Yama Nim and a comply/constrain operator of combinatorial games

• Item type: SIG Technical Reports(1)
• 公開日: 2023-07-01
• タイトル: Yama Nim and a comply/constrain operator of combinatorial games
• タイトル / 言語: en
• タイトル: Yama Nim and a comply/constrain operator of combinatorial games
• 言語: eng
• キーワード / 主題Scheme: Other
• キーワード / 主題: ゲーム・パズルの解析
• 資源タイプ / 資源タイプ識別子: http://purl.org/coar/resource_type/c_18gh
• 資源タイプ: technical report
• 著者所属: National Institute of Informatics
• 著者所属: Osaka Metropolitan University
• 著者所属: Indian Institute of Technology Bombay
• 著者所属: Kyushu University
• 著者所属: National Institute of Informatics
• 著者所属: Hiroshima University
• 著者所属(英): en
• 著者所属(英): National Institute of Informatics
• 著者所属(英): en
• 著者所属(英): Osaka Metropolitan University
• 著者所属(英): en
• 著者所属(英): Indian Institute of Technology Bombay
• 著者所属(英): en
• 著者所属(英): Kyushu University
• 著者所属(英): en
• 著者所属(英): National Institute of Informatics
• 著者所属(英): en
• 著者所属(英): Hiroshima University
• 著者名: Tomoaki, Abuku; Hironori, Kiya; Urban, Larsson; Indrajit, Saha; Koki, Suetsugu; Takahiro, Yamashita
• 著者名(英): Tomoaki, Abuku; Hironori, Kiya; Urban, Larsson; Indrajit, Saha; Koki, Suetsugu; Takahiro, Yamashita
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: We introduce Yama Nim, a variation of Nim played on a two-dimensional semi-infinite game board, with terminal positions in the upper left corner. The player can move two or more up steps and one right step, or two or more left steps and one down step. If a player cannot move, they lose. We find the solution to this game. We also consider a comply/constrain operator on impartial rulesets. Applied to the rulesets A and B, on each turn the opponent proposes one of the rulesets and the current player complies, by playing a move in that ruleset. If the outcome table of the comply/constrain variation of A and B is the same as the outcome table of A, then we say that B is dominated by A. We show necessary and sufficient conditions of “A dominates B”. Yama Nim is a good example that dominates classical rulesets such as Nim and Wythoff Nim.
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: We introduce Yama Nim, a variation of Nim played on a two-dimensional semi-infinite game board, with terminal positions in the upper left corner. The player can move two or more up steps and one right step, or two or more left steps and one down step. If a player cannot move, they lose. We find the solution to this game. We also consider a comply/constrain operator on impartial rulesets. Applied to the rulesets A and B, on each turn the opponent proposes one of the rulesets and the current player complies, by playing a move in that ruleset. If the outcome table of the comply/constrain variation of A and B is the same as the outcome table of A, then we say that B is dominated by A. We show necessary and sufficient conditions of “A dominates B”. Yama Nim is a good example that dominates classical rulesets such as Nim and Wythoff Nim.
• 書誌レコードID / 収録物識別子タイプ: NCID
• 書誌レコードID / 収録物識別子: AA11362144
• 書誌情報: 研究報告ゲーム情報学（GI）; 巻 2023-GI-50, 号 6, p. 1-7, 発行日 2023-07-01
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 2188-8736
• Notice: SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc.
• 出版者 / 言語: ja
• 出版者: 情報処理学会