IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v114y2002i3d10.1023_a1016056327692.html
   My bibliography  Save this article

Nash Equilibria, Variational Inequalities, and Dynamical Systems

Author

Listed:
  • E. Cavazzuti

    (University of Modena and Reggio Emilia)

  • M. Pappalardo

    (University of Pisa)

  • M. Passacantando

    (University of Pisa)

Abstract

In this paper, we introduce some relationships between Nash equilibria, variational equilibria, and dynamical equilibria for noncooperative games.

Suggested Citation

  • E. Cavazzuti & M. Pappalardo & M. Passacantando, 2002. "Nash Equilibria, Variational Inequalities, and Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 491-506, September.
    • Handle: RePEc:spr:joptap:v:114:y:2002:i:3:d:10.1023_a:1016056327692
    DOI: 10.1023/A:1016056327692
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1016056327692
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1016056327692?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 search for a different version of it.

    References listed on IDEAS

    as
    1. M. Pappalardo & M. Passacantando, 2002. "Stability for Equilibrium Problems: From Variational Inequalities to Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 113(3), pages 567-582, June.
    2. Jen-Chih Yao, 1994. "Variational Inequalities with Generalized Monotone Operators," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 691-705, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Prasit Cholamjiak & Suthep Suantai, 2013. "Iterative methods for solving equilibrium problems, variational inequalities and fixed points of nonexpansive semigroups," Journal of Global Optimization, Springer, vol. 57(4), pages 1277-1297, December.
    2. Jacquot, Paulin & Wan, Cheng, 2022. "Nonatomic aggregative games with infinitely many types," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1149-1165.
    3. Chen, Li-Ming & Chang, Wei-Lun, 2020. "Under what conditions can an application service firm with in-house computing benefit from cloudbursting?," European Journal of Operational Research, Elsevier, vol. 282(1), pages 71-80.
    4. Bichler, Martin & Kohring, Nils & Oberlechner, Matthias & Pieroth, Fabian R., 2023. "Learning equilibrium in bilateral bargaining games," European Journal of Operational Research, Elsevier, vol. 311(2), pages 660-678.
    5. Pham Viet Hai & Phan Tu Vuong, 2024. "Third Order Dynamical Systems for the Sum of Two Generalized Monotone Operators," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 519-553, August.
    6. Phan Tu Vuong & Jean Jacques Strodiot, 2020. "A Dynamical System for Strongly Pseudo-monotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 767-784, June.
    7. Nils Langenberg, 2012. "Interior point methods for equilibrium problems," Computational Optimization and Applications, Springer, vol. 53(2), pages 453-483, October.
    8. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    9. Elodie Adida & Georgia Perakis, 2010. "Dynamic Pricing and Inventory Control: Uncertainty and Competition," Operations Research, INFORMS, vol. 58(2), pages 289-302, April.
    10. Anselmi, Jonatha & Ardagna, Danilo & Passacantando, Mauro, 2014. "Generalized Nash equilibria for SaaS/PaaS Clouds," European Journal of Operational Research, Elsevier, vol. 236(1), pages 326-339.
    11. Bichuch, Maxim & Hobbs, Benjamin F. & Song, Xinyue, 2023. "Identifying optimal capacity expansion and differentiated capacity payments under risk aversion and market power: A financial Stackelberg game approach," Energy Economics, Elsevier, vol. 120(C).
    12. Szilárd Nagy, 2013. "Stackelberg equilibria via variational inequalities and projections," Journal of Global Optimization, Springer, vol. 57(3), pages 821-828, November.
    13. Pham Ky Anh & Trinh Ngoc Hai, 2021. "Dynamical system for solving bilevel variational inequalities," Journal of Global Optimization, Springer, vol. 80(4), pages 945-963, August.
    14. Mauro Passacantando & Danilo Ardagna & Anna Savi, 2016. "Service Provisioning Problem in Cloud and Multi-Cloud Systems," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 265-277, May.
    15. Massimo Pappalardo & Giandomenico Mastroeni & Mauro Passacantando, 2016. "Merit functions: a bridge between optimization and equilibria," Annals of Operations Research, Springer, vol. 240(1), pages 271-299, May.

