Advanced Search
MyIDEAS: Login to save this paper or follow this series

Evolutionarily Stable Strategies of Random Games, and the Vertices of Random Polygons

Contents:

Author Info

  • Sergiu Hart

    ()

  • Yosef Rinott

    ()

  • Benjamin Weiss

    ()

Abstract

An evolutionarily stable strategy (ESS) is an equilibrium strategy that is immune to invasions by rare alternative ("mutant") strategies. Unlike Nash equilibria, ESS do not always exist in finite games. In this paper, we address the question of what happens when the size of the game increases: does an ESS exist for "almost every large" game? Letting the entries in the n x n game matrix be randomly chosen according to an underlying distribution F, we study the number of ESS with support of size 2. In particular, we show that, as n goes to infinity, the probability of having such an ESS: (i) converges to 1 for distributions F with "exponential and faster decreasing tails" (e.g., uniform, normal, exponential); and (ii) it converges to 1 - 1/sqrt(e) for distributions F with "slower than exponential decreasing tails" (e.g., lognormal, Pareto, Cauchy). Our results also imply that the expected number of vertices of the convex hull of n random points in the plane converges to infinity for the distributions in (i), and to 4 for the distributions in (ii).

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.ma.huji.ac.il/hart/abs/ess.html
Download Restriction: no

Bibliographic Info

Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp445.

as in new window
Length:
Date of creation: Jan 2007
Date of revision:
Publication status: Published in Annals of Applied Probability 18 (2008), 1, 259-287
Handle: RePEc:huj:dispap:dp445

Contact details of provider:
Postal: Feldman Building - Givat Ram - 91904 Jerusalem
Phone: +972-2-6584135
Fax: +972-2-6513681
Email:
Web page: http://www.ratio.huji.ac.il/
More information through EDIRC

Related research

Keywords:

Other versions of this item:

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. Bagnoli, M. & Bergstrom, T., 1989. "Log-Concave Probability And Its Applications," Papers 89-23, Michigan - Center for Research on Economic & Social Theory.
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:huj:dispap:dp445. 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: (Ilan Nehama).

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.