  The selfish mining attack, arguably the most famous game-theoretic attack in
blockchain, indicates that the Bitcoin protocol is not incentive-compatible.
Most subsequent works mainly focus on strengthening the selfish mining
strategy, thus enabling a single strategic agent more likely to deviate. In
sharp contrast, little attention has been paid to the resistant behavior
against the selfish mining attack, let alone further equilibrium analysis for
miners and mining pools in the blockchain as a multi-agent system.
  In this paper, first, we propose a strategy called insightful mining to
counteract selfish mining. By infiltrating an undercover miner into the selfish
pool, the insightful pool could acquire the number of its hidden blocks. We
prove that, with this extra insight, the utility of the insightful pool could
be strictly greater than the selfish pool's when they have the same mining
power. Then we investigate the mining game where all pools can either choose to
be honest or take the insightful mining strategy. We characterize the Nash
equilibrium of this mining game, and derive three corollaries: (a) each mining
game has a pure Nash equilibrium; (b) honest mining is a Nash equilibrium if
the largest mining pool has a fraction of mining power no more than 1/3; (c)
there are at most two insightful pools under equilibrium no matter how the
mining power is distributed.
