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Source: ยท
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.

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