Competitive location in the plane

Two questions in competitive environment are presented in the literature. One question deals with finding the best location for new facilities in order to attract the most buying power away from existing facilities. The second question is how to find the best location for the defending facilities, so that a future competitor will be able to capture the least buying power. In this paper, the authors study the second problem for the case of a large number of customers spread independently and uniformly over a given region A⊆ℝ² and a large number of original facilities. They show that, under these conditions, a very simple solution, the ‘honeycomb’ heuristic, is almost surely guaranteed to be within 2.5 percent from optimality. This is the case for any number of facilities contemplated by the competitor.