Replicator dynamics of an N-player snowdrift game with delayed payoffs

作者：

Highlights：

• The replicator dynamics for an N-player snowdrift game are examined under the context of a social-type time delay.

• The system dynamics approach a stable equilibrium for small time delays, but the dynamics lead to oscillatory behavior as the time delay increases.

• We analytically determine the critical time delay for the transition of stability using a Hopf bifurcation analysis.

• Numerical examples are presented to corroborate the analytical results.

摘要

•The replicator dynamics for an N-player snowdrift game are examined under the context of a social-type time delay.•The system dynamics approach a stable equilibrium for small time delays, but the dynamics lead to oscillatory behavior as the time delay increases.•We analytically determine the critical time delay for the transition of stability using a Hopf bifurcation analysis.•Numerical examples are presented to corroborate the analytical results.

论文关键词：Replicator dynamics,Evolutionary games,Snowdrift game,Delayed differential equation,Hopf bifurcation,Critical time delay

论文评审过程：Received 26 December 2020, Revised 10 March 2021, Accepted 12 March 2021, Available online 31 March 2021, Version of Record 31 March 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126204