The Bitcoin Mining Game

19 Pages Posted: 13 Mar 2014

See all articles by Nicolas Houy

Nicolas Houy

University of Lyon 2 - Groupe d'Analyse et de Théorie Economique (GATE)

Date Written: March 11, 2014


When processing transactions in a block, a miner increases his reward but also decreases his probability to earn any reward because the time needed for his block to reach consensus depends on its size. We show that this leads to a game situation between miners. We analytically solve this game for two miners. Then, we show that miners do not play a Nash equilibrium in the current Bitcoin mining environment, instead, they should not process any transaction. Finally, we show that the situation where no transaction is ever processed would stop being a Nash equilibrium if the transaction fee was multiplied or, equivalently, the fixed reward divided by a factor of about 12.

Keywords: Bitcoin, mining, crypto-currency, game

JEL Classification: C72, D62

Suggested Citation

Houy, Nicolas, The Bitcoin Mining Game (March 11, 2014). Available at SSRN: or

Nicolas Houy (Contact Author)

University of Lyon 2 - Groupe d'Analyse et de Théorie Economique (GATE) ( email )

93, chemin des Mouilles
Ecully, 69130

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