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arXiv · 1609.02764

When game comparison becomes play: Absolutely Categorical Game Theory

Urban Larsson·Richard J. Nowakowski·Carlos P. Santos
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Abstract

Absolute Universes of combinatorial games, as defined in a recent paper by the same authors, include many standard short normal- mis\`ere- and scoring-play monoids. In this note we show that the class is categorical, by extending Joyal's construction of arrows in normal-play games. Given $G$ and $H$ in an Absolute Universe $U$, we study instead the Left Provisonal Game $[G, H]$, which is a normal-play game, independently of the particular Absolute Universe, and find that $G\longrightarrow H$ (implying $G\succcurlyeq H$) corresponds to the set of winning strategies for Left playing second in $[G,H]$. By this we define the category ${\bf LNP(U)}$.

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Urban Larsson, Richard J. Nowakowski, Carlos P. Santos. 2016-09-09. When game comparison becomes play: Absolutely Categorical Game Theory. https://arxiv.org/abs/1609.02764

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