The dynamics of competitive intensity

Administrative Science Quarterly, March, 1997 by William P. Barnett

To see this, assume that organizations vary in their fitnesses at time 1 (say, the time of founding) and that fitnesses do not change for individual organizations over time. Assume also that there is some threshold level of fitness, such that those organizations above the threshold are likely to survive to time 2 and those below it are not. As long as environmental selection criteria do not change over time, then as of time 2 members of the population will now be more likely to survive, on average, even though individual organizations have not learned. This general result has been obtained also from models that combine these two extreme cases. Bruderl and Schussler (1990) explicitly modeled the initial variance posited in the mover-stayer model but then also allowed for learning after an initial period of low hazard. Levinthal (1991) got a similar result, using a modification of the mover-stayer model, in which variance develops through a random walk. Overall, these various models agree that, whether by selection or development, older organizations are more likely to survive, on average.

If we assume that more viable organizations are stronger competitors, then these arguments also imply that older organizations generate stronger competition: dw/[d.sub.Tau] [is greater than] 0. Assuming that the increase in competitive intensity over time is linear, [w.sub.j] = [sigma] [Gamma.sub.1][Tau.sub.j] and substituting into the original competition equation [Alpha.sub.kj] = [w.sub.j.p.sub.kj] results in [Alpha.sub.kj] = [Sigma][P.sub.kj] [Gamma.sub.1][T.sub.j][P.sub.kj]. Aggregating over j again depicts the total competition felt by organization k but now allows for rivals to evolve into stronger competitors:

[Alpha] = [Sigma.sub.j[not equal to]k][Alpha.sub.kj] = [nu]N [c.sub.1]T,

where [Eta] = [Sigma.sub.p], [Gamma.sub.1p], and T = [Sigma.sub.j[not equal to]k][T.sub.j]. Thus, if the strongest competitors survive, then competition at the population level is a function of both density and T, the aggregate ages of living organizations in the population. Incorporating this into the original density-dependent models result in:

(1a) [Lambda] = [Lambda]*[expla.sub.[Lambda]]N [b.sub.[Lambda]][N.sup.2] [c.sub.1[Lambda] T]

(1b) [mu.sub.k] = [mu.sub.k]*[expla.sub.[Mu]N [b.sub.[Mu]]N [b.sub.[Mu]] [N.sup.2] [c.sub.1[Mu]] T].

If the strong-survivor hypothesis is correct, then older organizations should generate stronger competition, such that estimates of equations 1a and 1b will show [c.sub.1] [Lambda] [is less than] 0 and [c.sub.1] [Mu] [is greater than] 0, where the aggregate ages of the members of an organizational population decreases the organizational founding rate and increases organizational death rates.

This is a useful result, making it possible to test the strong-survivor hypothesis, as well as alternative hypotheses about the development of competitive intensity over time. In particular, Barron, West, and Hannan (1994) argued that organizations tend to become obsolete because of structural inertia and that internal processes of organizations gradually deteriorate, so-called senescence (Hirschman, 1970). This would mean that organizations gradually become unfit as they age. Barron, West, and Hannan looked for this result in terms of organizational viability, predicting that organizational failure rates increase with age once size is controlled. In light of the competitive intensity model, their idea can also be tested in terms of ecological strength. Assuming that less viable organizations are weaker competitors, their theory implies that older organizations should generate weaker competition, so that equations 1a and 1b would instead show [c.sub.1][Lambda] [is greater than] 0 and [c.sub.1][Mu] [is less than] 0.