Computational and Applied Mathematics

, Volume 37, Issue 2, pp 1369–1378 | Cite as

Polynomial time winning strategies for three variants of (s, t)-Wythoff’s game

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Abstract

In this paper, we provide polynomial time winning strategies for three variants of (s, t)-wythoff’s game using some special numeration systems. The first one is the game of Liu and Zhou (Discrete Applied Math 179:28–43, 2014), which is an extension of (s, t)-Wythoff’s game by adjoining to it some subsets of its P-positions as additional moves. The second one is a restriction of (s, t)-Wythoff’s game, investigated by Liu and Li (Electron J Combin 21(2):\(\sharp \)P2.44, 2014), where players are restricted to take even tokes in every move. The final one is new defined and obtained from the second one by adjoining to it some of its P-positions as additional moves.

Keywords

Game theory Combinatorial games \((s, t)\)-Wythoff’s game Polynomial time 

Mathematics Subject Classification

91A46 Combinatorial games 
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Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grants 61373174.

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2016

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXidian UniversityXi’anChina

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