Circular Nim Games

Abstract

A circular Nim game is a two player impartial combinatorial game consisting of  $n$ stacks of tokens placed in a circle. A move consists of choosing $k$ consecutive stacks, and taking at least one token from one or more of the $k$ stacks.  The last player able to make a move wins.  We prove results on the structure of the losing positions for small $n$ and $k$ and pose some open questions for further investigations.