Voronoi game is a simple geometric model for competitive facility location problem that is done between two players in continues space. In some previous researches the problem has been studied with Euclidean distance. In this paper a new version of one-round Voronoi game is presented in which multiplicatively weighted Voronoi diagram is used. It is showed in this paper when two players have same points, there is a winning strategy for one of the players. Also we discuss on one dimensional spaces.
