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Stability of shares in the Proof of Stake Protocol -- Concentration and Phase Transitions

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  • Wenpin Tang

Abstract

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.

Suggested Citation

  • Wenpin Tang, 2022. "Stability of shares in the Proof of Stake Protocol -- Concentration and Phase Transitions," Papers 2206.02227, arXiv.org.
    • Handle: RePEc:arx:papers:2206.02227
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    References listed on IDEAS

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    Cited by:

    1. Wenpin Tang & David D. Yao, 2022. "Trading under the Proof-of-Stake Protocol -- a Continuous-Time Control Approach," Papers 2207.12581, arXiv.org, revised Jun 2023.
    2. Wenpin Tang & David D. Yao, 2023. "Transaction fee mechanism for Proof-of-Stake protocol," Papers 2308.13881, arXiv.org, revised Aug 2023.
    3. Wenpin Tang, 2023. "Trading and wealth evolution in the Proof of Stake protocol," Papers 2308.01803, arXiv.org, revised Aug 2023.

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