Horizontal product differentiation in Varian’s model of sales

We consider the explicit introduction of firms’ choice of location into Varian’s model of sales. In our model, firms compete for both uninformed and informed consumers in a two-stage spatial competition model in which firms choose price and location. We obtain a result where both prices and locations are randomized in the subgame perfect equilibrium. The difference between each firm’s choice of location in the subgame perfect equilibrium is neither purely maximized at both ends of a line nor purely minimized at the center. Also, the expected profits in a subgame perfect equilibrium are equal to the maximum profit from an uninformed market in the absence of informed consumers. Thus, even when product differentiation is explicitly introduced into a Varian-type model, Varian’s implication can be retained; the opportunity for profit in an informed market is lost due to competition.