Abstract
A subtraction gameS=(s 1, ...,s k)is a two-player game played with a pile of tokens where each player at his turn removes a number ofm of tokens providedmεS. The player first unable to move loses, his opponent wins. This impartial game becomes partizan if, instead of one setS, two finite setsS L andS R are given: Left removes tokens as specified byS L, right according toS R. We say thatS L dominatesS R if for all sufficiently large piles Left wins both as first and as second player. We exhibit a curious property of dominance and provide two subclasses of games in which a dominance relation prevails. We further prove that all partizan subtraction games areperiodic, and investigatepure periodicity.
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Supported, in part, by Canadian Research Grants NSERC A9232 and NSERC 69-0695.
Work done during visits at CRMA, Université de Montréal, Québec, Canada, June 1981, and at Department of Mathematics and Statistics, The University of Calgary, Calgary, Alberta, Canada, 1983.
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Fraenkel, A.S., Kotzig, A. Partizan octal games: Partizan subtraction games. Int J Game Theory 16, 145–154 (1987). https://doi.org/10.1007/BF01780638
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DOI: https://doi.org/10.1007/BF01780638