulation model includes two primary components: organization structure and

environment. We modeled organization structure as rules. Though we could have used other

types of structure (e.g., roles, networks) or other aspects of structure (e.g., centralization,

verticality), we chose rules in order to create a parsimonious model that captures the fundamental

features of structure. As Burton and Obel (1995) explained, effective simulation reveals the

minimal elements of the problem at hand and so uses the least complex conceptualization that

still captures the essence of the phenomenon. That is, the model’s purpose is to represent the core

features of the phenomenon (e.g., organization structure), not be a literal replication of the

phenomenon (Lave and March, 1975; Rivkin and Siggelkow, 2003). As described earlier, rules

are a particularly important type of structure in dynamic environments (Burgelman, 1994; Brown

and Eisenhardt, 1997; Rindova and Kotha, 2001; Zott, 2003). They also fit especially well with

our research because rules directly relate to how structure generates actions to execute (or fail to

execute) environmental opportunities (Bingham, Eisenhardt, and Furr, 2007; Bingham,

Eisenhardt, and Davis, 2009). Rules are also very commonly used to represent structure in

simulations (e.g., Baligh, 2006) because of their direct link to action (March, Schultz, and Zhou,

2000; Eisenhardt and Sull, 2001). Thus our study follows a long, influential tradition of simple

yet powerful computational models that rely on rules to represent structure (Nelson and Winter,

1982; March, 1991; Rivkin, 2000).

We modeled the environment as a flow of heterogeneous opportunities, consistent with our

earlier discussion that organizational structure constrains action in the capture and execution of

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varying environmental opportunities (Burgelman, 1996; Eisenhardt and Martin, 2000; Miner,

Bassoff, and Moorman, 2001). Our focus on heterogeneous opportunities is also consistent with

the Austrian economics (Hayek, 1945; Kirzner, 1997) and entrepreneurship (Shane, 2000;

Schoonhoven and Romanelli, 2001) literatures in which environmental dynamism is also a core

interest. Conceptualizing the environment as a flow of heterogeneous opportunities also permits

a rich modeling of environmental dimensions. It enables us to unpack and explore environmental

dynamism more fully, a key theoretical aim of our research.

To capture heterogeneity, we modeled each opportunity as having 10 features that can be either 1

or 0 (e.g., 0101101101) and included four environmental dynamism dimensions, described

below. In contrast, many simulation models assume a fixed environment, a single environmental

jolt, or a single environmental dimension and so preclude the kind of rich exploration of

environmental dynamism that we seek. Although a parsimonious simulation is important (Burton

and Obel, 1995), the richness of the simulation should focus on the part of the model in which

the primary exploration will occur (Burton and Obel, 1995; Davis, Eisenhardt, and Bingham,

2007).

As in all research, we made several assumptions, some fundamental to our modeling. For

instance, we assumed that organizations take actions to capture opportunities, actions require

attention, and attention is limited (Ocasio, 1997). We also assumed that organizations use a

combination of rule-based and improvised actions and that improvised actions require more

attention than rule-based ones because they involve real-time sensemaking (Weick, 1993).These

17

assumptions are well grounded in field studies of improvisation (Brown and Eisenhardt, 1997;

Miner, Bassoff, and Moorman, 2001; Baker and Nelson, 2005).

Other assumptions are less essential to the theory simplify the model. For example, to focus on

the effects of structure on performance, not learning, we assumed that the rules have already

been learned and that adaptation to new opportunities occurs through improvised actions in real

time. This is consistent with empirical research showing that heuristics are learned quickly and

stabilize rapidly (Bingham, Eisenhardt, and Davis, 2009) and that real-time, improvisational

learning is often not retained in new heuristics (Weick, 1996; Moorman and Miner, 1998).

Similarly, to focus on effects of structure, we assumed that all rules are appropriate for at least

some opportunities. We also assumed that the effects of competitors are realized through the

flow of opportunities, an assumption that mirrors the Austrian economics argument that market

dynamism is endogeneously created through competitive interaction and technological

innovation (Kirzner, 1997).

In our model, the organization has a set of rules to capture opportunities in its environment. In

each time step, the organization takes a combination of rule-based and improvised actions to

attempt to execute a given opportunity. When enough of these actions match the opportunity, the

opportunity is captured, and firm performance increases by the value of the opportunity. Because

attention is limited, and actions (rule-based and improvised) consume attention, however, the

organization can take only a limited number of actions in each time step.

Environmental Dynamism

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We modeled four environmental dynamism dimensions based on our review of the structure-

environment research in the organizational and strategy literatures: velocity, complexity,

ambiguity, and unpredictability (Burns and Stalker, 1961; Lawrence and Lorsch, 1967; March

and Olsen, 1976; D'Aveni, 1994; Eisenhardt and Tabrizi, 1995). These four dimensions are

important, frequently used, and distinct from each other, though some research uses alternative

terms for them. This is particularly true of unpredictability. For example, instead of

unpredictability, terms like uncertainty, turbulence, and volatility are also used to capture the

same notion of disorder or dissimilarity in the environment. Terms like turbulence and volatility

focus particularly on disorder, while terms like unpredictability and uncertainty focus more on

the lack of pattern that disorder implies. Finally, though there may be other dimensions of

environmental dynamism, these four are among the most important. A strength of our model is

its rich representation of the environment.

Velocity is the speed or rate at which new opportunities emerge. The Internet bubble is an

example of an environment with a high velocity of opportunities. We operationalized velocity as

the rate that new opportunities flow into the environment (Eisenhardt, 1989; Eisenhardt and

Tabrizi, 1995). We used a Poisson distribution to model the stochastic arrival time of

opportunities into the environment where velocity is lambda, λ. A Poisson distribution, p(k),

describes the probability of k opportunities arriving in t time steps and is determined by the

single rate parameter λ:

p(k) = (λt)e-λt / k! (1)

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Poisson is a well-known probability distribution used to model arrival flow (Cinlar, 1975; Glynn

and Whitt, 1992). It is attractive here and in many simulations because it makes few assumptions

about the timing of opportunities (Law and Kelton, 1991). Although lambda can range from 0 to

infinity, we fixed an upper bound on the rate of execution because bounded rationality and

limited attention constrain the number of opportunities that can be addressed (March and Simon,

1958; Shane, 2000).

Complexity was operationalized as the number of features of an opportunity that must be

correctly executed to capture that opportunity. Complexity increases the difficulty of capturing

opportunities because organizations have less latitude for errors when there are numerous,

relevant contingencies (Gavetti, Levinthal, and Rivkin, 2005). Like computational complexity,

complexity can be conceptualized as the minimum number of correct steps that are needed to

execute a plan (Simon, 1962; Sipser, 1997). Biotechnology is an example of a high-complexity

environment because many features of the opportunity must be correct to achieve success (Hill

and Rothaermel, 2003). Complexity is an integer indicating the number of actions that must be

correct in order to execute an opportunity successfully. Because each opportunity has 10

features, complexity ranges from 0 to 10.

Ambiguity was defined as lack of clarity such that it is difficult to interpret or distinguish

opportunities. Because ambiguity makes the misperception of opportunities more likely (March

and Olsen, 1976), we operationalized environmental ambiguity as the proportion of perceived

opportunity features that differ from actual ones. Nascent markets like nanotechnology are

typically highly ambiguous (Santos and Eisenhardt, 2009). The actual features of an opportunity

20

are represented by a 10-element bit string (i.e., vector) of 1s and 0s—e.g., 0100100110. The

misperceived features of the same opportunity are also a 10-element bit string of 1s and 0s but

differ from the actual features by those features for which perception does not match reality—

e.g., 0110100110. Ambiguity was operationalized as the proportion of misperceived opportunity

features. For example, the actual and perceived features of the two bit strings above differ by one

element of 10, so the ambiguity = .1. This is an especially useful way to model ambiguity

because it allows us to capture the difficulty of interpretation that leads to misperception of

opportunities. Ambiguity ranges from 0 to 1.

Unpredictability was defined as the amount of disorder or turbulence in the flow of opportunities

such that there is no consistent similarity or pattern. An implication of increasing unpredictability

is that managers are less able to adjust or “tune” their structures to the environment because there

is less pattern to match (Galbraith, 1973).4 We manipulated unpredictability by changing the

probability that any opportunity feature will be a 1 or a 0—i.e., p(1) and p(0). Opportunities with

features that have a higher probability of 1 or 0 are less unpredictable than opportunities with

features having an equal probability of 1 or 0. This approach has the advantage of stochastically

generating similar opportunities without the researcher’s bias as to what those patterns should be.

To have a monotonically increasing measure of unpredictability, we converted these probabilities

using a well-known disorder computation from mathematical information theory (Cover and

Thomas, 1991). Unpredictability, U, of a flow of opportunities depends on the probability, p, of a

feature being either a 1 or a 0 and is given by:

21

U = - ∑ p * log2(p) (2)

To illustrate, when p(1) = .7 and p(0) = .3, then unpredictability is relatively low. There is a

70/30 split of 1s and 0s in the features vector of each opportunity (making 1s more likely than

0s) such that U = –.7*log2(.7) + .3*log2(.3) = .88. By contrast, when unpredictability is high

[p(1) = p(0) = .5 and U = 1], the distribution of 1s and 0s in the opportunity features is random.

