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Evolutionary dynamics in discrete time for the perturbed positive definite replicator equation

Abstract : The population dynamics for the replicator equation are well studied in continuous time but there is less work that explicitly considers the evolution in discrete time. The discrete-time dynamics can often be justified indirectly, by establishing the relevant evolutionary dynamics for the corresponding continuous-time system, and then appealing to an appropriate approximation property. In this paper we study the discrete-time system directly, and establish basic stability results for the evolution of a population defined by a positive definite system matrix, where the population is disrupted by random perturbations to the genotype distribution either through migration or mutation, in each successive generation.
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https://hal.inria.fr/hal-02892186
Contributor : Konstantin Avrachenkov <>
Submitted on : Tuesday, July 7, 2020 - 1:36:00 PM
Last modification on : Tuesday, November 17, 2020 - 12:10:13 PM
Long-term archiving on: : Friday, November 27, 2020 - 1:25:00 PM

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  • HAL Id : hal-02892186, version 1

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Amie Albrecht, Konstantin Avrachenkov, Phil Howlett, Geetika Verma. Evolutionary dynamics in discrete time for the perturbed positive definite replicator equation. The ANZIAM Journal, Cambridge University Press, In press. ⟨hal-02892186⟩

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