  GHOST, like the longest-chain protocol, is a chain selection protocol and its
capability in resisting selfish mining attack has been validated in imperfect
blockchains of Bitcoin and its variants (Bitcoin-like). This paper explores an
analytical-model-based method to investigate the impact of stubborn mining
attack in imperfect GHOST Bitcoin-like blockchains. We first quantify chain
dynamics based on Markov chain and then derive the formulas of miner revenue
and system throughput. We also propose a new metric, "Hazard Index", which can
be used to compare attack severity and also assist attacker in determining
whether it is profitable to conduct an attack. The experiment results show that
1) An attacker with more than 30% computing power can get huge profit and
extremely downgrade system throughput by launching stubborn mining attack. 2) A
rational attacker should not launch stubborn mining attack if it has less than
25% computing power. 3) Stubborn mining attack causes more damage than selfish
mining attack under GHOST. Our work provides insight into stubborn mining
attack and is helpful in designing countermeasures.