Both opportunities and rules have a 50/50 split of 1s and 0s (making 1s and 0s equally likely),

and there is no consistent similarity or pattern in the flow of opportunities. Unpredictability

ranges from 0 to 1.

Organizational Structure as Rules

We modeled structure as a set of rules for capturing opportunities, with each rule specifying

particular actions for executing opportunities. Rules as structure are common in our focal

literatures. For example, Galunic and Eisenhardt (2001) described rules for carrying out

“patching” opportunities in a high-performing, multi-business corporation, including that new

product-market charters should always be assigned to business units that (1) have relevant

product-market experience and (2) are currently assigned charters with shrinking markets or

fading profit margins. Similarly, Rindova and Kotha (2001) described rules for executing

alliance opportunities at Yahoo!, such as (1) making the basic service free and (2) having no

exclusive deals. Overall, rules specify actions for addressing opportunities and are central to

organizational processes and capabilities such as interfirm collaboration, product development,

and country entry (Burgelman, 1996; Eisenhardt and Sull, 2001; Rindova and Kotha, 2001;

Bingham, Eisenhardt, and Furr, 2007; Davis, 2008).

22

Rules were operationalized with a 10-element vector of 1s, 0s, and ?s (e.g., 0?1?10???0). When

an organization attempts to execute an opportunity with a rule, it generates 10 specific actions.

That is, each 1 or 0 generates a rule-based action in that position. The proportion of 1s and 0s in

a rule was set equal to the probability of 1s and 0s in the flow of opportunities. This captures the

insight noted earlier that organizations can adjust their structures to approximately match

patterns in the flow of opportunities if they exist (March and Simon, 1958). Additionally, for

each “?” the organization improvises either a 1 or 0 “improvised action” with a 50/50 likelihood.

For example, a combination of rule-based and improvised (underlined) actions using the rule

above could produce the vector 0111100110. The computer program then compares this set of 10

actions to the opportunity’s 10 features. If the number of actions (both rule-based and

improvised) that match the actual features of the opportunity equals or exceeds the value of the

environmental complexity parameter, then the opportunity is executed and the firm gains the

payoff value of that opportunity. For example, if complexity = 6 and the actions above—

0111100110—are compared to the opportunity 0110101010, then the opportunity is successfully

executed because 7 of the actions were correct. This operationalization captures the idea that

structure constrains some actions, while others are left open to improvisation (Brown and

Eisenhardt, 1997; Miner, Bassoff, and Moorman, 2001).

Amount of structure. We operationalized the amount of structure as simply the number of rule-

based actions specified by each rule (i.e., number of 1s and 0s). For example, the amount of

structure in the rule 01?0??011? is 6. Thus increasing the amount of structure for an

organization’s set of rules increases their constraint on action. For ease of exposition, we term

rules with little to moderate structure (i.e., 3 to 5) simple rules. This operationalization is

23

consistent with theoretical notions of structure such as Simon’s (1962) and Daft’s (1992), in

which the amount of structure is associated with the number of components. It is in contrast to

some prior research (Rivkin and Siggelkow, 2003) emphasizing the interactions among structural

features and putting less emphasis on the number of structural features. By emphasizing the

number of structural features, we focus on the amount of structure in rules. Structure, however,

constrains action in both. Thus, for the same research questions, the results should be

qualitatively consistent.

Performance. Each opportunity is associated with a randomly determined payoff value.

Performance was operationalized as the sum of all payoffs from every opportunity executed,

across all time steps. This is particularly appropriate for our research because it is consistent with

the empirical studies of dynamic environments indicating that performance is derived from a

series of temporary advantages and related payoffs (D'Aveni, 1994; Roberts, 1999; Rindova and

Kotha, 2001; Chen et al., 2009).

Simulating the Model

We implemented this model in Matlab software. The computer program flow is outlined below,

and the Technical Appendix provides more details. In the beginning, the organization’s structure

(i.e., its rules) and environment (i.e., flow of heterogeneous opportunities determined by the

velocity, complexity, ambiguity, and unpredictability parameters) are randomly initialized using

draws from probability distributions (Law and Kelton, 1991). In each time step, opportunities

flow into the environment at velocity lambda. When the organization tries to capture an

opportunity with a rule, the organization generates both rule-based and improvised actions.

24

When the number of these actions that match the opportunity is greater than the environmental

complexity, the opportunity is executed and performance increases by the payoff value.

As discussed above, the firm’s actions (both rule-based and improvised) require attention, which

is limited (Cyert and March, 1963; Ocasio, 1997), so the organization has a limited number of

actions that it can take in any time step. When attention runs out, the organization can take no

further actions. At the end of t = 200 time steps, the simulation run ends and performance is

computed. We chose this number of time steps because it is large enough to allow sufficient

opportunities to flow into the environment such that any initialization effects on the findings are

mitigated (Law and Kelton, 1991), but we also experimented with multiple values for the amount

of attention required for improvised action relative to rule-based action, as described further in

the Technical Appendix. We found no qualitative differences in the findings and so present the

results for this representative value.

Monte Carlo Simulation Experiments

We used Monte Carlo simulation techniques. In the Monte Carlo approach, an experiment is a

simulation with fixed parameter settings that is run multiple times (Law and Kelton, 1991). The

results are then averaged and confidence intervals calculated (Kalos and Whitlock, 1986). Thus

for any given experiment, the result is the mean performance (and confidence interval) over

multiple simulation runs, which better reflects the underlying processes under investigation than

those produced by a single simulation run.

25

Each experiment consists of 30 or 50 simulation runs. We selected n = 30 as the number of

simulation runs for all experiments, except those on the basic relationship between structure and

performance, because exploratory analyses revealed that values of n greater than 30 yielded

insignificantly small incremental gains on reliability. We used n = 50 for the basic relationship

between the amount of structure and performance because the larger range of structure values

adds precision to our illustration of this relationship. These results are representative of the

findings produced by other construct values during our exploration of the parameter space (see

the Technical Appendix for more details).

We ran experiments for a wide range of values for each environmental dimension (e.g., velocity).

Given space limitations, we report only relationships using representative low and high values

from those experiments. Specifically, we plotted the relationship between the amount of structure

and performance for these representative values of the environmental dimensions.5 Confidence

intervals in the form of error bars (i.e., the square root of the variance over the number of trials)

are included to enable more accurate statistical interpretation of the results, as is standard in

Monte Carlo experiments (Kalos and Whitlock, 1986).

RESULTS

Amount of Structure and Performance

[Figure 1 about here]

We begin by examining the two propositions that form the baseline theory. P1 proposed that the

amount of structure has an inverted U-shaped relationship with performance. Figure 1 plots the

relationship between performance and the amount of structure, with each point representing the

26

average over 50 simulations. The results show that organizations with low or high structure rules

perform worse than those with moderate structure (optimal structure at a value of 3). Optimal

structure exists, but unexpectedly, the curve is asymmetric. That is, the performance decline

from the left endpoint to the optimum is steeper than the performance decline from the right

endpoint to the optimum.6 Within the bounds of these simulation experiments, too much

structure produces a more gradual decline, while too little structure produces a steeper drop in

performance for all deviations from the optimum. Thus there is an asymmetric relationship,

which suggests a more complicated theoretical logic than a simple tension between too much and

too little structure.

Our model offers some insight into this logic. In particular, rule-based actions are relatively

automatic, and so they conserve attention. This enables more actions in a given time frame to

capture additional opportunities. So although more structure narrows the range of potential

opportunities that can be addressed, there is an “attention advantage” of added structure that

partially compensates. This advantage occurs at relatively high values of structure across a broad

range of environmental conditions and so favors erring on the side of structure in these

environments. This suggests the following modified proposition:

Proposition 1a (P1a): Performance has a unimodal, asymmetric right relationship with the

amount of structure.

Unpacking the Dimensions of Environmental Dynamism

27

P2 proposed an environmental contingency that the optimal amount of structure decreases with

increasing environmental dynamism. We used four experiments to understand which dimensions

explain this shifting optimum: we examined P2 by comparing curves with high and low values of

each dimension of environmental dynamism (i.e., velocity, complexity, ambiguity, and

unpredictability) while holding the other three constant at moderate values.

Environmental velocity. Figure 2 depicts the effect of increasing environmental velocity (i.e.,

rate of opportunity flow) on performance by superimposing the resulting curves of two

representative values. That is, we plotted the results that correspond to low and high values of

velocity (λ = .6 and 1.4) to examine the effects of velocity. P1a is roughly supported in both

environments.

