2020/04/17 by Charles Bertucci, Louis Bertucci, Bertucci, Charles +7 · 5 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #Blockchain #Blockchain Technology Applications and Security #Characterization (materials science) #Complex Systems and Time Series Analysis #Computer science #Computer security #Constant (computer programming) #Cryptocurrency #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Field (mathematics) #Game theory #General Finance (q-fin.GN) #Mathematical economics #Mathematics #Simple (philosophy) #Theoretical Economics (econ.TH) #econ.TH #math.AP #q-fin.GN
paper · pdf · doi:10.48550/arxiv.2004.08167
published in RePEc: Research Papers in Economics (Federal Reserve Bank of St. Louis) · 35 pages, 3 figures
arxiv created 2020/04/17 · openalex publication_date 2020/04/17 · arxiv updated 2020/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.