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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
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    Citations

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    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. 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.
    3. Drezner, Zvi & Eiselt, H.A., 2024. "Competitive location models: A review," European Journal of Operational Research, Elsevier, vol. 316(1), pages 5-18.
    4. 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.
    5. Abdullah Dasci & Gilbert Laporte, 2005. "A Continuous Model for Multistore Competitive Location," Operations Research, INFORMS, vol. 53(2), pages 263-280, April.
    6. 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.
    7. 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.
    8. Buechel, Berno & Roehl, Nils, 2015. "Robust equilibria in location games," European Journal of Operational Research, Elsevier, vol. 240(2), pages 505-517.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Teodora Dan & Patrice Marcotte, 2019. "Competitive Facility Location with Selfish Users and Queues," Operations Research, INFORMS, vol. 67(2), pages 479-497, March.
    16. 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.

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