[Figure 2 about here]

In contrast, the results do not support P2. Within the precision of this simulation experiment, the

optimal amount of structure—i.e., the amount of structure producing the highest performance—

is the same for both high- and low-velocity environments. Further, although the optimal amount

of structure is the same in the two velocity conditions, their performance is not. For a given

amount of structure, firms in high-velocity environments have higher performance than those in

low-velocity ones. In fact, increasing velocity appears to amplify performance and shift the

entire curve upward. Overall, this suggests that the large number of opportunities that emerge in

high-velocity environments (e.g., Internet bubble, Web 2.0) yields better performance for all

levels of structure, other things being equal.

28

[Figure 3 about here]

Environmental complexity. Figure 3 depicts the effects of increasing environmental

complexity (i.e., the difficulty of capturing opportunities, given numerous relevant

contingencies) on performance by superimposing the results of representative low and high

values of complexity (4 and 8). P1a is roughly supported in both high- and low-complexity

environments by unimodal, asymmetric curves. P2 is again not supported. Within the precision

of this simulation experiment, the optimal amount of structure is the same for both high and low

environmental complexity. Performance at the optimal structure differs in the two environments,

however, with increasing complexity shifting the curve downward. Firms perform worse in high-

complexity environments in which opportunities involve many contingencies (e.g., “green”

power, biotechnology), in contrast to the velocity findings.

[Figure 4 about here]

Environmental ambiguity. Figure 4 shows the effect of increasing environmental ambiguity

(i.e., lack of clarity of opportunities) on performance by superimposing the results of the two

representative cases that correspond to low and high values of ambiguity (0 and 0.2). P1a is

again roughly supported in both environments: the curves have unimodal, asymmetric shapes.

P2 is again not supported. The optimal amount of structure is the same in both low- and high-

ambiguity environments within the precision of this simulation experiment. Yet both the range of

29

optimal structures and the peak performance at the optimal structure differ in the low- versus the

high-ambiguity environments. When ambiguity is low, there is a narrow range of optimal

structures and a higher level of peak performance. This suggests an environment in which it is

difficult for managers to find and maintain an optimal structure, but they will achieve

particularly high performance when they do. To the extent that skilled executives more easily

locate and maintain the optimal structure, this is consistent with a skill-dominated environment.

In contrast, when ambiguity is high, as in nascent markets, there is a wide range of optimal

structures and lower peak performance. This suggests an environment in which it is easy for

managers to find and maintain an optimal structure, but they will not achieve particularly high

performance. This suggests a chance-dominated environment.

[Figure 5 about here]

Environmental unpredictability. Figure 5 illustrates the effects of environmental

unpredictability (i.e., disorder in the flow of opportunities) on performance by superimposing the

results of two representative cases of low and high unpredictability (U = .72 and 1). Again, a

unimodal, asymmetric relationship, supporting P1a, is found in both environments. But unlike

the results for velocity, complexity, and ambiguity, we find a shifting optimum, as predicted by

P2, as the optimal amount of structure decreases with higher unpredictability. Thus

unpredictability is the environmental dimension that shifts the optimal amount of structure.

Moreover, our model offers insight into the logic: the optimal structure decreases with increasing

unpredictability because managers are less able to adjust structure to fit the environment when

the presence of consistent patterns in the opportunity flow declines. In these environments,

30

managers must rely more on real-time improvised actions and less on structure because there is

less pattern in the environment that can be mirrored in organizational structure. This suggests a

modified proposition:

Proposition 2a (P2a): As environmental unpredictability increases, the optimal amount of

structure decreases.

There are also unexpected findings related to the range of optimal structures. As figure 5 shows,

when environments have low unpredictability, the relationship between structure and

performance forms a broad plateau. This suggests a forgiving environment in which there is a

wide range of optimal structures with roughly the same performance outcomes. In contrast, when

environments have high unpredictability, there is an inverted-V relationship between structure

and performance. This suggests a punishing environment in which there is a narrow range of

optimal structures, such that it is challenging to find the optimal amount of structure, hard to

maintain the optimal structure even when perturbations of structure are small, and very low

performance when the optimal structure is not achieved. Even small changes in structure have

large effects on performance, consistent with an edge of chaos in which only a narrow range of

structures leads to superior performance. Thus, in contrast to forgiving low-unpredictability

environments, high-unpredictability environments are punishing, with a narrow range of optimal

structures.

Analyzing mistakes. Because mistakes are likely to be relevant in a more complete theoretical

logic linking structure, performance, and environment, we next examined mistakes. We define a

31

mistake as an application of any action (rule-based or improvised) to an opportunity feature that

does not match, and mistake size as the number of mistakes (i.e., count of mismatches of actions

with opportunity features) committed in an attempt to capture an opportunity.

We computed the frequency distributions of mistake size, focusing on unpredictability because of

its role in shifting the optimal structure. We ran the simulation at multiple unpredictability and

structure settings and then tabulated the number of attempts to capture an opportunity for each

mistake size. As shown in figure 6, we have nine values of structure, from low = 1 to high = 9,

down the rows (omitting the value of 10 because it produced undefined endpoint values), and

three values of unpredictability—high, low, and very low (U = 1, .72, and .47)—across the

columns. The sum of each distribution is normalized to 1 for easy comparison across

distributions. Each of the resulting 27 distributions is a mini-graph that plots the proportion of

attempts to capture opportunities at each mistake size for specific values of unpredictability and

structure.

[Insert Figure 6 about here]

The mistakes analysis sheds light on the theoretical logic for why the range of optimal structures

decreases (i.e., from a broad plateau to an inverted-V) as unpredictability increases. First, in low-

unpredictability environments (column 2 in figure 6), the analysis indicates that increasing

structure reduces the mean mistake size and eliminates large mistakes. These trends are

accentuated in environments with very low unpredictability (column 3 in figure 6). The

underlying reasoning is as follows. When unpredictability is low, opportunities are more

32

homogeneous and there are recognizable patterns occurring in the opportunities. This

predictability allows managers to adjust their structures to more closely fit the opportunities. So a

structured action is more likely to be successful for capturing an opportunity. This means that

although increasing structure narrows the range of opportunities that can be addressed, the

elimination of large mistakes and the drop in mean mistake size partially offset this

disadvantage, such that there is a “mistakes advantage” for structure in less unpredictable

environments. This suggests a relatively broad range of successful structures (i.e., plateau) in

low-unpredictable environments, as observed in figure 5.

In contrast, in high-unpredictability environments, the mistakes analysis indicates that

organizations at all levels of structure are likely to commit multiple mistakes of varying size,

including some very large mistakes (column 1 in figure 6). When unpredictability is high,

opportunities are very heterogeneous and there is very little pattern in the flow of opportunities.

Thus managers cannot adjust their structures to fit environmental opportunities because they do

not know what those opportunities will be. The result is mistakes of varying sizes (even large

ones) at all levels of structure, including the optimal structure. So there is no “mistakes

advantage” for structure that compensates for the loss of flexibility when structure is added.

Rather, there is a narrow range of optimal structures, making the tradeoff between efficiency and

flexibility more severe in highly unpredictable environments.

Modeling structure and performance. To gain added theoretical insights, we next created a

simple mathematical formalization. This model formulates the theoretical logics of efficiency,

33

flexibility, and unpredictability more precisely in terms of specific functional forms (Davis,

Eisenhardt, and Bingham, 2007).7

Let e(x) and f(x) represent efficiency and flexibility as functions of structure, respectively. Prior

researchers have argued that efficiency and flexibility have interdependent, non-substitutable

effects on how structure influences performance (Adler, Goldoftas, and Levine, 1999; Gibson

and Birkinshaw, 2004) in which the aggregate effect on performance, A(x), is a roughly inverted

U-shaped curve of the following form:

A(x) = e(x)*f(x). (3)

Yet not all e(x) and f(x) functions produce a unimodal A(x) curve and shift the optimal structure,

x’, as unpredictability increases. As shown in the Mathematical Appendix, the requirements for

such a curve and shifting optimum put strong constraints on the forms of e(x) and f(x).8

Consistent with our mistakes analysis and prior research, we assume that increasing structure

increases efficiency—i.e., e’ (x) > 0 (Brown and Eisenhardt, 1997; Siggelkow, 2001)—such that

more structure enables faster, more reliable execution of those opportunities for which the

structure is appropriate. But as structure increases, the number of opportunities that fit the

structure decreases, and the gains to efficiency of economizing on attention grow more slowly

(Donaldson, 2001). So there are likely to be decreasing efficiency returns for added increments

of structure that we capture with a logarithmic function of efficiency:

34

e(x) = ln(x) (4)

The logarithmic form of e(x) satisfies the important condition that e’(x) > 0 because e’(x) = 1/x >

0 for x > 0 and captures the intuition that efficiency increases, albeit at a declining rate, as

structure increases.

Conversely, the literature suggests that flexibility declines as structure increases—i.e., f’(x) < 0

(Brown and Eisenhardt, 1997; Miner, Bassoff, and Moorman, 2001). On the one hand, less

structure enables organizations to use improvised actions to address more different opportunities.

