Hotelling model with heterogeneous firms

• Main Authors: Ler, Jun Yi, Low, Jing Mei Cheryl, Ng, Qin Hui
• Other Authors: School of Humanities and Social Sciences
• Format: Final Year Project
• Language: English
• Published: 2017
• Subjects: DRNTU::Social sciences
• Online Access: http://hdl.handle.net/10356/72733
• Institution: Nanyang Technological University

The Hotelling model is the workhorse model in the study of spatial competition since it was first proposed in Hotelling (1929), and has been widely applied to various fields of studies, such as industrial organization, urban planning and political economy. A notable finding, due to Eaton and Lipsey (1975), is that a pure-strategy Nash equilibrium does not exist with three competing firms in the Hotelling model. This finding is quite counter-intuitive, as pure-strategy Nash equilibria exist for any other number of firms. Moreover, the existing literature has focused mainly on the case of identical firms, and overlooked the location competition among heterogeneous firms, a case that is clearly of greater empirical relevance. This paper aims to advance our understanding of location competition by addressing the two aforementioned issues. Specifically, we investigate a standard Hotelling model with three firms and identify conditions under which a pure-strategy Nash equilibrium exists with three identical firms. We then incorporate quality variation into the benchmark Hotelling model, and characterize a pure-strategy Nash equilibrium. In the equilibrium, higher quality firms would locate themselves near the corners, whereas the lowest quality firms would locate itself in the middle. This finding is in sharp contrast to the Principle of Minimal Differentiation (Boulding, 1966), which asserts that firms would congregate at the middle when positioning their products.