One-Pile Nim games with arbitrarily many random players

Krawec (2015) developed a method of analyzing n-player games where a subset of players plays randomly. In this paper, we use this method to analyze a class of combinatorial games “One-Pile Nim with n players”, denoted by OPNim(n), which allows arbitrarily many players to play randomly. We analyze th...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2019-02, Vol.255, p.56-74
Main Authors: Liu, Wen An, Wang, Jing, Duan, Jia Wei
Format: Article
Language:English
Subjects:
Alliance matrix
Combinatorial analysis
Games
Impartial combinatorial games
Multi-player games
Nim
Players
Random player
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Summary:Krawec (2015) developed a method of analyzing n-player games where a subset of players plays randomly. In this paper, we use this method to analyze a class of combinatorial games “One-Pile Nim with n players”, denoted by OPNim(n), which allows arbitrarily many players to play randomly. We analyze the general structure of random players. The game values of OPNim(n) are determined for the general structure, assuming that a particular alliance matrix A0 defined by Krawec is adopted. We next try to answer the question: Fix a structure of random players, does there exist an alliance matrix A′ different from A0 such that the game values under A′ are the same with that under A0? We find a class of alliance matrices As which give this question a positive answer for any structure of random players.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2018.09.006