{
  "annotation_id": "80daca5f-9751-45e3-99b3-fc5e944de0de",
  "date_created": "2026-02-17T05:53:16.141000Z",
  "date_modified": "2026-02-17T05:53:16.141000Z",
  "file_hash": "13bf13311faca389042ea563667d94985e3564a0151690297283eb26612441c5",
  "private": false,
  "record": {
    "abstract": "We provide a criterion for determining the winner in two-player win-lose alternating-move games on trees, in terms of the Hausdorff dimension of the target set. We focus our study on special cases, including the Gale-Stewart game on the complete binary tree and a family of Schmidt games. Building on the Hausdorff dimension games originally introduced by Das, Fishman, Simmons, and Urba{\\\u0027n}ski, which provide a game-theoretic approach for computing Hausdorff dimensions, we employ a generalized family of these games, and show that they are useful for analyzing sets underlying the win-lose games we study.",
    "arxiv_id": "2601.08359",
    "authors": [
      "Itamar Bella\u00efche",
      "Auriel Rosenzweig"
    ],
    "categories": [
      "math.DS",
      "cs.GT",
      "math.LO",
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "title": "Determining the Winner in Alternating-Move Games",
    "url": "https://arxiv.org/abs/2601.08359",
    "version": "v2"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f3f397b3-611a-40e4-8a44-3d981651655f",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}