Trading and wealth evolution in the Proof of Stake protocol

Paper: arXiv 2308.01803

Authors: Wenpin Tang

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical framework using stochastic tools, optimal control, and mean field models to analyze Proof of Stake economics. However, it functions predominantly as a mathematical and survey-style chapter with limited empirical validation or data-driven backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze Wealth Evolution & Trading Incentives in PoS Blockchain] --> B[Phase 1: Pure PoS Wealth Model]
    A --> C[Phase 2: Single Miner Optimal Control Model]
    A --> D[Phase 3: Multi-Miner Mean Field Model]
    
    B --> E[Stochastic & Analytic Evaluation]
    C --> E
    D --> E
    
    E --> F[Findings: Decentralization Trends, Optimal Mining/Trading Strategies & Open Problems]