Trading and wealth evolution in the Proof of Stake protocol

TL;DR

This paper surveys the economic dynamics of Proof of Stake (PoS) blockchains, analyzing wealth evolution, trading incentives, and collective miner behavior using stochastic and analytical methods.

Contribution

It introduces a comprehensive framework combining wealth evolution, trading strategies, and mean field models for PoS blockchain economies, highlighting new insights into decentralization and miner incentives.

Findings

Wealth distribution dynamics depend on trading and staking strategies.

Miner trading incentives influence the degree of decentralization.

Mean field models reveal collective behavior patterns of miners.

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.