Location games on multiple disjoint spaces: circles and lines.

Location games are games where players select a subsets of points of some space, determining the division of this spaces into areas of points that are closer to the points of one of the players than to the points of other players. Because of many possible interpretations that abstraction of space offers, problems such as positioning production plants, proposing a political position in an issue space, locating a brand in a feature space, or locating a server in a computer network, can all be modelled as location problems and whenever any competition is involved, as location games. I will present results concerning certain multiround two player location game played on disjoint circles and disjoint line segments of equal sizes. In this game players move alternately selecting one or more locations in each move, having the same total numbers of points to select throughout the game. I will show tying or winning strategies for the players for different variants of this game (i.e. different total numbers of locations to select and different numbers of spaces). Additionally I will present an open problem concerning a multiplayer sequential location game played on a single line segment.