IDEAS home Printed from https://ideas.repec.org/a/oup/restud/v67y2000i1p17-45..html
   My bibliography  Save this article

Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution

Author

Listed:
  • Glenn Ellison

Abstract

The paper examines the behaviour of "evolutionary" models with ɛ-noise like those which have been used recently to discuss the evolution of social conventions. The paper is built around two main observations: that the "long run stochastic stability" of a convention is related to the speed with which evolution toward and away from the convention occurs, and that evolution is more rapid (and hence more powerful) when it may proceed via a series of small steps between intermediate steady states. The formal analysis uses two new measures, the radius and modified coradius, to characterize the long run stochastically stable set of an evolutionary model and to bound the speed with which evolutionary change occurs. Though not universally powerful, the result can be used to make many previous analyses more transparent and extends them by providing results on waiting times. A number of applications are also discussed. The selection of the risk dominant equilibrium in 2 × 2 games is generalized to the selection of ½-dominant equilibria in arbitrary games. Other applications involve two-dimensional local interaction and cycles as long run stochastically stable sets.

Suggested Citation

  • Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Oxford University Press, vol. 67(1), pages 17-45.
  • Handle: RePEc:oup:restud:v:67:y:2000:i:1:p:17-45.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/1467-937X.00119
    Download Restriction: Access to full text is restricted to subscribers.

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

    More about this item

    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:oup:restud:v:67:y:2000:i:1:p:17-45.. 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: (Oxford University Press) or (Christopher F. Baum). General contact details of provider: .

    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.