Substitutes in Creating Complementarities

5 August 2008 at 7:04 am 6 comments

| Lasse Lien |

I have just been reading the Porter and Siggelkow paper in the most recent issue of Academy of Mgmt. Perspectives. The paper summarizes the status of the “complementarity/NK-modelling/activity systems” perspective in competitive strategy. I am anything but an expert in this theory, but I thought I would share one reflection, mainly because it allows me to use the fancy title above.

As many O&M readers will know, a main take-away from this perspective is that an activity system with strong complementarities may enjoy protection against imitation. Some choices in an activity system will presumably be unobservable for outsiders, and getting everything right at once is less likely the more linkages there are between activities. Furthermore, the penalty for failing to get everything right increases with the strength of the complementarities.

My problem is that more and stronger complementarities should presumably speed up learning, because there are more and stronger feedback mechanisms putting pressure to move each activity in the beneficial direction. An increasing number of complementary activities presumably imply that each individual activity is encouraged to move in the “right” direction by many other activities, and stronger complementarities imply stronger pressure from each of them.

So while many and strong complementarities reduce the likelihood of perfect imitation and increase the penalty for imperfection, the rapid learning produced by an improved feedback mechanism may conceivably make the road to perfection rather short. Couldn’t these effects conceivably cancel each other out, or the latter effect even dominate the former? Or in other words — forgive the pun — aren’t these two mechanisms (precise imitation and rapid learning) substitutes in the pursuit of complementarity?

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6 Comments Add your own

  • 1. spostrel  |  5 August 2008 at 7:17 pm

    How would the feedback work? To the extent that not exploiting a complementarity across departmental lines results in a lost opportunity, who would notice this and be motivated to fix it?

    Suppose the IT group buys some new software whose capabilites can only be fully exploitied if marketing reorganizes or changes its basic practices. It’s not obvious how that complementarity would be detected, who would be motivated to do something about it, or how resistance (possibly well-founded) to the changes would be overcome. It certainly wouldn’t be something that would happen “automatically” but would probably require managerial work to accomplish.

    The article has some conceptual and technical problems, but I don’t think this feedback idea is one of them.

  • 2. Lasse  |  6 August 2008 at 3:43 am

    Steven, thanks for your comment. I certainly agree that there is nothing automatic about detecting and exploiting complementarities, but my point was merely that if many other activities (besides IT) would benefit from a particular change/reorganization in the marketing department, and these benefits were strong, the probability of the people in marketing noticing and acting on the opportunity should increase. In other words, misalignment between activities might be less stable the more and stronger complementarities there are. Anyway, I use a lot of wording like “could, might, may conceivably, and so on, so I’m not trying to argue a deterministic conclusion here, merely a logical possibility.
    But more importantly, the end of your comment made me really curious. What are the main problems with the article as you see it?

  • 3. spostrel  |  7 August 2008 at 5:01 pm

    The article in general is quite good at what it tries to do. It gives a clear review of the NK and supermodularity literatures and how they have been used in management, and it points out some important limitations and goals for future research. But to some extent, reliance on these frameworks to the exclusion of the older and deeper theory of production throws away critical information and makes things more confusing.

    The main problem I see in the article is that it blurs the distinction between quasi-concavity or quasi-convexuity and concavity or convexity. For most purposes in strategy, it is quasi-concavity or quasi-convexity that is the relevant consideration in deciding whether two activities are complements or substitutes, but the article looks at concavity and convexity. Thus it mixes up the elasticity of substitution (curvature of isoquants) with the presence of overall economies or diseconomies of scale.

    A simple example: Suppose we have output z = (x + y)^a, with x and y inputs and technical parameter a > 0. From a management perspective, x and y are perfect substitutes regardless of whether a 1 (increasing returns).

    But from the definitions used in the article, x and y are complements when a > 1 and substitutes when a 0, the article says to look at these inputs as complements and then says that when activities are complements you need to do them all to successfully imitate. But with the actual relationship given here, that conclusion is dead wrong. If a rival is using all x, you could achieve the same results using all y. The article’s presentation is unnecessarily misleading and could have been avoided by going back to the basics in any microtheory textbook. It would be a pity if this confusion were to propogate.

  • 4. spostrel  |  7 August 2008 at 5:03 pm

    Sorry, some less-than signs got eaten up by the HTML syntax reader.

  • 5. spostrel  |  7 August 2008 at 5:09 pm

    Simple clarification for notational clarity. According to the definition in the article, x and y are complements if z = (x + y)^a with a bigger than 1. But the isoquants are still linear, even with a above 1, so the implication that complements implies greater difficulty of imitation does not follow, since you can use x and y in any proportion to accomplish the same thing. Also, unlike with true complements, extreme solutions of all x or all y are more likely to be optimal, and the proportions of x and y used are likely to be very sensitive to small changes in relative prices.

  • 6. Lasse  |  11 August 2008 at 2:52 am

    Thanks Steven. Great comment!

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