Infinite cyclic impartial games

Details Infinite cyclic impartial games Infinite cyclic impartial games

1998-09-15

arxiv.org/abs/math/9809077v1

Mathematics

Combinatorics

To appear in Proc. Computer Games 1998

Scientific paper

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.

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