Competition in Multi-characteristics Spaces: Hotelling was Almost Right

Lancasterian models of product differentiation typically assume a one-dimensional characteristics space. We show that standard results on prices and locations no longer hold when firms compete in a multi-characteristics space. In the location game with n characteristics, firms choose to maximize differentiation in the dominant characteristic and to minimize differentiation in the others when the salience coefficient of the former is sufficiently large. Thus, the principle of minimum differentiation holds for all but one characteristic. Furthermore, prices do not necessarily fall when products get closer in the characteristics space because price competition is relaxed when products are differentiated enough in the dominant characteristic.