On the other hand, more structure constrains improvised actions, forces more rule-based actions,

and limits the heterogeneity of opportunities that can be addressed (Weick, 1993; Baker and

Nelson, 2005). Empirical studies of structural inertia have found that this decline in flexibility

occurs most dramatically at low levels of structure, at which even small additions of structure

can greatly constrain organizational actions (Greve, 1999). This is consistent with the argument

that the effect of incremental additions of structure is to eliminate successive fractions of

opportunities that could have been flexibly addressed by less structure. This implies that

flexibility is rapidly declining and inversely proportional to structure, a relationship that we

capture as follows:

f(x) = 1/x (5)

This function satisfies the important condition that f’(x) < 0 because f’(x) = –1/(x^2) < 0 for x >

0. As described in the Mathematical Appendix, this function is a particularly appropriate choice

35

because it captures the effect of eliminating successive fractions of opportunities with each

increment of structure. Finally, because efficiency and flexibility are interdependent and non-

substitutable (Gibson and Birkinshaw, 2004), aggregate performance is:

A(x) = ln(x)/x (6)

Though other functional forms for efficiency and flexibility may be possible, this A(x) produces

a unimodal, asymmetric right relationship between structure and performance that is consistent

with our simulation results and theory, as noted in the Mathematical Appendix.9

Next, we move to unpredictability. Though researchers have simply argued that flexibility

becomes more influential than efficiency as environmental dynamism increases, we show in the

Mathematical Appendix that simply increasing flexibility does not shift the optimal structure.

Instead, unpredictability, u, has two separate effects on performance that shift the optimum.

First, as unpredictability increases, the heterogeneity of opportunities increases. Organizations

with less structure can potentially capture at least some of these more varied opportunities

through improvisation. But executing these additional opportunities critically depends on having

the greater latitude of action (i.e., flexibility) that less structure provides and so is inversely

proportional to structure, 1/x. Also, though additional opportunities can be addressed, the number

of opportunities that can be captured grows increasingly slowly as unpredictability increases.

The reason is that less structure slows down improvisation and takes more attention because the

number of opportunity features that must be successfully improvised at once grows. So although

36

there are more opportunities available, the number of additional opportunities that can be

successfully captured increases at a decreasing rate. We represent this increasing difficulty with a

logarithmic function of unpredictability, ln(u). Thus we model the added performance

improvement that occurs with increasing unpredictability by ln(u)/x. Combining this effect with

A(x) changes performance to A(x) + ln(u)/x = ln(x)/x + ln(u)/x = ln(ux)/x.

Second, as unpredictability increases, it becomes more challenging to capture opportunities

regardless of whether improvised or rule-based actions are used. Adding structure is ineffective

in this environment because there is little predictable pattern in the flow of opportunities that

managers can use to adjust their organizational structures to the environment. Subtracting

structure is helpful, as noted above, in terms of adding opportunities that can potentially be

addressed. But it is also harmful because improvisation is more difficult. Improvisation demands

more attention, has more degrees of freedom, and generates many mistakes (including large

ones) and so becomes more challenging as unpredictability increases. We represent this overall

declining performance with a dampening parameter, 1/u. Adding this second effect of

unpredictability generates a performance function, P(x,u):

P(x,u) = 1/u [ln(ux)/x] = ln(ux)/ux (6)

As noted in the Mathematical Appendix, this function satisfies the conditions for P1a, generating

a unimodal, asymmetric right relationship between structure and performance. It also satisfies the

conditions for P2a that as unpredictability, u, increases, the optimal structure, x’ = e/u, decreases.

Overall, the mathematical model is consistent with our simulation results and theory.

37

This mathematical model offers several useful extensions. First, it clarifies the approximate

functional forms and rates of change of efficiency and flexibility that contribute to the

asymmetry between structure and performance. Performance is asymmetric because efficiency

and especially flexibility are changing more rapidly at low structure than at high. When structure

is low, even small increments in structure create large increases in efficiency, ln(x), and large

decreases in flexibility, 1/x. Thus there is a severe tradeoff between efficiency and flexibility. In

contrast, when structure is high, performance is much less sensitive to structure. Efficiency

improves very gradually with added structure. Flexibility is already so low that increases in

structure have little effect. Thus there is only a modest tradeoff between efficiency and

flexibility. Overall, having too little structure is particularly risky because efficiency and

flexibility are highly sensitive to even small changes in structure when structure is low.

Second, this model clarifies the inverted-V curve and related edge of chaos in highly

unpredictable environments. According to prior research, less structure is better in highly

dynamic environments because flexibility is more advantageous than efficiency. In contrast, a

core insight of our model is that neither efficiency nor flexibility works very well in highly

unpredictable environments. As expected, extensive structure and so efficiency are ineffective

because they are overly rigid. But unexpectedly, improvised actions and so flexibility are not

very effective either. With so little structure, improvisation consumes a lot of attention, is fraught

with mistakes, and is very slow. As a result, the organization can only capture a few

opportunities, and risks falling into an “error catastrophe,” in which it lacks enough traction to

improvise fast enough to capture opportunities before they disappear. So the optimal structure is

38

a narrow range (i.e., at the edge of chaos) of just enough structure to capture at least a few

opportunities.

DISCUSSION AND CONCLUSION

[TAB 1]

Using computational and mathematical modeling, we added to theory on the fundamental

relationships among structure, performance, and environment. As summarized in table 1, our

core contribution is a more precise theory of how the locus, asymmetry, and range of optimal

structures are grounded in the tradeoff between efficiency and flexibility in differing

environments. First, we clarify this tradeoff between flexibility and efficiency. Prior theory

focuses on balancing efficiency and flexibility (Tushman and O'Reilly, 1996; Brown and

Eisenhardt, 1997; Uzzi, 1997; Rowley, Behrens, and Krackhardt, 2000). In contrast, we find that

this tradeoff is more accurately the flexible capture of widely varying opportunities vs. efficient

execution of specific opportunities.10 Less structure opens up the organization to the possibility

of addressing a wider range of opportunities that serendipitously occur, but it also hinders the

rapid, mistake-free execution of those opportunities. Conversely, more structure enables the

efficient execution of particular opportunities that can be anticipated. But too much structure is

more than just too rigid. It also narrows the range of possible opportunities, suggesting that

structure is most valuable when many similar opportunities are available.

Second, the relationship between structure and performance is unexpectedly asymmetric:

performance gradually fades with too much structure but drops catastrophically with too little.

Thus structure and performance do not have an inverted-U relationship, as argued previously

39

(Brown and Eisenhardt, 1997; Gibson and Birkinshaw, 2004; Rothaermel, Hitt, and Jobe, 2006).

Rather, efficiency and flexibility are distinct functions that change increasingly slowly when

structure is high. In contrast, efficiency and especially flexibility are changing more rapidly

when structure is low, creating a more acute tradeoff between efficiency and flexibility. The

consequential implication is that it is safer to err on the side of too much structure (efficiency)

than on the side of too little (flexibility).

Third, our results show that simple rules and other semi-structures are surprisingly robust across

multiple environments, in contrast with research arguing that they are best only in highly

dynamic environments (Burns and Stalker, 1961; Rowley, Behrens, and Krackhardt, 2000;

Eisenhardt and Sull, 2001).11 In predictable environments, there is a broad plateau of optimal

structures, and so numerous high-performing structures exist. The tension between too much and

too little structure is easy to manage in this forgiving environment in which many structures are

roughly equivalent. So executives can rely on simple rules, loose coupling, and other semi-

structures that favor flexibility (albeit with more attention and mistakes) or elaborate structures

with tight coupling that favor efficiency (albeit with a narrower range of opportunities) without

sacrificing much performance. For example, executives who need to minimize mistakes (e.g.,

nuclear power plants, aircraft carriers) can design highly reliable organizations that utilize very

extensive structure (Perrow, 1984; Weick and Roberts, 1993) with little performance penalty.

In contrast, in unpredictable environments, there is an inverted-V relationship between structure

and performance with only a narrow band of optimal structures. Even minor perturbations in

structure can be catastrophic in these punishing environments in which performance is precarious

40

and mistakes can be many, large, and fatal. The tension between too much and too little structure

is challenging and crucial to manage. The mistakes advantage of structure vanishes, and

improvisation is difficult. Here, only simple rules are high performing. The overall implication is

that simple rules and other semi-structures are robust across diverse environments—i.e., they are

viable in predictable environments and essential in unpredictable ones.

Underlying the robustness of simple rules across environments are the dynamics of

unpredictability that shape the locus and range of optimal structure. Prior research has included

velocity (Eisenhardt, 1989), complexity (Gavetti, Levinthal, and Rivkin, 2005), and ambiguity

(March and Olsen, 1976; Rindova and Kotha, 2001) as major dimensions of environmental

dynamism. But though these dimensions have intriguing implications for strategy and

performance (see below), only unpredictability influences optimal structure. Underlying this

finding is the insight that structure is valuable when there are consistent patterns in the flow of

environmental opportunities and when managers have adjusted their structures to match these

patterns. But as our simulation suggests, these tuning adjustments need not be exactly accurate.

