IDEAS home Printed from https://ideas.repec.org/h/spr/spschp/978-3-319-29254-0_5.html
   My bibliography  Save this book chapter

Existence and Uniqueness of Nash Equilibrium in Aggregative Games: An Expository Treatment

In: Equilibrium Theory for Cournot Oligopolies and Related Games

Author

Listed:
  • Richard Cornes
  • Takashi Sato

    (Shimonoseki City University)

Abstract

In this study, we present an elementary treatment of Cournot’s oligopolistic competition model in which an industry’s demand function has a constant elasticity and technology has a convex cost function. Our treatment uses the ‘share function’, which exploits the aggregative structure of the resulting game. In this setting, the best response functions are not monotonic, ruling out the use of techniques previously applied to analyze submodular and supermodular games. Share functions, which model each firm’s most preferred share of total output as a proportion of total output, allow for a direct and transparent method to derive the properties of a Nash equilibrium. To illustrate this, we establish the existence of a unique equilibrium and examine its response to exogenous shocks.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:spschp:978-3-319-29254-0_5
    DOI: 10.1007/978-3-319-29254-0_5
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Peter Hubert Mathieu Mouche & Ferenc Szidarovszky, 2023. "Aggregative Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 1056-1092, March.
    2. Dmitry B. Rokhlin & Anatoly Usov, 2017. "Asymptotic efficiency of the proportional compensation scheme for a large number of producers," Papers 1701.06038, arXiv.org.

    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:spschp:978-3-319-29254-0_5. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.