Stability of shares in the Proof of Stake Protocol -- Concentration and Phase Transitions
Stability of shares in the Proof of Stake Protocol -- Concentration and Phase Transitions
复制标题
权益证明协议中股份的稳定性——集中和相变
DOI：
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Wenpin Tang
中科院分区：
文献类型：
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作者：
Wenpin Tang
本文关注的是加密货币中股票的稳定性，其中新硬币是根据权益证明协议发行的。我们识别了不同奖励方案下的大、中、小投资者，发现这些投资者的限制行为是不同的，大投资者的股票是稳定的，而中小投资者的股票可能是波动的，甚至缩水为零。例如，在几何回报的情况下，会出现混乱的集中化，所有的股份最终都会随机地集中在一个投资者身上。这导致了相变现象，和稳定的阈值的特点。为了应对区块链网络中越来越多的活动，我们还提出并分析了PoS协议的动态人口模型，该模型允许投资者的数量随着时间的推移而增长。数值实验证实了我们的理论。
This paper is concerned with the stability of shares in a cryptocurrency where the new coins are issued according to the Proof of Stake protocol. We identify large, medium and small investors under various rewarding schemes, and show that the limiting behaviors of these investors are different -- for large investors their shares are stable, while for medium to small investors their shares may be volatile or even shrink to zero. For instance, with a geometric reward there is chaotic centralization, where all the shares will eventually concentrate on one investor in a random manner. This leads to the phase transition phenomenon, and the thresholds for stability are characterized. In response to the increasing activities in blockchain networks, we also propose and analyze a dynamical population model for the PoS protocol, which allows the number of investors to grow over the time. Numerical experiments are provided to corroborate our theory.