IDEAS home Printed from https://ideas.repec.org/p/drm/wpaper/2023-22.html
   My bibliography  Save this paper

Noncooperative Oligopoly in Markets with a Continuum of Traders and a Strongly Connected Set of Commodities: A Limit Theorem

Author

Listed:
  • Ludovic A. Julien
  • Francesca Busetto
  • Giulio Codognato
  • Sayantan Ghosal
  • Damiano Turchet

Abstract

We consider a mixed version of the Shapley window model, where large traders are represented as atoms and small traders are represented by an atomless part. Our main theorem shows that any sequence of Cournot-Nash allocations of the strategic market games associated with the partial replications of the exchange economy has a limit point for each trader and that the assignment determined by these limit points is a Walrasian allocation of the original economy. Instead of relying on restrictive assumptions on the characteristics of atoms, as in Busetto et al. (2017), our limit theorem relies on the characteristics of agents in the atomless part and their endogenously price-taking behavior.

Suggested Citation

  • Ludovic A. Julien & Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Damiano Turchet, 2023. "Noncooperative Oligopoly in Markets with a Continuum of Traders and a Strongly Connected Set of Commodities: A Limit Theorem," EconomiX Working Papers 2023-22, University of Paris Nanterre, EconomiX.
    • Handle: RePEc:drm:wpaper:2023-22
    as

