Pyramid Nim is played on a directed acyclic graph. Players remove vertices of a path of undominated vertices. We determine Grundy-values for some small games of Pyramid Nim, and Grundy-values for a special class of directed acyclic graphs called triangular pyramids. The rules of the game are quite simple, and the analysis in general may be difficult. These two properties make Pyramid Nim an appealing game.
University of Pittsburgh
Mathematics and Statistics
Stephen J. Curran, Daniel Gray, Stephen C. Locke, and Richard M. Low. "PYRAMID NIM" Integers (2022).