IDEAS home Printed from https://ideas.repec.org/a/spr/etbull/v9y2021i1d10.1007_s40505-020-00193-6.html
   My bibliography  Save this article

On the insufficiency of some conditions for minimal product differentiation

Author

Listed:
  • Kali P. Rath

    (University of Notre Dame)

  • Gongyun Zhao

    (National University of Singapore)

Abstract

The basic framework is Hotelling’s model of product choice with quadratic transportation cost. Duopolists choose locations in the initial period and compete in prices in subsequent infinite periods. The firms share profits on the profit possibility frontier. Friedman and Thisse (Rand J Econ 24:631–645, 1993) provides a set of sufficient conditions for a unique equilibrium and minimal product differentiation in this setting. This paper reexamines those conditions. In the presence of some mild continuity requirements, there is exactly one profit sharing rule which satisfies those conditions. Furthermore, given any discount factor(s), the corresponding profits cannot be the outcome of a subgame perfect Nash equilibrium at every pair of locations. This brings out an inconsistency in the conditions. A slight weakening of the conditions, to allow for a wider class of profit sharing rules, can result in multiple equilibria and minimal product differentiation need not obtain. Two examples demonstrate this. Thus, neither those conditions nor their weaker variants can be used to characterize a unique equilibrium.

Suggested Citation

  • Kali P. Rath & Gongyun Zhao, 2021. "On the insufficiency of some conditions for minimal product differentiation," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 53-65, April.
    • Handle: RePEc:spr:etbull:v:9:y:2021:i:1:d:10.1007_s40505-020-00193-6
    DOI: 10.1007/s40505-020-00193-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40505-020-00193-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s40505-020-00193-6?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Philip J. Reny, 2016. "Introduction to the symposium on discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 423-429, March.
    2. Jehiel, Philippe, 1992. "Product differentiation and price collusion," International Journal of Industrial Organization, Elsevier, vol. 10(4), pages 633-641, December.
    3. Matsumura, Toshihiro & Matsushima, Noriaki, 2011. "Collusion, agglomeration, and heterogeneity of firms," Games and Economic Behavior, Elsevier, vol. 72(1), pages 306-313, May.
    4. Crawford, Gregory S., 2012. "Endogenous product choice: A progress report," International Journal of Industrial Organization, Elsevier, vol. 30(3), pages 315-320.
    5. 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.
    6. 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.
    7. 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.
    8. Kali P. Rath, 1998. "Stationary and nonstationary strategies in Hotelling's model of spatial competition with repeated pricing decisions," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(4), pages 525-537.
    9. Crawford, Gregory S., 2012. "Endogenous Product Choice: A Progress Report," Economic Research Papers 270745, University of Warwick - Department of Economics.
    10. Rath, Kali P. & Zhao, Gongyun, 2003. "Nonminimal product differentiation as a bargaining outcome," Games and Economic Behavior, Elsevier, vol. 42(2), pages 267-280, February.
    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. Becchetti, Leonardo & Palestini, Arsen & Solferino, Nazaria & Elisabetta Tessitore, M., 2014. "The socially responsible choice in a duopolistic market: A dynamic model of “ethical product” differentiation," Economic Modelling, Elsevier, vol. 43(C), pages 114-123.
    2. Amit Pazgal & David Soberman & Raphael Thomadsen, 2016. "Maximal or Minimal Differentiation in a Hotelling Market? A Fresh Perspective," Customer Needs and Solutions, Springer;Institute for Sustainable Innovation and Growth (iSIG), vol. 3(1), pages 42-47, March.
    3. Heijnen, Pim & Soetevent, Adriaan R., 2018. "Price competition on graphs," Journal of Economic Behavior & Organization, Elsevier, vol. 146(C), pages 161-179.
    4. M. Ali Khan & Metin Uyanık, 2021. "Topological connectedness and behavioral assumptions on preferences: a two-way relationship," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 411-460, March.
    5. Dilek, Hande & Karaer, Özgen & Nadar, Emre, 2018. "Retail location competition under carbon penalty," European Journal of Operational Research, Elsevier, vol. 269(1), pages 146-158.
    6. Jen-Te Yao, 2019. "The impact of transportation asymmetry on the choice of a spatial price policy," Asia-Pacific Journal of Regional Science, Springer, vol. 3(3), pages 793-811, October.
    7. Bester, H. & de Palma, A. & Leininger, W. & Thomas, J.P., 1991. "The Missing Equilibria in Hotelling's Location Game," Discussion Paper 1991-63, Tilburg University, Center for Economic Research.
    8. Vincenzo Scalzo, 2013. "Essential equilibria of discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 27-44, September.
    9. Krol Michal, 2011. "On the Existence and Social Optimality of Equilibria in a Hotelling Game with Uncertain Demand and Linear-Quadratic Costs," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-22, March.
    10. Oriol Carbonell-Nicolau & Richard P. McLean, 2019. "Nash and Bayes–Nash equilibria in strategic-form games with intransitivities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 935-965, November.
    11. Iskakov, M., 2022. "Existence theorems for Nash equilibrium and equilibrium in secure strategies," Journal of the New Economic Association, New Economic Association, vol. 56(4), pages 12-27.
    12. D. Glycopantis, 2020. "Two-person Bargaining with Lexicographic Preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 13-23, April.
    13. 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.
    14. Iskakov, M. & Iskakov, A. & d'Aspremont, C., 2018. "Games for cautious players: The Equilibrium in Secure Strategies," Games and Economic Behavior, Elsevier, vol. 110(C), pages 58-70.
    15. Drezner, Zvi & Eiselt, H.A., 2024. "Competitive location models: A review," European Journal of Operational Research, Elsevier, vol. 316(1), pages 5-18.
    16. Sudipta Sarangi & Hrachya Kyureghian, 2001. "Transport Cost Sharing and Spatial Competition," Departmental Working Papers 2001-03, Department of Economics, Louisiana State University.
    17. Torbenko, A., 2015. "Linear City Models: Overview and Typology," Journal of the New Economic Association, New Economic Association, vol. 25(1), pages 12-38.
    18. Matsumura, Toshihiro & Matsushima, Noriaki, 2011. "Collusion, agglomeration, and heterogeneity of firms," Games and Economic Behavior, Elsevier, vol. 72(1), pages 306-313, May.
    19. Pierre Fleckinger & Thierry Lafay, 2003. "Horizontal differentiation and price competition with sequential entry," Working Papers hal-00243021, HAL.
    20. Sudipta Sarangi & Hrachya Kyureghian, 2002. "Transport Cost Sharing," Departmental Working Papers 2002-08, Department of Economics, Louisiana State University.

    More about this item

    Keywords

    Minimal product differentiation; Profit possibility frontier; Profit sharing rule; Subgame perfect Nash equilibrium; Unique equilibrium;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    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:spr:etbull:v:9:y:2021:i:1:d:10.1007_s40505-020-00193-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.