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Evolutionary Variational Formulation for Oligopolistic Market Equilibrium Problems with Production Excesses

Author

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  • Annamaria Barbagallo

    (University of Naples “Federico II”)

  • Paolo Mauro

    (University of Catania)

Abstract

The paper is devoted to generalize a previous model of the dynamic oligopolistic market equilibrium problem allowing the presence of production excesses and assuming, in a more reasonable way that the total amounts of commodity shipments from a firm to all the demand markets be upper bounded. First, we give equilibrium conditions in terms of the well-known dynamic Cournot–Nash equilibrium principle. Then we show that such conditions can be expressed in terms of Lagrange multipliers; namely, by means of an utility function, prove that both equilibrium conditions can be equivalently expressed by a variational inequality. The variational formulation allows us to provide existence theorems and qualitative properties for equilibrium solutions. At last, a numerical example illustrates the results obtained.

Suggested Citation

  • Annamaria Barbagallo & Paolo Mauro, 2012. "Evolutionary Variational Formulation for Oligopolistic Market Equilibrium Problems with Production Excesses," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 288-314, October.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:1:d:10.1007_s10957-012-0056-z
    DOI: 10.1007/s10957-012-0056-z
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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. A. Maugeri & F. Raciti, 2010. "Remarks on infinite dimensional duality," Journal of Global Optimization, Springer, vol. 46(4), pages 581-588, April.
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    Citations

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    Cited by:

    1. John Cotrina & Javier Zúñiga, 2018. "Time-Dependent Generalized Nash Equilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 1054-1064, December.
    2. Patrizia Daniele & Sofia Giuffrè & Mariagrazia Lorino, 2016. "Functional inequalities, regularity and computation of the deficit and surplus variables in the financial equilibrium problem," Journal of Global Optimization, Springer, vol. 65(3), pages 575-596, July.
    3. Annamaria Barbagallo & Serena Guarino Lo Bianco, 2023. "A random time-dependent noncooperative equilibrium problem," Computational Optimization and Applications, Springer, vol. 84(1), pages 27-52, January.
    4. B. Jadamba & F. Raciti, 2015. "Variational Inequality Approach to Stochastic Nash Equilibrium Problems with an Application to Cournot Oligopoly," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 1050-1070, June.
    5. Carlos Hervés-Beloso & Monica Patriche, 2014. "A Fixed-Point Theorem and Equilibria of Abstract Economies with Weakly Upper Semicontinuous Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 719-736, December.
    6. Francesca Faraci & Baasansuren Jadamba & Fabio Raciti, 2016. "On Stochastic Variational Inequalities with Mean Value Constraints," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 675-693, November.
    7. Annamaria Barbagallo & Stéphane Pia, 2015. "Weighted Quasi-Variational Inequalities in Non-pivot Hilbert Spaces and Applications," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 781-803, March.
    8. Patrizia Daniele & Sofia Giuffrè, 2015. "Random Variational Inequalities and the Random Traffic Equilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 363-381, October.
    9. Chan, Chi Kin & Zhou, Yan & Wong, Kar Hung, 2018. "A dynamic equilibrium model of the oligopolistic closed-loop supply chain network under uncertain and time-dependent demands," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 325-354.
    10. Annamaria Barbagallo & Bruno Antonio Pansera & Massimiliano Ferrara, 2024. "Notes on random optimal control equilibrium problem via stochastic inverse variational inequalities," Computational Management Science, Springer, vol. 21(1), pages 1-21, June.
    11. Annamaria Barbagallo & Paolo Mauro, 2016. "A General Quasi-variational Problem of Cournot-Nash Type and Its Inverse Formulation," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 476-492, August.

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