Interacting Branching Process as a Simple Model of Innovation
Physical Review Letters, 105 (17):
178701+ (October 2010)DOI: 10.1103/physrevlett.105.178701
Abstract
We describe innovation in terms of a generalized branching process. Each new invention pairs with any existing one to produce a number of offspring, which is Poisson distributed with mean p. Existing inventions die with probability p/τ at each generation. In contrast with mean field results, no phase transition occurs; the chance for survival is finite for all p>0. For τ=∞, surviving processes exhibit a bottleneck before exploding superexponentially—a growth consistent with a law of accelerating returns. This behavior persists for finite τ. We analyze, in detail, the asymptotic behavior as p→0.