A Percolation Model of Innovation in Complex Technology Spaces

Innovations are known to arrive more highly clustered than if they were purely random. 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. However, for ‘richer’ technological environments, a ‘trough’ separates myopic from long-range search due to the effect of r&d duplication. The distribution of innovation sizes is highly skewed and may resemble a pareto distribution near the critical percolation probability.