Simon's model displays a first-mover advantage

Peter Dodds, myself, and some other friendly folks affiliated with the Computational Story Lab just published a paper in Physical Review E detailing an inherent first-mover advantage in Herbert Simon’s preferential attachment model. Check it out!

Re-analysis of the generative algorithm led us to the discovery that the first group actually has a size advantage proportional to $$1/\rho$$, where $$\rho$$ is the innovation probability. As $$\rho$$ is typically quite small–on the order of $$10^{-2}$$ to $$10^{-5}$$–this results in the first group being from 100 to 100000 times (respectively) as large as the mean-field analysis of the algorithm dictates. There’s even evidence for this mechanism in real-world citation counts (props to Dodds for wrangling this data…expert emacs skills were on display).

Written on May 11, 2017