  We study efficiency in a proof-of-work blockchain with non-zero latencies,
focusing in particular on the (inequality in) individual miners' efficiencies.
Prior work attributed differences in miners' efficiencies mostly to attacks,
but we pursue a different question: Can inequality in miners' efficiencies be
explained by delays, even when all miners are honest? Traditionally, such
efficiency-related questions were tackled only at the level of the overall
system, and in a peer-to-peer (P2P) setting where miners directly connect to
one another. Despite it being common today for miners to pool compute
capacities in a mining pool managed by a centralized coordinator, efficiency in
such a coordinated setting has barely been studied.
  In this paper, we propose a simple model of a proof-of-work blockchain with
latencies for both the P2P and the coordinated settings. We derive a
closed-form expression for the efficiency in the coordinated setting with an
arbitrary number of miners and arbitrary latencies, both for the overall system
and for each individual miner. We leverage this result to show that
inequalities arise from variability in the delays, but that if all miners are
equidistant from the coordinator, they have equal efficiency irrespective of
their compute capacities. We then prove that, under a natural consistency
condition, the overall system efficiency in the P2P setting is higher than that
in the coordinated setting. Finally, we perform a simulation-based study to
demonstrate that even in the P2P setting delays between miners introduce
inequalities, and that there is a more complex interplay between delays and
compute capacities.
