Abstract
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.
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There are many implicit axioms in the DEU model formula, see [FL02] for a comprehensive overview. In particular, since the DEU model treats utility as linearly additive over time-separated consumptions, it implicitly assumes that the consumer is risk-neutral to aggregated utilities over time, even if the consumer is risk-averse in each time period. Intertemporal risk-aversion has also been considered in the economics literature and there are modified DEU models where aggregation of discounted utilities is nonlinear [FL02, EZ89, KP78].
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Convergence in \(\mathbb {R}^\infty \) can be defined with respect to the standard Euclidean norm restricted to points in \(\mathbb {R}^\infty \) that have finite norm. All the points in the sequence of maximizers lie in this subspace because they have a finite number of nonzero components. The limit point of this sequence satisfies the optimization constraint (i.e. has a bounded L1 norm) and thus also lies in this subspace.
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Fisch, B., Pass, R., Shelat, A. (2017). Socially Optimal Mining Pools. In: R. Devanur, N., Lu, P. (eds) Web and Internet Economics. WINE 2017. Lecture Notes in Computer Science(), vol 10660. Springer, Cham. https://doi.org/10.1007/978-3-319-71924-5_15
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DOI: https://doi.org/10.1007/978-3-319-71924-5_15
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