IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v257y2025ics0165176525005476.html

Bertrand competition and captive customers

Author

Listed:
  • Myatt, David P.
  • Ronayne, David

Abstract

We study a Bertrand oligopoly with asymmetric costs in which each seller has some “captive” buyers. In the limit as captive buyers vanish, the lowest-cost firm sells to all buyers at a price equal to the second-lowest marginal cost. However, the closest competing price arises from non-degenerate mixed strategies, firms play exclusively undominated strategies, and with positive probability all but one firm sets the monopoly price.

Suggested Citation

  • Myatt, David P. & Ronayne, David, 2025. "Bertrand competition and captive customers," Economics Letters, Elsevier, vol. 257(C).
    • Handle: RePEc:eee:ecolet:v:257:y:2025:i:c:s0165176525005476
    DOI: 10.1016/j.econlet.2025.112710
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176525005476
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2025.112710?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Blume, Andreas, 2003. "Bertrand without fudge," Economics Letters, Elsevier, vol. 78(2), pages 167-168, February.
    2. Kartik, Navin, 2011. "A note on undominated Bertrand equilibria," Economics Letters, Elsevier, vol. 111(2), pages 125-126, May.
    3. Romain de Nijs, 2012. "Further results on the Bertrand game with different marginal costs," PSE-Ecole d'économie de Paris (Postprint) halshs-00916558, HAL.
    4. Mark Armstrong & John Vickers, 2022. "Patterns of Competitive Interaction," Econometrica, Econometric Society, vol. 90(1), pages 153-191, January.
    5. Garrod, Luke & Li, Ruochen & Wilson, Chris M., 2023. "Automated switching services," Economics Letters, Elsevier, vol. 232(C).
    6. Narasimhan, Chakravarthi, 1988. "Competitive Promotional Strategies," The Journal of Business, University of Chicago Press, vol. 61(4), pages 427-449, October.
    7. Sandro Shelegia & Chris M. Wilson, 2021. "A Generalized Model of Advertised Sales," American Economic Journal: Microeconomics, American Economic Association, vol. 13(1), pages 195-223, February.
    8. Baye, Michael R. & Kovenock, Dan & de Vries, Casper G., 1992. "It takes two to tango: Equilibria in a model of sales," Games and Economic Behavior, Elsevier, vol. 4(4), pages 493-510, October.
    9. De Nijs, Romain, 2012. "Further results on the Bertrand game with different marginal costs," Economics Letters, Elsevier, vol. 116(3), pages 502-503.
    10. repec:hal:pseose:halshs-00916558 is not listed on IDEAS
    11. Michael R. Baye & John Morgan, 2001. "Information Gatekeepers on the Internet and the Competitiveness of Homogeneous Product Markets," American Economic Review, American Economic Association, vol. 91(3), pages 454-474, June.
    12. Romain de Nijs, 2012. "Further results on the Bertrand game with different marginal costs," Post-Print halshs-00916558, HAL.
    13. Harrington, Joseph Jr., 1989. "A re-evaluation of perfect competition as the solution to the Bertrand price game," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 315-328, June.
    14. David Ronayne, 2021. "Price Comparison Websites," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(3), pages 1081-1110, 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. Joao Montez & Nicolas Schutz, 2021. "All-Pay Oligopolies: Price Competition with Unobservable Inventory Choices [Extremal Equilibria of Oligopolistic Supergames]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(5), pages 2407-2438.
    2. Johannes Johnen & David Ronayne, 2021. "The only Dance in Town: Unique Equilibrium in a Generalized Model of Price Competition," Journal of Industrial Economics, Wiley Blackwell, vol. 69(3), pages 595-614, September.
    3. Garella, Paolo G. & Laussel, Didier & Resende, Joana, 2021. "Behavior based price personalization under vertical product differentiation," International Journal of Industrial Organization, Elsevier, vol. 76(C).
    4. David P. Myatt, 2019. "A Theory of Stable Price Dispersion," Economics Series Working Papers 873, University of Oxford, Department of Economics.
    5. Mark Armstrong & John Vickers, 2018. "Patterns of Competition with Captive Customers," Economics Series Working Papers 864, University of Oxford, Department of Economics.
    6. David Ronayne & Greg Taylor, 2022. "Competing Sales Channels with Captive Consumers," The Economic Journal, Royal Economic Society, vol. 132(642), pages 741-766.
    7. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2021. "Search, Information, and Prices," Journal of Political Economy, University of Chicago Press, vol. 129(8), pages 2275-2319.
    8. Wilson, Chris M., 2010. "Ordered search and equilibrium obfuscation," International Journal of Industrial Organization, Elsevier, vol. 28(5), pages 496-506, September.
    9. Anderson, Simon & Baik, Alicia & Larson, Nathan, 2015. "Personalized pricing and advertising: An asymmetric equilibrium analysis," Games and Economic Behavior, Elsevier, vol. 92(C), pages 53-73.
    10. Chioveanu, Ioana, 2008. "Advertising, brand loyalty and pricing," Games and Economic Behavior, Elsevier, vol. 64(1), pages 68-80, September.
    11. Greg Taylor, 2020. "Competing Sales Channels," Economics Series Working Papers 843, University of Oxford, Department of Economics.
    12. Armstrong, Mark & John, Vickers, 2023. "Multibrand price dispersion," MPRA Paper 119322, University Library of Munich, Germany.
    13. Sandro Shelegia & Chris M. Wilson, 2021. "A Generalized Model of Advertised Sales," American Economic Journal: Microeconomics, American Economic Association, vol. 13(1), pages 195-223, February.
    14. Shelegia, Sandro & Wilson, Christopher, 2022. "Costly Participation and Default Allocations in All-Pay Contests," CEPR Discussion Papers 17611, Centre for Economic Policy Research.
    15. Florian Morath & Johannes Münster, 2018. "Online Shopping and Platform Design with Ex Ante Registration Requirements," Management Science, INFORMS, vol. 64(1), pages 360-380, January.
    16. Chris M. Wilson & Sandro Shelegia, 2016. "A Generalized Model of Sales," Working Papers 934, Barcelona School of Economics.
    17. Il-Horn Hann & Kai-Lung Hui & Sang-Yong Tom Lee & Ivan P.L. Png, 2005. "Sales and Promotions: A More General Model," Industrial Organization 0508014, University Library of Munich, Germany.
    18. David P. Myatt & David Ronayne, 2026. "Asymmetric Models of Sales," American Economic Journal: Microeconomics, American Economic Association, vol. 18(1), pages 281-311, February.
    19. Sinitsyn, Maxim, 2009. "Price dispersion in duopolies with heterogeneous consumers," International Journal of Industrial Organization, Elsevier, vol. 27(2), pages 197-205, March.
    20. Michael R. Baye & John Morgan & Patrick Scholten, 2004. "Temporal Price Dispersion: Evidence from an Online Consumer Electronics Market," Working Papers 2004-04, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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:eee:ecolet:v:257:y:2025:i:c:s0165176525005476. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ecolet .

    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.