The Pure Price of Anarchy of Pool Block Withholding Attacks in Bitcoin Mining


  • Colleen Alkalay-Houlihan University of Toronto
  • Nisarg Shah University of Toronto



Bitcoin, a cryptocurrency built on the blockchain data structure, has generated significant academic and commercial interest. Contrary to prior expectations, recent research has shown that participants of the protocol (the so-called “miners”) are not always incentivized to follow the protocol. We study the game induced by one such attack – the pool block withholding attack – in which mining pools (groups of miners) attack other mining pools. We focus on the case of two pools attacking each other, with potentially other mining power in the system.

We show that this game always admits a pure Nash equilibrium, and its pure price of anarchy, which intuitively measures how much computational power can be wasted due to attacks in an equilibrium, is at most 3. We conjecture, and prove in special cases, that it is in fact at most 2. Our simulations provide compelling evidence for this conjecture, and show that players can quickly converge to the equilibrium by following best response strategies.




How to Cite

Alkalay-Houlihan, C., & Shah, N. (2019). The Pure Price of Anarchy of Pool Block Withholding Attacks in Bitcoin Mining. Proceedings of the AAAI Conference on Artificial Intelligence, 33(01), 1724-1731.



AAAI Technical Track: Game Theory and Economic Paradigms