Kuninori Nakagawa

Abstract 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.

This paper aims at providing a brief review over the literature on spatial competition a la Hotelling and its major extensions. We also explore an economic implication embedded in its mathematical structure. In section 1, we survey the Hotelling spatial competition and its major extensions. In section 2, we discuss its mathematical structure, focusing mainly on consumer preferences and those distributions.