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International Journal of Game Theory

, Volume 47, Issue 2, pp 577–594 | Cite as

Rulesets for Beatty games

  • Lior Goldberg
  • Aviezri S. Fraenkel
Original Paper
  • 84 Downloads

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.

Keywords

Subtraction games Beatty games P-positions 

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Computer Science and Applied MathematicsWeizmann Institute of ScienceRehovotIsrael

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