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All Stackelberg Location Equilibria in the Hotelling's Duopoly Model on a Tree with Parametric Prices

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  • María García Pérez
  • Blas Pelegrín

Abstract

The sequential Hotelling's duopoly model on a tree was studied by Eiselt (1992), who developed conditions for the existence of location equilibria when location decisions are nodes and prices are parametric. In this paper, this competition model is also analyzed, but considering that locations for the two firms can be any pair of points on the tree, nodes or points in the edges. First, a condition is given under which both the leader and the follower get a positive profit. In this setting, the problem of finding optimal locations for each of them is studied with different and equal prices. In both cases, the set of optimal locations for the follower is generated for any location of the leader as well as the set of optimal locations for the leader. As a consequence the entire set of Stackelberg solutions to this competition model is obtained. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • María García Pérez & Blas Pelegrín, 2003. "All Stackelberg Location Equilibria in the Hotelling's Duopoly Model on a Tree with Parametric Prices," Annals of Operations Research, Springer, vol. 122(1), pages 177-192, September.
    • Handle: RePEc:spr:annopr:v:122:y:2003:i:1:p:177-192:10.1023/a:1026150608051
    DOI: 10.1023/A:1026150608051
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    Cited by:

    1. Arbib, Claudio & Pınar, Mustafa Ç. & Tonelli, Matteo, 2020. "Competitive location and pricing on a line with metric transportation costs," European Journal of Operational Research, Elsevier, vol. 282(1), pages 188-200.

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