IDEAS home Printed from https://ideas.repec.org/a/ecm/emetrp/v73y2005i1p141-174.html
   My bibliography  Save this article

The Expected Number of Nash Equilibria of a Normal Form Game

Author

Listed:
  • Andrew McLennan

Abstract

Fix finite pure strategy sets S1 , … , Sn , and let S= S1 ×⋯× Sn . In our model of a random game the agents' payoffs are statistically independent, with each agent's payoff uniformly distributed on the unit sphere in R -super-S. For given nonempty T1 ⊂ S1 , … , Tn ⊂ Sn we give a computationally implementable formula for the mean number of Nash equilibria in which each agent i's mixed strategy has support T i . The formula is the product of two expressions. The first is the expected number of totally mixed equilibria for the truncated game obtained by eliminating pure strategies outside the sets T i . The second may be construed as the "probability" that such an equilibrium remains an equilibrium when the strategies in the sets Si ∖ Ti become available. Copyright The Econometric Society 2005.

Suggested Citation

  • Andrew McLennan, 2005. "The Expected Number of Nash Equilibria of a Normal Form Game," Econometrica, Econometric Society, vol. 73(1), pages 141-174, January.
    • Handle: RePEc:ecm:emetrp:v:73:y:2005:i:1:p:141-174
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2005.00567.x
    File Function: link to full text
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative 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:ecm:emetrp:v:73:y:2005:i:1:p:141-174. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    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.