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A R T I C L E S

Contextuality Within Activity Systems andSustainability of Competitive Advantageby Michael Porter and Nicolaj Siggelkow

Executive OverviewResearch on the interactions among activities in firms and the extent to which these interactions helpcreate and sustain competitive advantage has rapidly expanded in recent years. In this research, the twomost common approaches have been the complementarity framework, as developed by Milgrom andRoberts (1990), and the NK-model (Kauffman, 1993) for simulation studies. This paper provides anintroduction to these approaches, summarizes key results, and points to an aspect of interactions that hasnot found much attention because neither of the two approaches is well-suited to address it: contextualinteractions, i.e., interactions that are influenced by other activity choices made by a firm. We provide anumber of examples of contextual interactions drawn from in-depth studies of individual firms and outlinesuggestions for future research.

The importance of fit and consistency among afirm’s activities1 is one of strategy’s most long-standing notions (Drazin & Van de Ven, 1985;

Khandwalla, 1973; Learned, Christensen, An-drews, & Guth, 1961). While earlier work stressedthe consistency among higher level concepts suchas “strategy” and “structure” (Chandler, 1962),more recent work has emphasized interdependen-cies at a lower level, among the various activitiesa firm is engaged in (Milgrom & Roberts, 1990;Porter, 1996).

Consider the example of Urban Outfitters, a$1.1 billion specialty retail store chain whose salesand profits have been growing at about 30% a year

for the last 15 years. It has adopted a set ofactivities and practices that are highly interdepen-dent and quite distinctive (Bhakta et al., 2006).Its stores create a bazaar-like ambience with eclec-tic and nonstandardized merchandise, includingclothes and home accessories, and the assortmentin each store is broad but shallow, underscoringthe atmosphere. Each store has a unique design;some occupy buildings previously used as movietheaters, banks, or stock exchanges. Store manag-ers have considerable authority to, for instance,change the store layout, or to experiment with themusic being played. Strengthening this shoppingexperience is a substantial investment of 2% to3% of annual revenue into visual display teamswho change the layout of each store every twoweeks, creating a new shopping experience when-ever customers return. As a result, customersspend considerably more time in Urban Outfittersstores than in other specialty stores (three to four

We would like to thank Dan Levinthal and Jan Rivkin for helpfuldiscussions. Financial support by Harvard Business School and the MackCenter for Technological Innovation at the University of Pennsylvania isgratefully acknowledged.

1 An activity is a discrete economic process within the firm, such asdelivering finished products to customers or training employees, that can beconfigured in a variety of ways (Porter, 1985).

Michael E. Porter ([email protected]) is Bishop William Lawrence University Professor, Harvard Business School.* Nicolaj Siggelkow ([email protected]) is Associate Professor of Management, the Wharton School, University of Penn-sylvania.

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times as much). To finance this investment, thecompany shuns traditional forms of advertisingsuch as print, radio, and television.

Urban Outfitters’ choices are clearly interde-pendent. For instance, the unique real estate playswell with the nonstandardized merchandise mix;both in turn make it more beneficial to grant moreauthority to store managers, as standardized ap-proaches are unlikely to work well. Similarly, fre-quent changes in store layout are particularly ben-eficial given the quick turnover of merchandise.Lastly, Urban Outfitters can afford not to usetraditional media outlets given the substantialword of mouth its unusual stores generate.

While such interdependencies among a firm’sactivities are widespread, the strategy field hasstruggled for many years to find a structured way toanalyze the consequences of such interactions.Two fairly recent advances have made it possibleto more systematically analyze the strategic andorganizational implications of interdependenciesamong a firm’s activities. One is agent-based simu-lation modeling using the NK model (Kauffman,1993); the other is the complementarity frameworkdeveloped by Milgrom and Roberts (1990). In thispaper, we provide an introduction to each of theseapproaches, summarize a range of research findingsthat have emerged from them, and discuss an im-portant feature of interdependencies among activi-ties that neither approach is well-suited to address.

Both approaches have focused on the contextu-ality of activities—the fact that the value of indi-vidual activities is influenced by other activitychoices made by a firm (i.e., Urban Outfitters’choice to create a bazaar-like setting influenced itsinventory levels and affected its decision to shuntraditional advertising).

Using large samples of firms, the empiricalwork based on the complementarity frameworkhas concentrated on identifying precisely whichactivities affect each other in many firms, i.e., onunderstanding where contextual activities tend toarise. The agent-based simulation work has fo-cused on analyzing the consequences that arise ascontextuality of activities (i.e., the number ofinterdependencies among activities) increases.

While contextuality of activities is an impor-tant phenomenon, our research conducted at the

firm level suggests that a second type of contex-tuality is important to further our understandingof the sustainability of competitive advantage: thecontextuality of interactions. Whether and how ac-tivities interact—for instance, whether they arecomplements and reinforce each other, orwhether they are substitutes2—can also dependon other activity choices made by a firm. Thus,the nature of the interaction among activities maynot be an inherent property of the activities, but afunction of the other choices made by a firm.

As an example, consider a firm such as the Gapthat operates a distribution system linking ware-houses and stores. Assume that the firm’s orderingsystem is configured to allow stores to order goodsonce a week. In this case, the benefit of increasingdelivery frequency of ordered goods from weeklyto daily is quite low (i.e., if the ordering systemallows buyers to order goods only once a week,there is little value in daily deliveries). If storeswere to order daily, though, the benefit of increas-ing the delivery frequency from once a week todaily would be higher. Thus, the marginal benefitof increasing the ordering frequency increases asthe delivery frequency increases, that is, orderingfrequency and delivery frequency are complemen-tary. However, this complementarity is contextualto the firm’s in-store information system. It existsonly if the firm has relevant information neededfor ordering on a daily basis, for instance througha point-of-sales (POS) system that tracks itemssold in real time. It is the presence of the POSsystem that makes the relationship complemen-tary. (Without a POS system, the two activitiesare not complementary.)

The rest of this paper is organized as follows. Inthe next section, we provide more detail on con-textuality of activities. We continue with an over-view of existing work that has focused on contex-tuality of activities based on the NK simulationmodel and with empirical investigations that weregrounded in the complementarity framework. Inthe subsequent section, we show several ways inwhich contextual interactions can arise and pro-

2 Two activities are complements if the presence of one activity in-creases the marginal benefit of the other, and substitutes if the presence ofone decreases the marginal benefit of the other.

2008 35Porter and Siggelkow

vide examples of contextual interactions drawnfrom detailed firm-level analyses. Finally, we dis-cuss the effect of contextuality on the difficulty ofimitation and adaptation and explore the impli-cations of contextuality for research using simula-tions and for empirical investigations.

ContextualityofActivities

One way to classify activities is by the degree towhich their value is affected by other activi-ties, i.e., the extent to which they interact.

Accordingly, activities can be arrayed along a con-tinuum of increasing interdependence (see the hor-izontal dimension in Figure 1). At one extreme (lowinterdependence) lie activities that are not affectedby any other activity choices. Since their value iscontext independent, these activities have the sameoptimal configuration for all firms in the economy.In other words, they are generic. For instance, the useof computers for accounting is an optimal activitychoice for (practically) all firms in the economy.3

At the other extreme (high interdependence)are activities whose value is affected by manyother firm choices; consequently, they have firm-or strategy-specific optimal configurations.4 Forinstance, the U.S. mutual fund provider Vanguardconfigured its employee incentive system so thatpay was based on the extent of cost savings forfund shareholders. This configuration was partic-ularly beneficial to Vanguard given many of Van-guard’s other choices, such as its organizationalstructure in which fund shareholders were also theowners of the asset management company, itsemphasis on funds for which low costs were com-petitively important such as index funds, and itsculture of keeping costs low in all of its operations(Siggelkow, 2002a). Between these two extremeslie activities that have generically optimal config-urations within particular industries, or that arespecific to a particular strategic group within anindustry (Caves & Porter, 1977; Hatten & Schen-del, 1977).

Generic activities are not unimportant—quitethe contrary. They set the bar for competition. A

3 Even at the extreme end of genericity one can have gradations. Forinstance, the use of computers presumes some computer literacy of employ-ees in the accounting department of a firm. For some parts of the world thisassumption may not hold, making the use of computers in those areas nota generic activity.

4 We use the term strategy here as a shorthand for many other activitychoices a firm has taken. Strategy by itself is not a special activity, but it arisesfrom the set of activities a firm has put in place.

