Classification of crypto-coins and tokens from the dynamics of their power law capitalisation distributions

We empirically verify that the market capitalisations of coins and tokens in the cryptocurrency universe follow power law distributions with significantly different values, with the tail exponent falling between 0.5 and 0.7 for coins, and between 1.0 and 1.3 for tokens. We provide a rational for this, based on a simple birth-proportional growth-death model previously introduced to describe firms, cities, webpages, etc. We validate the model and its main predictions, in terms of proportional growth and linear versus square-root growth law of the mean and standard deviation of market capitalisation as a function of time interval. Estimating the main parameters of the model, the theoretical predictions for the power law exponents of coins and tokens distribution are in remarkable agreement with the empirical estimations, given the simplicity of the model in the face of the complexity and non-stationarity of the crypto-currency world. Our results clearly characterizes 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.