Abstract
We describe a ruleset for a 2-pile subtraction game with P-positions \(\{(\lfloor \alpha n \rfloor ,\lfloor \beta n \rfloor ) : n \in \mathbb Z_{\ge 0} \}\) for any irrational \(1< \alpha < 2\), and \(\beta \) such that \(1/\alpha +1/\beta = 1\). We determine the \(\alpha \)’s for which the game can be represented as a finite modification of t-Wythoff (Holladay, Math Mag 41:7–13, 1968; Fraenkel, Am Math Mon 89(6):353–361, 1982) and describe this modification.
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Goldberg, L., Fraenkel, A.S. Rulesets for Beatty games. Int J Game Theory 47, 577–594 (2018). https://doi.org/10.1007/s00182-017-0594-6
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DOI: https://doi.org/10.1007/s00182-017-0594-6