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 lawof 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.
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 rationale for this, based on a simple proportional growth with birth 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.
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power law
power-law
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rational
rationale
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birth-proportional growth-death model previously introduced to describe
proportional growth with birth
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death model previously employed to describe the size distribution of
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empirically
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and linear versus square-root growth lawof the mean and standard deviation of market capitalisation as a function of time interval
(Gibrat's law) of the coins and tokens
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power law exponents of coins and tokens distribution
power-law exponents of coin and token distributions
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in the face of the complexity and non-stationarity of the crypto-currency world
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characterizes
characterize