Combinatorial Game Complexity: An Introduction with Poset Games

TL;DR

This paper introduces the fundamentals of combinatorial game theory with a focus on poset games, discussing their mathematical properties and recent computational complexity results, including the complexity of Nim and related games.

Contribution

It provides a comprehensive overview of the computational complexity of poset games, including recent findings, filling a gap in the literature on their algorithmic properties.

Findings

Poset games have complex computational properties.

Recent results show certain poset games are PSPACE-complete.

The paper summarizes known complexity classifications of poset games.

Abstract

Poset games have been the object of mathematical study for over a century, but little has been written on the computational complexity of determining important properties of these games. In this introduction we develop the fundamentals of combinatorial game theory and focus for the most part on poset games, of which Nim is perhaps the best-known example. We present the complexity results known to date, some discovered very recently.