On competition in a Stackelberg location-design model with deterministic supplier choice

Abstract

We study a market situation where two firms maximize market capture by deciding on the location in the plane and investing in a competing quality against investment cost. Clients choose one of the suppliers; i.e. deterministic supplier choice. To study this situation, a game theoretic model is formulated. We show that for the modelled situation no Nash equilibrium exists. However, a so-called Stackelberg equilibrium, where one of the firms (the leader) is aware of what the other (follower) is going to do, exists. The questions under study is whether co-location is a natural phenomenon in this case and in which situation one of the firms is not entering the market. The study requires a multi-level thinking where the decisions on location follow from the known quality investment behavior and the actions of the leader take the decisions of the follower into account.