Competitive location under proportional choice: 1-suboptimal points on networks - Kress, Dominik; Pesch, Erwin (Decision Making in Manufacturing and Services, 2012)
This paper is concerned with a competitive or voting location problem on networks under a proportional choice rule that has previously been introduced by Bauer et al. (1993). We refine a discretization result of the authors by proving convexity and concavity properties of related expected payoff functions. Furthermore, we answer the long time open question whether 1-suboptimal points are always vertices by providing a counterexample on a tree network.