A Mean Field Games Model for Cryptocurrency Mining

Understand

We propose a mean field game model to study the question of how centralization of reward and computational power occur in Bitcoin-like cryptocurrencies.

• Miners compete against each other for mining rewards by increasing their computational power.
• This leads to a novel mean field game of jump intensity control, which we solve explicitly for miners maximizing exponential utility, and handle numerically in the case of miners with power utilities.
• We show that the heterogeneity of their initial wealth distribution leads to greater imbalance of the reward distribution, and increased wealth heterogeneity over time, or a "rich get richer" effect.