Equilibrium analysis of block withholding attack: an evolutionary game perspective - Yukun Cheng; Zhanghao Yao; Zhiqi Xu; Xiaojing Ye (Blockchain)
With the development of blockchain technology, blockchain-based digital cryptocurrencies, such as Bitcoin, have received broad interest. Due to the permissionless environment, the blockchain is vulnerable to different kinds of attacks, including the block withholding (BWH) attack. BWH attack is one of the common selfish mining attacks, by which the attacking pool infiltrates the attacked pool by sending some infiltrating miners. These infiltrating miners try to find (partial) proof-of-work solutions and share the reward of the attacked pool, but discard the solution that can actually create blocks. Therefore, the attacking pool benefits by withholding blocks from the infiltrating miners, while damaging the benefits of victim pools. In this paper, we introduce the reward reallocation mechanism by paying additional rewards to the miners who successfully mine blocks, and propose an evolutionary game model for BWH attack among pools to study the strategy selection of pools. By constructing the replicator dynamic equations, the evolutionary stable strategies of pools are explored based on different levels of additional rewards. Our results provide enlightening significance to mitigate the negative influence from BWH attacks in practice.