We investigate the nature of competitive equilibrium for brands competing in a multi-attribute product space when consumer preferences for product attributes follow nonuniform distributions. We establish subgame-perfect equilibria in a two-stage game, where firms choose positions in the first stage and prices in the second stage. Two types of entry scenarios are investigated. In the first, the number of brands is given exogenously, and all of them choose positions simultaneously. In the second scenario, firms enter in sequence, and the early entrants can choose strategies to deter the entry of later entrants. We find the equilibria for two, three, and four brands for consumer preferences that follow a beta distribution. Nonuniform distributions result in equilibrium configurations that are substantially different from those obtained for uniform consumer distributions. In the two brands case, for sufficiently concentrated distributions we find asymmetric position equilibria with one firm at the corner of the market and one firm at an interior position. In the case of three brands, for sufficiently concentrated preferences we find symmetric equilibria that do not yield maximal differentiation. We also establish an equilibrium for the case of four competing brands. In addition we characterize entry deterring positioning strategies and examine how they vary with the distribution of consumer preferences.

Published in Marketing Science, vol. 13, no. 3, pp. 248-273, (Summer 1994).

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