Figure1Activity/Interaction Typology


firm that does not attain parity on such activitiesis at a competitive disadvantage. Yet, at the sametime, since these activities are beneficial for allfirms, other firms have a high incentive to pursuesuch activities as well. As a result, firms are un-likely to attain a sustainable competitive advan-tage from these activities. Competitive advantageis more likely to be sustainable if it arises fromactivities that have more than one optimal con-figuration, i.e., from strategy-specific activities.Since these activities are more beneficial to thefirm than they are to its rivals, incentives forimitation are muted (and more difficult, as we willargue in more depth below). In addition, contex-tual activities can lead to different strategic posi-tionings within an industry. Consider the follow-ing two examples:

In the wine industry, Robert Mondavi and E. &J. Gallo compete successfully with very differentsystems of activities. Mondavi, the leading pre-mium wine producer, produces high-quality winewith premium grapes, many grown in its ownvineyards. Grapes sourced from outside growersare purchased under long-term contracts from sup-pliers with whom the company has deep relation-ships, sharing knowledge and technology exten-sively. Grapes are handled with great care inMondavi’s sophisticated production process,which involves extensive use of hand methodsand batch technologies. Wine is fermented inredwood casks and extensively aged in small oakbarrels. Mondavi makes heavy use of wine tast-ings, public relations, and wine tours in marketingrelative to media advertising.

Gallo, in contrast, produces large volumes ofpopularly priced wine using highly automated pro-duction methods. The company purchases the ma-jority of its grapes from outside growers via arm’s-length relationships and is also a major importer ofbulk wine for use in blending. Gallo’s productionfacilities look more like oil refineries than winer-ies. Bulk aging takes place in stainless-steel tankfarms. Gallo spends heavily on media advertisingand is the leading advertiser among Californiawineries. In sum, Mondavi and Gallo have chosenvery different systems of contextual activities—activities that fit together and reflect the firms’different positionings.

A second example of different activity setswithin the same industry can be found in theautomobile insurance industry. There are twobroad types of insurance providers: those servingstandard (low-risk) drivers, such as State Farm,and those serving to a considerable degree non-standard (high-risk) drivers, such as ProgressiveCorporation. As a consequence of their differenttarget customers, these companies have pursuedtwo different systems of activity configurations.Specifically, we look at how the firms differ interms of settling customer claims. The activitydesign followed by most standard insurers is toinvestigate and settle claims deliberately in orderto hold down costs and earn further returns on theinvested premium. Most standard auto insurers(including State Farm) register operating losses intheir insurance business, i.e., claims and operatingexpenses exceed premiums, and profitability de-pends on the returns earned on the float beforeclaims are settled.

A different set of interdependent activities, putinto practice by Progressive, revolves around pay-ing as quickly as possible. Progressive makes per-sonal contact with more than 75% of claimantswithin 24 hours and settles more than 55% of allclaims within seven days. In many cases, a Pro-gressive adjuster will come to the accident sceneand issue a check on the spot. The rationalebehind this choice is to reduce the number oflawsuits, which tend to escalate costs but do notultimately benefit the insured.5 Many other activ-ities influence the time between an accident andthe final issuing of a check. Activity configura-tions that lead to quicker responses include edu-cating customers to call an 800 number right afteran accident, staffing the telephone support sys-tem, equipping adjusters with vans and havingthem on call around the clock, extensively train-ing adjusters and allowing them to write a checkon the scene, contacting policyholders veryquickly after accidents, and improving back-officeprocesses that allow rapid settlement.

While both approaches to claims settlement

5 A study conducted by the independent Insurance Research Councilshowed that after paying lawyer fees, policyholders who hire an attorneyend up with less compensation on average than those who do not involvea lawyer (Fierman, 1995).


represent coherent sets of interdependent activi-ties, the profitability of each approach depends onthe type of customers served. For Progressive,which concentrates on nonstandard customerswho are more likely to be involved in an accidentand who generally choose only the lowest cover-age levels required by law, a fast settlement pro-cess is optimal because the margin for error byadjusters is limited. Moreover, facing less compe-tition to insure high-risk drivers, Progressive canearn operating income on the underwriting and isthus less dependent on the float to become prof-itable. In contrast, for standard insurers, whosecustomers choose much larger coverages, this re-sponse approach tends not to be optimal.

In sum, the value of individual activities can bedependent on the configuration of other activitychoices of a firm; the benefit of activities is con-textual. While some activities might be generi-cally beneficial, and thereby form the competitivebedrock of an industry, strategy-specific activitiesallow firms to create and implement different stra-tegic positionings in the market.

To gain a better understanding of how interac-tions among activities—i.e., the presence of strat-egy-specific activities—can create a number ofdifferent positionings, the framework of perfor-mance landscapes is very helpful (Kauffman,1993; Levinthal, 1997; Wright, 1931). To illus-trate the idea of a performance landscape, con-sider a simple world in which a firm needs only tomake a decision of how much to invest in twoactivities, A and B. For instance, a firm mightinvest very much in both A and B, or very little inA and a medium amount in B, etc. On a horizon-tal plane with two axes, we could capture thesechoices by plotting along the x-axis the degree ofinvestment in A and along the y-axis the degree ofinvestment in B. Since in our simple world thefirm can engage in only two activities, the firm’sperformance is determined by these two invest-ments. Thus, for every combination of invest-ments there arises a particular performance for thefirm. This performance is dependent on all factorsthat affect the value of an activity configuration,such as customer preferences, available technolo-gies, and competitors’ current positionings. Foreach combination of investments in A and B, we

now plot the ensuing performance on the verticalz-axis. This procedure creates a performance land-scape, i.e., a mapping from activity configurationsonto performance values (see Figure 2a). Concep-tually, the idea of a performance landscape caneasily be extended to more than two choice di-mensions (A, B, C, D, . . .), collectively leading toa performance outcome for a firm. For illustrativepurposes, we will continue, however, with twodimensions.

Consistency, or “internal fit” within a set ofactivities, is represented by a peak in the land-scape. A set of activities is said to be consistent ifchanging any single activity (and not changingany other activity) leads to a performance decline.Thus, consistency of fit among activities is repre-sented by a peak in the landscape: Any incremen-tal move leads the firm to a lower elevation, i.e.,to lower performance.

At the same time, the overall shape of theperformance landscape is intimately affected bythe degree of interaction among the activities. Ifactivities are generic (i.e., have an optimal con-figuration that is independent of other activityconfigurations), then the landscape is smooth andcontains only a single peak. This peak consists ofthe optimal configuration of each individual ac-tivity (see Figure 2a). The more interactions arepresent among the activities of firms, the morerugged the performance landscape becomes. Withmany strategy-specific activities (i.e., activitiesthat are highly interdependent with each other),many peaks arise (see Figure 2b). In this case, notonly one “global” (highest) peak exists, but manyother “local” peaks exist, too.6 If a performancelandscape represents a particular industry, thepresence of multiple peaks implies that severalconsistent sets of activities, several valuable posi-tionings, exist in the landscape. We illustratedsuch multiple positionings that arose from contex-tual activities with our examples of the wine andthe automobile insurance industries.

More generally, generic (independent) activi-ties lead to smooth plateaus, to “mesas” in the

6 This terminology is common in the context of optimization. Theperformance function, which takes activity choices as arguments and pro-vides performance as output, does not have a single “global” maximum, butalso several “local” maxima.


landscape.7 In a sense, the presence of genericactivities reduces the number of dimensions onwhich firms can differentiate themselves (becauseall firms have the same optimal configuration forthis activity). Figure 2c depicts the case in which

Activity B is generic. Regardless of the level ofActivity A, the highest performance is achievedfor a medium level of B. Thus, a medium level ofB constitutes a best practice for all firms and doesnot provide an opportunity for differentiation.

Contextuality of activities has been the focusof two current streams of research. First, agent-based simulation work based on the NK model hassought to analyze the consequences that arise asthe degree of interdependence among the activ-ities of a firm increases, and thus, as a perfor-mance landscape becomes more rugged. Second,the work on complementarities has focused on

7 Assume A is an independent activity that leads to high performanceif it is configured as A� (e.g., use computers in your accounting depart-ment). Since A is independent, A� always leads to high performanceregardless of the configuration of other activities. As a result, the heights onthe landscape of sets of activities that contain A� have a high correlationwith each other, i.e., the landscape is smooth. In contrast, if A is notindependent, the value of A� is changing when the configuration of otheractivities is changing. In this case, the heights of sets of activities thatcontain A� are less correlated with each other.

Figure2Performance Landscapes


providing empirical evidence for interaction ef-fects among activities in larger samples of firms.In the next two sections, we review each re-search stream.

