IDEAS home Printed from https://ideas.repec.org/p/mcm/deptwp/1985-02.html
   My bibliography  Save this paper

Equilibrium in Hotelling's Model of Spatial Competition

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://socserv.socsci.mcmaster.ca/econ/rsrch/papers/archive/85-19.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. Gal-or, Esther, 1982. "Hotelling's spatial competition as a model of sales," Economics Letters, Elsevier, vol. 9(1), pages 1-6.
    5. Varian, Hal R, 1981. "A Model of Sales: Errata," American Economic Review, American Economic Association, vol. 71(3), pages 517-517, June.
    6. 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.
    7. 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.
    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. Sinitsyn, Maxim, 2008. "Characterization of the support of the mixed strategy price equilibria in oligopolies with heterogeneous consumers," Economics Letters, Elsevier, vol. 99(2), pages 242-245, May.
    2. Dimitrios Xefteris & Iván Barreda‐Tarrazona & Aurora García‐Gallego & Nikolaos Georgantzís, 2023. "Catalog competition: Theory and experimental evidence," Economic Inquiry, Western Economic Association International, vol. 61(1), pages 122-137, January.
    3. Sinitsyn, Maxim, 2009. "Price dispersion in duopolies with heterogeneous consumers," International Journal of Industrial Organization, Elsevier, vol. 27(2), pages 197-205, March.
    4. Paul Heidhues & Botond Köszegi, 2004. "The Impact of Consumer Loss Aversion on Pricing," CIG Working Papers SP II 2004-17, Wissenschaftszentrum Berlin (WZB), Research Unit: Competition and Innovation (CIG).
    5. Kuninori Nakagawa, 2023. "Horizontal product differentiation in Varian’s model of sales," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(2), pages 607-627, June.
    6. Wilfred Amaldoss & Sanjay Jain, 2002. "David vs. Goliath: An Analysis of Asymmetric Mixed-Strategy Games and Experimental Evidence," Management Science, INFORMS, vol. 48(8), pages 972-991, August.
    7. Marceau, Nicolas & Mongrain, Steeve, 2011. "Competition in law enforcement and capital allocation," Journal of Urban Economics, Elsevier, vol. 69(1), pages 136-147, January.
    8. Jianqiang Zhang & Weijun Zhong & Shue Mei, 2012. "Competitive effects of informative advertising in distribution channels," Marketing Letters, Springer, vol. 23(3), pages 561-584, September.
    9. Raymond J. Deneckere & Dan Kovenock, 1988. "Capacity-Constrained Price Competition When Unit Costs Differ," Discussion Papers 861, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Anindya Ghose & Tridas Mukhopadhyay & Uday Rajan, 2007. "The Impact of Internet Referral Services on a Supply Chain," Information Systems Research, INFORMS, vol. 18(3), pages 300-319, September.
    11. Li, Chenguang & Sexton, Richard J., 2009. "Impacts of Retailers’ Pricing Strategies for Produce Commodities on Farmer Welfare," 2009 Conference, August 16-22, 2009, Beijing, China 51720, International Association of Agricultural Economists.
    12. Oliver Hinz & Jochen Eckert, 2010. "The Impact of Search and Recommendation Systems on Sales in Electronic Commerce," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 2(2), pages 67-77, April.
    13. De los Santos, Babur & Kim, In Kyung & Lubensky, Dmitry, 2018. "Do MSRPs decrease prices?," International Journal of Industrial Organization, Elsevier, vol. 59(C), pages 429-457.
      • Babur De los Santos & In Kyung Kim & Dmitry Lubensky, 2013. "Do MSRPs Decrease Prices?," Working Papers 2013-13, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.
    14. Edgardo Arturo Ayala Gaytán, 2009. "Social network externalities and price dispersion in online markets," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(2), pages 1-28, November.
    15. Karle, Heiko & Schumacher, Heiner & Vølund, Rune, 2023. "Consumer loss aversion and scale-dependent psychological switching costs," Games and Economic Behavior, Elsevier, vol. 138(C), pages 214-237.
    16. Etienne Gagnon & David López-Salido & Nicolas Vincent, 2013. "Individual Price Adjustment along the Extensive Margin," NBER Macroeconomics Annual, University of Chicago Press, vol. 27(1), pages 235-281.
    17. Andrew Rhodes & Jidong Zhou, 2019. "Consumer Search and Retail Market Structure," Management Science, INFORMS, vol. 67(6), pages 2607-2623, June.
    18. Benaïm, Michel & Hofbauer, Josef & Hopkins, Ed, 2009. "Learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1694-1709, July.
    19. Pedro M. Gardete & Liang Guo, 2021. "Prepurchase Information Acquisition and Credible Advertising," Management Science, INFORMS, vol. 67(3), pages 1696-1717, March.
    20. Blázquez de Paz, Mario, 2018. "Electricity auctions in the presence of transmission constraints and transmission costs," Energy Economics, Elsevier, vol. 74(C), pages 605-627.

    More about this item

    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:mcm:deptwp:1985-02. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/demcmca.html .

    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.