Rather, sometimes matches may occur by chance, and sometimes structure helps just by

diminishing the degrees of freedom in mistake-prone improvisation. The key implication is that

adding structure when unpredictability decreases can be valuable (or at least not harmful), even

when it is not completely clear what exactly that structure should be. Thus our results support a

structural explanation for Weick’s (1990) well-known observation of the success of a European

army in navigating the Alps based on a map of the Pyrenees (see also Gavetti, Levinthal, and

Rivkin, 2005).

41

A particularly intriguing optimum in the structure-performance-environment relationship is

simple rules in highly unpredictable environments. Prior researchers have argued that favoring

flexibility leads to high performance (Burns and Stalker, 1961; Brown and Eisenhardt, 1998).

But though we find that flexibility is helpful, this argument is too simplistic because neither

structure nor improvisation is very effective in these environments. As a result, the optimal

structure not only diminishes, but its range unexpectedly shrinks from a broad plateau to an

inverted-V (i.e., edge of chaos). And more unexpectedly, the number of opportunities that can be

successfully executed also drops as improvisation becomes more difficult. A consequential

implication is that the content of a high-performing simple-rules strategy will likely focus on

capturing a few, high-payoff opportunities – i.e., a small number of rules to quickly select a few

“home-run” opportunities and to quickly exit those opportunities when they do not pan out. This

implication also helps explain why heuristics that focus on prioritizing and exiting opportunities

are particularly high performing in highly dynamic environments (Bingham, Eisenhardt, and

Furr, 2007).

Finally, we contribute insights into the edge-of-chaos concept from the complexity sciences

(Kauffman, 1993; Carroll and Burton, 2000). Research has defined the edge-of-chaos as a phase

transition between order and disorder (Kauffman, 1993), and it is often described more colorfully

with phrases like “snooze, you lose” and “only the paranoid survive” (Brown and Eisenhardt,

1998; Burgelman, 2002). Our contribution is theoretical insights into this intriguing construct,

and its role within our elaborated theory of structure, performance, and the environment. First,

we identify where the edge of chaos is likely to occur: in highly unpredictable environments. In

these environments, the relationship between structure and performance is an inverted-V with

42

tipping points on both sides of the optimal structure, consistent with an edge-of-chaos. Second,

we explain why the edge of chaos occurs—when structure is low, rapidly changing efficiency

and flexibility with difficult improvisation create a thin range of optimal structures. Third, we

characterize the distribution of mistakes at the edge of chaos—many errors of widely varying

size and including some large errors. Managers are likely to experience both small oversights

and debilitating miscalculations. Note that we did not find an inverse power law distribution of

many small mistakes and few large ones (Bak, 1996). Rather, the distribution is roughly normal.

Finally, we provide insight into the energy required to maintain a position at the edge of chaos.

Researchers have argued that the edge of chaos is a dissipative equilibrium, an unstable critical

point that requires constant energy to maintain (Prigogine and Stengers, 1984). We extend this

notion to our focal literatures by clarifying that managerial energy at the edge of chaos centers on

real-time improvisation of opportunities, recovery from the inevitable mistakes that will occur,

and continuous monitoring of the amount of structure to avoid drift from the optimum.

Toward a Pluralistic View of Strategies

More broadly, our work also contributes to strategy and its mandate to develop theoretical logics

explaining variance in firm performance. First, we contribute to the strategic logic of opportunity

and the related strategy as simple rules (Eisenhardt and Martin, 2000; Eisenhardt and Sull, 2001).

According to the logic of opportunity, firms achieve high performance in dynamic markets by

using a few simple rules to guide the capture of opportunities (e.g., Gersick, 1994; Burgelman,

1996; Galunic and Eisenhardt, 2001; Miner, Bassoff, and Moorman, 2001; Rindova and Kotha,

2001; Bingham, Eisenhardt, and Furr, 2007). Our research extends this view with support and

insights into the core theoretical logic by clarifying the implications of limited attention,

43

mistakes, and the fleeting and varied nature of opportunities. These dynamics place a premium

on using increasingly simple rules to capture increasingly unpredictable opportunities. Thus, like

other simulations that provide internal validation of theory (e.g., Sastry, 1997), our simulation

helps to sharpen the theory that underlies the strategic logic of opportunity.

Second, we contribute insights into the boundary conditions of several strategic logics. In

positioning logic, executives achieve high performance by building tightly linked activity

systems in valuable strategic positions, such as low-cost or high-differentiation (Porter, 1985;

Rivkin, 2000). Our findings add to this view by clarifying that such high-structure strategies are

effective in predictable markets. Further, our findings contribute to a deeper understanding of

why tightly linked activity systems are high performing in such predictable markets—i.e., while

fewer opportunities may fit these highly structured strategies, their tightly linked activity systems

produce both few and small mistakes. Therefore they efficiently execute a flow of similar

opportunities. In addition, given that there are many possible high-performing structures in

predictable markets (i.e., a plateau relationship between structure and performance), our findings

indicate why executives can achieve good performance with many alternative strategies. These

numerous optimal strategic alternatives help to explain why multiple differentiated positions are

often viable in predictable markets (Porter, 1985). Finally, our findings clarify why, once

achieved, competitive advantage gained through positioning is relatively robust to environmental

and structural perturbations, creating a foundation for sustainable competitive advantage and

superior performance.

44

By contrast, in opportunity logic, executives achieve high performance by using a few simple

rules or heuristics to capture varied opportunities (Eisenhardt and Sull, 2001; Bingham and

Eisenhardt, 2008). Our findings contribute to this view by indicating that low-structure

opportunity logic is particularly essential in unpredictable markets, while positioning logic is

most effective in predictable markets, thereby sketching a boundary condition between these

strategic logics. Our findings further contribute a subtle insight into the precarious nature of

competitive advantage (D'Aveni, 1994; Lenox, Rockart, and Lewin, 2006). Though prior

researchers have argued that firms should seek a series of short-term, competitive advantages in

dynamic environments (Roberts and Amit, 2003; Chen et al., 2009), our results indicate that

competitive advantage in these environments is unstable and its duration unforeseeable (but not

necessarily short-term). Overall, this suggests that firms with a strategic logic of opportunity are

threatened by internal collapse—i.e., they can fail as a result of having too much or too little

structure and not just as a result of external competition. This potential for internal collapse

offers an alternative explanation of intraindustry performance heterogeneity that differs from

path dependent and competitive explanations (McGahan and Porter, 1997; Bowman and Helfat,

2001). Thus a key insight is that the managerial challenges of finding and maintaining optimal

structure at the edge of chaos may contribute to heterogeneous firm performance within dynamic

industries.

A Richer View of Environments

Our work also contributes to a better understanding of distinct environments. Prior research tends

to focus on single environmental dimensions or mix several dimensions together. The result is an

imprecise understanding of different environments. In contrast, we highlighted four distinct,

45

widely used environmental dynamism dimensions (i.e., velocity, complexity, ambiguity, and

unpredictability) and developed their unique implications for strategy and performance. We

covered unpredictability above and now turn to the remaining three dimensions.

High velocity environments are particularly attractive. Because they are opportunity-rich,

managers can be selective, and so choose many, high-payoff opportunities. In addition, this

finding offers further insight into why rapid executive actions and processes such as fast strategic

decision making (Eisenhardt, 1989) and fast product innovation (Eisenhardt and Tabrizi, 1995)

are so effective in high-velocity environments. In these opportunity-rich environments, there are

likely to be many high-payoff opportunities. By acting quickly, executives can secure a larger

number of these superior payoffs for a longer time and so achieve high performance. In contrast,

by acting slowly, executives are likely to secure fewer opportunities and to exploit them for less

time, leading to low performance. The attractiveness of high-velocity environments may also

explain why the Internet era (with its high velocity of opportunities) had a surprisingly low

failure rate. Although many firms died, the death rate was unusually low when compared with

the total number of foundings (Goldfarb, Kirsch, and Miller, 2007). Overall, we found that high-

velocity environments are attractive for achieving high performance.

In contrast, complex environments are particularly unattractive. In highly complex environments,

opportunities have many features that executives must execute correctly. Thus these

opportunities are challenging to capture, and performance is correspondingly low. This finding

extends prior research by helping to explain why firms in complex environments such as

biotechnology (Owen-Smith and Powell, 2003) and “green” power (Sine, Mitsuhashi, and

46

Kirsch, 2006) often perform poorly even when their executives have high domain expertise. In

these technically and institutionally complex environments, executives must achieve success in

many areas (e.g., technical, manufacturing, safety, regulatory, marketing) to capture an

opportunity. When organizations fail to capture some opportunities, attention is wasted that

could have been used to address other opportunities. Thus organizations in complex

environments can address relatively few opportunities and are likely to have a low probability of

success when they do. Overall, we find that high-complexity environments are unattractive for

gaining high performance.

Our findings for environmental ambiguity are especially intriguing. When ambiguity is high,

executives are unable to perceive opportunities accurately and have a wide range of reasonably

optimal structures that produce roughly equivalent, albeit mediocre, performance. By contrast,

when ambiguity is low, the range of optimal structures narrows and so favors executives who are

able to locate and maintain optimal structure. Thus performance at the optimal structure

improves because executives can more accurately perceive opportunities and so more precisely

match structure to them.

