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 \(SSAM^r\) 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 \(N\ge 1\) is the number of piles and \(n\ge 3\) is the number of players and we will present the possible \(n\le N\)and determine the game value in this case.
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References
Bouton CL (1901) Nim, a game with a complete mathematical theory. Ann Math 3:35-39.
Fraenkel AS, Lorberbom M (1991) Nimhoff games. J Combin Theory Ser A 58:1-25.
Flammenkamp A, Holshouser A, ReiterH(2003) Dynamic one-pile blocking Nim. Electr J Combin 10:Article N4.
Holshouser A, Reiter H, Rudzinski J (2003) Dynamic one-pile Nim. Fibonacci Q 41(3):253-262.
Albert MH, Nowakowski RJ (2004) Nim restrictions. Int Electron J Combin Number Theory 4:Article G01.
Liu WA, Zhao X (2016) Nim with one or two dynamic restrictions. Discr Appl Math 198:48-64.
Albert MH, Nowakowski RJ (2001) The game of End-Nim. Electr J Combin 8:Article R1.
Friedman E (2000) Variants of Nim. Math Magic Game Arch. Accessed Nov 2000.
Li SYR (1978) N-person Nim and n-person Moore’s Games. Int J Game Theory 7:31-36.
Straffin PD (1985) Three-person winner-take-all games with Mc-Carthys revenge rule. Coll JMath 16:386-394.
Loeb DE (1996) Stable winning coalitions. In: Nowakowski RJ (ed) Proc MSRI workshop on combinatorial games, games of no chance 29:451-471. Cambridge University Press, Cambridge.
Propp J (1996) Three-player impartial games. Theor Comput Sci 233:263-278.
Cincotti A (2010) N-player partizan games. Theor Comput Sci 411:3224-3234
Kelly AR (2006) One-pile misère Nim for three or more players. Int J Math Math Sci 2006:1-8. https://doi.org/10.1155/IJMMS/2006/40796
Kelly AR (2011) Analysis of one pile misère Nim for two alliances. Rock Mt J Math 41(6):1895-1906.
Zhao X, Liu WA (2016) One pile misère bounded Nim with two alliances. Discr Appl Math 214:16-33.
Krawec WO (2012) Analyzing n-player impartial games. Int J Game Theory 41:345-367.
KrawecWO(2015) n-Player impartial combinatorial games with random players. TheorComput Sci 569:1-12.
Wen An Liu , Juan Yang (2017)Multi-player Last Nim with Passes.Int J Game Theory
wen An Liu, Jing Jing Zhou (2017) Multi-Player Small Nim with Passes.Discrete applied mathematics.
Guy RK, Nowakowski RJ (2009) Unsolved problems in combinatorial games. In: Games of no chance 3, Math. Sci. Res. Inst. Publ, vol 56. Cambridge Univ Press, Cambridge, pp 475-500
Morrison RE, Friedman EJ, Landsberg AS (2012) Combinatorial games with a pass: a dynamical systems approach. arXiv:1204.3222
Low RM, Chan WH (2015) An atlas of N- and P-positions in ‘Nim with a pass’. Int Electron J Combin Number Theory 15:Article G02
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Communicated by Sharad S Sane.
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Alqady, H., El-Seidy, E. Last Nim Game With Shifted Alliance System. Indian J Pure Appl Math 52, 799–806 (2021). https://doi.org/10.1007/s13226-021-00145-1
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DOI: https://doi.org/10.1007/s13226-021-00145-1