Strictly Dominated Strategies in the Replicator-Mutator Dynamics
AbstractThe replicator-mutator dynamics is a set of differential equations frequently used in biological and socioeconomic contexts to model evolutionary processes subject to mutation, error or experimentation. The replicator-mutator dynamics generalizes the widely used replicator dynamics, which appears in this framework as the extreme case where replication is perfectly precise. This paper studies the influence of strictly dominated strategies on the location of the rest points of the replicator-mutator dynamics, at the limit where the mutation terms become arbitrarily small. It can be proved that such limit rest points for small mutation are Nash equilibria, so strictly dominated strategies do not occur at limit stationary points. However, we show through a simple case how strictly dominated strategies can have an influence on the location of the limit rest points for small mutation. Consequently, the characterization of the limit rest points of the replicator-mutator dynamics cannot in general proceed safely by readily eliminating strictly dominated strategies.
Download InfoIf 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.
Bibliographic InfoArticle provided by MDPI, Open Access Journal in its journal Games.
Volume (Year): 2 (2011)
Issue (Month): 3 (September)
Contact details of provider:
Web page: http://www.mdpi.com/
replicator-mutator; dominated strategies; limit stationary states; limit rest points;
Find related papers by JEL classification:
- C - Mathematical and Quantitative Methods
- C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
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.:
- Samuelson, L. & Zhang, J., 1990.
"Evolutionary Stability In Symmetric Games,"
90-24, Wisconsin Madison - Social Systems.
- Hofbauer, Josef & Weibull, Jorgen W., 1996.
"Evolutionary Selection against Dominated Strategies,"
Journal of Economic Theory,
Elsevier, vol. 71(2), pages 558-573, November.
- Hofbauer, Josef & Weibull, Jîrgen W., 1995. "Evolutionary selection against dominated strategies," CEPREMAP Working Papers (Couverture Orange) 9506, CEPREMAP.
- J. Hofbauer & J. Weibull, 2010. "Evolutionary Selection against dominated strategies," Levine's Working Paper Archive 444, David K. Levine.
- Hofbauer, Josef & Weibull, Jörgen W., 1995. "Evolutionary Selection against Dominated Strategies," Working Paper Series 433, Research Institute of Industrial Economics.
- Binmore, Ken & Samuelson, Larry, 1999. "Evolutionary Drift and Equilibrium Selection," Review of Economic Studies, Wiley Blackwell, vol. 66(2), pages 363-93, April.
- Sandholm, William H. & Hofbauer, Josef, 2011. "Survival of dominated strategies under evolutionary dynamics," Theoretical Economics, Econometric Society, vol. 6(3), September.
- Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
- Situngkir, Hokky & Prasetyo, Yanu Endar, 2012. "On social and economic spheres: an observation of the “gantangan” Indonesian tradition," MPRA Paper 39671, University Library of Munich, Germany.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (XML Conversion Team).
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.