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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
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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 

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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.

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