Socially optimal mining pools

Mining for Bitcoins is a high-risk high-reward activity. Miners, seeking to reduce their variance and earn steadier rewards, collaborate in so-called pooling strategies where they jointly mine for Bitcoins. Whenever some pool participant is successful, the earned rewards are appropriately split among all pool participants. Currently a dozen of different pooling strategies are in use for Bitcoin mining. We here propose a formal model of utility and social optimality for Bitcoin mining (and analogous mining systems) based on the theory of discounted expected utility, and next study pooling strategies that maximize the utility of participating miners in this model. We focus on pools that achieve a steady-state utility, where the utility per unit of work of all participating miners converges to a common value. Our main result shows that one of the pooling strategies actually employed in practice—the so-called geometric pay pool—achieves the optimal steady-state utility for miners when its parameters are set appropriately. Our results apply not only to Bitcoin mining pools, but any other form of pooled mining or crowdsourcing computations where the participants engage in repeated random trials towards a common goal, and where “partial” solutions can be efficiently verified.