Suppose that homogenous agents fully consume their time to invent new
ideas and learn ideas from their friends. If the social network is
complete and agents pick friends and ideas of friends uniformly at
random, the distribution of ideas’ popularity is an extension of the
Yule-Simon distribution. It has a power-law tail, with an upward or
downward curvature. For infinite population it converges to the
Yule-Simon distribution. The power law is steeper when innovation is
high. Diffusion follows S-shaped curves.
Keywords: innovation, diffusion, two-mode networks, cumulative advantage, quadratic attachment kernel, power law, Yule-Simon distribution, generalized hypergeometric distribution.
JEL classification: D83, D85, O31, O33