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Abstract and Applied Analysis
Volume 2013, Article ID 952915, 12 pages
Research Article

A Quasi-Variational Approach for the Dynamic Oligopolistic Market Equilibrium Problem

1Department of Mathematics and Applications “R. Caccioppoli”, University of Naples “Federico II”, Via Cintia, 80126 Naples, Italy
2Department of Mathematics and Computer Science, University of Catania, Viale A. Doria 6, 95125 Catania, Italy

Received 18 July 2013; Accepted 19 September 2013

Academic Editor: Abdellah Bnouhachem

Copyright © 2013 Annamaria Barbagallo and Paolo Mauro. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper is concerned with the dynamic oligopolistic market equilibrium problem in the realistic case in which we allow the presence of capacity constraints and production excesses and, moreover, we assume that the production function depends not only on the time but also on the equilibrium distribution. As a consequence, we introduce the generalized dynamic Cournot-Nash principle in the elastic case and prove the equivalence between this equilibrium definition and a suitable evolutionary quasi-variational inequality. For completeness we make the analysis of existence, regularity, and sensitivity of the solution. In the end, a numerical example is provided.