{"paper":{"title":"Bitcoin: A Natural Oligopoly","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"cs.CR","authors_text":"Nick Arnosti, S. Matthew Weinberg","submitted_at":"2018-11-21T02:41:52Z","abstract_excerpt":"Although Bitcoin was intended to be a decentralized digital currency, in practice, mining power is quite concentrated. This fact is a persistent source of concern for the Bitcoin community.\n  We provide an explanation using a simple model to capture miners' incentives to invest in equipment. In our model, $n$ miners compete for a prize of fixed size. Each miner chooses an investment $q_i$, incurring cost $c_i q_i$, and then receives reward $\\frac{q_i^\\alpha}{\\sum_j q_j^\\alpha}$, for some $\\alpha \\geq 1$. When $c_i = c_j$ for all $i,j$, and $\\alpha = 1$, there is a unique equilibrium where all "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08572","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}