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The Proof-of-Stake (PoS) consensus algorithm has been criticized, in the literature and in several cryptocurrencies communities, due to the so-called compounding effect: who is richer has more coins to stake, therefore higher probability of being selected as a block validator and obtaining the corresponding rewards, thus becoming even richer. In this paper, we present a PoS simulator written in the Julia language that allows one to test several variants of PoS-based consensus algorithms, tweaking their parameters, and observe how the distribution of cryptocurrency coins among the users evolves over time. Such a tool can be used to investigate which combinations of parameters values allow to obtain a "fair" and stable consensus algorithm, in which, over the long term, no one gets richer or poorer by the mere act of validating blocks. Based on this investigation, we also introduce a new PoS-based consensus mechanism that allows the system to keep the wealth distribution stable even after a large number of epochs.
Leporati et al. (Mon,) studied this question.