Last Nim Game With Shifted Alliance System

Hassan Alqady () and Essam El-Seidy ()
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Hassan Alqady: Ain Shams University
Essam El-Seidy: Ain Shams University

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 3, 799-806

Abstract: Abstract We introduce a class of impartial combinatorial game which is the multiple-player last Nim game denoted by MLNim(N, n) in which there are N piles of counters which are linearly ordered and the move will be, the n-player will remove any positive integer of counters from the last pile, we will introduce this MLNim(N, n) with Shifted Standard alliance system by r, denoted by $$SSAM^r$$ S S A M r in which each player will prefer winning for another player over himself. The Aim is to determine the Game value of the positions of MLNim(N, n) where $$N\ge 1$$ N ≥ 1 is the number of piles and $$n\ge 3$$ n ≥ 3 is the number of players and we will present the possible $$n\le N$$ n ≤ N and determine the game value in this case.

Keywords: Shifted; Alliance; MLNim(N; n); Nim and Impartial combinatorial Game; 91A46; 91A06 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00145-1

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