A criterion based on the Hausdorff dimension of the target set determines the winner in alternating-move win-lose games on trees, generalizing prior results on Schmidt games to arbitrary complete metric spaces.
Schmidt (1965) On badly approximable numbers and certain games, Transactions of the American Mathematical Society, vol
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Determining the Winner in Alternating-Move Games
A criterion based on the Hausdorff dimension of the target set determines the winner in alternating-move win-lose games on trees, generalizing prior results on Schmidt games to arbitrary complete metric spaces.