The Max-Min-Min Principle of Product Differentiation

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. * Graduate School of Business, Columbia University, New York, NY, U.S.A; (212) 854-3476, e-mail [email protected]. ** 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 ( 2 1 2 ) 9 9 5 4 2 1 8 , ( 4 1 5 ) 7 2 3 8 6 1 1 , e m a i l n e c o n o m i @ s t e r n . n y u . e d u , http://edgar.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 [email protected]. The Max-Min-Min Principle of Product Differentiation