2024-03-29T10:17:53Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/574192022-11-24T20:01:04Zcom_10324_1180com_10324_931com_10324_894col_10324_1375
Strictly dominated strategies in the replicator-mutator dynamics
Izquierdo Millán, Segismundo Samuel
Izquierdo, Luis R.
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.
2022-11-24T12:31:38Z
2022-11-24T12:31:38Z
2022-11-24T12:31:38Z
2011
info:eu-repo/semantics/article
Games, 2011, vol. 2, n. 3, p. 355-364
2073-4336
https://uvadoc.uva.es/handle/10324/57419
10.3390/g2030355
355
3
364
Games
2
2073-4336
eng
https://www.mdpi.com/2073-4336/2/3/355
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/3.0/
© 2011 The Author(s)
Attribution 3.0 Unported
MDPI