IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v196y2023i3d10.1007_s10957-023-02164-w.html
   My bibliography  Save this article

Aggregative Variational Inequalities

Author

Listed:
  • Peter Hubert Mathieu Mouche

    (Wageningen University
    Corvinus Institute of Advanced Studies)

  • Ferenc Szidarovszky

    (Corvinus University of Budapest)

Abstract

We enrich the theory of variational inequalities in the case of an aggregative structure by implementing recent results obtained by using the Selten–Szidarovszky technique. We derive existence, semi-uniqueness and uniqueness results for solutions and provide a computational method. As an application we derive very powerful practical equilibrium results for Nash equilibria of sum-aggregative games and illustrate with Cournot oligopolies.

Suggested Citation

  • Peter Hubert Mathieu Mouche & Ferenc Szidarovszky, 2023. "Aggregative Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 1056-1092, March.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:3:d:10.1007_s10957-023-02164-w
    DOI: 10.1007/s10957-023-02164-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-023-02164-w
    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/s10957-023-02164-w?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. Szidarovszky, F & Yakowitz, S, 1977. "A New Proof of the Existence and Uniqueness of the Cournot Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(3), pages 787-789, October.
    2. Pierre von Mouche & Federico Quartieri (ed.), 2016. "Equilibrium Theory for Cournot Oligopolies and Related Games," Springer Series in Game Theory, Springer, number 978-3-319-29254-0, March.
    3. Gérard Gaudet & Stephen W. Salant, 1991. "Uniqueness of Cournot Equilibrium: New Results From Old Methods," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 399-404.
    4. Okuguchi, Koji, 1983. "The cournot oligopoly and competitive equilibria as solutions to non-linear complementarity problems," Economics Letters, Elsevier, vol. 12(2), pages 127-133.
    5. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, December.
    6. Muhammad Aslam Noor & Khalida Inayat Noor & Bandar Mohsen & Michael Th. Rassias & Andrei Raigorodskii, 2022. "General Preinvex Functions and Variational-Like Inequalities," Springer Optimization and Its Applications, in: Nicholas J. Daras & Themistocles M. Rassias (ed.), Approximation and Computation in Science and Engineering, pages 643-666, Springer.
    7. Richard Cornes & Takashi Sato, 2016. "Existence and Uniqueness of Nash Equilibrium in Aggregative Games: An Expository Treatment," Springer Series in Game Theory, in: Pierre von Mouche & Federico Quartieri (ed.), Equilibrium Theory for Cournot Oligopolies and Related Games, pages 47-61, Springer.
    8. Charles D. Kolstad & Lars Mathiesen, 1987. "Necessary and Sufficient Conditions for Uniqueness of a Cournot Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(4), pages 681-690.
    9. Shumei Hirai & Ferenc Szidarovszky, 2013. "Existence And Uniqueness Of Equilibrium In Asymmetric Contests With Endogenous Prizes," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-9.
    10. Szidarovszky, Ferenc & Okuguchi, Koji, 1997. "On the Existence and Uniqueness of Pure Nash Equilibrium in Rent-Seeking Games," Games and Economic Behavior, Elsevier, vol. 18(1), pages 135-140, 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. Koji Okuguchi & Takeshi Yamazaki, 2018. "Existence of Unique Equilibrium in Cournot Mixed Oligopoly," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-13, September.
    2. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2013. "The empirical content of Cournot competition," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1552-1581.
    3. Magnus Hoffmann & Grégoire Rota‐Graziosi, 2020. "Endogenous timing in the presence of non‐monotonicities," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(1), pages 359-402, February.
    4. Alex Dickson & Roger Hartley, 2013. "Bilateral oligopoly and quantity competition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(3), pages 979-1004, April.
    5. Christian Ewerhart & Federico Quartieri, 2020. "Unique equilibrium in contests with incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(1), pages 243-271, July.
    6. Ewerhart, Christian, 2014. "Cournot games with biconcave demand," Games and Economic Behavior, Elsevier, vol. 85(C), pages 37-47.
    7. Van Long, Ngo & Soubeyran, Antoine, 2000. "Existence and uniqueness of Cournot equilibrium: a contraction mapping approach," Economics Letters, Elsevier, vol. 67(3), pages 345-348, June.
    8. Simon Cowan, 2023. "Welfare-increasing monopolization," Economics Series Working Papers 1006, University of Oxford, Department of Economics.
    9. Martin Peitz & Markus Reisinger, 2014. "Indirect Taxation in Vertical Oligopoly," Journal of Industrial Economics, Wiley Blackwell, vol. 62(4), pages 709-755, December.
    10. Hogan Seamus D, 2011. "A New Existence and Uniqueness Theorem for Continuous Games," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-28, August.
    11. Pierre Fleckinger, 2007. "Collective Reputation and Market Structure: Regulating the Quality vs Quantity Trade-of," Working Papers hal-00243080, HAL.
    12. Walter Ferrarese, 2022. "Equilibrium effort in games with homogeneous production functions and homogeneous valuation," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(2), pages 195-212, June.
    13. R Cornes & R Hartley, 2005. "The Geometry of Aggregative Games," Economics Discussion Paper Series 0514, Economics, The University of Manchester.
    14. Yi, Sang-Seung, 1997. "On the existence of a unique correlated equilibrium in Cournot oligopoly," Economics Letters, Elsevier, vol. 54(3), pages 235-239, July.
    15. Awi Federgruen & Ming Hu, 2019. "Stability in a general oligopoly model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(1), pages 90-102, February.
    16. Chaiken, Benjamin & Duggan, Joseph E. & Sioshansi, Ramteen, 2021. "Paid to produce absolutely nothing? A Nash-Cournot analysis of a proposed power purchase agreement," Energy Policy, Elsevier, vol. 156(C).
    17. Dmitry B. Rokhlin & Anatoly Usov, 2017. "Asymptotic efficiency of the proportional compensation scheme for a large number of producers," Papers 1701.06038, arXiv.org.
    18. Alex Dickson & Roger Hartley, 2006. "On a foundation for Cournot equilibrium," Economics Discussion Paper Series 0638, Economics, The University of Manchester.
    19. Long, Ngo Van & Soubeyran, Antoine, 2001. "Cost Manipulation Games in Oligopoly, with Costs of Manipulating," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(2), pages 505-533, May.
    20. Krishnendu Ghosh Dastidar & Sugata Marjit, 2022. "Market size, entry costs and free entry Cournot equilibrium," Journal of Economics, Springer, vol. 136(2), pages 97-114, July.

    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:196:y:2023:i:3:d:10.1007_s10957-023-02164-w. 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.