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Time‐Dependent Variational Inequality for an Oligopolistic Market Equilibrium Problem with Production and Demand Excesses

Author

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  • Annamaria Barbagallo
  • Paolo Mauro

Abstract

The paper is concerned with the variational formulation of the oligopolistic market equilibrium problem in presence of both production and demand excesses. In particular, we generalize a previous model in which the authors, instead, considered only the problem with production excesses, by allowing also the presence of demand excesses. First we examine the equilibrium conditions in terms of the well‐known dynamic Cournot‐Nash principle. Next, the equilibrium conditions will be expressed in terms of Lagrange multipliers by means of the infinite dimensional duality theory. Then, we show the equivalence between the two conditions that are both expressed by an appropriate evolutionary variational inequality. Moreover, thanks to the variational formulation, some existence and regularity results for equilibrium solutions are proved. At last, a numerical example, which illustrates the features of the problem, is provided.

Suggested Citation

  • Annamaria Barbagallo & Paolo Mauro, 2012. "Time‐Dependent Variational Inequality for an Oligopolistic Market Equilibrium Problem with Production and Demand Excesses," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:651975
    DOI: 10.1155/2012/651975
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    References listed on IDEAS

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    1. SALINETTI, Gabriella & WETS, Roger J.-B., 1979. "On the convergence of sequences of convex sets in finite dimensions," LIDAM Reprints CORE 352, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. repec:bla:econom:v:36:y:1969:i:141:p:58-68 is not listed on IDEAS
    3. Johannes Jahn, 1996. "Introduction to the Theory of Nonlinear Optimization," Springer Books, Springer, edition 0, number 978-3-662-03271-8, March.
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    Cited by:

    1. Annamaria Barbagallo & Paolo Mauro, 2013. "A Quasi‐Variational Approach for the Dynamic Oligopolistic Market Equilibrium Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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