IDEAS home Printed from
   My bibliography  Save this paper

Symmetric and Asymmetric Equilibria in a Spatial Duopoly


  • Marcella Scrimitore



We describe a spatial duopoly in a Hotelling model with quadratic transportation costs where consumers are distributed according to a symmetric density whose degree of concentration is variable. By solving the two-stage game in prices and locations as a function of the concentration index, we analyse the effects on the firms’optimal choices in a unbounded strategy space of an increasing agglomeration of consumers in the middle. Traditional horizontal differentiation-locational models assume that consumers are uniformly distributed over the characteristics space. With a few exceptions, the situations in which the consumers' preferences are concentrated on a subsection of the available varieties have been neglected. This issue was successfully addressed by Tabuchi and Thisse (1995), who explicitly solved the price-location problem for two firms in the presence of a symmetric triangular consumers’ distribution. They showed that in this case any symmetric location cannot be an equilibrium, due to a discontinuity of the reactions functions generated by the non-differentiability of the consumers’ density at its modal value; rather, their model exhibits two subgame perfect asymmetric equilibria characterised by strong product differentiation. In this paper, we assume that consumers are distributed according to a trapezoid distribution. This allows a simple parametrization of the degree of consumers' concentration, which includes the uniform and the triangular distribution as limit cases, and makes possible to solve the price-location problem as a function of the concentration index. Therefore we are able to find a more general explicit solution which covers those previously discussed in the literature. The basic results of the paper are the following. A symmetric equilibrium exists for all values of the concentration parameter, provided that the density is differentiable at the centre of its support. A higher degree of the consumers’ concentration around the middle induces firms to move inwards, in order to locate closer to the growing share of consumers: competition in the highly populated central area of the market reduces differentiation and strengthens price competition. The overall equilibrium shows clearly that the demand effect outweighs the strategic effect. However the symmetric equilibrium may be not unique. When concentration becomes sufficiently high, two asymmetric specular equilibria coexist with the symmetric one. They arise for a degree of concentration lower than that implied by a triangular distribution, with price-location choices collapsing in the limit to those identified by Tabuchi and Thisse. At these equilibria one firm locates in the central area of the market, while the other locates outside the market space. These results are consistent with the idea that a higher concentration of consumers around the centre induces firms to reduce the optimal product differentiation and offer theoretical support to the intuition that homogeneity of consumers might have important implications in terms of reducing the firms' market power. However, our findings suggest that in models of spatial competition realistic representations of the demand side may generate a ‘strange’ interplay between the strategic effect and the demand effect which may cause a failure of the uniqueness property and weakens the economic interpretation of equilibria.

Suggested Citation

  • Marcella Scrimitore, 2003. "Symmetric and Asymmetric Equilibria in a Spatial Duopoly," ERSA conference papers ersa03p194, European Regional Science Association.
  • Handle: RePEc:wiw:wiwrsa:ersa03p194

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. repec:kap:jeczfn:v:82:y:2003:i:4:p:555-568 is not listed on IDEAS
    2. 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.
    3. Caplin, Andrew S & Nalebuff, Barry J, 1986. "Multi-dimensional Product Differentiation and Price Competition," Oxford Economic Papers, Oxford University Press, vol. 38(0), pages 129-145, Suppl. No.
    4. Tabuchi, Takatoshi & Thisse, Jacques-Francois, 1995. "Asymmetric equilibria in spatial competition," International Journal of Industrial Organization, Elsevier, vol. 13(2), pages 213-227.
    5. Economides, Nicholas, 1986. "Minimal and maximal product differentiation in Hotelling's duopoly," Economics Letters, Elsevier, vol. 21(1), pages 67-71.
    6. Beath,John & Katsoulacos,Yannis, 1991. "The Economic Theory of Product Differentiation," Cambridge Books, Cambridge University Press, number 9780521335263, October.
    7. Alessandra Chirco & Luca Lambertini & Fabio Zagonari, 2003. "How demand affects optimal prices and product differentiation," Economics of Governance, Springer, vol. 82(4), pages 555-568, November.
    8. Neven, D. & Thisse, J-F., 1989. "On Quality And Variety Competition," CORE Discussion Papers 1989020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Tabuchi, Takatoshi, 1994. "Two-stage two-dimensional spatial competition between two firms," Regional Science and Urban Economics, Elsevier, vol. 24(2), pages 207-227, April.
    10. Corrado Benassi & Alessandra Chirco & Marcella Scrimitore, 2002. "Income concentration and market demand," Oxford Economic Papers, Oxford University Press, vol. 54(4), pages 584-596, October.
    11. Hinloopen, Jeroen & van Marrewijk, Charles, 1999. "On the limits and possibilities of the principle of minimum differentiation1," International Journal of Industrial Organization, Elsevier, vol. 17(5), pages 735-750, July.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Michal Król, 2009. "The role of demand uncertainty in the two stage Hotelling model," The School of Economics Discussion Paper Series 0904, Economics, The University of Manchester.
    2. Torrisi, Gianpiero, 2008. "The model of the linear city under a triangular distribution of consumers: an empirical analysis on price and location of beverage kiosks in Catania," MPRA Paper 12694, University Library of Munich, Germany.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wiw:wiwrsa:ersa03p194. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Gunther Maier). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.