IDEAS home Printed from https://ideas.repec.org/p/wrk/warwec/866.html
   My bibliography  Save this paper

Noncooperative Oligopoly in Markets with a Continuum of Traders

Author

Listed:
  • Busetto, Francesca

    (Dipartimento di Scienze Economiche, Universitµa degli Studi di Udine)

  • Codognato, Giulio

    (Dipartimento di Scienze Economiche, Universitµa degli Studi di Udine)

  • Ghosal, Sayantan

    (Department of Economics, University of Warwick)

Abstract

In this paper, we study three prototypical models of noncooperative oligopoly in markets with a continuum of traders : the model of Cournot-Walras equilibrium of Codognato and Gabszewicz (1991), the model of Cournot-Nash equilibrium of Lloyd S. Shapley, and the model of Cournot-Walras equilibrium of Busetto et al. (2008). We argue that these models are all distinct and only the Shapley's model with a continuum of traders and atoms gives an endogenous explanation of the perfectly and imperfectly competitive behavior of agents in a one-stage setting. For this model, we prove a theorem of existence of a Cournot-Nash equilibrium.

Suggested Citation

  • Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2008. "Noncooperative Oligopoly in Markets with a Continuum of Traders," The Warwick Economics Research Paper Series (TWERPS) 866, University of Warwick, Department of Economics.
    • Handle: RePEc:wrk:warwec:866
    as

    Download full text from publisher

    File URL: https://warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp_866.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jaskold Gabszewicz, Jean & Vial, Jean-Philippe, 1972. "Oligopoly "A la cournot" in a general equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 4(3), pages 381-400, June.
    2. Jean-Marc Bonnisseau & Michael Florig, 2003. "Existence and optimality of oligopoly equilibria in linear exchange economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 727-741, November.
    3. Jean Gabszewicz & Giulio Codognato, 1991. "Équilibres de Cournot-Walras dans une économie d'échange," Revue Économique, Programme National Persée, vol. 42(6), pages 1013-1026.
    4. d'Aspremont, Claude & Dos Santos Ferreira, Rodolphe & Gerard-Varet, Louis-Andre, 1997. "General Equilibrium Concepts under Imperfect Competition: A Cournotian Approach," Journal of Economic Theory, Elsevier, vol. 73(1), pages 199-230, March.
    5. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2008. "Cournot-Walras Equilibrium as a Subgame Perfect Equilibrium," The Warwick Economics Research Paper Series (TWERPS) 837, University of Warwick, Department of Economics.
    6. B. C. Eaton & Richard G. Harris (ed.), 1997. "Trade, Technology and Economics," Books, Edward Elgar Publishing, number 1020.
    7. Amir, Rabah & Sahi, Siddharta & Shubik, Martin & Yao, Shuntian, 1990. "A strategic market game with complete markets," Journal of Economic Theory, Elsevier, vol. 51(1), pages 126-143, June.
    8. Roberts, John & Sonnenschein, Hugo, 1977. "On the Foundations of the Theory of Monopolistic Competition," Econometrica, Econometric Society, vol. 45(1), pages 101-113, January.
    9. Codognato, Giulio & Gabszewicz, Jean J, 1993. "Cournot-Walras Equilibria in Markets with a Continuum of Traders," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(3), pages 453-464, July.
    10. Postlewaite, A & Schmeidler, David, 1978. "Approximate Efficiency of Non-Walrasian Nash Equilibria," Econometrica, Econometric Society, vol. 46(1), pages 127-135, January.
    11. Peck, James & Shell, Karl & Spear, Stephen E., 1992. "The market game: existence and structure of equilibrium," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 271-299.
    12. Codognato, Giulio, 1995. "Cournot-Walras and Cournot Equilibria in Mixed Markets: A Comparison," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 361-370, March.
    13. Gabszewicz, J. & Michel, P., 1992. "Oligopoly Equilibria in Exchange Economies," Papiers d'Economie Mathématique et Applications 92.26, Université Panthéon-Sorbonne (Paris 1).
    14. repec:cor:louvrp:-1265 is not listed on IDEAS
    15. Benyamin Shitovitz, 1997. "A comparison between the core and the monopoly solutions in a mixed exchange economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(3), pages 559-563.
    16. Dubey, Pradeep & Shapley, Lloyd S., 1994. "Noncooperative general exchange with a continuum of traders: Two models," Journal of Mathematical Economics, Elsevier, vol. 23(3), pages 253-293, May.
    17. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
    18. 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.
    19. 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.
    20. 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.
    21. Martin Shubik & Jingang Zhao, 1990. "A Strategic Market Game of a Finite Economy with a Mutual Bank," Cowles Foundation Discussion Papers 961, Cowles Foundation for Research in Economics, Yale University.
    22. Shapley, Lloyd S & Shubik, Martin, 1977. "Trade Using One Commodity as a Means of Payment," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 937-968, October.
    23. Codognato, G., 1995. "Cournot-Walras and Cournot equilibria in mixed markets: A comparison," LIDAM Reprints CORE 1134, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    24. Shitovitz, Benyamin, 1973. "Oligopoly in Markets with a Continuum of Traders," Econometrica, Econometric Society, vol. 41(3), pages 467-501, May.
    25. Roberts, Kevin, 1980. "The limit points of monopolistic competition," Journal of Economic Theory, Elsevier, vol. 22(2), pages 256-278, April.
    26. 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).
    27. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    28. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, September.
    29. Lahmandi-Ayed, R, 1996. "Oligopoly Equilibria in Exchange Economies : Limit Theorems," Papiers d'Economie Mathématique et Applications 96.07, Université Panthéon-Sorbonne (Paris 1).
    30. 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)

