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Spatial competition with unit-demand functions

Author

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  • Fournier, Gaëtan
  • Van Der Straeten, Karine
  • Weibull, Jörgen W.

Abstract

This paper studies a spatial competition game between two firms that sell a homogeneous good at some pre-determined fixed price. A population of consumers is spread out over the real line, and the two firms simultaneously choose location in this same space. When buying from one of the firms, consumers incur the fixed price plus some transportation costs, which are increasing with their distance to the firm. Under the assumption that each consumer is ready to buy one unit of the good whatever the locations of the firms, firms converge to the median location: there is minimal differentiation. In this article, we relax this assumption and assume that there is an upper limit to the distance a consumer is ready to cover to buy the good. We show that the game always has at least one Nash equilibrium in pure strategy. Under this more general assumption, the "minimal differentiation" principle no longer holds in general. At equilibrium, firms choose "minimal", "intermediate" or "full" differentiation, depending on this critical distance a consumer is ready to cover and on the shape of the distribution of consumers' locations.

Suggested Citation

  • Fournier, Gaëtan & Van Der Straeten, Karine & Weibull, Jörgen W., 2020. "Spatial competition with unit-demand functions," TSE Working Papers 20-1072, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:124019
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    References listed on IDEAS

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    1. A. Smithies, 1941. "Optimum Location in Spatial Competition," Journal of Political Economy, University of Chicago Press, vol. 49(3), pages 423-423.
    2. de Palma, A, et al, 1985. "The Principle of Minimum Differentiation Holds under Sufficient Heterogeneity," Econometrica, Econometric Society, vol. 53(4), pages 767-781, July.
    3. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, December.
    4. Gaëtan Fournier, 2019. "General distribution of consumers in pure Hotelling games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 33-59, March.
    5. Dimitrios Xefteris & Didier Laussel & Michel Le Breton, 2017. "Simple centrifugal incentives in spatial competition," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 357-381, May.
    6. 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.
    7. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65(2), pages 135-135.
    8. d'Aspremont, C & Gabszewicz, Jean Jaskold & Thisse, J-F, 1979. "On Hotelling's "Stability in Competition"," Econometrica, Econometric Society, vol. 47(5), pages 1145-1150, September.
    9. Hinich, Melvin J. & Ordeshook, Peter C., 1970. "Plurality Maximization vs Vote Maximization: A Spatial Analysis with Variable Participation," American Political Science Review, Cambridge University Press, vol. 64(3), pages 772-791, September.
    10. Meagher, Kieron J. & Zauner, Klaus G., 2004. "Product differentiation and location decisions under demand uncertainty," Journal of Economic Theory, Elsevier, vol. 117(2), pages 201-216, August.
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