2022/06/05 by Wenpin Tang, Tang, Wenpin · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #FOS: Economics and business #General Economics (econ.GN) #General Finance (q-fin.GN) #Opinion Dynamics and Social Influence
paper · pdf · doi:10.48550/arxiv.2206.02227
openalex publication_date 2022/06/05 · openalex created_date 2022/11/27 · openalex updated_date 2026/07/28
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.