Combinatorial Game Complexity: An Introduction with 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.