A model of three cities: the locations of two firms with different types of competition

We develop a spatial model representing three cities of different size and connected by a road. We study two versions of a two-stage game where firms first decide where to locate and then set quantities or prices. We show that, in the case of quantity competition, maximal dispersion or agglomeration arises. Also, multiple equilibria are possible. In the case of price competition, maximal dispersion or partial dispersion arises. An asymmetric spatial equilibrium is possible even if the model is completely symmetric ex ante. A number of results are also derived when comparing the Cournot and the Bertrand locational equilibria in terms of profits, consumer surplus, and total welfare, and with respect to the welfare-maximizing locations.