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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
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    References listed on IDEAS

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    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.
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    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. 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.
    3. Nils Langenberg, 2012. "Interior point methods for equilibrium problems," Computational Optimization and Applications, Springer, vol. 53(2), pages 453-483, October.
    4. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    5. Elodie Adida & Georgia Perakis, 2010. "Dynamic Pricing and Inventory Control: Uncertainty and Competition," Operations Research, INFORMS, vol. 58(2), pages 289-302, April.
    6. Szilárd Nagy, 2013. "Stackelberg equilibria via variational inequalities and projections," Journal of Global Optimization, Springer, vol. 57(3), pages 821-828, November.
    7. 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.
    8. 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.
    9. 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.
    10. Jacquot, Paulin & Wan, Cheng, 2022. "Nonatomic aggregative games with infinitely many types," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1149-1165.
    11. 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.
    12. 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.
    13. 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).
    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.

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