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Market And Locational Equilibrium For Two Competitors

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  • Labbe, Martine
  • Hakimi, S. Louis

Abstract

We consider the following 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

  • Labbe, Martine & Hakimi, S. Louis, 1989. "Market And Locational Equilibrium For Two Competitors," Econometric Institute Archives 272383, Erasmus University Rotterdam.
    • Handle: RePEc:ags:eureia:272383
    DOI: 10.22004/ag.econ.272383
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    References listed on IDEAS

    as
    1. Hakimi, S. Louis, 1983. "On locating new facilities in a competitive environment," European Journal of Operational Research, Elsevier, vol. 12(1), pages 29-35, January.
    2. Pierre Hansen & Martine Labbé, 1988. "Algorithms for Voting and Competitive Location on a Network," Transportation Science, INFORMS, vol. 22(4), pages 278-288, November.
    3. Wendell, R. E. & McKelvey, R. D., 1981. "New perspectives in competitive location theory," European Journal of Operational Research, Elsevier, vol. 6(2), pages 174-182, February.
    4. Patrick T. Harker, 1986. "Alternative Models of Spatial Competition," Operations Research, INFORMS, vol. 34(3), pages 410-425, June.
    5. Gregory Dobson & Uday S. Karmarkar, 1987. "Competitive Location on a Network," Operations Research, INFORMS, vol. 35(4), pages 565-574, August.
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    Keywords

    Agricultural and Food Policy; Marketing;

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