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

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 i...

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Bibliographic Details
Published in:Computational & applied mathematics 2018-05, Vol.37 (2), p.1369-1378
Main Authors: Li, Haiyan, Liu, Sanyang, Yi, Guisheng
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Game theory
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Polynomials
Set theory
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Summary: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): ♯ 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.
ISSN:0101-8205
2238-3603
1807-0302
DOI:10.1007/s40314-016-0405-x