IDEAS home Printed from https://ideas.repec.org/p/gla/glaewp/2014_01.html
   My bibliography  Save this paper

Noncooperative oligopoly in markets with a continuum of traders: a limit theorem a la Cournot

Author

Listed:
  • Francesca Busetto
  • Giulio Codognato
  • Sayantan Ghosal

Abstract

In this paper, we consider an exchange economy `a la Shitovitz (1973), with atoms and an atomless set. We associate with it a strategic market game of the kind first proposed by Lloyd S. Shapley and known as the Shapley window model. We analyze the relationship between the set of the Cournot-Nash equilibrium allocations of the strategic market game and the Walras equilibrium allocations of the exchange economy with which it is associated. We show, with an example, that even when atoms are countably infinite, any Cournot-Nash equilibrium allocation of the game is not a Walras equilibrium of the underlying exchange economy. Accordingly, in the original spirit of Cournot (1838), we partially replicate the mixed exchange economy by increasing the number of atoms, without affecting the atomless part, and ensuring that the measure space of agents remains finite. We show that any sequence of Cournot-Nash equilibrium allocations of the strategic market games associated with the partially replicated exchange economies approximates a Walras equilibrium allocation of the original exchange economy.

Suggested Citation

  • 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.
    • Handle: RePEc:gla:glaewp:2014_01
    as

    Download full text from publisher

    File URL: http://www.gla.ac.uk/media/media_307052_en.pdf
    Download Restriction: no
    ---><---

    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. 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.
    3. B. C. Eaton & Richard G. Harris (ed.), 1997. "Trade, Technology and Economics," Books, Edward Elgar Publishing, number 1020.
    4. 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.
    5. 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.
    6. 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.
    7. Charles R. Frank, 1965. "Entry in a Cournot Market," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(3), pages 245-250.
    8. Novshek, William & Sonnenschein, Hugo, 1987. "General Equilibrium with Free Entry: A Synthetic Approach to the Theory of Perfect Competition," Journal of Economic Literature, American Economic Association, vol. 25(3), pages 1281-1306, September.
    9. 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.
    10. 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.
    11. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
    12. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    13. 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.
    14. 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.
    15. GABSZEWICZ, Jean & MICHEL, Philippe, 1992. "Oligopoly equilibria in exchange economies," LIDAM Discussion Papers CORE 1992047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. 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.
    17. Novshek, William & Sonnenschein, Hugo, 1983. "Walrasian equilibria as limits of noncooperative equilibria. Part II: Pure strategies," Journal of Economic Theory, Elsevier, vol. 30(1), pages 171-187, June.
    18. Francesca Busetto & Giulio Codognato & Sayantan Ghosal, 2013. "Three Models of Noncooperative Oligopoly in Markets with a Continuum of Traders," Recherches économiques de Louvain, De Boeck Université, vol. 79(4), pages 15-32.
    19. 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.
    20. William Novshek, 1980. "Cournot Equilibrium with Free Entry," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(3), pages 473-486.
    21. R. J. Ruffin, 1971. "Cournot Oligopoly and Competitive Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(4), pages 493-502.
    22. 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.
    23. Mas-Colell, Andreu, 1983. "Walrasian equilibria as limits of noncooperative equilibria. Part I: Mixed strategies," Journal of Economic Theory, Elsevier, vol. 30(1), pages 153-170, June.
    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. Francesca BUSETTO & Giulio CODOGNATO & Sayantan GHOSSAL, 2013. "Three Models of Noncooperative Oligopoly in Markets with a Continuum of Traders," Discussion Papers (REL - Recherches Economiques de Louvain) 2013041, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    27. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, January.
    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 & 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).
    2. 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.
    3. Francesca Busetto & Giulio Codognato & Sayantan Ghosal, 2012. "Noncooperative Oligopoly in Markets with a Continuum of Traders: A Limit Theorem," EconomiX Working Papers 2012-49, University of Paris Nanterre, EconomiX.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Julien, Ludovic A., 2013. "On Stackelberg competition in strategic multilateral exchange," Research in Economics, Elsevier, vol. 67(1), pages 59-75.
    10. 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.
    11. Codognato, Giulio & Ghosal, Sayantan & Tonin, Simone, 2015. "Atomic Cournotian traders may be Walrasian," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 1-14.
    12. Ludovic A. Julien & Fabrice Tricou, 2008. "Market Price Mechanisms and Stackelberg General Equilibria," Working Papers hal-04140726, HAL.
    13. Zigrand, Jean-Pierre, 2004. "A general equilibrium analysis of strategic arbitrage," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 923-952, December.
    14. 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.
    15. Julien, Ludovic A., 2011. "Unemployment equilibrium and economic policy in mixed markets," Economic Modelling, Elsevier, vol. 28(4), pages 1931-1940, July.
    16. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
    17. Busetto, Francesca & Codognato, Giulio & Julien, Ludovic, 2021. "Atomic Leontievian Walrasian traders are always Cournotian," Economics Letters, Elsevier, vol. 207(C).
    18. 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).
    19. 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.
    20. 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.

    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

    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:gla:glaewp:2014_01. 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: Business School Research Team (email available below). General contact details of provider: https://edirc.repec.org/data/dpglauk.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.