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In the context of the `selfish-mine' strategy proposed by Eyal and Sirer, westudy the effect of propagation delay on the evolution of the Bitcoinblockchain. First, we use a simplified Markov model that tracks the contrastingstates of belief about the blockchain of a small pool of miners and the `restof the community' to establish that the use of block-hiding strategies, such asselfish-mine, causes the rate of production of orphan blocks to increase. Thenwe use a spatial Poisson process model to study values of Eyal and Sirer'sparameter $\gamma$, which denotes the proportion of the honest community thatmine on a previously-secret block released by the pool in response to themining of a block by the honest community. Finally, we use discrete-eventsimulation to study the behaviour of a network of Bitcoin miners, a proportionof which is colluding in using the selfish-mine strategy, under the assumptionthat there is a propagation delay in the communication of information betweenminers.

Bitcoin Blockchain Dynamics: the Selfish-Mine Strategy in the Presence of Propagation Delay