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Aggregative Variational Inequalities

Author

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  • 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
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    References listed on IDEAS

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    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, June.
    3. Gérard Gaudet & Stephen W. Salant, 1991. "Uniqueness of Cournot Equilibrium: New Results From Old Methods," The Review of Economic Studies, Review of Economic Studies Ltd, 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, April.
    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.
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    1. von Mouche, Pierre & Szidarovszky, Ferenc, 2024. "Aggregative games with discontinuous payoffs at the origin," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 77-84.

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