A game theoretic analysis on block withholding attacks using the zero-determinant strategy

In Bitcoin's incentive system that supports open mining pools, block withholding attacks incur huge security threats. In this paper, we investigate the mutual attacks among pools as this determines the macroscopic utility of the whole distributed system. Existing studies on pools' interactive attacks usually employ the conventional game theory, where the strategies of the players are considered pure and equal, neglecting the existence of powerful strategies and the corresponding favorable game results. In this study, we take advantage of the Zero-Determinant (ZD) strategy to analyze the block withholding attack between any two pools, where the ZD adopter has the unilateral control on the expected payoffs of its opponent and itself. In this case, we are faced with the following questions: who can adopt the ZD strategy? individually or simultaneously? what can the ZD player achieve? In order to answer these questions, we derive the conditions under which two pools can individually or simultaneously employ the ZD strategy and demonstrate the effectiveness. To the best of our knowledge, we are the first to use the ZD strategy to analyze the block withholding attack among pools.