Mean Field Game Approach to Bitcoin Mining

Charles Bertucci, Louis Bertucci, Jean-Michel Lasry and Pierre-Louis Lions
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Charles Bertucci: CMAP, Ecole Polytechnique, Palaiseau, France
Louis Bertucci: Institut Louis Bachelier, Paris, France
Jean-Michel Lasry: Universit\'e Paris-Dauphine, PSL Research University, CEREMADE, Paris, France
Pierre-Louis Lions: Universit\'e Paris-Dauphine, PSL Research University, CEREMADE, Paris, France

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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.

Date: 2020-04
New Economics Papers: this item is included in nep-gth and nep-pay
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