Can Rivalry Increase Prices?

Spatially differentiated duopolists set higher-than-monopoly prices at some distances. This phenomenon is shown to occur in any finite- dimensional space for a class of reservation prices that covers concavity and convexity in perceived distance from a design. But an upper bound on the equilibrium duopoly price converges monotonically and quickly to the monopoly price in dimensionality. If consumers care about sufficiently many features of the product (a very small number of criteria is enough), monopoly nearly leads to an extreme price.