Infinite cyclic impartial games
Combinatorics
2007-05-23 v1
Abstract
We define the family of {\it locally path-bounded} digraphs, which is a class of infinite digraphs, and show that on this class it is relatively easy to compute an optimal strategy (winning or nonlosing); and realize a win, when possible, in a finite number of moves. This is done by proving that the Generalized Sprague-Grundy function exists uniquely and has finite values on this class.
Cite
@article{arxiv.math/9809077,
title = {Infinite cyclic impartial games},
author = {Aviezri S. Fraenkel and Ofer Rahat},
journal= {arXiv preprint arXiv:math/9809077},
year = {2007}
}
Comments
To appear in Proc. Computer Games 1998