Stability analysis of game models with fixed and stochastic delays

Limi Hu and Xiaoling Qiu

Applied Mathematics and Computation, 2022, vol. 435, issue C

Abstract: In this paper, we combine evolutionary game with dynamics, and discuss two kinds of game models with time delay. First, based on continuous distributed (kernel function) stochastic delay, we give the asymptotic stability condition of general three-strategy game model. Second, we study the replicator dynamics of two-community three-strategy game model with two fixed time delays (i.e. τ1 within the community and τ2 between different communities). Based on Hopf bifurcation theory, by calculating the critical conditions for the existence of bifurcation, the influence of bifurcation on the stability of equilibrium points is analyzed. Finally, we take rock-paper-scissors game as an example to verify the correctness of the theoretical results, when the delay τ meets certain conditions or doesn’t exceed the critical value, the stability of the system will not change.

Keywords: Evolutionary games; Time delay; Stability; Kernel function; Hopf bifurcation (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:435:y:2022:i:c:s0096300322005471

DOI: 10.1016/j.amc.2022.127473

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