Abstract
We empirically verify that the market capitalizations of coins and tokens in the cryptocurrency universe follow power-law distributions with significantly different values for the tail exponent falling between 0.5 and 0.7 for coins, and between 1.0 and 1.3 for tokens. We provide a rationale for this, based on a simple proportional growth with birth and death model previously employed to describe the size distribution of firms, cities, webpages, etc. We empirically validate the model and its main predictions, in terms of proportional growth (Gibrat's Law) of the coins and tokens. Estimating the main parameters of the model, the theoretical predictions for the power-law exponents of coin and token distributions are in remarkable agreement with the empirical estimations, given the simplicity of the model. Our results clearly characterize coins as being 'entrenched incumbents' and tokens as an 'explosive immature ecosystem', largely due to massive and exuberant Initial Coin Offering activity in the token space. The theory predicts that the exponent for tokens should converge to 1 in the future, reflecting a more reasonable rate of new entrants associated with genuine technological innovations.