Networks and Spatial Economics

, Volume 18, Issue 4, pp 999–1017 | Cite as

Computation of Multi-facility Location Nash Equilibria on a Network Under Quantity Competition

  • Blas PelegrínEmail author
  • Pascual Fernández
  • María Dolores García


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.


Multi-facility location Nash equilibria Network optimization Spatial Cournot competition 



This research has been supported by the Ministry of Economy and Competitiveness of Spain under the research project MTM2015-70260-P, and the Fundación Séneca (The Agency of Science and Technology of the Region of Murcia) under the research project 19241/PI/14.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Blas Pelegrín
    • 1
    Email author
  • Pascual Fernández
    • 1
  • María Dolores García
    • 2
  1. 1.Department Statistics and Operatinal ResearchUniversity of MurciaMurciaSpain
  2. 2.Department of Business Administration, Law, and Social SciencesSan Antonio Catholic University of MurciaMurciaSpain

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