A Mean Field Games Model for Cryptocurrency Mining

Zongxi Li, A. Max Reppen, Ronnie Sircar

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)2188-2208
Number of pages21
JournalManagement Science
Issue number4
StatePublished - 2024
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Strategy and Management
  • Management Science and Operations Research


  • Bitcoin
  • cryptocurrencies
  • cryptocurrency
  • mean field games
  • mining


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