The Stability of Two-Community Replicator Dynamics with Discrete Multi-Delays

Jinxiu Pi, Hui Yang, Yadong Shu, Chongyi Zhong and Guanghui Yang
Additional contact information
Jinxiu Pi: School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
Hui Yang: School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
Yadong Shu: School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
Chongyi Zhong: School of Mathematics and Big data, Guizhou Education University, Guiyang 550018, China
Guanghui Yang: School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China

Mathematics, 2020, vol. 8, issue 12, 1-17

Abstract: This article investigates the stability of evolutionarily stable strategy in replicator dynamics of two-community with multi-delays. In the real environment, players interact simultaneously while the return of their choices may not be observed immediately, which implies one or more time-delays exists. In addition to using the method of classic characteristic equations, we also apply linear matrix inequality (i.e., LMI) to discuss the stability of the mixed evolutionarily stable strategy in replicator dynamics of two-community with multi-delays. We derive a delay-dependent stability and a delay-independent stability sufficient conditions of the evolutionarily stable strategy in the two-community replicator dynamics with two delays, and manage to extend the sufficient condition to n time delays. Lastly, numerical trials of the Hawk–Dove game are given to verify the effectiveness of the theoretical consequences.

Keywords: replicator dynamics; asymptotical stability; two-community; discrete multi-delays (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/12/2120/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/12/2120/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:12:p:2120-:d:451840

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().