The Shifted Alliance System of Last Nim Game
Hassan El Kady, Essam El-Seidy · Journal of Game Theory · 2019
We introduce a class of impartial combinatorial game which is the multi-player Last Nim game, denoted by in which there are N piles of counters which are linearly ordered, the move will be, the n-player will remove any positive integer of counters from the last pile, we will introduce this with Shifted Standard alliance system by 1, denoted by in which each player will prefer winning for another player over himself. The Aim is to determine the game value of the positions of where is the number of piles and is the number of players and we will present the possible and determine the game value in this case.