The Miner's Dilemma With Migration

Abstract

As an important example of the application of blockchain technology, the Bitcoin network has achieved great success. The network is secured by miners who are nowadays organized in mining pools. In this paper, we consider the “block withholding attack” as introduced by Eyal, where mining pools may infiltrate others to decrease their revenues. However, when two mining pools attack each other and neither controls a strict majority, the so-called miner's dilemma arises. Both pools are worse off than without an attack. Knowing this, pools may make implicit non-attack agreements. Having said this, the miner's dilemma is known to emerge only if no pool controls the majority of the mining power. In this work, we extend the original model to include miner migration and show that the miner's dilemma emerges even for pools whose mining power exceeds 50%. We construct a game, where two mining pools attack each other and use simulation analysis methods to analyze the evolution the pools' mining power, infiltration preferences and revenue densities under the influence of different mining pool sizes and miner migration preferences. The results show that underlying game experiences a phase transition fueled by miners' migration preference. Without migration, it is profitable for a large mining pool to attack the other pool. The higher the migration preference of the miners, the more the game transitions into the miner's dilemma and attacking makes both pools worse off. Once the pools violate their implicit non-attack agreements, their revenues decrease.