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Stability of Replicator Dynamics with Bounded Continuously Distributed Time Delay

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School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
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School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 431; https://doi.org/10.3390/math8030431
Received: 9 January 2020 / Revised: 8 March 2020 / Accepted: 12 March 2020 / Published: 16 March 2020
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. View Full-Text
Keywords: evolutionary games; replicator dynamics; time delay; stability; hawk–dove game evolutionary games; replicator dynamics; time delay; stability; hawk–dove game
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Zhong, C.; Yang, H.; Liu, Z.; Wu, J. Stability of Replicator Dynamics with Bounded Continuously Distributed Time Delay. Mathematics 2020, 8, 431.

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