Stability of evolutionarily stable strategies in discrete replicator dynamics with time delay

Journal of Theoretical Biology
Jan Alboszta, Jacek MieKisz

Abstract

We construct two models of discrete-time replicator dynamics with time delay. In the social-type model, players imitate opponents taking into account average payoffs of games played some units of time ago. In the biological-type model, new players are born from parents who played in the past. We consider two-player games with two strategies and a unique mixed evolutionarily stable strategy. We show that in the first type of dynamics, it is asymptotically stable for small time delays and becomes unstable for big ones when the population oscillates around its stationary state. In the second type of dynamics, however, evolutionarily stable strategy is asymptotically stable for any size of a time delay.

References

Sep 1, 1974·Journal of Theoretical Biology·J M Smith
Jul 7, 1997·Journal of Theoretical Biology·T Yi, W Zuwang
Jul 1, 1982·Journal of the History of Biology·C U Smith

❮ Previous
Next ❯

Citations

Jan 7, 2011·Bulletin of Mathematical Biology·Jacek MiękiszUrszula Foryś
Jan 24, 2012·Journal of Theoretical Biology·Ryota Iijima
Jan 17, 2012·Journal of Theoretical Biology·João A MoreiraJorge M Pacheco
Nov 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·James Burridge
Nov 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tobias Brett, Tobias Galla
May 20, 2020·Physical Review. E·Sourabh MittalSagar Chakraborty
Feb 20, 2021·Physical Review. E·Jacek Miękisz, Marek Bodnar

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Wen-Xu WangBing-Hong Wang
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Zhaojin XuLianzhong Zhang
Proceedings of the National Academy of Sciences of the United States of America
Dirk Helbing, Wenjian Yu
Journal of Theoretical Biology
Mendeli H VainsteinJeferson J Arenzon
© 2021 Meta ULC. All rights reserved