Hotelling was Right

• Published date: 01 December 2013
• Author: Dimitrios Xefteris
• Date: 01 December 2013
• DOI: http://doi.org/10.1111/jems.12032

Hotelling was Right

DIMITRIOS XEFTERIS

Department of Economics,

University of Cyprus,

Nicosia, Cyprus

xefteris.dimitrios@ucy.ac.cy

This paper proves existence of a subgame perfect equilibrium in Hotelling’s original (unidimen-

sional city, linear transportation costs, uniform distribution of the consumers, two firms with

identical and constant marginal cost, perfectly inelastic demand) location–price game such that

in the location subgame the location choices of the firms are pure and identical. The result can

be extended to variations of the original setup (multidimensional city, nonlinear transportation

costs, nonuniform distribution of consumers, many firms with identical and constant marginal

costs, two or more firms with nonidentical but constant marginal costs).

1. Introduction

Hotelling’s (1929) model of spatial differentiation is one of the most influential con-

tributions in economic theory. It is the cornerstone of a whole literature that studies

issues in industrial organization and political economics and it has been modified in

numerous ways.1In industrial organization it still provides the basic framework for

product differentiation analysis and in political economics it paved the way for the most

popular model of electoral competition; the spatial competition model which dates back

to Downs (1957) and which, in the case of two candidates, produces the well-known

minimum differentiation result.

As far as the original first-location-then-price model of Hotelling (1929) is con-

cerned, there are two important papers that shed some light on the nature of its equilib-

ria. d’Aspremont et al. (1979) showed that there is no subgame perfect equilibrium in

pure strategies and Osborne and Pitchik (1987) added that in Hotelling’s (1929) model

“there is a unique (up to symmetry) subgame perfect equilibrium in which the location

choices of the firms are pure; in it, the firms locate 0.27 from the ends of the market.”

This equilibrium was identified in a computational manner, and it is in fact only proved

to be an ε-equilibrium. That is, our present knowledge about equilibrium behavior in

the original model is relatively limited. Formally speaking, we do not have even one

subgame equilibrium of such a celebrated model.

To the author’s knowledge there have been no further studies that investigated

equilibrium behavior in Hotelling’s (1929) original game. Osborne and Pitchik (1987)

proved that full equilibrium characterization for each price subgame is, essentially, im-

plausible and it was quite natural that the debate ended there. But there is a minor

detail that deserves some attention. While studying this game, Osborne and Pitchik

(1987) made a modification to Hotelling’s (1929) assumptions. Unlike Hotelling (1929)

1. Examples of notable variations of the original model are Irmen and Thisse (1998), who study a multidi-

mensional differentiation setup, and Grilo et al. (2001), who consider consumption externalities.

C2013 Wiley Periodicals, Inc.

Journal of Economics & Management Strategy, Volume22, Number 4, Winter 2013, 706–712