Horizontal Product Differentiation in Varian's Model of Sales

We consider the explicit introduction of firms’ choice of location to Varian’s model of sales for a two-stage spatial competition model based on a standard Hotelling’s linear city model. This model is the formalization of Varian’s model of sales in the context of Hotelling’s spatial competition. We obtain three main results. First, we show that there exists a symmetric subgame perfect equilibrium in which each firm chooses a symmetric mixed strategy equilibrium profile. This equilibrium includes symmetric location pairs and asymmetric location pairs. Second, the equilibrium behaviors in our model are randomized at both location and price stages. Third, we show that expected profits in a subgame perfect equilibrium are equal to the maximum monopoly profit. 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 with competition. I am grateful to Tadashi Sekiguchi for his guidance over the past decade. Without his helpful advice, I would not have been able to complete this study. I am also grateful to Haruo Imai, my supervisor, for his long direction. I also would like to thank Noriaki Matsushima, Takanori Maehara, and seminar participants at Kyoto University, National Graduate Institute for Policy Studies, the ARSC2011(Applied Regional Science Conference), and the NARSC2012(the North American Meeting of Regional Science Association International) for comments and suggestions. All errors are my own. Shizuoka University, Suruga-ku Ohya 836, Shizuoka, 422-8529, Japan. Tel: +81-54-2375474. E-mail: [email protected] ORCID iD 0000-0003-2429-7630