Self-organization of R&D search in complex technology spaces

Abstract

We extend an earlier model of innovation dynamics based on percolation by adding endogenous R&D search by economically motivated firms. The {0,1} seeding of the technology lattice is now replaced by draws from a lognormal distribution for technology ‘difficulty’. Firms are rewarded for successful innovations by increases in their R&D budget. We compare two regimes. In the first, firms are fixed in a region of technology space. In the second, they can change their location by myopically comparing progress in their local neighborhoods and probabilistically moving to the region with the highest recent progress. We call this the moving or self-organizational regime (SO). We find that as the mean and standard deviation of the lognormal distribution are varied, the relative rates of aggregate innovation switches between the two regimes. The SO regime has higher innovation rates, other things being equal, for lower means or higher standard deviations of the lognormal distribution. These results hold for increasing size of the search radius. The clustering of firms in the SO regime grows rapidly and then fluctuates in a complex way around a high value that increases with the search radius. We also investigate the size distributions of the innovations generated in each regime. In the fixed one, the distribution is approximately lognormal and certainly not fat tailed. In the SO regime, the distributions are radically different. They are much more highly right skewed and show scaling over at least two decades with a slope of almost exactly one, independently of parameter settings. Thus we argue that firm self-organization leads to self-organized criticality.