Universal partisan rulesets and a universal partisan dicotic ruleset

Koki Suetsugu ()
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Koki Suetsugu: National Institute of Informatics

International Journal of Game Theory, 2024, vol. 53, issue 4, No 14, 1385-1406

Abstract: Abstract In combinatorial game theory, we study the set of game values $$\mathbb {G}$$ G , whose elements are mapped from positions of rulesets. In many cases, given a ruleset, not all elements of $$\mathbb {G}$$ G can be assigned positions in the ruleset. An intriguing question is: what ruleset would allow all of them to appear? In this paper, we introduce a ruleset named blue-red turning tiles and prove that it is a universal partisan ruleset; that is, every element in $$\mathbb {G}$$ G can occur as a position in the ruleset. This is the second universal partisan ruleset after portuguese konane. In addition, we introduce two rulesets go on lattice and beyond the door and prove that they are also universal partisan rulesets using a game-tree-preserving reduction from blue-red turning tiles. Furthermore, we consider a dicotic version of beyond the door, and we prove that the ruleset is a universal partisan dicotic ruleset.

Keywords: Combinatorial game theory; Universal ruleset; Partisan games; Dicotic games (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00182-024-00920-4

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