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Open AccessArticle

Strictly Dominated Strategies in the Replicator-Mutator Dynamics

1
Department of Industrial Organization, Universidad de Valladolid, Valladolid, 47011 Spain
2
Social Systems Engineering Centre (InSiSoc), Valladolid, 47011 Spain
3
Department of Civil Engineering, Universidad de Burgos, Burgos, 09001 Spain
*
Author to whom correspondence should be addressed.
Games 2011, 2(3), 355-364; https://doi.org/10.3390/g2030355
Received: 27 June 2011 / Revised: 2 September 2011 / Accepted: 2 September 2011 / Published: 14 September 2011
The 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. View Full-Text
Keywords: replicator-mutator; dominated strategies; limit stationary states; limit rest points replicator-mutator; dominated strategies; limit stationary states; limit rest points
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Izquierdo, S.S.; Izquierdo, L.R. Strictly Dominated Strategies in the Replicator-Mutator Dynamics. Games 2011, 2, 355-364.

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