Multiplayer games as extension of misère games

Abstract

We introduce i-misere play to multiplayer impartial games, which is an extension of Li’s rank-based play and, at the same time, which contains the normal play and the misere play as special cases when the number of players is two. We characterize losing positions of such plays for both NIM and Moore’s game. i-misere play is defined as a special case of a more general notion of preference-based play, and we also study properties of some other preference-based plays.