ResearchBasedon theNKModel

While the organization literature has a longtradition of recognizing the importance ofinteractions (e.g., Thompson, 1967), formal

studies have only recently come to the fore. Alarge number of studies have employed simulationtechniques based on the NK framework developedby Kauffman (1993) to study the consequences ofinteraction effects (for an overview, see Sorenson,2002). Simulation models based on the NK frame-work have two parts: the creation of a perfor-mance landscape and the modeling of “agents”(e.g., firms) that try to find high peaks on theselandscapes.

As described above, in our context, perfor-mance landscapes represent a mapping betweendifferent sets of (more or less interdependent)activity choices and performance outcomes. Thechallenge for researchers was how to create aparsimonious mechanism that would allow thegeneration of such performance landscapes andprovide the researcher with control over the de-gree of interdependence among the activitychoices. It turned out that a similar problem hadarisen in the field of theoretical biology. Thefitness of an organism is to a large extent deter-mined by its genetic makeup, i.e., the outcomefrom a large set of genes. Moreover, many genesinteract with each other. Building on prior workby Wright (1931), who had visualized organismsas trying to achieve high locations on fitness land-scapes, Kauffman (1993) proposed the NK modelto represent possible payoffs to various combina-tions of genes, i.e., to create performance land-scapes. Work by Levinthal (1997) and Rivkin(2000) imported this technique to the field oforganizational studies.

As the name implies, the NK model has twokey parameters: N represents the number of activ-ities (or genes, in the original setting); K capturesthe degree of interdependence among the activi-ties. More specifically, if we apply the NK modelto business, each firm is assumed to make choices

with respect to N binary activities (a1, a2, . . . aN),each contributing to firm performance.8 For in-stance, firms need to decide whether to introducea new product (a1 � 1) or not (a1 � 0), whetherto provide more sales force training (a2 � 1) ornot (a2 � 0), or whether to upgrade productionfacilities (a3 � 1) or not (a3 � 0). Each activity,ai, contributes to the overall performance of thefirm. The contribution of each activity, ci(ai, a-i),is assumed to depend on how activity ai is config-ured and how K related activities (a-i) are config-ured. Thus, the notion of contextual activities—the value of an activity is dependent on how otheractivities are configured—is a central aspect ofthis type of modeling. Which K activities interactwith any activity ai is specified either by the mod-eler (e.g., Ghemawat & Levinthal, 2000) or ran-domly by the computer (e.g., Rivkin, 2000). Foreach possible combination of activity ai and its Krelated activities, value contributions ci are drawnrandomly from a uniform distribution over theunit interval. For instance, assume activity a1 isaffected by activity a2. Then the model wouldcreate four possible contributions for a1: c1(00),the contribution of a1 if a1 is set to 0 and a2 is setto 0; c1(10), the contribution if a1 is set to 1 and a2

is set to 0; and likewise c1(01) and c1(11). Each ofthese contributions would be determined by a ran-dom draw from the uniform distribution u[0, 1].

The resulting overall performance of a particularactivity combination is then given by the averageof the contributions, i.e., V(a1a2 . . . aN) �

1N

�i�1

N

ci(ai, a�i). For instance, for a case with N � 3,

the firm may have chosen the activity configura-tion 101; then V(101) � 1/3 * [(c1(101) �c2(101) � c3(101)].

The procedure thus allows researchers to createperformance landscapes that have a certain degreeof ruggedness, which is controlled by the param-eter K. If K � 0—i.e., each activity’s contributiondepends only on how that activity is config-ured—a landscape is smooth and single-peaked.As K increases, up to its maximum of N � 1,

8 The assumption that decisions are binary is not crucial. The modelcould easily be extended to have more than two choices for each decision.


landscapes become increasingly rugged. Sincecontributions are drawn randomly, landscapeswith the same level of K still differ in the locationof the various peaks on them.

The second part of the simulation models com-prises the agents that are “released” on these land-scapes. Considerable modeling advances havebeen made on how to represent these agents in thecontext of business firms. While early work as-sumed that firms explore performance landscapesby randomly changing (“mutating”) individual ac-tivities (Levinthal, 1997), more recent work hasput significantly more organizational structure onthe firms, modeling, for instance, hierarchy, ver-tical information flow, and incentives (Rivkin &Siggelkow, 2003; Siggelkow & Rivkin, 2005,2006), or different cognitive representations ofmanagers (Gavetti & Levinthal, 2000).

A simulation would then proceed as follows:First the researcher specifies the landscape char-acteristics N and K; then, using the NK modelprocedure a landscape is created. Onto this land-scape firms with various characteristics are re-leased; these firms are observed for a certain num-ber of periods (e.g., until each firm has found apeak and is not moving anymore) and their per-formance is recorded. Then a new landscape withsimilar characteristics is generated, and so on.Since each landscape differs in detail (due to therandom generation of the contributions), this loopis usually repeated many times (e.g., 1,000 times).Results are then averaged over these 1,000 obser-vations. Lastly, the landscape characteristics—say,K—would be changed. And again 1,000 land-scapes with this new level of K would be gener-ated, and firms would be observed on each of theselandscapes.

The key focus of this work has been on exam-ining the effects of different degrees of interaction(different levels of K). For instance, Levinthal(1997) found that firms operating on high-K land-scapes are subject to high rates of failure in chang-ing environments. Similarly, Rivkin (2000)showed that as K increases, the probability of afirm’s reaching the global peak decreases dramat-ically. As a result, imitating a firm that occupiesthe global peak within a landscape is very unlikelyto succeed if the leading firm’s strategy is based on

a large set of interdependent activity choices. Inan extension of this work, Rivkin (2001) analyzedthe problem faced by firms (e.g., franchise opera-tions) that, after finding the global peak, mightwant to replicate this performance. If a firm’sstrategy is complex, a firm that tries to replicateitself might encounter similar obstacles to thoseencountered by other firms that try to imitate it.Assuming that a replicator has a higher probabil-ity of correctly duplicating each individual activ-ity than an imitator does, Rivkin (2001) foundthat the gap between replicability by the samefirm and imitability by other firms tends to begreatest at moderate levels of K.9

An attractive feature of the NK model is thatthe degree of interdependence can be controlledby only one parameter, K. The downside of thissimplicity is that the modeler has no control overwhich types of interactions arise. In any givensimulation involving a significant degree of inter-action, a broad distribution of different types ofinteractions is present, rendering the study of theeffects of particular types of interactions, and ofcontextual interactions, impossible. For instance,activities A and B might be complements (i.e., themarginal benefit of A increases with the level ofB, and vice versa), while the interaction betweenA and C is one of substitutes (i.e., the marginalbenefit of A decreases with the level of C). Un-fortunately, the modeler has no control overwhich of these types of interactions arise. Thislimitation of the NK model stems from the ran-dom assignment of contributions to activities (seeAppendix 1 for more details).

In sum, while the studies of the effects of dif-ferent degrees of interaction have produced anumber of interesting insights, it is important tonote that these results are mean tendencies across

9 Further studies employing the NK methodology include McKelvey(1999) and Lenox, Rockart, and Lewin (2006), whose models includeinteractions between different firms; Levinthal and Warglien (1999), whoincluded interactions among different decision makers; Marengo et al.(2000), who examined the effects of various decomposition schemes;Siggelkow and Levinthal (2003, 2005), who analyzed different sequences oforganizational structures; Sommer and Loch (2004), who studied differentlearning mechanisms; and Ethiraj and Levinthal (2004a, 2004b), whofocused on the effects of different degrees of modularity among the activitychoices. Empirical studies testing the NK-framework are few. Notableexceptions are Sorenson (1997), Fleming and Sorenson (2001), and So-renson, Rivkin, and Fleming (2006).


a wide range of different types of interactions,potentially hiding important phenomena. For in-stance, as Siggelkow (2002b) showed using ananalytically solvable mathematical model, theconsequences of misperceiving interactions be-tween activities are markedly different when in-teractions are between substitutes than when theyare between complements. With the NK ap-proach, such distinctions relating to the types ofinteractions cannot be explored.

ResearchBasedon theComplementarityFramework

Besides the simulation work in the organizationliterature, a large stream of the recent work oninteraction effects among firms’ activities—

both empirical and theoretical—has built on thework of Milgrom and Roberts (1990, 1995).Guided by the observation that many firms in theAmerican economy were shifting from mass pro-duction to lean manufacturing, Milgrom and Rob-erts (1990) proposed an optimizing model of thefirm that generated many of the observed patternsin the transition from one system to the other. Inparticular, the model accounted for the observa-tion that a successful transformation from onesystem to the other required substantial changes ina wide range of a firm’s activities.

