当前位置: X-MOL 学术arXiv.cs.DM › 论文详情
Cumulative subtraction games
arXiv - CS - Discrete Mathematics Pub Date : 2018-05-23 , DOI: arxiv-1805.09368
Gal Cohensius; Urban Larsson; Reshef Meir; David Wahlstedt

We study zero-sum games, a variant of the classical combinatorial Subtraction games (studied for example in the monumental work "Winning Ways", by Berlekamp, Conway and Guy), called Cumulative Subtraction (CS). Two players alternate in moving, and get points for taking pebbles out of a joint pile. We prove that the outcome in optimal play (game value) of a CS with a finite number of possible actions is eventually periodic, with period $2s$, where $s$ is the size of the largest available action. This settles a conjecture by Stewart in his Ph.D. thesis (2011). Specifically, we find a quadratic bound, in the size of $s$, on when the outcome function must have become periodic. In case of two possible actions, we give an explicit description of optimal play. We generalize the periodicity result to games with a so-called reward function, where at each stage of game, the change of `score' does not necessarily equal the number of pebbles you collect.
更新日期:2020-02-14

 

全部期刊列表>>
宅家赢大奖
向世界展示您的会议墙报和演示文稿
全球疫情及响应:BMC Medicine专题征稿
新版X-MOL期刊搜索和高级搜索功能介绍
化学材料学全球高引用
ACS材料视界
x-mol收录
自然科研论文编辑服务
南方科技大学
南方科技大学
西湖大学
中国科学院长春应化所于聪-4-8
复旦大学
课题组网站
X-MOL
深圳大学二维材料实验室张晗
中山大学化学工程与技术学院
试剂库存
天合科研
down
wechat
bug