  We introduce the game INFLUENCE, a scoring combinatorial game, played on a
directed graph where each vertex is either colored black or white. The two
players, Black and White play alternately by taking a vertex of their color and
all its successors (for Black) or all its predecessors (for White). The score
of each player is the number of vertices he has taken.
  We prove that INFLUENCE is a nonzugzwang game, meaning that no player has
interest to pass at any step of the game, and thus belongs to Milnor's
universe. We study this game in the particular class of paths where black and
white are alternated. We give an almost tight strategy for both players when
there is one path. More precisely, we prove that the first player always gets a
strictly better score than the second one, but that the difference between the
score is bounded by 5. Finally, we exhibit some graphs for which the initial
proportion of vertices of the color of a player is as small as possible but
where this player can get almost all the vertices.
