Two-stage two-dimensional spatial competition between two firms

Abstract

In this paper we analyze the Hotelling's model of spatial duopoly on two-dimensional space, where the first stage is the location game, and the second stage is the price game. In the case of a uniform rectangular distribution of consumers, we prove that (i) two firms maximize their distance in one dimension, but minimize their distance in the other dimension, (ii) the firms are better off if they locate sequentially rather than simultaneously, and (iii) the welfare loss in equilibrium is 1.6 to 4 times as large as that in optimum.