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One-pile misère Nim for three or more players

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  • Annela R. Kelly

Abstract

The analysis of the classical game of Nim relies on binaryrepresentation of numbers as shown in the books of Berlekamp andGardener. There is considerable interest in generalizations andmodifications of the game. We will consider one-pile misère Nimfor more than two players. In the case of three or more players,the impartial game theory results rarely apply. In this note, weanalyze the game in a variety of cases where alliances are formedamong the players.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jijmms:040796
    DOI: 10.1155/IJMMS/2006/40796
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    Cited by:

    1. Wen An Liu & Juan Yang, 2018. "Multi-player Last Nim with Passes," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(2), pages 673-693, May.
    2. 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.

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