IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v39y1991i5p749-756.html
   My bibliography  Save this article

Market and Locational Equilibrium for Two Competitors

Author

Listed:
  • Martine Labbé

    (Erasmus Universiteit, Rotterdam, The Netherlands)

  • S. Louis Hakimi

    (University of California, Davis, California)

Abstract

We consider a two-stage location and allocation game involving two competing firms. The firms first select the location of their facility on a network. Then the firms optimally select the quantities each wishes to supply to the markets, which are located at the vertices of the network. The criterion for optimality for each firm is maximizing its profit, which is the total revenue minus the production and transportation costs. Under reasonable assumptions regarding the revenue, the production cost and the transportation cost functions, we show that there is a Nash equilibrium for the quantities offered at the markets by each firm. Furthermore, if the quantities supplied (at the equilibrium) by each firm at each market are positive, then there is also a Nash locational equilibrium, i.e., no firm finds it advantageous to change its location.

Suggested Citation

  • Martine Labbé & S. Louis Hakimi, 1991. "Market and Locational Equilibrium for Two Competitors," Operations Research, INFORMS, vol. 39(5), pages 749-756, October.
    • Handle: RePEc:inm:oropre:v:39:y:1991:i:5:p:749-756
    DOI: 10.1287/opre.39.5.749
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.39.5.749
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.39.5.749?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Drezner, Zvi & Wesolowsky, George O., 1996. "Location-allocation on a line with demand-dependent costs," European Journal of Operational Research, Elsevier, vol. 90(3), pages 444-450, May.
    2. Drezner, Zvi & Eiselt, H.A., 2024. "Competitive location models: A review," European Journal of Operational Research, Elsevier, vol. 316(1), pages 5-18.
    3. Blas Pelegrín & Pascual Fernández & María Dolores García, 2018. "Computation of Multi-facility Location Nash Equilibria on a Network Under Quantity Competition," Networks and Spatial Economics, Springer, vol. 18(4), pages 999-1017, December.
    4. Abdullah Dasci & Gilbert Laporte, 2005. "A Continuous Model for Multistore Competitive Location," Operations Research, INFORMS, vol. 53(2), pages 263-280, April.
    5. Diego Ruiz-Hernández & Javier Elizalde & David Delgado-Gómez, 2017. "Cournot–Stackelberg games in competitive delocation," Annals of Operations Research, Springer, vol. 256(1), pages 149-170, September.
    6. Marianov, Vladimir & Rí­os, Miguel & Icaza, Manuel José, 2008. "Facility location for market capture when users rank facilities by shorter travel and waiting times," European Journal of Operational Research, Elsevier, vol. 191(1), pages 32-44, November.
    7. Godinho, Pedro & Dias, Joana, 2010. "A two-player competitive discrete location model with simultaneous decisions," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1419-1432, December.
    8. Mayadunne, Sanjaya & Johar, Monica & Saydam, Cem, 2018. "Competitive store closing during an economic downturn," International Journal of Production Economics, Elsevier, vol. 199(C), pages 162-178.
    9. Konur, Dinçer & Geunes, Joseph, 2012. "Competitive multi-facility location games with non-identical firms and convex traffic congestion costs," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 373-385.
    10. Küçükaydin, Hande & Aras, Necati & Kuban AltInel, I., 2011. "Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution," European Journal of Operational Research, Elsevier, vol. 208(3), pages 206-220, February.
    11. 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.
    12. Buechel, Berno & Roehl, Nils, 2015. "Robust equilibria in location games," European Journal of Operational Research, Elsevier, vol. 240(2), pages 505-517.
    13. Rhim, Hosun & Ho, Teck H. & Karmarkar, Uday S., 2003. "Competitive location, production, and market selection," European Journal of Operational Research, Elsevier, vol. 149(1), pages 211-228, August.
    14. Blas Pelegrín & Pascual Fernández & María Dolores García, 2023. "On the Existence and Computation of Nash Equilibrium in Network Competitive Location Under Delivered Pricing and Price Sensitive Demand," Networks and Spatial Economics, Springer, vol. 23(4), pages 825-843, December.
    15. Iida, Tetsuya & Matsubayashi, Nobuo, 2011. "Strategic multi-store opening under financial constraint," European Journal of Operational Research, Elsevier, vol. 210(2), pages 379-389, April.
    16. Teodora Dan & Patrice Marcotte, 2019. "Competitive Facility Location with Selfish Users and Queues," Operations Research, INFORMS, vol. 67(2), pages 479-497, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:39:y:1991:i:5:p:749-756. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.