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

In the context of the `selfish-mine' strategy proposed by Eyal and Sirer, we\nstudy the effect of propagation delay on the evolution of the Bitcoin\nblockchain. First, we use a simplified Markov model that tracks the contrasting\nstates of belief about the blockchain of a small pool of miners and the `rest\nof the community' to establish that the use of block-hiding strategies, such as\nselfish-mine, causes the rate of production of orphan blocks to increase. Then\nwe use a spatial Poisson process model to study values of Eyal and Sirer's\nparameter $\\gamma$, which denotes the proportion of the honest community that\nmine on a previously-secret block released by the pool in response to the\nmining of a block by the honest community. Finally, we use discrete-event\nsimulation to study the behaviour of a network of Bitcoin miners, a proportion\nof which is colluding in using the selfish-mine strategy, under the assumption\nthat there is a propagation delay in the communication of information between\nminers.\n