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Evolutionary Variational Inequality Formulation of the Generalized Nash Equilibrium Problem

Author

Listed:
  • Didier Aussel

    (Lab. PROMES, UPR CNRS 8521, University of Perpignan Via Domitia)

  • Rachana Gupta

    (Indian Institute of Technology - Delhi)

  • Aparna Mehra

    (Indian Institute of Technology - Delhi)

Abstract

The formulation of the generalized Nash Equilibrium problem as an evolutionary variational inequality problem is proved in the general setting of quasiconvex decision functions. An existence result for the time-dependent generalized Nash equilibrium problem is deduced, and an application to the dynamic electricity market is also considered.

Suggested Citation

  • Didier Aussel & Rachana Gupta & Aparna Mehra, 2016. "Evolutionary Variational Inequality Formulation of the Generalized Nash Equilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 74-90, April.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:1:d:10.1007_s10957-015-0859-9
    DOI: 10.1007/s10957-015-0859-9
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    References listed on IDEAS

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    1. D. Aussel & N. Hadjisavvas, 2004. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 445-450, May.
    2. WEI, Jing-Yuan & SMEERS, Yves, 1999. "Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices," LIDAM Reprints CORE 1454, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Barbagallo, Annamaria & Daniele, Patrizia & Giuffrè, Sofia & Maugeri, Antonino, 2014. "Variational approach for a general financial equilibrium problem: The Deficit Formula, the Balance Law and the Liability Formula. A path to the economy recovery," European Journal of Operational Research, Elsevier, vol. 237(1), pages 231-244.
    4. Annamaria Barbagallo & Patrizia Daniele & Mariagrazia Lorino & Antonino Maugeri & Cristina Mirabella, 2014. "A Variational Approach to the Evolutionary Financial Equilibrium Problem with Memory Terms and Adaptive Constraints," Springer Optimization and Its Applications, in: Valery A. Kalyagin & Panos M. Pardalos & Themistocles M. Rassias (ed.), Network Models in Economics and Finance, edition 127, pages 13-23, Springer.
    5. Edward Anderson & Huifu Xu, 2006. "Optimal Supply Functions in Electricity Markets with Option Contracts and Non-smooth Costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 387-411, July.
    6. Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, January.
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    8. Wei Jing-Yuan & Yves Smeers, 1999. "Spatial Oligopolistic Electricity Models with Cournot Generators and Regulated Transmission Prices," Operations Research, INFORMS, vol. 47(1), pages 102-112, February.
    9. Patrizia Daniele, 2006. "Dynamic Networks and Evolutionary Variational Inequalities," Books, Edward Elgar Publishing, number 3516.
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    Cited by:

    1. Shipra Singh & Aviv Gibali & Simeon Reich, 2021. "Multi-Time Generalized Nash Equilibria with Dynamic Flow Applications," Mathematics, MDPI, vol. 9(14), pages 1-23, July.
    2. Orestes Bueno & John Cotrina, 2021. "Existence of Projected Solutions for Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 344-362, October.
    3. 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.
    4. John Cotrina & Javier Zúñiga, 2019. "Quasi-equilibrium problems with non-self constraint map," Journal of Global Optimization, Springer, vol. 75(1), pages 177-197, September.

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