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Izquierdo, Segismundo S. Izquierdo Millán, Luis Rodrigo 2015-08-25T10:18:27Z 2015-08-25T10:18:27Z 2011-09 2073-4336 http://hdl.handle.net/10259/3811 10.3390/g2030355 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 JCyL (GREX251-2009 and VA006B09), Ministry of Science and Innovation (TIN2008-06464-C03-02, DPI2010-16920 and CSD2010-00034), Ministry of Education (grant JC2009-00263) application/pdf eng MDPI Games (2011), v.2, n.4, p.355-364 http://www.mdpi.com/2073-4336/2/3/355 info:eu-repo/grantAgreement/JCyL/GREX251-2009 info:eu-repo/grantAgreement/JCyL/VA006B09 info:eu-repo/grantAgreement/MICINN/TIN2008-06464-C03-02 info:eu-repo/grantAgreement/MICINN/DPI2010-16920 info:eu-repo/grantAgreement/MICINN/CSD2010-00034 Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess Replicator-mutator Dominated strategies Limit stationary states Limit rest points Industrial management Gestión de empresas Strictly Dominated Strategies in the Replicator-Mutator Dynamics info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion