Authors: Popović, Danijela 
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On emulational equivalence of combinatorial games and the game Hackenforb
First page: 41
Related Publication(s): Book of abstracts
Conference: Maribor Graph Theory Conference (MGTC 2022), 11-15. septembar, 2022, Maribor, Slovenija
Issue Date: 2022
In combinatorial game theory, two impartial games are considered equiv-
alent if their corresponding Grundy values are equal. Although the
developed theory is an irreplaceable tool when questions of the winner
and the optimal strategy are concerned, it does not tell too much about
the structural (dis)similarity between games. In this presentation we
shall talk about another notion of equivalence of impartial combina-
torial games, the so-called “emulational equivalence." This concept is
stronger than the Grundy equivalence, but weaker than the isomor-
phism between the game graphs. Intuitively, two games are emulation-
ally equivalent if they reduce to the same game when positions that
are “essentially the same" are not treated as distinct. We also define
a new impartial combinatorial game on graphs called Hackenforb and
show that various well-known combinatorial games (such as Nim, Sub-
traction game, Notakto, Chomp) are emulationally equivalent to an
instance of Hackenforb. We hope that it is not too ambitious to believe
that, in some future, Hackenforb can establish itself as a new common
“language" for studying many different games, and that this could help
in bringing out some new possible directions from which we can ap-
proach various open questions on combinatorial games and shed some
light on them.
Joint work with Bojan Bašić and Nikola Milosavljević.
Keywords: combinatorial games | emulational equivalence | games on graphs | Hackenforb
Publisher: Faculty of Natural Sciences and Mathematics, University of Maribor

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