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Competitive location under proportional choice: 1-suboptimal points on networks

Kress D., Pesch E.

Decision Making in Manufacturing and Services

2012

Vol. 6, no. 1-2

53--64

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.