We define the family of 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. (C) 2001 Elsevier Science B.V. All rights reserved. [References: 16]
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