IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2001.11422.html
   My bibliography  Save this paper

Spatial competition with unit-demand functions

Author

Listed:
  • Gaetan Fournier
  • Karine Van Der Straeten
  • Jorgen Weibull

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

  • Gaetan Fournier & Karine Van Der Straeten & Jorgen Weibull, 2020. "Spatial competition with unit-demand functions," Papers 2001.11422, arXiv.org.
    • Handle: RePEc:arx:papers:2001.11422
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2001.11422
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, April.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. A. Smithies, 1941. "Optimum Location in Spatial Competition," Journal of Political Economy, University of Chicago Press, vol. 49(3), pages 423-423.
    11. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Buechel, Berno & Roehl, Nils, 2015. "Robust equilibria in location games," European Journal of Operational Research, Elsevier, vol. 240(2), pages 505-517.
    2. Zsolt Katona, 2015. "Democracy in product design: Consumer participation and differentiation strategies," Quantitative Marketing and Economics (QME), Springer, vol. 13(4), pages 359-394, December.
    3. Zsolt Katona, 2015. "Democracy in product design: Consumer participation and differentiation strategies," Quantitative Marketing and Economics (QME), Springer, vol. 13(4), pages 359-394, December.
    4. Matteo Bassi & Marco Pagnozzi & Salvatore Piccolo, 2015. "Product Differentiation by Competing Vertical Hierarchies," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 24(4), pages 904-933, October.
    5. G. Bertuzzi & L. Lambertini, 2001. "Advertising in a Differential Game of Spatial Competition," Working Papers 400, Dipartimento Scienze Economiche, Universita' di Bologna.
    6. Aurélie Bonein & Stéphane Turolla, 2023. "Spatial competition with demand uncertainty: A laboratory experiment," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 32(4), pages 906-939, October.
    7. Webers, H.M., 1996. "The Location Model with Reservation Prices," Other publications TiSEM f2c29198-01e5-4c50-8c27-b, Tilburg University, School of Economics and Management.
    8. Drezner, Zvi & Eiselt, H.A., 2024. "Competitive location models: A review," European Journal of Operational Research, Elsevier, vol. 316(1), pages 5-18.
    9. Bertrand Ottino-Loffler & Forrest Stonedahl & Vipin Veetil & Uri Wilensky, 2017. "Spatial Competition with Interacting Agents," International Journal of Microsimulation, International Microsimulation Association, vol. 10(3), pages 75-91.
    10. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107687899.
    11. Buechel, Berno & Klein, Jan, 2014. "Do Consumers' Preferences Really Matter? - A Note on Spatial Competition with Restricted Strategies," MPRA Paper 55288, University Library of Munich, Germany.
    12. Thomas Grandner, 2010. "A Note On Product Differentiation In A Linear City And Wage Bargaining," Bulletin of Economic Research, Wiley Blackwell, vol. 62(4), pages 407-416, October.
    13. Vermeulen, Ben & La Poutré, Han & de Kok, Ton, 2012. "Dynamics and equilibria under incremental horizontal differentiation on the Salop circle," MPRA Paper 51449, University Library of Munich, Germany.
    14. 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.
    15. Borenstein, Severin & Netz, Janet, 1999. "Why do all the flights leave at 8 am?: Competition and departure-time differentiation in airline markets," International Journal of Industrial Organization, Elsevier, vol. 17(5), pages 611-640, July.
    16. Gianmarco I P Ottaviano & Jacques-François Thisse, 2005. "New Economic Geography: What about the N?," Environment and Planning A, , vol. 37(10), pages 1707-1725, October.
    17. Fujita, Masahisa & Thisse, Jacques-François, 2009. "New Economic Geography: An appraisal on the occasion of Paul Krugman's 2008 Nobel Prize in Economic Sciences," Regional Science and Urban Economics, Elsevier, vol. 39(2), pages 109-119, March.
    18. Salvanes, Kjell G. & Steen, Frode & Sorgard, Lars, 2005. "Hotelling in the air? Flight departures in Norway," Regional Science and Urban Economics, Elsevier, vol. 35(2), pages 193-213, March.
    19. Mayer, Thierry, 2000. "Spatial Cournot competition and heterogeneous production costs across locations," Regional Science and Urban Economics, Elsevier, vol. 30(3), pages 325-352, May.
    20. Barigozzi, Francesca & Ma, Ching-to Albert, 2018. "Product differentiation with multiple qualities," International Journal of Industrial Organization, Elsevier, vol. 61(C), pages 380-412.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    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:arx:papers:2001.11422. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.