Preservation of P-Positions between a Game and Its Restricted Game

E. Duchene et al investigate games whose sets of allowed moves are subsets of Wythoff´s one, and whose set of P-positions is exactly Wythoff´s sequence. Their results show that such a game does not exist. In this paper, we find a pair of games, one is the restricted version of the other, such that they have the same set of P-positions. We also find another pair of games, one is the restricted version of the other, such that they do not have the same set of P-positions. This means that the preservation of P-positions between a game and its restricted game depends on the game itself.