A Percolation Model of Innovation in Complex Technology

Innovations are known to arrive more highly clustered than if they werepurely random, and their rate of arrival has been increasing nearlyexponentially for several centuries. Their distribution of importance ishighly skewed and appears to obey a power law or lognormal distribution.Technological change has been seen by many scholars as followingtechnological trajectories and being subject to ‘paradigm’ shifts fromtime to time. To address these empirical observations, we introduce acomplex technology space based on percolation theory. This space issearched randomly in local neighborhoods of the current best-practicefrontier. Numerical simulations demonstrate that with increasing radiusof search, the probability of becoming deadlocked declines and the meanrate of innovation increases until a plateau is reached. Thedistribution of innovation sizes is highly skewed and heavy tailed. Forpercolation probabilities near the critical value, it seems to resemblean infinite-variance Pareto distribution in the tails. For highervalues, the lognormal appears to be preferred.