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Equilibrium in Hotelling's Model of Spatial Competition

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  • Martin J Osborne
  • Carolyn Pitchik

Abstract

Using a partly analytical, partly computational approach we find and study a mixed strategy equilibrium in Hotelling's model of spatial competition (in which each of two firms chooses a location in a line segment, and a price). In the equilibrium we find, the firms randomize only over prices. They choose locations close to the quartiles of the market. The support of the equilibrium price strategy of each firm is the union of two short iintervals, and has an atom of approximate size 0.73 at the highest price. The equilibrium can be interpreted as one in which firms charge a relatively high price most of the time, and occaisionally hold a "sale".

Suggested Citation

  • Martin J Osborne & Carolyn Pitchik, 1985. "Equilibrium in Hotelling's Model of Spatial Competition," Department of Economics Working Papers 1985-02, McMaster University.
  • Handle: RePEc:mcm:deptwp:1985-02
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    References listed on IDEAS

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    1. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-659, September.
    2. A. Smithies, 1941. "Optimum Location in Spatial Competition," Journal of Political Economy, University of Chicago Press, vol. 49(3), pages 423-423.
    3. A. P. Lerner & H. W. Singer, 1937. "Some Notes on Duopoly and Spatial Competition," Journal of Political Economy, University of Chicago Press, vol. 45(2), pages 145-145.
    4. Paul Milgrom & Robert Weber, 1981. "Distributional Strategies for Games with Incomplete Information," Discussion Papers 428R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Gal-or, Esther, 1982. "Hotelling's spatial competition as a model of sales," Economics Letters, Elsevier, vol. 9(1), pages 1-6.
    6. R. J. Aumann & Y. Katznelson & R. Radner & R. W. Rosenthal & B. Weiss, 1983. "Approximate Purification of Mixed Strategies," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 327-341, August.
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