EVOLUTIONARY DYNAMICS IN DISCRETE TIME FOR THE PERTURBED POSITIVE DEFINITE REPLICATOR EQUATION

The population dynamics for the replicator equation has been 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 corre...

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Bibliographic Details
Published in:The ANZIAM journal Vol. 62; no. 2; pp. 148 - 184
Main Authors: ALBRECHT, AMIE, AVRACHENKOV, KONSTANTIN, HOWLETT, PHIL, VERMA, GEETIKA
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01.04.2020
Subjects:
Computer Science
Computer Science and Game Theory
Continuous time systems
Discrete time systems
Dynamical Systems
Dynamics
Evolution
Genotype & phenotype
Mathematical analysis
Mathematics
Matrices (mathematics)
Mutation
Perturbation
Population
Probability
discrete time
93C55
93C10
92D25
93E15
replicator equation
93C73
random perturbations
Replicator equation
discrete-time
ISSN:1446-1811, 1446-8735
Online Access:Get full text
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Summary:The population dynamics for the replicator equation has been 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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ISSN:1446-1811
1446-8735
DOI:10.1017/S1446181120000140