    Citations

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


    Cited by:

    1. David Mayer-Foulkes, 2011. "Vulnerable Markets," DEGIT Conference Papers c016_040, DEGIT, Dynamics, Economic Growth, and International Trade.
    2. Perets, Hovav & Shitovitz, Benyamin & Spiegel, Menahem, 2012. "Trading equilibrium in a public good economy with smooth preferences and a mixed measure space of consumers," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 163-169.
    3. Codognato, Giulio & Ghosal, Sayantan & Tonin, Simone, 2015. "Atomic Cournotian traders may be Walrasian," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 1-14.
    4. 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.
    5. Chatterji, Shurojit; Ghosal, Sayantan, 2010. "Liquidity, moral hazard and bank crises," CAGE Online Working Paper Series 27, Competitive Advantage in the Global Economy (CAGE).
    6. 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.
    7. Julien, Ludovic A., 2013. "On Stackelberg competition in strategic multilateral exchange," Research in Economics, Elsevier, vol. 67(1), pages 59-75.
    8. 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.
    9. Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Ludovic A. Julien & Damiano Turchet, 2023. "Noncooperative Oligopoly in Markets with a Continuum of Traders and a Strongly Connected Set of Commodities: A Limit Theorem," Working Papers hal-04194965, HAL.
    10. 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.
    11. Busetto, Francesca & Codognato, Giulio & Julien, Ludovic, 2021. "Atomic Leontievian Walrasian traders are always Cournotian," Economics Letters, Elsevier, vol. 207(C).
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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).

    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 & Ghosal, Syantan, 2008. "Cournot-Walras Equilibrium as a Subgame Perfect Equilibrium," Economic Research Papers 269786, University of Warwick - Department of Economics.
    2. 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.
    3. 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).
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Ludovic A. Julien & Fabrice Tricou, 2008. "Market Price Mechanisms and Stackelberg General Equilibria," Working Papers hal-04140726, HAL.
    10. Julien, Ludovic A., 2013. "On Stackelberg competition in strategic multilateral exchange," Research in Economics, Elsevier, vol. 67(1), pages 59-75.
    11. Busetto, Francesca & Codognato, Giulio & Julien, Ludovic, 2021. "Atomic Leontievian Walrasian traders are always Cournotian," Economics Letters, Elsevier, vol. 207(C).
    12. 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.
    13. 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.
    14. Zigrand, Jean-Pierre, 2004. "A general equilibrium analysis of strategic arbitrage," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 923-952, December.
    15. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
    16. Ghosal, Sayantan & Tonin, Simone, 2014. "Non-Cooperative Asymptotic Oligopoly in Economies with Infinitely Many Commodities," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-23, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    17. Desgranges, Gabriel & Ghosal, Sayantan, 2010. "P-Stable Equilibrium: Definition And Some Properties," Economic Research Papers 270772, University of Warwick - Department of Economics.
    18. Alex Dickson & Roger Hartley, 2013. "Bilateral oligopoly and quantity competition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(3), pages 979-1004, April.
    19. Julien, Ludovic A., 2011. "Unemployment equilibrium and economic policy in mixed markets," Economic Modelling, Elsevier, vol. 28(4), pages 1931-1940, July.
    20. 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.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • 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:wrk:warwec:866. 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: Margaret Nash (email available below). General contact details of provider: https://edirc.repec.org/data/dewaruk.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.