Mean Field Game Approach to Bitcoin Mining

TL;DR

This paper models Bitcoin mining using a Mean Field Game framework, providing equilibrium insights into hashrate dynamics and blockchain security under various assumptions.

Contribution

It introduces a master equation approach to analyze Bitcoin mining, allowing for model enrichments while preserving core game structure.

Findings

Hashrate reaches a steady state in deterministic models.

In stochastic models, hashrate targets depend on random states.

Blockchain security can be constant or increase with demand.

Abstract

We present an analysis of the Proof-of-Work consensus algorithm, used on the Bitcoin blockchain, using a Mean Field Game framework. Using a master equation, we provide an equilibrium characterization of the total computational power devoted to mining the blockchain (hashrate). From a simple setting we show how the master equation approach allows us to enrich the model by relaxing most of the simplifying assumptions. The essential structure of the game is preserved across all the enrichments. In deterministic settings, the hashrate ultimately reaches a steady state in which it increases at the rate of technological progress. In stochastic settings, there exists a target for the hashrate for every possible random state. As a consequence, we show that in equilibrium the security of the underlying blockchain is either $i)$ constant, or $ii)$ increases with the demand for the underlying cryptocurrency.