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{ń}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.

翻译：我们提出了一种基于目标集豪斯多夫维度的判定准则，用于确定树状结构上双人零和交替移动博弈的获胜方。本研究聚焦于若干特例，包括完全二叉树上的盖尔-斯图尔特博弈及一类施密特博弈。基于Das、Fishman、Simmons和Urbański最初提出的豪斯多夫维度博弈——该博弈为计算豪斯多夫维度提供了博弈论方法，我们采用该博弈的广义族系，并证明其在分析我们所研究的零和博弈基础集合方面具有重要价值。