A Mean Field Games Model for Cryptocurrency Mining.

This article develops a novel mean field game model to analyze how centralization of mining rewards and computational power arises in Bitcoin-like proof-of-work cryptocurrencies. Miners compete by adjusting their computational power (hash rates) to maximize expected utility, balancing mining rewards against electricity costs. The model yields explicit equilibrium solutions for miners with exponential (constant absolute risk aversion, CARA) utility and numerical solutions for miners with power (constant relative risk aversion, CRRA) utility, revealing that initial wealth heterogeneity leads to increasing wealth inequality and mining centralization over time—a "rich get richer" effect. Additionally, the presence of a cost-advantaged miner (e.g., with cheaper electricity) significantly increases mining power concentration, consistent with empirical observations of dominant mining pools. The paper also discusses extensions including stochastic rewards, mining pools, and heterogeneous costs, providing a computationally tractable framework for studying decentralization and centralization dynamics in cryptocurrency mining.