Milgrom and Roberts’ work contained two keyinsights, one conceptual, one mathematical. First,they observed that many activities within a givenproduction system were complementary to eachother. They defined two activities to be comple-mentary if the marginal benefit of one activity wasincreased by the level of the other activity. Sec-ond, they developed mathematical methods build-ing on the supermodularity work by Topkis (1978)that allowed a particular but exact formulation ofthe notion of complementarities involving a largeset of choices. With these methods, models withan unusually large number of variables and rela-tively weak assumptions (by economics standards)were amenable to tractable analysis. (We will re-turn to these assumptions at the end of this sec-tion.)

The complementarity framework has spurredboth theoretical and empirical research. A grow-

ing body of literature has continued to developand apply the mathematical apparatus of super-modularity in a wide variety of formal models,addressing issues such as investments in productand process flexibility, optimal partitioning of de-sign problems, modes of organizing innovationactivities, and convergence to equilibria in learn-ing games (e.g., Athey & Schmutzler, 1995; Bag-well & Ramey, 1994; Chen & Gazzale, 2004;Holmstrom & Milgrom, 1994; Leiponen, 2005;Milgrom, Qian, & Roberts, 1991; Milgrom &Shannon, 1994; Schaefer, 1999; Topkis, 1995;Vives, 2005).

Empirical work in this line of research haspursued two main directions: finding support forcomplementarity among various activities bystudying the performance implications of adoptingindividual activities versus entire sets of activities,and inferring complementarities by studying adop-tion patterns of new technologies and practices.For a thorough exposition of the inherent econo-metric problems involved in identifying comple-mentarities, see Athey and Stern (1998) andArora (1996). For a testing strategy to detectsupermodularity given discrete choices, seeMohnen and Roller (2005).

A notable example of the first type of empiricalstudy is Ichniowski, Shaw, and Prennushi (1997),who studied the effect on the productivity of steelfinishing lines of adopting individual human re-source management (HRM) practices versus en-tire sets of HRM practices. They found “consistentsupport for the conclusion that groups or clustersof complementary HRM practices have large ef-fects on productivity, while changes in individualwork practices have little or no effect on produc-tivity” (p. 291). Ichniowski and Shaw (1999) re-ported a similar finding using an expanded sampleincluding both U.S. and Japanese steel finishinglines. Likewise, MacDuffie and Krafcik (1992)found for firms in the U.S. automobile industry asynergistic payoff between the adoption of “lean”production processes and a set of HRM practices,including shop floor work organization and incen-tive clauses in employment contracts. MacDuffie(1995) extended this work to a larger set of auto-mobile assembly plants located worldwide, findinga complementary relationship between team-


based work systems, high-commitment HRMpractices, and low inventory and repair buffers.Also focusing on high-performance work prac-tices, such as profit sharing, formal teams, and jobrotation, Colombo, Delmastro, and Rabbiosi(2007), using longitudinal data on 109 Italianmanufacturing firms, found that the value of thesepractices was enhanced by a decentralized organi-zational structure. Thus, in this case, a comple-mentarity between work practices and an elementof organization structure was detected.

Focusing on investments in information tech-nology, Bresnahan, Brynjolfsson, and Hitt (2002)found in a sample of 300 large U.S. manufacturingand service firms that the benefits to informationtechnology investments increase in the level ofworker human capital, and vice versa, indicatingcomplementarity. Likewise, the relationship be-tween workers’ skill level and organizationalchanges, such as decentralization of authority anddelayering of managerial functions, was shown tobe complementary in a sample of French manu-facturing plants (Caroli & Van Reenen, 2001).

On a broader organizational level, Whittingtonet al. (1999) studied the performance implicationsof 10 distinct changes in organizational structure,processes, and firm boundaries using a survey of383 European firms. Consistent with complemen-tarities, they found that piecemeal changes (withthe exception of investments in information tech-nology) delivered little performance benefit, whileexploitation of the full set of innovations wasassociated with high performance. In particular, apositive performance effect arose only if changesto structures, processes, and firm boundaries werecombined. No performance effect, or even a neg-ative effect, was found when changes addressedonly two of these areas. For a broader exposition ofthese results, see Pettigrew et al. (2003).

One should note that not every empirical testof complementarity has yielded confirming results.For instance, Cappelli and Neumark (2001), usingU.S. Census Bureau survey data covering 1977through 1996, found very few complementaritiesamong work practices. In addition, they made theinteresting observation that complementaritydoes not necessarily imply that joint adoption isbetter than no adoption. While it may be true that

adopting practice A alone is worse than adoptingpractices A and B together, the net benefit ofpractices A and B may still be zero if the directeffects (e.g., costs) of A and B are negative. Theyfound such a relationship for the practices of jobrotation and self-managed teams. These two prac-tices do benefit from each other, yet both haveindividual negative effects on performance (mea-sured by labor productivity), creating an overallinsignificant performance effect.10

Similarly, Black and Lynch (2001), studyingthe effects of work practices in a broad sample ofU.S. manufacturing businesses over the period1987 through 1993, found a significant interac-tion effect only between unionization and profitsharing for nonmanagerial workers, yet no inter-action effects among any of the workplace prac-tices themselves. Lastly, in a detailed study of theeffects of improved information technology inemergency response systems (9-1-1), Athey andStern (2002) did not find evidence for comple-mentarity between information technology in-vestments and investments in the human skills ofthe call-takers.

Empirical studies in the second stream of liter-ature, examining adoption patterns of new prac-tices and technologies, include Colombo andMosconi (1995), who investigated the adoptionpatterns of flexible manufacturing systems, newdesign/engineering technologies, and new man-agement techniques such as JIT and total qualityprocedures in the Italian metalworking industry.They observed that all of these innovationstended to be adopted together, providing an indi-cation of complementarity among them. Focusingon the adoption of different types of incentives,Cockburn, Henderson, and Stern (1999) showedin a sample of large pharmaceutical firms that acomplementary relationship exists between the

10 Sometimes the adoption of “practices” may be forced by otherconsiderations. For instance, Van Biesebroeck (2006), studying automobileplants in the United States, found that an increase in product variety ledto lower labor productivity. In this case, competitive forces may require afirm to increase its product variety. Moreover, Van Biesebroeck found thatan increase in vertical integration (insourcing) and an increase in the useof flexible technology also led to lower labor productivity. However, if theincrease in product variety was coupled with a higher degree of insourcingor a more extensive use of flexible technology, the negative effects weremuted, thus showing a complementary relationship between product vari-ety and flexibility and product variety and insourcing.


degree to which publications in scientific journalsare important for career advancement and inten-sity of incentives to conduct applied research.

Concentrating on interdependencies amongoutsourcing decisions, Novak and Stern (2007),using detailed data from the global auto industry,found that contractual complementarities exist. Inparticular, they showed that the probability that afirm chooses to vertically integrate an automobilesystem (e.g., the brake system) increases with thenumber of other systems the firm integrates.Moreover, these complementarities are particu-larly strong for systems that have tight interdepen-dencies and for which coordination is difficult tomonitor.

Hitt and Brynjolfsson (1997), in a study of 273firms from the Fortune 1000 list, found that firmsthat were extensive users of information technol-ogy tended to adopt a complementary set of orga-nizational practices that included decentralizationof decision authority, emphasis on subjective in-centives, and greater reliance on skills and humancapital. Similarly focusing on the adoption of in-formation technologies, Bocquet, Brossard, andSabatier (2007), using data on 136 French firms,found that positive reinforcements appeared toexist between Enterprise Resource Planning(ERP) systems and Electronic Data Interchange(EDI) systems, and between ERP and Internet-based exchange systems. At the same time, theyconcluded that EDI systems and Internet-basedexchange systems were independent choices, notaffecting each other.

In sum, studies have generally explored activityconfigurations that are beneficial for many firmsand activities that are complementary in the samemanner for all firms within an industry or acrossindustries. (For a recent study that starts to addresscontextual interactions, see Cassiman andVeugelers, 2006, to be discussed in more detaillater.) While these are important situations tostudy, they represent only a subset of the ways inwhich activity choices can interact and how theseinteractions affect competition. Moreover, an ex-planation for sustainable competitive advantage,i.e., for long-term superior profitability, may notbe found in such cases. If a particular activityconfiguration is beneficial for all firms within a

given industry, competitors will have strong in-centives to adopt this configuration sooner orlater.

