On the non-existence of oligopolistic equilibria in differentiated products spaces

In a large class of product differentiation models á la Hotelling, the firms' payoffs in the game involving location in the differentiated products space exclusively depends on the distance to their neighbouring firms, rather than on the firms' locations proper. This leads to a degeneracy on the firms' strategy space. Using alternative equilibrium concepts, this is shown to be the reason for the non-existence of non-cooperative equilibria, especially if the firms' technologies are not identical.