Epidemiography. II: Games with a dozing yet winning player
[For part I see the first and third author, Pac. J. Math. 118, 369-381 (1985; Zbl 0574.90110).] Epidemiography designates a class of games played on directed graphs. At step k of the game, the move made on a digraph G is replicated onto f(k) isomorphic copies of G. The player first unable to move is the loser; his opponent the winner. We show that if G is finite and acyclic, then the game terminates for every function \(f: Z^ k\to Z^ 0\), and we construct classes of digraphs and functions f for which the first (second) player can win. Many epidemiography games are robust: the outcome depends only on the ``foliage'' of G, and the winner can play randomly during much of the time. Play is very long even if f grows only linearly. Bounds on the length of play are provided.
scientific article; zbMATH DE number 4061030
scientific article