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Enforce and selective operators of combinatorial games

Author

Listed:
  • Tomoaki Abuku

    (National Institute of Informatics
    Gifu University)

  • Shun-ichi Kimura

    (Hiroshima University)

  • Hironori Kiya

    (Osaka Metropolitan University)

  • Urban Larsson

    (Indian Institute of Technology Bombay)

  • Indrajit Saha

    (Kyushu University)

  • Koki Suetsugu

    (National Institute of Informatics
    Waseda University)

  • Takahiro Yamashita

    (Hiroshima University)

Abstract

We consider an enforce operator on impartial rulesets similar to the Muller Twist and the comply/constrain operator of Smith and Stănică, 2002. Applied to the rulesets A and B, on each turn the opponent enforces one of the rulesets and the current player complies, by playing a move in that ruleset. If the outcome table of the enforce variation of A and B is the same as the outcome table of A, then we say that A dominates B. We find necessary and sufficient conditions for this relation. Additionally, we define a selective operator and explore a distributive-lattice-like structure within applicable rulesets. Lastly, we define nim-values under enforce-rulesets, and establish that the Sprague–Grundy theory continues to hold, along with illustrative examples.

Suggested Citation

  • Tomoaki Abuku & Shun-ichi Kimura & Hironori Kiya & Urban Larsson & Indrajit Saha & Koki Suetsugu & Takahiro Yamashita, 2024. "Enforce and selective operators of combinatorial games," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(4), pages 1249-1273, December.
    • Handle: RePEc:spr:jogath:v:53:y:2024:i:4:d:10.1007_s00182-024-00910-6
    DOI: 10.1007/s00182-024-00910-6
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