Similar to the NK model, the complementarityframework is not well-suited to deal with contex-tual interactions. While in the NK model any andall types of interactions can arise, the complemen-tarity framework, as the name implies, constrainsitself to a single and very specific type of interac-tion. In particular, in the formal analyses thatform the background for the empirical studies, twoactivities, A and B, are said to be complements ifand only if three conditions hold (see Appendix 2for a more general and formal statement of theseconditions):

1. The marginal benefit of A has to increase withthe level of B, and vice versa.

2. Relationship 1 has to hold for all levels of Aand B.

3. Relationship 1 has to hold regardless of how afirm configures its remaining activities.

This definition of complementarity is conve-nient because it yields robust comparative staticsproperties: Any exogenous decrease in the mar-ginal cost of any element in a system of comple-ments will (weakly) increase the optimal level ofall elements in the system (for more details, see,e.g., Milgrom & Roberts, 1990; Milgrom & Shan-non, 1994; Topkis, 1995). This formulation alsoholds mathematical interest because conditions 1through 3 describe the weakest sufficient condi-tions to yield these comparative statics results(Milgrom, Roberts, & Athey, 1996). However, forthe central question of strategy—how firms candistinguish themselves and achieve above-averageperformance—an exclusive focus on complemen-tarities as defined above is less satisfying for threereasons.

First, complementarity is but one case of howactivities interact. Activities within firms can in-teract as substitutes as well.11 For instance, as afirm increases its investment in quality control,leading to fewer defects in its products, the mar-

11 The complementarity framework can incorporate only a limitednumber of substitutes. If activity ai is a substitute to all other activities of afirm, it can be formally replaced by –ai, thereby making it complementary(de Groote, 1994).


ginal benefits of increasing after-sale service sup-port dealing with faulty products is likely to de-crease.

Second, the type of interaction among activi-ties may not be constant for all levels of theseactivities, i.e., condition 2 may be violated. Twoactivities might be complementary over a range oftheir values, but not complementary outside therange.

Third, interactions among activities are notalways independent of other activity choices, ascondition 3 requires. As a result, two activitiesmight be complementary in one firm and substi-tutes in another. (For an illustration of how re-strictive the complementarity conditions are, seeAppendix 3.) Similarly, as a firm changes some ofits activities, the nature of the interactions amongits activities might change over time.

To summarize, both the NK model and thecomplementarity framework have been success-fully used to study the issue of interdependenciesamong a firm’s activity choices. At the same time,both approaches make it difficult to study contextualinteractions. In the remainder of this paper, we willillustrate contextual interactions in their variousforms and outline implications of contextual inter-actions for both managers and researchers.

We first describe violations of condition 2, i.e.,contextuality that is caused by the level of theactivities. Second, we will explore examples ofviolations of condition 3. In one case we describehow the same activities can have different inter-actions in different firms because the activities areembedded in different activity systems; in theother case we describe how contextuality can leadto interactions that change their nature over time.

Contextuality CreatedbyDifferentActivityLevels

To illustrate a situation in which activities may becomplementary only over certain ranges of theirlevels (violation of condition 2), we continue withthe example of the auto insurer Progressive Corpo-ration. Progressive’s quick-response approach tohandling clients’ claims allows the company to lowertotal costs by reducing the frequency of litigation inserving high-risk customers. Let T � t1 � . . . � tNbe the total time between accident and issuing a

check, i.e., the time required for the N activitiesthat lie between accident and the issuing of acheck. For instance, t1 might be the time until acustomer notifies an agent after an accident hashappened, t2 the time between the notification ofthe agent and personal face-to-face contact, and t3the time between agent contact and claim settle-ment. Let P(T) be the net benefit function ofhaving a response time T. Since shorter responsetimes are beneficial for Progressive, P(T) is de-creasing in T. Depending on the shape of P(T),investments in activities that shorten the totaltime to settlement are complementary, or not.Strict complementarity requires that P(T) is con-vex over the entire range of T. While an argumentcan be made that P(T) may be convex within acertain range of T, the convexity of P(T) is un-likely to hold over all possible levels of T. Forinstance, if it takes a relatively long time to settleclaims (two weeks is not uncommon in the indus-try), a reduction in the time it takes for an agentto have contact with the claimant and to start theclaims process, say from three days to one day, isquite likely to go unnoticed by customers andcreates no benefit for the insurance company (theinvestments are not complementary). If, however,claims settlement can actually occur within a day,the same reduction in time of contacting a claim-ant (from three days to one day) may have con-siderable benefit to the insurance company (interms of both customer satisfaction and likelihoodof involving a lawyer), as the insured party mayrespond positively to the noticeable reduction oftotal processing time. (In other words, the effi-ciency improvement is not swamped by large de-lays introduced by other parts of the settlementprocess.) Thus, the investment in one activityincreases the marginal benefit of investing in theother activity—the activities are complementary.Finally, once both contact and settlement timehave been reduced to very short levels, the mar-ginal benefit of decreasing one even further islikely to decline again, i.e., the investments ceaseto be complementary. (In other words, as T getscloser to zero, P(T) is not going to infinity but willlevel out.)

This example also illustrates the empiricalchallenge of choosing the correct level at which to


measure the effects of complementarity. Using theprevious notation, a common question would bewhether investments that reduce, say, t1 and t2 arecomplementary. Assume that an investment thatreduces t1 does not lead to a reduction in t2, andvice versa, i.e., reductions in T through invest-ments in t1 and t2 are strictly additive. In this case,if the efficiency of the process is measured by T,no complementarity between the investments willbe found. At the same time, if P(T) is used tomeasure the effects and T is in the range in whichP(T) is convex, one would empirically find acomplementarity between the investments.

Contextuality Leading toDifferent Interactions inDifferent Firms

An even more interesting departure from thestrict complementarity assumptions for companystrategy is the case when the type of interaction isaffected by other choices (violation of condition3). A firm’s existing set of activities can transformthe relationship between activities from one ofcomplements to one of substitutes and vice versa.For example, in the automobile insurance setting,we described two different kinds of strategies withrespect to response times. Given a strategy ofpostponing payments (up to the point when reg-ulators step in), all activities that lead to a reduc-tion in response times are substitutes. Any invest-ment that reduces the time of one activity wouldlead to a decrease of the marginal benefit of speed-ing up another activity. However, with a strategyof decreasing total response time, these choicesare complementary (at least over a certain range,as discussed in the previous section).

A more elaborate example of contextuality canbe found in the mutual fund industry. In 1974, themutual fund provider Vanguard was formed. Orig-inally, Vanguard, like other mutual fund provid-ers, outsourced investment management to an in-vestment management company, WellingtonManagement (WM). As was industry practice inthe 1970s, Vanguard distributed its funds usingthe same investment management company thatmanaged the funds.

Vanguard differed from its competitors, how-ever, in various ways. First, administrative serviceswere not contracted out, but were provided at cost

by the Vanguard Group itself. Second, the Van-guard Group was owned by the fund shareholdersrather than by a separate set of shareholders.Lastly, Vanguard differed from its competitors inits overarching investment philosophy and thetype of funds it promoted. John Bogle, Vanguard’sCEO, believed that high and fairly predictablelong-run investment returns could be achieved byincurring very low expenses and attempting not tooutperform the market but to match it. Thus,Bogle introduced the industry’s first index fund(based on the S&P 500) in 1976 and increasedVanguard’s offering of bond funds. In 1977, Van-guard decided to bring the distribution functionin-house and to market its funds as no-loads, i.e.,not to charge any sales fees. In the following years,Vanguard also started to bring investment man-agement for all bond funds in-house.

The interplay between the insourcing of in-vestment management and the no-load, directdistribution system reveals the effect of contextu-ality. For Vanguard, bringing both investmentmanagement and distribution in-house was com-plementary, yet for other fund providers it wasnot. The benefit of internalizing investment man-agement was much greater after Vanguard hadgained control over distribution. It would havebeen unwise for Vanguard to take away the (verylucrative) investment management business fromWM while still relying on WM to distribute itsfunds. WM would have been much less motivatedto sell the funds. If insourcing investment man-agement and direct distribution are complemen-tary, the reverse is also true, i.e., changing fromload distribution to direct, no-load distribution ismore valuable in the presence of internal invest-ment management than with external investmentmanagement. This reverse argument holds forVanguard, but only in the context of its low-coststrategy, organizational structure, and fund port-folio. Internalization of investment managementand distribution each decreased costs. By virtue ofVanguard’s mutual structure these cost savingswere passed through to the funds, which thereforerecorded higher net returns. It has been shownthat fund inflows, in turn, respond in a convexmanner to higher relative returns (Sirri & Tufano,1998). Thus, the benefit to Vanguard—in terms


of asset growth—from decreasing its costs of in-vestment management became larger when thecosts of distribution were also reduced. Moreover,this effect was most pronounced for fund types forwhich small changes in expenses translated intolarge relative performance differences and werenot swamped by large performance fluctuations.Thus, the complementary relationship arosestrongly for the types of funds Vanguard was fo-cusing on and for which it was insourcing theinvestment management, i.e., low-risk and indexfunds. Consistent with this contextual comple-mentarity argument, Vanguard did not insourcethe investment management for actively tradedequity funds.

