IDEAS home Printed from https://ideas.repec.org/p/hal/cesptp/hal-00641873.html
   My bibliography  Save this paper

Product flexibility and price competition in Hotelling's duopoly

Author

Listed:
  • Pierre Fleckinger

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Thierry Lafay

    (PRISM Sorbonne - Pôle de recherche interdisciplinaire en sciences du management - UP1 - Université Paris 1 Panthéon-Sorbonne)

Abstract

In a Hotelling's duopoly with a general transportation cost function, we study competition through catalog: each firm chooses at the same time a price and a location. With simultaneous catalog offers, there is no equilibrium in pure strategies for high valuations of the consumers, while a Stackelberg equilibrium exists under mild conditions. The follower is better off than the leader, whose price is smaller: the location preemption effect is weaker than the price leadership effect. We obtain closed-form solutions for the linear and quadratic cost cases. Using these results, we discuss the nature of competition depending on the relative flexibility of products and prices.

Suggested Citation

  • Pierre Fleckinger & Thierry Lafay, 2010. "Product flexibility and price competition in Hotelling's duopoly," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00641873, HAL.
    • Handle: RePEc:hal:cesptp:hal-00641873
    Note: View the original document on HAL open archive server: https://hal.science/hal-00641873v1
    as

    Download full text from publisher

    File URL: https://hal.science/hal-00641873v1/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fudenberg, Drew & Tirole, Jean, 1984. "The Fat-Cat Effect, the Puppy-Dog Ploy, and the Lean and Hungry Look," American Economic Review, American Economic Association, vol. 74(2), pages 361-366, May.
    2. Osborne, Martin J & Pitchik, Carolyn, 1987. "Equilibrium in Hotelling's Model of Spatial Competition," Econometrica, Econometric Society, vol. 55(4), pages 911-922, July.
    3. Judith R. Gelman & Steven C. Salop, 1983. "Judo Economics: Capacity Limitation and Coupon Competition," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 315-325, Autumn.
    4. Anil K Kashyap, 1995. "Sticky Prices: New Evidence from Retail Catalogs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(1), pages 245-274.
    5. Anderson, Simon, 1987. "Spatial competition and price leadership," International Journal of Industrial Organization, Elsevier, vol. 5(4), pages 369-398.
    6. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
    7. Edward C. Prescott & Michael Visscher, 1977. "Sequential Location among Firms with Foresight," Bell Journal of Economics, The RAND Corporation, vol. 8(2), pages 378-393, Autumn.
    8. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    9. Emi Nakamura & Jón Steinsson, 2008. "Five Facts about Prices: A Reevaluation of Menu Cost Models," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(4), pages 1415-1464.
    10. Neven, Damien J., 1987. "Endogenous sequential entry in a spatial model," International Journal of Industrial Organization, Elsevier, vol. 5(4), pages 419-434.
    11. Lambertini, Luca, 2002. "Equilibrium locations in a spatial model with sequential entry in real time," Regional Science and Urban Economics, Elsevier, vol. 32(1), pages 47-58, January.
    12. Economides, Nicholas, 1984. "The principle of minimum differentiation revisited," European Economic Review, Elsevier, vol. 24(3), pages 345-368, April.
    13. Tabuchi, Takatoshi & Thisse, Jacques-Francois, 1995. "Asymmetric equilibria in spatial competition," International Journal of Industrial Organization, Elsevier, vol. 13(2), pages 213-227.
    14. Gal-Or, Esther, 1985. "First Mover and Second Mover Advantages," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 649-653, October.
    15. Lambertini, Luca, 1997. "Unicity of the equilibrium in the unconstrained Hotelling model," Regional Science and Urban Economics, Elsevier, vol. 27(6), pages 785-798, November.
    16. Paulo Monteiro & Frank Page, 2008. "Catalog competition and Nash equilibrium in nonlinear pricing games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(3), pages 503-524, March.
    17. MacLeod, W. Bentley, 1985. "On the non-existence of equilibria in differentiated product models," Regional Science and Urban Economics, Elsevier, vol. 15(2), pages 245-262, June.
    18. Pierre Fleckinger & Thierry Lafay, 2003. "Horizontal differentiation and price competition with sequential entry," Working Papers hal-00243021, HAL.
    19. Nicholas Economides & Jamie Howell & Sergio Meza, 2002. "Does it Pay to be First? Sequential Locational Choice and Foreclosure," Working Papers 02-19, New York University, Leonard N. Stern School of Business, Department of Economics.
    20. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
    21. Novshek, William, 1980. "Equilibrium in simple spatial (or differentiated product) models," Journal of Economic Theory, Elsevier, vol. 22(2), pages 313-326, April.
    22. Gotz, Georg, 2005. "Endogenous sequential entry in a spatial model revisited," International Journal of Industrial Organization, Elsevier, vol. 23(3-4), pages 249-261, April.
    23. 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

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


    Cited by:

