Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T11:04:42.882Z Has data issue: false hasContentIssue false
  • English
  • Français

Three Models of Noncooperative Oligopoly in Markets with a Continuum of Traders*

Published online by Cambridge University Press:  09 January 2015

Francesca Busetto ,
Giulio Codognato  and
Sayantan Ghosal
Get access

Summary

In this paper, we reconstruct the main developments of the theory of noncooperative oligopoly in general equilibrium, by focusing on the analysis of three prototypical models for pure exchange economies: the model of Cournot-Walras equilibrium of Codognato and Gabszewicz (1991); the model of Cournot-Nash equilibrium originally proposed by Lloyd S. Shapley and known as window model; the model of Cournot-Walras equilibrium of Busetto et al. (2008). We establish, in a systematic way, the relationship between the three notions of equilibrium proposed in these models and the notion of Walras equilibrium. Then, we investigate the relationships among those three notions of equilibrium.

Cet article propose une reconstruction de la théorie de l'oligopole en équilibre général en univers non coopératif. Trois types de modèles en échange pur sont étudiés : le modèle de Cournot-Walras analysé dans Codognato et Gabszewicz (1991) ; le modèle de jeu de marché à la Cournot-Nash proposé initialement par Shapley ; et le modèle de Cournot-Walras étudié par Busetto et al. (2008). Nous établissons la relation qui existe entre les équilibres de ces trois modèles avec l'équilibre concurrentiel walrassien. Ensuite, nous analysons les relations entre les trois équilibres stratégiques associés à ces trois modèles.

Keywords

Noncooperative oligopolyCournot-Walras equilibriaCournot-Nash equilibria.C72D51oligopole non coopératiféquilibre de Cournot-Walraséquilibre de Cournot-NashC72D51
Type
Research Article
Information
Recherches Économiques de Louvain/ Louvain Economic Review , Volume 79 , Issue 4 , December 2013 , pp. 15 - 32
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

*

We would like to thank an anonymous referee for his comments and suggestions. Francesca Busetto and Giulio Codognato gratefully acknowledge financial support from MIUR (PRIN 20103S5RN3).

†

Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Udine, Via Tomadlni 30, 33100 Udine, Italy.

‡

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

§

Department of Economics, University of Warwick, Coventry CV4 7AL, United Kingdom.

References

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
Aumann, R.J. (1964), “Markets with a continuum of traders,” Econometrica 32, 39–50.Google Scholar
Aumann, R.J. (1966), “Existence of competitive equilibria in markets with a continuum of traders,” Econometrica 24, 1–17.Google Scholar
Bonnisseau, J-M., Florig, M. (2003), “Existence and optimality of oligopoly equilibria in linear exchange economies,” Economic Theory 22, 727–741.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. (1995), “Cournot-Walras and Cournot equilibria in mixed markets: a comparison,” Economic Theory 5, 361–370.Google Scholar
Codognato, G., Gabszewicz, J.J. (1991), “Equilibres de Cournot-Walras dans une économie d'échange,” Revue Economique 42, 1013–1026.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, París.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 Economic Theory 73, 199–230.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 ‘á 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
Lahmandi-Ayed, R. (2001), “Oligopoly equilibria in exchange economies: a limit theorem,” Economic Theory 17, 665–674.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
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