Rev Ind Organ (2007) 30:29–38
On Stability in Competition: Tying and Horizontal
Published online: 28 February 2007
© Springer Science+Business Media B.V. 2007
Abstract We combine Hotelling’s model of product differentiation with
tie-in sales. A monopolist in one market competes with another ﬁrm in a second
market. In equilibrium ﬁrms choose zero product differentiation. Due to the
tying structure no ﬁrm can gain the whole market by a small price reduction. A
differentiation effect due to tie-in sales leads to this equilibrium stability.
Keywords Horizontal product differentiation · Hotelling · Tie-in sales ·
JEL-Classiﬁcations: D43, L10, L11, L13.
We address equilibrium existence for Hotelling’s model of horizontal prod-
uct differentiation. To address equilibrium existence for Hotelling’s model we
combine it with tie-in sales. Tie-in sales require consumers to buy a good as a
condition for buying another good.
Examples for tie-in sales motivate the widely used setting of a monopolist
in one market competing with another ﬁrm in a second market. In the second
A survey on tie-in sales goes beyond the scope of this paper. Therefore, we refer to the
extensive literature on tie-in sales and bundling for detailed deﬁnitions and examples.
References on deﬁnitions and examples are, e.g., Burstein (1960, 1988), Adams and Yellen (1976),
and Whinston (1990).
A. Egli (
University of Bern, Volkswirtschaftliches Institut, Abteilung für Wirtschaftstheorie,
Schanzeneckstrasse 1, Postfach 8573, CH-3001 Bern, Switzerland