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

30 Pages Posted: 7 Jun 2022

See all articles by Wenpin Tang

Wenpin Tang

Columbia University - Department of Industrial Engineering and Operations Research

Date Written: June 1, 2022

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.

Keywords: Blackwell-MacQueen urn, blockchain, concentration/anti-concentration, cryptocurrency, Polya urn, Proof of Stake

JEL Classification: C6, G11

Suggested Citation

Tang, Wenpin, Stability of shares in the Proof of Stake Protocol -- Concentration and Phase Transitions (June 1, 2022). Available at SSRN: https://ssrn.com/abstract=4124744 or http://dx.doi.org/10.2139/ssrn.4124744

Wenpin Tang (Contact Author)

Columbia University - Department of Industrial Engineering and Operations Research ( email )

500 W. 120th Street #315
New York, NY 10027
United States

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