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Dynamic Games and Applications

Erschienen in:

29.07.2017

Discrete and Continuous Distributed Delays in Replicator Dynamics

verfasst von: Nesrine Ben-Khalifa, Rachid El-Azouzi, Yezekael Hayel

Erschienen in: Dynamic Games and Applications | Ausgabe 4/2018

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Abstract

In this paper, we study evolutionary games and we examine the stability of the evolutionarily stable strategy (ESS) in the continuous-time replicator dynamics with distributed time delays. In many examples, the interactions between individuals take place instantaneously, but their impacts are not immediate and take a certain amount of time which is usually random. In this paper, we study the consequences of distributed delays on the stability of the replicator dynamics. The main results are that (i) under the exponential delay distribution, the ESS is asymptotically stable for any value of the rate parameter; (ii) the necessary and sufficient conditions for the asymptotic stability of the ESS under uniform and Erlang distributions; and (iii) for the discrete distributed delays, we derive a necessary and sufficient delay-independent stability conditions. We illustrate our results with numerical examples from the Hawk–Dove game.

Vorheriger Artikel Reach-Avoid Differential Games with Targets and Obstacles Depending on Controls

Nächster Artikel An Evolutionary Analysis of Growth and Fluctuations with Negative Externalities

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Titel: Discrete and Continuous Distributed Delays in Replicator Dynamics
verfasst von: Nesrine Ben-Khalifa
Rachid El-Azouzi
Yezekael Hayel
Publikationsdatum: 29.07.2017
Verlag: Springer US
Erschienen in: Dynamic Games and Applications / Ausgabe 4/2018
Print ISSN: 2153-0785
Elektronische ISSN: 2153-0793
DOI: https://doi.org/10.1007/s13235-017-0225-7

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