This contextuality can also be inferred fromthe following observation. Were insourcing in-vestment management and distribution comple-mentary for all firms, regardless of the firms’ otherchoices, then we should always see the choices ofin-house investment management and in-housedistribution go together. However, we can observequite a number of “mixed cases,” i.e., mutual fundproviders that focus only on asset managementand outsource distribution, and a number of pro-viders who specialize in distribution and outsourceinvestment management. Thus, insourcing invest-ment management and insourcing distribution donot seem to be context-free complements.

Contextuality Leading toChanges inActivityInteractionsOver Time

Violations of condition 3 can manifest themselvesnot only across firms but also over time in thesame firm. Two activities that were substitutes canbecome complements, and vice versa, as a firmadapts its activity system to changing industryconditions.

An example of how the relationship amongactivities can change over time can be found at LizClaiborne, the largest fashion apparel manufac-turer in the United States. In the 1980s, Liz Clai-borne focused on the apparel needs of the thenrapidly growing segment of professional women.Its collection provided high value to customerslooking for guidance about what constituted ac-ceptable professional women’s apparel and for anarray of items that were fashion coordinated. In its

early years, given its unique positioning, Liz Clai-borne was able to easily sell all of its output to itsdepartment store customers and required themto place binding orders at the beginning of theseason.

Consider the subset of activities that influencesthe lead time between design and final delivery ofthe product. Each of these activities, from designitself to the management of contract manufactur-ers, involves configuration choices: e.g., conven-tional design vs. computer-aided design, physicaldelivery of design and fabric samples to manufac-turers vs. using online technology, etc.

When Liz Claiborne was setting fashion trendsand was able to sell its entire output, the benefitsof decreasing its lead time were small. In fact, leadtime did not matter much as long as Liz Claibornewas able to ship its merchandise at the beginningof each season. For firms that were not able to“define” the market, shorter lead times were ben-eficial since they allowed the gathering of moreinformation about upcoming fashion trends.Hence for Liz Claiborne, improvements in activ-ities that led to a shortening of the total lead timewere substitutes. More formally, let T � t1 � t2� . . . � tN be the total lead time, with t1, . . . ,tN the time of the various activities from design todelivery. If there is no benefit in decreasing T(under the constraint that T is sufficiently small toguarantee shipment at the beginning of the sea-son), then a decrease, for instance, in t1, wouldlead to a reduction of the benefit of reducing t2,i.e., investments that reduce t1 and t2 are substi-tutes. For example, as IT systems improved, allow-ing faster communications with suppliers, themarginal benefit of investing in design technology(e.g., CAD systems) that would reduce lead timeeven further decreased for Liz Claiborne. Consis-tent with this relationship, Liz Claiborne investedvery little in upgrading design technology (Hen-ricks, 1995).

In the 1990s, however, Liz Claiborne’s compet-itive environment changed. First, the Liz Clai-borne brand became less important, leading todecreased consumer loyalty. With this change,shorter lead times, once unimportant for the com-pany, became valuable, since shorter lead timesallowed it to wait longer and discern emerging


fashion trends. Second, department stores experi-enced cash-flow problems as many chains hadbeen involved in leveraged buyouts or mergersinvolving high levels of debt. As a consequence,department stores sought to reduce inventories tofree up cash, and increasingly demanded the de-livery of merchandise in small lots and the optionto reorder items during a season. To allow reor-dering efficiently, manufacturers had to move toat least partial production to order (Hammond,1993). Production to order, in turn, was moreeffective with shorter overall lead times. Invest-ments that sped up the design process were mademore valuable by concurrent investments in in-formation technology. For Liz Claiborne, upgrad-ing design technology and upgrading informationtransmission technology had become comple-mentary.

Implicationsof Contextuality forManagementPractices

Contextuality has a number of implications formanagement practice. Here, we focus on theeffect of contextuality on the ease of imitation

and adaptation. Imitating complex systems of in-teractive activities is generally challenging be-cause entire systems (rather than individual activ-ities) must be replicated (Porter & Rivkin, 1998).Put differently, interactions cause the imitation-benefit relationship to be convex: If only a fewelements of a system are copied, no benefits (oreven negative results because of inconsistencies)are generated.

Contextuality further adds to the difficulty ofimitating a competitor’s activity system. First,strategy-specific activities, as compared to genericactivities, are inherently more difficult and costlyto imitate because their configurations are observ-able in fewer firms, and matching them oftenrequires imitators to suboptimize their current ac-tivity configurations (Porter, 1996).

Second, and more subtle, contextuality of in-teraction effects can lead to misguided imitationbehavior. Contextual interactions require imita-tors to learn not only about new activity config-urations (e.g., a new practice adopted by a com-petitor) but also about new activity interactions

(i.e., how this practice affects existing activitieswithin the imitating firm). In the presence ofcontextual interactions, managers who observethat two activities are complementary (or substi-tutes) for a competitor cannot conclude that thesame two choices are complementary (or substi-tutes) for their firm. As a result, imitating theinvestment behavior of competitors can backfire.For instance, a competitor for whom two activitiesare complementary would tend to co-invest inboth activities. Imitating this co-investment couldbe harmful to the imitator if the two activities,due to other activity choices, are actually substi-tutes in the imitating firm. For instance, whileinvesting in quick response capabilities and fasterclaims adjusting might be complements for Pro-gressive, they might very well be substitutes forstandard insurers.

Similarly, contextuality of interactions impliesthat the relationship between existing activitiescan change as new activity configurations areadopted. This means that established strategicheuristics or adjustment routines (Nelson & Win-ter, 1982) may fail. Consider a firm that is tryingto imitate a leading firm. If the imitator couldobserve the entire set of activity choices taken bythe leading firm, and if the imitator were capableof duplicating all these choices, the imitator couldimitate perfectly. However, in most cases, theimitator cannot observe the entire set of the lead-er’s activity configurations. Hence, the imitatorcan duplicate only the observable activity config-urations and subsequently attempt to deduce theremaining set of choices, hoping that its system ofroutines and traditional operating procedures, i.e.,its knowledge about how the new activity config-urations interact with its old activities, will bringabout optimal readjustments. Yet, if the nature ofthe relationship between existing activities haschanged after the adoption of new activities, ei-ther no or even counterproductive adjustmentswill be made.

The fact that interactions can change theirtype from substitutes to complements, or viceversa, when other activity configurations are al-tered has consequences not only for imitation butalso for the ability of firms to adapt their activitysystems, e.g., in response to an environmental


change. As a firm starts to incrementally changeits activity system, it may not be aware that inter-actions among its other activities have changedand will therefore operate with mistaken beliefsabout interactions, relying on outdated mentalmaps. For instance, Liz Claiborne’s existing man-agement did not fully realize that interactions hadchanged within its activity system after reorderingactivities had been adopted—e.g., creating acomplementarity between investments in fasterdesign capabilities and better capitalized suppli-ers—which contributed to its performance decline(Siggelkow, 2001).

Further examples of such consequences of con-textual interactions on imitation and adaptationare revealed in the innovation literature (Hender-son, 1993; Henderson & Clark, 1990). Incumbentfirms have been found to experience severe diffi-culties in responding to “architectural” innova-tions that are characterized not by new parts of asystem, but by new ways in which the parts of asystem interact with each other. The interactionsamong the components of a product, or, moregenerally, among activities of a firm, leave orga-nizational imprints, such as who communicateswith whom, what type of information is gatheredand shared, and what heuristics are used to solveproblems or to make investment decisions. If rel-evant interactions change, the existing organiza-tional structures and processes that arose in thecontext of the old set of interactions can becomevery misleading.

Recall the example of firms like the Gap thatoperate distribution systems linking warehousesand stores. For such firms ordering frequency anddelivery frequency are complementary, yet only ifrelevant information for ordering on a daily basisis available, e.g., through a POS system. Existinginvestment routines that were formed in the oldregime (i.e., in the absence of a POS system) willnot have incorporated a relationship between or-dering and delivery frequency. With these oldroutines in place, the installation of a POS system(e.g., a salient feature of a competitor that wasreplicated) may not be accompanied by increasedinvestment in ordering and distribution fre-quency. Moreover, even if the firm increased in-vestment in one of these activities, the old rou-

tines would not lead to a self-adjusting increase inthe investment in the other activity.

