Trading and Wealth Evolution in the Proof of Stake Protocol

23 Pages Posted: 15 Aug 2023

See all articles by Wenpin Tang

Wenpin Tang

Columbia University - Department of Industrial Engineering and Operations Research

Date Written: August 3, 2023

Abstract

With the increasing adoption of the Proof of Stake (PoS) blockchain, it is timely to study the economy created by such blockchain. In this chapter, we will survey recent progress on the trading and wealth evolution in a cryptocurrency where the new coins are issued according to the PoS protocol. We first consider the wealth evolution in the PoS protocol assuming no trading, and focus on the problem of decentralisation. Next we consider each miner’s trading incentive and strategy through the lens of optimal control, where the miner needs to trade off PoS mining and trading. Finally, we study the collective behavior of the miners in a PoS trading environment by a mean field model. We use both stochastic and analytic tools in our study. A list of open problems are also presented.

Keywords: Consumption-investment, continuous-time control, cryptocurrency, HJB equations, market impact, mean field, phase transition, Polya urn, Proof of Stake (PoS), stability

JEL Classification: C6, G11

Suggested Citation

Tang, Wenpin, Trading and Wealth Evolution in the Proof of Stake Protocol (August 3, 2023). Available at SSRN: https://ssrn.com/abstract=4530538 or http://dx.doi.org/10.2139/ssrn.4530538

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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