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Strictly Dominated Strategies in the Replicator-Mutator Dynamics
Department of Industrial Organization, Universidad de Valladolid, Valladolid, 47011 Spain
Social Systems Engineering Centre (InSiSoc), Valladolid, 47011 Spain
Department of Civil Engineering, Universidad de Burgos, Burgos, 09001 Spain
* Author to whom correspondence should be addressed.
Received: 27 June 2011; in revised form: 2 September 2011 / Accepted: 2 September 2011 / Published: 14 September 2011
Abstract: 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.
Keywords: 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.
Izquierdo SS, Izquierdo LR. Strictly Dominated Strategies in the Replicator-Mutator Dynamics. Games. 2011; 2(3):355-364.
Izquierdo, Segismundo S.; Izquierdo, Luis R. 2011. "Strictly Dominated Strategies in the Replicator-Mutator Dynamics." Games 2, no. 3: 355-364.