Cooperation and Optimization of Multi-Pool Mining Game With Zero Determinant Alliance

In blockchain technology, solving the SHA256 problem (also known as mining) is key for the proof-of-work (PoW)-based blockchain networks. However, selfish pools typically initiate block withholding attacks on others for greater rewards in the process of consensus, resulting in a decline of the social welfare and even posing a threat to the efficiency of the entire blockchain system. In this study, the multi-pool mining game in the blockchain network is applied to optimize the strategy selection of mining pools and to improve the mining efficiency. First, the multi-pool mining process is formulated as a multi-player game and then the zero determinant (ZD) strategy is utilized to resolve the mining pool dilemma. Thereafter, a ZD alliance mechanism is proposed to optimize the strategy selection of pools, aiming to effectively avoid block withholding attacks and to encourage cooperative mining among pools. Finally, numerical simulations show that the ZD alliance can significantly improve the social welfare and the cooperation probability of the mining pools, which verifies the theoretical results.