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

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  • Wettergren, Thomas A.

Abstract

We consider a version of the N-player snowdrift game in which the payoffs obtained by the players are delayed. The delay in payoffs is shown to lead to a Hopf bifurcation with an associated critical value of the time delay in the replicator dynamics. For time delays larger than the critical time delay, the replicator dynamics oscillate around the equilibrium instead of asymptotically approaching it. The dependence of this critical time delay on the parameters of the game is determined. After developing the analysis for the 2-player game, the same methodology is applied to the N-player version of the game to show how the results change as a function of N, concluding with an analysis of the limiting case of large numbers of players.

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  • Wettergren, Thomas A., 2021. "Replicator dynamics of an N-player snowdrift game with delayed payoffs," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    • Handle: RePEc:eee:apmaco:v:404:y:2021:i:c:s0096300321002940
    DOI: 10.1016/j.amc.2021.126204
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    Cited by:

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    6. Xinrong Yang & Zhenping Geng & Haitao Li, 2023. "Matrix-Based Method for the Analysis and Control of Networked Evolutionary Games: A Survey," Games, MDPI, vol. 14(2), pages 1-13, February.
    7. Xu, Yan & Feng, Meiling & Zhu, Yuying & Xia, Chengyi, 2022. "Multi-player snowdrift game on scale-free simplicial complexes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    8. Hu, Limi & Qiu, Xiaoling, 2022. "Stability analysis of game models with fixed and stochastic delays," Applied Mathematics and Computation, Elsevier, vol. 435(C).
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