Instability in the Hotelling’s Non-Price Spatial Competition Model

Yosuke Yasuda

doi:10.4236/tel.2013.33a002

Abstract

This note analyzes a slightly modified Hotelling model in which two firms are allowed to choose multiple store locations. Each firm can endogenously choose the number of stores while opening a store incurs a set-up cost. We show that the principle of minimum differentiation, i.e., both firms open a store each on the center, never holds when the set-up cost is decreasing in the number of stores. Under general cost functions that include non-linear and asymmetric set up costs, we characterize the conditions under which the principle holds. General payoff functions that are non-linear in the market share are also considered.

Highlights

IntroductionThe spatial competition model initiated by Hotelling [1] is widely used in many fields such as business, economics, regional science, political economics, and so forth
We show that the principle of minimum differentiation, i.e., both firms open a store each on the center, never holds when the set-up cost is decreasing in the number of stores
The spatial competition model initiated by Hotelling [1] is widely used in many fields such as business, economics, regional science, political economics, and so forth1

Summary

Introduction

The spatial competition model initiated by Hotelling [1] is widely used in many fields such as business, economics, regional science, political economics, and so forth. The striking implication of the Hotelling model is that, trying to steal more customers from the rival, both firms end up choosing the center This result, often referred as the principle of minimum differentiation, is employed to explain variety of concentrating phenomena, e.g., little product differentiation, agglomeration of shops, and similar target policies set by two political parties (the median voter theorem). In this short note, we revisit the Hotelling model by incorporating the possibility that firms can choose multiple store locations.

When Firms Agglomerate in the Center

Extension

Conclusion