Stability of Replicator Dynamics with Bounded Continuously Distributed Time Delay

Chongyi Zhong, Hui Yang, Zixin Liu and Juanyong Wu
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Chongyi Zhong: School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
Hui Yang: School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
Zixin Liu: School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
Juanyong Wu: School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China

Mathematics, 2020, vol. 8, issue 3, 1-12

Abstract: In this paper, we consider evolutionary games and construct a model of replicator dynamics with bounded continuously distributed time delay. In many circumstances, players interact simultaneously while impacts of their choices take place after some time, which implies a time delay exists. We consider the time delay as bounded continuously distributed other than some given constant. Then, we investigate the stability of the evolutionarily stable strategy in the replicator dynamics with bounded continuously distributed time delay in two-player game contexts. Some stability conditions of the unique interior Nash equilibrium are obtained. Finally, the simple but important Hawk–Dove game is used to verify our results.

Keywords: evolutionary games; replicator dynamics; time delay; stability; hawk–dove game (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: View citations in EconPapers (2)

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