A class of extensions of Restricted (s, t)-Wythoff’s game

Abstract

Restricted (s, t)-Wythoff’s game, introduced by Liu et al. in 2014, is an impartial combinatorial game. We define and solve a class of games obtained from Restricted (s, t)-Wythoff’s game by adjoining to it some subsets of its P-positions as additional moves. The results show that under certain conditions they are equivalent to one case in which only one P-position is adjoined as an additional move. Furthermore, two winning strategies of exponential and polynomial are provided for the games.

Keywords

• discrete mathematics
• combinatorial games
• wythoff’s game
• winning strategy
• computational complexity
• 91a46