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 vertices 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 scores 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.

我们介绍了游戏影响，一种得分组合游戏，在有向图上进行，其中每个顶点要么是黑色，要么是白色。黑棋和白棋这两个玩家通过取其颜色及其所有后继（对于黑）或其所有前驱（对于白）的顶点交替进行游戏。每个玩家的分数就是他所取的顶点数。我们证明影响是一个 nonzugzwang 游戏，这意味着没有玩家有兴趣在游戏的任何一步传球，因此属于米尔诺的宇宙。我们在黑白顶点交替的特定路径类中研究这个游戏。当有一条路径时，我们为两个玩家提供了一个几乎严格的策略。更准确地说，我们证明第一个玩家总是比第二个玩家获得严格的分数，但分数之间的差异以 5 为界。最后，我们展示了一些图表，其中 a 颜色顶点的初始比例player 尽可能小，但是这个玩家可以得到几乎所有的顶点。