Emperor nim and emperor sum: a new sum of impartial games

Koki Suetsugu ()
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Koki Suetsugu: National Institute of Informatics

International Journal of Game Theory, 2024, vol. 53, issue 4, No 1, 1089-1097

Abstract: Abstract The emperor sum of combinatorial games is discussed in this study. In this sum, a player moves arbitrarily many times in one component. For every other component, the player moves once at most. The $$\mathcal {P}$$ P -positions of emperor sums are characterized using a parameter referred to as $$\mathcal {P}$$ P -position length. An emperor sum is a $$\mathcal {P}$$ P -position if and only if every component is a $$\mathcal {P}$$ P -position and the nim-sum of the $$\mathcal {P}$$ P -position lengths of all components is 0. This is similar to using the nim-sum of $$\mathcal {G}$$ G -values to characterize the $$\mathcal {P}$$ P -positions of the disjunctive sum of games.

Keywords: Combinatorial game theory; Nim; Impartial game; Sum of games; $$\mathcal {P}$$ P -position length (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00182-021-00782-0

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