The Evolutionary Equilibrium of Block Withholding Attack

Bitcoin is the most famous and the most used cryptocurrency in the world, such that it has received extreme popularity in recent years. However the Bitcoin system is accompanied by different attacks, including the block withholding (BWH) attack. When a miner plays the BWH attack, it will withhold all the blocks newly discovered in the attack pool, damaging the honest miners’ right to obtain the fair reward. In this paper, we consider a setting in which two miners may honestly mine or perform the BWH attack in a mining pool. Different strategy profiles will bring different payoffs, in addition influence the selection of the strategies. Therefore, we establish an evolutionary game model to study the behavior tendency of the miners and the evolutionary stable strategies under different conditions, by formulating the replicator dynamic equations. Through numerical simulations, we further verify the theoretical results on evolutionary stable solutions and discuss the impact of the factors on miners’ strategic choice. Based on these simulation results, we also make some recommendations for the manager and the miners to mitigate the BWH attack and to promote the cooperation between miners in a mining pool.