These insights contribute to understanding effective institutional entrepreneurship in nascent

markets. Research indicates that entrepreneurs in these highly ambiguous markets often excel

when they shape industry structure to their advantage (Rao, 1994; Rindova and Fombrun, 1999;

Santos and Eisenhardt, 2009). For example, entrepreneurs succeed when they form portfolios of

relationships that shape the industry structure to gain a central network position (Ozcan and

Eisenhardt, 2008) or when they use analogies to provide some unique insight into the

47

opportunity structure of these novel markets that improves opportunity capture (Gavetti,

Levinthal, and Rivkin, 2005).12 We add to institutional entrepreneurship by revealing that these

actions are successful attempts to reduce ambiguity and so increase the possibility of very high

performance. Thus successful entrepreneurs seek to change nascent markets from games of luck

with likely mediocre performance in which the optimal structure is easy to find (high ambiguity)

to games of skill with potentially high performance in which the optimal structure is challenging

to find (low ambiguity).

Adaptation in Entrepreneurial vs. Established Organizations

Finally, our work contributes to organization theory. At the heart of our research is the core

tradeoff between flexibility and efficiency in dynamic environments. Less structure enables the

flexible capture of serendipitous opportunities. But with too much improvisation, the

organization runs the risk of incoherence, confusion, and drift. More structure enables tight focus

on the efficient execution of expected opportunities. With too much structure, however, the

organization runs the risk of stagnation and misalignment with fresh opportunities. The essence

of flexibility is thus the messy capture of the unexpected, while the essence of efficiency is the

smooth execution of the anticipated.

Our contribution is the insight that this core efficiency-flexibility tradeoff affects types of

organizations differently. For entrepreneurial organizations that typically have little structure, the

challenge in any environment is the same: to gain enough structure before failure ensues.

Legitimation and competition, of course, affect performance. But the key insight here is that

sufficient structure is also essential. Without sufficient structure, it is impossible to improvise

48

effectively and so to capture opportunities. Thus the well-known liability of newness may mask a

liability of too little structure.

In contrast, for established organizations that often have extensive structure, such as roles, rules,

and linkages among units, the imperative varies in different environments. If the environment is

predictable, this structure can be high-performing because it can take advantage of consistent

patterns in the environment that can be mirrored in structure. The number and size of mistakes

decreases with more structure in predictable environments, and only modest executive attention

is needed to retain an optimal amount of structure. Organizations can gain a stable equilibrium

that is robust to structural and environmental changes.

But as the environment becomes unpredictable or executives diversify into unpredictable

environments, our findings indicate major challenges for established organizations. One is

obviously to decrease the amount of structure. But a second, subtler challenge is the need for a

dramatically altered mindset. This mindset entails vigilantly managing the amount of structure

(not just its content), improvising to capture fresh opportunities, and quickly rebounding from

mistakes - all at the edge of chaos, where firms can at best capture only a few opportunities and

gain an unstable or dissipative equilibrium. Simply put, managing in unpredictable environments

is different, harder, and more precarious than in predictable environments. Overall, the irony of

adaptation is that, as it becomes more crucial for organizations to adapt, it also becomes more

challenging to do so. Thus the well-known liability of senescence may be as much a cognitive

phenomenon as an age phenomenon.

49

We began by noting that diverse literatures emphasized that balancing between too much and too

little structure is essential for high performance in dynamic environments. This consonance led

us to explore the theoretical logic of efficiency versus flexibility underlying fundamental

relationships at the heart of the science of organization. By incorporating limits on attention, time

delays, the inevitability of mistakes, and the fleeting and heterogeneous nature of opportunities,

we construct a more precise theory that links structure, performance, and environment. This

theoretical framework reveals the surprisingly wide applicability of a simple-rules strategy and

semi-structures, an asymmetry that favors more structure, and demanding managerial challenges

at the edge-of-chaos. Overall, we spotlight a research agenda that places complexity sciences

reasoning at the nexus of organizational studies, network sociology, and competitive strategy.

50

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TECHNICAL APPENDIX: Operationalization and Initialization of Opportunities

Each opportunity is composed of a 10-element vector of perceived features composed of either

1s or 0s (i.e., a bit string), a 10-element actual features bit string, and a randomly selected payoff

value. The feature vectors are produced by an algorithm that randomly assigns each element

either a 1 or 0. The probability of selecting a 1 or 0 is determined by the unpredictability

parameter. The perceived features vector differs from the actual features vector by a proportion

of elements as set by the environmental ambiguity parameter. The exact elements that differ are

randomly chosen. The payoff is drawn from a normal distribution with m = 30 and v = 5,

although sensitivity analyses showed that the results do not depend on these values. Moreover,

we assume that unexecuted opportunities stay in the environment for a random amount of time

drawn from a normal distribution with m = 20 and v = 5; sensitivity analyses showed that the

results do not depend on these values either.

Operationalization, Initialization, and Use of Rules

We initialized the rule structure in the computer program in a similar way as for the

opportunities. The rules are initialized as 10-element vectors but with ?s (elements that can be

improvised) scattered throughout a string of 1s and 0s. Thus the amount of structure is

operationalized by the number of 1s and 0s. Similar to the structure of opportunities, the

probability of selecting a 1 or 0 is determined by the unpredictability parameter. Thus our

computational model reflects that managers can adjust their structures to fit consistent patterns in

the flow of opportunities if such patterns exist, consistent with empirical evidence. Also, as in

actual organizations, there is typically an approximate fit but often not an exact one. Thus the

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probability of getting a 1 or 0 is the same in both the rules and opportunities and is determined

by the unpredictability parameter. This assumption could be relaxed in future work to explore the

impact of misfit between environmental unpredictability and organizational structure, for

example, in attempting to understand better the role of learning to fit structure to environmental

patterns.

The exact placement of 1s, 0s, and ?s is randomly assigned. For example, if a rule’s amount of

structure is set to 6, then 0?0?1?01?0 or any other permutation could result as long as four ?s

were assigned. After initialization of both rules and opportunities, all available opportunities

(both those that recently flowed into the environment and those not yet captured but still in the

pool of opportunities) can be captured in each time step.

Rules are used to capture opportunities by combining rule-based and improvised (described

below) actions that produce a 10-element bit string (e.g., 0111100110). These bits are compared

with each opportunity bit string (e.g., 0110101010). An opportunity is captured and its payoff is

gained when the number of actions that correctly match the opportunity’s features is greater than

the value of environmental complexity.

Improvisation and Attention

A key feature of our model is the improvisation of action. Some actions are rule-based and some

are improvised. When a rule (e.g., 0?1?10???0) is applied to a given opportunity, the

organization follows the rule for each element as specified by a 0 or a 1. These are the rule-based

actions. In addition, the organization randomly improvises a 0 or 1 action for each ? placeholder

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with a p = .5 likelihood of each outcome. Overall, this process produces a set of actions (e.g.,

0111100110 in which the 2nd, 4th, 7th, 8th, and 9th actions are improvised) that can be

compared with a given opportunity (e.g., 0110101010). When enough of the actions match the

opportunity features as specified by the environmental complexity parameter, the opportunity is

captured and the organization gains the opportunity’s payoff. When an insufficient number of

actions match the opportunity features, the opportunity remains in the environment to be

potentially captured using other actions. Depending on the attention available (see below), the

organization continues to try to capture an opportunity using improvisation again and in future

time steps until it disappears from the environment at a randomly determined time, as described

above.

In general, our operationalization of improvisation is consistent with existing research showing

that improvisation involves real-time action and that improvised action is not always correct

(Weick, 1993, 1998; Miner, Bassoff, and Moorman, 2001). As in actual organizations, only some

improvised actions are correct. We also found that different amounts of attention and ratios of

rule-based to improvised attention did not qualitatively change the results. As a manipulation

check, we also checked that the total number of mistakes decreased with increasing structure as

expected. We confirmed that, because decreasing structure increases the organization’s capacity

to improvise flexibly with a larger number of opportunities that potentially fit, there are more

mistakes. This result is similar for different rates of improvisation. We also conducted an

analysis of mistakes in figure 6 that normalizes the total number of mistakes to compare these

distributions across the mini-graphs, as described in the text. Overall, our approach is a

conservative one that nonetheless captures the fundamental features of improvisation—i.e.,

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improvising requires more attention than following rules and is not always accurate. Our

modeling of improvisation thus offers a reasonable abstraction of the actual process that is

appropriate for our research question and the objectives of simulation models (Burton and Obel,

1995).

