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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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    References listed on IDEAS

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    1. Wettergren, Thomas A., 2021. "Game-based modeling of independent searchers who share a common goal," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    2. Ji, M. & Xu, C. & Zheng, Da-Fang & Hui, P.M., 2010. "Enhanced cooperation and harmonious population in an evolutionary N-person snowdrift game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(5), pages 1071-1076.
    3. Chan, Chun-Him & Yin, Haiping & Hui, P.M. & Zheng, Da-Fang, 2008. "Evolution of cooperation in well-mixed N-person snowdrift games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2919-2925.
    4. James Burridge & Yu Gao & Yong Mao, 2017. "Delayed response in the Hawk Dove game," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(1), pages 1-6, January.
    5. Xu, Meng & Zheng, Da-Fang & Xu, C. & Zhong, Lixin & Hui, P.M., 2015. "Cooperative behavior in N-person evolutionary snowdrift games with punishment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 322-329.
    6. Wang, Xu-Wen & Nie, Sen & Jiang, Luo-Luo & Wang, Bing-Hong & Chen, Shi-Ming, 2017. "Role of delay-based reward in the spatial cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 153-158.
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    Cited by:

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    3. Liu, Siyuan & Zhang, Chunyan & Li, Kun & Zhang, Jianlei, 2022. "Exploring the inducement for social dilemma and cooperation promotion mechanisms in structured populations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
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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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    11. Han, Weiwei & Zhang, Zhipeng & Sun, Junqing & Xia, Chengyi, 2022. "Role of reputation constraints in the spatial public goods game with second-order reputation evaluation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

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