Bruno Biais, Christophe Bisière, Matthieu Bouvard, and Catherine Casamatta, The blockchain folk theorem, The Review of Financial Studies, 2018, forthcoming.


Blockchains are distributed ledgers, operated within peer-to-peer networks. We model the proof-of-work blockchain protocol as a stochastic game and analyze the equilibrium strategies of rational, strategic miners. Mining the longest chain is a Markov perfect equilibrium, without forking, in line with Nakamoto (2008). The blockchain protocol, however, is a coordination game, with multiple equilibria. There exist equilibria with forks, leading to orphaned blocks and persistent divergence between chains. We also show how forks can be generated by information delays and software upgrades. Last we identify negative externalities implying that equilibrium investment in computing capacity is excessive.

JEL codes

  • C73: Stochastic and Dynamic Games • Evolutionary Games • Repeated Games
  • G2: Financial Institutions and Services
  • L86: Information and Internet Services • Computer Software

Research partnership

Fédération des Banques Françaises Research Initiative