This paper is under CC 4.0 license. available on arxiv Authors: (1) Bartosz Kusmierz, IOTA Foundation 10405 Berlin, Germany & Department of Theoretical Physics, Wroclaw University of Science and Technology, Poland bartosz.kusmierz@pwr.edu.pl; (2) Roman Overko, IOTA Foundation 10405 Berlin, Germany roman.overko@iota.org. Table of Links Abstract and Introduction Related Work and Methodology Results Summary and References Abstract Rapidly growing distributed ledger technologies (DLTs) have recently received attention among researchers in both industry and academia. While a lot of existing analysis (mainly) of the Bitcoin and Ethereum networks is available, the lack of measurements for other crypto projects is observed. This article addresses questions about tokenomics and wealth distributions in cryptocurrencies. We analyze the time-dependent statistical properties of top cryptocurrency holders for 14 different distributed ledger projects. The provided metrics include approximated Zipf coefficient, Shannon entropy, Gini coefficient, and Nakamoto coefficient. We show that there are quantitative differences between the coins (cryptocurrencies operating on their own independent network) and tokens (which operate on top of a smart contract platform). Presented results show that coins and tokens have different values of approximated Zipf coefficient and centralization levels. This work is relevant for DLTs as it might be useful in modeling and improving the committee selection process, especially in decentralized autonomous organizations (DAOs) and delegated proof of stake (DPoS) blockchains. —Cryptocurrencies, Tokenomics, DPoS, Wealth Distribution, Zipf law Index Terms I. INTRODUCTION The advent of Bitcoin [13] has given rise to an increasing interest in distributed systems throughout the 2010s. The newly created space of cryptocurrencies has attracted many scientists, programmers, and business investors. Due to the complexity of Distributed Ledger Technologies (DLTs), their development requires expertise in many fields of science, including applied mathematics, cryptography, game theory, economics, peer-to-peer (p2p) networks, and coding theory. In the first years of DLTs, questions of technological nature received the most attention as the problems like consensus mechanism and peer-to-peer layer are at the core of any such technology. Unfortunately, questions about economics, cryptocurrencies distributions and tokenomics took a back seat in academic research of cryptocurrencies and have not been sufficiently addressed (with a few notable exceptions). This is unfortunate as the Bitcoin pseudo-anonymous account model allows for transaction transparency unprecedented in traditional financial systems, where almost all payments are private and highly sensitive. Furthermore, Bitcoin enabled new monetary models and deployed them on a global scale. Notably, the amount of Bitcoin currency units is capped at 21 million. However, due to some Bitcoin wallets being lost, as a result of negligence or human error, Bitcoin’s monetary policy is effectively deflationary. The monetary policy is not the only important factor cryptocurrency distribution. Even technology solutions like consensus mechanisms might influence cryptocurrency distribution. In this context, a comparison of Proofof-Work (PoW) and Proof-of Stake (PoS) consensus mechanisms is very informative. In PoW, newly created units of currency are rewarded to the specialized users, called miners, who have access to efficient Application-Specific Integrated Circuit (ASIC). PoW miners might hold a large number of cryptocurrency units; however, a large portion of mined rewards must be sold to cover expenses like electricity bills, rent, and amortization costs of ASIC machines. In PoS systems, however, new tokens are rewarded to stakers who hold a large number of cryptocurrency units. Unlike PoW miners, PoS stakers do not experience high costs and are incentivized not to sell their rewards as doing so increases their revenue in the future. This illustrates that even supposedly monetary-agnostic technology solutions might influence tokenomics. This paper partially addresses the questions of cryptocurrency tokenomics. We analyze the distribution of the top richest accounts in cryptocurrencies like Bitcoin, Ethereum, and selected ERC20 tokens. Our analysis involves in the data sets snapshotted at different dates with a given time interval. We use such data sets to measure different statistical metrics and analyze their evolution over time. Previous studies [6], [7], [10] showed that the distributions of the top richest balances might be modeled with Zipf’s law. We expand on these results and study the time evolution of Zipf’s law coefficient associated with such distributions. Notably, we analyze cryptocurrencies that, to our best knowledge, have never been analyzed before using similar methods. Next, we proceed with a thorough analysis of a series of centralization metrics like Shannon entropy, Gini index, and Nakamoto coefficient. These metrics are used to answer the main question addressed in this paper, which is formulated as follows: Are there any quantitative differences between top account balances in cryptocurrency “coins” and “tokens”? Therefore, the novelty of this work comprises the following two aspects: (i) studying quantitative differences between coins and tokens and (ii) examining cryptocurrencies whose analysis is missed in the literature. A distinction between cryptocurrency coins and tokens was made in [22], where authors define coins as operating on their own independent ledger/network and tokens as operating on top of a coin network (typically smart contract platforms as Ethereum or Cardano). For the purposes of this paper, we use the same definitions. This research might be particularly interesting for DLTs, where a group of top cryptocurrency holders fulfills a special role. Examples include Decentralized Autonomous Organizations (DAOs) in which a committee of top token holders is responsible for DAO governance or treasury management. Other examples are Delegated Proof-of-Stake (DPoS) blockchains, where a relatively small committee of block validators issues ledger updates or distributed random number generators based on the threshold signature scheme. Since our research is focused on a relatively small group of top token holders, it can be directly applied to modeling the aforementioned examples. This is also reasonable as the typical size of the threshold signature committee is limited by the message complexity (up to 50—100 nodes). Our research might help to improve the committee selection process as we provide a range of parameters of Zipf’s law coefficient, which might be used as a model of cryptocurrency distribution. The structure of the paper is as follows. In the next section, we discuss related work and introduce the methods and tools used in this paper. Section III is devoted to the presentation and analysis of the results. In the last section, we conclude our findings and discuss future research.

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