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Last Nim Game With Shifted Alliance System

Author

Listed:
  • Hassan Alqady

    (Ain Shams University)

  • Essam El-Seidy

    (Ain Shams University)

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.

Suggested Citation

  • Hassan Alqady & Essam El-Seidy, 2021. "Last Nim Game With Shifted Alliance System," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(3), pages 799-806, September.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:3:d:10.1007_s13226-021-00145-1
    DOI: 10.1007/s13226-021-00145-1
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    References listed on IDEAS

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    1. Annela R. Kelly, 2006. "One-pile misère Nim for three or more players," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-8, October.
    2. Walter Krawec, 2012. "Analyzing n-player impartial games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 345-367, May.
    Full references (including those not matched with items on IDEAS)

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