In sum, the extent of contextual interactions isan important dimension that characterizes systemsof activities. While considerable research efforthas been extended on the horizontal axis of Figure1, the contextuality of activities, much less atten-tion has been spent on the vertical dimension, thecontextuality of interactions. Combining the dis-tinction between generic and strategy-specific ac-tivities and between interactions that are contex-tual or not creates the typology shown in Figure 1.When no interactions are present optimal config-urations can be found that are not different acrossfirms. In other words, these activity configurationsrepresent universal best practices. As the interac-tions among activities becomes more dense (i.e.,the value of activities is more likely dependent onother activity choices), the optimal configurationof activities becomes a function of industry, stra-tegic group, or even firm-level strategy. At each ofthese levels of activity contextuality, interactionsthemselves can be either contextual or similarwithin all firms at the respective level. Given thatcontextuality of interactions has not been a focusof past research, in the next two sections, we willspell out implications for both simulation andempirical work.

Implicationsof Contextualityof Interactionsfor Simulation Studies

Formal modeling can be very useful in trying tounderstand the often complex effects of activityinteractions. Traditional closed-form modeling

approaches, however, become quickly intractablewhen dealing with interactions unless restrictionsare imposed, such as the Milgrom and Robertsdefinition of complementarities. Agent-based sim-ulations building on the NK model can addressthis challenge. Yet, as noted before, the NK sim-ulation framework is limited because it does notprovide control over which types of interactionscan arise in a performance landscape.

To study the effects of contextual interactionsdirectly, such control would be very useful. Oneway to achieve such control would be to start witha performance function, rather than to assign con-


tributions to individual activities. Consider a caseof N � 4, where each activity ai can take on twovalues, 1 and 0. The following function includesall possible interactions among the activities:

V(a1, a2, a3, a4) � �1a1 � �2a2 � �3a3 � �4a4 �

�1a1a2 � �2a1a3 � �3a1a4 � �4a2a3 � �5a2a4 �

�6a3a4 � �1a1a2a3 � �2a1a2a4 � �3a1a3a4 �

�4a2a3a4 � �a1a2a3a4

By choosing appropriate values, or distribu-tions, for the parameters �i, �i, �i, and �, dif-ferent types of interactions can be created. Forexample, if �i � �i � � � 0, all activities areindependent; in this case, landscapes that aregenerated by drawing random values for �i havesimilar properties to K � 0 landscapes createdby the NK model. If �i � 0, �i � 0 and � � 0,all interactions among activities satisfy the Mil-grom and Roberts definition of complementar-ity, as all cross-partial derivatives are positive. If1 � �i � 0, �i � –1 and � � 0, all activitieshave contextual interaction effects.12

First exploratory characterizations of perfor-mance landscapes created with this methodologyshow that having control over the types of inter-actions can create new insights. For instance, oneof the main findings of NK models is that as Kincreases—often interpreted as an increase in in-teraction intensity (e.g., Levinthal, 1997)—per-formance landscapes become more rugged (Kauff-man, 1993), making imitation more difficult(Rivkin, 2000). Yet, if landscapes are composedentirely of complementary activities, stronger in-teractions can actually lead to smoother land-scapes, making imitation potentially easier (resultsavailable from the authors).

Implicationsof Contextualityof Interactionsfor Empirical Research

Contextuality of both activity configurationsand interactions poses significant challengesfor empirical work because identifying contex-

tuality often requires an in-depth knowledge ofthe activity systems of each firm, or data point.Such in-depth knowledge is difficult to obtain forlarge samples. However, our framework suggestspractical directions for large-sample research. Forinstance, assume that the benefit of adopting abundle of production practices (say, A, B, and C)has been found to yield higher labor efficiency fora sample of firms than adopting the practicesseparately. Our framework suggests the additionalquestion of whether the configuration is particu-larly beneficial (or detrimental) for firms withspecific strategies, i.e., for firms with certain sets ofother activity choices. By pooling across all obser-vations, we know only that the bundle of practicesis beneficial on average. However, it may be thatA, B, and C are beneficial (and/or mutually rein-forcing) only for companies that produce stan-dardized outputs, while they are detrimental(and/or mutually independent or even substitutes)for companies that produce highly customizedoutputs (or vice versa).

Contextuality of interactions can be exploredby testing whether interaction effects are constantover entire samples, including firms with signifi-cant differences. Interaction effects are frequentlystudied by including the product of two variablesin a regression model. Thus, if the interactionbetween A and B is tested, the regression modelwould include a term such as �*A*B. Contextu-ality due to the level of activities could be testedby exploring whether � is a function of the levelof A and B. This could be explored by splitting thesample into groups depending on their levels of Aand B and testing whether � is different across thegroups.

Contextuality due to other activities could betested by exploring whether � is a function ofother variables, C. Dividing the sample into sub-groups using C and testing for differences in �, orincluding higher-order interaction terms such asA*B*C, would be a first step to explore this type

12 To see that all activities have contextual interaction effects when1 � �i � 0, �i � �1 and � � 0, consider, e.g., the cross-partial derivativeof a1 and a2, �1 � �1a3 � �2a4. It equals �1 if a3 � 0 and a4 � 0. Since �1 �0, a1 and a2 are in this case complements. Yet, if a3 � 1 and a4 � 0, thecross-partial derivative equals �1 � �1 � 0; thus, in this case, a1 and a3 aresubstitutes. Likewise for a3 � 0 and a4 � 1. In other words, the type of theinteraction between a1 and a2 is contextually determined by the configu-rations of a3 and a4.


of contextuality. Similarly, if A and B are shownto be complementary on average, finding variablesC that drive the joint adoption of A and B, butnot of A or B alone, can point to sources ofcontextuality. For an interesting test along theselines, see Cassiman and Veugelers (2006). Inves-tigating whether internal R&D and externalknowledge acquisition are complementary forfirms, they “identify reliance on basic R&D—theimportance of universities and research centers asan information source for the innovation pro-cess—as an important contextual variable affect-ing complementarity between internal and externalinnovation activities” (p. 68).

If no such contextuality effects among a partic-ular set of performance-enhancing activities canbe detected, then the range of firms included inthe sample speaks to the degree to which theseactivities are generic. For instance, if the sampleincludes firms from a broad swath of industries,the set of activities would be universal best prac-tices. If firms from only one industry are included,the set of activities would be (at the minimum)industry best practices. If contextuality effects aredetected, the degree of specificity of the contex-tual variable determines the degree of specificityof this effect. For instance, if the contextual vari-able is constant for firms within a strategic group,yet differs across strategic groups, the identifiedactivities are strategic-group best practices with orwithout contextual interactions, depending onthe presence of contextual interactions.

As an illustration of how taking contextualityinto account can refine empirical findings, wereanalyzed the data from MacDuffie’s (1995) studyof automobile assembly plants. MacDuffie (1995)investigated the productivity and quality effects ofinnovative human resource practices, work poli-cies that govern shop floor production activity,and the use of inventory buffers in production.MacDuffie analyzed both the direct effects andinteraction effects of these practices and con-cluded that “plants using flexible production sys-tems, which bundle human resource practices intoa system that is integrated with production/busi-ness strategy, outperform plants using more tradi-tional mass production systems in both productiv-ity and quality” (p. 218). The results implied that

the identified practices were generically beneficialand interacted similarly in all firms, i.e., a case ofindustry best practices.

Our subsequent analysis of the data reveals,however, that only the work practices, such as thedegree to which workers are in formal work teams,were truly industry best practices, showing no con-textual effects. The human resource and inventorybuffer practices prove to have both contextualbenefits and contextual interactions. For instance,the benefit of the human resource practices, suchas the level of ongoing training, was higher forplants that assembled relatively new models, i.e.,for firms that had shorter product life cycles. Sim-ilarly, we found that the complementary interac-tion between human resource and inventorybuffer practices was influenced by the degree ofvariation among those parts that were required forall models assembled in a plant (MacDuffie &Siggelkow, 2002).

