Hostname: page-component-6d856f89d9-8l2sj Total loading time: 0 Render date: 2024-07-16T08:08:34.619Z Has data issue: false hasContentIssue false
  • English
  • Français

Noncooperative Oligopoly in Markets with a Cobb-Douglas Continuum of Traders

Published online by Cambridge University Press:  09 January 2015

Giulio Codognato  and
Ludovic A. Julien
Get access

Summary

In this paper, we reconsider two models of noncooperative oligopoly in general equilibrium proposed by Busetto et al. ((2008), (2011)): a version of the Shapley's window model for mixed exchange economies a la Shitovitz and its reformulation a la Cournot-Walras. We introduce the assumption that preferences of the traders belonging to the atomless part are represented by Cobb-Douglas utility functions. This assumption permits us to prove the existence of a Cournot-Nash equilibrium of the Shapley's window model - called Cobb-Douglas-Cournot-Nash equilibrium - without introducing further assumptions on atoms' endowments and preferences previously used by Busetto et al. (2011). Then, we show that the set of the Cobb-Douglas-Cournot-Nash equilibrium allocations coincides with the set of the Cournot-Walras equilibrium allocations.

Dans cet article, nous considérons les deux modèles d'oligopole équilibre général analysés dans Busetto et al. (2008), (2011). Ces modèles constituent deux transpositions dans le cadre d'analyse des marchés mixtes rationalisés par Shitovitz : la première est une version du modèle de Shapley et la deuxième une reformulation du modèle Cournot-Walras. Nous supposons que les agents dont la taille est négligeable ont des préférences représentées par des fonctions de type Cobb-Douglas. Cette hypothèse nous permet de construire un concept d'équilibre général stratégique, l'équilibre de Cobb-Douglas Cournot-Nash. Nous prouvons l'existence d'un tel équilibre. De plus, nous montrons l'ensemble des allocations associées à l'équilibre de Cobb-Douglas Cournot-Nash coïncide avec l'ensemble des allocations de l'équilibre Cournot-Walras.

Keywords

strategic market gamesnoncooperative oligopolyatomsatomless partC72D51jeux stratégiques de marchéoligopole non coopératifatomesnon atomicitéC72D51
Type
Research Article
Information
Recherches Économiques de Louvain/ Louvain Economic Review , Volume 79 , Issue 4 , December 2013 , pp. 75 - 88
Copyright
Copyright © Université catholique de Louvain, Institut de recherches économiques et sociales 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Udine, Via Tomadini 30, 33100 Udine, Italy, and EconomiX, Université de Paris Ouest Nanterre la Défense, 200 Avenue de la République, 92001 Nanterre Cedex, France.

‡

LEG, Université de Dijon, 2 boulevard Gabriel, 21066, Dijon Cedex, France, and EconomiX, Université de Paris Ouest Nanterre la Défense, 200 Avenue de la République, 92001 Nanterre Cedex, France.

