The Missing Equilibria in Hotelling's Location Game

We study the location equilibrium in Hotelling's model of spatial competition. As d'Aspremont et al. (1979) have shown, with quadratic consumer transportation cost the two sellers will seek to move as far away from each other as possible. This generates a coordination problem which the literature typically ignores by restricting firm 1 to locate in the first half and firm 2 in the second half of market. We study the non-cooperative outcome in the absence of such a coordination device and find that the location game possesses an infinity of mixed strategy Nash equilibria. in these equilibria coordination failure invalidates the principle of 'maximum differentiation' and firms may even locate at the same point.