Product differentiation and location decisions under demand uncertainty

We investigate Hotelling's duopoly game of location-then-price choices with quadratic transportation costs and uniformly distributed consumers under the assumption that firms are uncertain about the exact location of demand. We characterize the unique equilibrium and the socially optimal locations. Contrary to the individual-level random utility models, location uncertainty is a differentiation force. In equilibrium, increases in the variance of the uncertainty lead to greater differentiation, higher expected equilibrium prices and profits, and a greater welfare loss.