Inferring final organizational outcomes from intermediate outcomes of exploration and exploitation: the complexity link

Abstract

The difficulty in definitively linking outcomes of managerial action to organizational outcomes has been a festering issue in organizational research. The problem arises because it is not easy to separate the distinctive contributions of managers at intermediate stages, as well as the contribution of external factors beyond the control of managers. Specifically, certain managerial actions focusing on exploratory or exploitative innovation produce an intermediate output, organizational knowledge. From this base of organizational knowledge, further management actions craft the final output that eventually faces the market test. Drawing from complexity concepts, I argue that the probability of correctly fashioning the subset of key elements in the intermediate output may be a good measure of the probability of organizational success. I use March’s iconic computational simulation model to demonstrate the merits of this principle. I model the effect of complexity on managerial intentionality towards exploratory and exploitative innovation. I elicit important insights for research and practice by comparing organizational knowledge outcomes with the outcomes for probability of organizational success, in stable and moderately turbulent environment.

Appendix: Mathematical structure underlying the complexity framing for computation of probability of organizational success

The essential nature of the problem addressed in the paper constitutes matching a randomly generated reality string R, of size m bits, each of which can have one of two state values (let us call them A and B, standing for “1” and “−1”, respectively), with the corresponding values of another string, MyString (that stands for the organizational code), whose m dimensions can take values from the set {A, B, C}, where “C” stands for a value “0” or no opinion. MyString is generated by March’s adoption of the genetic algorithm, drawing from the work of Holland (1975). Thus, in the paper, different combinations of exploitation (p ₁) and exploration (p ₃) enable us to generate distinct MyString. Comparing MyString with R, we assess organizational knowledge and success probability.

Let us consider a simplified situation where the R string is generated with a probability P01 for a bit turning up with value “A” and probability (1 − P01) for a bit turning up with a value of “B”. Further, assume that MyString is generated with a probability P02 for a bit turning up with value “A” and probability (1 − P02) for a bit turning up with a value of “B”. Also, let k stand for the proportion of bits that must match in order that MyString may be given payoff. Accordingly, the total number of bits that need to match is given by m * k.

Now, consider a particular bit position, in both R and MyString. In the former, the probability of getting an “A” is P01, in the latter the same probability is P02. Thus, Q, the probability of getting the same value in that particular bit position, is given by:

$$Q = P01\,*\,P02 + (1 - P01)\,*\,(1 - P02).$$

(1)

Accordingly, the expected number of matches is given by m * Q.

Thus, by random draw without replacement from a pool of size m, the probability P _overall of getting (m * k) exact matches, is given by:

$$P_{\_ \text{overall}} \,=\, {^{m\,*\,Q} {\rm C}_{m\,*\,k}} /^{m} {\rm C}_{m\,*\,k} .$$

(2)

P _overall can be calculated by computational simulation as well. Suppose that, instead of generating MyString by the genetic algorithm (as in the reported results), we generate MyString with a process involving random draws with probability P02. Thereafter we pick random sets of m * k bits, say L = 500 of them in all, and assign payoff of 1 unit only if MyString and R match in all the bit-positions in a given random set. We compute the value of P _overall as the proportion of L evaluations that is non-zero.

We observe in Table 3 that that this process generates values fairly close to that given by (2). However, the deviation from the formulaic prediction increases as complexity increases, since smaller numbers introduce larger rounding errors. Using a higher value of L (say L = 1000) does not get a significantly closer match. Moreover, using a high L where each experiment is performed I = 10,000 times becomes quite computation intensive. Therefore we recommend L = 500 for future studies of this kind.

Table 3 Comparison of P _overall values attained for P01 = 0.50 by formula and by simulation