Charles Bertucci, Louis Bertucci, Jean-Michel Lasry, Pierre-Louis Lions
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SIAM Journal on Financial Mathematics, Volume 15, Issue 3, Page 960-987, September 2024. 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). This class of models allows us to adapt to many different situations. 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 only. 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 and the energy consumption either are constant or increase with the price of the underlying cryptocurrency.
期刊介绍：
SIAM Journal on Financial Mathematics (SIFIN) addresses theoretical developments in financial mathematics as well as breakthroughs in the computational challenges they encompass. The journal provides a common platform for scholars interested in the mathematical theory of finance as well as practitioners interested in rigorous treatments of the scientific computational issues related to implementation. On the theoretical side, the journal publishes articles with demonstrable mathematical developments motivated by models of modern finance. On the computational side, it publishes articles introducing new methods and algorithms representing significant (as opposed to incremental) improvements on the existing state of affairs of modern numerical implementations of applied financial mathematics.
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