Product and Price Competition in a Two-Dimensional Vertical Differentiation Model

In this paper, the one-dimensional vertical differentiation model (Shaked and Sutton [Shaked, A., J. Sutton. 1982. Relaxing price competition through product differentiation. Rev. Econom. Stud. 49 3–13.], Moorthy [Moorthy, K. S. 1988. Product and price competition in a Duopoly. Marketing Sci. 7(Spring) 141–168.]) is extended to two dimensions and an analysis of product and price competition is presented. A two-stage game theoretic analysis in which two firms compete first on product positions and then on price is conducted. Closed form equilibrium solutions are obtained for each stage in which competitors are unrestricted in their choices of price or product positions. A significant finding of this research is that unlike the one-dimensional vertical differentiation model, firms do not tend towards maximum differentiation, although this solution is possible under certain conditions. When the range of positioning options on each of the dimensions is equal, MaxMin product differentiation occurs. That is, in equilibrium, the two firms tend to choose positions which will represent maximum differentiation on one dimension and minimum differentiation on the other dimension.