A limit to price-increasing competition

Differentiated entry may cause an incumbent firm to increase its price if the entering brand attracts price-sensitive consumers. This paper generalizes from the known cases with one-dimensional and two-dimensional products, showing for a finite number of attributes that there is scope for price-increasing competition, depending on the entrant's product positioning. The extension is critical because it leads to a reversal that has not been considered. The highest possible duopoly price converges to the monopoly price as the dimensionality increases. Intuitively, when the product is more complex, tastes in the intersection of two brand markets (at any prices) are more specific and less frequent. This thinning of the fringe diminishes the effect of competitive entry.