Undercutting Bitcoin Is Not Profitable

A fixed block reward and voluntary transaction fees are two sources of economic incentives for mining in Bitcoin and other cryptocurrencies. For Bitcoin, the block reward halves every 210,000 blocks and it is supposed to vanish gradually. The remaining incentive of transaction fees is optional and arbitrary, and an undercutting attack becomes a potential threat, where the attacker deliberately forks an existing chain by leaving wealthy transactions unclaimed to attract other miners. We look into the profitability of the undercutting attack in this work. Our numerical simulations and experiments demonstrate that (i) only miners with mining power > 40% have a reasonable probability of successfully undercutting. (ii) As honest miners do not shift to the fork immediately in the first round, an undercutter's profit drops with the number of honest miners. Given the current transaction fee rate distribution in Bitcoin, with half of the miners being honest, undercutting cannot be profitable at all; With 25% honest mining power, an undercutter with > 45% mining power can expect income more than its "fair share"; With no honest miners present, the threshold mining power for a profitable undercutting is 42%. (iii) For the current largest Bitcoin mining pool with 17.2% mining power, the probability of successfully launching an undercutting attack is tiny and the expected returns are far below honest mining gains. (iv) While the larger the prize the undercutter left unclaimed, the higher is the probability of the attack succeeding but the attack's profits also go down. Finally, we analyze the best responses to undercutting for other rational miners. (v) For two rational miners and one of them being the potential undercutter with 45% mining power, we find the dominant strategy for the responding rational miner is to typical rational.