Another key feature of the model is attention. As in actual organizations, we assumed that the

organization has a finite amount of attention. In particular, the organization has a fixed attention

budget. In each time step, the attention budget is decremented for each application of rules to

opportunities, each rule-based action, and each improvised action. Consistent with research on

improvisation (Weick, 1993; Miner, Bassoff, and Moorman, 2001) and the use of rules (Cyert

and March, 1963), we assumed that an improvised action takes more attention than simply

checking whether a rule matches an opportunity or a rule-based action, because improvisation

has enhanced demands for real-time sensemaking and the convergence of figuring out actions

and executing them (Weick, 1993; Miner, Bassoff, and Moorman, 2001). Thus we set the

attention required to check the match of a rule with an opportunity or take a rule-based action at

1 unit of attention and each improvised action at 10 units of attention. Though we chose 10 as a

representative value, our sensitivity analyses indicated that the findings are robust to a broad

range of variations in the amount of attention that an improvised action requires. In general, the

robustness of our findings to a broad range of variations in attention suggests that a more

discriminate improvisation process (i.e., one requiring more attention or more improvisational

skill) is likely to yield qualitatively similar results. Similarly, sensitivity analysis indicated that

our findings are qualitatively robust to different orderings for addressing opportunities. So

although we address opportunities by their performance payoffs, other orders (such as random)

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qualitatively produce the same results. In any given time step, the attention budget is

decremented until the attention budget is depleted or the time step ends. Action stops if the

attention budget is completely depleted. It is then replenished at the beginning of each new time

step. We set the attention budget to 2800 attention units. Sensitivity analyses that varied the

attention budget showed that increasing this budget increases the number of opportunities that

can be executed in a given time step, as expected, but that these variations (above a minimal

threshold) do not produce qualitatively different findings. Therefore we chose this representative

value for our simulation runs. Finally, in any given time step, rules are checked against

opportunities for a match, and rule-based and improvised actions are taken as long as attention is

still available.

Performance and Error Constructs in Monte Carlo Experiments

We used standard Monte Carlo techniques (Law and Kelton, 1991). Each experiment consists of

30 or 50 simulation runs. We selected n = 30 as the number of simulation runs for all

experiments, except those on the basic relationship between structure and performance, because

exploratory analyses revealed that values of n greater than 30 yielded insignificantly small

incremental gains on reliability. We used n = 50 for the basic relationship between the amount of

structure and performance because the larger range of structure values adds precision to our

illustration of this relationship. The results of these simulation experiments are graphed

consistently across figures 1-5: each point represents the results for one simulation experiment,

including the mean performance (Y-axis) computed across all simulation runs for a given

amount of structure (X-axis). A curve is then interpolated between the mean performance values

by connecting the points with a straight line.

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As in all stochastic processes and related phenomena (regardless of whether empirical or

simulated), the results of experiments may typically vary across simulation runs even when the

construct parameter values are fixed (Law and Kelton, 1991). Therefore we computed not only

the mean performance for a given experiment but also its variability in terms of error variances.

We then plotted both a performance mean for each value of the amount of structure and

associated “error bar” confidence intervals, which indicate the variability of each result, a

standard graphical method used in Monte Carlo outputs (Kalos and Whitlock, 1986). We

computed the length of the error bar as the square root of the error variance of each experiment

over the number of trials (i.e., simulation runs) of these experiments. These error bars provide an

intuitive and visual display of the confidence intervals surrounding a result. As a rule of thumb,

if the mean of one result is contained within the error bars of another result, then the two are not

significantly different. For example, this implies that the peak performance can be generated by a

range of optimal structural values. These structural values can be characterized by their own

range intervals (e.g., 3–6) and medians (e.g., 4.5).

Comparing medians is necessary when optimal structure is a range of values. For instance, to

assess the shifting optimum in P2, we compared median structures when the optimum was a

range of values. P2 is confirmed when these median optimal structures differ. In addition, to

assess asymmetry, we compared the slope of the line from the median optimal structure to the

endpoint on the left side to the slope of the line from optimal structure to the endpoint on the

right side. Curves are asymmetric right when the absolute value of the left slope is higher than

the right slope.

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Sensitivity Analyses

We performed extensive sensitivity analyses for all of the structure/performance relationships

reported in the Results section, thoroughly exploring the parameter space to discover if a given

finding remained when construct values (i.e., parameters) were varied. To ensure the robustness

of the results, we not only varied the amount of structure measure, but also secondary constructs

such as the environmental dynamism dimensions. We chose the specific values for presentation

because they represent extreme values of a parameter or the midpoint values between already

tested values, as appropriate. Thus we explored the parameter space in a very fine-grained way.

We paid special attention to exploring the full range of the environmental dimension values—

velocity, complexity, ambiguity, and unpredictability. Because velocity (λ) is unbounded in a

Poisson distribution, but actual organizations are both cognitively and resource bounded, we

placed an upper bound on λ at the value for which the number of opportunities is an order of

magnitude greater than the organization could capture in any time step. We then thoroughly

explored velocity at a variety of parameter values, including 0, .4, .6, .8, 1.2, 1.4, 1.6, 1.8, 2.0,

2.2, 2.4, 2.6, 2.8, 3, 4, and 5. All results are consistent with figure 2. We also explored

complexity, which ranges from 0 to 1, with a variety of parameter values, including 0, .2, .3, .4,

.5, .6, .7, .8, .85, and .9. All results are consistent with those in figure 3. We tested ambiguity,

which ranges from 0 to 1, with a variety of parameter values, including 0, .1, .2, .25, .3, .4, .6, .8,

and 1.0. All results are consistent with those in figure 4. Unpredictability ranges from 0 to1 in

our tests. We tested the sensitivity of the unpredictability results with a variety of parameter

values for the proportion of 1s, including 0, .1, .2, .3, .4, .5, .6, .7, .8, .9, and 1.0. All results are

consistent with those in figure 5.

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MATHEMATICAL APPENDIX

The mathematical formalization that we constructed sheds light on the logic underlying P1a, P2a,

and the varying range of optimal structures from our simulation experiments. In this appendix,

we perform some of the mathematical operations that underlie this logic. We are especially

grateful to an anonymous reviewer who encouraged our building this interpretive model and

developing this line of thinking.

Though the literature is mostly silent about the specific functional forms underlying the

relationship between structure and performance, there is consensus that flexibility and efficiency

are inversely interdependent and have non-substitutable effects on how structure influences

performance (e.g., Gibson and Birkinshaw, 2004). Let x be the amount of organizational

structure. We begin by representing the aggregate effect of structure on performance by A(x) =

f(x)*e(x), where f(x) and e(x) are the non-negative functions of flexibility and efficiency.

Broadly, the literature suggests that efficiency increases and flexibility decreases as the amount

of structure increases, respectively: f’(x) < 0, e’(x) > 0.

This representation allows us to demonstrate that not all flexibility and efficiency functions

generate a unimodal curve, as predicted in P1a. Specifically, for a unimodal curve to exist, we

require that [A’(x) > 0 for x < x’] and [A’(x) < 0 for x > x’], where x’ is the optimal amount of

structure (i.e., at the performance “peak”).

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Applying the chain rule [A’(x) = (e(x)*f’(x)) + (e’(x)*f(x))] and the absolute value equation [–

f’(x) = |f’(x)| when f’(x) < 0] yields these two important conditions for unimodal functions of the

type A(x) = f(x)*e(x):

|f’(x)| < f(x)*e’(x)/e(x) for x < x’ (1) and

e’(x) < |f’(x)|*e(x)/f(x) for x > x’ (2).

These constraints on the two underlying functions, f(x) and e(x), are necessary to predict a

unimodal relationship.

In addition, we can show that the argument that the shifting optimum predicted in P2a is

generated because of the increasing importance of flexibility is not correct. Let a > 0 represent

the importance of flexibility in A(x) = a*f(x)*e(x). Then, applying the chain rule again yields

A’(x) = a[f(x)*e’(x) + f’(x)*e(x)]. Inspecting this A’(x) reveals that simply increasing the

importance of flexibility by increasing the coefficient a does not affect the position of the

optimum given that the critical point of A’(x) is independent of a.

Instead, logical argument and empirical literature suggest functional forms that do satisfy the

conditions underlying P1a and P2a. For instance, the literature suggests an increasing function of

structure for efficiency such that e’(x) > 0. Examining the impact of adding a marginal amount of

structure sheds further light on the shape of e(x). One possibility is that each incremental

application of structure generates a constant improvement, e’(x) = c, where c is a constant. But a

constant improvement is unlikely over the full range of x. Instead, it is more likely that

increasing structure has a diminishing marginal effect on efficiency. A marginal improvement in

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efficiency, de, is derived from a smaller set of opportunities and a smaller efficiency gain from

economizing on attention. Thus the marginal improvement in efficiency, de , derived from

applying a marginal amount of structure dx is inversely dependent on the base level of structure,

x, suggesting an inversely proportional relationship: de ∝ dx/x where x > 0. Integrating yields a

logarithmic efficiency function:

e(x) = ln(x)

which satisfies e’(x) > 0 as e’(x) = 1/x > 0 when x > 0. Moreover, this logarithmic efficiency

function has the important property of being unbounded —increasing structure always increases

efficiency, although at a diminishing rate.

