Imitation dynamics with time delay.
J Theor Biol
; 420: 8-11, 2017 05 07.
Article
em En
| MEDLINE
| ID: mdl-28257762
ABSTRACT
Based on the classic imitation dynamics (Hofbauer and Sigmund, 1998, Evolutionary Games and Population Dynamics, Cambridge University Press), the imitation dynamics with time delay is investigated, where the probability that an individual will imitate its opponent's own strategy is assumed to depend on the comparison between the past expected payoff of this individual's own strategy and the past expected payoff of its opponent's own strategy, i.e. there is a time delay effect. For the two-phenotype model, we show that if the system has an interior equilibrium and this interior equilibrium is stable when there is no time delay, then there must be a critical value of time delay such that the system tends to a stable periodic solution when the time delay is larger than the critical value. On the other hand, for three-phenotype (rock-scissors-paper) model, the numerical analysis shows that for the stable periodic solution induced by the time delay, the amplitude and the period will increase with the increase of the time delay. These results should help to understand the evolution of behavior based on the imitation dynamics with time delay.
Palavras-chave
Texto completo:
1
Coleções:
01-internacional
Base de dados:
MEDLINE
Assunto principal:
Comportamento
/
Dinâmica Populacional
/
Evolução Biológica
/
Teoria dos Jogos
Tipo de estudo:
Prognostic_studies
Limite:
Humans
Idioma:
En
Revista:
J Theor Biol
Ano de publicação:
2017
Tipo de documento:
Article
País de afiliação:
China