https://hal.inria.fr/hal-02892186Albrecht, AmieAmieAlbrechtUniversity of South Australia [Adelaide]Avrachenkov, KonstantinKonstantinAvrachenkovNEO - Network Engineering and Operations - CRISAM - Inria Sophia Antipolis - MÃ©diterranÃ©e - Inria - Institut National de Recherche en Informatique et en AutomatiqueHowlett, PhilPhilHowlettUniversity of South Australia [Adelaide]Verma, GeetikaGeetikaVermaUniversity of South Australia [Adelaide]Evolutionary dynamics in discrete time for the perturbed positive definite replicator equationHAL CCSD2020Replicator equationdiscrete-timerandom perturbations[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-PR] Mathematics [math]/Probability [math.PR][INFO.INFO-GT] Computer Science [cs]/Computer Science and Game Theory [cs.GT]Avrachenkov, Konstantin2020-07-07 13:36:002023-03-15 08:58:092020-07-07 15:08:03enJournal articlesapplication/pdf1The 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.