Compounding of Wealth in Proof-of-Stake Cryptocurrencies


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Academic research paper -

Abstract.

Proof-of-stake (PoS) is a promising approach for designing efficient blockchains, where block
proposers are randomly chosen with probability proportional to their stake. A primary concern with
PoS systems is the “rich getting richer” phenomenon, whereby wealthier nodes are more likely to get
elected, and hence reap the block reward, making them even wealthier. In this paper, we introduce the
notion of equitability, which quantifies how much a proposer can amplify her stake compared to her
initial investment. Even with everyone following protocol (i.e., honest behavior), we show that existing
methods of allocating block rewards lead to poor equitability, as does initializing systems with small
stake pools and/or large rewards relative to the stake pool. We identify a geometric reward function, which we prove is maximally equitable over all choices of reward functions under honest behavior and bound the deviation for strategic actions; the proofs involve the study of optimization problems and stochastic dominances of P ́olya urn processes, and are of independent mathematical interest. These results allow us to provide a systematic framework to choose the parameters of a practical incentive system for PoS cryptocurrencies.