IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v188y2021i2d10.1007_s10957-020-01777-9.html
   My bibliography  Save this article

Variational Inequality Type Formulations of General Market Equilibrium Problems with Local Information

Author

Listed:
  • Igor Konnov

    (Kazan Federal University)

Abstract

We suggest a new approach to creation of general market equilibrium models involving economic agents with local and partial knowledge about the system and under different restrictions. The market equilibrium problem is then formulated as a quasi-variational inequality that enables us to establish existence results for the model in different settings. We also describe dynamic processes, which fall into information exchange schemes of the proposed market model. In particular, we propose an iterative solution method for quasi-variational inequalities, which is based on evaluations of the proper market information only in a neighborhood of the current market state without knowledge of the whole feasible set and prove its convergence.

Suggested Citation

  • Igor Konnov, 2021. "Variational Inequality Type Formulations of General Market Equilibrium Problems with Local Information," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 332-355, February.
    • Handle: RePEc:spr:joptap:v:188:y:2021:i:2:d:10.1007_s10957-020-01777-9
    DOI: 10.1007/s10957-020-01777-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-020-01777-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-020-01777-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. I. V. Konnov, 2019. "Equilibrium formulations of relative optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(1), pages 137-152, August.
    2. Igor Konnov, 2009. "Decomposition Approaches for Constrained Spatial Auction Market Problems," Networks and Spatial Economics, Springer, vol. 9(4), pages 505-524, December.
    3. D. Chan & J. S. Pang, 1982. "The Generalized Quasi-Variational Inequality Problem," Mathematics of Operations Research, INFORMS, vol. 7(2), pages 211-222, May.
    4. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    5. I. V. Konnov, 2016. "Selective bi-coordinate variations for resource allocation type problems," Computational Optimization and Applications, Springer, vol. 64(3), pages 821-842, July.
    6. Harker, Patrick T., 1991. "Generalized Nash games and quasi-variational inequalities," European Journal of Operational Research, Elsevier, vol. 54(1), pages 81-94, September.
    7. Elisabetta Allevi & Adriana Gnudi & Igor V. Konnov & Giorgia Oggioni, 2017. "Dynamic Spatial Auction Market Models with General Cost Mappings," Networks and Spatial Economics, Springer, vol. 17(2), pages 367-403, June.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    2. Giancarlo Bigi & Mauro Passacantando, 2016. "Gap functions for quasi-equilibria," Journal of Global Optimization, Springer, vol. 66(4), pages 791-810, December.
    3. Laura Scrimali, 2012. "Infinite Dimensional Duality Theory Applied to Investment Strategies in Environmental Policy," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 258-277, July.
    4. L. F. Bueno & G. Haeser & F. Lara & F. N. Rojas, 2020. "An Augmented Lagrangian method for quasi-equilibrium problems," Computational Optimization and Applications, Springer, vol. 76(3), pages 737-766, July.
    5. Francisco Facchinei & Christian Kanzow & Sebastian Karl & Simone Sagratella, 2015. "The semismooth Newton method for the solution of quasi-variational inequalities," Computational Optimization and Applications, Springer, vol. 62(1), pages 85-109, September.
    6. Giorgia Oggioni & Yves Smeers & Elisabetta Allevi & Siegfried Schaible, 2012. "A Generalized Nash Equilibrium Model of Market Coupling in the European Power System," Networks and Spatial Economics, Springer, vol. 12(4), pages 503-560, December.
    7. Alexey Izmailov & Mikhail Solodov, 2014. "On error bounds and Newton-type methods for generalized Nash equilibrium problems," Computational Optimization and Applications, Springer, vol. 59(1), pages 201-218, October.
    8. J. Contreras & J. B. Krawczyk & J. Zuccollo, 2016. "Economics of collective monitoring: a study of environmentally constrained electricity generators," Computational Management Science, Springer, vol. 13(3), pages 349-369, July.
    9. Migot, Tangi & Cojocaru, Monica-G., 2020. "A parametrized variational inequality approach to track the solution set of a generalized nash equilibrium problem," European Journal of Operational Research, Elsevier, vol. 283(3), pages 1136-1147.
    10. Anna Schwele & Christos Ordoudis & Pierre Pinson & Jalal Kazempour, 2021. "Coordination of power and natural gas markets via financial instruments," Computational Management Science, Springer, vol. 18(4), pages 505-538, October.
    11. James Ang & Masao Fukushima & Fanwen Meng & Takahiro Noda & Jie Sun, 2013. "Establishing Nash equilibrium of the manufacturer–supplier game in supply chain management," Journal of Global Optimization, Springer, vol. 56(4), pages 1297-1312, August.
    12. ABADA, Ibrahim & EHRENMANN, Andreas & SMEERS, Yves, 2014. "Endogenizing long-term contracts in gas market models," LIDAM Discussion Papers CORE 2014036, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Han, Deren & Zhang, Hongchao & Qian, Gang & Xu, Lingling, 2012. "An improved two-step method for solving generalized Nash equilibrium problems," European Journal of Operational Research, Elsevier, vol. 216(3), pages 613-623.
    14. 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.
    15. Ankur A. Kulkarni & Uday V. Shanbhag, 2012. "Revisiting Generalized Nash Games and Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 175-186, July.
    16. I. V. Konnov, 2021. "A general class of relative optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 501-520, June.
    17. Zhou, Jing & Lam, William H.K. & Heydecker, Benjamin G., 2005. "The generalized Nash equilibrium model for oligopolistic transit market with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 39(6), pages 519-544, July.
    18. SCRIMALI, Laura, 2006. "A quasi-variational inequality approach to the financial equilibrium problem," LIDAM Discussion Papers CORE 2006108, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. Jiawang Nie & Xindong Tang & Lingling Xu, 2021. "The Gauss–Seidel method for generalized Nash equilibrium problems of polynomials," Computational Optimization and Applications, Springer, vol. 78(2), pages 529-557, March.
    20. Elnaz Kanani Kuchesfehani & Georges Zaccour, 2015. "S-adapted Equilibria in Games Played Over Event Trees with Coupled Constraints," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 644-658, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:188:y:2021:i:2:d:10.1007_s10957-020-01777-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.