Publication: Computation of multi-facility location Nash equilibria on a network under quantity competition.
Authors
Pelegrín Pelegrín, Blas ; Fernández Hernández, Pascual ; García Pérez, María Dolores
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Publisher
SPRINGER
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DOI
https://doi.org/10.1007/s11067-019-09463-8
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info:eu-repo/semantics/article
Description
©2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
This document is the Accepted, version of a Published Work that appeared in final form in Networks and Spatial Economics. To access the final edited and published work see https://doi.org/10.1007/s11067-019-09463-8
Abstract
We deal with the location-quantity problem for competing firms when they locate multiple facilities and offer the same type of product. Competition is performed under delivered quantities that are sent from the facilities to the customers. This problem is reduced to a location game when the competing firms deliver the Cournot equilibrium quantities. While existence conditions for a Nash equilibrium of the location game have been discussed in many contributions in the literature, computing an equilibrium on a network when multiple facilities are to be located by each firm is a problem not previously addressed. We propose an integer linear programming formulation to fill this gap. The formulation solves the profit maximization problem for a firm, assuming that the other firms have fixed their facility locations. This allows us to compute location Nash equilibria by the best response procedure. A study with data of Spanish municipalities under different scenarios is presented and conclusions are drawn from a sensitivity analysis.
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Citation
Networks and Spatial Economics 18 (2018), 999-1017
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