Moral hazard in games of miners

Cryptocurrency mining, which has attracted substantial attention recently is a game where miners cost mining power and compete for an amount of digital token. In this paper, we revisit this game under new settings that miners' maximal mining powers, i.e. capacities, are disparate. We show it has a unique pure Nash-equilibrium and derive the closed-form. In the PNE, miners fall into two types: half-hearted and all-out, the former of which owns more capacity than the latter. An all-out miner mines with her full capacity while a half-hearted miner does not. Compared with the desired equilibrium that every miner does her best, our result reveals that the disparity of capacity leads to less total mining power, compromising the security of cryptocurrency systems.