MERIT-Infonomics Research Memorandum series A Percolation Model of Innovation in Complex Technology Spaces

Innovations are known to arrive more highly clustered than if they were purely random, and their rate of arrival has been increasing nearly exponentially for several centuries. Their distribution of importance is highly skewed and appears to obey a power law or lognormal distribution. Technological change has been seen by many scholars as following technological trajectories and being subject to ‘paradigm’ shifts from time to time. To address these empirical observations, we introduce a complex technology space based on percolation theory. This space is searched randomly in local neighborhoods of the current best-practice frontier. Numerical simulations demonstrate that with increasing radius of search, the probability of becoming deadlocked declines and the mean rate of innovation increases until a plateau is reached. The distribution of innovation sizes is highly skewed and heavy tailed. For percolation probabilities near the critical value, it seems to resemble an infinite-variance Pareto distribution in the tails. For higher values, the lognormal appears to be preferred.