Epidemiography designates a class of combinatorial 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 loses and his opponent wins. Let G be any finite acyclic digraph. We determine the winner for several classes of growth functions f and show that in each case the winner has a semi-robust strategy: He can play almost randomly during the play except at the end. We also determine the strategy for shortest and longest play.
