The existence of mining pools in Bitcoin enables the miners to gain more stable reward. However, it is proved that the pools are vulnerable for security attacks. A strategic pool manager has strong incentive to launch pool block withholding attack by sending some of her miners to infiltrate the other pools. The infiltrating miners try to find (partial) proof-of-work solutions but discard the solution that can actually create blocks. As it is hard to recognize malicious miners,these miners still get reward in the infiltrated pools. In this work, we revisit the game-theoretic model for pool block withholding attacks and propose a revised approach to reallocate the reward to the miners. Instead of proportionally allocating the reward to all miners, a pool manager deducts a fraction from the reward to award the miner who actually mined the block. Accordingly, we prove that, under our scheme, for any number of mining pools, no-pool-attacks is always a Nash equilibrium. Moreover, with only two minority mining pools, no-pool-attacks is the unique Nash equilibrium

比特币矿池的存在使矿工可以获得更稳定的奖励。然而，事实证明这些池容易受到安全攻击。一位战略矿池经理有强烈的动机通过派遣她的一些矿工渗透其他矿池来发起矿池区块扣留攻击。渗透的矿工试图找到（部分）工作量证明解决方案，但丢弃可以实际创建区块的解决方案。由于很难识别恶意矿工，这些矿工仍然在渗透池中获得奖励。在这项工作中，我们重新审视了矿池区块扣留攻击的博弈论模型，并提出了一种修改后的方法来重新分配给矿工的奖励。矿池经理不是按比例将奖励分配给所有矿工，而是从奖励中扣除一小部分来奖励实际开采该区块的矿工。因此，我们证明，根据我们的方案，对于任意数量的矿池，无矿池攻击始终是纳什均衡。此外，只有两个少数矿池，无矿池攻击是唯一的纳什均衡