    Download full text from publisher

    File URL: https://economix.fr/pdf/dt/2023/WP_EcoX_2023-22.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Codognato, Giulio & Ghosal, Sayantan & Tonin, Simone, 2015. "Atomic Cournotian traders may be Walrasian," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 1-14.
    2. Gabszewicz, Jean Jaskold & Mertens, Jean-Francois, 1971. "An Equivalence Theorem for the Core of an Economy Whose Atoms Are Not 'Too' Big," Econometrica, Econometric Society, vol. 39(5), pages 713-721, September.
    3. Francesca Busetto & Giulio Codognato & Sayantan Ghosal, 2017. "Asymptotic equivalence between Cournot–Nash and Walras equilibria in exchange economies with atoms and an atomless part," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 975-990, November.
    4. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan & Julien, Ludovic & Tonin, Simone, 2018. "Noncooperative oligopoly in markets with a continuum of traders and a strongly connected set of commodities," Games and Economic Behavior, Elsevier, vol. 108(C), pages 478-485.
    5. David M. Kreps, 2012. "Microeconomic Foundations I: Choice and Competitive Markets," Economics Books, Princeton University Press, edition 1, volume 1, number 9890.
    6. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2011. "Noncooperative oligopoly in markets with a continuum of traders," Games and Economic Behavior, Elsevier, vol. 72(1), pages 38-45, May.
    7. Sahi, Siddhartha & Yao, Shuntian, 1989. "The non-cooperative equilibria of a trading economy with complete markets and consistent prices," Journal of Mathematical Economics, Elsevier, vol. 18(4), pages 325-346, September.
    8. Okuno, Masahiro & Postlewaite, Andrew & Roberts, John, 1980. "Oligopoly and Competition in Large Markets," American Economic Review, American Economic Association, vol. 70(1), pages 22-31, March.
    9. Codognato, Giulio & Ghosal, Sayantan, 2000. "Cournot-Nash equilibria in limit exchange economies with complete markets and consistent prices," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 39-53, August.
    10. Shitovitz, Benyamin, 1973. "Oligopoly in Markets with a Continuum of Traders," Econometrica, Econometric Society, vol. 41(3), pages 467-501, May.
    11. CODOGNATO, Giulio, 2000. "Cournot-Nash equilibria in limit exchange economies with complete markets: A comparison between two models," LIDAM Reprints CORE 1445, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Gabszewicz, Jean J. & Shitovitz, Benyamin, 1992. "The core in imperfectly competitive economies," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 15, pages 459-483, Elsevier.
    13. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
    14. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, September.
    15. Codognato, Giulio, 2000. "Cournot-Nash Equilibria in Limit Exchange Economies with Complete Markets: A Comparison between Two Models," Games and Economic Behavior, Elsevier, vol. 31(1), pages 136-146, April.
    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. Busetto, Francesca & Codognato, Giulio & Julien, Ludovic, 2020. "Atomic Leontievian Cournotian traders are always Walrasian," Games and Economic Behavior, Elsevier, vol. 122(C), pages 318-327.
    2. Alex Dickson & Simone Tonin, 2021. "An introduction to perfect and imperfect competition via bilateral oligopoly," Journal of Economics, Springer, vol. 133(2), pages 103-128, July.
    3. Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Ludovic Julien & Simone Tonin, 2020. "Existence and optimality of Cournot–Nash equilibria in a bilateral oligopoly with atoms and an atomless part," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 933-951, December.
    4. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan & Julien, Ludovic & Tonin, Simone, 2018. "Noncooperative oligopoly in markets with a continuum of traders and a strongly connected set of commodities," Games and Economic Behavior, Elsevier, vol. 108(C), pages 478-485.
    5. Codognato, Giulio & Ghosal, Sayantan & Tonin, Simone, 2015. "Atomic Cournotian traders may be Walrasian," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 1-14.
    6. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2012. "Noncooperative Oligopoly in Markets with a Continuum of Traders: A Limit Theorem," The Warwick Economics Research Paper Series (TWERPS) 994, University of Warwick, Department of Economics.
    7. Francesca Busetto & Giulio Codognato & Sayantan Ghosal, 2017. "Asymptotic equivalence between Cournot–Nash and Walras equilibria in exchange economies with atoms and an atomless part," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 975-990, November.
    8. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2011. "Noncooperative oligopoly in markets with a continuum of traders," Games and Economic Behavior, Elsevier, vol. 72(1), pages 38-45, May.
    9. Busetto, Francesca & Codognato, Giulio & Julien, Ludovic, 2021. "Atomic Leontievian Walrasian traders are always Cournotian," Economics Letters, Elsevier, vol. 207(C).
    10. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2014. "Noncooperative Oligopoly in Markets with a Continuum of Traders: A Limit Theorem µa la Cournot," SIRE Discussion Papers 2014-019, Scottish Institute for Research in Economics (SIRE).
    11. Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Damiano Turchet, 2023. "On the foundation of monopoly in bilateral exchange," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(4), pages 1261-1290, December.
    12. Busetto, Francesca & Codognato, Giulio & Ghosal, Syantan, 2008. "Cournot-Walras Equilibrium as a Subgame Perfect Equilibrium," Economic Research Papers 269786, University of Warwick - Department of Economics.
    13. Francesca Busetto & Giulio Codognato & Sayantan Ghosal, "undated". "Noncooperative oligopoly in markets with a continuum of traders: a limit theorem a la Cournot," Working Papers 2014_01, Business School - Economics, University of Glasgow.
    14. Ghosal, Sayantan & Tonin, Simone, 2018. "Noncooperative oligopoly in economies with infinitely many commodities and traders," Games and Economic Behavior, Elsevier, vol. 109(C), pages 184-200.
    15. Desgranges, Gabriel & Ghosal, Sayantan, 2010. "P-Stable Equilibrium: Definition And Some Properties," Economic Research Papers 270772, University of Warwick - Department of Economics.
    16. Julien, Ludovic A., 2013. "On Stackelberg competition in strategic multilateral exchange," Research in Economics, Elsevier, vol. 67(1), pages 59-75.
    17. David Mayer-Foulkes, 2011. "Vulnerable Markets," DEGIT Conference Papers c016_040, DEGIT, Dynamics, Economic Growth, and International Trade.
    18. Cato, Susumu, 2021. "Preference aggregation and atoms in measures," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    19. Jonathan H. Hamilton & W. Bentley MacLeod & Jacques-François Thisse, 1991. "Spatial Competition and the Core," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(3), pages 925-937.
    20. Ludovic A. Julien, 2017. "Hierarchical Competition and Heterogeneous Behavior in Noncooperative Oligopoly Markets," Post-Print hal-01637298, HAL.

    More about this item

    Keywords

    Cournot-Nash equilibrium; Walras equilibrium; Asymptotic equivalence;
    All these keywords.

    JEL classification:

    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

    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:drm:wpaper:2023-22. 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: Valerie Mignon (email available below). General contact details of provider: https://edirc.repec.org/data/modemfr.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.