International Journal of Game Theory

, Volume 16, Issue 2, pp 145–154 | Cite as

Partizan octal games: Partizan subtraction games

  • A. S. Fraenkel
  • A. Kotzig


A subtraction gameS=(s1, ...,sk)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 setsSL andSR are given: Left removes tokens as specified bySL, right according toSR. We say thatSL dominatesSR 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.


Economic Theory Game Theory Dominance Relation Large Pilis Curious Property 
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  1. 1.
    Austin R (1976) Impartial and partisan games. M.Sc. Thesis, Univ of CalgaryGoogle Scholar
  2. 2.
    Berlekamp ER, Conway JH, Guy RK (1982) Winning ways. Academic Press, LondonGoogle Scholar
  3. 3.
    Conway JH (1976) On numbers and games. Academic Press, LondonGoogle Scholar
  4. 4.
    Guy RK, Smith CAB (1956) TheG-values of various games. Proc Cambridge Phil Soc 52:514–526Google Scholar

Copyright information

© Physica-Verlag 1987

Authors and Affiliations

  • A. S. Fraenkel
    • 1
  • A. Kotzig
    • 2
  1. 1.Department of Applied MathematicsThe Weizmann Institute of ScienceRehovotIsrael
  2. 2.Centre de Recherches MathématiquesUniversité des MontréalMontréalCanada

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