Abstract
We consider how three firms compete in a Salop location model and how cooperation in location choice by two of these firms affects the outcomes. We consider the classical case of linear transportation costs as a two-stage game in which the firms select first a location on a unit circle along which consumers are dispersed evenly, followed by the competitive selection of a price. Standard analysis restricts itself to purely competitive selection of location; instead, we focus on the situation in which two firms collectively decide about location, but price their products competitively after the location choice has been effectuated. We show that such partial coordination of location is beneficial to all firms, since it reduces the number of equilibria significantly and, thereby, the resulting coordination problem. Subsequently, we show that the case of quadratic transportation costs changes the main conclusions only marginally.
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Notes
- 1.
We refer to Walras [28] for a translation of this seminal work.
- 2.
Hotelling [13] himself used the metaphor of consumers located along a “high street”, who incur costs to travel to the location of the store of each producer. These travel or transportation costs now represent the disutility from consuming a product that is imperfectly fitting with the exact location of the consumer on this high street.
- 3.
The introduction of this minimal distance guarantees the existence of an equilibrium in this model.
- 4.
Calculations regarding the reported outcomes here are available upon request.
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Acknowledgements
We thank an anonymous referee for valuable comments. We are grateful for the support of Emiliya Lazarova and Lina Mallozzi in the development of this paper.
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Chakrabarti, S., Gilles, R.P. (2017). Partial Cooperation in Location Choice: Salop’s Model with Three Firms. In: Mallozzi, L., D'Amato, E., Pardalos, P. (eds) Spatial Interaction Models . Springer Optimization and Its Applications, vol 118. Springer, Cham. https://doi.org/10.1007/978-3-319-52654-6_2
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