{"paper":{"title":"Asymptotics for the Time of Ruin in the War of Attrition","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ilie Grigorescu, Philip Ernst","submitted_at":"2016-07-26T10:53:46Z","abstract_excerpt":"We consider two players, starting with $m$ and $n$ units, respectively. In each round, the winner is decided with probability proportional to each player's fortune, and the opponent loses one unit. We prove an explicit formula for the probability $p(m,n)$ that the first player wins. When $m\\sim Nx_{0}$, $n\\sim N y_{0}$, we prove the fluid limit as $N\\to \\infty$. When $x_{0}=y_{0}$, then $z\\to p(N,N+z\\sqrt{N})$ converges to the standard normal CDF and the difference in fortunes scales diffusively. The exact limit of the time of ruin $\\tau_{N}$ is established as $(T-\\tau_N) \\sim N^{-\\beta}W^{\\fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07636","kind":"arxiv","version":2},"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"}