We analyze two and three-dimensional variants of Hotelling's model of differentiated products. In our setup, consumers can place different importance on each product attribute; this is measured by a weight in 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. We seek subgame-perfect equilibria. We find 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. Thus, depending on the importance consumers place on each attribute, in two dimensions there is a max-min equilibrium, a min-max equilibrium, or both. In three dimensions, depending on the weights, there can be a max-min-min equilibrium, a min-max-min equilibrium, a min-min-max equilibrium, any two of them, or all three.

Journal of Regional Science vol. 38 (1998), pp. 207-230.

^* Graduate School of Business, Columbia University, New York, NY, U.S.A; (212) 854-3476, e-mail aansari@research.gsb.columbia.edu.

^** Stern School of Business, New York University, New York, U.S.A., and Center for Economic Policy Research, Stanford University, Stanford, U.S.A; (212) 998-0864, (212) 725-9415, FAX (212) 995-4218, (415) 723-8611, e-mail neconomi@stern.nyu.edu, http://www.stern.nyu.edu/networks/

^*** Stern School of Business, New York University, New York, U.S.A., (212) 998-0521, FAX (212) 995-4006, e-mail jsteckel@stern.nyu.edu.

in Acrobat format. If you do not have an Acrobat reader, you can download it free from Adobe.