The effect of propagation delay on the dynamic evolution of the Bitcoin blockchain

This paper analyzes the selfish-mine strategy in the Bitcoin blockchain introduced in 2013 by I. Eyal and E. G. Sirer. This strategy could be used by a colluding pool of miners to earn more than their fair share of the mining revenue and in consequence to force other honest miners to join them to decrease the variance of their revenues and make their monthly revenues more predictable. It is a very dangerous dynamic that could allow the rogue pool of miners to go toward a majority by accumulating powers of news adherents and control the entire network. Considering that the propagation delay of information between any two miners in the network, which is not negligible and follows a normal distribution with mean proportional to the physical distance between the two miners, and a constant variance independent of others' delays, we prove that no guarantee can be given about the success or failure of the selfish-mine attack because of the variability of information propagation in the network.