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The Interacting Branching Process as a Simple Model of Innovation

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/τat each generation. In contrast to mean field results, no phase transition occurs; the chance for survival is finite for all p > 0. For τ= \infty, surviving processes exhibit a bottleneck before exploding super-exponentially - a growth consistent with a law of accelerating returns. This behavior persists for finite τ. We analyze, in detail, the asymptotic behavior as p \to 0.