IDEAS home Printed from https://ideas.repec.org/h/wsi/wschap/9789814513449_0005.html
   My bibliography  Save this book chapter

Epistemic Conditions for Nash Equilibrium

In: The Language of Game Theory Putting Epistemics into the Mathematics of Games

Author

Listed:
  • Robert Aumann
  • Adam Brandenburger

Abstract

Sufficient conditions for Nash equilibrium in an n-person game are given in terms of what the players know and believe — about the game, and about each other's rationality, actions, knowledge, and beliefs. Mixed strategies are treated not as conscious randomizations, but as conjectures, on the part of other players, as to what a player will do. Common knowledge plays a smaller role in characterizing Nash equilibrium than had been supposed. When n = 2, mutual knowledge of the payoff functions, of rationality, and of the conjectures implies that the conjectures form a Nash equilibrium. When n ≥ 3 and there is a common prior, mutual knowledge of the payoff functions and of rationality, and common knowledge of the conjectures, imply that the conjectures form a Nash equilibrium. Examples show the results to be tight.

Suggested Citation

  • Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136 World Scientific Publishing Co. Pte. Ltd..
  • Handle: RePEc:wsi:wschap:9789814513449_0005
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/pdf/10.1142/9789814513449_0005
    Download Restriction: Ebook Access is available upon purchase.

    File URL: http://www.worldscientific.com/doi/abs/10.1142/9789814513449_0005
    Download Restriction: Ebook Access is available upon purchase.

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    More about this item

    Keywords

    Game Theory; Epistemic Game Theory; Foundations; Applied Mathematics; Social Neuroscience; Rationalizability; Nash Equilibrium; Probability; Uncertainty;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

    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:wsi:wschap:9789814513449_0005. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tai Tone Lim). General contact details of provider: http://www.worldscientific.com/page/worldscibooks .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.