By contrast, empirical literature and logical argument suggest decreasing flexibility as a function

of structure such that f’(x) < 0. Flexibility involves using improvisation to capture a variety of

opportunities that could not be captured by structure-based actions alone. Logic suggests that

adding structure eliminates successive fractions of opportunities, and so the amount of structure

is inversely proportional to the fraction of opportunities that could have been captured with

improvisation. Thus it is most rapidly decreasing at low structure, an argument that is also

consistent with empirical evidence (Greve, 1999). This suggests the following function:

f(x) = 1/x

which satisfies f’(x) < 0 as f’(x) = –1/(x^2) < 0 when x > 0. In our rule-based model, a simple

interpretation of the effect of increasing structure on flexible opportunity execution is to decrease

the pool of opportunities available to improvisational execution by successive fractions for each

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addition of structure. That is, flexibility is the product of these fractional losses of opportunities

at each level of structure, n: f(x) = ∏ [1 – (1/n)] = ∏[(n – 1)/n] = (x – 1)!/x! = 1/x. A natural

interpretation, then, is that increasing structure quickly eliminates opportunities from the pool of

opportunities available for improvised actions. This modeling of flexibility also has the

important property of approaching a limit of 0 as structure increases.

Returning to an objective for this mathematical formalization, it can be shown that these

functional forms are consistent with P1a:

Let A(x) = f(x)*e(x) = ln(x)/x.

Recall that for A(x) to be unimodal, it is required that

|f’(x)| < f(x)*e’(x)/e(x) for x < x’ (1) and

e’(x) < |f’(x)|*e(x)/f(x) for x > x’ (2).

Substituting f(x), e(x), f’(x), and e’(x) into A’(x) = [e(x)*f’(x)] + [e’(x)*f(x)] generates A’(x) =

(1 – ln(x))/(x^2), while letting A’(x) = 0 yields x’ = e as the optimum.

Substituting f(x) = 1/x and e(x) = ln(x) into the inequalities above also reveals that these

functions satisfy the conditions for P1a. For example, after reducing the equations, we find the

following true inequalities:

1 < ln(x) x < x’ (1) and

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1 > ln(x) x > x’ (2).

These functions produce a unimodal, asymmetric right curve as predicted by P1a.

It can also be shown that these basic functional shapes are consistent with P2a as well. Consider

unpredictability, the key dimension of environmental dynamism underlying the logic in P2a. An

important insight is that unpredictability, u, shapes both flexibility and efficiency by affecting

how firms use structure to execute opportunities in two ways. One effect of increasing

unpredictability is that some additional opportunities can occasionally be captured in a more

unpredictable stream of heterogeneous opportunities. But this increment varies inversely with the

amount of structure—1/x—and grows increasingly slowly with increasing unpredictability –

ln(u)—because opportunity capture becomes increasingly difficult at lower levels of structure,

both of which we represent with ln(u)/x. Combining this with A(x) changes the performance

function: A(x) + ln(u)/x = ln(x)/x + ln(u)/x = ln(ux)/x. Another important effect of

unpredictability is to reduce the effectiveness of both structure and improvisation, which is

represented as a simple dampening parameter reducing the magnitude of performance, 1/u,

which can be applied to the performance equation above: (1/u)*ln(ux)/x. Although there are

potentially many ways to represent these effects, the resulting model is a simple one that

nonetheless captures the dual effects of unpredictability, u:

P(x,u) = ln(ux)/ux, where u > 0.

This modification of A(x) to include unpredictability, u, retains its key properties. For instance,

P(x,u) also satisfies the conditions for P1a:

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Differentiating yields P’(x,u) = [1-ln(ux)]/ux^2 and setting P’(x,u) = 0 yields x’ = e/u.

Deriving the conditions again yields

1 > ln(ux) x < e/u (1) and

1 < ln(ux) x > e/u (2)

which are true for u > 0.

Turning back to P2a, this model is consistent with a shifting optimum because x’ = e/u depends

on u. Consistent with P2a, as u increases, x’ decreases. Moreover, this P(x,u) also shares other

important features of our simulation findings, such as the unimodal, asymmetric right shape and

the shift from a broad plateau to a sharp inverted-V edge of chaos as unpredictability increases.

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Table 1: Comparison of Theoretical Frameworks for Structure-Environment-Performance Relationships

Framework Feature Prior Revised Core tradeoff Flexibility vs. Efficiency

Flexible capture of varying opportunities vs.

efficient execution of specific opportunities. Relevance of limited attention, mistakes, time

delays, and fleeting and varied opportunities.

Structure- performance relationship

Inverted-U Flexibility and efficiency are

opposing, approximately linear processes

Unimodal, asymmetric right. Attention advantage of increasing structure. Efficiency increases at a decreasing rate;

flexibility more rapidly decreases at decreasing rate.

Major environmental constructs

Environmental dynamism shifts locus of optimal structure

Unpredictability shifts the locus and range of optimal structure.

High velocity raises performance. High complexity lowers performance. High ambiguity lowers performance and

broadens the range of optimal structure. Robustness of simple

rules Necessary in highly dynamic

environments Simple rules are robust across a wide range of

environments. Viable in predictable environments. Necessary in unpredictable environments.

Range of optimal structures

Constant In predictable environments, plateau of many optimal structures.

In unpredictable environments, inverted-V of a few optimal structures, selection and exit rules for opportunities.

Edge-of-chaos Highly dynamic environments Inverse power law distribution of

mistakes High managerial energy focused on

staying poised at the optimal structure or edge-of-chaos

Highly unpredictable environments. Many mistakes of varying sizes, including

large ones, roughly normal distribution. Mistakes advantage of increasing structure in

less unpredictable environments. High managerial energy focused on

improvisation, mistake recovery, and staying poised at the optimal structure or edge-of-chaos

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Endnotes • We appreciate the generous support of the National Science Foundation (IOC Award

#0323176), the Stanford Technology Ventures Program, and the MIT Sloan School of

Management. We also thank multiple individuals for their helpful comments, including Phil

Anderson, Steve Barley, Diane Burton, Tim Carroll, Rebecca Henderson, Pankaj Ghemawat,

Clark Gilbert, Riitta Katila, Bruce Kogut, Dan Levinthal, Tammy Madsen, Anne Miner, Woody

Powell, Jan Rivkin, Simon Rodan, Lori Rosenkopf, Nicolaj Siggelkow, Wesley Sine, Bob

Sutton, Brian Uzzi, Christoph Zott; participants at the Academy of Management Conference,

Atlanta Competitive Advantage Conference, West Coast Research Symposium on Technology

Entrepreneurship, Wharton Technology Conference, BYU/Utah Winter Strategy Conference;

and seminar participants at Stanford University, INSEAD, and the Harvard Business School. The

paper benefited greatly from the comments of Elaine Romanelli and three anonymous reviewers.

1 We appreciate the suggestion of an anonymous reviewer to focus on the relationships of

structure with efficiency and flexibility.

2 We develop a matching model whose fundamental feature is to allow for varying degrees of

match between opportunities and rules, something that is not present in other, more constrained

modeling approaches. We appreciate the comments of an anonymous reviewer in suggesting that

we make this point in explaining our use of stochastic process modeling.

3 Stochastic process modeling is more fully described in references such as Burton and Obel

(1995) and Davis, Eisenhardt, and Bingham (2007). Interested readers can also refer to the

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exemplars cited in the text, such as March (1991) and Carroll and Harrison (1998). We

appreciate the comments of an anonymous reviewer that we provide more information about this

modeling approach.

4 We appreciate the insightful recommendation of an anonymous reviewer that we clarify the

meaning of unpredictability and its implications for whether there are patterns in the

environment that managers can use to adjust or “tune” their organizational structures to better

match the environment.

5 Additional results for other values of the environmental dimensions are available from the

authors.

6 To assess asymmetry, we compared the slope of the line from optimal structure to the endpoint

on the left side to the slope of the line from optimal structure to the endpoint on the right side.

Median values are used if optimal structure is a range of values. Curves are asymmetric right

when the absolute value of the left slope is higher than the right slope.

7 This mathematical formalization is not intended to be a formal derivation of our simulation

results. Rather, its aim is to build an interpretive model that increases understanding of the theory

and enhances confidence in the simulation results. We appreciate the encouragement and

guidance of an anonymous reviewer to add this formalization.

8 We thank an anonymous reviewer for this formulation and other helpful insights.

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9 We tried other functional forms for efficiency and flexibility, including linear forms, which do

not reproduce these results. We chose these two functional forms because they also fit with

empirical literature and logical argument. More details are in the Mathematical Appendix.

10 We appreciate the advice of an anonymous reviewer to include this more nuanced

understanding of the core tradeoff between efficiency and flexibility.

11 We appreciate the suggestion of an anonymous reviewer to consider the robustness of a

simple-rules strategy.

12 We appreciate the observation of an anonymous reviewer that unique insight into the

opportunity structure can potentially provide large returns in highly ambiguous environments.

This observation suggests that these managers could use such insights (e.g., as derived from

analogies) to lower ambiguity. We use this interpretation as part of our explanation of the

behavior of successful executives in highly ambiguous markets, including nascent markets. In

addition, this reviewer also noted that such unique insights might also be effective in highly

unpredictable environments. Here, also, analogies may be a concrete example of the kind of

unique insights to which this reviewer referred.