2024-06-17T19:28:30Zhttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_oaipmhoai:ipsj.ixsq.nii.ac.jp:002268132024-03-29T05:26:34Z01164:05305:11215:11287
Yama Nim and a comply/constrain operator of combinatorial gamesYama Nim and a comply/constrain operator of combinatorial gamesengゲーム・パズルの解析http://id.nii.ac.jp/1001/00226704/Technical Reporthttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_action_common_download&item_id=226813&item_no=1&attribute_id=1&file_no=1Copyright (c) 2023 by the Information Processing Society of JapanNational Institute of InformaticsOsaka Metropolitan UniversityIndian Institute of Technology BombayKyushu UniversityNational Institute of InformaticsHiroshima UniversityTomoaki, AbukuHironori, KiyaUrban, LarssonIndrajit, SahaKoki, SuetsuguTakahiro, YamashitaWe 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.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.AA11362144研究報告ゲーム情報学（GI）2023-GI-506172023-07-012188-87362023-06-28