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The Existence of Equilibria in the 3-Facility Hotelling Model in a Tree

Author

Listed:
  • H. A. Eiselt

    (University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3)

  • Gilbert Laporte

    (École des Hautes Études Commerciales, Montreal, Canada H3T 1V6)

Abstract

This paper considers the location of three market share maximizing facilities on a tree network. Assume that the demand originates at the vertices of the tree and that the facilities can locate at the vertices or on the edges of the tree. It is shown that the problem may have agglomerated, dispersed, or have no equilibria at all. Conditions for these cases are developed in the paper.

Suggested Citation

  • H. A. Eiselt & Gilbert Laporte, 1993. "The Existence of Equilibria in the 3-Facility Hotelling Model in a Tree," Transportation Science, INFORMS, vol. 27(1), pages 39-43, February.
    • Handle: RePEc:inm:ortrsc:v:27:y:1993:i:1:p:39-43
    DOI: 10.1287/trsc.27.1.39
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    Cited by:

    1. Drezner, Zvi & Eiselt, H.A., 2024. "Competitive location models: A review," European Journal of Operational Research, Elsevier, vol. 316(1), pages 5-18.
    2. Gaëtan Fournier & Marco Scarsini, 2019. "Location Games on Networks: Existence and Efficiency of Equilibria," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 212-235, February.
    3. Berno Buechel, 2014. "Condorcet winners on median spaces," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 735-750, March.
    4. Buechel, Berno & Roehl, Nils, 2015. "Robust equilibria in location games," European Journal of Operational Research, Elsevier, vol. 240(2), pages 505-517.
    5. Gaëtan Fournier & Marco Scarsini, 2014. "Hotelling Games on Networks: Efficiency of Equilibria," Post-Print halshs-00983085, HAL.
    6. Rahul Swamy & Timothy Murray, 0. "Computing equilibrium in network utility-sharing and discrete election games," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-29.
    7. Rahul Swamy & Timothy Murray, 2022. "Computing equilibrium in network utility-sharing and discrete election games," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 2056-2084, October.
    8. Mercedes Pelegrín & Blas Pelegrín, 2017. "Nash equilibria in location games on a network," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(3), pages 775-791, July.
    9. Daniel Serra & Charles Revelle, 1994. "Competitive location in discrete space," Economics Working Papers 96, Department of Economics and Business, Universitat Pompeu Fabra.

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