IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2013y2013i1n952915.html

A Quasi‐Variational Approach for the Dynamic Oligopolistic Market Equilibrium Problem

Author

Listed:
  • Annamaria Barbagallo
  • Paolo Mauro

Abstract

The paper is concerned with the dynamic oligopolistic market equilibrium problem in the realistic case in which we allow the presence of capacity constraints and production excesses and, moreover, we assume that the production function depends not only on the time but also on the equilibrium distribution. As a consequence, we introduce the generalized dynamic Cournot‐Nash principle in the elastic case and prove the equivalence between this equilibrium definition and a suitable evolutionary quasi‐variational inequality. For completeness we make the analysis of existence, regularity, and sensitivity of the solution. In the end, a numerical example is provided.

Suggested Citation

  • Annamaria Barbagallo & Paolo Mauro, 2013. "A Quasi‐Variational Approach for the Dynamic Oligopolistic Market Equilibrium Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:952915
    DOI: 10.1155/2013/952915
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/952915
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/952915?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
    ---><---

    References listed on IDEAS

    as
    1. Nagurney, Anna & Dupuis, Paul & Zhang, Ding, 1994. "A Dynamical Systems Approach for Network Oligopolies and Variational Inequalities," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 28(3), pages 263-283, September.
    2. 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).
    3. Annamaria Barbagallo & Paolo Mauro, 2012. "Time-Dependent Variational Inequality for an Oligopolistic Market Equilibrium Problem with Production and Demand Excesses," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-35, July.
    4. repec:bla:econom:v:36:y:1969:i:141:p:58-68 is not listed on IDEAS
    5. Annamaria Barbagallo & Paolo Mauro, 2012. "Time‐Dependent Variational Inequality for an Oligopolistic Market Equilibrium Problem with Production and Demand Excesses," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    6. Johannes Jahn, 1996. "Introduction to the Theory of Nonlinear Optimization," Springer Books, Springer, edition 0, number 978-3-662-03271-8, October.
    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. 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.
    2. Annamaria Barbagallo & Paolo Mauro, 2012. "Time‐Dependent Variational Inequality for an Oligopolistic Market Equilibrium Problem with Production and Demand Excesses," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Tan Miller & Terry Friesz & Roger Tobin & Changhyun Kwon, 2007. "Reaction Function Based Dynamic Location Modeling in Stackelberg–Nash–Cournot Competition," Networks and Spatial Economics, Springer, vol. 7(1), pages 77-97, March.
    4. 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.
    5. Grechuk, Bogdan, 2023. "Extended gradient of convex function and capital allocation," European Journal of Operational Research, Elsevier, vol. 305(1), pages 429-437.
    6. Anna Nagurney & Dong Li, 2015. "A supply chain network game theory model with product differentiation, outsourcing of production and distribution, and quality and price competition," Annals of Operations Research, Springer, vol. 226(1), pages 479-503, March.
    7. Cojocaru, Monica-Gabriela & Daniele, Patrizia & Nagurney, Anna, 2006. "Double-layered dynamics: A unified theory of projected dynamical systems and evolutionary variational inequalities," European Journal of Operational Research, Elsevier, vol. 175(1), pages 494-507, November.
    8. 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.
    9. Anna Nagurney & Min Yu & Jonas Floden, 2013. "Supply chain network sustainability under competition and frequencies of activities from production to distribution," Computational Management Science, Springer, vol. 10(4), pages 397-422, December.
    10. Rida Laraki & William D. Sudderth, 2004. "The Preservation of Continuity and Lipschitz Continuity by Optimal Reward Operators," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 672-685, August.
    11. Yu, Min & Nagurney, Anna, 2013. "Competitive food supply chain networks with application to fresh produce," European Journal of Operational Research, Elsevier, vol. 224(2), pages 273-282.
    12. Anna Nagurney & Dong Li & Tilman Wolf & Sara Saberi, 2013. "A network economic game theory model of a service-oriented internet with choices and quality competition," Netnomics, Springer, vol. 14(1), pages 1-25, November.
    13. 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.
    14. Anna Nagurney & Ke Ke & Jose Cruz & Kitty Hancock & Frank Southworth, 2002. "Dynamics of Supply Chains: A Multilevel (Logistical–Informational–Financial) Network Perspective," Environment and Planning B, , vol. 29(6), pages 795-818, December.
    15. Patrick Lahr & Axel Niemeyer, 2024. "Extreme Points in Multi-Dimensional Screening," Papers 2412.00649, arXiv.org, revised Oct 2025.
    16. Alberto Del Pia & Robert Weismantel, 2016. "Relaxations of mixed integer sets from lattice-free polyhedra," Annals of Operations Research, Springer, vol. 240(1), pages 95-117, May.
    17. Giovanna Redaelli, 1998. "Convergence problems in stochastic programming models with probabilistic constraints," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 21(1), pages 147-164, June.
    18. Chuang-Liang Zhang, 2026. "Levitin-Polyak Well-Posedness and Stability in Multiobjective Interval-Valued Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 209(1), pages 1-20, April.
    19. Dong Li & Anna Nagurney, 2017. "Supply chain performance assessment and supplier and component importance identification in a general competitive multitiered supply chain network model," Journal of Global Optimization, Springer, vol. 67(1), pages 223-250, January.
    20. Anna Nagurney & Dong Li, 2014. "Equilibria and dynamics of supply chain network competition with information asymmetry in quality and minimum quality standards," Computational Management Science, Springer, vol. 11(3), pages 285-315, July.

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnlaaa:v:2013:y:2013:i:1:n:952915. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.