This was part of Applications of Mean Field Games

Bitcoin Mining as a Mean Field Game

Louis Bertucci, Institut Louis Bachelier
Tuesday, November 16, 2021

Abstract: We present an analysis of the Proof-of-Work (PoW) 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). This new class of models allows us to adjust to many different situations. The PoW consensus algorithm has an intrinsic stability that makes it very suitable for creating a strong form of consensus. We show that a homogenous version of the model is able to explain well the Bitcoin data. In equilibrium, the revenue per unit of real hashrate follows a mean reverting process even with an unbounded reward process. We also show that, in the long run, R&D expenses, as well as the blockchain security and the bitcoin energy consumption, are all proportional to the total miners reward (i.e. the bitcoin price).