References

Aliprantis, C.D., Border, K.C. (2006), Infinite dimensional analysis, Springer, New York.Google Scholar
Amir, R., Sahi, S., Shubik, M., Yao, S. (1990), “A strategic market game with complete markets,” Journal of Economic Theory 51, 126–143.Google Scholar
Busetto, F., Codognato, G., Ghosal, S. (2008), “Cournot-Walras equilibrium as a subgame perfect equilibrium,” International Journal of Game Theory 37, 371–386.Google Scholar
Busetto, F., Codognato, G., Ghosal, S. (2011), “Noncooperative oligopoly in markets with a continuum of traders,” Games and Economic Behavior, 72, 38–45.Google Scholar
Busetto, F., Codognato, G., Ghosal, S. (2012), “Noncooperative oligopoly in markets with a continuum of traders: a limit theorem,” Working Paper n. 2012–49, EconomiX, Université de Paris Ouest Nanterre la Défense.Google Scholar
Codognato, G., Gabszewicz, J.J. (1993), “Cournot-Walras equilibria in markets with a continuum of traders,” Economic Theory 3, 453–464.Google Scholar
Codognato, G., Ghosal, S. (2000), “Cournot-Nash equilibria in limit exchange economies with complete markets and consistent prices,” Journal of Mathematical Economics 34, 39–53.Google Scholar
Cournot, A. (1838), Recherches sur les principes mathématiques de la théorie des richesses, Hachette, Paris.Google Scholar
d'Aspremont, C., Dos, Santos Ferreira R., Gérard-Varet, L.-A. (1997), “General equilibrium concepts under imperfect competition: a Cournotian approach,” Journal of Economie Theory 73, 199–230.Google Scholar
Dierker, H., Grodal, B. (1986), “Nonexistence of Cournot-Walras equilibrium in a general equilibrium model with two oligopolists,” in Hildenbrand, W., Mas-Colell, A. (eds), Contributions to mathematical economics in honor of Gérard Debreu, North-Holland, Amsterdam.Google Scholar
Dubey, P., Shapley, L.S. (1994), “Noncooperative general exchange with a continuum of traders: two models,” Journal of Mathematical Economics 23, 253–293.Google Scholar
Dubey, P., Shubik, M. (1978), “The noncooperative equilibria of a closed trading economy with market supply and bidding strategies,” Journal of Economic Theory 17, 1–20.Google Scholar
Gabszewicz, J.J., Michel, P. (1997), “Oligopoly equilibrium in exchange economies,” in Eaton, B.C., Harris, R. G. (eds), Trade, technology and economics. Essays in honour of Richard G. Lipsey, Edward Elgar, Cheltenham.Google Scholar
Gabszewicz, J.J., Vial, J.-P. (1972), “Oligopoly ‘à la Cournot-Walras’ in a general equilibrium analysis,” Journal of Economic Theory 4, 381–400.Google Scholar
Julien, L.A., Tricou, F. (2005), “Specialized oligopolies in a pure exchange economy: the symmetric Cournot-Walras equilibrium,” Research in Economics 59, 280–292.Google Scholar
Julien, L.A., Tricou, F. (2009), “Preferences, market power and oligopolistic competition: an example,” Economics Bulletin 29, 2918–2923.Google Scholar
Okuno, M., Postlewaite, A., Roberts, J. (1980), “Oligopoly and competition in large markets,” American Economic Review 70, 22–31.Google Scholar
Mas-Colell, A. (1982), “The Cournotian foundations of Walrasian equilibrium theory,” in Hildenbrand, W. (ed), Advances in economic theory, Cambridge University Press, Cambridge.Google Scholar
Peck, J., Shell, K., Spear, S.E. (1992), “The market game: existence and structure of equilibrium,” Journal of Mathematical Economics 21, 271–299.Google Scholar
Postlewaite, A., Schmeidler, D. (1978), “Approximate efficiency of non-Walrasian Nash equilibria,” Econometrica 46, 127–137.Google Scholar
Roberts, D.J., Sonnenschein, H. (1977), “On the foundations of the theory of monopolistic competition,” Econometrica 45, 101–114.Google Scholar
Roberts, K. (1980), “The limit points of monopolistic competition,” Journal of Economic Theory 22, 256–278.Google Scholar
Sahi, S., Yao, S. (1989), “The noncooperative equilibria of a trading economy with complete markets and consistent prices,” Journal of Mathematical Economics 18, 325–346.Google Scholar
Shapley, L.S., Shubik, M. (1977), “Trade using one commodity as a means of payment,” Journal of Political Economy 85, 937–968.Google Scholar
Shitovitz, B. (1973), “Oligopoly in markets with a continuum of traders,” Econometrica 41, 467–501.Google Scholar
Shitovitz, B. (1997), “A comparison between the core and the monopoly solutions in a mixed exchange economy,” Economic Theory 10, 559–563.Google Scholar