Compounding of Wealth in Proof-of-Stake Cryptocurrencies

TL;DR

This paper analyzes wealth distribution in proof-of-stake cryptocurrencies, introducing a geometric reward function that maximizes fairness and provides a framework for designing equitable incentive systems.

Contribution

It introduces the concept of equitability in PoS systems and proves the geometric reward function is maximally equitable under honest behavior.

Findings

Geometric reward function maximizes equitability.

Existing reward methods lead to poor equitability.

Framework for selecting incentive parameters.

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 \emph{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 Polya 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.