A further important avenue for empirical workis to examine a broader array of measures of per-formance, specifically measures of overall perfor-mance. Many studies of complementarities haveemployed narrow efficiency measures such as laborinput per unit of output (i.e., labor productivity).These measures offer comparability across pro-cesses, but have differing relevance for firms withdifferent strategies. Ideally, performance measuresshould incorporate both the cost and the priceelements of the business (i.e., some form of marginor profit contribution measure). For instance, afirm that produces highly customized productsmay not want to adopt the bundle A, B, and C, ifadopting this bundle hampers the ability to cus-tomize products and thereby command higherprices. In this case, the firm might pursue a differ-entiation strategy (Porter, 1985). While a differ-ent optimal bundle might result in lower (labor)efficiency in producing standardized outputs, theprice premium for the customized products canoutweigh the efficiency loss. A focus on narrowmeasures of efficiency, then, implicitly suppressesstrategy differences by assuming that all firmsvalue the measure similarly, i.e., that all firmsfollow the same strategy. This neglects importantdimensions of competition and can create mis-leading interpretations of empirical results.


Conclusion

In recent years, the idea of firms as systems ofinterdependent activities has found renewed in-terest. Both the NK model and the complemen-

tarity framework have allowed researchers to ap-proach this topic in a more systematic manner.For future research, we would suggest increasingthe focus on sets of activities whose interactioneffects are contextual, because these activities aremore difficult to imitate and, thus, more likely torepresent sources of competitive advantage. Moregenerally, as our examples show, to gain a richerunderstanding of the role played by interactionsamong activities in creating and sustaining com-petitive advantage, research needs to encompass awider range of interactions than the strictly de-fined complementarities that have served as thetheoretical model underlying many empiricalanalyses. Similarly, simulation research will needto be extended. To study the effects of differenttypes of interactions and of contextuality, simula-tion models will have to allow more control thanthe frequently used NK model grants.

Empirical support for the existence of contex-tual interactions is so far mainly derived fromin-depth field research. Future research on largersamples is needed. Reanalyzing prior studies tolook explicitly for contextualities might be a firststep. A more ambitious approach would be toassemble data sets in which fuller interactionstructures of the activities of firms are docu-mented. Due to the high cost of assembling suchdata, research treading a middle ground betweenindividual case studies and large-sample researchmay prove to be the most feasible next step. Incor-porating the possibility of contextual relationship infuture research is certainly no small task, but will beessential to further our understanding of the role ofinteractions in competitive advantage.

Appendix1:Different typesof interactionswithin theNKmodel

The random assignment of contributions to activitiesgives rise to a variety of types of interactions, yet providesthe researcher with no control over which types of interac-tions do arise. A simple example illustrates this point. Sayactivities A and B can be configured in two ways (0 or 1)and B affects A. In this case, the NK model would assign

four random contributions to A: cA(0, 0), the contributionof A when A � 0 and B � 0; cA(1, 0), the contributionwhen A � 1 and B � 0; and likewise cA(0, 1) and cA(1, 1).Consider the case cA(0, 0) � 0.1, cA(1, 0) � 0.4, cA(0, 1) �0.3, and cA(1, 1) � 0.8. In this case, when B � 0, themarginal benefit of changing A from 0 to 1 equals 0.3 (�0.4 � 0.1), and it equals 0.5 (� 0.8 � 0.3) when B � 1.Thus, the marginal benefit of A is increasing in the level ofB; A and B are complements. Yet the NK model could quiteas likely assign cA(1, 1) � 0.5. Now, the marginal benefit ofchanging A from 0 to 1 when B � 1 is only 0.2 (0.5 � 0.3),less than the marginal benefit when B � 0. In this case, Aand B would be substitutes. Thus, given the stochasticdetermination of contributions—and thereby implicitly ofthe types of interactions among activities—it is impossibleto control what types of interactions will be present in anygiven simulation run.

Appendix2: Complementarityandsupermodularity

Milgrom and Roberts define complementarity as follows:Let f(x, y, z) be a (benefit) function where z is a vector ofvariables. The variables x and y are complements, if f issupermodular, i.e., has the following property:

f( x�, y�, z) � f( x�, y�, z) � f( x�, y�, z) � f( x�, y�, z)

(1)

for all x� x�, y� y� (2)

and all values of z (3)

Complementarity is, thus, defined to occur when increasingthe variable x from its lower level x� to the higher level x� ismore beneficial when the second variable y is at the higherlevel y� than at the lower level y�. Condition 2 states thatthis relationship between x and y has to hold at all levels ofx and y. Condition 3 requires that this relationship hold forall values of all the other variables z. Only if the aboveconditions hold for all pairs of variables (between x, y, andz and among the variables constituting z), does the set ofvariables {x, y, z} form a system of complements.13

Translated into our activity terminology, each variablecorresponds to an activity, while x�, x�, etc. are differentconfigurations of activity x. Note that the Milgrom and

13 For clarity, we chose to unpack the definition given by Milgrom andRoberts (1990, p. 516): “A function f: Rn3 R is supermodular if for all a,a��Rn, f(a) � f(a�) � f(min(a, a�)) � f(max(a, a�)).” Rewrite a, a� as: a �(x�, y�, z) and a� � (x�, y�, z) with x�, x�, y�, y�� R and z � Rn-2. Sincethe above definition of supermodularity has to hold for all vectors a, a�,consider a and a� that fulfill: x� � x� and y� � y� (our condition 2) for anyz � Rn-2 (our condition 3). Then max(a, a�) � (x�, y�, z) and min(a, a�) �(x�, y�, z). Substituting into the above definition yields: f(x�, y�, z) � f(x�,y�, z) � f(x�, y�, z) � f(x�, y�, z), which can be rewritten as f(x�, y�, z) –f(x�, y�, z) � f(x�, y�,z) – f(x�, y�, z) (our condition 1). (R denotes the setof real numbers.)


Roberts framework requires that the possible choices foreach activity can be ordered, e.g., small vs. large investmentsin flexible machinery. All statements of activity “levels” arethus to be understood with respect to such an order.

Appendix3: Complementarityand contextualinteractions

The following example illustrates the concept of contex-tuality while revealing the restrictiveness of the comple-mentarity conditions. Consider the case of three activities,A, B, and C. Each activity can be configured in two ways,which we denote by 0 and 1. Hence, the firm can considereight possible combinations of ABC: 000, 001, . . . , 111.We normalize the payoff of the combination 000 to be zero.Figure A1 displays a case in which A, B, and C are com-plements. In this case, changing one and only one activityfrom 0 to 1 yields a benefit of 1, changing two activitiesyields a benefit of 3, and changing all three activities yieldsa benefit of 6. Thus, the payoffs of the eight combinationsare given as follows: �(000) � 0; �(100) � �(010) ��(001) � 1; �(110) � �(101) � �(011) � 3; �(111) �6. To check the complementarity between A and B, forinstance, note that changing A from 0 to 1 is more benefi-cial if B is at 1 rather than at 0. Similarly, changing B from0 to 1 is more beneficial if A is at 1 rather than at 0.Moreover, note that these relationships hold regardless ofthe level of C.For C � 0:A’s marginal benefit is larger at the higher level of B:

�2 �(110) � �(010) �(100) � �(000) 1

B’s marginal benefit is larger at the higher level of A:

2 �(110) � �(100) �(010) � �(000) 1

Similarly for C � 1:

3 �(111) � �(011) �(101) � �(001) 2

3 �(111) � �(101) �(011) � �(001) 2

Similar calculations reveal that the interactions betweenactivities A and C as well as between B and C are alwayscomplementary. Now consider a single modification to thepayoff structure: Assume that changing all three activitiesyields a benefit of 4 rather than 6, i.e., �(111) � 4; chang-ing all three activities is still more beneficial than changingany two, but less so than previously. With this single mod-ification, all three interactions between A, B, and C becomecontextual. Consider, for instance, A and B. When C is at0, A and B are still complements, yet when C is at 1, A andB are now substitutes.For C � 0: payoffs are as given above.For C � 1:A’s marginal benefit is smaller at the higher level of B:

1 �(111) � �(011) � �(101) � �(001) 2

B’s marginal benefit is smaller at the higher level of A:

1 �(111) � �(101) � �(011) � �(001) 2

The same relationships are found between A and C (bothare complements if B � 0 and substitutes if B � 1) andbetween B and C (complements if A � 0 and substitutes ifA � 1). Similar results are achieved for other modificationsof the payoff structure (e.g., changing �(001) from 1 to 3creates contextual interactions between A and C, and B andC, while retaining the unconditional complementarity be-tween A and B). While not every modification to the payoffstructure eliminates the generic complementarity among A,B and C (e.g., increasing �(111) to 7 leaves the uncondi-tional complementarity intact), the strict conditions re-quired by complementarity are easily violated, creatingcontextual interactions.

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