Competitive location problems: balanced facility location and the One-Round Manhattan Voronoi Game

Abstract We study competitive location problems in a continuous setting, which facilities have to be placed rectangular domain R of normalized dimensions 1 and $$\rho \ge 1$$ ρ ≥ 1 , distances are measured according the Manhattan metric. show that family balanced facility configurations (in Voronoi cells individual equalized with respect number geometric properties) is considerably richer this metric than for Euclidean distances. Our main result considers One-Round Game distances, first player White then Black each place n points ; scores area one its closer opponent. give tight characterization: has winning strategy if only n$$ n all other cases, we present Black.