IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v112y2002i2d10.1023_a1013658023971.html
   My bibliography  Save this article

On the Tikhonov Well-Posedness of Concave Games and Cournot Oligopoly Games

Author

Listed:
  • M. Margiocco

    (University of Genova)

  • F. Patrone

    (University of Genova)

  • L. Pusillo

    (University of Genova)

Abstract

The purpose of this paper is to investigate whether theorems known to guarantee the existence and uniqueness of Nash equilibria, provide also sufficient conditions for the Tikhonov well-posedness (T-wp). We consider several hypotheses that ensure the existence and uniqueness of a Nash equilibrium (NE), such as strong positivity of the Jacobian of the utility function derivatives (Ref. 1), pseudoconcavity, and strict diagonal dominance of the Jacobian of the best reply functions in implicit form (Ref. 2). The aforesaid assumptions imply the existence and uniqueness of NE. We show that the hypotheses in Ref. 2 guarantee also the T-wp property of the Nash equilibrium. As far as the hypotheses in Ref. 1 are concerned, the result is true for quadratic games and zero-sum games. A standard way to prove the T-wp property is to show that the sets of ∈-equilibria are compact. This last approach is used to demonstrate directly the T-wp property for the Cournot oligopoly model given in Ref. 3. The compactness of ∈-equilibria is related also to the condition that the best reply surfaces do not approach each other near infinity.

Suggested Citation

  • M. Margiocco & F. Patrone & L. Pusillo, 2002. "On the Tikhonov Well-Posedness of Concave Games and Cournot Oligopoly Games," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 361-379, February.
    • Handle: RePEc:spr:joptap:v:112:y:2002:i:2:d:10.1023_a:1013658023971
    DOI: 10.1023/A:1013658023971
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1013658023971
    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:1013658023971?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. Watts, Alison, 1996. "On the Uniqueness of Equilibrium in Cournot Oligopoly and Other Games," Games and Economic Behavior, Elsevier, vol. 13(2), pages 269-285, April.
    2. 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.
    3. M. Margiocco & F. Patrone & L. Pusillo Chicco, 1999. "Metric Characterizations of Tikhonov Well-Posedness in Value," Journal of Optimization Theory and Applications, Springer, vol. 100(2), pages 377-387, February.
    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. San-hua Wang & Nan-jing Huang & Donal O’Regan, 2013. "Well-posedness for generalized quasi-variational inclusion problems and for optimization problems with constraints," Journal of Global Optimization, Springer, vol. 55(1), pages 189-208, January.
    2. Yi-bin Xiao & Nan-jing Huang, 2011. "Well-posedness for a Class of Variational–Hemivariational Inequalities with Perturbations," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 33-51, October.
    3. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    4. Fang, Ya-Ping & Huang, Nan-Jing & Yao, Jen-Chih, 2010. "Well-posedness by perturbations of mixed variational inequalities in Banach spaces," European Journal of Operational Research, Elsevier, vol. 201(3), pages 682-692, March.

    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. Ewerhart, Christian, 2014. "Cournot games with biconcave demand," Games and Economic Behavior, Elsevier, vol. 85(C), pages 37-47.
    2. Watts, Alison, 1998. "Insolvency and Division of Cleanup Costs," International Review of Law and Economics, Elsevier, vol. 18(1), pages 61-76, March.
    3. R Cornes & R Hartley, 2005. "The Geometry of Aggregative Games," Economics Discussion Paper Series 0514, Economics, The University of Manchester.
    4. Alex Dickson & Roger Hartley, 2006. "On a foundation for Cournot equilibrium," Economics Discussion Paper Series 0638, Economics, The University of Manchester.
    5. 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.
    6. Matt Van Essen, 2013. "Regulating the Anticommons: Insights from Public‐Expenditure Theory," Southern Economic Journal, John Wiley & Sons, vol. 80(2), pages 523-539, October.
    7. Martimort, David & Stole, Lars, 2012. "Representing equilibrium aggregates in aggregate games with applications to common agency," Games and Economic Behavior, Elsevier, vol. 76(2), pages 753-772.
    8. Attila Tasnádi, 2010. "Quantity-setting games with a dominant firm," Journal of Economics, Springer, vol. 99(3), pages 251-266, April.
    9. Cars H. Hommes & Marius I. Ochea & Jan Tuinstra, 2018. "Evolutionary Competition Between Adjustment Processes in Cournot Oligopoly: Instability and Complex Dynamics," Dynamic Games and Applications, Springer, vol. 8(4), pages 822-843, December.
    10. Hervé Moulin & Alison Watts, 1996. "Two versions of the tragedy of the commons," Review of Economic Design, Springer;Society for Economic Design, vol. 2(1), pages 399-421, December.
    11. Quartieri, Federico, 2017. "Are vessel sharing agreements pro-competitive?," Economics of Transportation, Elsevier, vol. 11, pages 33-48.
    12. Jan Zouhar & Martina Zouharova, 2020. "Stackelberg versus Cournot duopoly with asymmetric costs: primary markups, entry deterrence, and a comparison of social welfare and industry profits," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 89-96, April.
    13. Domenico Buccella & Luciano Fanti & Luca Gori, 2024. "Competitive wages and tax evasion in a Cournot duopoly," Theory and Decision, Springer, vol. 97(3), pages 585-594, November.
    14. Watts, Alison, 2002. "Uniqueness of equilibrium in cost sharing games," Journal of Mathematical Economics, Elsevier, vol. 37(1), pages 47-70, February.
    15. Kumar, Rajnish, 2013. "Secure implementation in production economies," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 372-378.
    16. 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.
    17. Fabio Manenti & Ernesto Somma, 2008. "One-Way Compatibility, Two-Way Compatibility and Entry in Network Industries," International Journal of the Economics of Business, Taylor & Francis Journals, vol. 15(3), pages 301-322.
    18. Einy, Ezra & Haimanko, Ori & Moreno, Diego & Shitovitz, Benyamin, 2010. "On the existence of Bayesian Cournot equilibrium," Games and Economic Behavior, Elsevier, vol. 68(1), pages 77-94, January.
    19. Collie, David, 1992. "International Trade and Cournot Equilibrium: Existence, Uniqueness and Comparative Statics," Bulletin of Economic Research, Wiley Blackwell, vol. 44(1), pages 55-66, January.
    20. Hélène Le Cadre, 2019. "On the efficiency of local electricity markets under decentralized and centralized designs: a multi-leader Stackelberg game analysis," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(4), pages 953-984, December.

    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:112:y:2002:i:2:d:10.1023_a:1013658023971. 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.