Advanced Search
MyIDEAS: Login

Distribution of pure Nash equilibria in n-person games with random best replies

Contents:

Author Info

  • Klaus Kultti
  • Hannu Salonen
  • Hannu Vartiainen

    ()

Abstract

In this paper we study the number of pure strategy Nash equilibria in large finite n-player games. A distinguishing feature of our study is that we allow general - potentially multivalued - best reply correspondences. Given the number K of pure strategies to each player, we assign to each player a distribution over the number of his pure best replies against each strategy profile of his opponents. If the means of these distributions have a limit (mu)i for each player i as the number K of pure strategies goes to infinity, then the limit number of pure equilibria is Poisson distributed with a mean equal to the product of the limit means (mu)i. In the special case when all best reply mappings are equally likely, the probability of at least one pure Nash equilibrium approaches one and the expected number of pure Nash equilibria goes to infinity.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.ace-economics.fi/kuvat/dp71.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Aboa Centre for Economics in its series Discussion Papers with number 71.

as in new window
Length: 21
Date of creation: Dec 2011
Date of revision:
Handle: RePEc:tkk:dpaper:dp71

Contact details of provider:
Postal: Rehtorinpellonkatu 3, FIN-20500 TURKU
Phone: +358 2 333 51
Web page: http://ace-economics.fi
More information through EDIRC

Related research

Keywords: random games; pure Nash equilibria; n players;

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Sophie Bade & Guillaume Haeringer & Ludovic Renou, 2005. "More Strategies, More Nash Equilibria," School of Economics Working Papers 2005-01, University of Adelaide, School of Economics.
  2. Andrew McLennan, 2005. "The Expected Number of Nash Equilibria of a Normal Form Game," Econometrica, Econometric Society, vol. 73(1), pages 141-174, 01.
  3. Powers, Imelda Yeung, 1990. "Limiting Distributions of the Number of Pure Strategy Nash Equilibria in N-Person Games," International Journal of Game Theory, Springer, vol. 19(3), pages 277-86.
  4. Stanford, William, 1997. "On the distribution of pure strategy equilibria in finite games with vector payoffs," Mathematical Social Sciences, Elsevier, vol. 33(2), pages 115-127, April.
  5. McLennan, Andrew & Berg, Johannes, 2005. "Asymptotic expected number of Nash equilibria of two-player normal form games," Games and Economic Behavior, Elsevier, vol. 51(2), pages 264-295, May.
Full references (including those not matched with items on IDEAS)

Citations

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:tkk:dpaper:dp71. 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: (Aleksandra Maslowska).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.