Two and three-dimensional variants of Hotelling's (1929) model of differentiated products are analyzed. In the setup, consumers can place different importances on each product attribute; these are measured by weights on the disutility of distance in each dimension. Two firms play a two-stage game; they choose locations in stage 1 and prices in stage 2. Subgame-perfect equilibria are sought. It is found that all such equilibria have maximal differentiation in one dimension only; in all other dimensions they have minimum differentiation. An equilibrium with maximal differentiation in a certain dimension occurs when consumers place sufficient importance (weight) on that attribute.
Ansari, Asim, Nicholas Economides, and Joel Steckel. "The Max-Min-Min Principle of Product Differentiation." Journal of Regional Science 38, no. 2 (May 1998): 207-31.
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