Stability for Take-Away Games

Abstract

In this paper, we study a family of take-away games called α-tag, parametrized by a real number α ≥ 1. We show that for any given α, there is a half-open interval I α containing α such that the set of losing positions for α-tag is the same as the set of losing positions for β-tag if and only if β ∈ I α . We then end with some results and conjectures on the nature of these intervals.