    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. Mostafa Ghadampour & Ebrahim Soori & Ravi P. Agarwal & Donal O’Regan, 2022. "A Strong Convergence Theorem for Solving an Equilibrium Problem and a Fixed Point Problem Using the Bregman Distance," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 854-877, December.
    2. L. C. Zeng & J. C. Yao, 2007. "Existence Theorems for Variational Inequalities in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 132(2), pages 321-337, February.
    3. Yonghong Yao & Yeong-Cheng Liou & Shin Kang, 2013. "Two-step projection methods for a system of variational inequality problems in Banach spaces," Journal of Global Optimization, Springer, vol. 55(4), pages 801-811, April.
    4. Massimo Pappalardo & Giandomenico Mastroeni & Mauro Passacantando, 2016. "Merit functions: a bridge between optimization and equilibria," Annals of Operations Research, Springer, vol. 240(1), pages 271-299, May.
    5. Vu Thi Huong & Jen-Chih Yao & Nguyen Dong Yen, 2017. "On the Stability and Solution Sensitivity of a Consumer Problem," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 567-589, November.
    6. Pham Ky Anh & Trinh Ngoc Hai, 2021. "Dynamical system for solving bilevel variational inequalities," Journal of Global Optimization, Springer, vol. 80(4), pages 945-963, August.
    7. Monica Bianchi & Siegfried Schaible, 2004. "Equilibrium Problems under Generalized Convexity and Generalized Monotonicity," Journal of Global Optimization, Springer, vol. 30(2), pages 121-134, November.
    8. L. C. Zeng & N. C. Wong & J. C. Yao, 2007. "Convergence Analysis of Modified Hybrid Steepest-Descent Methods with Variable Parameters for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 51-69, January.
    9. Phan Tu Vuong & Xiaozheng He & Duong Viet Thong, 2021. "Global Exponential Stability of a Neural Network for Inverse Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 915-930, September.
    10. Lai-Jiu Lin & Zenn-Tsun Yu & Chih-Sheng Chuang, 2013. "Weak and strong convergence theorems for asymptotically pseudo-contraction mappings in the intermediate sense in Hilbert spaces," Journal of Global Optimization, Springer, vol. 56(1), pages 165-183, May.
    11. N. El Farouq, 2001. "Pseudomonotone Variational Inequalities: Convergence of the Auxiliary Problem Method," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 305-322, November.
    12. Phan Tu Vuong, 2022. "The Global Exponential Stability of a Dynamical System for Solving Variational Inequalities," Networks and Spatial Economics, Springer, vol. 22(2), pages 395-407, June.
    13. Fabián Flores-Bazán & Ruben López, 2005. "The Linear Complementarity Problem Under Asymptotic Analysis," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 73-90, February.
    14. L. C. Ceng & S. Schaible & J. C. Yao, 2008. "Existence of Solutions for Generalized Vector Variational-like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 121-133, April.
    15. Lateef Olakunle Jolaoso & Adeolu Taiwo & Timilehin Opeyemi Alakoya & Oluwatosin Temitope Mewomo, 2020. "A Strong Convergence Theorem for Solving Pseudo-monotone Variational Inequalities Using Projection Methods," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 744-766, June.
    16. Y. S. Xia, 2004. "Further Results on Global Convergence and Stability of Globally Projected Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 627-649, September.
    17. Y. B. Zhao & G. Isac, 2000. "Quasi-P*-Maps, P(τ, α, β)-Maps, Exceptional Family of Elements, and Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 213-231, April.
    18. B. T. Kien & M. M. Wong & N. C. Wong & J. C. Yao, 2009. "Solution Existence of Variational Inequalities with Pseudomonotone Operators in the Sense of Brézis," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 249-263, February.
    19. L. C. Zeng & S. Schaible & J. C. Yao, 2009. "Hybrid Steepest Descent Methods for Zeros of Nonlinear Operators with Applications to Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 75-91, April.
    20. Ahmed, Md. Tanveer & Kwon, Changhyun, 2012. "Pricing game of online display advertisement publishers," European Journal of Operational Research, Elsevier, vol. 219(2), pages 477-487.

    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:114:y:2002:i:3:d:10.1023_a:1016056327692. 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.