Dynamic Stability in Perturbed Games
The effect that exogenous mistakes, made by players choosing their strategies, have on the dynamic stability for the replicator dynamic is analyzed for both asymmetric and symmetric normal form games. Through these perturbed games, the dynamic solution concept of limit asymptotic stability is motivated by insisting that such solutions be asymptotically stable for all sufficiently small perturbations (a robustness property). Limit asymptotic stability is then a refinement of the Nash equilibrium. For asymmetric normal form games, it is shown that a strategy pair is limit asymptotically stable if and only if it is a pure strategy pair that weakly dominates alternative best replies. For symmetric normal form games, all evolutionarily stable strategies (ESS's), whether pure or mixed, are limit asymptotically stable. Here, conditions are established for limit asymptotic stability of completely mixed (i.e. interior) strategies as well as strategies on the boundary. Consistency with solutions found by backwards and/or forwards induction is shown for elementary extensive form games. Limit asymptotically stable sets are introduced that generalize other set-valued solution concepts such as the ``strict equilibrium set'' and the ``ES set'' for asymmetric and symmetric normal form games respectively.
|Date of creation:||Jul 1995|
|Contact details of provider:|| Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany|
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de
When requesting a correction, please mention this item's handle: RePEc:bon:bonsfb:321. 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: (BGSE Office)
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.