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The Miner’s Dilemma With Migration: The Control Effect of Solo-Mining

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 allow for 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. In a second step, we introduce solo-mining into the system. Introducing solo-mining cannot prevent the miner’s dilemma, however, it improves the efficiency of the mining process as the infiltration preferences of the mining pools are lowered. Thus, solo-mining has a control effect on the miner’s dilemma by keeping the infiltration preference below a certain threshold.