多人Large Nim博弈的最优策略

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摘要:

研究包含任意多个竞争者的Large Nim博弈模型,它是传统的Large Nim由两个竞争者到多个竞争者的一般化.在标准联盟矩阵下,运用递归函数,针对竞争者人数与堆数的三大类关系,得到了相应的博弈值和获胜的最优策略.

This paper is devoted to the gameMulti-player Large Nim Gameswhich is the generalization of the classic Large Nim games from two players to arbitrarily many players.Assuming that the standard alliance matrix be adopted,by using a recursive function,the game values are completely determined for three kinds of relation between the numbers of players and piles.These game values are capable of determining which of the players has a winning optimal strategy.

作者:

刘文安肖亚

Liu Wenan;Xiao Ya(College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China)

机构地区:

betway官方app 数学与信息科学学院

出处:

《betway官方app 学报：自然科学版》 CAS 北大核心 2021年第2期1-6,F0002,共7页

基金:

国家自然科学基金(11171368)。

关键词:

多人公平组合博弈 Large Nim博弈联盟矩阵博弈值

multi-player impartial combinatorial game Large Nim alliance matrix game value