  The arisen of Bitcoin has led to much enthusiasm for blockchain research and
block mining, and the extensive existence of mining pools helps its
participants (i.e., miners) gain reward more frequently. Recently, the mining
pools are proved to be vulnerable for several possible attacks, and pool block
withholding attack is one of them: one strategic pool manager sends some of her
miners to other pools and these miners pretend to work on the puzzles but
actually do nothing. And these miners still get reward since the pool manager
can not recognize these malicious miners. 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. Fortunately, in the new model,
the pool managers have strong incentive to not launch such attacks. We show
that for any number of mining pools, no-pool-attacks is always a Nash
equilibrium. Moreover, with only two minority mining pools participating,
no-pool-attacks is actually the unique Nash equilibrium.
