A Mean Field Games Model for Cryptocurrency Mining

Zongxi Li (), A. Max Reppen () and Ronnie Sircar ()
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Zongxi Li: Operations Research & Financial Engineering Department, Princeton University, Princeton, New Jersey 08540
A. Max Reppen: Questrom School of Business, Boston University, Boston, Massachusetts 02215; Rafik B. Hariri Institute for Computing and Computational Science & Engineering, Boston, Massachusetts 02215
Ronnie Sircar: Operations Research & Financial Engineering Department, Princeton University, Princeton, New Jersey 08540

Management Science, 2024, vol. 70, issue 4, 2188-2208

Abstract: We propose a mean field game model to study the question of how centralization of reward and computational power occur in Bitcoin-like cryptocurrencies. Miners compete against each other for mining rewards by increasing their computational power. This leads to a novel mean field game of jump intensity control, which we solve explicitly for miners maximizing exponential utility and handle numerically in the case of miners with power utilities. We show that the heterogeneity of their initial wealth distribution leads to greater imbalance of the reward distribution, and increased wealth heterogeneity over time, or a “rich get richer” effect. This concentration phenomenon is aggravated by a higher Bitcoin mining reward and reduced by competition. Additionally, an advantaged miner with cost advantages such as access to cheaper electricity, contributes a significant amount of computational power in equilibrium, unaffected by competition from less efficient miners. Hence, cost efficiency can also result in the type of centralization seen among miners of cryptocurrencies.

Keywords: cryptocurrencies; cryptocurrency; Bitcoin; mining; mean field games (search for similar items in EconPapers)
Date: 2024
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