ISSN:
1432-1270
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Economics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01780638
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