    1. Javier Elizalde & Markus Kinateder & Ignacio Rodríguez-Carreño, 2015. "Entry regulation, firm’s behaviour and social welfare," European Journal of Law and Economics, Springer, vol. 40(1), pages 13-31, August.
    2. Han, Haipeng & Lien, Donald & Lien, Jaimie W. & Zheng, Jie, 2022. "Online or face-to-face? Competition among MOOC and regular education providers," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 857-881.
    3. Dimitrios Xefteris & Iván Barreda-Tarrazona & Aurora García-Gallego & Nikolaos Georgantzis, 2018. "Catalog Competition: Equilibrium Characterization and experimental evidence," Working Papers 2018/08, Economics Department, Universitat Jaume I, Castellón (Spain).
    4. Kress, Dominik & Pesch, Erwin, 2012. "Sequential competitive location on networks," European Journal of Operational Research, Elsevier, vol. 217(3), pages 483-499.
    5. Javier Elizalde & Markus Kinateder & Ignacio Rodríguez-Carreño, 2014. "Entry Regulation in a Linear Market with Elastic Demand," Faculty Working Papers 02/14, School of Economics and Business Administration, University of Navarra.
    6. Sun, Shuzhen & Liu, Tieming, 2023. "Pricing and sales-effort coordination facing free riding behaviors between a brick-and-mortar retailer and a platform store owned by the manufacturer," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 179(C).
    7. 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.
    8. Scott M. Gilpatric & Youping Li, 2021. "Endogenous Price Leadership and Product Positioning," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 58(2), pages 287-302, March.
    9. Guo, Wen-Chung & Lai, Fu-Chuan & Zeng, Dao-Zhi, 2015. "A Hotelling model with production," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 40-49.

    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. Fleckinger, Pierre & Lafay, Thierry, 2010. "Product flexibility and price competition in Hotelling's duopoly," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 61-68, July.
    2. Pierre Fleckinger & Thierry Lafay, 2006. "Concurrence en catalogue dans le duopole d'Hotelling," Revue économique, Presses de Sciences-Po, vol. 57(3), pages 573-581.
    3. Javier Elizalde & Markus Kinateder & Ignacio Rodríguez-Carreño, 2015. "Entry regulation, firm’s behaviour and social welfare," European Journal of Law and Economics, Springer, vol. 40(1), pages 13-31, August.
    4. Javier Elizalde & Markus Kinateder & Ignacio Rodríguez-Carreño, 2014. "Entry Regulation in a Linear Market with Elastic Demand," Faculty Working Papers 02/14, School of Economics and Business Administration, University of Navarra.
    5. Pierre Fleckinger & Thierry Lafay, 2003. "Horizontal differentiation and price competition with sequential entry," Working Papers hal-00243021, HAL.
    6. Iskakov, M. & Iskakov, A., 2012. "Complete Solution of the Hotelling Problem: Equilibrium in Secure Strategies for the Price Subgame," Journal of the New Economic Association, New Economic Association, vol. 13(1), pages 10-33.
    7. Brito, Duarte & Pereira, Pedro, 2009. "Product differentiation when competing with the suppliers of bottleneck inputs," Regional Science and Urban Economics, Elsevier, vol. 39(1), pages 43-53, January.
    8. Torbenko, A., 2015. "Linear City Models: Overview and Typology," Journal of the New Economic Association, New Economic Association, vol. 25(1), pages 12-38.
    9. Lambertini, Luca, 2002. "Equilibrium locations in a spatial model with sequential entry in real time," Regional Science and Urban Economics, Elsevier, vol. 32(1), pages 47-58, January.
    10. Jean J. Gabszewicz & Jacques-François Thisse, 2000. "Microeconomic theories of imperfect competition," Cahiers d'Économie Politique, Programme National Persée, vol. 37(1), pages 47-99.
    11. Rhee, Byong-Duk, 2006. "First-mover disadvantages with idiosyncratic consumer tastes along unobservable characteristics," Regional Science and Urban Economics, Elsevier, vol. 36(1), pages 99-117, January.
    12. Dragone, Davide & Lambertini, Luca, 2020. "Equilibrium existence in the Hotelling model with convex production costs," Regional Science and Urban Economics, Elsevier, vol. 84(C).
    13. Ebina, Takeshi & Matsushima, Noriaki & Shimizu, Daisuke, 2015. "Product differentiation and entry timing in a continuous time spatial competition model," European Journal of Operational Research, Elsevier, vol. 247(3), pages 904-913.
    14. Ralph Braid, 2013. "The locations of firms on intersecting roadways," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 50(3), pages 791-808, June.
    15. 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.
    16. Scott M. Gilpatric & Youping Li, 2021. "Endogenous Price Leadership and Product Positioning," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 58(2), pages 287-302, March.
    17. Drezner, Zvi & Eiselt, H.A., 2024. "Competitive location models: A review," European Journal of Operational Research, Elsevier, vol. 316(1), pages 5-18.
    18. Kress, Dominik & Pesch, Erwin, 2012. "Sequential competitive location on networks," European Journal of Operational Research, Elsevier, vol. 217(3), pages 483-499.
    19. Kats, Amoz, 1995. "More on Hotelling's stability in competition," International Journal of Industrial Organization, Elsevier, vol. 13(1), pages 89-93, March.
    20. Ralph Braid, 2014. "The socially optimal and equilibrium locations of two stores or libraries with consumer search," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 53(1), pages 123-136, August.

    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:hal:cesptp:hal-00641873. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.